Structural Damage Detection using Nonlinear and Noncontact …ssslab.kaist.ac.kr/article/pdf/Ph.D_Dissertation_LiuPP.pdf · 2017-06-06 · Damage often causes a structure to exhibit

박 사 학 위 논 문

Ph.D. Dissertation

비선형 및 비접촉식 레이저 초음파 기술을

이용한 구조물 손상 감지 기술

Structural Damage Detection using Nonlinear and Noncontact Laser Ultrasonic Techniques

2017

Peipei Liu (劉沛沛)

한 국 과 학 기 술 원

Korea Advanced Institute of Science and Technology

박 사 학 위 논 문



2017

Peipei Liu

한 국 과 학 기 술 원

건설 및 환경공학과



Peipei Liu

위 논문은 한국과학기술원 박사학위논문으로

학위논문 심사위원회의 심사를 통과하였음

2017 년 05 월 31 일

심사위원장 손 훈 (인 )

심 사 위 원 안 윤 규 (인 )

심 사 위 원 정 형 조 (인 )

심 사 위 원 조 윤 호 (인 )

심 사 위 원 홍 정 욱 (인 )

Structural Damage Detection using Nonlinear and Noncontact

Laser Ultrasonic Techniques

Peipei Liu

Advisor: Hoon Sohn

A dissertation/thesis submitted to the faculty of

Korea Advanced Institute of Science and Technology in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in Civil and Environmental Engineering

Daejeon, Korea

May 31, 2017

Approved by

Hoon Sohn

Professor of Civil and Environmental Engineering

The study was conducted in accordance with Code of Research Ethics1).

1) Declaration of Ethical Conduct in Research: I, as a graduate student of Korea Advanced Institute of Science and Technology, hereby declare that I have not committed any act that may damage the credibility of my research. This includes, but is not limited to, falsification, thesis written by someone else, distortion of research findings, and plagiarism. I confirm that my dissertation contains honest conclusions based on my own careful research under the guidance of my advisor.

초 록

구조물에 발생한 손상은 구조물의 비선형 거동을 유발하며, 이러한 비선형 거동에 의해 발생하는

응답 특성은 선형 거동의 응답 특성보다 손상에 더욱 민감하다. 또한 비접촉식 레이저 초음파

기술은 비접촉식 작동으로 작동하고 높은 공간 분해능의 측정이 가능해 구조물 손상 감지

분야에서 각광 받고 있다. 본 학위논문에서는 비선형 초음파 기술 및 비접촉식 레이저 초음파

기술을 이용한 구조물 손상 감지 기술을 개발하고자 한다. 세부 개발목표는 (1) 광대역 펄스

레이저 입력 비선형 초음파 변조 기법, (2) 비선형 응답 특성 추출을 통한 손상 감지 기법 및 (3)

개발 기법의 수치/실험적 검증으로 이루어져 있다.

손상이 있는 구조물에 서로 다른 주파수의 두 입력 초음파 신호가 가해지게 되면, 비선형

거동에 의해 구조물 응답에서 비선형 변조 (측파대)가 발생한다. 그러나 측파대의 발생을

위해서는 입력 초음파 신호의 주파수들이 특정 생성 조건을 만족시켜야 하며, 이 조건은 대상

구조물의 환경 및 구동 조건에 영향을 받는다. 따라서 본 연구에서는 광대역 초음파를 생성하는

펄스 레이저를 입력 신호로 사용하여, 측파대 생성 조건에 대한 복잡한 고려 없이도 측파대가

발생할 수 있도록 했다.

광대역 초음파 입력에 의해 얻어진 구조물 응답에서 비선형 응답 특성을 추출하기 위한 두 가지

기법이 제안되었다. 먼저, 비선형 응답 특성을 주파수 영역에서 추출하기 위한 측파대 피크

카운팅 (SPC) 기반 손상 감지 기법을 개발하였다. 손상 비선형성에 의해 상대적으로 약한

스펙트럼 피크가 발생되며, 이를 파악하여 비선형 손상 특성을 정의하였다. 이를 스펙트럼

상관관계 영역에서 적용함으로써 손상에 대한 민감도 및 노이즈 간섭에 대한 견고성을 향상시키는

데 성공하였다. 다른 하나는 상태공간 기반의 손상 감지 기법으로, 측정된 광대역 응답을 고차원

상태공간으로 투사한 후 재구축된 상태공간 끌개의 기하학적 변화 확인을 통해 비선형 응답 특성

추출이 가능하다. 또한 레이저 스캐닝 시스템을 개발하여 인접 지점에서 얻은 비선형 응답 특성을

기저 데이터로 활용함으로써 환경 및 구동 조건 변화에 의해 발생하는 영향을 줄일 수 있으며,

이를 통해 정상 상태에서 수집한 기저 데이터 없이도 손상을 감지 및 시각화 할 수 있다.

개발된 손상 감지 기술의 성능은 마이크로 균열이 있는 알루미늄 평판에 대해 수치적으로

검증되었으며, 이 과정에서 레이저 유발 초음파 모사를 위한 다중 물리 시뮬레이션을 개발하였다.

또한, 알루미늄 평판의 피로균열, 탄소 섬유 강화 플라스틱 (CFRP) 평판의 박리 및 유리 섬유

강화 플라스틱 (GFRP) 풍력 발전기 블레이드의 박리/분리 손상 검출을 통해 제안된 손상 감지

기술의 성능을 실험적으로도 검증하였다.

핵 심 낱 말 비접촉식 레이저 초음파, 비선형 초음파 모듈레이션, 손상 감지, 측파대 피크 카운팅,

상태공간 끌개, 스펙트럼 상관관계, 무기저

DCE

20125557

Peipei Liu. 비선형 및 비접촉식 레이저 초음파 기술을 이용한

구조물 손상 감지 기술. 건설 및 환경공학과. 2017년. 143+x 쪽. 지도교수: 손훈. (영문 논문)

Peipei Liu. Structural Damage Detection using Nonlinear and Noncontact Laser Ultrasonic Techniques. Department of Civil and Environmental Engineering. 2017. 143+x pages. Advisor: Hoon Sohn. (Text in English)

Abstract

Damage often causes a structure to exhibit severe nonlinear behaviors, and the resulting nonlinear features are

much more sensitive to damage than their linear counterparts. Also in structural damage detection field,

noncontact laser ultrasonic techniques have gained great popularity with their noncontact nature and high spatial

resolution. This dissertation mainly aims at structural damage detection by taking advantages of both nonlinear

ultrasonic and noncontact laser ultrasonic techniques. The detailed objectives are: (1) Nonlinear ultrasonic

modulation with a wideband laser pulse input; (2) Nonlinear damage feature extraction from wideband ultrasonic

responses; and (3) Numerical and experimental validation of the developed techniques.

When two distinct frequencies are applied on a target structure, nonlinear modulation (sideband)

components are created due to nonlinear ultrasonic modulation mechanism at the existence of structural damage.

However, the choice of two input frequencies needs to satisfy some binding conditions for nonlinear modulation

generation and can be affected by environmental and operational variations of the target structure. Here,

nonlinear ultrasonic modulation is extended by using a pulse laser as the driving signal. Nonlinear ultrasonic

modulation can occur among multiple frequency peaks, which highly increases the chance for the binding

conditions to be satisfied.

For extracting nonlinear features from the wideband ultrasonic responses, first, a sideband peak count (SPC)

based damage detection technique is developed to analyze the nonlinearity caused by structural damage in the

frequency domain. A nonlinear damage feature is defined by keeping track of the relatively weak spectral peaks

generated due to damage induced nonlinearity. This SPC based technique is further optimized by operating SPC

in the spectral correlation domain, which increases its sensitivity to damage and its robustness against noise

interference. Second, a state space based damage detection technique is proposed by projecting the wideband

response into a high-order state space and reconstructing its state space attractor. Another nonlinear damage

feature is obtained by checking the geometrical variations of the reconstructed attractors. Moreover, to eliminate

the influence caused by varying operational and environmental conditions, with a laser ultrasonic scanning

system, a baseline-free damage detection technique is proposed by using the ultrasonic responses acquired from

adjacent scanning points as references. Thus, damage can be detected and even visualized without relying on the

baseline data obtained from the intact condition.

A multi-physics simulation scheme is developed for simulating laser-induced ultrasonic waves on aluminum

plates and validating the proposed damage detection techniques with a simulated micro crack. The proposed

damage detection techniques are also experimentally validated by detecting fatigue crack in an aluminum plate,

delamination in a carbon fiber reinforced polymer (CFRP) plate, and delamination/ debonding in a glass fiber

reinforced polymer (GFRP) wind turbine blade.

Keywords Noncontact laser ultrasonics, Nonlinear ultrasonic modulation, Damage detection, Sideband peak

count, State space attractor, Spectral correlation, Baseline-free

Contents Contents .................................................................................................................................................. i

List of Figures and Tables .................................................................................................................... v

Chapter 1. Introduction

1.1 Motivation ..................................................................................................................................... 1

1.2 Techniques for structural damage detection ................................................................................. 2

1.3 Linear/ Nonlinear ultrasonic techniques ....................................................................................... 3

1.3.1 Linear ultrasonic techniques .................................................................................................. 3

1.3.2 Nonlinear ultrasonic techniques ............................................................................................. 4

1.4 Contact/ Noncontact ultrasonic techniques ................................................................................... 6

1.4.1 Contact ultrasonic techniques ................................................................................................ 6

1.4.2 Noncontact ultrasonic techniques .......................................................................................... 7

1.5 Research objectives and uniqueness ............................................................................................. 8

1.6 Organization and chapter summary ............................................................................................ 10

Chapter 2. Theoretical Background of Nonlinear Ultrasonic Modulation

2.1 Working principle ....................................................................................................................... 13

2.2 Binding conditions ...................................................................................................................... 15

2.3 Literature review for nonlinear ultrasonic modulation ............................................................... 17

2.4 Nonlinear ultrasonic modulation with a wideband input ............................................................ 19

2.5 Chapter summary ........................................................................................................................ 20

Chapter 3. Noncontact Laser Ultrasonic System and Numerical Simulation

3.1 Laser ultrasonic generation ......................................................................................................... 23

3.2 Laser ultrasonic measurement ..................................................................................................... 25

3.3 Laser ultrasonic scanning system ................................................................................................ 27

3.3.1 System configuration ........................................................................................................... 27

3.3.2 Scanning strategy ................................................................................................................. 29

3.4 Literature review for noncontact laser ultrasonics ...................................................................... 31

3.5 Numerical simulation for laser-induced ultrasonic waves .......................................................... 32

3.5.1 Governing equations ............................................................................................................ 32

3.5.2 Plate modeling ..................................................................................................................... 34

i

3.5.3 Comparison between simulations and experiments ............................................................. 37

3.5.4 Crack modeling .................................................................................................................... 42

3.6 Chapter summary ........................................................................................................................ 44

Chapter 4. Structural Damage Detection using Sideband Peak Count

4.1 Sideband peak count (SPC) ......................................................................................................... 45

4.2 Baseline-free damage detection by spatial comparison .............................................................. 47

4.3 Numerical validation ................................................................................................................... 49

4.4 Fatigue crack detection in aluminum plate ................................................................................. 52

4.4.1 Experimental setup .............................................................................................................. 52

4.4.2 Test results ........................................................................................................................... 55

4.5 Delamination detection in CFRP plate ........................................................................................ 58


5.5.2 Test results ........................................................................................................................... 59

4.6 Delamination and debonding detection in GFRP wind turbine blade ......................................... 59


4.6.2 Test results ........................................................................................................................... 61

4.7 Chapter summary ........................................................................................................................ 62

Chapter 5. Structural Damage Detection using State Space Attractor

5.1 State space attractor .................................................................................................................... 65

5.2 Attractor reconstruction .............................................................................................................. 67

5.3 Bhattacharyya distance (BD) ...................................................................................................... 70

5.4 Baseline-free damage detection by spatial comparison .............................................................. 72

5.5 Numerical validation ................................................................................................................... 74

5.6 Fatigue crack detection in aluminum plate ................................................................................. 78


5.6.2 Test results ........................................................................................................................... 79

5.7 Delamination detection in CFRP plate ........................................................................................ 84


5.7.2 Test results ........................................................................................................................... 84

5.8 Delamination and debonding detection in GFRP wind turbine blade ......................................... 85


5.8.2 Test results ........................................................................................................................... 86

5.9 Chapter summary ........................................................................................................................ 87

ii

Chapter 6. Structural Damage Detection using Spectral Correlation of Nonlinear Modulations

6.1 Limitation of sideband peak count (SPC) ................................................................................... 89

6.2 Spectral correlation technique ..................................................................................................... 91

6.2.1 Definition of spectral correlation ......................................................................................... 91

6.2.2 Spectral correlation between nonlinear modulation components ........................................ 93

6.2.3 Properties of spectral correlation ......................................................................................... 95

6.3 Experimental validation using inputs at two single frequencies ................................................. 98


6.3.2 Fatigue crack detection results through spectral correlation .............................................. 100

6.3.3 Fatigue crack detection results with simulated noise interference ..................................... 102

6.4 Spectral correlation enhancement by a wideband input ............................................................ 104

6.4.1 Spectral correlation with a wideband input........................................................................ 104

6.4.2 Sideband peak count (SPC) in spectral correlation domain ............................................... 108

6.5 Numerical validation ................................................................................................................. 111

6.6 Fatigue crack detection in aluminum plate ............................................................................... 114

6.7 Delamination detection in CFRP plate ...................................................................................... 116

6.8 Delamination and debonding detection in GFRP wind turbine blade ....................................... 117

6.9 Chapter summary ...................................................................................................................... 118

Chapter 7. Concluding Remarks

7.1 Conclusions ............................................................................................................................... 121

7.2 Future work ............................................................................................................................... 123

Bibliography ...................................................................................................................................... 125

Acknowledgement ............................................................................................................................. 137

Curriculum Vitae .............................................................................................................................. 139

iii

iv

List of Figures and Tables

Figure 1.1 Catastrophic incidents due to structural failure in history .................................................... 1

Figure 1.2 Illustration of multiple nonlinear ultrasonic phenomena ...................................................... 5

Figure 2.1 Illustration of nonlinear ultrasonic modulation using two distinct frequency inputs ......... 13

Figure 2.2 Three basic moving crack modes in plates ......................................................................... 14

Figure 2.3 A simple model for nonlinear ultrasonic modulation at the presence of a crack ............... 15

Figure 2.4 Investigation of nonlinear ultrasonic modulation with different input frequencies ........... 17

Figure 2.5 The first sideband spectrogram obtained from aluminum specimens by sweeping the high-

frequency inputs from 10 to 20 kHz and the low-frequency inputs from 80 to 110 kHz ..................... 19

Figure 2.6 Illustration of nonlinear ultrasonic modulation using a wideband input ............................ 20

Figure 3.1 Ultrasonic generation by a laser ......................................................................................... 24

Figure 3.2 Schematic of a typical laser Doppler vibrometer based on two-beam heterodyne

method .................................................................................................................................................. 26

Figure 3.3 Schematic diagram of the noncontact laser ultrasonic scanning system ............................ 28

Figure 3.4 Four different scanning strategies ...................................................................................... 30

Figure 3.5 Example of Lamb wave propagation contour plots in the time domain ............................. 32

Figure 3.6 Illustration of the ultrasonic wave generated by a pulse laser beam .................................. 34

Figure 3.7 Spatial and temporal distributions of the pulse laser intensity ........................................... 35

Figure 3.8 Schematic of the 3D FEM model (cross-section drawn).................................................... 36

Figure 3.9 Geometric dimensions of the circular aluminum plates and placements of the excitation

and sensing points ................................................................................................................................. 38

Figure 3.10 Experimental setup for simulation model validation using noncontact laser ultrasonic

scanning system .................................................................................................................................... 38

Figure 3.11 Temperature distribution irradiated by a pulse laser ........................................................ 39

Figure 3.12 The effect of the depth 𝛬𝛬𝑑𝑑 of the thermal wave region on simulated ultrasound ........... 40

Figure 3.13 Comparison of the velocity signals obtained from numerical simulations and

experimental tests with varying thicknesses ......................................................................................... 41

Figure 3.14 Modeling of a micro crack in the 3D FEM model ........................................................... 42

Figure 3.15 Plane extraction for observing crack opening and closing ............................................... 42

Figure 3.16 Crack opening and closing during ultrasonic wave propagation ...................................... 43

v

Figure 4.1 Illustration of nonlinear ultrasonic modulation using a wideband input ............................ 45

Figure 4.2 Description of sideband peak count (SPC) and SPC difference ......................................... 47

Figure 4.3 Raster scanning of the target inspection area using a noncontact laser ultrasonic scanning

system ................................................................................................................................................... 47

Figure 4.4 Illustration for spatially adjacent ultrasonic response comparison using MSPCD ............ 48

Figure 4.5 Illustration of data extraction in simulation model for MSPCD calculation ...................... 49

Figure 4.6 SPC and SPC difference values obtained from three selected points in simulation

model .................................................................................................................................................... 50

Figure 4.7 Baseline-free simulated crack detection result using SPC based damage detection

technique ............................................................................................................................................... 51

Figure 4.8 Dimensions of the specimen, crack location, and laser excitation and sensing

arrangement........................................................................................................................................... 52

Figure 4.9 Fatigue test and microscopic image of the aluminum plate specimen with a fatigue

crack ...................................................................................................................................................... 53

Figure 4.10 Experimental setup for fatigue crack detection using noncontact laser ultrasonic scanning

system ................................................................................................................................................... 54

Figure 4.11 Representative response signals from path 2 in the plate specimen ................................. 55

Figure 4.12 SPC and SPC difference values obtained from the intact and damage cases for the plate

specimen ............................................................................................................................................... 56

Figure 4.13 MSPCD values obtained from all six paths in the aluminum plate specimen .................. 57

Figure 4.14 Baseline-free fatigue crack detection result using SPC based damage detection

technique ............................................................................................................................................... 58

Figure 4.15 Carbon fiber reinforced polymer (CFRP) plate and laser excitation and sensing

arrangement........................................................................................................................................... 58

Figure 4.16 Baseline-free delamination detection result in CFRP plate using SPC based

technique ............................................................................................................................................... 59

Figure 4.17 Dimensions of a full scale wind turbine blade, and locations of simulated delamination

and debonding ....................................................................................................................................... 60

Figure 4.18 Enlarged view of the damages and the laser scanning region .......................................... 61

Figure 4.19 Experimental setup for delamination and debonding detection using noncontact laser

ultrasonic scanning system ................................................................................................................... 61

Figure 4.20 Baseline-free delamination/ debonding detection results in wind turbine blade using SPC

based technique ..................................................................................................................................... 62

vi

Figure 5.1 State space attractor reconstructed from an accelerometer ................................................ 66

Figure 5.2 Limit cycle state space attractor achieved from Equation (5.2) ......................................... 67

Figure 5.3 Illustration of state space attractor reconstruction from a single time series ...................... 67

Figure 5.4 Example for state space attractor reconstruction ................................................................ 68

Figure 5.5 Overview of the BD computation between the current and reference state space

attractors ................................................................................................................................................ 72

Figure 5.6 Illustration for spatially adjacent ultrasonic response comparison using BD .................... 73

Figure 5.7 Illustration of a scanning region in simulation model for BD calculation ......................... 74

Figure 5.8 Singular values obtained from SVD of a state space attractor matrix, which is built from a

single scanning signal after applying a low-pass filter with a varying cut-off frequency, fc ................ 75

Figure 5.9 The effect of the embedding dimension 𝑚𝑚 on damage detection (𝑚𝑚 = 1, 2, 3, 4, 5, 10, 15

and 20, fc = 200 kHz) ............................................................................................................................ 76

Figure 5.10 The effect of the frequency band on damage detection (fc = 350, 300, 250, 200, 150 and

100 kHz, m =15) ................................................................................................................................... 77

Figure 5.11 Damage detection result with a high embedding dimension (𝑚𝑚 = 25) and a high cut-off

frequency (fc = 350 kHz)....................................................................................................................... 78

Figure 5.12 Fatigue crack detection using correlation coefficient obtained from six paths on the

aluminum plate specimen ..................................................................................................................... 79

Figure 5.13 Parameter selection for state space attractor reconstruction for the six paths in the plate

specimen ............................................................................................................................................... 80

Figure 5.14 The effect of embedding dimension 𝑚𝑚 on Bhattacharyya distance (BD) and fatigue

crack detection (m = 1, 2, 3, 4, 5, 10, 15, 20) ........................................................................................ 81

Figure 5.15 Parameter selection for state space attractor reconstruction using 10 randomly selected

ultrasonic response signals from the scanning area .............................................................................. 82

Figure 5.16 Baseline-free fatigue crack detection using BD feature with different embedding

dimension m (m = 1, 2, 3, 4, 5 and 10).................................................................................................. 83


ultrasonic response signals from the CFRP plate .................................................................................. 85

Figure 5.18 Baseline-free delamination detection in CFRP plate using state space based

technique ............................................................................................................................................... 85

Figure 5.19 Parameter selection for state space attractor reconstruction with 10 randomly selected

ultrasonic response signals from the wind turbine blade ...................................................................... 86

Figure 5.20 Baseline-free delamination/ debonding detection in wind turbine blade using state space

based technique ..................................................................................................................................... 87

vii

Figure 6.1 Comparison in the time domain between an original test signal and the signal

contaminated with simulated noise ....................................................................................................... 90

Figure 6.2 Comparison in the frequency domain between an original test signal and the signal

contaminated with simulated noise ....................................................................................................... 90

Figure 6.3 Spectral correlation results (ignoring symmetric values at α < 0) for 𝑥𝑥(𝑡𝑡) = 𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑎𝑎𝑡𝑡 +

𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑏𝑏𝑡𝑡 ................................................................................................................................................... 93


𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑏𝑏𝑡𝑡 + 𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑎𝑎+𝑓𝑓𝑏𝑏)𝑡𝑡 + 𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑎𝑎−𝑓𝑓𝑏𝑏)𝑡𝑡 ................................................................................................... 94

Figure 6.5 Stationary noise signal exhibits no spectral correlation ..................................................... 96

Figure 6.6 Two statistically weak-linked components exhibit weak spectral correlation ................... 96

Figure 6.7 Different components contributing to the response of the spectral density function

at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 .............................................................................................................................................. 97

Figure 6.8 Aluminum plate with fatigue crack .................................................................................... 99

Figure 6.9 Experimental setup ............................................................................................................. 99

Figure 6.10 Spectral correlation values obtained from the intact and damaged specimens for multiple

frequency combinations ...................................................................................................................... 101

Figure 6.11 Spectral correlation values 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) calculated from the noise contaminated test

signals with different SNRs ................................................................................................................. 103

Figure 6.12 Spectral density values �𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏, 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 , 0) calculated from the noise

contaminated test signals with different SNRs .................................................................................... 104

Figure 6.13 Illustration of structural response in the frequency domain under a wideband pulse laser

excitation ............................................................................................................................................. 105

Figure 6.14 Sideband peak count (SPC) in spectral correlation domain ........................................... 109

Figure 6.15 SPC and SPC difference values obtained in the spectral correlation domain for three

selected points in simulation model .................................................................................................... 112

Figure 6.16 MSPCD values calculated from signals contaminated with different SNRs .................. 113


technique in the spectral correlation domain ...................................................................................... 114

Figure 6.18 MSPCD values obtained in the spectral correlation domain from all six paths in the

aluminum plate specimen ................................................................................................................... 115

Figure 6.19 Baseline-free fatigue crack detection result using SPC based damage detection technique

in the spectral correlation domain ....................................................................................................... 116

Figure 6.20 Baseline-free delamination detection in CFRP plate using SPC based technique in the

spectral correlation domain ................................................................................................................. 117

viii

Figure 6.21 Baseline-free delamination/ debonding detection in wind turbine blade using SPC based

technique in the spectral correlation domain ...................................................................................... 118

Table 3.1 Properties of the aluminum used for numerical simulations ................................................ 35

Table 6.1 Summary of the peak coordinates in spectral correlation (α > 0) ....................................... 94

Table 6.2 Sensitivities of different spectral correlation values to a fatigue crack shown

in Figure 6.10 ...................................................................................................................................... 102

Table 6.3 Comparison of the MSPCD values between Figure 4.6 and Figure 6.15 ........................... 113

ix

x

Chapter 1. Introduction

1.1 Motivation

(a) (b)

(c) (d) (e)

Figure 1.1 Catastrophic incidents due to structural failure in history: (a) the downfall of a whole

single span of Sungsoo Grand Bridge in Korea (1994), (b) the collapse of Sampoong Department

Store in Korea (1995), (c) the derailment of ICE train in Germany (1998), (d) the aircraft crash of

China Airlines Flight 611 (2002), and (e) the collapse of Yangmingtan Bridge in China (2012).

Structural damage often starts with material and/or geometrical property changes of the target

structure. When the structural damage grows, it will reach a point where the target structure is no

longer acceptable to the users. Here, this point is referred to as structural failure (Farrar and Worden,

2007). In history, there are numerous catastrophic incidents caused by structural failure. To name a

few (Figure 1.1), the downfall of a whole single span of Sungsoo Grand Bridge in Korea (1994), the

collapse of Sampoong Department Store in Korea (1995), the derailment of ICE train in Germany

(1998), the aircraft crash of China Airlines Flight 611 (2002), and the collapse of Yangmingtan

Bridge in China (2012). In order to prevent these catastrophes in civil, mechanical, aerospace and

transportation infrastructure, almost all private and government industries tried their best to detect

- 1 -

structural damage at the earliest possible time. The early detection enables to take a step in advance to

prevent structural failure, making it possible to alleviate maintenance costs and extend residual life of

the target structure. Multiple technologies have been developed or under development to replace the

conventional regular visual inspection, which is quite labor-intensive, time-consuming and entirely

expertized. Especially in these days, many portions of the existing infrastructure are approaching or

exceeding their initial design life. However, due to economic issues, these civil, mechanical and

aerospace structures are still being used in spite of aging and the associated damage accumulation.

Therefore, the demand for effective damage detection techniques has been raising dramatically.

1.2 Techniques for structural damage detection

In general, structural damage detection techniques can be divided into two categories, namely,

global and local damage detection techniques, respectively (Giurgiutiu, 2008). For the global damage

detection technique, it is used to evaluate and assess the global dynamic characteristics such as

resonance frequency, mode shape and modal damping ratio and overall condition of a target structure

(Yun and Bahng, 2000, Brownjohn et al., 2003, Lee et al., 2005, Koo et al., 2008, Jin et al., 2015).

And it is often achieved by observing structural vibrations under a low-frequency excitation (typically

below 1 kHz). However, the global technique is not sensitive to local incipient damage, and is hard to

detect the structural damage at its earliest stage (Chang et al., 2003, Lynch, 2007). For the local

damage detection technique, there exist various different techniques such as ultrasonic, acoustic

emission, thermography, eddy current, magnetic particle inspection, X-ray and etc. (Ho et al., 1990,

Zilberstein et al., 2001, Kundu et al., 2012, Williams et al., 2013, An et al., 2014). Among all these

local damage detection techniques, the ultrasonic based damage detection technique is one of the most

promising approaches and has proven its effectiveness in achieving a reasonable compromise among

resolution, practicality and detectability.

Ultrasound is sound with a frequency greater than the upper limit of human hearing (great than

20 kHz) and it has been applied in various fields in recent years. Among all, ultrasonic waves in

structures have become a critically significant subject for structural damage detection. In ultrasonic

based damage detection techniques, an ultrasound transducer connected to a diagnostic equipment is

passed to the structure under inspection. The transducer is typically attached to the target structure by

a couplant (such as adhesive and oil) or by water. However, when ultrasonic testing is conducted with

a noncontact transducer, such as an electromagnetic acoustic transducer (EMAT) or laser, the use of

couplant is not required. Normally, the ultrasonic waves with center frequencies from 0.1 to 1.5 MHz,

- 2 -

and occasionally up to 50 MHz, are transmitted into structures to detect internal flaws or to

characterize materials. Two basic testing strategies are often used: pulse-echo and pitch-catch. In

pulse-echo mode, the transducer performs both the sending and the receiving of the ultrasonic waves

as the waves are reflected back to the device. Damage is often detected by the appearance of a new

reflected signal. In pitch-catch mode, a transmitter sends ultrasonic waves, and a separate receiver

detects the response that has reached it over a distance or on another surface. Damage or other

conditions in the space between the transmitter and the receiver is detected by variations of the

amplitude, phase and mode conversion of ultrasonic waves which are either transmitted or reflected

from the damage. Nowadays, small defect can also be detected by looking into the nonlinearity of the

ultrasonic waves, like distortion, accompanying wave harmonics, and in sum and difference frequency

generation (sidebands).

Overall, some of the advantages of ultrasonic based damage detection that are often cited include:

(1) It is sensitive to both surface and subsurface damages; (2) Only one surface needs to be accessible

for most cases; (3) It owns high accuracy in determining damage position and estimating its size and

shape; and (4) It is capable of portable or highly automated operation. Meanwhile, as with all the

damage detection techniques, ultrasonic based damage detection also has its own limitations, which

include: (1) It normally requires a couplant to promote the transfer of ultrasonic energy into the target

structure unless a noncontact transducer is used; (2) Damage oriented parallel to the ultrasonic waves

may go undetected; (3) Structures that are rough, irregular in shape, very small or thin, or not

homogeneous are difficult to inspect; and (4) Ultrasonic waves may also be affected by temperature or

various loading conditions.

1.3 Linear/ Nonlinear ultrasonic techniques

1.3.1 Linear ultrasonic techniques

Linear ultrasonic techniques use linear features of ultrasonic waves, such as variations of the

amplitude, phase, and mode conversion of the transmitted or reflected ultrasonic waves for structural

damage detection. For example, Shan and Dewhurst investigated the arrival time of the transmitted

ultrasonic waves through a crack for surface-breaking crack detection in steel samples (Shan and

Dewhurst, 1993). Cook and Berthelot detected the presence of crack and monitored its growth in flat

steel bars by observing the amplitude of the scattered ultrasonic waves (Cook and Berthelot, 2001).

Sohn et al. detected delamination in composite structures based on the energy attenuation of the

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ultrasonic waves that is correlated to the amount of energy dissipated by the delamination damage

(Sohn et al., 2004). Ihn and Chang also developed a damage index related to the change in energy

content of a specific ultrasonic wave mode for detecting cracks and debondings in metallic and

composite structures, and a piezoelectric sensor network was included to characterize the damage (i.e.,

location and size) (Ihn and Chang, 2004, Ihn and Chang, 2008). Staszewski et al. showed a wavefield

image where the wave scattered at the crack tip by spatial scanning using a 3D laser Doppler

vibrometer (LDV) (Staszewski et al., 2007). Cai et al. took advantage of time reversal technique for

clearly distinguishing the arrival time of the scattered ultrasonic waves and locating multiple

simulated damage in aluminum plates (Cai et al., 2011). Qiu et al. studied the attenuation of the

ultrasonic wave peak value caused by crack damage in a full-scale aircraft fatigue test under time-

varying conditions (Qiu et al., 2016). These linear features have been widely studied and showed a

great capability for various gross structural damage detection. However, when dealing with small

damage (e.g., micro fatigue crack), linear ultrasonic techniques may lose their effectiveness and

practicability (Kim et al., 2006, Liu et al., 2014).

1.3.2 Nonlinear ultrasonic techniques

Different from linear ultrasonic techniques, nonlinear ultrasonic techniques mainly focus on

nonlinearity induced by structural damage and investigate frequency variations of the acquired

ultrasonic waves. More specifically, nonlinearity due to structural damage can distort ultrasonic

waves, create accompanying harmonics (sub-harmonics) and modulations of different input

frequencies, and change resonance frequencies as the amplitude of the driving input changes (Jhang,

2009). As this nonlinearity even comes from a very small initial damage, it can detect the structural

damage effectively at its very early stage. For brief introduction, different nonlinear ultrasonic

phenomena are summarized as follows (Figure 1.2):

(1) Harmonic: When the waveform of the incident wave at frequency 𝑓𝑓𝑎𝑎 is distorted by a

nonlinear source, higher harmonic waves are generated with frequencies at 2𝑓𝑓𝑎𝑎, 3𝑓𝑓𝑎𝑎, etc., as shown

in Figure 1.2(a). Cantrell and Yost investigated the presence of second harmonic existing in fatigued

aluminum alloy (Cantrell and Yost, 1994). Li et al. used the second harmonic waves to detect material

nonlinearity due to damage mechanism in tube-like structure (Li et al., 2016). Shah and Ribakov used

both the second and third harmonics for early stage damage detection in concrete (Shah and Ribakov,

2009).

(2) Sub-harmonic: Sub-harmonic is a nonlinear wave distortion resulting in the doubling of the

period with frequencies of 𝑓𝑓𝑎𝑎/2, 𝑓𝑓𝑎𝑎/3, etc., as shown in Figure 1.2(b). Korshak et al. observed the

- 4 -

sub-harmonic showing up in a substrate with a crack of irregular shape (Korshak et al., 2002).

Solodov et al. also investigated the sub-harmonic generation due to nonbonded contact interfaces and

demonstrated that the sub-harmonic owns a high localization around a fatigue crack and can provide

opportunities for early detection and recognition of damaged areas (Solodov et al., 2002, Solodov et

al., 2004).

(a) (b)

(c) (d)

Figure 1.2 Illustration of multiple nonlinear ultrasonic phenomena: (a) harmonic, (b) sub-harmonic,

(c) nonlinear ultrasonic modulation, and (d) resonance frequency shift.

(3) Nonlinear ultrasonic modulation: When two input waves at distinct frequencies 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏

(𝑓𝑓𝑎𝑎 > 𝑓𝑓𝑏𝑏) encounter a nonlinear source, modulated components are generated at frequencies 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏,

𝑓𝑓𝑎𝑎 ± 2𝑓𝑓𝑏𝑏 , 2𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , etc., as shown in Figure 1.2(c). Here, when 𝑓𝑓𝑎𝑎 = 𝑓𝑓𝑏𝑏 , the corresponding

modulation components become harmonics. Sutin and Donskoy detected multiple contact-type defects

by checking the modulation of an ultrasonic wave by a hammer-induced low-frequency vibration

(Sutin and Donskoy, 1998). Didenkulov et al. demonstrated that nonlinear ultrasonic modulation can

be a novel tool for crack inspection in concrete (Didenkulov et al., 1999). Sohn et al. developed a

fatigue crack detection technique based on nonlinear ultrasonic modulation using two piezoelectric

transducers (PZTs) for generating both 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏, and showed its ability to detect micro fatigue

crack in metallic specimens (Sohn et al., 2013).

- 5 -

(4) Resonance frequency shift: The resonance frequency is studied as a function of the excitation

level. In the presence of a nonlinear source, as the excitation level increases, it is manifested by a shift

in the resonance frequency, as shown in Figure 1.2(d). Payan et al. took use of the resonance

frequency shift method to monitor progressive thermal damage of concrete and showed its advantages

over some classical linear methods (Payan et al., 2007). Meo et al. applied this resonance frequency

shift method to detect delamination damage in various composite plates (Meo et al., 2008). Eiras et al.

monitored the aging processing of glass fiber reinforced cement by investigating its resonance

frequency shift behavior (Eiras et al., 2013).

1.4 Contact/ Noncontact ultrasonic techniques

1.4.1 Contact ultrasonic techniques

For ultrasonic techniques, contact transducers are typically surface-mounted on or embedded in

the target structure. The most often used contact transducers are wedge transducer, piezoelectric

transducer (PZT), fiber optic sensor, acoustic emission sensor and etc. Davies et al. installed a

circumferential array of PZTs to record backscattered signals from a crack and visualize the crack

(Davies et al., 2009). Sohn et al. used PZTs, together with an enhanced time reversal method, to

detect the internal delamination in composite plates (Sohn et al., 2007). Qiu et al. scanned multiple

actuator-sensor channels in a dense PZT array on a carbon fiber composite wing box of an unmanned

aerial vehicle (Qiu et al., 2009). Lim et al. investigated the nonlinearity in ultrasonic responses

received from PZT sensors and developed a reference-free fatigue crack detection method based on

nonlinear ultrasonic modulation applied on complex aircraft fitting-lugs (Lim et al., 2014). Cuc et al.

took advantage of guided Lamb waves for disbonding detection in adhesively bonded joints between

metallic and composite plates using piezoelectric wafer active sensors (PWAS) (Cuc et al., 2004).

Scholey et al. reported quantitative measurements of the amplitude and angular variations of acoustic

emission events duo to matrix cracking and delamination in large quasi-isotropic composite plates

(Scholey et al., 2010). Betz et al. developed a new way of fiber-optic detection of Lamb waves, which

allows the use of Bragg gratings for both high-resolution strain and high-speed ultrasound detection

(Betz et al., 2003). Guo et al. reviewed the application of fiber Bragg grating (FBG) sensor

technology for load monitoring and damage detection of air platforms (Guo et al., 2011).

Though these ultrasonic techniques, which rely on contact transducers, have been widely

investigated and applied, they may suffer from the following limitations: (1) The couplant layer is a

- 6 -

source of considerable variability in sensitivity and also in bandwidth; (2) High spatial resolution is

hard to achieve using contact transducers; (3) Transducer installation and cabling are costly and labor-

intensive, and they might be the weakest link in the whole test system, especially under harsh

environments; and (4) For some applications, there is no access to attach transducers on the target

structure.

1.4.2 Noncontact ultrasonic techniques

In recent years there has been a growing interest in using noncontact transducers for structural

damage detection. Noncontact ultrasonics is a method where ultrasonic wave is generated or received

to or from the target structure without making direct or indirect contact. In this way, noncontact

ultrasonics allows some structures to be inspected without fear of contamination from couplants. Also,

noncontact ultrasonics would facilitate testing of structures or components that are continuously rolled

on a production line, in extremely hot environments, coated, oxidized, or just difficult to physically

contact. Noncontact ultrasonics, which have been investigated or applied for structural damage

detection, mainly include air-coupled transducer (ACT), electromagnetic acoustic transducer (EMAT),

electronic speckle pattern interferometry (ESPI), laser and so on. Here, brief explanations will be

given for some of the noncontact techniques.

Air-coupled transducer (ACT), just as its name implies, transfer the ultrasonic wave to the target

structure through air. However, only few part of the sound energy can be transmitted to the target

structure due to large acoustic impedance mismatch between air and the target material (Castaings and

Cawley, 1996). Methods for overcoming the acoustic impedance mismatch have been investigated

frequently in the past. Electrostatic air-coupled and piezoelectric air-coupled transducers have

constituted the most popular design and many applications for damage detection have been achieved.

Kažys et al. carried out experimental investigation with different arrangements of ACTs and their

proposed method enabled delamination and impact induced damage detection in honeycomb materials

(Kažys et al., 2006). Ballad et al. used a pair of focused ACTs to generate and receive longitudinal or

flexural ultrasonic waves in plate-like samples and nonlinear modulation technique was included for

crack detection (Ballad et al., 2004).

Electromagnetic acoustic transducer (EMAT) is a transducer for noncontact wave generation and

reception using electromagnetic mechanisms. The biggest advantage of EMAT is its ability to

generate a specific ultrasonic wave mode. EMAT can generate various ultrasonic waves such as shear

horizontal (SH) bulk waves, surface waves, and Lamb waves in conductive and ferromagnetic

materials (Thompson, 1990). Hirao and Ogi generated and received SH waves using EMATs to detect

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corrosion defects on the outer surfaces of steel pipelines (Hirao and Ogi, 1999). Vasiljevic et al.

detected pipe dent by monitoring longitudinal waves in a metal pipe using EMATs (Vasiljevic et al.,

2008). Murayama and Ayaka observed the harmonic components by generating Lamb waves in a thin

steel sheet using EMATs for fatigue crack detection (Murayama and Ayaka, 2007). However, when it

comes to real applications, the spacing between the transducer and the structure becomes hard to

control and maintain, making its noncontact nature a drawback rather than an advantage. Additionally,

its application is limited to metallic or magnetic materials.

Laser is entirely couplant free, noncontact and can be remote from the target structure. It is also

capable of flat spectral response over large bandwidth. Laser beams can be made extremely small to

give good access in confined spaces and to give high spatial resolution, and can be scanned readily

across the target structure. It has now been established as a viable noncontact alternative to contact

transducers for generating and receiving ultrasonic waves. More details about laser ultrasonic

techniques will be given in Chapter 3.

1.5 Research objectives and uniqueness

This dissertation aims at extracting nonlinear features from wideband ultrasonic responses and

using these nonlinear features for structural damage detection. Also, taking advantages of laser

ultrasonic techniques with their noncontact nature and high spatial resolution, a fully noncontact laser

ultrasonic scanning system is introduced and used for wideband ultrasonic signal generation and

measurement. The scope and uniqueness of this dissertation are summarized as follows:

(1) Nonlinear ultrasonic modulation with a wideband input

Normally, a high-frequency and a low-frequency inputs are applied on a target structure and

detect structural damage based on the generated nonlinear modulation components. However, the

choice of two input frequencies needs to satisfy some binding conditions for nonlinear modulation

generation and can be affected by variations in the environmental and operational conditions of the

target structure. In the proposed techniques, a wideband excitation signal is used as the driving signal,

nonlinear ultrasonic modulation can occur among multiple frequency peaks at the existence of

structural damage, which highly increases the chance for the binding conditions to be satisfied. Also,

the test data collection time can also be highly reduced compared with sweeping different input

frequency combinations.

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(2) Nonlinear damage feature extraction from wideband ultrasonic responses

For extracting nonlinear features from the wideband ultrasonic responses, first, a sideband peak

count (SPC) based damage detection technique is developed to analyze the nonlinearity caused by

structural damage in the frequency domain. A corresponding nonlinear damage feature does not count

the dominant spectral peaks but keeps track of the relatively weak peaks in the neighborhood of the

strong peaks generated due to the damage induced nonlinearity. Second, a state space based damage

detection technique is proposed by projecting the wideband response into a high-order state space and

reconstructing its state space attractor. The state space attractor is the geometric representation of a

dynamical system, and thus will reflect a loss of dynamical similarity due to damage, especially the

nonlinear one. Another nonlinear damage feature is obtained by checking the geometrical variations

of the reconstructed attractor from a reference one.

To eliminate the influence caused by varying operational and environmental conditions on the

test results, taking use of a laser ultrasonic scanning system, a baseline-free damage detection

technique is proposed by using the ultrasonic responses acquired from the adjacent points as

references. In this way, damage can be detected and even visualized without relying on the baseline

data obtained from the intact condition.

(3) Technique optimization against noise interference

Considering the noise effect on SPC based damage detection technique, an optimized SPC

technique is developed by introducing spectral correlation technique, which investigates the spectral

correlation between nonlinear modulation components. The major advantage of the spectral

correlation over conventional spectral density function is that the modulation components of interest

can be reliably extracted even when the measured ultrasonic signals are heavily contaminated by

noise. Also, when dealing with a wideband ultrasonic signal, the contrast of the spectral correlation

values caused by nonlinear modulation components is enhanced between the intact and damage

conditions, which increases its sensitivity to damage. The SPC based technique is then optimized by

conducting SPC operation in the spectral correlation domain for structural damage detection with a

higher sensitivity to damage and higher robustness against noise interference.

(4) Numerical and experimental validations of the developed damage detection techniques

First, a multi-physics simulation scheme is developed for simulating laser-induced ultrasonic

waves on an aluminum plate. For efficient computation, the simulation model is divided into two sub-

regions, thermal and ultrasonic wave regions, by theoretically investigating the effect of thermal

diffusion caused by laser excitation. A simulated micro crack is also introduced into this simulation

- 9 -

model, and its nonlinear feature is verified by observing the crack opening and closing during wave

propagation. The proposed damage detection techniques are then validated by detecting the simulated

micro crack in the simulation model. Second, the proposed damage detection techniques are

experimentally validated by detecting fatigue crack in an aluminum plate, delamination in a carbon

fiber reinforced polymer (CFRP) plate, and delamination/ debonding in a glass fiber reinforced

polymer (GFRP) wind turbine blade.

1.6 Organization and chapter summary

This dissertation is organized with seven chapters and summarized as follows:

Chapter 1 presents the motivation of this research, literature review of existing ultrasonic

techniques for structural damage detection. Objectives, scopes and organization of the dissertation are

also stated in this chapter.

Chapter 2 explains the basic working principle of nonlinear ultrasonic modulation and the

binding conditions for modulation generation. Previous researches for nonlinear ultrasonic modulation

based structural damage detection are presented. This chapter also extends the nonlinear ultrasonic

modulation technique from using two single frequencies as inputs to a wideband input.

Chapter 3 discusses the working principles and characteristics for laser based ultrasonic wave

generation and measurement. A noncontact laser ultrasonic scanning system is introduced in this

chapter with detailed description for the system compositions. Different laser based scanning

strategies are then provided and compared. In addition, this chapter also develops a 3D simulation

model with a micro crack for analyzing laser-induced ultrasonic waves and validating the damage

detection techniques developed in the following chapters.

Chapter 4 proposes a new damage detection method called sideband peak count (SPC) for the

pulse laser-induced wideband ultrasonic responses. SPC detects the damage induced nonlinearity by

counting the sideband spectral peaks in the frequency domain. Also, together with laser scanning,

damage can be detected using the SPC based method without relying on any baseline data obtained

from the pristine condition of the target structure. This technique is numerically and experimentally

validated in this chapter.

- 10 -

Chapter 5 introduces another analysis method for damage detection using the wideband

ultrasonic responses. A state space attractor is reconstructed from the acquired wideband ultrasonic

response for damage detection. The proposed state space based damage detection technique is

numerically and experimentally validated and discussed with different parameters for attractor

reconstruction.

Chapter 6 analyzes the noise effect on the proposed damage detection methods in Chapters 4

and 5. In order to tackle this problem, spectral correlation technique is adopted and extended for

wideband ultrasonic responses acquired under a pulse laser input. The SPC technique developed in

Chapter 4 is then conducted in the new spectral correlation domain for structural damage detection. Its

advantages over SPC in the conventional frequency domain are explained and validated numerically

and experimentally in this chapter.

Chapter 7 concludes this dissertation with summary, uniqueness and future work.

- 11 -

- 12 -

Chapter 2. Theoretical Background of Nonlinear Ultrasonic Modulation

This chapter introduces the theoretical background for nonlinear ultrasonic modulation, including

its working principle and binding conditions for nonlinear modulation generation. Previous researches

for nonlinear ultrasonic modulation based structural damage detection are also presented. Furthermore,

nonlinear ultrasonic modulation with a wideband input is proposed and discussed in this chapter.

2.1 Working principle

(a)

(b)

Figure 2.1 Illustration of nonlinear ultrasonic modulation using two distinct frequency inputs: (a)

intact case, and (b) damage case.

When two inputs with different frequencies 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 (𝑓𝑓𝑎𝑎 > 𝑓𝑓𝑏𝑏) are applied to a linear system,

the system response contains the output frequency components corresponding only to the input

frequencies (Figure 2.1(a)). However, if the system behaves nonlinearly (e.g., due to fatigue crack

existence), the system response will contain not only the input frequencies but also their harmonics

(multiplies of input frequencies, i.e., 2𝑓𝑓𝑎𝑎 and 2𝑓𝑓𝑏𝑏 ) and modulations (linear combinations or

- 13 -

sidebands of input frequencies, i.e., 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏, 𝑓𝑓𝑎𝑎 ± 2𝑓𝑓𝑏𝑏, 2𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏, etc.) (Figure 2.1(b)) (Van Den

Abeele et al., 2000, de Lima and Hamilton, 2003). This phenomenon is called nonlinear ultrasonic

modulation or nonlinear wave modulation. Because this phenomenon occurs only if there are

nonlinear sources, it can be considered a signature of the presence of nonlinearity, and thus the

existence of nonlinear damage, assuming that the inherent material nonlinearity is weak and

negligible. Indeed, most structural damage evolves in a nonlinear manner, causing an intact structure

with predominantly linear properties to exhibit nonlinear properties.

Take the crack damage as an example (Zagrai et al., 2008). During fatigue process, structural

material develops imperfections progressing from micro- (several μm) to macro-scale (several mm

and above). At the early stage of structural degradation, damage accumulates in the form of submicro-

and micro defects. Micro defects grow within individual grains/grain boundaries interacting with each

other and producing small initial micro cracks. Coalescences of advancing micro cracks form clusters

of cracks in the structure and essentially initiate dynamic growth of one or a few micro cracks into

macro cracks, which cause structural failure. At initial stages of structural degradation, micro defects

and micro cracks are considerably smaller than the wavelengths commonly used in the ultrasonic

damage detection, linear characteristics such as amplitude, speed of ultrasound, or damping manifest

limited sensitivity to the micro-scale damage. Hence, most of the linear ultrasonic techniques focus on

detecting relatively large (i.e., macro) cracks. However, compared to the micro crack initiation and

development stage, time needed for formation and growth of the macro crack is extremely short,

which makes it necessary to detect the crack at its initial stage. In contrast to linear ultrasonic

techniques, the nonlinear responses (i.e., nonlinear ultrasonic modulation) exist persistently when the

crack damage progresses from micro- to macro-scale (Jhang and Kim, 1999, Zagrai et al., 2008).

Figure 2.2 Three basic moving crack modes in plates.

Though full mechanism of nonlinear ultrasonic modulation at the presence of crack is not yet

well discovered, one of the main reasons is due to the ‘breathing’ of micro or macro cracks (Klepka et

al., 2011, Jhang, 2009). In general, the breathing crack could exhibit three different crack modes in

plates, as illustrated in Figure 2.2 (Klepka et al., 2011): (1) Opening and closing mode – crack faces

- 14 -

move directly apart from each other; (2) Sliding mode – crack faces slide on each other in the

direction perpendicular to the leading edge of the crack; and (3) Tearing mode – crack faces move

relative to each other and parallel to the leading edge of the crack. Let us consider a crack with an

opening and closing mode when 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 are applied as inputs (Jhang, 2009). The low-frequency

input 𝑓𝑓𝑏𝑏 changes the width of the crack depending on the phase of the induced low-frequency

vibration. During the dilation phase of the low-frequency cycle, the high-frequency signal 𝑓𝑓𝑎𝑎 is

partially decoupled by the open crack. This reduces the amplitude of the high-frequency signal

passing through the crack. In the other half of the low-frequency cycle, the closed crack does not

interrupt the high-frequency signal 𝑓𝑓𝑎𝑎. This results in an amplitude modulation of the ultrasonic

signal as shown in Figure 2.3. Thus, in the frequency domain, this signal reveals sideband frequencies

(nonlinear modulation frequencies at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏). This simple model provides physical intuition but

cannot be used for quantitative assessment. More realistic crack models can be found by describing

cracks as contacting rough surfaces (Nazarov and Sutin, 1997, Solodov and Korshak, 2002). Besides

crack damage, the nonlinear responses have been further studied and experimentally validated at

unbonded planner interfaces (Buck et al., 1978, Richardson, 1979), and unbonded rough interfaces

(Sutin and Nazarov, 1995, Klepka, et al., 2014).

Figure 2.3 A simple model for nonlinear ultrasonic modulation at the presence of a crack.

2.2 Binding conditions

Note that even for a structure that behaves nonlinearly, nonlinear ultrasonic modulation does not

always occur. Previous studies have theoretically and experimentally investigated the binding

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conditions for nonlinear wave modulation with localized nonlinear damage (Zaitsev et al., 2009, Lim

et al., 2014), and these studies can be briefly summarized as follows:

(1) Crack perturbation condition: The strain (displacement) at the location with damage should be

oscillated by both input waves (or vibrations). That is, if the crack is located at the node of one of the

input waves, the nonlinear components are not generated. However, in wave propagation, this

condition does not need to be considered because the node/anti-node is varied as the wave propagates.

(Zaitsev et al., 2009)

(2) Mode matching condition: The motion induced by one of the two inputs should modulate the

other input at the location of the nonlinear damage. That is, the high amplitude of the nonlinear

ultrasonic modulation can be obtained when the ultrasonic signal is modulated due to the crack

motion. (Klepka, et al., 2011)

(3) Nonlinear resonance condition: In the case of vibration, the amplitude of the modulated

vibration mode can be further amplified when the modulation frequency coincides with one of the

resonance frequencies of the structure. (Lim et al., 2014)

That is, the generation of nonlinear modulation is heavily dependent on the choice of 𝑓𝑓𝑎𝑎 and

𝑓𝑓𝑏𝑏 and can be easily affected by the configuration of the damage as well as by variations in the

environmental and operational conditions (e.g., temperature and loading) of the target structure.

Figure 2.4 shows an investigation result got from an aluminum plate with a fatigue crack (25

mm long and 15 μm width) (Lim et al., 2014). The experiment was conducted by applying two

continuous sine signals (vibration case) and two tone-burst signals (wave propagation case) with

multiple combinations of 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 , respectively, on the aluminum plate via piezoelectric

transducers (PZTs). It shows that when the inputs (𝑓𝑓𝑎𝑎 = 217 kHz, 𝑓𝑓𝑏𝑏 = 33 kHz) satisfy the binding

conditions, nonlinear modulation components appear in the response singals (Figure 2.4(a)). However,

if the inputs (𝑓𝑓𝑎𝑎 = 504 kHz, 𝑓𝑓𝑏𝑏 = 33 kHz) do not satisfy the binding conditions, nonlinear ultrasonic

modulation does not occur even when there is a fatigue crack in the target aluminum plate (Figure

2.4(b)). In practice, it is challenging to find the optimal combination of two input frequencies 𝑓𝑓𝑎𝑎 and

𝑓𝑓𝑏𝑏, which satisfies all the binding conditions.

- 16 -

Vibration Wave propagation

(a)

Vibration Wave propagation

(b)

Figure 2.4 Investigation of nonlinear ultrasonic modulation with different input frequencies: (a) 𝑓𝑓𝑎𝑎 =

217 kHz, 𝑓𝑓𝑏𝑏 = 33 kHz, satisfying the binding conditions, and (b) 𝑓𝑓𝑎𝑎 = 504 kHz, 𝑓𝑓𝑏𝑏 = 33 kHz, not

satisfying the binding conditions. (Lim et al., 2014)

2.3 Literature review for nonlinear ultrasonic modulation

Nonlinear ultrasonic modulation techniques with a low-frequency and a high-frequency inputs

have been widely studied for structural damage detection over the past decades. For examples, fatigue

crack in an aluminum plate was detected using a piezoelectric stack actuator for generation of the

low-frequency input and a surface-mounted PZT for creation of the high-frequency input (Parsons and

Staszewski, 2006). Croxford et al. detected a fatigue damage introduced in aluminum alloy and

investigated the nonlinear responses with respect to the number of fatigue cycles using two oblique

incidence shear transducers (Croxford et al., 2009). Warnemuende and Wu detected microcracking

and deterioration in concretes using an impact hammer for low-frequency input generation and a PZT

for high-frequency excitation (Warnemuende and Wu, 2004). With the similar test setup, Chen et al.

- 17 -

detected and tracked the evolution of micro cracks in Portland cement mortar samples (Chen et al.,

2008). Aymerich and Staszewski demonstrated the application of the nonlinear ultrasonic modulation

technique for damage detection in composite resulting from a low-velocity impact (Aymerich and

Staszewski, 2010). An electromagnetic shaker was used to introduce the low-frequency input, and a

surface-mounted PZT was used for high-frequency excitation. The results showed that the amplitude

of the modulations is related to the severity of damage. Meo et al. also applied this technique to detect

delamination damage due to low-velocity impact on various composite plates (Meo et al., 2008). The

input frequencies were chosen as the first and the third resonance modes of these test plates. Klepka et

al. applied an electromagnetic shaker to generate low-frequency input and surface-mounted PZT for

high-frequency excitation, and a scanning laser vibrometry was applied to acquire the responses from

the composite plates for impact damage detection and localization (Klepka et al., 2014). Ballad et al.

developed a noncontact damage visualization technique for simulated defects in a thin plate (Ballad et

al., 2004). Two focused air-coupled transducers with scanning equipment were used for high-

frequency ultrasonic excitation and sensing. For low-frequency excitation, a mechanical shaker or a

loud speaker was used. Lim et al. used two air-coupled transducers for generation both low-frequency

and high-frequency inputs and a 3D laser Doppler vibrometer was adopted for fatigue damage

visualization in an aluminum plate (Lim et al., 2015).

There are also some works about the binding conditions for nonlinear modulation generation.

Didenkulov et al. found that cracks in concrete beams generated significant modulation components

when a low-frequency sweeping signal was used (Didenkulov et al., 1999). The dependence of high-

frequency input on the modulation amplitude was studied by Duffour et al. (Duffour et al., 2006).

This frequency dependence was also noted by Courtney et al. (Courtney et al., 2008). A fixed low-

frequency and a swept high-frequency were used to find an optimal combination that can amplify the

modulation level caused by a crack (Yoder and Adams, 2010). Similarly, a first sideband spectrogram

was created by sweeping both the low-frequency and high-frequency inputs over specified frequency

ranges to study the effect of input frequency combination on the modulation amplitude (Sohn et al.,

2013). This experiment was conducted on aluminum plate specimens with a fatigue crack and Figure

2.5 gives an example of the first sideband spectrogram by sweeping the low-frequency inputs from 10

to 20 kHz and the high-frequency inputs from 80 to 110 kHz. It can be seen that only for a subset of

low-frequency and high-frequency combinations, the nonlinear modulation components have higher

amplitude in the presence of a fatigue crack.

- 18 -

(a) (b)

Figure 2.5 The first sideband spectrogram obtained from aluminum specimens by sweeping the high-

frequency inputs from 10 to 20 kHz and the low-frequency inputs from 80 to 110 kHz: (a) intact case,

and (b) damage case. (Sohn et al., 2013)

2.4 Nonlinear ultrasonic modulation with a wideband input

Since it is not easy to find the optimal frequency combination which satisfies all the binding

conditions, and sweeping input frequency combinations decreases the test efficiency, this chapter

explores the nonlinear ultrasonic modulation technique with a wideband input. That is, rather than

using two distinct input frequencies, a single wideband excitation is used instead.

When a wideband excitation signal (e.g., a pulse laser) is used as the driving signal, different

frequency peaks will be generated due to different guided wave modes (Lamb wave modes)

propagating in a plate, standing wave modes or resonance modes of a structure. The nonlinear

ultrasonic modulation can occur among these frequency peaks when the structure is damaged as

shown in Figure 2.6. In this way, the wideband input guarantees that the binding conditions can be

satisfied among at least some frequency peaks in the generated frequency band. Also, the test data

collection time can be highly reduced compared with sweeping different input frequency

combinations.

One issue to be concerned is that the energy level for each frequency component under a

wideband input might be much lower than the energy level achieved with two single distinct input

frequencies. However, the feasibility of this nonlinear wave modulation technique with a wideband

input has been proven in several related articles. de Lima et al. showed that the dislocation, friction,

stress concentration and temperature gradient due to crack damage can produce nonlinear modulation

even at a very low strain level (de Lima et al. 2003). Van Den Abeele et al. studied the relationship

- 19 -

between the sideband energy and the strength of the low-frequency input signal and showed that, even

when the low-frequency signal has almost zero strength, the sideband energy in a nonlinear structure

is significant and measurable (Van Den Abeele et al., 2000). Sohn et al. succeeded in observing the

nonlinear modulation with low strength input for both low-frequency and high-frequency signals

(Sohn et al., 2013). Therefore, even when the energy for each frequency component caused by a

wideband excitation is relatively weak, the nonlinear behavior of a damaged structure can still be

expected and monitored. In addition, because multiple frequency peaks were generated by a wideband

excitation, higher-order nonlinear modulations (cascade cross modulations) could be generated as

well in the presence of damage (Zaitsev et al., 2011).

(a)

(b)

Figure 2.6 Illustration of nonlinear ultrasonic modulation using a wideband input: (a) intact case, and

(b) damage case.

2.5 Chapter summary

This chapter describes the working principle and binding conditions for nonlinear ultrasonic

modulation, and reviews a bunch of related researches for nonlinear ultrasonic modulation based

structural damage detection. Among the previous researches, in order to guarantee that nonlinear

ultrasonic modulation occurs in the presence of damage, the inputs applied on the target structure are

often swept over multiple frequency combinations. Different from previous researches, nonlinear

- 20 -

ultrasonic modulation with a wideband input is proposed and explained in this chapter. Under a

wideband input, the binding conditions for nonlinear ultrasonic modulation can be satisfied among at

least some frequency peaks in the generated frequency band. The test data collection time can also be

highly reduced compared with sweeping different frequency combinations. However, under a

wideband input, since the nonlinear modulation components and the linear response components

overlap in the frequency domain, it requires additional signal processing methods to diagnose the

condition of the target structure using the wideband structural responses.

- 21 -

- 22 -

Chapter 3. Noncontact Laser Ultrasonic System and Numerical Simulation

This chapter explains the working principles and characteristics for laser based ultrasonic wave

generation and measurement. A noncontact laser ultrasonic scanning system is introduced in this

chapter with detailed description for all the system compositions. A 3D simulation model for laser-

induced ultrasonic waves is developed and described in this chapter as well, and the simulation results

are validated with experimental tests using the noncontact laser ultrasonic scanning system. In

addition, a simulated micro crack is created in the model for validating the damage detection

techniques developed in the following chapters, and the nonlinear character of the simulated micro

crack is proved by observing its closing and opening motion during ultrasonic wave propagation.

3.1 Laser ultrasonic generation

Laser based ultrasound can be divided into two categories: one for ultrasound generation and the

other for sensing. It often requires a pulse laser to generate the ultrasonic waves and a continuously

running laser to receive the responses.

For ultrasonic generation, the laser is a device which amplifies the intensity of light by means of

a quantum process known as stimulated emission. The generated lasers are short pulse (from tens of

nanoseconds to femtoseconds) and high peak power lasers. Common lasers used for ultrasonic

generation are solid state Q-switched Nd:YAG lasers and gas lasers (CO2 or Excimers), and they are

used principally as a transient source of high-power localized heat. A number of different physical

processes may take place when a solid surface is illuminated by a laser (Scruby and Drain, 1990). At

lower incident powers these include heating, generation of thermal waves, elastic waves (ultrasound)

and, in materials such as semiconductors, electric currents may be caused to flow. At higher powers,

material may be ablated from the surface and a plasma formed, while in the sample there may be

melting, plastic deformation and even the formation of cracks. With a high power level, these ablation

phenomena are mostly used for welding or cutting of the target sample.

Here, the discussion is focused on laser power regimes that are suitable for structural damage

detection, and therefore focus most of our attention on the localized heating produced by a laser,

which in turn generates the thermoelastic stresses and strains that act as an ultrasonic source. The laser

ultrasonic generation is actually a complex multi-physics procedure. As shown in Figure 3.1,

electromagnetic radiation from the laser is absorbed in the surface region of a sample, causing heating.

- 23 -

https://en.wikipedia.org/wiki/Solid-state_laser

https://en.wikipedia.org/wiki/Q-switching

https://en.wikipedia.org/wiki/Nd:YAG_laser

https://en.wikipedia.org/wiki/Gas_laser

https://en.wikipedia.org/wiki/Carbon_dioxide_laser

https://en.wikipedia.org/wiki/Excimer_laser

Thermal energy then propagates into the specimen as thermal waves. For typical Q-switched laser

pulse duration, the thermal wave field only extends a few micrometers even in good conductors. The

heated region undergoes thermal expansion, and thermoelastic stresses generate elastic waves

(ultrasound) which propagate deep within the sample. All types of elastic waves can be generated,

including bulk waves (compression and shear), surface waves (including Rayleigh) and guided waves

(e.g., Lamb waves in plates, extensional and flexural waves in rods). And a wide range of ultrasonic

amplitudes can be generated by varying the incident laser power. Note that, the thermal expansion

level is proportional to the gradient of the thermal energy, thus it indicates that a high-power short-

pulse laser is suitable for ultrasonic generation with a high efficiency.

Figure 3.1 Ultrasonic generation by a laser.

Several characteristics should be taken into consideration when a pulse laser is used for

ultrasonic generation, including wavelength, pulse energy, beam profile, pulse duration and pulse

repetition rate. A brief discussion is given as follows (Scruby and Drain, 1990):

(1) For most purposes, the choice of optical wavelength is not that critical. The main effect of

changing the wavelength of the incident electromagnetic radiation is to modify the reflectivity of the

solid surface, and hence the efficiency with which the incident radiant energy is converted into

elastic-wave energy. Compared with metals, the situation may be more complicated in certain non-

metals, where the absorption of electromagnetic radiation is strongly frequency dependent.

(2) Pulse energy is a very important factor in determining the characteristics of laser-generated

ultrasonic waves. There are two conflicting considerations. On one hand, the ultrasonic amplitude in

the truly non-destructive thermoelastic regime is proportional to optical power, i.e. proportional to

pulse energy for a fixed duration pulse. Thus, to enhance ultrasonic amplitudes and thereby improve

the sensitivity of, for example, laser-ultrasonic based damage detection, as high a pulse energy as

possible is desirable. On the other hand, however, increasing the pulse energy brings the source closer

- 24 -

to the threshold for surface damage, and a certain amount of unwanted plastic deformation, melting or

vaporization may occur. However, this threshold depends on power density rather than energy, so that

it can sometimes be avoided by enlarging the irradiated area but such an action may significantly

change the characteristics of the generated ultrasonic waves.

(3) The area of the incident radiation on the sample surface is important because it affects both

the power density (and hence the threshold for ablation and surface damage) and the characteristics of

the generated ultrasonic waves. Many commercial lasers produce beams with diameter of the order of

a centimeter, but optical components such as lenses are often used to tailor the dimensions of the

beams. Thus, particular ultrasonic characteristics can readily be obtained by changing the irradiated

area from a circular region, to a point, to a line, to a circular line, or even to phased arrays.

(4) Pulse duration is another relatively important parameter since it also influences both the

generation mechanism and the characteristics of the generated ultrasonic waves. The optical energy

must be compressed into a very short pulse in order to obtain a sufficiently high instantaneous power

(>105 W) to generate useful ultrasonic amplitudes. The preferred pulse duration depends upon the

desired ultrasonic waveform. A pulse duration of 20 ns or less is required to generate adequate

ultrasonic energy up to 20 MHz. However, if lower ultrasonic frequencies (< 1 MHz) are required, it

is arguably still better to employ a pulse duration in the range 10-50ns than switch to a normal pulse

laser. This is because the generation efficiency in metals falls with longer pulse duration and probably

more than compensates for any advantage gained by compressing the energy into a narrower

frequency band. In addition, the possibly complicating effects of thermal conductivity also increase

with pulse duration.

(5) The desired repetition rate is likely to depend upon the intended applications. The advantage

of a high repetition rate for damage detection, for instance, is that extensive, rapid signal averaging

can be carried out to improve signal to noise ratios. High repetition rates also mean that large areas

can be rapidly scanned. However, in specimens where there is much ultrasonic reverberation, higher

repetition rates are not preferred, because the ultrasonic waveforms from successive pulses, which last

many milliseconds, may overlap.

3.2 Laser ultrasonic measurement

There are various means for laser ultrasonic measurement such as two-beam homodyne, two-

beam heterodyne, time-delay, Fabry-Perot, dynamic holographic, multi-beam, fiber interferometry,

optical beam deflection, and knife edge detection (Scruby and Drain, 1990). Among these, laser

- 25 -

Doppler vibrometer (LDV) using the Doppler effect, which is one type of the two-beam heterodyne

interferometers, is one of the most widely used because of its sensitivity and stability compared to

other intensity modulation interferometers.

If a beam is reflected by a moving object and detected by a measurement system, the measured

Doppler frequency shift of the beam can be described as (Drain, 1980):

𝑓𝑓𝑑𝑑 = 2 ∙ 𝑣𝑣/𝜆𝜆 (3.1)

where 𝑣𝑣 is the object’s velocity and 𝜆𝜆 is the wavelength of the emitted beam. To be able to

determine the velocity of an object, the Doppler frequency shift has to be measured at a known

wavelength. This can be done by using a LDV. A LDV is generally a two beam laser interferometer

that measures the frequency difference between an internal reference beam and a test beam. The most

common type of laser in an LDV is the helium-neon laser, although laser diodes, fiber lasers, and

Nd:YAG lasers are also used. Most commercial LDVs work in a heterodyne regime by adding a

known frequency shift (typically 30 - 40 MHz) to one of the beams. This frequency shift is usually

generated by a Bragg cell, or acousto-optic modulator. The frequency shift is greater than the

maximum Doppler frequency shift, so that the frequency at the detector never falls to zero and thus

sign ambiguity does not arise.

Figure 3.2 Schematic of a typical laser Doppler vibrometer based on two-beam heterodyne method.

The working procedure of a typical LDV is briefly given here (Figure 3.2). The beam from the

laser, which has a frequency 𝑓𝑓0, is divided into a reference beam and a test beam with a beam splitter.

The test beam then passes through the Bragg cell, which adds a frequency shift 𝑓𝑓𝑏𝑏. This frequency

shifted beam is then directed to the target. The motion of the target adds a Doppler shift to the beam

given by 𝑓𝑓𝑑𝑑. Light scatters from the target in all directions, but some portion of the light is collected

by the LDV and reflected by the beam splitter to the photodetector. This light has a frequency equal to

𝑓𝑓0 + 𝑓𝑓𝑏𝑏 + 𝑓𝑓𝑑𝑑. This scattered light is combined with the reference beam at the photodetector. The

initial frequency of the laser is very high (> 1014 Hz), which is higher than the response ability of the

- 26 -

detector. The detector does respond, however, to the beat frequency between the two beams, which is

at 𝑓𝑓𝑏𝑏 + 𝑓𝑓𝑑𝑑 (typically in the tens of MHz range). The output of the photodetector is a standard

frequency modulated signal, with the Bragg cell frequency 𝑓𝑓𝑏𝑏 as the carrier frequency, and the

Doppler shift 𝑓𝑓𝑑𝑑 as the modulation frequency. This signal can be demodulated to derive the velocity

of the vibrating target.

Note that, there are some fundamental limitations when use LDV for measurement (Johansmann

et al., 2005, Scruby and Drain, 1990, Martin and Rothberg, 2009): (1) Sensitivity limit: Higher

intensity of the reference and the test beams leads to more effective Doppler frequency shift

measurement, but induces severer photon noise. Therefore, LDV devices try to supply enough laser

intensity to ensure the measurement sensitivity while minimize the photon noise; (2) Intermode

beating: As the laser source is not an ideal single mode laser, undesirable spurious signals are

generated by beating between the laser modes. This fluctuates the measurement according to the path

length difference between the reference and the test beams; and (3) Speckle noise: When the incident

laser beam irradiated on a rough surface, the scattered light intensity has an irregular angular

distribution, called speckle pattern. The speckle pattern will reduce the reflectivity of the laser signal

from the target surface, disturbing proper ultrasonic measurement. Hence, special surface treatment is

needed in some test cases to enhance the reflectivity of the returned laser signal.

3.3 Laser ultrasonic scanning system

3.3.1 System configuration

A complete noncontact laser ultrasonic scanning system is introduced in this section (An et al.,

2013). This system is composed of an excitation unit, a sensing unit and a control unit, as illustrated in

Figure 3.3. The excitation unit is comprised of a Q-switched Nd:YAG pulse laser (Quantel Ultra

Laser), a galvanometer and a focal lens. The Nd:YAG pulse laser has a wavelength of 532 nm and a

maximum peak power of 3.7 MW, and generates a pulse with 8 ns pulse duration at a repetition rate

of 20 Hz. The galvanometer (Scanlab Scancube10) has a maximum rotating speed of 5730 °/s, angular

resolution of 6.6 × 10-4 ° and an allowable scan angle of ± 21.8 °. Through the galvanometer, the

pulse laser can be shot at the desired excitation points. The focal lens installed in front of the

galvanometer adjusts the laser beam size to less than 0.5 mm at the optical focal length of 2 m for

achieving high spatial resolution.

For the sensing unit, a commercial scanning LDV (Polytec PSV-400-M4) with a built-in

- 27 -

galvanometer and an auto-focal lens is used. The laser source of this LDV is a helium neon (He-Ne)

laser with a wavelength of 633nm. The maximum angular scan range and scanning speed are ± 20 °

and 2000 °/s, respectively. This one-dimensional (1D) LDV measures the out-of-plane velocity in the

range of 0.01 μm/s to 10 m/s over a target surface based on the Doppler effect. Here, the intensity of

the reflected laser beam governs the sensitivity of the LDV, and the intensity of the reflected laser

beam highly depends on the surface condition. For a rough surface, a special surface treatment is

often necessary to enhance the reflectivity of the returned laser beam. Moreover, the system here can

be extended to conduct 3D measurement by using a 3D LDV.

The control unit consists of a personal computer (PC), controller, velocity decoder with the

maximum sensitivity of 1 mm/s/V and a 14-bit digitizer with a maximum sampling frequency of 2.56

MHz. The controller sends out trigger signals to launch the excitation laser beam and to

simultaneously start the data collection. In addition, the controller generates control signals to aim the

excitation and sensing laser beams to desired target positions. The velocity decoder computes the out-

of-plane velocity by relating it to the frequency shift of the laser beam reflected from the target

surface. The measured signals are then stored and processed in PC.

Figure 3.3 Schematic diagram of the noncontact laser ultrasonic scanning system. (An et al., 2013)

The overall working principle is as follows. First, virtual grid points on the target surface are

- 28 -

created using a built-in digital camera and a software program. Also, the sequences of excitation and

sensing scanning points are predetermined. Note that different scanning strategies can be employed at

this stage, and these strategies will be given in next subsection. Once the grid points and scanning

sequences are predetermined, the controller in the control unit sends out a trigger signal to the

excitation unit to fire the excitation laser beam to the first prescribed excitation point. The same

trigger signal is simultaneously transmitted to the sensing unit to activate data acquisition. Then, the

response signal is collected at a specified measurement point, transmitted to and stored in the control

unit. Next, the control unit moves the excitation or sensing laser beam or both laser beams

automatically to the next scanning point(s) by sending control signals to the relevant galvanometer(s).

By repeating the ultrasonic excitation and sensing over the prescribed grid points, all the

corresponding response signals can be acquired, and they can be used for further signal processing,

such as ultrasonic wavefield imaging, damage detection and visualization.

The laser ultrasonic scanning system introduced here has the following advantages: (1) The

system can be rapidly deployed and requires less maintenance since no sensors are needed to place on

the target structure; (2) The system can achieve high temporal and spatial resolutions and is effective

for incipient damage detection; and (3) The system is applicable to harsh environments and even on

moving structures. However, a main concern about usage of the laser ultrasonic scanning system is

the safety issue. Very carefully cautions are needed to handle lasers. In particular, retinal or skin

damage might be caused when the high-power laser beam is directly or indirectly exposed to eye or

skin. Thus, it is important to know the risk level of each laser in advance. For the laser ultrasonic

scanning system introduced in this chapter, the He-Ne laser used for ultrasonic wave measurement

and the Nd:YAG laser for ultrasonic wave generation are classified as Class 2 (safe except long-time

naked eye exposure) and Class 4 (danger in eye and skin exposure by direct or indirect laser beam),

respectively. Therefore, special caution is required when use this laser ultrasonic scanning system.

3.3.2 Scanning strategy

Four different scanning strategies are given and compared (An et al., 2013). Using this laser

ultrasonic scanning system, two scanning strategies can be realized. That is, fixed laser excitation and

scanning laser sensing (Figure 3.4(a)), and scanning laser excitation and fixed laser sensing (Figure

3.4(b)). When the laser ultrasonic scanning system is used together with a surface mounted

piezoelectric transducer (PZT) or a noncontact air-coupled transducer (ACT), we can achieve two

more scanning strategies, namely, fixed PZT/ACT excitation and scanning laser sensing (Figure

3.4(c)), and scanning laser excitation and fixed PZT/ACT sensing (Figure 3.4(d)). All these four

- 29 -

scanning strategies have their own advantages and disadvantages, and suit for different applications.

A brief comparison and discussion is given below.

Theoretically, based on the linear reciprocity of ultrasonic waves (Fink and Prada, 2001), the

scanning strategies shown in Figures 3.4(a) and (b) offer the identical scanning results. However, in

practice, scanning the excitation laser is more effective than scanning the sensing laser. This is

because the ultrasonic generation by Nd:YAG laser is little affected by the surface irregularity and the

incident angle of the excitation beam, while the sensitivity of LDV heavily depends on the surface

condition of the sensing points and the incident angle of the sensing laser beam. Therefore, a retro-

reflective tape or special coating is often applied to the sensing surface to increase the light intensity

of the backscattered laser beam along the incident angle and to improve the LDV sensitivity.

Typically, the allowable incident angle for an excitation laser is up to ± 70 ° (Lee et al., 2011) while

± 20 ° for a sensing laser (Scruby and Drain, 1990).

(a) (b)

(c) (d)

Figure 3.4 Four different scanning strategies: (a) fixed laser excitation and scanning laser sensing, (b)

scanning laser excitation and fixed laser sensing, (c) fixed PZT/ACT excitation and scanning laser

sensing, and (d) scanning laser excitation and fixed PZT/ACT sensing.

For the scanning strategy shown in Figure 3.4(c), when a fixed PZT or ACT is used for ultrasonic

generation, any arbitrary waveform such as a narrowband tone-burst signal can be exerted to an

excitation point with high energy level. The desired narrowband excitation and high excitation energy

- 30 -

can simplify the subsequent signal processing process to a certain extent. Also, the high excitation

energy may augment inspection speed by reducing the time averaging for ultrasonic measurement

with LDV. Note that, though the input waveform of a laser excitation is limited to a wideband pulse in

this discussion, there still exist some special techniques to generate narrowband inputs with laser.

(Huang et al., 1992, Kim et al., 2006).

A similar wavefield image can be created by the scanning strategy shown in Figure 3.4(d) unless

the excitation is limited to a pulse input. However, for some specific applications such as curved

surfaces or large scanning areas, the scanning strategy shown in Figure 3.4(d) is more effective than

the strategy shown in Figure 3.4(c), because the ultrasonic generation by Nd:YAG laser is less

affected by the surface irregularity and the incident angle of the excitation beam, comparing with the

ultrasonic sensing by LDV. Moreover, when PZT or ACT is used for sensing, multiple ultrasonic

wave modes can be acquired.

3.4 Literature review for noncontact laser ultrasonics

Noncontact laser ultrasonic techniques have been extensively studied by nondestructive testing

(NDT) community, to structural health monitoring (SHM) applications. Besides the noncontact laser

ultrasonic scanning system introduced above (An et al., 2013), several similar laser based system have

been developed and used for modal analysis (Sriram et al., 1992, Stanbridge and Ewins, 1999) and

structural damage detection (Dixon et al., 2010, Yashiro et al., 2008, Lee et al., 2007a, Lee et al.,

2007b, Mallet et al., 2004, Staszewski et al., 2007). For example, Dixon et al. performed an A-scan

by scanning the excitation laser over a target surface and measured ultrasonic signals with an

electromagnetic acoustic transducer (EMAT) to detect cracks in metal sheets (Dixon et al., 2010).

Similarly, Yashiro et al. and Lee et al. proposed the test systems using a Q-switched pulse laser for

ultrasonic excitation scanning and a fixed piezoelectric transducer (PZT) for ultrasonic response

measurement, and they showed the system capability through damage detection in pipe and composite

structures (Yashiro et al., 2008, Lee et al., 2007a, Lee et al., 2007b). On the other hand, Mallet et al.

visualized Lamb wave propagation using a commercial LDV for sensing scanning and a PZT for

excitation (Mallet et al., 2004). Cracks in a metallic structure were also detected using a 3D LDV for

sensing scanning along three spatial axes and a PZT for excitation (Staszewski et al., 2007). Figure

3.5 gives an example of the Lamb wave propagation contour plots visualized using the out-of-plane

sensing scanning signals (Staszewski et al., 2007). And it shows that the wave interaction with a crack

can be seen from the wave propagation imaging results.

However, in some cases, especially when the damage is at its initial stage, the wave interaction

- 31 -

with the damage cannot be directly seen from the reconstructed wave propagation imaging, thus

multiple signal processing methods have been proposed. An adjacent wave subtraction method was

proposed for structural damage diagnosis (Lee et al., 2012). Instantaneous wavenumber, relying on

the effective thickness of the target structure, was extracted to detect the delamination and estimate

the delamination depth in composite structures (Mesnil et al., 2014). A frequency-wavenumber

filtering method, which makes it possible to separate wave propagation depending on its directionality,

was proposed to enhance damage detectability (Ruzzene, 2007, Michaels et al., 2011, Sohn et al.,

2011a), and for structures with additional structural complexities (An et al., 2013). Based on the

frequency-wavenumber filtering method, standing waves were also extracted for detecting

delamination in composites (Sohn et al., 2011b, Park et al., 2014). Nonlinear ultrasonic modulation

technique was adopted and the sensing scanning signals by LDV under two single frequency inputs

generated by ACTs were used to extract the nonlinear modulation components for fatigue crack

detection and visualization (Lim et al., 2015). Also, nonlinear features were extracted from the

response signals from a wideband pulse laser input, and micro damage was detected and visualized

through laser excitation scanning (Liu et al., 2014, Liu et al., 2015). Moreover, several techniques

were developed to accelerate the laser scanning procedure via two-stage scanning (Park and Sohn,

2014, Park et al., 2016), compressed sensing schemes (Donoho, 2016, Park et al., 2017), and with a

continuous-scanning (fast scan) LDV for measurement (Flynn, 2014).

Figure 3.5 Example of Lamb wave propagation contour plots in the time domain. (Staszewski et al.,

2007)

3.5 Numerical simulation for laser-induced ultrasonic waves

3.5.1 Governing equations

- 32 -

A number of different physical processes may take place when a specimen surface is illuminated

by a pulse laser beam. At a low power level of the laser beam, these processes include heating and the

generation of thermal and elastic waves (ultrasound). At a high power level, the surface of the

specimen may be ablated and a plasma formed, causing melting and plastic deformation of the

specimen and even the formation of cracks (Scruby and Drain, 1990). Here, the discussion of the laser

power is restricted to a low power level so that ultrasonic waves can be generated and used for

structural damage detection without harming the target specimens.

When the surface of an isotropic specimen is illuminated by a pulse laser, the surface region

absorbs the electromagnetic radiation from the laser, causing heating. The resulting thermal

conduction can be expressed in a cylindrical coordinate system, illustrated in Figure 3.6, as follows

(Xu et al., 2004):

𝜌𝜌𝐶𝐶𝑝𝑝𝜕𝜕𝜕𝜕(𝑟𝑟, 𝑧𝑧, 𝑡𝑡)

𝜕𝜕𝑡𝑡= ∇�𝑘𝑘∇𝜕𝜕(𝑟𝑟, 𝑧𝑧, 𝑡𝑡)� + 𝑄𝑄 (3.2)

where 𝜕𝜕(𝑟𝑟, 𝑧𝑧, 𝑡𝑡) represents the temperature distribution at time 𝑡𝑡, 𝑟𝑟 is along the radial direction, 𝑧𝑧

is along the depth direction. 𝜌𝜌, 𝐶𝐶𝑝𝑝 and 𝑘𝑘 are the density, specific heat capacity at a constant

pressure, and thermal conductivity, respectively. 𝑄𝑄 is the power density of a heat source. Because the

pulse laser is often treated as a heat flux rather than a heat source (𝑄𝑄 = 0), Equation (3.2) can be

simplified as:

𝜌𝜌𝐶𝐶𝑝𝑝𝜕𝜕𝜕𝜕(𝑟𝑟, 𝑧𝑧, 𝑡𝑡)

𝜕𝜕𝑡𝑡=

1𝑟𝑟𝜕𝜕𝜕𝜕𝑟𝑟 �

𝑟𝑟𝑘𝑘𝜕𝜕𝜕𝜕(𝑟𝑟, 𝑧𝑧, 𝑡𝑡)

𝜕𝜕𝑟𝑟 � +𝜕𝜕𝜕𝜕𝑧𝑧 �

𝑘𝑘𝜕𝜕𝜕𝜕(𝑟𝑟, 𝑧𝑧, 𝑡𝑡)

𝜕𝜕𝑧𝑧 � (3.3)

The normal boundary conditions are listed as follows:

−𝑘𝑘𝜕𝜕𝜕𝜕(𝑟𝑟, 𝑧𝑧, 𝑡𝑡)

𝜕𝜕𝑧𝑧�𝑧𝑧=0

= 𝐼𝐼𝑓𝑓(𝑟𝑟)𝑔𝑔(𝑡𝑡), 𝜕𝜕𝜕𝜕(𝑟𝑟, 𝑧𝑧, 𝑡𝑡)

𝜕𝜕𝑧𝑧�𝑧𝑧=ℎ

= 0 (3.4)

where 𝐼𝐼 is the power intensity of the absorbed laser beam, and 𝑓𝑓(𝑟𝑟) and 𝑔𝑔(𝑡𝑡) are the spatial and

temporal distributions of the pulse laser beam, respectively. 𝑧𝑧 = 0 is at the top surface and 𝑧𝑧 = ℎ is

at the bottom surface (Figure 3.6). ℎ is the thickness of the specimen.

Then, the thermal energy acquired from the pulse laser propagates into the specimen as thermal

waves. Also, the thermal wave region is accompanied by thermal expansion, which in turn generates

stresses and strains within the specimen. The sudden change in stress within a region of the specimen

will act as a source of elastic waves (ultrasound) which then redistribute the stress throughout the

specimen and produce a transient displacement field (ultrasonic wave region), as illustrated in Figure

3.6. In an isotropic specimen, the displacement satisfies (Xu et al., 2004, Scruby and Drain, 1990):

(𝜆𝜆 + 2𝜇𝜇)∇�∇ ∙ 𝑼𝑼(𝑟𝑟, 𝑧𝑧, 𝑡𝑡)� − 𝜇𝜇∇ × ∇ × 𝑼𝑼(𝑟𝑟, 𝑧𝑧, 𝑡𝑡)

−𝛼𝛼𝑡𝑡(3𝜆𝜆 + 2𝜇𝜇)∇𝜕𝜕(𝑟𝑟, 𝑧𝑧, 𝑡𝑡) = 𝜌𝜌𝜕𝜕2𝑼𝑼(𝑟𝑟, 𝑧𝑧, 𝑡𝑡)

𝜕𝜕2𝑡𝑡

(3.5)

- 33 -

where 𝑼𝑼(𝑟𝑟, 𝑧𝑧, 𝑡𝑡) is the time-dependent displacement, 𝜆𝜆 and 𝜇𝜇 are the Lamé constants, and 𝛼𝛼𝑡𝑡 is

the thermoelastic expansion coefficient of the isotropic specimen.

Figure 3.6 Illustration of the ultrasonic wave generated by a pulse laser beam.

3.5.2 Plate modeling

Numerical simulation models have been developed for simulating laser-generated ultrasound (Xu

et al., 2004, Xu et al., 2006, Cavuto et al., 2013, Liu et al., 2015), but some of the models simplify the

laser source as an effective elastic source, neglecting its thermoelastic nature. Here, ultrasonic wave

propagation induced by a pulse laser is modelled and analyzed using the commercial finite element

software COMSOL Multiphysics. A 3D model (cylindrical coordinate system, 𝑟𝑟, 𝜃𝜃 and 𝑧𝑧) is built

to simulate a circular aluminum plate with a radius (𝑟𝑟 direction) of 75 mm and varying thicknesses (𝑧𝑧

direction). The material properties of the aluminum plate used for the numerical simulations are listed

in Table 3.1. A pulse laser beam with 1 mm radius is exerted onto the center of the plate. The pulse

laser delivers 10 mJ of energy for 8 ns. The energy from the laser is treated as a heat flux and applied

on the top surface of the plate. Except this top surface exposed to the pulse laser, all other boundaries

are assumed to be thermally insulated. The inward heat flux on the surface boundary can be described

as follows:

𝐼𝐼𝑖𝑖𝑖𝑖(𝑟𝑟, 𝑡𝑡) = 𝐼𝐼0(1− 𝑅𝑅𝐶𝐶)(1𝜋𝜋𝜎𝜎2

)𝑒𝑒−�𝑟𝑟22𝜎𝜎2�𝑔𝑔(𝑡𝑡) (3.6)

where 𝐼𝐼0 is the peak power of the pulse laser, and 𝑅𝑅𝐶𝐶 is the reflection coefficient of the aluminum

plate surface. The power intensity of the laser beam is assumed to follow a Gaussian distribution in

the 𝑟𝑟 direction, and the standard deviation of the Gaussian laser beam, 𝜎𝜎, is assumed to be 0.3 mm as

shown in Figure 3.7(a). The temporal function of the laser beam, 𝑔𝑔(𝑡𝑡), is assumed to be a pulse

function as shown in Figure 3.7(b).

- 34 -

Table 3.1 Properties of the aluminum used for numerical simulations

Density 𝜌𝜌

(kg/m3)

Young’s modulus

𝐸𝐸 (GPa)

Poisson’s ratio 𝜈𝜈

Coefficient of thermal expansion

𝛼𝛼𝑡𝑡 (K-1)

Thermal conductivity

𝑘𝑘 (W/(m·K))

Heat capacity at constant pressure 𝐶𝐶𝑝𝑝

(J/(kg·K))

Reflection coefficient

𝑅𝑅𝐶𝐶

2700 68.9 0.33 2.34×10-5 170 900 0.95

(a) (b)

Figure 3.7 Spatial and temporal distributions of the pulse laser intensity: (a) spatial distribution of the

laser intensity over the irradiated region, and (b) temporal distribution in the time domain.

To represent multi-physical phenomena occurring after the impingement of the laser beam onto

the plate, the numerical model is divided into two sub-regions, thermal and ultrasonic wave regions

(Figure 3.8(a)). Within the thermal wave region, each node of the element has one thermal and three

mechanical degrees of freedom (DOFs). Within the ultrasonic wave region, each node has only three

mechanical DOFs.

Based on Equation (3.3), the thermal energy can be expressed as a Gaussian spread in space and

time, and a thermal diffusion length 𝜇𝜇𝑡𝑡 is described as (Marín, 2010):

𝜇𝜇𝑡𝑡 = 2√𝜅𝜅𝑡𝑡 (3.7)

where the diffusivity 𝜅𝜅:

𝜅𝜅 = 𝑘𝑘 𝜌𝜌𝐶𝐶𝑝𝑝⁄ (3.8)

This thermal diffusion length gives a distance at which the amplitude of the heat flux reduces 𝑒𝑒

times from its value on the top surface at each specific time 𝑡𝑡. To define the thermal wave region, 𝑡𝑡

in Equation (3.7) is set to the time where the surface temperature falls below 1% of the initial

temperature increase due to the pulse laser irradiation. Since the standard deviation of the Gaussian

- 35 -

spread of thermal energy is 𝜇𝜇𝑡𝑡/√2, the dimensions of the thermal wave region, within which over 99%

of the temperature changes occur, can be defined as:

𝛬𝛬𝑑𝑑 = 3√2𝜇𝜇𝑡𝑡 , 𝛬𝛬𝑙𝑙 = 𝑟𝑟𝑙𝑙𝑎𝑎𝑙𝑙𝑙𝑙𝑟𝑟 + 3

√2𝜇𝜇𝑡𝑡 (3.9)

where 𝑟𝑟𝑙𝑙𝑎𝑎𝑙𝑙𝑙𝑙𝑟𝑟 is the radius of the pulse laser beam, 𝛬𝛬𝑑𝑑 and 𝛬𝛬𝑙𝑙 are the depth and radius of the thermal

wave region, respectively. Assuming an 8 ns pulse laser, 𝑡𝑡 = 10 µs, 𝜇𝜇𝑡𝑡 = 53 μm, 𝛬𝛬𝑑𝑑 = 110 µm

and 𝛬𝛬𝑙𝑙 = 1110 µm are selected, respectively.

(a)

(b)

Figure 3.8 Schematic of the 3D FEM model (cross-section drawn): (a) geometry of the laser

irradiating plate, and (b) finite element meshes.

The entire model is meshed with tetrahedral elements, and a multi-scale element length is used to

reduce computation burden. For the thermal wave region, the pulse laser can be treated as the

superposition of multiple harmonic heat sources, and a thermal wavelength 𝜆𝜆 of a heat source with a

specific frequency is defined as (Mandelis, 2001):

𝜆𝜆 = 2𝜋𝜋�2𝜅𝜅/𝜔𝜔 (3.10)

- 36 -

Note that the thermal wavelength 𝜆𝜆 decreases when 𝜔𝜔 increases. For example, when the upper limit

of the interested frequency range is 350 kHz, which is the cut-off frequency of laser Doppler

vibrometer (LDV) used in later experiments, the corresponded thermal wavelength becomes around

50 μm. Hence, the maximum length of the tetrahedral mesh within the thermal wave regions is set to

one tenth of the thermal wavelength, 5 μm, as shown in Figure 3.8(b).

Inside the ultrasonic wave region, the recommended element length can be expressed as (Xu et

al., 2006):

𝑙𝑙𝑐𝑐 = 𝜆𝜆𝑚𝑚𝑖𝑖𝑖𝑖/20 (3.11)

where 𝑙𝑙𝑐𝑐 is the recommended element length and 𝜆𝜆𝑚𝑚𝑖𝑖𝑖𝑖 is the shortest wavelength of interest.

Assuming that we are mainly interested in ultrasonic responses up to 350 kHz, the wavelengths of

antisymmetric A0 and symmetric S0 modes in a 3 mm-thick aluminum plate become around 10 mm

and 14 mm, respectively. Considering the shortest wavelength of interest, the element length in the

ultrasonic wave region should be less than 0.5 mm. Note that, as the plate becomes thinner, the

shortest wavelength and the corresponding element length decrease as indicated in Figure 3.8(b).

The initial temperature and displacement field values at 𝑡𝑡 = 0 are set to 𝜕𝜕 = 293.15 𝐾𝐾,𝑼𝑼 =

(0,0,0) in 𝑟𝑟, 𝜃𝜃 and 𝑧𝑧 directions. The total running time of each simulation is set to be 100 µs. 1 ns

time step is used for the first 8 ns of the simulation, and then the time step is increased to 150 ns for

the rest of the simulation based on:

𝛥𝛥𝑡𝑡 = 1/(20𝑓𝑓𝑚𝑚𝑎𝑎𝑥𝑥) (3.12)

where 𝑓𝑓𝑚𝑚𝑎𝑎𝑥𝑥 is the highest frequency of interest, 𝑓𝑓𝑚𝑚𝑎𝑎𝑥𝑥 = 350 kHz.

3.5.3 Comparison between simulations and experiments

Three circular aluminum plates were prepared with the same geometric dimensions as the

simulation models, as shown in Figure 3.9. The excitation point was set at the center of the plate and

the sensing point was 40 mm away from it. Ultrasonic responses were measured using the noncontact

laser ultrasonic scanning system introduced in Section 3.3. Figure 3.10 shows the actual hardware

components used in this experiment. A peak power of around 1.25 MW was used in this validation

experiment, and the ultrasonic responses were measured with a sampling frequency of 2.56 MHz for

100 μs. The distances between the Nd:YAG laser head and the plate and between LDV and the plate

were set to 1 m. To improve the signal to noise ratio, the responses were measured 100 times and

averaged in the time domain.

- 37 -

Figure 3.9 Geometric dimensions of the circular aluminum plates and placements of the excitation

and sensing points.

Figure 3.10 Experimental setup for simulation model validation using noncontact laser ultrasonic

scanning system.

First, the time history of temperature increase (in Kelvin) in the 𝑧𝑧 and r directions obtained from

the numerical simulation model are shown in Figures 3.11(a) and (b), respectively. It is observed that

the temperature increase induced by the pulse laser is confined to a considerably small region

enclosing the spot where simulated laser heat flux is directed. The temperature distribution matches

well with the thermal diffusion length 𝜇𝜇𝑡𝑡 estimated using Equation (3.7) for each time instant. The

maximum temperature increase observed in the numerical simulation is around 135 K.

- 38 -

(a)

(b)

Figure 3.11 Temperature distribution irradiated by a pulse laser: (a) temperature distributions at

different depths at r = 0, and (b) surface temperature distributions at different radial distances.

The selection of the thermal wave region in this simulation model was then numerically verified.

A proper selection of the dimensions of this thermal wave region is critical to reduce the computation

burden of simulation but needs to still maintain its accuracy. The effect of the depth 𝛬𝛬𝑑𝑑 of the thermal

wave region on the simulated ultrasounds is shown in Figure 3.12. The value of 𝛬𝛬𝑑𝑑 was varied from 5

μm to 300 μm, and the ultrasonic wave velocities 𝒗𝒗𝑖𝑖 corresponding to varying 𝛬𝛬𝑑𝑑 (𝑖𝑖 =

5, 10, 20, … , 300 µm) were acquired at the sensing point (Figure 3.8(a)) of the 3 mm thick plate

model and plotted in Figure 3.12(a). The waveform converges when the depth 𝛬𝛬𝑑𝑑 increases.

Specifically, once the depth reaches 100 μm, there is no much improvement in the waveform. When

𝒗𝒗300 is designated as the baseline signal, the error ratio of each velocity signal 𝒗𝒗𝑖𝑖 with respect to

𝒗𝒗300 is defined as [(𝒗𝒗𝑖𝑖 − 𝒗𝒗300)T(𝒗𝒗𝑖𝑖 − 𝒗𝒗300)]/[(𝒗𝒗5 − 𝒗𝒗300)T(𝒗𝒗5 − 𝒗𝒗300)] and shown in Figure

3.12(b). Figure 3.12(b) substantiates the fact that the previously estimated theoretical value for 𝛬𝛬𝑑𝑑

- 39 -

(𝛬𝛬𝑑𝑑 = 110 µm) is proper. A similar parameter study performed for the radius 𝛬𝛬𝑙𝑙 of the thermal wave

region indicates the same convergence trend and substantiates the appropriateness of the estimated

theoretical value of 𝛬𝛬𝑙𝑙 as well.

(a)

(b)

Figure 3.12 The effect of the depth 𝛬𝛬𝑑𝑑 of the thermal wave region on simulated ultrasound: (a)

velocity signals simulated by varying the depth 𝛬𝛬𝑑𝑑 in the numerical simulation model, and (b) error

ratio of each velocity signal with respect to the baseline signal simulated with 𝛬𝛬𝑑𝑑 = 300 μm.

Figure 3.13 compares the normal (out-of-plane) velocities numerically and experimentally

acquired at the sensing point of the aluminum plates with varying thicknesses. Because the LDV used

in the experiments holds the frequency components only up to 350 kHz, the velocity signals obtained

from the simulations are pre-processed with a low-pass filter (cut-off frequency: 350 kHz) though the

- 40 -

higher frequency components cannot be totally removed. Furthermore, due to the energy loss (e.g.,

reflection) in the experiment, the laser power illuminated on the specimen is most likely not the same

for the simulations and experiments. Therefore, the velocity signals shown in Figure 3.13 are

amplitude normalized. By comparison, the velocities acquired from the simulations and experiments

share similar wave shapes.

Figure 3.13 Comparison of the velocity signals obtained from numerical simulations and

experimental tests with varying thicknesses.

- 41 -

3.5.4 Crack modeling

Figure 3.14 Modeling of a micro crack in the 3D FEM model.

Figure 3.15 Plane extraction for observing crack opening and closing.

For investigating the structural damage detection techniques developed in the following chapters,

a micro crack is then introduced into the 3D FEM plate model with a thickness of 3 mm. It has been

reported that the contacts between two rough surfaces of a real crack can generate local nonlinear

waves even when the crack is not fully open and closed (Van Den Abeele et al., 2000, Lee and Hong,

2015). So, it is critical to properly simulate the generation of nonlinearity in a simplified crack model

(Lee and Hong, 2015). In this study, the crack is modeled as the intersection of two circles, and then

stretched in its length direction as shown in Figure 3.14. In this way, the simulated crack will have an

- 42 -

extremely narrow width at the crack tips, allowing crack opening and closing during wave

propagation. The simulated crack is 10 mm long and 10 μm wide at its center.

Figure 3.16 Crack opening and closing during ultrasonic wave propagation.

In order to verify the crack opening and closing during wave propagation, a 2D plane is selected

passing through the simulated crack near its tip location, as shown in Figure 3.15. In this way, the

selected 2D plane is broken into two parts with a narrow gap in between. By observing the change of

the gap during wave propagation, opening and closing of the simulated micro crack can be verified.

Figure 3.16 gives several snapshots for different states of the gap during wave propagation, and it

shows that the gap caused by the simulated crack opens and closes at staggered times. This is further

evidence that, during wave propagation, opening and closing of the simulated crack occurs especially

near the crack tips, which makes the simulated crack a nonlinear source.

- 43 -

3.6 Chapter summary

This chapter explains the working principles for laser ultrasonic generation and measurement. A

noncontact laser ultrasonic scanning system is introduced by integrating and synchronizing a Q-

switched Nd:YAG laser for ultrasonic wave generation and a LDV for ultrasonic wave measurement.

Different scanning strategies are also discussed in this chapter. The system provides the following

advantages: (1) The system can be rapidly deployed and requires less maintenance since no sensors

are needed to place on the target structure; (2) The system can achieve high temporal and spatial

resolutions and is effective for incipient damage detection, and (3) The system is applicable to harsh

environments and even on moving structures. However, this laser ultrasonic scanning system is likely

to be less sensitive than a conventional system with contact transducers under some practical

conditions. It is possible to raise its sensitivity by using higher laser intensity, but costs and operating

problems escalate in consequence. Also, we cannot ignore the safety hazards associated with lasers,

and the intrusion of the various safety requirements into the working environment. Nevertheless

noncontact laser ultrasonics are beginning to make a significant impact in some applications where

their benefits over other transducers outweigh their disadvantages.

In addition, a multi-physics simulation scheme for simulating laser-induced ultrasonic waves on

an aluminum plate is developed in this chapter. For efficient computation, the simulation model is

divided into two sub-regions, thermal and ultrasonic wave regions, by theoretically investigating the

effect of thermal diffusion caused by pulse laser excitation. The effectiveness of the proposed

simulation scheme is validated with experimental results and shows a good correspondence with the

test results. Then a simulated micro crack is introduced into this simulation model, and its nonlinear

feature is verified by observing the crack opening and closing during wave propagation. This

simulation model developed in this chapter will be used to validate the proposed structural damage

detection techniques in the following chapters.

- 44 -

Chapter 4. Structural Damage Detection using Sideband Peak Count

In Chapter 2, nonlinear ultrasonic modulation with a wideband input is proposed. However,

under a wideband excitation like a pulse laser, since the nonlinear modulation components and the

linear response components overlap in the frequency domain, it requires additional signal processing

methods. This chapter develops a new analysis method called sideband peak count (SPC) for the

wideband ultrasonic responses. Also, in conjunction with laser scanning, damage can be detected

using the SPC technique without relying on any baseline data obtained from the pristine condition of

the target structure. This new damage detection technique is numerically and experimentally validated

in this chapter.

4.1 Sideband peak count (SPC)

As explained in Section 2, when a wideband signal is used as input, nonlinear ultrasonic

modulation can occur among various frequency components caused by the input and multiple

frequency peaks are generated as shown in Figure 4.1 (Liu et al., 2014). The basic assumption is that

nonlinear ultrasonic modulation can occur among these frequency peaks when the structure is

damaged, and the wideband input guarantees that the binding conditions can be satisfied among at

least some frequency peaks in the generated frequency band.

(a) (b)

Figure 4.1 Illustration of nonlinear ultrasonic modulation using a wideband input: (a) intact case, and

(b) damage case.

To statistically quantify the nonlinearity in a damaged structure from its response to a wideband

excitation, a new feature extraction technique by counting sideband peaks is proposed in this chapter.

- 45 -

This technique does not count the dominant peaks but keeps track of the relatively weak peaks in the

neighborhood of the strong peaks generated due to the damage induced nonlinearity. Similarly, Eiras

et al. discussed the variation of the sideband energy for monitoring the aging process of Glass Fiber

Reinforced Cement (GRC) using two piezoelectric transducers (PZTs) for excitation and sensing

(Eiras et al., 2013). They observed that a greater number of relatively stronger minor peaks appear as

the degree of material nonlinearity increases.

In this study, firstly, spectral density function is used to get the spectral density distribution

𝑃𝑃𝑥𝑥(𝑓𝑓) of the wideband ultrasonic response signal 𝑥𝑥(𝑡𝑡) in the frequency domain:

𝑃𝑃𝑥𝑥(𝑓𝑓) = 𝐸𝐸[𝑋𝑋(𝑓𝑓)𝑋𝑋∗(𝑓𝑓)] (4.1)

where 𝑋𝑋(𝑓𝑓) is the Fourier transform of 𝑥𝑥(𝑡𝑡) and * denotes the complex conjugate. Then, the

sideband peak count (SPC) is defined as the ratio of the number of spectral density peaks (𝑁𝑁𝑝𝑝) over a

moving threshold (𝑡𝑡ℎ) to the total peak number (𝑁𝑁𝑡𝑡) within a specified normalized frequency range:

𝑆𝑆𝑃𝑃𝐶𝐶(𝑡𝑡ℎ) = 𝑁𝑁𝑝𝑝(𝑡𝑡ℎ)𝑁𝑁𝑡𝑡

(4.2)

where all peaks – the dominant peaks as well as the sideband peaks above the threshold level – are

counted as shown in Figure 4.2(a). Since the number of dominant peaks is negligible in comparison to

the number of the smaller sideband peaks, it is not necessary to separate the dominant peaks from the

sideband peaks. Because of the nonlinearity induced by structural damage, more sideband peaks show

up in the spectrum or the sideband energy grows as a consequence. Therefore, the SPC value for the

damage case should be larger than that for the intact case, especially when the threshold value is

relatively low.

Figure 4.2(b) shows a representative plot of SPC difference obtained from the later experiments

presented in this chapter. Here, the SPC difference (SPCD) is defined as the difference between the

SPC values obtained from the current 𝑆𝑆𝑃𝑃𝐶𝐶𝑐𝑐 and reference 𝑆𝑆𝑃𝑃𝐶𝐶𝑟𝑟 statuses:

𝑆𝑆𝑃𝑃𝐶𝐶𝑆𝑆 = 𝑆𝑆𝑃𝑃𝐶𝐶𝑐𝑐 − 𝑆𝑆𝑃𝑃𝐶𝐶𝑟𝑟 (4.3)

The SPCD is positive when there is a damage in the target structure, and the maximum SPCD

(MSPCD) can be obtained when the threshold value is relatively low. In this study, the MSPCD

defined below is selected as a new nonlinear damage feature and used to detect structural damage:

𝑀𝑀𝑆𝑆𝑃𝑃𝐶𝐶𝑆𝑆 = 𝑀𝑀𝑀𝑀𝑥𝑥 (𝑆𝑆𝑃𝑃𝐶𝐶𝑐𝑐 − 𝑆𝑆𝑃𝑃𝐶𝐶𝑟𝑟) (4.4)

- 46 -

(a) (b)

Figure 4.2 Description of sideband peak count (SPC) and SPC difference: (a) SPC is defined as the

ratio of the number of frequency peaks over a moving threshold to the total number of peaks in the

frequency domain, and (b) the SPC difference, which is defined as the difference between the SPC

values obtained from the current and the reference conditions, increases as more spectral peaks show

up for the damaged specimen especially when the threshold is relatively low.

4.2 Baseline-free damage detection by spatial comparison

Figure 4.3 Raster scanning of the target inspection area using a noncontact laser ultrasonic scanning

system.

Majority of the existing damage detection techniques detect damage by comparing the data

obtained from the current state of the target structure with the baseline data obtained from its intact

condition. However, the varying operational and environmental conditions of the structure could

adversely influence the collected data and cause false alarms. To address this problem, taking

advantages of the laser ultrasonic scanning system, ultrasonic response obtained from a specific

Control UnitNd:Yag Laser

Laser Doppler Vibrometer (LDV)

Galvanometer

Galvanometer

Excitation Unit

Sensing Unit

Synchronization

Trigger/Control Signals

Trigger/Control Signals

DataTransmission Scanning Area

Fixed Sensing Point

Scanning Excitation Points

- 47 -

spatial point is compared with other responses obtained from its spatially adjacent points. In this way,

damage can be detected and even visualized without relying on the baseline data obtained from the

intact condition. Figure 4.3 shows the overall schematic of the nonlinear laser ultrasonic system and

how raster scanning of the target area is performed (An et al., 2013). In this chapter, the sensing laser

beam is fixed at a single point and the excitation laser beam is scanned over the target area with a

constant pitch. When the excitation laser beam is aimed at a specific excitation point, ultrasonic waves

are generated and measured at a fixed sensing point using a sensing laser. The resultant time response

is stored and assigned to the coordinate of the corresponding excitation point. The scanning process

continues until the scanning covers the entire target area. Note that, other scanning strategies

mentioned in Chapter 3 can also be used for this proposed baseline-free damage detection method,

such as fixing the excitation point and scanning the sensing laser, which depends on the condition of

each specific test application.

Figure 4.4 Illustration for spatially adjacent ultrasonic response comparison using MSPCD.

Then, the SPC curve is calculated for each excitation point, and the MSPCD value for each

excitation point is computed by comparing the SPC curve obtained from the current excitation point

with the reference SPC curves obtained from its adjacent points as shown in Figure 4.4. Slightly

different from Equation (4.4), the MSPCD here is redefined as:

𝑀𝑀𝑆𝑆𝑃𝑃𝐶𝐶𝑆𝑆 = 𝑀𝑀𝑀𝑀𝑥𝑥 (|𝑆𝑆𝑃𝑃𝐶𝐶𝑐𝑐 − 𝑆𝑆𝑃𝑃𝐶𝐶𝑟𝑟|) (4.5)

The calculation of MSPCD here is based on the premise that the waves from spatially adjacent points

are similar unless there is anomaly (e.g., damage) among these points. Therefore, the MSPCD value

increases when the SPC curve from the center point deviates from its spatially adjacent SPC curves

due to damage. Except the points at the edge of the scanning area, there are totally 8 adjacent points

for each point and multiple MSPCDi values can be calculated using Equation (4.5) as illustrated in

Figure 4.4. The mean value of these MSPCDi values is chosen as the damage index for each point:

𝑀𝑀𝑆𝑆𝑃𝑃𝐶𝐶𝑆𝑆 =1𝑛𝑛�𝑀𝑀𝑆𝑆𝑃𝑃𝐶𝐶𝑆𝑆𝑖𝑖

𝑖𝑖

𝑖𝑖=1

(4.6)

- 48 -

where 𝑛𝑛 is the number of adjacent points for each current point. This mean MSPCD value can be

visualized for the entire target area, and spatial points with high MSPCD values indicate the existence

and the location of the damage. Thus, baseline-free damage detection or visualization is realized. Also,

note that the damage detection method presented here is different from the traditional phased array

ultrasonic imaging techniques, in which time-of-flight or wave attenuation characteristics are used to

image damage in target structures (Giurgiutiu and Bao, 2004, Yan et al., 2010).

4.3 Numerical validation

(a) (b)

Figure 4.5 Illustration of data extraction in simulation model for MSPCD calculation: (a) a scanning

area covering the simulated micro crack, and (b) three points from the selected scanning area, where

Point B is near the crack tip while Point A and Point C are far from the crack location.

This section validates the proposed SPC based damage detection technique in the numerical

simulation model developed in Chapter 3. As mentioned in Chapter 3, a micro crack is introduced in

the simulated aluminum plate model, and the nonlinearity of the simulated micro crack is verified by

observing the crack opening and closing during wave propagation. To validate the proposed damage

detection technique, a scanning area of 40 mm × 35 mm was defined, covering the entire micro crack

as shown in Figure 4.5(a). A total of 1400 (40 × 35) scanning points were assigned within this

scanning area, achieving a spatial resolution of 1 mm. A 100 μs velocity signal with a sampling time

step of 150 ns was obtained from each scanning point.

- 49 -

(a)

(b)

(c)

Figure 4.6 SPC and SPC difference values obtained from three selected points in simulation model:

(a) Point A, far away from the crack location, (b) Point B, near the crack tip, and (c) Point C, far away

from the crack location.

- 50 -

First, three points from the scanning area were selected, named Point A, B and C, respectively.

As shown in Figure 4.5(b), Point B is located near the simulated crack tip, while Point A and C are far

away from the crack location. Also, the velocity responses from these three selected points were

acquired from the same simulation model without the micro crack. Hence, we achieve the velocity

response signals from both the intact and damage conditions for the three selected points. For these

three points, the SPC curves are calculated for both the intact and damage conditions, and the SPC

difference (SPCD) is computed using Equation (4.3) by treating the SPC curves got under the intact

condition as reference.

Figure 4.6 shows the SPC curves and the corresponding SPC difference for the three points. Here,

a frequency band of 20 to 350 kHz was selected for computing SPC curves and the corresponding

SPC difference. From Figures 4.6(a) and (c), it can be seen that, when the probing points are far away

from the crack location, the difference of the SPC curves between the damage and intact conditions is

not obvious and it can be clearly verified by checking the corresponding SPC difference. However, in

Figure 4.6(b), when Point B locates near the crack tip, the difference of the SPC curves between the

damage and intact conditions becomes distinguishable, and the maximum difference (MSPCD) shows

up when the threshold value is relatively low.

Then, all the SPC curves for all the scanning points were calculated for the simulation model

with the micro crack, and the corresponding MSPCD value for each scanning point in the selected

area was computed using Equations (4.5) and (4.6). Accordingly, the crack detection or visualization

result is shown in Figure 4.7. In Figure 4.7, it can be clearly seen that the scanning points near the

simulated crack own higher MSPCD values. Hence, the simulated micro crack is successfully

detected using the proposed SPC based damage detection technique.


technique.

- 51 -

4.4 Fatigue crack detection in aluminum plate

4.4.1 Experimental setup

To experimentally examine the performance of the proposed SPC based damage detection

technique, a 3 mm thick aluminum plate specimen, fabricated using 6061-T6 aluminum alloy, was

prepared. All the geometrical information of this specimen can be found in Figure 4.8. A notch was

introduced in the middle of one edge of the specimen so that fatigue crack can initiate from this notch.

A fatigue crack was introduced using an INSTRON 8801 system as shown in Figure 4.9(a). The

specimen was tested under tension-tension cycling of a maximum load of 25 kN and a minimum load

of 2.5 kN at a frequency of 10 Hz. A 15 mm long crack was produced after 18,793 loading cycles.

The width of the fatigue crack is overall less than 10 μm and even less than 5 μm near the crack tip as

shown in Figure 4.9(b).

(a)

(b)

Figure 4.8 Dimensions of the specimen, crack location, and laser excitation and sensing arrangement:

(a) six excitation-sensing paths, and (b) fixed sensing point and excitation area scanning.

90 mm

50m

m

120

mm

80 m

m

300 mm

Thickness: 3 mm

Excitation Points Sensing Points

60m

m

40m

m30

mm

20m

m10

mmCrack1

23456

Path

35 mm 120

mm

80 m

m

300 mm

Thickness: 3 mm

Sensing PointExcitation

Scanning Area(19×19 points)

35 m

m

Crack25 mm

- 52 -

(a) (b)

Figure 4.9 Fatigue test and microscopic image of the aluminum plate specimen with a fatigue crack:

(a) fatigue test setup, and (b) microscopic image of the crack tip.

The noncontact laser ultrasonic scanning system introduced in Chapter 3 was adopted in this

experiment (An et al., 2013). To shortly review this laser ultrasonic scanning system, it is composed

of an excitation unit (a Q-switched Nd:YAG pulse laser, a galvanometer and a focal lens), a sensing

unit (a commercial scanning laser Doppler vibrometer, LDV) and a control unit. Parameters for the

excitation unit should be carefully selected to avoid surface damage such as ablation. The Q-switched

Nd:YAG pulse laser employed in this system has a wavelength of 532 nm and a maximum peak

power of 3.7 MW, and generates a pulse with 8 ns pulse duration at a repetition rate of 20 Hz. A peak

power of around 0.2 MW was selected for the Q-switched Nd:YAG pulse laser as excitation in this

experiment. The laser source of the LDV in the sensing unit is a helium neon (He-Ne) laser with a

wavelength of 633 nm. This one-dimensional LDV measures the out-of-plane velocity in the range of

0.01 um/s to 10 m/s over a target surface based on the Doppler effect (Scruby and Drain, 1990). The

accuracy of velocity measurement highly depends on the intensity of the returned laser beam. Thus,

the incident angle of the LDV laser beam should be carefully controlled to maximize the intensity of

the returned beam and minimize speckle noises (Martin and Rothberg, 2009). Occasionally, a special

surface treatment is also necessary for increasing the measurement accuracy. In this experiment, a

retro-reflective tape was pasted on the sensing point to enhance the intensity of the returned laser

beam. The ultrasonic responses were measured with a sampling frequency of 2.56 MHz for 25.6 ms.

To improve the signal to noise ratio, the responses were measured 100 times and averaged in the time

domain. The PC in the control unit sends out a trigger signal to launch the excitation laser beam and

to simultaneously start the data collection. Also, the PC generates control signals to aim the excitation

- 53 -

and sensing laser beams to the desired target positions. Figure 4.10 shows the actual hardware

components and the system setup in this experiment.

Figure 4.10 Experimental setup for fatigue crack detection using noncontact laser ultrasonic scanning

system.

Two different experiments were conducted here. First, as shown in Figure 4.8(a), six pairs of

excitation and sensing laser beam points were selected to examine the sensitivity of the proposed

nonlinear damage feature, MSPCD, extracted from each path to the fatigue crack by comparing with

the reference signal acquired in its intact condition. Among all these six paths, path 1 passes through

the crack, and path 2 passes through the crack tip, while other paths do not. For the intact condition of

the plate specimen, ultrasonic responses were recorded three times from each path. One of them was

used as the reference signal (Reference), and the other two as the test signals acquired from the intact

case (Intact I and Intact II). To take into account variations caused by resetting of the laser ultrasonic

scanning system and the specimen after fatigue test, the whole measurement system was reconfigured

even for the intact case. After the crack formation, ultrasonic response signals (Damage) were

collected again following the same measurement procedure in the intact case.

Second, in order to validate the proposed baseline-free damage detection technique by spatial

comparison, a laser excitation scanning area was selected with a 35 mm × 35 mm square area, located

close to one edge of the specimen and covering the entire fatigue crack, as shown in Figure 4.8(b). A

total of 361 (19 × 19) scanning points were assigned within this scanning area, achieving a spatial

resolution less than 2 mm. The fixed sensing point was located outside the scanning area and was 25

mm away from the closest excitation point. This second experiment was conducted after the fatigue

test.

- 54 -

4.4.2 Test results

(a)

(b)

(c)

Figure 4.11 Representative response signals from path 2 in the plate specimen: (a) time histories, (b)

normalized frequency spectra, and (c) close-up view of the frequency spectra.

For the first experiment, representative ultrasonic responses (Intact I and Damage) obtained from

- 55 -

path 2 of the plate specimen in both time and frequency domains are displayed in Figures 4.11(a) and

(b). The frequency content of the response signal spans up to 400 kHz. A close-up view of the

frequency spectra is shown in Figure 4.11(c) and it displays that more sideband peaks appear when

the specimen is damaged after fatigue test. A frequency band of 20 to 400 kHz was selected for

conducting the SPC operation and calculating the MSPCD values.

(a)

(b)

Figure 4.12 SPC and SPC difference values obtained from the intact and damage cases for the plate

specimen: (a) path 2 passing through the crack tip, and (b) path 3 not passing through the crack.

Figure 4.12 shows the SPC value and its difference from the reference case for all the intact and

damage cases. Figure 4.12(a) shows the SPC and its difference from path 2, which passes through the

crack tip. The MSPCD reaches above 0.15 for the damage case when the threshold is quite low

(around 0.4% of the largest peak value in the frequency domain). Figure 4.12(b) shows the SPC and

its difference for path 3, which does not directly pass through the crack. The MSPCD values keep low

and similar for all the intact and damage cases. Therefore, it can be seen that the MSPCD obtained

- 56 -

from the damage case shows a much higher value compared to the intact cases when the propagating

ultrasonic waves pass directly through the crack tip. Therefore, a fatigue crack can be detected and

located based on this finding.

Figure 4.13 shows the MSPCD values obtained from all six paths in the plate specimen for all the

intact and damage cases, using Equation (4.4). It can be clearly seen that the MSPCD value whose

path passes through the crack, especially through the crack tip, is much higher than the others mainly

caused by the measurement noises and the measurement system reconfiguration after each

measurement test. It seems that, in this experiment, the laser excitation can well ‘activate’ crack

opening and closing only when the direct propagating waves directly pass through the crack.

Furthermore, this crack opening and closing is most prominent near the crack tip where the crack

width is minimum.

Figure 4.13 MSPCD values obtained from all six paths in the aluminum plate specimen.

For the second excitation area scanning test, the baseline-free damage detection technique by

spatial comparison was used to detect the fatigue crack in the selected scanning area. Here, Equations

(4.5) and (4.6) were used to calculate the MSPCD value for each scanning point. Figure 4.14 gives the

fatigue crack detection or visualization result composed by the MSPCD values. In Figure 4.14, it

again shows that the MSPCD values near the fatigue crack, especially the crack tip, own higher values.

However, by comparing the crack detection result (Figure 4.14) from the result achieved in the

simulation model (Figure 4.7), we can find that Figure 4.7 from the simulation model gives a better

detection result. And the MSPCD values near the crack in the simulation model is much higher than

the MSPCD values in this experiment. This observation indicates that test noise or environmental

variation in real field application might deteriorate the effectiveness of the proposed SPC based

damage detection technique. More detailed discussions and an optimization method will be provided

in the following chapters.

- 57 -

Figure 4.14 Baseline-free fatigue crack detection result using SPC based damage detection technique.

4.5 Delamination detection in CFRP plate


Another specimen for experimental validation of the proposed SPC based damage detection

technique is a carbon fiber reinforced polymer (CFRP) plate, as shown in Figure 4.15. This plate is

composed of IM7 graphite fibers with 97703 resin material and 12 piles with a layup of [0/±45/0/

±45]s. A 1 cm diameter delamination was introduced at the center of the plate through impact testing.

Figure 4.15 Carbon fiber reinforced polymer (CFRP) plate and laser excitation and sensing

arrangement.

A laser excitation scanning area was selected with a 60 mm × 60 mm square area, covering the

delamination damage, as shown in Figure 4.15. A total of 1225 (35 × 35) scanning points were

- 58 -

assigned within this scanning area, achieving a spatial resolution less than 2 mm. The fixed sensing

point was located outside the scanning area and was 20 mm away from the closest excitation point.

The same noncontact laser ultrasonic scanning system introduced in Chapter 3 was used in this

experiment. Each ultrasonic response was measured with a sampling frequency of 2.56 MHz for 0.4

ms and averaged 100 times in the time domain for improving the signal to noise ratio. All the other

experimental setup was identical to the one used in the previous experiment.

4.5.2 Test results

Since the frequency content of the response signals spans up to 100 kHz, a frequency band from

20 to 100 kHz was selected for conducting the SPC operation and estimating the MSPCD values. The

SPC curve was computed for each scanning point in the selected excitation scanning area, and the

corresponding MSPCD value is calculated by comparing with the SPC curves got from its spatially

adjacent scanning points, using Equations (4.5) and (4.6). The corresponding delamination detection

result is shown in Figure 4.16. It shows that the scanning points near the delamination location have

higher MSPCD values, which represent the existence of damage. It also indicates that the damage-

induced nonlinearity mostly concentrates at the edge of the delamination. Note, besides the damage

location, there also exist some relatively high MSPCD values in Figure 4.16, which might be caused

by test noise interference.

Figure 4.16 Baseline-free delamination detection result in CFRP plate using SPC based technique.

4.6 Delamination and debonding detection in GFRP wind turbine blade


- 59 -

An actual 10 kW wind turbine blade (Figure 4.17) was fabricated for additional validation of the

proposed SPC based damage detection technique. The wind turbine blade is made of glass fiber

reinforced polymer (GFRP) material, has rough dimensions of 3500 mm × 450 mm × 3 mm, and

consists of 6 piles with a layup of [0/±45]s. The elastic modulus 𝐸𝐸1, shear modulus 𝐺𝐺12, and poisson

ratio 𝜈𝜈12 of the GFRP material are 24.65 GPa, 8.532 GPa, and 0.476, respectively (Park et al., 2014).

In real applications, since the wind turbine blade will be in a rotation mode, the noncontact laser

ultrasonic scanning system introduced in Chapter 3 might be a practical solution for damage detection

in the wind turbine blade.

Figure 4.17 Dimensions of a full scale wind turbine blade, and locations of simulated delamination

and debonding.

Because composite structures are fabricated by bonding multilayers of laminates with resins, they

are inherently vulnerable to delamination and debonding. These two types of damage were

intentionally produced in this wind turbine blade as shown in Figure 4.17. For simulating internal

delamination, a circular Teflon tape with 15 mm diameter was inserted between 3rd and 4th ply

during fabrication of the blade. For debonding, some of the glue used to attach a stiffener to the blade

skin was removed, introducing a small localized gap (debonding) between the stiffener and the blade

skin. Close views of these two damages are shown in Figure 4.18.

As shown in Figure 4.18, a 50 mm × 50 mm square area was scanned with 400 (20 × 20)

excitation scanning points for both delamination and debonding detection, achieving a spatial

resolution around 2.5 mm. The fixed sensing point was located 20 mm away from the closest

excitation point. Figure 4.19 shows the actual experimental setup. The same laser ultrasonic scanning

system adopted in the previous experiment was used here. The ultrasonic responses from each

excitation point were measured with a sampling frequency of 2.56 MHz for 0.4 ms and averaged 100

times in the time domain for improving the signal to noise ratio. All the other experimental setup and

- 60 -

parameter setting was identical to the one used in the previous experiment. One thing to be cautious is

that GFRP used for the wind turbine blade is more vulnerable to ablation due to its lower thermal

conductivity.

(a) (b) (c)

Figure 4.18 Enlarged view of the damages and the laser scanning region: (a) delamination, (b)

debonding (front view), and (c) debonding (back view).

Figure 4.19 Experimental setup for delamination and debonding detection using noncontact laser

ultrasonic scanning system.

4.6.2 Test results

The frequency content of the response signal acquired from the wind turbine blade spans up to

350 kHz. A frequency band of 20 to 350 kHz was selected for conducting the SPC operation and

calculating the MSPCD values.

- 61 -

(a) (b)

Figure 4.20 Baseline-free delamination/ debonding detection results in wind turbine blade using SPC

based technique: (a) delamination, and (b) debonding (the dashed line indicates the location of the

hidden stiffener).

The SPC curve was computed for each scanning point in the selected excitation scanning areas,

and the corresponding MSPCD value was calculated by comparing with the SPC curves got from the

spatially adjacent scanning points, using Equations (4.5) and (4.6). The corresponding damage

detection results are shown in Figure 4.20. It can be seen that the excitation scanning points near the

damage location have higher MSPCD values, which indicate the existence of structural damage. Also,

besides the damage location, there exist some relatively high MSPCD values, especially in Figure

4.20(a), which might be caused by test noise interference. Within a certain level of test noise

interference, these noise interferences on Figure 4.20 can be removed by further image processing.

The proposed technique again successfully detects both delamination and debonding in the GFRP

wind turbine blade.

4.7 Chapter summary

This chapter proposes a sideband peak count (SPC) based damage detection technique to

statistically quantify the nonlinearity caused by structural damage. A nonlinear damage feature called

maximum sideband peak count difference (MSPCD) is extracted by comparing the SPC curves got

under current condition and a reference condition. Here, the reference condition can be when the

target structure is in its initial intact status. Moreover, to eliminate the influence caused by varying

operational and environmental conditions on the test results, a baseline-free damage detection

- 62 -

technique is proposed by using the SPC curves acquired from the adjacent points as reference. In this

way, damage can be detected or even visualized without relying on the baseline data obtained from

the intact condition. The proposed damage detection technique is validated using the simulation

model with a micro crack developed in the previous chapter. Also, experimental validation tests are

also successfully conducted to detect fatigue crack in an aluminum plate, delamination in a CFRP

plate, delamination and debonding in a GFRP wind turbine blade, respectively. However, by

comparing the test results from numerical simulation and experimental tests, it indicates that noise

interference in field applications might deteriorate the effectiveness of the proposed SPC based

damage detection technique. To tackle this problem, more detailed discussions and an optimization

method are provided in the following chapters.

- 63 -

- 64 -

Chapter 5. Structural Damage Detection using State Space Attractor

Different from the sideband peak count (SPC) based analysis in the frequency domain, this

chapter introduces another analysis method conducted directly in the time domain using the wideband

ultrasonic responses. State space technique is introduced and a state space attractor is reconstructed

from the acquired wideband ultrasonic response for damage detection. The proposed state space based

damage detection technique is validated using the simulation model. Also, in this chapter, the

proposed state space based damage detection technique is used to detect fatigue crack in aluminum

plate and delamination/ debonding in CFRP plate and GFRP wind turbine blade.

5.1 State space attractor

Recently, the geometric variations of data-driven dynamic state space attractors under

deterministic or stochastic excitations have been shown sensitive to nonlinear damage (Nichols, 2003,

Moniz et al., 2005, Overbey et al., 2007, Liu et al., 2014). An attractor is firstly reconstructed in the

state space from a scalar vibration response. Then, damage features representing geometrical changes

of the attractor, such as prediction error, average local attractor variance ratio, correlation dimension

of attractors, are extracted by comparing the attractors between the intact and damage conditions.

Figure 5.1 gives an example for detecting a simulated crack damage in an aluminum three-story test

bed. Multiple test conditions were prepared to acquire different response signals from an

accelerometer. By comparing Figures 5.1(a) and (b), when simulated damage exists in the test bed, a

clear geometrical change of the reconstructed state space attractors between the baseline and the

current conditions can be observed (Liu et al., 2014).

This chapter uses the geometric variation of the state space attractors reconstructed from the

wideband response signals to detect structural damage. The major departure of this study from the

aforementioned studies (Nichols, 2003, Moniz et al., 2005, Overbey et al., 2007, Liu et al., 2014) is

that the state space attractor is applied to ultrasonic signals for local micro damage detection, the

frequency band of which is far above the frequency ranges explored by the previous studies. Also, in

conjunction with laser scanning, it can be used for baseline-free damage detection or visualization.

- 65 -

(a) (b)

Figure 5.1 State space attractor reconstructed from an accelerometer under (a) condition 5 which is

undamaged, and (b) condition 14 which is damaged. (Liu et al., 2014)

Considering the target structure as a dynamical system, and let us assume the dynamical system

can be described by a first order differential equation:

�̇�𝒙 = 𝑓𝑓(𝒙𝒙, 𝑡𝑡) (5.1)

The solution to this problem with an initial value 𝒙𝒙(0) (boldface type denotes a vector) will trace out

a trajectory in a state space defined by the system variables 𝒙𝒙. As transients die out, the trajectory

will approach the system dynamical attractor, which is a geometric object in the state space to which

all trajectories belong (Nichols, 2003). As an example, consider a system described by the following

equations:

𝑑𝑑𝑥𝑥1𝑑𝑑𝑡𝑡

= 𝑥𝑥1(1 − 𝑥𝑥12)

𝑑𝑑𝑥𝑥2𝑑𝑑𝑡𝑡

= 1 (5.2)

The state space for this system is defined in polar coordinates by the variables 𝑥𝑥1 and 𝑥𝑥2. The

variable 𝑥𝑥1 denotes the radial direction and 𝑥𝑥2 the angle. Time is implicitly reflected in the

constantly increasing angle. Several different initial conditions (denoted with black circles) are placed

in the state space and quickly approach the state space attractor, in this example a one-dimensional

limit cycle as shown in Figure 5.2. Arrows on the figure denote the vector field associated with this

attractor. Other initial conditions placed in this state space field will flow along these arrows toward

the limit cycle. Therefore, the state space attractor is the geometric representation of this dynamical

system, and thus will reflect a loss of dynamical similarity due to damage, especially the nonlinear

one (Liu et al., 2014).

- 66 -

Figure 5.2 Limit cycle state space attractor achieved from Equation (5.2). (Nichols, 2003)

5.2 Attractor reconstruction

Figure 5.3 Illustration of state space attractor reconstruction from a single time series.

In practice, it is difficult to gain access to each of the system variables. Instead, based on the

mathematical embedding proposed by Takens, the dynamics of the unobserved variables can be

qualitatively reconstructed from a single time series of the system response data (Takens, 1981). The

reconstruction procedure is accomplished by concatenating lag copies of the single measured time

series 𝑥𝑥(𝑛𝑛) (𝑛𝑛 = 1,2, … ,𝑁𝑁). Here 𝑛𝑛 is the discrete time index corresponding to the value of 𝑥𝑥

sampled at time 𝑛𝑛∆t and ∆t is the sampling interval. Each discrete time instance of the attractor 𝑿𝑿

at time 𝑛𝑛∆t can be expressed as:

- 67 -

𝑿𝑿(𝑛𝑛) = �𝑥𝑥(𝑛𝑛),𝑥𝑥�𝑛𝑛 + 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙�, … , 𝑥𝑥�𝑛𝑛 + (𝑚𝑚 − 1)𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙��

𝑛𝑛 = 1, 2 , … ,𝑁𝑁 − (𝑚𝑚− 1)𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 (5.3)

where 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 is the time lag and 𝑚𝑚 is the embedding dimension (Figure 5.3). With proper time lag

𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 and embedding dimension 𝑚𝑚, a state space attractor, which preserves the ‘true’ underlying

system dynamics, can be reconstructed. Figure 5.4 gives an example about the reconstruction of state

space attractor for a single degree-of-freedom Duffing system (expressed by displacement 𝑥𝑥1 and

velocity 𝑥𝑥2 ) under sinusoidal excitation (Liu et al., 2014). Figures 5.4(a) and (b) plot the

displacement 𝑥𝑥1 and the trajectory {𝑥𝑥1,𝑥𝑥2}𝑇𝑇 (the actual state space attractor) in the state space of

this system, respectively. Figure 5.4(c) gives the reconstructed attractor from displacement 𝑥𝑥1 with

𝑚𝑚 = 2 and 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 = 12. Compared with the actual attractor in Figure 5.4(b), only the direction of the

attractor changes, without affecting the manifold topology.

(a)

(b) (c)

Figure 5.4 Example for state space attractor reconstruction: (a) the time series of 𝑥𝑥1, (b) the

trajectory plotted from {𝑥𝑥1,𝑥𝑥2 }𝑇𝑇, and (c) the attractor reconstructed from 𝑥𝑥1. (Liu et al., 2014)

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For selection of time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙, there are two common techniques: one uses the autocorrelation

function and the other uses the average mutual information (AMI) function. The first method makes

use of the autocorrelation function to determine the time lag at which a vector is least correlated with

itself (Abarbanel, 1996). Thus, a frequently chosen time lag, 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙, is taken to be at the first zero

crossing of the autocorrelation function. The normalized estimated autocorrelation function can be

calculated as:

𝐶𝐶𝑥𝑥𝑥𝑥(𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙) =∑ [𝑥𝑥(𝑛𝑛) − �̅�𝑥][𝑥𝑥�𝑛𝑛 + �𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙�� − �̅�𝑥]𝑖𝑖

∑ [𝑥𝑥(𝑛𝑛)− �̅�𝑥]2𝑖𝑖 (5.4)

The downside of this autocorrelation method is that the autocorrelation captures only the linear

relationships within time series.

The second method for more general dynamic systems makes use of the average mutual

information (AMI) function (Fraser and Swinney, 1986). The AMI function measures the average

amount of information learned about 𝑥𝑥�𝑛𝑛 + 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙� from 𝑥𝑥(𝑛𝑛):

𝐴𝐴𝑀𝑀𝐼𝐼(𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙) = ��̂�𝑝(𝑥𝑥(𝑛𝑛),𝑥𝑥(𝑛𝑛 + 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙))log2�̂�𝑝(𝑥𝑥(𝑛𝑛), 𝑥𝑥(𝑛𝑛 + 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙))�̂�𝑝(𝑥𝑥(𝑛𝑛))�̂�𝑝(𝑥𝑥(𝑛𝑛 + 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙))

𝑖𝑖

(5.5)

where �̂�𝑝(𝑥𝑥(𝑛𝑛))and �̂�𝑝 �𝑥𝑥�𝑛𝑛 + 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙�� are the estimated probability densities of 𝑥𝑥(𝑛𝑛) and 𝑥𝑥�𝑛𝑛 +

𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙�, respectively, and �̂�𝑝(𝑥𝑥(𝑛𝑛),𝑥𝑥(𝑛𝑛 + 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙)) is the estimated joint density. When AMI value

becomes zero, 𝑥𝑥�𝑛𝑛 + 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙� is completely independent of 𝑥𝑥(𝑛𝑛) and the coordinate independence is

ensured for the reconstructed attractor. The general prescription is to choose the value of 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙

corresponding to the first minimum AMI value, although this is not a prescription rooted in theoretical

rigor but rather a practical interpretation of AMI.

However, in theory, the choice of time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 is not that important but mainly to minimize

redundancy in the resulting reconstructed attractors. And it has been shown that often the selection of

the embedding dimension 𝑚𝑚 has a more significant impact on the dynamic characteristics of the

reconstructed state space attractor than the time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 has (Overbey et al., 2007). Embedding an

attractor in too few dimensions can result in trajectories being falsely projected on top of one another.

For example, consider the limit cycle oscillation shown in Figure 5.2. The state space for this system

consists of two state variables and therefore requires at least 𝑚𝑚 = 2 coordinates in order to

reconstruct its attractor. If the system is embedded in one dimension the circle would be collapsed

onto a line in state space resulting in a very different topology.

For selection of embedding dimension 𝑚𝑚, two commonly-used methods are the singular system

analysis and the false nearest neighbors (FNNs) method. In the first method, a singular value

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decomposition (SVD) is performed on the measured vector (Broomhead and King, 1986):

[𝑿𝑿]𝑁𝑁×𝑃𝑃 = [𝑼𝑼]𝑁𝑁×𝑃𝑃[𝑾𝑾]𝑃𝑃×𝑃𝑃[𝑽𝑽]𝑃𝑃×𝑃𝑃𝑇𝑇 (5.6)

where [𝑿𝑿] is an 𝑁𝑁 × 𝑃𝑃 matrix made up of the measured vector with 𝑁𝑁 time points and 𝑃𝑃 − 1

delayed copies representing the other columns, similar to the final form of the reconstructed attractor.

[𝑾𝑾] is a 𝑃𝑃 × 𝑃𝑃 diagonal matrix whose elements are the singular values of the system. If the singular

values are sorted, normalized, and plotted as a function of their indices, 𝑝𝑝, they give a representation

of the variance contained in each of the 𝑝𝑝 dimensions. The proper embedding dimension 𝑚𝑚 can

then be chosen as the number of indices needed for the singular values to drop to an insignificant

number.

As for the false nearest neighbors (FNNs) method, it calculates the percentage of false neighbors

when a state space attractor is reconstructed with dimension 𝑚𝑚 (Kennel and Abarbanel, 1992). A

false neighbor is defined as a pair of closely positioned points whose distance substantially increases

as the dimension increases from 𝑚𝑚 to 𝑚𝑚 + 1. As the embedding dimension expands, the percentage

of false nearest neighbors will decline to a suitably small value. In this method, the lowest embedding

dimension, which corresponds to the first near zero percentage of FNNs, is often chosen as the

optimal embedding dimension 𝑚𝑚.

5.3 Bhattacharyya distance (BD)

In order to quantitatively indicate the geometric variation of the state space attractors, a statistical

distance call Bhattacharyya distance (BD) is introduced as the nonlinear damage feature in this

chapter (Nichols, 2003, Overbey et al., 2007). Once the state space attractor is reconstructed, BD is

extracted from the reconstructed state space attractor as described in Figure 5.5. Here, two time series

are needed, one from the current condition of the target structure, and the other from a reference

condition. Thus, two attractors can be reconstructed, namely, current attractor 𝑿𝑿 and reference

attractor Y, respectively.

In the first step, a set of 𝑄𝑄 fiducial points 𝒀𝒀(𝑖𝑖) (1 ≤ 𝑖𝑖 ≤ 𝑁𝑁 − (𝑚𝑚 − 1)𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙) is randomly

selected from 𝒀𝒀. The number of the fiducial points should be chosen so that the feature extraction

results are insensitive to the addition of successive fiducial points. A convenient rule is to choose

𝑄𝑄 = 𝑁𝑁/100 (Pecora and Carroll, 1996).

In the second step, a set of 𝑃𝑃 nearest neighbors 𝑿𝑿𝑐𝑐𝑖𝑖(𝑗𝑗) (1 ≤ 𝑗𝑗 ≤ 𝑁𝑁 − (𝑚𝑚 − 1)𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙) to each

fiducial point 𝒀𝒀(𝑖𝑖) is selected from 𝑿𝑿. Here, 𝑃𝑃 should be selected so that the local dynamics of the

attractor can be captured, and it also should be large enough to be insensitive to noise. An optimal

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choice is 𝑃𝑃 = 𝑁𝑁/1000 (Overbey and Todd, 2008). To prevent temporal correlations between the

fiducial point and the selected neighbors, a Theiler window with step 2𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 is adopted so that any

selected neighbor point will be separated from the fiducial point by at least 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 points in time. Then,

the fiducial points and neighbors are evolved in time with a time step 𝐿𝐿 (in most cases, 𝐿𝐿 = 1), and

the mass centroid of the time-evolved neighborhood in the current attractor is computed by:

𝒀𝒀�𝑐𝑐(𝑖𝑖 + 𝐿𝐿) = 1𝑃𝑃

� 𝑿𝑿𝑐𝑐𝑖𝑖(𝑗𝑗 + 𝐿𝐿)1≤𝑗𝑗≤𝑁𝑁−(𝑚𝑚−1)𝑇𝑇𝑙𝑙𝑎𝑎𝑙𝑙

(5.7)

The error for each chosen fiducial point becomes:

𝑒𝑒𝑐𝑐𝑖𝑖 = �𝒀𝒀�𝑐𝑐(𝑖𝑖 + 𝐿𝐿) − 𝒀𝒀(𝑖𝑖 + 𝐿𝐿)� (5.8)

where ‖∙‖ denotes the Euclidean norm, and the total number of 𝑒𝑒𝑐𝑐𝑖𝑖 is 𝑄𝑄. Next, the reference

attractor itself is treated as the current attractor and a set of 𝑃𝑃 nearest neighbors 𝑿𝑿𝑟𝑟𝑖𝑖(𝑗𝑗) to each

fiducial point are selected from the reference attractor itself. Similarly, the time-evolved error 𝑒𝑒𝑟𝑟𝑖𝑖 for

each chosen fiducial point can be calculated using Equations (5.7) and (5.8).

In the last step, BD is computed to statistically estimate the difference between 𝑒𝑒𝑟𝑟𝑖𝑖 and 𝑒𝑒𝑐𝑐𝑖𝑖

obtained from the reference and current attractors:

BD = 14

(𝜇𝜇𝑐𝑐 − 𝜇𝜇𝑟𝑟)2

𝜎𝜎𝑐𝑐2 + 𝜎𝜎𝑟𝑟2+

12𝑙𝑙𝑛𝑛 �

𝜎𝜎𝑐𝑐2 + 𝜎𝜎𝑟𝑟2

2𝜎𝜎𝑐𝑐𝜎𝜎𝑟𝑟� (5.9)

where 𝜇𝜇𝑟𝑟, 𝜎𝜎𝑟𝑟 and 𝜇𝜇𝑐𝑐, 𝜎𝜎𝑐𝑐 represent the mean and standard deviation of 𝑒𝑒𝑟𝑟𝑖𝑖 and 𝑒𝑒𝑐𝑐𝑖𝑖, respectively.

The first term in Equation (5.9) is a scaled Fisher exponent, the deflection coefficient, which may be

unable to differentiate some situations if the mean shift and variance between the current and

reference conditions are equally significant. Therefore, the second term is introduced in BD only

considering the case of variance change. Here, large BD value implies a big geometrical difference

between the current attractor and the reference attractor, and the current condition of the structure

significantly deviates from the reference condition of the structure.

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Figure 5.5 Overview of the BD computation between the current and reference state space attractors.

5.4 Baseline-free damage detection by spatial comparison

Same as proposed in Chapter 4, the ultrasonic response obtained from a specific spatial point is

compared with the other responses obtained from its spatially adjacent points. In this way, damage

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can be detected and even visualized without relying on the baseline data obtained from the intact

condition. The proposed noncontact laser ultrasonic scanning system is adopted to scan over a

selected target scanning area with a constant pitch. Also, in this chapter, the scanning strategy with a

fixed sensing laser and a scanning excitation laser is selected. The major difference from Chapter 4 is

that, the new developed BD feature is used, instead of maximum sideband peak count difference

(MSPCD).

The BD value for each excitation point is computed by comparing the current attractor obtained

from the current excitation point with the reference attractors reconstructed from its adjacent points as

shown in Figure 5.6. The calculation of BD here is based on the premise that the waves from spatially

adjacent points are similar unless there is anomaly (e.g., damage) among these points. Therefore, the

BD value increases when the state space attractor reconstructed from the center point deviates from its

spatially adjacent attractors due to damage. Except the points at the edge of the scanning area, there

are totally 8 adjacent points for each point and multiple BDi values can be calculated using Equation

(5.9) as shown in Figure 5.6. The mean value of these BDi values is chosen as the damage index for

each scanning point:

𝐵𝐵𝑆𝑆 =1𝑛𝑛�𝐵𝐵𝑆𝑆𝑖𝑖

𝑖𝑖

𝑖𝑖=1

(5.10)

where 𝑛𝑛 is the number of adjacent points for each scanning point. This mean BD value can be

visualized for the entire scanning area, and spatial points with higher BD values indicate the existence

and the location of damage. Thus, baseline-free damage detection or visualization technique using the

developed BD feature is realized.

Figure 5.6 Illustration for spatially adjacent ultrasonic response comparison using BD.

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This section validates the proposed state space based damage detection technique with the

numerical simulation model developed in Chapter 3. As mentioned in Chapter 3, a micro crack is

introduced in the simulated aluminum plate model, and the nonlinearity of the simulated micro crack

is verified by observing the crack opening and closing during wave propagation. Same as Chapter 4,

to validate the proposed state space based damage detection technique, a scanning area of 40 mm × 35

mm was defined, covering the entire micro crack as shown in Figure 5.7. A total of 1400 (40 × 35)

scanning points were assigned within this scanning area, achieving a spatial resolution of 1 mm. A

100 μs velocity signal with a sampling time step of 150 ns was obtained from each scanning point and

used to reconstruct the state space attractors and calculate the BD values.

Figure 5.7 Illustration of a scanning region in simulation model for BD calculation.

It has been shown that often the selection of the embedding dimension 𝑚𝑚 has a more significant

impact on the dynamic characteristics of the reconstructed state space attractor than the time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙

has (Overbey et al., 2007). Therefore, in this validation, the time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 was fixed to be 5 using the

average mutual information (AMI) function, and only the effect of the embedding dimension 𝑚𝑚 on

the damage detection performance was investigated.

Singular value decomposition (SVD) was used to determine the dimension, 𝑚𝑚 (Broomhead and

King, 1986). The matrix of a state space attractor was built using Equation (5.3) with a large

dimension 𝑚𝑚 (𝑚𝑚 = 𝑃𝑃 = 25) from a single scanning signal. Then, SVD was performed on this matrix,

and 𝑃𝑃 singular values were computed. When the singular values are sorted in a descending order,

normalized with respect to the maximum singular value, and then plotted as a function of their

indices, 𝑝𝑝 (𝑝𝑝 = 1,2, … ,𝑃𝑃) as shown in Figure 5.8, each normalized singular value represents the

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information (variance) contained in each principal axis. The proper embedding dimension can then be

chosen based on the information contained in the retained singular values. Figure 5.8 shows the

normalized singular values of a randomly selected signal after applying a low-pass filter with a

varying cut-off frequency fc. When the frequency band of the signal is wider (i.e. when the signal is

filtered with a higher cut-off frequency), a higher embedding dimension is necessary for properly

reconstructing its state space attractor. In fact, a broadband signal theoretically has an infinite

dimension.

Figure 5.8 Singular values obtained from SVD of a state space attractor matrix, which is built from a

single scanning signal after applying a low-pass filter with a varying cut-off frequency, fc.

Next, the effect of the embedding dimension on damage detection was investigated with fc =

200 kHz. The state space attractors were reconstructed with a varying dimension, 𝑚𝑚 (𝑚𝑚 = 1, 2, 3, 4,

5, 10, 15 and 20), and the corresponding BD values were calculated and visualized in Figure 5.9.

When 𝑚𝑚 is less than 4, the corresponding damage detection result does not properly indicate the

crack. As 𝑚𝑚 increases, the BD values drastically increase near the crack tip and undesired high BD

values away from the crack disappear, improving the damage detection result. As the embedding

dimension 𝑚𝑚 increases over 15, the improvement of crack detection result becomes insignificant, as

shown in Figure 5.9. This observation matches with the small singular values of the filtered signal (fc

= 200 kHz) at the index of 15 or higher in Figure 5.8.

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Figure 5.9 The effect of the embedding dimension 𝑚𝑚 on damage detection (𝑚𝑚 = 1, 2, 3, 4, 5, 10, 15

and 20, fc = 200 kHz).

- 76 -

In Figure 5.10, the effect of the cut-off frequency on damage detection was investigated by

varying the cut-off frequency (fc = 350, 300, 250, 200, 150 and 100 kHz), but fixing the embedding

dimension, 𝑚𝑚 = 15. The results in Figure 5.10 imply that, though the high-frequency components are

more sensitive to micro damage, the results obtained with a narrow-band frequency are as good as the

ones obtained with a wider frequency band. As the frequency band decreases, the BD values near the

crack become more distinguishable. This is because a higher embedding dimension m is needed to

well reconstruct the state space attractors for the response signals with a wider frequency band.

Figure 5.10 The effect of the frequency band on damage detection (fc = 350, 300, 250, 200, 150 and

100 kHz, m =15).

In Figure 5.11, the damage detection performance for signals filtered with a high cut-off

frequency (fc = 350 kHz) was improved by choosing a higher embedding dimension (𝑚𝑚 = 25). It

indicates that a better damage detection result can be achieved by using a wider frequency band and a

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higher embedding dimension. However, compromise needs to be made between the damage detection

performance and its computation burden.

Figure 5.11 Damage detection result with a high embedding dimension (𝑚𝑚 = 25) and a high cut-off

frequency (fc = 350 kHz).



To experimentally examine the performance of the proposed state space based damage detection

technique, same aluminum plate specimen with a fatigue crack was used in this chapter. All the

geometrical information of this specimen can be found in Figure 4.8. All the experimental setup and

parameter setting are same as the experiment conducted on the same aluminum plate specimen in

Chapter 4.

For review, two different experiments were conducted. First, as shown in Figure 4.8(a), six pairs

of excitation and sensing laser beam points were selected to examine the sensitivity of the proposed

damage feature, BD, extracted from each path to the fatigue crack by comparing with the reference

signal acquired in its intact condition. Among all these six paths, path 1 passes through the crack, and

path 2 passes through the crack tip, while other paths do not. For the intact condition of the plate

specimen, ultrasonic responses were recorded three times from each path. One of them was used as

the reference signal (Reference), and the other two as the test signals acquired from the intact case

(Intact I and Intact II). After the crack formation, ultrasonic response signals (Damage) were collected

again following the same measurement procedure as in the intact case.

Second, in order to validate the proposed baseline-free damage detection technique by spatial

comparison, a laser excitation scanning area was selected with a 35 mm × 35 mm square area, located

close to one edge of the specimen and covering the entire fatigue crack, as shown in Figure 4.8(b). A

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total of 361 (19 × 19) scanning points were assigned within this scanning area, achieving a spatial

resolution less than 2 mm. The fixed sensing point was located outside the scanning area and was 25

mm away from the closest excitation point. This second experiment was conducted after the fatigue

test.

5.6.2 Test results

For comparison with the proposed state space based technique, a linear feature called correlation

coefficient was first calculated for the six paths (Figure 4.8(a)). The correlation coefficient of the two

intact and one damage cases (Damage, Intact I and Intact II) were computed with respect to the

reference case (Reference). Figure 5.12 summarizes the correlation coefficient values calculated from

the six paths. It is concluded that the linear correlation coefficient is not an effective feature for

fatigue crack detection because the difference between the damage and intact cases is small.

Figure 5.12 Fatigue crack detection using correlation coefficient obtained from six paths on the

aluminum plate specimen.

In this experiment, average mutual information (AMI) function and false nearest neighbors

(FNNs) function were used to choose the optimal time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 and dimension 𝑚𝑚 for state space

attractor reconstruction, respectively. For a given measured time series 𝑥𝑥(𝑛𝑛) (𝑛𝑛 = 1,2, … ,𝑁𝑁), the

AMI function measures the average amount of information learned about 𝑥𝑥�𝑛𝑛 + 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙� by measuring

𝑥𝑥(𝑛𝑛). If 𝑥𝑥�𝑛𝑛 + 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙� is completely independent from 𝑥𝑥(𝑛𝑛), AMI value becomes zero. Figure 5.13(a)

shows the AMI values of the reference responses obtained from the six paths with respect to time lag

𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙. For all six paths, the AMI values approach to almost zero when the time lag 𝜕𝜕 is bigger than 5.

Therefore, 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 = 5 was selected in this experiment.

If the distance between two closely positioned points substantially increase as the embedding

dimension increases from m to m + 1 dimensional space, this pair of points is named a false neighbor

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due to improper unfolding. As the embedding dimension expands, the percentage of false nearest

neighbors declines to a suitably small value. The lowest embedding dimension, which corresponds to

the first near zero percentage of FNNs, is often chosen as the appropriate embedding dimension. The

FNNs functions for the reference responses from the six paths are depicted in Figure 5.13(b). The

percentage of FNNs functions declines rapidly and approaches to the minimum values at 𝑚𝑚 = 5 for

all the six paths. Therefore, the embedding dimension should be selected as 5 or higher. Note that the

FNNs value does not converge to zero even after 𝑚𝑚 increases over 5. Because the laser pulse

excitation is neither a purely stochastic process nor a fully deterministic sequence, there are still some

information retained in higher dimensions although the majority of information is contained in the

first few dimensions.

(a) (b)

Figure 5.13 Parameter selection for state space attractor reconstruction for the six paths in the plate

specimen: (a) average mutual information (AMI) for time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙, and (b) false nearest neighbors

(FNNs) for dimension m.

First, the effect of the embedding dimension m on crack detection was investigated. The state

space attractors for the damage and intact cases were reconstructed with varying dimensions (𝑚𝑚 = 1, 2,

3, 4, 5, 10, 15 and 20) and compared with the reference attractors with the same dimension for all the

six paths. Then, the Bhattacharyya distance (BD) was calculated to assess the deviation of the current

(either intact or damage) attractor from the reference one using Equation (5.9). The results are

summarized in Figure 5.14. As the dimension increases beyond 5, the damage and intact attractors are

clearly distinguished and the wave propagation path (path 2) crossing the crack tip is easily identified.

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Figure 5.14 The effect of embedding dimension 𝑚𝑚 on Bhattacharyya distance (BD) and fatigue

crack detection (m = 1, 2, 3, 4, 5, 10, 15, 20).

- 81 -

For the second excitation area scanning test, the baseline-free damage detection technique by

spatial comparison was used to detect the fatigue crack in the selected scanning area. Also, AMI

function and FNNs function were used to choose the optimal time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 and dimension 𝑚𝑚 for

state space attractor reconstruction, respectively. Figure 5.15(a) shows the AMI values of 10

randomly selected ultrasonic responses from the scanning area with respect to time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙. Figure

5.15(b) shows the FNNs values of the 10 randomly selected ultrasonic responses with respect to

dimension 𝑚𝑚. Based on Figure 5.15, the time lag was chosen as 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 = 5, and the dimension 𝑚𝑚 was

selected as 𝑚𝑚 = 5, respectively. Once the parameters were selected for state space attractor

reconstruction, the BD value for each scanning point was calculated by comparing its attractor with

the reference attractors obtained from its adjacent points. Here, the effect of the embedding dimension

𝑚𝑚 was investigated as well. The attractors were reconstructed with varying dimensions (𝑚𝑚 = 1, 2, 3,

4, 5 and 10) and corresponding BD values were calculated and visualized for fatigue crack detection.

The results are summarized in Figure 5.16. When 𝑚𝑚 = 1 or 2, the FNNs function shows a

percentage for false neighbors over 50%, the corresponding result cannot indicate the fatigue crack,

but produces a false indication of damage. As the percentage of false neighbors decreases below 20%

(𝑚𝑚 is equal or larger than 3), the damage detection results are improved. Furthermore, it is clearly

demonstrated that the strongest nonlinearity is observed near the crack tip (Lim et al., 2014). Figure

5.16 demonstrates that the proposed technique can successfully locate the fatigue crack and is quite

sensitive to damage induced nonlinearity. Moreover, by comparing with the result (Figure 4.14)

achieved with MSPCD in Chapter 4, it shows that the state space based technique is more sensitive to

damage and less affected by test noise interference.

(a) (b)


ultrasonic response signals from the scanning area: (a) average mutual information (AMI) for time lag

𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙, and (b) false nearest neighbors (FNNs) for embedding dimension m.

- 82 -

Figure 5.16 Baseline-free fatigue crack detection using BD feature with different embedding

dimension m (m = 1, 2, 3, 4, 5 and 10).

- 83 -



The same carbon fiber reinforced polymer (CFRP) plate (Figure 4.15) in Chapter 4 was used for

experimental validation. The target damage is a 1 cm diameter delamination introduced at the center

of the plate through impact testing.

For review, as shown in Figure 4.15, a laser excitation scanning area was selected with a 60 mm

× 60 mm square area, covering the delamination damage. A total of 1225 (35 × 35) scanning points

were assigned within this scanning area, achieving a spatial resolution less than 2 mm. The fixed

sensing point was located outside the scanning area and was 20 mm away from the closest excitation

point. Each ultrasonic response was measured with a sampling frequency of 2.56 MHz for 0.4 ms and

averaged 100 times in the time domain for improving the signal to noise ratio. Other detailed

information about this CFRP plate and the experimental setup can be found in Chapter 4.

5.7.2 Test results

Firstly, the parameters for state space attractor reconstruction were selected. Figure 5.17 shows

the selections of time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 using AMI function and embedding dimension 𝑚𝑚 using FNNs

function, respectively. The AMI values of 10 randomly selected ultrasonic responses from the laser

excitation scanning area are shown with respect to time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 in Figure 5.17(a). The AMI values

approach to almost zero when time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 reaches 20. Hence, 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 = 20 was selected in this

experiment. Figure 5.17(b) displays the FNNs values for the same 10 randomly selected ultrasonic

responses. The FNNs values decline to the minimum values when 𝑚𝑚 = 10. Therefore, the embedding

dimension was set to 10.

The BD values for all the scanning points in the selected scanning area were then calculated from

the reconstructed state space attractors with the selected parameters. The corresponding delamination

detection result is shown in Figure 5.18. It shows that the proposed technique successfully detects the

delamination in the CFRP plate specimen, and the BD value increases as the scanning moves toward

the edge of the damaged area. Once again, by comparing with the result (Figure 4.16) achieved with

MSPCD in Chapter 4, it shows that the state space based technique is more sensitive to damage and

less affected by test noise interference.

- 84 -

(a) (b)


ultrasonic response signals from the CFRP plate: (a) average mutual information (AMI) for time lag

𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙, and (b) false nearest neighbors (FNNs) for embedding dimension m.

Figure 5.18 Baseline-free delamination detection in CFRP plate using state space based technique.



Same as in Chapter 4, an actual 10 kW GFRP (glass fiber reinforced polymer) wind turbine blade

(Figure 4.17) was selected for additional validation of the proposed state space based damage

detection technique. Two types of damages, delamination and debonding, were intentionally produced

in this wind turbine blade. Close views of these two damages can be seen in Figure 4.18.

For review, as shown in Figure 4.18, a 50 mm × 50 mm square area was scanned with 400 (20 ×

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20) scanning points for both delamination and debonding detection, achieving a spatial resolution

around 2.5 mm. The fixed sensing point was located 20 mm away from the closest excitation point.

The ultrasonic responses from all excitation points were measured with a sampling frequency of 2.56

MHz for 0.4 ms and averaged 100 times in the time domain for improving the signal to noise ratio.

Other detailed information about this GFRP wind turbine blade and the experimental setup can be

found in Chapter 4.

5.8.2 Test results

The parameters for state space attractor reconstruction were first selected. Figure 5.19 shows the

selections of time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 using AMI function and embedding dimension 𝑚𝑚 using FNNs function,

respectively. The AMI values of 10 randomly selected ultrasonic responses from two scanning areas

are shown with respect to time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 in Figure 5.19(a). The AMI values approach to almost zero

when time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 reaches 30. Hence, 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙 = 30 was selected in this experiment. Figure 5.19(b)

displays the FNNs values for the same 10 randomly selected ultrasonic responses. The FNNs values

decline to the minimum values when 𝑚𝑚 = 6. Therefore, the embedding dimension was set to 6.

(a) (b)

Figure 5.19 Parameter selection for state space attractor reconstruction with 10 randomly selected

ultrasonic response signals from the wind turbine blade: (a) average mutual information (AMI) for

time lag 𝜕𝜕𝑙𝑙𝑎𝑎𝑙𝑙, and (b) false nearest neighbors (FNNs) for dimension m.

The BD values for two scanning areas were then calculated from the reconstructed state space

attractors with the selected parameters. The corresponding damage detection results are shown in

Figure 5.20. It shows again that if the scanning is performed in the middle of the damaged area, BD

- 86 -

value does not increase much since the other adjacent points are also affected by the damage.

However, as the scanning moves toward the edge of the damaged area, the BD value increases

significantly as demonstrated in Figure 5.20. The proposed technique again successfully detects and

even visualizes both delamination and debonding in the GFRP wind turbine blade. Once again, by

comparing with the results (Figure 4.20) got with MSPCD in Chapter 4, it shows that the state space

based technique is more sensitive to damage induced nonlinearity and less affected by test noise

interference. However, considering the computation burden, since the BD feature is computed in the

state space with a high dimension, compromise needs to be made between the damage detection

performance and its computation burden.

(a) (b)

Figure 5.20 Baseline-free delamination/ debonding detection in wind turbine blade using state space

based technique: (a) delamination, and (b) debonding (the dashed line indicates the location of the

hidden stiffener).

5.9 Chapter summary

This chapter projects the acquired wideband ultrasonic responses into a state space and

reconstructs its state space attractor. The state space attractor is the geometric representation of a

dynamical system, and thus will reflect a loss of dynamical similarity due to damage, especially the

nonlinear one. A new nonlinear damage feature called Bhattacharyya distance (BD) is obtained by

checking the geometrical variations of the reconstructed current state space attractor from a reference

attractor. Also, by examining the spatial distribution of the BD values over an inspection area via laser

scanning, damage can be detected and even visualized without referencing temporal baseline

ultrasonic signals corresponding to the pristine condition of the target structure. Simulation model

- 87 -

with a micro crack proposed in Section 3 is used to validate the proposed state space based damage

detection technique. Moreover, fatigue crack in an aluminum plate, delamination in a CFRP plate, and

delamination and hidden debonding in a GFRP wind turbine blade are also successfully detected

using the proposed technique. By comparing with the test results using the maximum sideband peak

count (MSPCD) feature in Chapter 4, the state space based technique shows higher sensitivity to

structural damage, and is more robust against test noise interference. However, compromise needs to

be made between damage detection performance and its computation burden.

- 88 -

Chapter 6. Structural Damage Detection using Spectral Correlation of Nonlinear

Modulations

This chapter analyzes the limitation of the proposed sideband peak count (SPC) technique. In

order to tackle this limitation, spectral correlation technique is adopted and its properties against noise

interference are presented and validated through experiments on an aluminum plate with two single

frequencies as inputs. Then the spectral correlation technique is extended for wideband structural

ultrasonic responses acquired under the pulse laser input, and the SPC technique is conducted in the

new spectral correlation domain for damage detection. Its advantages over SPC in the conventional

frequency domain are explained and validated numerically and experimentally with the same model

and specimens shown in Chapter 4.

6.1 Limitation of sideband peak count (SPC)

In the previous chapters, sideband peak count (SPC) and state space based damage detection

techniques have been presented and shown their feasibility both numerically and experimentally.

However, by comparing the damage detection results achieved from the proposed two damage

detection techniques, the SPC based technique seems more susceptible to test noise interference. This

technical hurdle needs to be overcome before the SPC based technique can make transitions to real

field applications.

In general, at the presence of structural damage, the amplitude of the damage-induced modulation

components is at least one or two orders of magnitude smaller than that of the linear components. It

indicates that the energy level of nonlinear modulation components is much closer to the test noise

level. Hence, the test noise, varying with environmental and operational conditions, might badly

interfere with the proposed techniques. Also, because the noise interference normally covers over the

entire frequency band, it is impossible to remove the noise interference simply through a band-pass

filtering.

Figures 6.1 and 6.2 compare a test signal (randomly selected from the previous chapters) before

and after contaminating with simulated test noise in the time and frequency domains, respectively.

The comparison results show that the test signal, contaminated with simulated noise, varies a lot in

both the time and frequency domains. However, for the state space based damage detection technique,

- 89 -

as explain in Chapter 5, a set of 𝑃𝑃 nearest neighbors are picked for each fiducial point in the

reconstructed state space attractor. And this 𝑃𝑃 number is selected so that the local dynamics of the

attractor can be captured, and the 𝑃𝑃 number should also be large enough so that the mass centroid of

the 𝑃𝑃 selected neighborhood and its time-evolved neighborhood are insensitive to noise interference

(Overbey and Todd, 2008). In this way, the noise interference on the state space based damage

detection technique can be removed or at least weakened. On the other hand, for the SPC based

damage detection technique developed in Chapter 4, because more small spectral peaks rise up in the

frequency domain due to test noise (Figure 6.2), all these small spectral peaks will be counted during

the SPC operation and increase the MSPCD value, which in turn will greatly affect the damage

detection results using the SPC based technique.

Figure 6.1 Comparison in the time domain between an original test signal and the signal

contaminated with simulated noise.

Figure 6.2 Comparison in the frequency domain between an original test signal and the signal

contaminated with simulated noise.

- 90 -

6.2 Spectral correlation technique

In order to increase the robustness of the proposed SPC based damage detection technique

against noise interference, spectral correlation technique is adopted in this chapter. Using spectral

correlation, noise or other interference, which is spectrally overlapped with the nonlinear modulation

components in the ultrasonic responses, can be effectively removed or highly reduced. Since this

noise issue also exists while using two single frequencies as inputs, all the contents below in this

chapter start from two single frequency inputs, as well as for better explanation.

6.2.1 Definition of spectral correlation

Based on nonlinear ultrasonic modulation, when two input with different frequencies 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏

(𝑓𝑓𝑎𝑎 > 𝑓𝑓𝑏𝑏) are applied to a system behaves nonlinearly, the system response will contain not only the

input frequencies but also their modulations (linear combinations of input frequencies, 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏) (Van

Den Abeele et al., 2000, de Lima and Hamilton, 2003). Here, only the first-order nonlinear

modulations at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 are considered. Typically, spectral density function is used to analyze the

frequency contents in the response and extract the modulations. Given a random signal 𝑥𝑥(𝑡𝑡), its

spectral density function (power spectrum) is given by:

𝑃𝑃𝑥𝑥(𝑓𝑓) = 𝐸𝐸[𝑋𝑋(𝑓𝑓)𝑋𝑋∗(𝑓𝑓)] (6.1)

where 𝑋𝑋(𝑓𝑓) is the Fourier transform of 𝑥𝑥(𝑡𝑡) and * denotes the complex conjugate. And the

corresponding nonlinear modulation components at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 can be expressed as:

𝑃𝑃𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏) = 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏)] (6.2)

As mentioned before, because the amplitude of the nonlinear modulation components is at least one or

two orders of magnitude smaller than that of the linear components, it is difficult to extract the

nonlinear modulation using this conventional spectral density function under noisy conditions,

especially when the noise overlaps with the nonlinear modulation components in the frequency

domain.

In this chapter, spectral correlation technique is adopted, and the spectral correlation between

nonlinear modulation components is used instead of the conventional spectral density value of the

modulation components. In past decades, spectral correlation has been exploited in various fields,

such as diagnosis of gear faults in moving mechanical systems (Dalpiaz et al., 2000, Bouillaut and

Sidahmed, 2001, Antoni, 2009), and channel sensing and spectrum allocation in wireless

- 91 -

communication (Fehske et al., 2005, Han et al., 2006, Yoo et al., 2014). Normally, spectral correlation

is used to identify second-order cyclostationary stochastic processes whose autocorrelation functions

𝑅𝑅𝑥𝑥(𝑡𝑡, 𝜏𝜏) vary periodically with time (Gardner, 2001):

𝑅𝑅𝑥𝑥(𝑡𝑡, 𝜏𝜏) = 𝑅𝑅𝑥𝑥�𝑡𝑡 + 𝜕𝜕𝑝𝑝, 𝜏𝜏�

𝑅𝑅𝑥𝑥(𝑡𝑡, 𝜏𝜏) = 𝐸𝐸[𝑥𝑥 �𝑡𝑡 +𝜏𝜏2� 𝑥𝑥∗ �𝑡𝑡 −

𝜏𝜏2�]

(6.3)

where 𝜏𝜏 is the time lag, 𝜕𝜕𝑝𝑝 is the cyclic period, 𝐸𝐸 is the expectation operation with respect to time

𝑡𝑡. Spectral correlation is then a double Fourier transform of the 𝑅𝑅𝑥𝑥(𝑡𝑡, 𝜏𝜏) with respect to 𝑡𝑡 and 𝜏𝜏

(Gardner, 2001):

𝑆𝑆𝑥𝑥(𝑓𝑓,𝛼𝛼) = �𝑅𝑅𝑥𝑥(𝑡𝑡, 𝜏𝜏)𝑒𝑒−𝑖𝑖2𝜋𝜋𝜋𝜋𝑡𝑡𝑒𝑒−𝑖𝑖2𝜋𝜋𝑓𝑓𝜋𝜋d𝑡𝑡 d𝜏𝜏 (6.4)

where 𝛼𝛼 is the cyclic frequency and 𝑓𝑓 is the spectral frequency. Equation (6.4) can also be written

as:

𝑆𝑆𝑥𝑥(𝑓𝑓,𝛼𝛼) = 𝐸𝐸[𝑋𝑋(𝑓𝑓 + 𝛼𝛼/2)𝑋𝑋∗(𝑓𝑓 − 𝛼𝛼/2)] (6.5)

To interpret the results brought by spectral correlation, let us consider a signal (Bouillaut and

Sidahmed, 2001):

𝑥𝑥(𝑡𝑡) = 𝑀𝑀(𝑡𝑡)𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑎𝑎𝑡𝑡 + 𝑏𝑏(𝑡𝑡)𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑏𝑏𝑡𝑡 (6.6)

where 𝑀𝑀(𝑡𝑡) and 𝑏𝑏(𝑡𝑡) are two low-pass filtered random amplitude coefficients. This signal 𝑥𝑥(𝑡𝑡) can

also present the response of a linear system subjected to inputs at frequencies 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏. The

calculation of the autocorrelation of 𝑥𝑥(𝑡𝑡) will furnish the following equation:

𝑅𝑅𝑥𝑥(𝑡𝑡, 𝜏𝜏) = 𝐸𝐸 �𝑀𝑀 �𝑡𝑡 +𝜏𝜏2� 𝑀𝑀∗ �𝑡𝑡 −

𝜏𝜏2�� 𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑎𝑎𝜋𝜋

+𝐸𝐸 �𝑏𝑏 �𝑡𝑡 +𝜏𝜏2� 𝑏𝑏∗ �𝑡𝑡 −

𝜏𝜏2�� 𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑏𝑏𝜋𝜋

+𝐸𝐸 �𝑀𝑀 �𝑡𝑡 +𝜏𝜏2� 𝑏𝑏∗ �𝑡𝑡 −

𝜏𝜏2�� 𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑎𝑎−𝑓𝑓𝑏𝑏)𝑡𝑡𝑒𝑒𝑖𝑖2𝜋𝜋

𝑓𝑓𝑎𝑎+𝑓𝑓𝑏𝑏2 𝜋𝜋

+𝐸𝐸 �𝑏𝑏 �𝑡𝑡 +𝜏𝜏2� 𝑀𝑀∗ �𝑡𝑡 −

𝜏𝜏2�� 𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑏𝑏−𝑓𝑓𝑎𝑎)𝑡𝑡𝑒𝑒𝑖𝑖2𝜋𝜋

𝑓𝑓𝑏𝑏+𝑓𝑓𝑎𝑎2 𝜋𝜋

(6.7)

Next, by calculating the double Fourier transform of Equation (6.7) with respect to 𝑡𝑡 and 𝜏𝜏, we

obtain the following spectral correlation equation:

𝑆𝑆𝑥𝑥(𝑓𝑓,𝛼𝛼) = 𝛾𝛾𝑎𝑎(𝑓𝑓 − 𝑓𝑓𝑎𝑎)𝛿𝛿(𝛼𝛼) + 𝛾𝛾𝑏𝑏(𝑓𝑓 − 𝑓𝑓𝑏𝑏)𝛿𝛿(𝛼𝛼)

+𝛾𝛾𝑎𝑎𝑏𝑏 �𝑓𝑓 − �𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏

2��𝛿𝛿�𝛼𝛼 − (𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)�

+𝛾𝛾𝑏𝑏𝑎𝑎 �𝑓𝑓 − �𝑓𝑓𝑏𝑏 + 𝑓𝑓𝑎𝑎

2��𝛿𝛿�𝛼𝛼 − (𝑓𝑓𝑏𝑏 − 𝑓𝑓𝑎𝑎)�

(6.8)

where 𝛿𝛿 is the Dirac delta function, 𝛾𝛾𝑎𝑎 and 𝛾𝛾𝑏𝑏 are the spectra densities of 𝑀𝑀(𝑡𝑡) and 𝑏𝑏(𝑡𝑡), 𝛾𝛾𝑎𝑎𝑏𝑏

and 𝛾𝛾𝑏𝑏𝑎𝑎 are the cross-spectral densities between 𝑀𝑀(𝑡𝑡) and 𝑏𝑏(𝑡𝑡), respectively. Here, 𝛾𝛾𝑎𝑎, 𝛾𝛾𝑏𝑏, 𝛾𝛾𝑎𝑎𝑏𝑏,

and 𝛾𝛾𝑏𝑏𝑎𝑎 are functions with a zero-centered peak.

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As shown in Equation (6.8), for 𝛼𝛼 = 0, the first two terms on the right side of the equation

represent spectral correlation values at 𝑓𝑓 = 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏, respectively, and 𝑆𝑆𝑥𝑥(𝑓𝑓, 0) becomes 𝑃𝑃𝑥𝑥(𝑓𝑓),

as defined in Equation (6.1). For 𝛼𝛼 ≠ 0, we can find two symmetric spectral correlation values at

(𝑓𝑓 = 𝑓𝑓𝑎𝑎+𝑓𝑓𝑏𝑏2

,𝛼𝛼 = ±(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)). Figure 6.3 presents the spectral correlation of the response signal 𝑥𝑥(𝑡𝑡)

obtained from a linear system (ignoring symmetric values at 𝛼𝛼 < 0). For simplicity, we set 𝑀𝑀(𝑡𝑡) =

𝑏𝑏(𝑡𝑡) = 1 in Figure 6.3.


𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑏𝑏𝑡𝑡.

6.2.2 Spectral correlation between nonlinear modulation components

For a nonlinear system, there are two additional modulated frequency components 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 and

𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 in the response signal besides 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏. By expanding Equation (6.8) with four input

frequencies, a total of ten peak values appear in the spectral correlation, as shown in Figure 6.4. For

𝛼𝛼 = 0, we again encounter its spectral density function with four peak values at 𝑓𝑓𝑎𝑎, 𝑓𝑓𝑏𝑏, 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏, and

𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏. When 𝛼𝛼 ≠ 0, six peaks are produced among the frequency components 𝑓𝑓𝑎𝑎, 𝑓𝑓𝑏𝑏, 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 and

𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 and their (𝑓𝑓,𝛼𝛼) coordinates in spectral correlation are listed in Table 6.1.

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𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑏𝑏𝑡𝑡 + 𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑎𝑎+𝑓𝑓𝑏𝑏)𝑡𝑡 + 𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑎𝑎−𝑓𝑓𝑏𝑏)𝑡𝑡.

Table 6.1 Summary of the peak coordinates in spectral correlation (𝛼𝛼 > 0)

Frequency combination Coordinate of spectral correlation peak (𝑓𝑓,𝛼𝛼)

Linear 𝑓𝑓𝑎𝑎, 𝑓𝑓𝑏𝑏 𝑓𝑓𝑎𝑎, 𝑓𝑓𝑏𝑏 (

𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏2

,𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)

Nonlinear 𝑓𝑓𝑎𝑎, 𝑓𝑓𝑏𝑏,

𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏, 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏

𝑓𝑓𝑎𝑎, 𝑓𝑓𝑏𝑏 (𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏

2,𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)

𝑓𝑓𝑎𝑎, 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 (𝑓𝑓𝑎𝑎 −𝑓𝑓𝑏𝑏2

,𝑓𝑓𝑏𝑏)

𝑓𝑓𝑎𝑎, 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 (𝑓𝑓𝑎𝑎 +𝑓𝑓𝑏𝑏2

,𝑓𝑓𝑏𝑏)

𝑓𝑓𝑏𝑏, 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 (𝑓𝑓𝑎𝑎2

, |𝑓𝑓𝑎𝑎 − 2𝑓𝑓𝑏𝑏|)

𝑓𝑓𝑏𝑏, 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 (𝑓𝑓𝑏𝑏 +𝑓𝑓𝑎𝑎2

,𝑓𝑓𝑎𝑎)

𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏, 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 (𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏)

Comparison of Figures 6.3 and 6.4 shows that there are five more peaks (𝛼𝛼 > 0) in spectral

correlation when nonlinear modulation components exist in the response signal. That is, the spectral

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correlation values at those five coordinates will increase when damage exists in the target structure

and causes nonlinear ultrasonic modulation. The major departure of this study from the

aforementioned studies is that spectral correlation is used to detect the nonlinear modulations instead

of the cyclostationarity of signal 𝑥𝑥(𝑡𝑡), or the statistical link between the original input frequencies 𝑓𝑓𝑎𝑎

and 𝑓𝑓𝑏𝑏. In this study, we mainly consider the spectral correlation value 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) between the two

nonlinear modulation components at 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 and 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏:

𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) = 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)] (6.9)

6.2.3 Properties of spectral correlation

Two notable properties of spectral correlation are that (Gardner, 1986): (1) Stationary noise

exhibits no spectral correlation (for 𝛼𝛼 ≠ 0); and (2) Two statistically weak-linked components exhibit

weak spectral correlation (for 𝛼𝛼 ≠ 0). To illustrate these two properties, simulation results are plotted

in Figures 6.5 and 6.6.

Figure 6.5 shows the spectral correlation of stationary white noise, whose spectral correlation

values appear only at 𝛼𝛼 = 0. Figures 6.6(a) and (b) show the spectral correlation of signal 𝑥𝑥(𝑡𝑡)

defined in Equation (6.6). In the first case, 𝑀𝑀(𝑡𝑡) and 𝑏𝑏(𝑡𝑡) are strongly correlated when 𝑀𝑀(𝑡𝑡) =

𝑏𝑏(𝑡𝑡) = 1, as shown in Figure 6.6(a). This also indicates a strong statistical link between the two

frequency components at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 . On the other hand, when 𝑀𝑀(𝑡𝑡) and 𝑏𝑏(𝑡𝑡) are stastically

independent (not statistically linked), the last two terms on the right side of Equations (6.7) and (6.8)

become zero and the peak value at (𝑓𝑓𝑎𝑎+𝑓𝑓𝑏𝑏2

,𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏) vanishes, as shown in Figure 6.6(b). That is, the

spectral correlation of 𝑥𝑥(𝑡𝑡) in Figure 6.6(b) contains only two peaks at 𝛼𝛼 = 0. Actually, the spectral

correlation value 𝑆𝑆𝑥𝑥 �𝑓𝑓𝑎𝑎+𝑓𝑓𝑏𝑏2

,𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏� (= 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎)𝑋𝑋∗(𝑓𝑓𝑏𝑏)]) can be estimated as (Gardner, 1986):

𝑆𝑆𝑥𝑥 �𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏

2,𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏� ~ 𝑐𝑐𝑎𝑎,𝑏𝑏�𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑏𝑏, 0)

𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎)𝑋𝑋∗(𝑓𝑓𝑏𝑏)]~ 𝑐𝑐𝑎𝑎,𝑏𝑏�𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎)𝑋𝑋∗(𝑓𝑓𝑎𝑎)]𝐸𝐸[𝑋𝑋(𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑏𝑏)] (6.10)

where 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 0) (= 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎)𝑋𝑋∗(𝑓𝑓𝑎𝑎)]) and 𝑆𝑆𝑥𝑥(𝑓𝑓𝑏𝑏 , 0) (= 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑏𝑏)]) are the spectral density

values of 𝑥𝑥(𝑡𝑡) at frequencies 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏, respectively, and 𝑐𝑐𝑎𝑎,𝑏𝑏 (≤ 1) is the correlation coefficient,

reflecting the statistical link between the two components at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏.

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Figure 6.5 Stationary noise signal exhibits no spectral correlation, 𝑥𝑥(𝑡𝑡) = 𝑠𝑠𝑡𝑡𝑀𝑀𝑡𝑡𝑖𝑖𝑠𝑠𝑛𝑛𝑀𝑀𝑟𝑟𝑠𝑠 𝑤𝑤ℎ𝑖𝑖𝑡𝑡𝑒𝑒 𝑛𝑛𝑠𝑠𝑖𝑖𝑠𝑠𝑒𝑒.

(a)

(b)

Figure 6.6 Two statistically weak-linked components exhibit weak spectral correlation,

𝑥𝑥(𝑡𝑡) = 𝑀𝑀(𝑡𝑡)𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑎𝑎𝑡𝑡 + 𝑏𝑏(𝑡𝑡)𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑏𝑏𝑡𝑡: (a) 𝑀𝑀(𝑡𝑡) = 𝑏𝑏(𝑡𝑡) = 1, and (b) 𝑀𝑀(𝑡𝑡) and 𝑏𝑏(𝑡𝑡) are independent

from each other.

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Figure 6.7 Different components contributing to the response in spectral density function at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏.

Here, let us take a look into the different components contributing to the response of the spectral

density function at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 . As shown in Figure 6.7, there are many components 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ±

𝑓𝑓𝑏𝑏 , 0)𝑖𝑖 contributing to the spectral responses at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏. Here, 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , 0)𝑖𝑖 are the spectral density

values of the ith component at the modulation frequencies 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 . First, there are the ‘real’

modulations 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , 0)1 caused by two inputs at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 . Second, modulations 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ±

𝑓𝑓𝑏𝑏 , 0)2 among noise at other frequencies, can occur at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 (e.g., 𝑓𝑓𝑎𝑎1 − 𝑓𝑓𝑏𝑏1 = 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏, 𝑓𝑓𝑎𝑎2 +

𝑓𝑓𝑏𝑏2 = 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏). Third, harmonics 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , 0)3 caused by noise inputs at (𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)/2 and (𝑓𝑓𝑎𝑎 +

𝑓𝑓𝑏𝑏)/2, can appear at 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 and 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏, respectively. Fourth, additional noise 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , 0)4 at

𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 can be added to the modulation components at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏. Under harsh test conditions, the

effect of the true modulation can be smeared by the aforementioned noise components. In the

presence of the noise components, similar to Equation (6.10), 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) (= 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 −

𝑓𝑓𝑏𝑏)]) can be revised as follows:

𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) ~ � 𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏𝑖𝑖�𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 0)𝑖𝑖𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 , 0)𝑖𝑖𝑖𝑖

𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)]~� 𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏𝑖𝑖�𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)]𝑖𝑖𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)]𝑖𝑖𝑖𝑖

(6.11)

where 𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏𝑖𝑖 is the corresponding correlation coefficient indicating the statistical link between

the ith components at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏. For 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , 0)1, because they are produced by the common input

at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏, they are strongly correlated with a high 𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏1 value. On the other hand, the

modulation components 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏, 0)2 caused by frequencies 𝑓𝑓𝑎𝑎1, 𝑓𝑓𝑏𝑏1 and 𝑓𝑓𝑎𝑎2, 𝑓𝑓𝑏𝑏2 (𝑓𝑓𝑎𝑎1 ≠ 𝑓𝑓𝑎𝑎2 ≠

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𝑓𝑓𝑎𝑎 ,𝑓𝑓𝑏𝑏1 ≠ 𝑓𝑓𝑏𝑏2 ≠ 𝑓𝑓𝑏𝑏 ), and the harmonics 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , 0)3 caused by frequencies (𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)/2 and

(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)/2 exhibit weak spectral correlations (𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏2 ≈ 𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏3 ≈ 0) because their noise

inputs are at different frequencies and uncorrelated. Moreover, most of the experimental noises

𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , 0)4 are stationary, and a stationary signal exhibits no spectral correlation (𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏4 = 0).

Hence, the spectral correlation 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) (= 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)]) between the two

nonlinear modulation components at 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 and 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 can be properly measured, even when the

signal is contaminated by noise.

6.3 Experimental validation using inputs at two single frequencies


The effectiveness of the proposed spectral correlation technique was examined using the test data

obtained from two identical aluminum plate (6061-T6) specimens. The geometrical dimensions of the

specimens are presented in Figure 6.8(a). Packaged piezoelectric transducers (Liu et al., 2016), named

PZT1, PZT2, and PZT3 (Figure 6.8(b)), are attached to each plate specimen. The three PZTs are

packaged by a flexible printed circuit board with SMA connectors. PZT1 and PZT2 were used for

generating high-frequency 𝑓𝑓𝑎𝑎 and low-frequency 𝑓𝑓𝑏𝑏 input signals, respectively, while PZT3 was used

for sensing. A 15 mm fatigue crack propagated from the center hole, as shown in Figure 6.8(c), was

induced in one plate specimen after 37,000 cycles of a cyclic loading test. A universal testing machine

(INSTRON 8801) with a 10 Hz cycle rate, a maximum load of 25 kN, and a stress ratio of 0.1 was

used for this cyclic loading test.

The packaged PZTs were connected to a data acquisition system (Figure 6.9) (Lim et al., 2014),

which consists of two National Instruments (NI) NI-PXI-5421 arbitrary waveform generators (AWGs),

a NI-PXI-5122 high-speed digitizer (DIG) and a NI-PXI-8105 embedded controller. One AWG is

used to generate the high-frequency input signal on PZT1 and the other to generate the low-frequency

input signal on PZT2. The response from PZT3 is measured by DIG. The AWGs and DIG are

synchronized and controlled by LabVIEW software in the embedded controller.

- 98 -

(a)

(b) (c)

Figure 6.8 Aluminum plate with fatigue crack: (a) geometrical dimensions and PZT transducer

arrangement, (b) packaged piezoelectric transducer, and (c) a close-up of the fatigue crack.

(a) (b)

Figure 6.9 Experimental setup: (a) test schematic, and (b) hardware and specimen configurations.

The amplitudes of the high-frequency and low-frequency input signals were set to a peak-to-peak

voltage of 20 V. The responses were measured with 1 MHz sampling rate for 0.25 s. Each response

was measured 10 times and averaged in the time domain to improve the signal to noise ratio. In this

experiment, both 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 were swept over certain frequency ranges, increasing the possibility of

- 99 -

modulation generation at the presence of a fatigue crack. For the sweeping of high-frequency and

low-frequency inputs, 𝑓𝑓𝑎𝑎 was swept from 183 to 185 kHz, and 𝑓𝑓𝑏𝑏 from 30 to 40 kHz both in 1 kHz

increments, resulting in a total of 33 input frequency combinations. These 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 combinations

were selected because the responses had relatively large amplitudes at the corresponding input and

modulation frequencies.

6.3.2 Fatigue crack detection results through spectral correlation

Figure 6.10 displays the spectral correlation values obtained at six different coordinates listed

under ‘nonlinear’ case in Table 6.1. The spectral correlation values from Figures 6.10(a) to (d) show

the spectral correlation between one of two linear components (𝑓𝑓𝑎𝑎 or 𝑓𝑓𝑏𝑏), and one of the nonlinear

modulation components (𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 or 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 ). As a fatigue crack is formed, these four spectral

correlation values increase overall for most of the input frequency combinations investigated. Figure

6.10(e) shows the spectral correlation value between two nonlinear modulation components at 𝑓𝑓𝑎𝑎 ±

𝑓𝑓𝑏𝑏. Comparison of Figure 6.10(e) with Figures 6.10(a) to (d) indicates that the spectral correlation

value between two nonlinear modulation components is more sensitive to the fatigue crack than the

spectral correlation values between the linear and modulation components. On the other hand, the

spectral correlation value between the two linear components at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 is insensitive to the fatigue

crack, as displayed in Figure 6.10(f).

The sensitivities of different spectral correlation values shown in Figure 6.10 to the fatigue crack

are quantitatively compared using the following index:

𝑠𝑠 = �1𝑁𝑁�(

𝑆𝑆𝑑𝑑,𝑖𝑖

𝑆𝑆𝑖𝑖,𝑖𝑖)2

𝑁𝑁

𝑖𝑖=1

(6.12)

where 𝑆𝑆𝑑𝑑,𝑖𝑖 and 𝑆𝑆𝑖𝑖,𝑖𝑖 represent the spectral correlation values obtained from the damaged and intact

specimens, respectively, and N is the total number of 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 combinations (𝑁𝑁 = 33). Table 6.2

demonstrates that the spectral correlation value 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) (= 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)]) between

two modulation components at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 shown in Figure 6.10(e) has the highest sensitivity to fatigue

crack among all investigated spectral correlation values.

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(a) 𝑓𝑓𝑏𝑏,𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 (b) 𝑓𝑓𝑎𝑎,𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏

(c) 𝑓𝑓𝑏𝑏,𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 (d) 𝑓𝑓𝑎𝑎,𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏

(e) 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 ,𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 (f) 𝑓𝑓𝑎𝑎 ,𝑓𝑓𝑏𝑏

Figure 6.10 Spectral correlation values obtained from the intact and damaged specimens for multiple

frequency combinations.

- 101 -

Table 6.2 Sensitivities of different spectral correlation values to a fatigue crack shown in Figure 6.10.

Spectral correlation value between 𝑠𝑠

𝑓𝑓𝑏𝑏 ,𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 (Figure 6.10(a)) 12.65

𝑓𝑓𝑎𝑎 ,𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 (Figure 6.10(b)) 7.09

𝑓𝑓𝑏𝑏 ,𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 (Figure 6.10(c)) 40.96

𝑓𝑓𝑎𝑎 ,𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 (Figure 6.10(d)) 20.46

𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 ,𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 (Figure 6.10(e)) 93.21

𝑓𝑓𝑎𝑎 ,𝑓𝑓𝑏𝑏 (Figure 6.10(f)) 1.06

6.3.3 Fatigue crack detection results with simulated noise interference

To investigate the effect of noise on the spectral correlation value 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) between two

modulation components at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏, simulated stationary white noises with different signal to noise

ratios (SNRs) were added to the acquired test signals. Here, the SNR is defined as:

𝑆𝑆𝑁𝑁𝑅𝑅 = 10𝑙𝑙𝑠𝑠𝑔𝑔10𝐸𝐸𝑙𝑙𝐸𝐸𝑖𝑖

(dBW) (6.13)

where 𝐸𝐸𝑙𝑙 and 𝐸𝐸𝑖𝑖 are the energy of the acquired test signal and the added white noise, respectively.

SNR was varied from 60 to 30 dBW, with 10 dBW decrement, and the spectral correlation value

𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) was calculated using these noise contaminated test signals. For comparison, the

modulation components �𝑃𝑃𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑃𝑃𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏) in the conventional spectral density function,

which is equal to �𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏, 0) in Equation (6.11), was also calculated. Figures 6.11

and 6.12 present the spectral correlation value 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) (= 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)]) and the

corresponding conventional spectral density value �𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏, 0) (=

�𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)]𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)]) obtained from the noise contaminated test

signals with 𝑆𝑆𝑁𝑁𝑅𝑅 = 60, 50, 40 and 30 dBW, respectively. It can be seen that 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) was much

more robust against the white noise interference, while it became difficult to differentiate the damaged

specimen from the intact one as SNR decreased for �𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 , 0).

Here, note that, in high SNR condition (e.g., Figure 6.11(a) and Figure 6.12(a)), the spectral

correlation value 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) and the spectral density value �𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 , 0) show

- 102 -

nearly identical values, which means they own the same sensitivity to structural damage. This can be

explained by investigating Equation (6.11). In high SNR condition (ignoring all the interferences), the

connection between 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) and �𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 , 0) is the correlation coefficient

𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏 (𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) = 𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏�𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 , 0)). In this experiment, when inputs

with two distinct frequencies 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 are applied on the target structure, the linear responses at 𝑓𝑓𝑎𝑎

and 𝑓𝑓𝑏𝑏 and their modulations at 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 and 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 (due to weak material nonlinearity in intact

condition) are all statistically linked (𝑐𝑐𝑎𝑎,𝑏𝑏 = 𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏 = 1), regardless of the condition of the target

structure (Gardner, 1986). Thus, 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) and �𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 , 0) become

theoretically identical to each other, and with same sensitivity to structural damage.

(a) SNR = 60 dBW (b) SNR = 50 dBW

(c) SNR = 40 dBW (d) SNR = 30 dBW

Figure 6.11 Spectral correlation values 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) calculated from the noise contaminated test

signals with different SNRs.

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(a) SNR = 60 dBW (b) SNR = 50 dBW

(c) SNR = 40 dBW (d) SNR = 30 dBW

Figure 6.12 Spectral density values �𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 , 0) calculated from the noise

contaminated test signals with different SNRs.

6.4 Spectral correlation enhancement by a wideband input

6.4.1 Spectral correlation with a wideband input

When a pulse laser is applied on a target structure, a wideband response with multiple frequency

peaks will be generated, as illustrated in Figure 6.13. When the structure is damaged, nonlinear

ultrasonic modulation occurs among these frequency peaks and induce nonlinear modulation

components overlapping with the initial linear components. In this section, spectral correlation

(𝑆𝑆𝑥𝑥(𝑓𝑓,𝛼𝛼) = 𝐸𝐸[𝑋𝑋(𝑓𝑓 + 𝛼𝛼/2)𝑋𝑋∗(𝑓𝑓 − 𝛼𝛼/2)]) is extended to analyze the wideband responses. Here, for

two frequency components 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 from a wideband response signal, given that the resolution of

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Fourier transfer is ∆𝑓𝑓 in the frequency domain for spectral correlation, the two components we

considered are actually two narrowband components centered at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 with a narrow frequency

band equal to ∆𝑓𝑓 (Figure 6.13). These narrowband components can be represented as a summation

of pure sinusoidal signals with varying frequencies around 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏:

𝑀𝑀(𝑡𝑡) ∙ 𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑎𝑎𝑡𝑡 = � 𝑀𝑀𝑝𝑝𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑎𝑎+𝑓𝑓𝑝𝑝)𝑡𝑡

𝑝𝑝

𝑏𝑏(𝑡𝑡) ∙ 𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑏𝑏𝑡𝑡 = � 𝑏𝑏𝑞𝑞𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑏𝑏+𝑓𝑓𝑞𝑞)𝑡𝑡

𝑞𝑞

(6.14)

where 𝑓𝑓𝑝𝑝 and 𝑓𝑓𝑞𝑞 are frequencies within the range of −12∆𝑓𝑓 ≤ 𝑓𝑓𝑝𝑝/𝑞𝑞 < 1

2∆𝑓𝑓 and they satisfy 𝑓𝑓𝑝𝑝 =

−𝑓𝑓−𝑝𝑝, 𝑓𝑓𝑞𝑞 = −𝑓𝑓−𝑞𝑞, 𝑀𝑀𝑝𝑝 and 𝑏𝑏𝑞𝑞 are the amplitudes of the corresponding components at 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑝𝑝 and

𝑓𝑓𝑏𝑏 + 𝑓𝑓𝑞𝑞, respectively. 𝑀𝑀(𝑡𝑡) and 𝑏𝑏(𝑡𝑡) represent the amplitude coefficients for the two narrowband

frequency components centered at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏:

𝑀𝑀(𝑡𝑡) = � 𝑀𝑀𝑝𝑝𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑝𝑝𝑡𝑡𝑝𝑝

𝑏𝑏(𝑡𝑡) = � 𝑏𝑏𝑞𝑞𝑒𝑒𝑖𝑖2𝜋𝜋𝑓𝑓𝑞𝑞𝑡𝑡𝑞𝑞

(6.15)

Figure 6.13 Illustration of structural response in the frequency domain under a wideband pulse laser

excitation.

Considering the first-order nonlinear modulations at 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 and 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏, their amplitudes 𝑚𝑚+

and 𝑚𝑚− are proportional to the amplitude coefficients at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 based on the classical two-fold

nonlinear interaction between 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 (Van Den Abeele et al., 2000):

𝑚𝑚+(𝑡𝑡) ∙ 𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑎𝑎+𝑓𝑓𝑏𝑏)𝑡𝑡 = � 𝛽𝛽𝑝𝑝,𝑞𝑞+ 𝑀𝑀𝑝𝑝𝑏𝑏𝑞𝑞𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑎𝑎+𝑓𝑓𝑏𝑏+𝑓𝑓𝑝𝑝+𝑓𝑓𝑞𝑞)𝑡𝑡

𝑝𝑝,𝑞𝑞

𝑚𝑚−(𝑡𝑡) ∙ 𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑎𝑎−𝑓𝑓𝑏𝑏)𝑡𝑡 = � 𝛽𝛽𝑝𝑝,𝑞𝑞− 𝑀𝑀𝑝𝑝𝑏𝑏𝑞𝑞𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑎𝑎−𝑓𝑓𝑏𝑏+𝑓𝑓𝑝𝑝−𝑓𝑓𝑞𝑞)𝑡𝑡

𝑝𝑝,𝑞𝑞

(6.16)

where 𝛽𝛽𝑝𝑝,𝑞𝑞± is the nonlinear coefficient between 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑝𝑝 and 𝑓𝑓𝑏𝑏 + 𝑓𝑓𝑞𝑞, respectively, and the value of

- 105 -

the nonlinear coefficient depends on the corresponding input frequencies (Zaitsev et al., 2009, Lim et

al., 2014). Here, because all the 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑝𝑝 and 𝑓𝑓𝑏𝑏 + 𝑓𝑓𝑞𝑞 are centered at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 within a narrow

bandwidth ∆𝑓𝑓, the absolute difference between these 𝛽𝛽𝑝𝑝,𝑞𝑞± is insignificant. 𝑚𝑚+(𝑡𝑡) and 𝑚𝑚−(𝑡𝑡) can

be presented as:

𝑚𝑚+(𝑡𝑡) = � 𝛽𝛽𝑝𝑝,𝑞𝑞+ 𝑀𝑀𝑝𝑝𝑏𝑏𝑞𝑞𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑝𝑝+𝑓𝑓𝑞𝑞)𝑡𝑡

𝑝𝑝,𝑞𝑞

𝑚𝑚−(𝑡𝑡) = � 𝛽𝛽𝑝𝑝,𝑞𝑞− 𝑀𝑀𝑝𝑝𝑏𝑏𝑞𝑞𝑒𝑒𝑖𝑖2𝜋𝜋(𝑓𝑓𝑝𝑝−𝑓𝑓𝑞𝑞)𝑡𝑡

𝑝𝑝,𝑞𝑞

(6.17)

As shown in Figure 6.6, two statistically weak-linked components exhibit weak spectral

correlation, and it highly depends on the correlation between the amplitude coefficients of these two

components. Take 𝑀𝑀(𝑡𝑡) and 𝑏𝑏(𝑡𝑡) (Equation (6.15)) as an example, if they are totally independent

from each other, 𝑀𝑀𝑝𝑝 = 0 or 𝑏𝑏𝑞𝑞 = 0 should be satisfied when �𝑓𝑓𝑝𝑝� = �𝑓𝑓𝑞𝑞� (Kreyszig, 2006). In this

case, the corresponding correlation coefficient 𝑐𝑐𝑎𝑎,𝑏𝑏 (Equation (6.10)), between the two narrowband

frequency components centered at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏, becomes zero. For 𝑚𝑚+(𝑡𝑡) and 𝑚𝑚−(𝑡𝑡) in Equation

(6.17), it is worth mentioning that the same frequency component 𝑓𝑓𝑝𝑝 + 𝑓𝑓𝑞𝑞 has different amplitudes

𝛽𝛽𝑝𝑝,𝑞𝑞+ 𝑀𝑀𝑝𝑝𝑏𝑏𝑞𝑞 and 𝛽𝛽𝑝𝑝,−𝑞𝑞

− 𝑀𝑀𝑝𝑝𝑏𝑏−𝑞𝑞 in 𝑚𝑚+(𝑡𝑡) and 𝑚𝑚−(𝑡𝑡) , respectively. Here, 𝛽𝛽𝑝𝑝,−𝑞𝑞− is the nonlinear

coefficient between 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑝𝑝 and 𝑓𝑓𝑏𝑏 − 𝑓𝑓𝑞𝑞. If the structure is intact, 𝛽𝛽𝑝𝑝,𝑞𝑞± is weak (close to zero), and

the insignificant variations among different 𝛽𝛽𝑝𝑝,𝑞𝑞± become dominant in comparison to the amplitudes

of 𝛽𝛽𝑝𝑝,𝑞𝑞± . Thus, the amplitudes of 𝛽𝛽𝑝𝑝,𝑞𝑞

+ 𝑀𝑀𝑝𝑝𝑏𝑏𝑞𝑞 and 𝛽𝛽𝑝𝑝,−𝑞𝑞− 𝑀𝑀𝑝𝑝𝑏𝑏−𝑞𝑞 vary a lot for the same frequency

component 𝑓𝑓𝑝𝑝 + 𝑓𝑓𝑞𝑞 in 𝑚𝑚+(𝑡𝑡) and 𝑚𝑚−(𝑡𝑡), and the corresponding correlation coefficient 𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏,

between the two narrowband frequency components centered at 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 and 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏, becomes low.

On the other hand, for the damage case, since 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑝𝑝 and 𝑓𝑓𝑏𝑏 + 𝑓𝑓𝑞𝑞 vary within a narrow bandwidth

∆𝑓𝑓, all 𝛽𝛽𝑝𝑝,𝑞𝑞± will increase if 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 satisfy the binding conditions. In this case, the initial

variations among different 𝛽𝛽𝑝𝑝,𝑞𝑞± become negligible in comparison to the increased amplitudes of 𝛽𝛽𝑝𝑝,𝑞𝑞

± ,

and 𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏 will increase in return. Note that, however, in Equation (6.17), when 𝑓𝑓𝑝𝑝 ± 𝑓𝑓𝑞𝑞 = 0, the

induced time-invariant terms in 𝑚𝑚+(𝑡𝑡) and 𝑚𝑚−(𝑡𝑡) might increase the value of 𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏 to some

extent regardless of the condition of the target structure (Bouillaut and Sidahmed, 2001).

Since the resolution of Fourier transfer is ∆𝑓𝑓 in the frequency domain, we can rewrite Equation

(6.17) as:

�𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏, 0)~𝛽𝛽𝑎𝑎,𝑏𝑏± �𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑏𝑏 , 0)

�𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏)]~𝛽𝛽𝑎𝑎,𝑏𝑏± �𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎)𝑋𝑋∗(𝑓𝑓𝑎𝑎)]𝐸𝐸[𝑋𝑋(𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑏𝑏)]

(6.18)

where 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , 0)(= 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏)]) is the spectral density value at the modulation

- 106 -

frequencies centered at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 0) (= 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎)𝑋𝑋∗(𝑓𝑓𝑎𝑎)]) and 𝑆𝑆𝑥𝑥(𝑓𝑓𝑏𝑏 , 0) (= 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑏𝑏)])

are the spectral density values at frequencies centered at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏, respectively. Here, 𝛽𝛽𝑎𝑎,𝑏𝑏± can be

seen as the averaged nonlinear coefficients of 𝛽𝛽𝑝𝑝,𝑞𝑞± between frequencies centered at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏. Also,

based on Equation (6.11), we can estimate the spectral correlation value 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) (= 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 +

𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)]) as:

𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) ~𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏�𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏, 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏, 0)

𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)]~𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏�𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)]𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)] (6.19)

Substitute Equation (6.18) into Equation (6.19), we can achieve:

𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) ~𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏𝛽𝛽𝑎𝑎,𝑏𝑏+ 𝛽𝛽𝑎𝑎,𝑏𝑏

− 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 , 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑏𝑏 , 0)

𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)]~𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏𝛽𝛽𝑎𝑎,𝑏𝑏+ 𝛽𝛽𝑎𝑎,𝑏𝑏

− 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎)𝑋𝑋∗(𝑓𝑓𝑎𝑎)]𝐸𝐸[𝑋𝑋(𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑏𝑏)] (6.20)

And for better comparison, the spectral density values at the modulation frequencies in Equation (6.18)

are modified as:

�𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 , 0) ~𝛽𝛽𝑎𝑎,𝑏𝑏+ 𝛽𝛽𝑎𝑎,𝑏𝑏

− 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑏𝑏, 0)

�𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏)]�𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏)]~𝛽𝛽𝑎𝑎,𝑏𝑏+ 𝛽𝛽𝑎𝑎,𝑏𝑏

− 𝐸𝐸[𝑋𝑋(𝑓𝑓𝑎𝑎)𝑋𝑋∗(𝑓𝑓𝑎𝑎)]𝐸𝐸[𝑋𝑋(𝑓𝑓𝑏𝑏)𝑋𝑋∗(𝑓𝑓𝑏𝑏)] (6.21)

By comparing between Equation (6.20) and Equation (6.21), it can be seen that, when the inputs

are composed of two narrowband frequency components centered at 𝑓𝑓𝑎𝑎 and 𝑓𝑓𝑏𝑏 , the spectral

correlation value 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏) has higher sensitivity to structural damage than the conventional

spectral density value �𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 0)𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 , 0), because both the nonlinear coefficient 𝛽𝛽𝑎𝑎,𝑏𝑏±

and the correlation coefficient 𝑐𝑐𝑎𝑎+𝑏𝑏,𝑎𝑎−𝑏𝑏 increase when the structure is damaged, enhancing the

contrast between intact and damage conditions.

Now, let us consider the whole wideband response, and there are a few points to note. First, there

must exist linear responses 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , 0)1 overlapping with the modulation components centered at

𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏. However, since the linear components are not sensitive to micro damage, their changes are

relatively ignorable and the corresponding spectral correlation value 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏)1 does not change no

matter the two linear responses 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏, 0)1 are statistically-linked or not.

Second, modulations 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 , 0)2 between other frequencies in the wideband response can

occur at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏 (e.g., 𝑓𝑓𝑎𝑎1 − 𝑓𝑓𝑏𝑏1 = 𝑓𝑓𝑎𝑎 − 𝑓𝑓𝑏𝑏 , 𝑓𝑓𝑎𝑎2 + 𝑓𝑓𝑏𝑏2 = 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 , 𝑓𝑓𝑎𝑎1 ≠ 𝑓𝑓𝑎𝑎2 ≠ 𝑓𝑓𝑎𝑎,𝑓𝑓𝑏𝑏1 ≠ 𝑓𝑓𝑏𝑏2 ≠ 𝑓𝑓𝑏𝑏).

In this case, modulation components 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏, 0)2 caused by frequencies 𝑓𝑓𝑎𝑎1, 𝑓𝑓𝑏𝑏1 and 𝑓𝑓𝑎𝑎2, 𝑓𝑓𝑏𝑏2

might exhibit weak spectral correlation value 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏)2 because their linear sources are at

different frequencies and possibly be uncorrelated. However, the modulation components 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ±

𝑓𝑓𝑏𝑏 , 0)2 caused by frequencies 𝑓𝑓𝑎𝑎1, 𝑓𝑓𝑏𝑏1 and 𝑓𝑓𝑎𝑎2, 𝑓𝑓𝑏𝑏2 will be presented in other spectral correlation

coordinates, 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎1, 2𝑓𝑓𝑏𝑏1) and 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎2, 2𝑓𝑓𝑏𝑏2), in conjunction with their corresponding nonlinear

- 107 -

modulation pairs and with an enhanced contrast between intact and damage conditions.

Third, in noisy conditions, additional noise interference 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏, 0)3 may exist at 𝑓𝑓𝑎𝑎 ± 𝑓𝑓𝑏𝑏.

However, since most of the experimental noises are stationary, and stationary noise exhibits no

spectral correlation, spectral correlation value 𝑆𝑆𝑥𝑥(𝑓𝑓𝑎𝑎, 2𝑓𝑓𝑏𝑏)3 becomes zero for the additional noise

interference.

In conclusion, when a wideband response signal is analyzed using spectral correlation, it shows

the following advantages over the conventional spectral density function: (1) The contrast of the

spectral correlation values caused by nonlinear modulation components is enhanced between the

intact and damage conditions of the target structure; (2) For the linear components in the wideband

response, the corresponding spectral correlation values depend on the initial statistical links between

these linear components, regardless of the condition of the target structure; and (3) Spectral

correlation of a wideband response is robust against noise interference.

6.4.2 Sideband peak count (SPC) in spectral correlation domain

Considering all the advantages of spectral correlation over the conventional spectral density

function when dealing with a wideband ultrasonic response signal, the SPC technique is conducted in

the spectral correlation domain.

First, spectral correlation is used to transform the wideband ultrasonic response signal into the

spectral correlation domain. If the selected frequency range is from 𝑓𝑓𝑟𝑟1 to 𝑓𝑓𝑟𝑟2 in the frequency

domain (α = 0) for SPC operation, the corresponding spectral correlation region, containing the

spectral correlation values among all the frequency components in the selected frequency range, can

be defined with the following constraints (Gardner, 1986):

𝑓𝑓𝑟𝑟1 +12𝛼𝛼 ≤ 𝑓𝑓 ≤ 𝑓𝑓𝑟𝑟2 −

12𝛼𝛼 (6.22)

The corresponding spectral correlation region is shown in Figure 6.14(a). In the spectral correlation

domain, when the cyclic frequency α = 0, 𝑆𝑆𝑥𝑥(𝑓𝑓, 0) is equal to the conventional spectral density

distribution 𝑃𝑃𝑥𝑥(𝑓𝑓). If SPC is conducted in 𝑆𝑆𝑥𝑥(𝑓𝑓, 0) (= 𝑃𝑃𝑥𝑥(𝑓𝑓)) as shown in Figure 6.14(b), the results

will be identical with the results shown in Chapter 4. Here, we consider all the spectral correlation

values in the corresponding spectral correlation region when α ≠ 0 (Figure 6.14(c)).

- 108 -

(a)

(b)

(c)

Figure 6.14 Sideband peak count (SPC) in spectral correlation domain: (a) spectral correlation of a

wideband response signal, (b) SPC in the conventional frequency domain (𝛼𝛼 = 0), and (c) SPC in the

spectral correlation domain (𝛼𝛼 ≠ 0).

- 109 -

Here, the SPC is defined as the ratio of the number of the spectral correlation peaks (𝑁𝑁𝑝𝑝) over a

moving threshold plane (𝑡𝑡ℎ) to the total peak number (𝑁𝑁𝑡𝑡) within a selected normalized spectral

correlation region:

𝑆𝑆𝑃𝑃𝐶𝐶(𝑡𝑡ℎ) = 𝑁𝑁𝑝𝑝(𝑡𝑡ℎ)𝑁𝑁𝑡𝑡

(6.23)

where all peaks are counted as shown in Figure 6.14(c), because the number of dominant spectral

correlation peaks is negligible in comparison to the number of the smaller spectral correlation peaks,

and the linear responses and the nonlinear modulation responses overlap in the spectral correlation

domain. Due to the nonlinearity induced by structural damage, more spectral correlation peaks caused

by nonlinear modulations show up and the spectral correlation peaks with smaller values grow as a

consequence. Therefore, the SPC value for the damage case should be larger than that for the intact

case, especially when the threshold value is relatively low.

Then, SPC difference (SPCD) is defined as the difference between the SPC values obtained from

the current 𝑆𝑆𝑃𝑃𝐶𝐶𝑐𝑐 and a reference 𝑆𝑆𝑃𝑃𝐶𝐶𝑟𝑟:

𝑆𝑆𝑃𝑃𝐶𝐶𝑆𝑆 = 𝑆𝑆𝑃𝑃𝐶𝐶𝑐𝑐 − 𝑆𝑆𝑃𝑃𝐶𝐶𝑟𝑟 (6.24)

where the 𝑆𝑆𝑃𝑃𝐶𝐶𝑟𝑟 can be the SPC curve obtained in the pristine condition of the target structure. The

acquired SPCD curve shows high positive values when there is a damage in the target structure, and

the maximum SPCD (MSPCD) can be obtained when the threshold value is relatively low. Same as

Chapter 4, the MSPCD is selected as the nonlinear damage feature, defined as:

𝑀𝑀𝑆𝑆𝑃𝑃𝐶𝐶𝑆𝑆 = 𝑀𝑀𝑀𝑀𝑥𝑥 (𝑆𝑆𝑃𝑃𝐶𝐶𝑐𝑐 − 𝑆𝑆𝑃𝑃𝐶𝐶𝑟𝑟) (6.25)

Also, the 𝑆𝑆𝑃𝑃𝐶𝐶𝑟𝑟 can be the SPC curve obtained from the adjacent scanning points in the target

structure. In this case, the baseline-free damage detection can be achieved by spatial comparison, as

proposed in the previous chapters. For baseline-free damage detection by spatial comparison, the

MSPCD is modified as:

𝑀𝑀𝑆𝑆𝑃𝑃𝐶𝐶𝑆𝑆𝑖𝑖 = 𝑀𝑀𝑀𝑀𝑥𝑥 (�𝑆𝑆𝑃𝑃𝐶𝐶𝑐𝑐 − 𝑆𝑆𝑃𝑃𝐶𝐶𝑟𝑟,𝑖𝑖�)

𝑀𝑀𝑆𝑆𝑃𝑃𝐶𝐶𝑆𝑆 =1𝑛𝑛�𝑀𝑀𝑆𝑆𝑃𝑃𝐶𝐶𝑆𝑆𝑖𝑖

𝑖𝑖

𝑖𝑖=1

(6.26)

where 𝑆𝑆𝑃𝑃𝐶𝐶𝑟𝑟,𝑖𝑖 is the SPC curve obtained from the ith adjacent point, and 𝑛𝑛 is the total number of

adjacent points for the current point. This mean MSPCD value can be visualized for the entire target

area, and spatial points with high MSPCD values indicate the existence and the location of the

damage.

- 110 -


This section validates the proposed SPC technique in the spectral correlation domain using the

simulation model developed in Chapter 3. For comparing with the SPC results in Chapter 4, same

scanning area of 40 mm × 35 mm was defined, covering the entire micro crack as shown in Figure

4.5(a). A total of 1400 (40 × 35) scanning points were assigned within this scanning area, achieving a

spatial resolution of 1 mm. A 100 μs velocity signal with a sampling time step of 150 ns was obtained

from each scanning point and used to validate the new optimized SPC technique.

Same as Chapter 4, three points from the scanning area were selected, named Point A and B and

C, respectively. As shown in Figure 4.5(b), Point B is located near the simulated crack tip, while Point

A and C are far away from the crack location. Also, the velocity responses from these three selected

points were acquired from the same simulation model before introducing the micro crack. Hence, the

velocity responses were achieved from both the intact and damage conditions for the three selected

points. Then, the SPC curves were calculated in the spectral correlation domain for both the intact and

damage conditions, and the SPC difference (SPCD) is computed using Equation (6.25) by treating the

SPC curve got under the intact condition as reference.

Using the same frequency range selected in Chapter 4, the spectral correlation region (based on

Equation (6.22)) corresponding to 20 to 350 kHz was used for computing the SPC curves and the

corresponding SPC differences. Figure 6.15 plots the SPC curves calculated in the spectral correlation

domain and the corresponding SPC difference for the three points. Figures 6.15(a) and (c) show that

the difference of the SPC curves between the damage and the intact conditions is not obvious when

the testing points are far away from the crack location. However, in Figure 6.15(b), when Point B

locates near the crack tip, the SPC difference becomes distinguishable, and the maximum difference

(MSPCD) shows up when the threshold is relatively low. Moreover, by comparing with the SPC

results calculated in the conventional frequency domain (Figure 4.6), it can be seen that the SPC

difference between the damage and intact conditions is enhanced when the SPC is computed in the

spectral correlation domain (Figure 6.15(b)), and all the MSPCD values for Figure 4.6 and Figure

6.15 are extracted and listed in Table 6.3.

- 111 -

(a)

(b)

(c)

Figure 6.15 SPC and SPC difference values obtained in the spectral correlation domain for three

selected points in simulation model: (a) Point A, far away from the crack location, (b) Point B, near

the crack tip, and (c) Point C, far away from the crack location.

- 112 -

Table 6.3 Comparison of the MSPCD values between Figure 4.6 and Figure 6.15

Point A Point B Point C

SPC in the frequency domain (Figure 4.6) 0.04 0.76 0.04

SPC in the spectral correlation domain (Figure 6.15) 0.03 0.88 0.04

Also, to investigate the noise effect on the MSPCD value calculated in the spectral correlation

domain, simulated white noises with different signal to noise ratios (SNRs) were added to the velocity

responses acquired from the three points in the damage condition. Here, the SNR has the same

definition as in Equation (6.13), and it varies from 40 to 20 dBW with 2 dBW decrement. The

contaminated signals were used to calculate the SPC curves in the spectral correlation domain and

obtain the MSPCD values. For comparison, the SPC curves and the MSPCD values were also

calculated with the contaminated signals in the frequency domain. Figures 6.16(a) and (b) shows the

MSPCD values calculated from the contaminated signals in the frequency domain and in the spectral

correlation domain, respectively. It proves that, when the SPC curve and the MSPCD value are

computed in the spectral correlation domain, they are more robust against noise interference.

(a) (b)

Figure 6.16 MSPCD values calculated from signals contaminated with different SNRs: (a) SPC in the

frequency domain, and (b) SPC in the spectral correlation domain.

Then, all the SPC curves for all the scanning points were calculated in the spectral correlation

domain for the simulation model with micro crack, and the corresponding MSPCD value for each

scanning point in the selected area was computed using Equation (6.26). Accordingly, the crack

detection or visualization result can be shown in Figure 6.17. By comparing with the crack detection

- 113 -

result using the MSCPD values obtained in the frequency domain (Figure 4.7), it shows that the

contrast of the MSCPD values between the points near the crack location and the points in the intact

region is enhanced in Figure 6.17.


technique in the spectral correlation domain.


To experimentally examine the performance of the optimized SPC technique in the spectral

correlation domain, the same test on an aluminum plate with a fatigue crack in Chapter 4 was adopted

and the test data was used to validate the proposed technique in this chapter and to compare with the

test results shown in Chapter 4. Detailed information about the test specimen and experimental setup

can be found in Chapter 4.

For review, two different experiments were conducted. First, as shown in Figure 4.8(a), six pairs

of excitation and sensing laser beam points were selected to examine the sensitivity of the proposed

damage feature, MSPCD, extracted from each path to the fatigue crack by comparing with the

reference signal acquired in its intact condition. Among all these six paths, path 1 passes through the

crack, and path 2 passes through the crack tip, while other paths do not. For the intact condition of the

plate specimen, ultrasonic responses were recorded three times from each path. One of them was used

as the reference signal (Reference), and the other two as the test signals acquired from the intact case

(Intact I and Intact II). After the crack formation, ultrasonic response signals (Damage) were collected

again following the same measurement procedure as in the intact case. Second, in order to validate the

proposed baseline-free damage detection technique by spatial comparison, a laser excitation scanning

area was selected with a 35 mm × 35 mm square area, located close to one edge of the specimen and

covering the entire fatigue crack, as shown in Figure 4.8(b). A total of 361 (19 × 19) scanning points


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point. The second experiment was conducted after the fatigue test.

Figure 6.18 MSPCD values obtained in the spectral correlation domain from all six paths in the

aluminum plate specimen.

A frequency band of 20 to 400 kHz was selected for conducting SPC operation in Chapter 4, thus

the corresponding spectral correlation region was used to estimate the MSPCD values in this

validation experiment. For the six paths in the first experiment, Figure 6.18 shows the MSPCD values

calculated in the spectral correlation domain for all the intact and damage cases, using Equation (6.25).

It can be seen that the MSPCD value whose path passes through the crack, especially through the

crack tip, is much higher than the other MSPCD values. Also, by comparing with the MSPCD values

calculated in the frequency domain as shown in Figure 4.13, it shows that the contrast of the MSPCD

values between Path 1, 2 and Path 3 to 6 is enhanced when the SPC is conducted in the spectral

correlation domain. Moreover, by comparing the MSPCD values among Path 3 to 6, it again shows

that the SPC technique in the spectral correlation domain is less affected by the noise interference.

For the second excitation scanning test, Equation (6.26) was used to calculate the MSPCD values

by spatial comparison in the selected scanning area. Figure 6.19 gives the fatigue crack detection

result composing by the MSPCD values obtained in the spectral correlation domain. Again, by

comparing with the crack detection result shown in Figure 4.14 in Chapter 4, it shows that the

MSPCD values calculated in the spectral correlation domain own much higher values when the

scanning points are near the crack location, especially near the crack tip. Also, this fatigue crack

detection result shown in Figure 6.19 is much less affected by test noise interference than the result

plotted in Figure 4.14.

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Figure 6.19 Baseline-free fatigue crack detection result using SPC based damage detection technique

in the spectral correlation domain.


The second specimen for experimental validation of the optimized SPC technique in the spectral

correlation domain is the same carbon fiber reinforced polymer (CFRP) plate, as shown in Figure 4.15

in Chapter 4. A 1 cm diameter delamination was introduced at the center of the plate through impact

testing.

For review, as shown in Figure 4.15, a laser excitation scanning area was selected with a 60 mm

× 60 mm square area, covering the delamination damage. A total of 1225 (35 × 35) scanning points



point. Each ultrasonic response was measured with a sampling frequency of 2.56 MHz for 0.4 ms and

averaged 100 times in the time domain for improving the signal to noise ratio. Detailed information

about this CFRP plate and the experimental setup can be found in Chapter 4.

A spectral correlation region corresponding to the frequency band of 20 to 100 kHz was selected

for conducting the SPC operation and estimating the MSPCD values. The SPC curve was computed

for each scanning point in the selected excitation scanning area, and the corresponding MSPCD value

was calculated by comparing with the SPC curves got from its spatially adjacent scanning points,

using Equation (6.26). The corresponding delamination detection result is shown in Figure 6.20. It

shows that the scanning points near the delamination location have higher MSPCD values, which

represent the existence of damage. Also, by comparing with the delamination detection result shown

in Figure 4.16 in Chapter 4, it shows that the MSPCD values calculated in the spectral correlation

domain is more sensitive to structural damage and is more robust against test noise interference.

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Figure 6.20 Baseline-free delamination detection in CFRP plate using SPC based technique in the

spectral correlation domain.


Same as in Chapter 4, an actual 10 kW GFRP (glass fiber reinforced polymer) wind turbine blade

(Figure 4.17) was selected as well for additional validation of the optimized SPC technique in the

spectral correlation domain. Two types of damages, delamination and debonding, were intentionally

produced in this wind turbine blade. For simulating internal delamination, a circular Teflon tape with

15 mm diameter was inserted between 3rd and 4th ply during fabrication of the blade. For debonding,

some of the glue used to attach a stiffener to the blade skin was removed, introducing a small

localized gap (debonding) between the stiffener and the blade skin. Close views of these two damages

are shown in Figure 4.18.

As shown in Figure 4.18, a 50 mm × 50 mm square area was scanned with 400 (20 × 20)

scanning points for both delamination and debonding detection, achieving a spatial resolution around

2.5 mm. The fixed sensing point was located 20 mm away from the closest excitation point. The

ultrasonic responses from all the excitation points were measured with a sampling frequency of 2.56

MHz for 0.4 ms and averaged 100 times in the time domain for improving the signal to noise ratio.

Detailed information about this GFRP wind turbine blade and the experimental setup can be found in

Chapter 4.

A spectral correlation region corresponding to the frequency band of 20 to 350 kHz was selected

for conducting the SPC operation and estimating the MSPCD values. The SPC curve was computed

for each scanning point in the selected excitation scanning areas, and the corresponding MSPCD

value was calculated by comparing with the SPC curves got from its adjacent scanning points, using

Equation (6.26). The corresponding damage detection results are shown in Figure 6.21. It can be seen

- 117 -

that the excitation scanning points near the damage location have higher MSPCD values, which

indicate the existence of structural damage. Moreover, by comparing with the delamination and

debonding detection results shown in Figure 4.20 in Chapter 4, it once again proves that the MSPCD

value calculated in the spectral correlation domain is more sensitive to structural damage and is more

robust against test noise interference.

(a) (b)

Figure 6.21 Baseline-free delamination/ debonding detection in wind turbine blade using SPC based

technique in the spectral correlation domain: (a) delamination, and (b) debonding (the dashed line

indicates the location of the hidden stiffener).

6.9 Chapter summary

In this chapter, the limitation of the sideband peak count (SPC) based damage detection technique

is analyzed, and it shows that the SPC based technique is susceptible to noise interference, which in

turn will affect the damage detection results and cause false alarms in noisy test environments. To

tackle this problem, instead of using the conventional spectral density function, spectral correlation

technique is proposed in this chapter to reliably extract damage induced nonlinear modulation

components from the ultrasonic response signals. When dealing with the structural response signals

caused by a wideband input, the spectral correlation technique offers the following two major

advantages: (1) The contrast of the spectral correlation values caused by nonlinear modulation

components is enhanced between the intact and damage conditions of the target structure; and (2)

Spectral correlation of a wideband response is robust against noise interference. Then, the SPC

technique is optimized by conducting SPC operation in the spectral correlation domain for structural

damage detection. The optimized SPC technique is validated numerically and experimentally with the

same model and specimens shown in Chapter 4, and its advantages over SPC in the conventional

- 118 -

frequency domain are proved as well. This optimized SPC technique conducted in the spectral

correlation domain shows its reliability and feasibility for field applications.

- 119 -

- 120 -

Chapter 7. Concluding Remarks

7.1 Conclusions

In this dissertation, a fully noncontact laser ultrasonic scanning system is introduced and used for

wideband ultrasonic wave generation and measurement with a high spatial resolution. Damage

induced nonlinearity is analyzed and extracted from the wideband ultrasonic responses, and the

extracted nonlinear features are used for structural damage detection, especially for micro damage

detection. The conclusions of this dissertation are provided as follows:

(1) Nonlinear ultrasonic modulation with a wideband input

A high-frequency and a low-frequency inputs are often applied on a target structure to detect

structural damage based on the generated nonlinear modulation components. However, it is not easy

to select the optimal frequency combination that needs to satisfy some binding conditions and can be

easily affected by environmental and operational variations of the target structure. In this dissertation,

nonlinear ultrasonic modulation is extended by using a wideband excitation signal as the driving

signal. In this way, nonlinear ultrasonic modulation can occur among multiple frequency peaks at the

existence of structural damage, which highly increases the chance for the binding conditions to be

satisfied. Also, the test data collection time can also be highly reduced compared with sweeping

different input frequency combinations within the same frequency band. However, since the nonlinear

modulation components and the linear response components overlap in the frequency domain under a

wideband excitation, additional signal processing methods are in need to extract nonlinear features

from the wideband ultrasonic responses.

(2) Multi-physics numerical simulation for laser generated ultrasound

A multi-physics simulation scheme is developed for simulating laser induced ultrasonic waves on

aluminum plates and validating the proposed damage detection techniques with a simulated micro

crack. The nonlinearity induced by the simulated micro crack is verified by observing the crack

opening and closing during wave propagation. For efficient computation, the simulation model is

divided into two sub-regions with different degrees of freedom, by theoretically investigating the

effect of thermal diffusion caused by a pulse laser excitation. A multi-scale element size is also

assigned in the two divided sub-regions, according to the wavelength of laser induced thermal waves

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and ultrasonic waves, respectively. The effectiveness of the developed simulation model is validated

with experimental tests conducted with a noncontact laser ultrasonic scanning system on aluminum

plates with different thicknesses, and the simulation results show a good correspondence with the test

results.

(3) Sideband peak count (SPC) based damage detection technique

A sideband peak count (SPC) based damage detection technique is developed to analyze the

nonlinearity caused by structural damage from the wideband ultrasonic responses. The response signal

is transformed into the frequency domain, a SPC curve is then calculated showing the ratio of the

number of spectral peaks over a moving threshold to the total peak numbers in the frequency domain.

The maximum difference between a current SPC curve and a reference SPC curve is defined as a new

nonlinear damage feature. Here, the reference SPC curve can be acquired when the target structure is

in its intact condition. Taking use of the laser ultrasonic scanning system, a baseline-free damage

detection technique is proposed by using the ultrasonic responses acquired from the adjacent points to

calculate the reference SPC curves. Thus, damage can be detected or even visualized without relying

on the baseline data obtained from the intact condition.

Considering the noise influence on SPC based damage detection technique, an optimized SPC

technique is developed by introducing spectral correlation technique, which investigates the spectral

correlation between nonlinear modulation components. The major advantage of the spectral

correlation over conventional spectral density function is that the modulation components of interest

can be reliably extracted even when the measured ultrasonic signals are heavily contaminated by

noise. Also, when dealing with a wideband ultrasonic signal, the contrast of the spectral correlation

values caused by nonlinear modulation components is enhanced between the intact and damage

conditions, increasing its sensitivity to damage. The SPC based technique is then optimized by

calculating SPC curves in the spectral correlation domain for structural damage detection with a

higher sensitivity to damage and higher robustness against noise interference. This SPC based damage

detection technique is numerically and experimentally validated in this dissertation.

(4) State space based damage detection technique

A state space based damage detection technique is also developed to detect the nonlinearity

caused by structural damage from the wideband ultrasonic responses. By concatenating lag copies of

the acquired wideband ultrasonic response, the response signal can be projected into a high-order state

space and a state space attractor can be reconstructed. The state space attractor is the geometric

representation of a dynamic system, and thus will reflect a loss of dynamical similarity due to damage,

- 122 -

especially the nonlinear one. Another new nonlinear damage feature is defined by checking the

geometrical variations of the current reconstructed attractor from a reference attractor. Here, the

reference attractor can be acquired when the target structure is in its intact condition. Similarly, the

proposed baseline-free damage detection technique can be realized by reconstructing the reference

attractors using the ultrasonic responses acquired from the adjacent points. Thus, damage can be

detected or even visualized without relying on the baseline data obtained from the intact condition.

The state space based damage detection technique is proved to be more robust against noise

interference than the SPC based technique conducted in the frequency domain. In this dissertation, the

state space based damage detection technique is also numerically and experimentally validated.

Parameters for attractor reconstruction has also been investigated, which shows that a higher

embedding dimension is needed to well reconstruct the attractors for the signals with a wider

frequency band. It is also concluded that a better damage detection result can be achieved by using a

wider frequency band and a higher embedding dimension. However, compromise needs to be made

between the damage detection performance and its computation burden.

7.2 Future work

For the improvement of this dissertation, following future work will be conducted.

(1) Further investigation of the proposed damage detection techniques

To improve and validate the performance of the proposed damage detection techniques, various

target structures and damage types are needed for further validation. Also, further investigation is in

need about the noise effect on the proposed techniques for real field applications.

(2) Development of a laser ultrasonic measurement system with two pulse laser excitations

Since the nonlinear modulation components and the linear response components overlap each

other in the frequency domain under a wideband excitation, it is hard to further quantify the damage

unless we are able to look into only the nonlinear modulation components. A new laser ultrasonic

measurement system is to be developed with two pulse laser excitation units. By controlling the beam

size or pulse duration of the pulse laser, the generated frequency band in the target structure can be

modified. In this way, signals with two distinct frequency bands can be generated in the target

structure and make it possible to separate the nonlinear modulation components from the linear

response components in the frequency domain.

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(3) Development of new structural damage detection techniques with two pulse laser inputs

Based on the future work (2), once the ultrasonic responses are required under two pulse laser

inputs with two different frequency bands generated on the target structure, the proposed damage

detection techniques can be modified to investigate only the nonlinear modulation components. For

example, for the state space based damage detection technique, a band-pass filter can be included so

that only the nonlinear modulation components within their corresponding frequency bands are kept

in the filtered ultrasonic responses and used for attractor reconstruction. For the SPC based damage

detection technique, the SPC operation can be conducted in the frequency range covering only the

nonlinear modulation components. Moreover, when the SPC is conducted in the spectral correlation

domain, it is possible to consider about the spectral correlation region composed only by the nonlinear

modulation components.

- 124 -

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Acknowledgement

After five years studying abroad in South Korea, the day finally comes to write this

acknowledgement as the finishing touch of my dissertation. Every moment with laughter or tears

during the past five years suddenly flashed into my mind and all have become my precious treasure,

not just in the scientific area, but more importantly on a personal level.

Back to the day I first entered this foreign country, I had a lot of doubts about my choice and

my future. It was also not easy to adjust to such a new environment with different cultural background.

I have to admit the journey here was not always successful and satisfactory, there are some moments I

do have regrets. I gained while I lost. But thanks to all these uncertainties and changes in life, I got a

chance to break the old self and rebuild another new me. I learned to view wider and further, remove

myself from the center in my heart, and to achieve from the differences we have among each other.

Also, I would like to express the deepest appreciation to my advisor, my labmates, my family,

my friends, and all the people we met in this wonderful and amazing journey. Thank you for your

kind support, wise counsel and sympathetic ear. I wish you all prosper in whatever you do. You were

there for me, and I will always be there for you.

I have no idea what life has for me in the future. And I don’t know how long it will take to find

all the answers in my life. But I don’t worry that much as I did before. For you are my shepherd, I

lack nothing.

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CURRICULUM VITAE

Peipei LIU

Ph.D.

Department of Civil and Environmental Engineering

Korea Advanced Institute of Science and Technology (KAIST)

291 Daehakro, Yuseong-gu, Daejeon, 34141, Republic of Korea

Phone: (82)+42-350-3665, Fax: (82)+42-350-3610

Email: [email protected]

RESEARCH INTERESTS

Structural Health Monitoring & Damage Detection, Non-destructive Testing, Sensing Technologies, Laser Ultrasonics, Nonlinear Ultrasonics, Statistical Pattern Recognition, Probability & Statistical Analysis, Image Processing, Finite Element Method.

EDUCATION

2012 - 2017 Ph.D., Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea

2010 - 2012 M.S., Instrument Science and Technology (Intelligent Monitor and Control), Aerospace Engineering, Nanjing University of Aeronautics and Astronautics (NUAA), People’s Republic of China

2006 - 2010 B.S., Aircraft Design and Engineering, Aerospace Engineering, Nanjing University of Aeronautics and Astronautics (NUAA), People’s Republic of China

DISSERTATION & THESIS

1. Peipei Liu, “Structural damage detection based on nonlinear and noncontact laser ultrasonic techniques,” Doctoral Dissertation, Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology (KAIST), May, 2017.

2. Peipei Liu, “Research on the integration approaches of the miniaturized piezoelectric structural health monitoring systems,” M.S. Thesis, Department of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics (NUAA), June, 2012. (Provincial Excellent M.S.

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mailto:[email protected]

Thesis Award)

3. Peipei Liu, “Development of an integrated piezoelectric structural health monitoring system based on PC104+ bus,” B.S. Thesis, Department of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics (NUAA), June, 2010. (Provincial Excellent B.S. Thesis Award)

JOURNAL PUBLICATIONS *11 published, 2 submitted, and 3 in preparation

* The corresponding author is underlined

1. Peipei Liu, Hoon Sohn, “Damage detection using sideband peak count in spectral correlation domain,” in preparation for Smart Materials and Structures, 2017.

2. Timotius Yonathan Sunarsa, Pouria Aryan, Ikgeun Jeon, Byeongjin Park, Peipei Liu, Hoon Sohn, “A reference‐free and non‐contact method for detection and imaging of defects in adhesive-bonded joints,” in preparation for a special issue in Materials, 2017.

3. Suyoung Yang, Sung-Youb Jung, Kiyoung Kim, Peipei Liu, Hoon Sohn, “Development of a tunable vibration energy harvester and its application to existing bridge,” in preparation for Smart Materials and Structures, 2017.

4. Peipei Liu, Hoon Sohn, “Development of nonlinear spectral correlation between ultrasonic modulation components,” submitted to NDT&E International, 2017.

5. Hyung Jin Lim, Yongtak Kim, Hoon Sohn, Ikgeun Jeon, Peipei Liu, “Improvement of nonlinear ultrasonic modulation based fatigue crack detection reliability with multiple damage classifiers,” submitted to Smart Structures and Systems, 2017.

6. Peipei Liu, Hoon Sohn, Ikgeun Jeon, “Nonlinear spectral correlation for fatigue crack detection in noisy environment,” Journal of Sound and Vibration, vol. 400, pp. 305-316, 2017.

7. Byeongjin Park, Hoon Sohn, Peipei Liu, “Accelerated noncontact laser ultrasonic scanning for damage detection using combined binary search and compressed sensing,” Mechanical Systems and Signal Processing, vol. 92, pp. 315-333, 2017.

8. Peipei Liu, Hoon Sohn, Suyoung Yang, Hyung Jin Lim, “Baseline-free fatigue crack detection based on spectral correlation and nonlinear wave modulation,” Smart Materials and Structures, vol. 25, pp. 125034, 2016.

9. Peipei Liu, Hyung Jin Lim, Suyoung Yang, Hoon Sohn, Yung Yi, Daewoo Kim, Cheul Hee Lee, In-hwan Bae, “Development of a “stick-and-detect” wireless sensor node for fatigue crack detection,” Structural Health Monitoring, vol. 16, pp. 153-163, 2016.

10. Peipei Liu, Nazirah Ab. Wahab, Hoon Sohn, “Numerical simulation for damage detection using laser-generated ultrasound,” Ultrasonics, vol. 69, pp. 248-258, 2016.

11. Peipei Liu, Hoon Sohn, Byeongjin Park, “Baseline-free damage visualization using noncontact laser nonlinear ultrasonics and state space geometrical changes,” Smart Materials and Structures, vol. 24, pp. 065036, 2015.

12. Peipei Liu, Hoon Sohn, Suyoung Yang, Tribikram Kundu, “Fatigue crack localization using noncontact laser ultrasonics and state space attractors,” Journal of the Acoustical Society of America, vol. 138, pp. 890-898, 2015.

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13. Jinyeol Yang, Peipei Liu, Suyoung Yang, Hyeonseok Lee, Hoon Sohn, “Laser based impedance measurement for pipe corrosion and bolt-loosening detection,” Smart Structures and Systems, vol. 15, pp. 41-55, 2015.

14. Peipei Liu, Hoon Sohn, Tribikram Kundu, “Fatigue crack localization using laser nonlinear wave modulation spectroscopy (LNWMS),” Journal of the Korean Society for Nondestructive Testing, vol. 34, pp. 419-427, 2014.

15. Peipei Liu, Hoon Sohn, Tribikram Kundu, Suyoung Yang, “Noncontact detection of fatigue cracks by laser nonlinear wave modulation spectroscopy (LNWMS),” NDT&E International, vol. 66, pp. 106-116, 2014.

16. Hyung Jin Lim, Hoon Sohn, Peipei Liu, “Binding conditions for nonlinear ultrasonic generation unifying wave propagation and vibration,” Applied Physics Letters, vol. 104, pp. 214103, 2014.

CONFERENCE PROCEEDINGS * The corresponding author is underlined

1. Peipei Liu, Hoon Sohn, “Fatigue crack detection by nonlinear spectral correlation with a wideband input,” SPIE Smart Structures/NDE, Portland, US, March 25-29, 2017.

2. Byeongjin Park, Hoon Sohn, Peipei Liu, “Accelerated laser ultrasonic scanning using binary search,” The 8th European Workshop on Structural Health Monitoring, Bilbao, Spain, July 5-8, 2016.

3. Hoon Sohn, Hyung Jin Lim, Ji-Min Kim, Suyoung Yang, Jun Lee, Yongtak Kim, Peipei Liu, Yujin Jang, Gun-Woo Moon, Yung Yi, Daewoo Kim, Jaeha Kim, Sung-Youb Jung, “Self-sufficient and self-contained sensing for local monitoring of in-situ bridge structures,” The 8th European Workshop On Structural Health Monitoring, Bilbao, Spain, July 5-8, 2016.

4. Nazirah Ab. Wahab, Peipei Liu, Hoon Sohn, “Finite element modeling of ultrasonic wave propagation induced by a pulse laser,” COSEIK, Daejeon, Korea, April 13-15, 2016.

5. Peipei Liu, Timotius Yonathan Sunarsa, Hoon Sohn, “Damage visualization using synchronized noncontact laser ultrasonic scanning,” SPIE Smart Structues/NDE, Las Vegas, US, March 20-24, 2016.

6. Hoon Sohn, Hyung Jin Lim, Byeongjin Park, Peipei Liu, Byeongju Song, Yongtak Kim, “Nonlinear ultrasonic modulation for damage detection,” International Conference Vibroengineering, Nanjing, China, September 26-28, 2015.

7. Peipei Liu, Nazirah Ab. Wahab, Hoon Sohn, “Numerical and experimental analyses of pulse laser-generated ultrasound,” CANSMART 2015 & SMN 2015, Vancouver, Canada, July 15-17, 2015.

8. Peipei Liu, Hoon Sohn, “Fatigue crack visualization using noncontact laser ultrasonics and state space geometrical changes,” SPIE Smart Structures/NDE, San Diego, US, March 8-12, 2015.

9. Peipei Liu, Hyung Jin Lim, Suyoung Yang, Hoon Sohn, Hyung Chul Park, Yung Yi, Dong Sam Ha, “Development of an active wireless sensor node for fatigue crack detection using nonlinear wave modulation,” The 2nd International Conference on Structural Health Monitoring and Integrity Management, Nanjing, China, September 24-26, 2014.

10. Hyung Jin Lim, Hoon Sohn, Peipei Liu, “Noncontact visualization of nonlinear ultrasonic

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modulation for reference-free fatigue crack detection,” SPIE Smart Structures/NDE, San Diego, US, March 9-13, 2014.

11. Peipei Liu, Suyoung Yang, Hyung Jin Lim, Hyung Chul Park, In Chang Ko, and Hoon Sohn, “Development of a wireless nonlinear wave modulation spectroscopy (NWMS) sensor node for fatigue crack detection,” SPIE Smart Structures/NDE, San Diego, US, March 9-13, 2014.

12. Peipei Liu, Hoon Sohn, Tribikram Kundu, “Noncontact fatigue crack detection using nonlinear wave modulation spectroscopy (NWMS),” The 166th Acoustical Society of America meeting, San Francisco, US, December 2-6, 2013.

PATENTS

1. Hoon Sohn, Byeongjin Park, Peipei Liu, “Accelerated damage detection using binary search aided compressed sensing,” KR Patent, June 22, 2016.

2. Hoon Sohn, Byeongju Song, Byeongjin Park, Peipei Liu, “Apparatus and technique for structural health monitoring based on nonlinear ultrasonic wave,” KR Patent (Application# 10-2016-0066363), May 30, 2016.

3. Hoon Sohn, Peipei Liu, Suyoung Yang, “Diagnosis method of structures and diagnosis system,” KR Patent (Publication# 10-1670819-0000), October 25, 2016.

4. Hoon Sohn, Peipei Liu, Suyoung Yang, “Diagnosis method of structures and diagnosis system (Divisional),” KR Patent (Application# 10-2016-0044533), April 8, 2016.

5. Hoon Sohn, Hyung Jin Lim, Suyoung Yang, Peipei Liu, “Wireless sensor using nonlinear ultrasonic wave modulation technique,” US Patent (Application# 14787127), October 26, 2015.

6. Hoon Sohn, Hyung Jin Lim, Suyoung Yang, Peipei Liu, “Wireless sensor using nonlinear ultrasonic wave modulation technique,” CN Patent (Application# 201380076095.9), October 29, 2015.

7. Hoon Sohn, Hyung Jin Lim, Suyoung Yang, Peipei Liu, “Wireless sensor using nonlinear ultrasonic wave modulation technique,” KR Patent (Publication# 10-1414520-0000), June 26, 2014.

8. Hoon Sohn, Hyung Jin Lim, Suyoung Yang, Peipei Liu, “Wireless sensor using nonlinear ultrasonic wave modulation technique,” PCT Patent (Application# PCT-KR2013-012037), December 23, 2013.

TECHNOLOGY TRANSFER

1. Hoon Sohn, Hyung Jin Lim, Suyoung Yang, Peipei Liu, “Wireless sensor using nonlinear ultrasonic wave modulation technique,” transformed to TM E&C Co. Ltd, October 30, 2014.

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PARTICIPATED PROJECTS

1. Characterization of guided wave propagation in aircraft structures: National Sciences and Engineering Research Council of Canada (Funded: 50,000 USD for 09/01/13 to 12/31/15).

2. Development of a self-sufficient wireless sensor node based structural health monitoring system for civil infrastructure: Global Frontier Project (CISS) at National Research Foundation of Korea (Funded: 608,580 USD for 09/29/11 to 08/31/20).

BOOK & BOOK CHAPTERS

1. Hoon Sohn, Peipei Liu, Hyung Jin Lim, Byeongjin Park, “Nonlinear ultrasonic wave modulation for fatigue crack and delamination detection,” a book chapter in Nonlinear Acoustic Techniques for Nondestructive Evaluation (Editor: Tribikram Kundu), Springer, in preparation.

2. Tribikram Kundu, Jesus Eiras, Weibin Li, Peipei Liu, Hoon Sohn, Jorge Juan Paya Bernabeau, “Fundamentals of nonlinear acoustic techniques and sideband peak count,” a book chapter in Nonlinear Acoustic Techniques for Nondestructive Evaluation (Editor: Tribikram Kundu), Springer, in preparation.

3. Hoon Sohn, Peipei Liu, “Non-contact laser ultrasonic for SHM in aerospace structures,” a book chapter in Structural Health Monitoring (SHM) in Aerospace Structures (Editor: Fuh-Gwo Yuan), Elsevier, 2016.

EDUCATIONAL EXPERIENCES

Summer, 2015 Teaching Assistant, CE580, “Statistical Pattern Recognition for Structural Health Monitoring,” KAIST.

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Documents

Structural Damage Detection using Nonlinear and Noncontact …ssslab.kaist.ac.kr/article/pdf/Ph.D_Dissertation_LiuPP.pdf · 2017-06-06 · Damage often causes a structure to exhibit