4
Ultrasonic Chirplet Signal Decomposition for Defect Evaluation and Pattern Recognition Yufeng Lu**, Erdal Oruklu* and Jafar Saniie* * Department of Electrical and Computer Engineering Illinois Institute of Technology Chicago, Illinois 60616 ** Department of Electrical and Computer Engineering Bradley University Peoria, Illinois 61625 Abstract—In this study, a quantitative method using chirplet signal decomposition (CSD) is presented for pattern recognition and defect characterization. The CSD algorithm is utilized to decompose the ultrasonic signal into a linear combination of chirplets, and efficiently estimate the echo parameters. These parameters can be correlated to the structure of defects. For experimental studies, planar and focused transducers with different center frequencies have been used for testing the embedded defects in specimen at normal or oblique refracted angles. It has been shown that the CSD successfully associates the estimated chirplets and their parameters as a quantitative method to characterize defects. Keywords- Chirplet signal decomposition, quantitative evaluation, pattern recognition, Ultrasonic NDE I. INTRODUCTION In ultrasonic nondestructive evaluation (NDE), the pattern of scattering echoes is highly dependent on impulse response of the ultrasonic transducers, physical properties of the propagation path, and the shape, size, orientation and location of defects. The inhomogeneity and/or structural disposition of materials result in nonstationary and dispersive ultrasonic scattering echoes. Therefore, for material characterization and flaw detection application, it becomes a challenging problem to unravel such complex signals using only direct measurement and conventional signal processing techniques. Chirplet is a type of wavelet model often used in ultrasound, radar, sonar, and seismic signals [1-5]. The chirplet signal decomposition (CSD) algorithm has been used to decompose the ultrasonic scattering signal into a linear combination of chirplets and efficiently estimate the echo parameters, which can be correlated to the structure of defects[6-9] . In our previous work[6], the CSD algorithm and its computation efficiency have been comprehensively discussed. Moreover, a fast implementation of the CSD algorithm has been proposed recently [7]. In this work, we present a quantitative method for pattern recognition and defect characterization using CSD. Geometry of defects contributes significantly to the echo shape when the defect size is about same or bigger than the wavelength of ultrasound. The time-of-arrival, amplitude and the number of estimated echoes (i.e., chirplets) are critical in quantitative evaluation of defects. For experimental studies, the benchmark data from world federation of NDE center has been evaluated for the proposed quantitative method using CSD. Planar and focused transducers with different center frequencies (i.e., 5 MHz and 10 MHz) have been used for testing the embedded defects in specimen at normal or oblique refracted angles. A variety of defects including disc- shaped cracks in a diffusion-bonded titanium alloy and a set of flat-bottom and side-drilled holes of different sizes positioned at various depths have been used to examine the echo scattering patterns and to predict the defect shapes and to validate the accuracy of the CSD algorithm. This paper is organized as follows: Section II briefly reviews the CSD algorithm. Section III presents the experimental study of quantitative evaluation using CSD algorithm. The CSD results in experimental studies including disc-shaped cracks and a set of side-drilled holes are discussed. II. CHIRPLET SIGNAL DECOMPOSITION The objective of the CSD algorithm is to decompose the ultrasonic signal, ) ( t s , into a linear expansion of chirp echoes and efficiently estimate the parameter vectors of these echoes[6]. () ) ( ) ( 1 0 t r t f t s M j j + = = Θ (1) where, ) ( t r denotes the residue of signal reconstruction , () ( ) ( ) ( ) ( ) 2 2 2 1 2 exp τ α φ τ π τ α β + + + = Θ t i i t f i t t f c represents a single ultrasonic chirp echo. ] , , , , , [ 1 2 α φ α β τ c j f = Θ stands for the parameter vector, τ is the time-of-arrival, c f is the center frequency, β is the amplitude, 2 α is the chirp rate, φ is the phase, and 1 α is the bandwidth factor of the ultrasonic echo. The parameter vector, j Θ , is estimated based on the chirplet transform of the ultrasonic signal. First, in the time- frequency signal representation based on chirplet transform, the dominant echo is localized. The time-of-arrival (TOA), center frequency and amplitude of the dominant echo are estimated. Then, the remaining parameters are successively estimated. The decomposition process is repeated by iteratively subtracting the estimated single dominant echo 2553 978-1-4244-4390-1/09/$25.00 ©2009 IEEE 2009 IEEE International Ultrasonics Symposium Proceedings 10.1109/ULTSYM.2009.0633 Authorized licensed use limited to: Illinois Institute of Technology. Downloaded on October 02,2020 at 05:58:02 UTC from IEEE Xplore. Restrictions apply.

Ultrasonic chirplet signal decomposition for defect evaluation ...ecasp.ece.iit.edu/publications/2000-2011/2009-12.pdfUltrasonic Chirplet Signal Decomposition for Defect Evaluation

  • Upload
    others

  • View
    3

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Ultrasonic chirplet signal decomposition for defect evaluation ...ecasp.ece.iit.edu/publications/2000-2011/2009-12.pdfUltrasonic Chirplet Signal Decomposition for Defect Evaluation

Ultrasonic Chirplet Signal Decomposition for

Defect Evaluation and Pattern Recognition Yufeng Lu**, Erdal Oruklu* and Jafar Saniie*

* Department of Electrical and Computer Engineering Illinois Institute of Technology

Chicago, Illinois 60616

** Department of Electrical and Computer Engineering

Bradley University Peoria, Illinois 61625

Abstract—In this study, a quantitative method using chirplet signal decomposition (CSD) is presented for pattern recognition and defect characterization. The CSD algorithm is utilized to decompose the ultrasonic signal into a linear combination of chirplets, and efficiently estimate the echo parameters. These parameters can be correlated to the structure of defects. For experimental studies, planar and focused transducers with different center frequencies have been used for testing the embedded defects in specimen at normal or oblique refracted angles. It has been shown that the CSD successfully associates the estimated chirplets and their parameters as a quantitative method to characterize defects.

Keywords- Chirplet signal decomposition, quantitative evaluation, pattern recognition, Ultrasonic NDE

I. INTRODUCTION

In ultrasonic nondestructive evaluation (NDE), the pattern of scattering echoes is highly dependent on impulse response of the ultrasonic transducers, physical properties of the propagation path, and the shape, size, orientation and location of defects. The inhomogeneity and/or structural disposition of materials result in nonstationary and dispersive ultrasonic scattering echoes. Therefore, for material characterization and flaw detection application, it becomes a challenging problem to unravel such complex signals using only direct measurement and conventional signal processing techniques.

Chirplet is a type of wavelet model often used in ultrasound, radar, sonar, and seismic signals [1-5]. The chirplet signal decomposition (CSD) algorithm has been used to decompose the ultrasonic scattering signal into a linear combination of chirplets and efficiently estimate the echo parameters, which can be correlated to the structure of defects[6-9] . In our previous work[6], the CSD algorithm and its computation efficiency have been comprehensively discussed. Moreover, a fast implementation of the CSD algorithm has been proposed recently [7]. In this work, we present a quantitative method for pattern recognition and defect characterization using CSD. Geometry of defects contributes significantly to the echo shape when the defect size is about same or bigger than the wavelength of ultrasound. The time-of-arrival, amplitude and the number of estimated echoes (i.e., chirplets) are critical in quantitative evaluation of defects. For experimental studies, the benchmark data from world federation of NDE center has

been evaluated for the proposed quantitative method using CSD. Planar and focused transducers with different center frequencies (i.e., 5 MHz and 10 MHz) have been used for testing the embedded defects in specimen at normal or oblique refracted angles. A variety of defects including disc-shaped cracks in a diffusion-bonded titanium alloy and a set of flat-bottom and side-drilled holes of different sizes positioned at various depths have been used to examine the echo scattering patterns and to predict the defect shapes and to validate the accuracy of the CSD algorithm.

This paper is organized as follows: Section II briefly reviews the CSD algorithm. Section III presents the experimental study of quantitative evaluation using CSD algorithm. The CSD results in experimental studies including disc-shaped cracks and a set of side-drilled holes are discussed.

II. CHIRPLET SIGNAL DECOMPOSITION

The objective of the CSD algorithm is to decompose the ultrasonic signal, )(ts , into a linear expansion of chirp echoes and efficiently estimate the parameter vectors of these echoes[6].

( ) )()(1

0

trtftsM

jj

+= −

=Θ (1)

where, )(tr denotes the residue of signal reconstruction ,

( ) ( ) ( ) ( )( )22

21 2exp ταφτπταβ −++−+−−=Θ tiitfittf c

represents a single ultrasonic chirp echo. ],,,,,[ 12 αφαβτ cj f=Θ stands for the parameter vector, τ

is the time-of-arrival, cf is the center frequency, β is the

amplitude, 2α is the chirp rate, φ is the phase, and

1α is the bandwidth factor of the ultrasonic echo.

The parameter vector, jΘ , is estimated based on the

chirplet transform of the ultrasonic signal. First, in the time-frequency signal representation based on chirplet transform, the dominant echo is localized. The time-of-arrival (TOA), center frequency and amplitude of the dominant echo are estimated. Then, the remaining parameters are successively estimated. The decomposition process is repeated by iteratively subtracting the estimated single dominant echo

2553978-1-4244-4390-1/09/$25.00 ©2009 IEEE 2009 IEEE International Ultrasonics Symposium Proceedings

10.1109/ULTSYM.2009.0633

Authorized licensed use limited to: Illinois Institute of Technology. Downloaded on October 02,2020 at 05:58:02 UTC from IEEE Xplore. Restrictions apply.

Page 2: Ultrasonic chirplet signal decomposition for defect evaluation ...ecasp.ece.iit.edu/publications/2000-2011/2009-12.pdfUltrasonic Chirplet Signal Decomposition for Defect Evaluation

from the signal until the residue of the reconstructed signal, r(t), satisfies a predefined condition (e.g., energy of the residue becomes less than a few percents of total signal energy).

III. QUANATATIVE EXPERIMENTAL STUDIES USING CSD

It has been shown that the CSD algorithm is capable of achieving a high resolution time-frequency representation and accurate estimation of parameters. Nevertheless, it is more valuable to link the results of CSD algorithm to the physical properties of the defects and validate its accuracy in practical applications for quantitative evaluation.

For experimental studies, two aluminum blocks with different size of side-drill hole (SDH) are manufactured [10]. One is with 1 mm diameter, another is 4 mm diameter. The experimental setting is shown in Figure 1. It can be seen that the water path is 50.8 mm and the depth of SDH is 25.4 mm ( i.e, from the water-aluminum interface to the center of SDH).

Figure 1. Experiment setup for SDH blocks

To provide a rigorous test, two 5 MHz transducers are used to acquire ultrasonic data at normal or oblique refracted angles, θ . One is planar transducer. Another is spherically focused transducer with 172.9 mm focal length.

To verify the experiment setup, the CSD is utilized to analyze the ultrasonic data from the front surface of the specimen. The ultrasonic data superimposed with the estimated chirplet is shown in Figure 2.

Figure 2. Ultrasonic data from the front surface superimposed with the estimated chirplet (depicted in dashed red color line). The estimated TOA is 68.71 sμ . The theoretical TOA is calculated as follows.

water

waterideal v

DTOA

×= 2 (2)

where, waterD denotes the water distance in the case of

incidence angle 0, which is 50.8 mm . waterv denotes the

wave speed in water, which is 1.484 smm μ/ . It can be

derived that the idealTOA is 68.47 sμ . Taken the bandwidth

factor of the chirplet into consideration, the estimated TOA is in agreement with idealTOA .

Furthermore, the estimated chirplet parameters for the block with 1mm SDH is shown in Table I. The estimated parameters of chirplets for the block with 4 mm SDH is shown in Table II. These results indicate that the estimated parameters from CSD algorithm track with reasonable accuracy the physical parameters of experimental setup. Moreover, the CSD algorithm provides more detailed information describing the reflected echoes such as phase, bandwidth factor and chirp rate that can be used for further analysis.

Table I. Estimated parameters of chirplets (Block with 1mm SDH)

Refracted angle

Chirplet

Parameters

00 300 450

Spherically

focused

transducer

Amplitude [m-Volt] 43 29 16

TOA [us] 76.6 82.6 89.5

Frequency [MHz] 4.6 4.6 4.3

Planar

transducer

Amplitude [m-Volt] 23 20 15

TOA [us] 76.6 82.8 89.8

Frequency [MHz] 4.5 4.7 4.8

Table II. Estimated parameters of chirplets (Block with 4mm SDH)

Refracted angle

Chirplet

Parameters

00 300 450

Spherically

focused

transducer

Amplitude [m-Volt] 88 59 33

Time-of-arrival [us] 76.1 82.1 88.9

Frequency [MHz] 4.6 4.5 4.4

Planar

transducer

Amplitude [m-Volt] 42 38 28

Time-of-arrival [us] 76.1 82.4 89.4

Frequency [MHz] 4.5 4.7 4.8

Additionally, an experiment is set up to evaluate disk-shaped cracks in a diffusion-bonded titanium alloy sample. The ultrasonic data of these synthetic cracks are obtained at normal or oblique refracted angles, θ using a 10 MHz planar

50.8 mm

25.4 mm

Side-drill hole

Water

Aluminum

θ

Transducer

2554 2009 IEEE International Ultrasonics Symposium ProceedingsAuthorized licensed use limited to: Illinois Institute of Technology. Downloaded on October 02,2020 at 05:58:02 UTC from IEEE Xplore. Restrictions apply.

Page 3: Ultrasonic chirplet signal decomposition for defect evaluation ...ecasp.ece.iit.edu/publications/2000-2011/2009-12.pdfUltrasonic Chirplet Signal Decomposition for Defect Evaluation

transducer. The diameter of the transducer is 6.35 mm . The water depth is 25.4 mm . The surface of diffusion bond is 13 mm below the front surface of water/titanium alloy interface. Two different sizes of cracks are made with the diameter 0.762 mm (i.e, crack D) and the diameter 1.905 mm (i.e, crack C). For the crack C, the responded ultrasonic data is recorded from the two edges of the crack, which are marked as point a and point b. The thickness of both disk-shaped cracks is 0.089 mm . Figure 3 shows the experiment setup for the alloy sample [11].

Figure 3. Experiment setup for disc-shaped cracks in a diffusion-bonded titanium alloy.

Figure 4. Experimental data of Crack C (with amplitude normalized to ±1) superimposed with the estimated chirplets . a) Front surface reference signal superimposed with sum of 2 chirplets. b) Experimental data (refracted angle 0) superimposed with sum of 2 chirplets. c) Experimental data (refracted angle 30 at point a) superimposed with sum of 4 chirplets. d) Experimental data (refracted angle 30 at point b) superimposed with sum of 4 chirplets. e) Experimental data (refracted angle 45 at point a) superimposed with sum of 4 chirplets. f) Experimental data (refracted angle 45 at point b) superimposed with sum of 4 chirplets.

Table III. Estimated parameters of chirplets (Crack C)

Figure 5. Experimental data of Crack D (with amplitude normalized to ±1) superimposed with the estimated chirplets (depicted in dashed red line). a) Front surface reference signal superimposed with sum of 2 chirplets. b) Experimental data (refracted angle 0) superimposed with sum of 2 chirplets. c) Experimental data (refracted angle 30) superimposed with sum of 4 chirplets. d) Experimental data (refracted angle 45) superimposed with sum of 4 chirplets.

TOA

[us]

Center

Frequency

[MHz]

Amplitude

[m-Volt]

Reference signal

34.583 9.42 363.4

34.711 10.68 47.9

Refracted angle 00

38.744 9.78 14.4

38.836 13.82 1.80

Refracted angle 300

(point a)

39.774 11.02 0.58

40.020 6.03 0.19

40.349 7.55 0.05

40.260 11.35 0.05

Refracted angle 450

(point a)

40.810 9.91 0.15

40.810 9.91 0.06

41.061 11.40 0.03

40.999 12.76 0.01

Refracted angle 300

(point b)

39.747 7.78 0.49

39.569 11.37 0.05

39.842 11.36 0.06

39.935 7.70 0.04

Refracted angle 450

(point b)

40.593 5.10 0.08

40.562 9.00 0.07

40.538 11.63 0.06

40.049 6.59 0.04

25.4 mm Water

Titanium Alloy

θ

Transducer

Diffusion bond

13 mm a b Disc-shaped cracks

Crack C Crack D

2555 2009 IEEE International Ultrasonics Symposium ProceedingsAuthorized licensed use limited to: Illinois Institute of Technology. Downloaded on October 02,2020 at 05:58:02 UTC from IEEE Xplore. Restrictions apply.

Page 4: Ultrasonic chirplet signal decomposition for defect evaluation ...ecasp.ece.iit.edu/publications/2000-2011/2009-12.pdfUltrasonic Chirplet Signal Decomposition for Defect Evaluation

Table IV. Estimated parameters of chirplets (Crack D)

Similar to the experiment of testing SDH discussed above, the ultrasonic data from the front surface of the specimen is obtained as the reference signal. The ultrasonic data from the crack C has been analyzed using CSD and its estimated parameters of the estimated chirplets are shown in Table III. The estimated parameters of crack D are shown in Table IV.

The ideal TOA of the crack at refracted angle θ is calculated as follows.

θθ cos

2

tan

__ ×

×+=

iumti

bonddiffusionreferenceangle v

DTOATOA (3)

Where referenceTOA denotes the estimated TOA of

reference signal, which is 34.583 sμ . bonddiffusionD _

denotes

the depth of the diffusion bond, which is 13 mm . iumtiv tan

denotes the wave speed in titanium, which is 6.2 smm μ/ .

Therefore, θ_angleTOA at the angle 00 is 38.78 sμ .

θ_angleTOA at the angle 300 is 39.43 sμ . θ_angleTOA at the

angle 450 is 40.51 sμ .

From Table III and Table IV, it can be seen that the estimated TOAs at angle 00 are 38.744 sμ and 38.766 sμ .

Taken the thickness of the cracks (0.089 mm) into consideration, it can be asserted that the estimated TOAs at refracted angle 00 are in good agreement with the calculation of experiment setup. Experimental signals of crack C and crack D (with amplitude normalized to ±1) superimposed with the estimated chirplets (depicted in dashed line and red color) are shown in Figure 4 and Figure 5. It also can be seen that the front surface reference signal and the experimental data obtained at angle 00 are well reconstructed by the CSD algorithm (see Figure 4a/4b and

Figure 5a/5b ). Nevertheless, with the increase of refracted angle, more chirplets needed to decompose the experimental data (see the refracted angle 30 and 45 degree cases). In addition, Table III and Table IV show that the signal energy is more evenly distributed to each chirplet in the high refracted angle cases. This spreading of signal is caused by geometrical effect of the beam profile of the planner transducer and corners/edges of disk-shape crack.

IV. CONCLUSION

In this study, the performance of CSD algorithm has been demonstrated for quantitative nondestructive evaluation using ultrasound. Through extensive experimental studies, it has been shown that the CSD algorithm offers an efficient approach for defect pattern recognition. Furthermore, the CSD algorithm successfully associates the estimated chirplets and their parameters as a quantitative approach to characterize defects. Numerical and experimental results signify that the CSD algorithm is successful for ultrasonic signal analysis accounting for a broad type of echoes including narrowband, broadband, symmetric, skewed, dispersive or nondispersive echoes.

REFERENCES [1] S. Mann, and S. Haykin, “ The chirplet transform: physical

consideration,” IEEE Transactions on Signal Porcessing, vol. 43, pp. 2745-2761, November 1995.

[2] W. Fan, H. Zou, Y.Sun, Z. Li, and R. Shi, “Decomposition of seismic signal via chirplet transform,” IEEE Proceedings of 6th International Conference on Signal Processing, pp. 1778-1782, August 2002.

[3] N. Ma, and D. Vray, “Bottom backscattered coefficient estimation from wideband chirp sonar echoes by chirp adapted time frquency representation,” IEEE Proceedings of International Conference on Acoustics and Speech Signal Processing, pp. 12-15, May 1998.

[4] M. Li, X. Gu, and P. Shan, “Time-frequency distribution of encountered waves using Hilbert-Huang transform,” International Journal of Mechanics, vol. 1, no. 2, pp. 27-32, 2007.

[5] J. Li, and H. Ling, “Application of adaptive chirplet representation for ISAR feature extraction from targets with rotating parts,” IEEE Proceedings on Radar, Sonar, and Navigation, vol. 150, pp. 284-291, August 2003.

[6] Y.Lu, R. Demirli, G.Cardoso, and J. Saniie, “A successive parameter estimation algorithm for chirplet signal decomposition,” IEEE Transaction on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 53, pp. 2121–2131, November 2006.

[7] Y.Lu, E. Oruklu, and J. Saniie, “Fast chirplet transform with FPGA-based implementation,” IEEE Signal Processing Letters, vol. 15, pp. 577-580, December 2008.

[8] Y.Lu, R. Demirli, G.Cardoso, and J. Saniie, “Chirplet transform for ultrasounic signal analysis and NDE applications,” IEEE Proceedings of Ultrasonic Symposium, vol. 1, pp. 18-21, September 2005.

[9] Y.Lu, R. Demirli, and J. Saniie, “A comparative study of echo estimation techniques for ultrasonic NDE applications,” IEEE Proceedings of Ultrasonic Symposium, pp. 536–539, October 2006.

[10] 2004 Ultrasonics Benchmarks, The World Federation of NDE Centers, “ftp://cnde:[email protected]”, April 2004.

[11] 2005Ultrasonics Benchmarks, The World Federation of NDE Centers, ftp://cnde:[email protected]”, July 2005.

ACKNOWLEDGMENT The authors wish to thank the World Federation of NDE Centers for the 2004 and 2005 ultrasonic benchmark experimental data and for the permission to use them in this paper.

TOA

[us]

Center

Frequency

[MHz]

Amplitude

[m-Volt]

Reference

signal

34.583 9.42 363.41

34.711 10.68 47.93

Refracted

angle 00

38.766 10.38 4.64

38.882 13.01 0.50

Refracted

angle 300

39.716 5.59 0.46

39.823 11.20 0.19

39.807 4.45 0.19

39.924 14.95 0.06

Refracted

angle 450

40.673 9.98 0.16

40.981 9.48 0.07

40.750 4.93 0.05

40.576 15.65 0.03

2556 2009 IEEE International Ultrasonics Symposium ProceedingsAuthorized licensed use limited to: Illinois Institute of Technology. Downloaded on October 02,2020 at 05:58:02 UTC from IEEE Xplore. Restrictions apply.