Health Monitoring System Large Structural Systems 1998

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A health monitoring system for large structural systems

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1998 Smart Mater. Struct. 7 606

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Health monitoring of large structural systems

1.00076 m

0.89876 m

0.051 m

0.003175 m

WT 2x6.5W 4x13

10.2 cm10.2 cm

0.8 cm

0.7 cm

10.8 cm

5.4 cm

0.7 cm

0.8 cm

0.051 m

0.44938 m

Section View Beam Dimension

0.44938 m

6.096 m (20 ft)

0.051 m

0.108 m

0.003175 m

1.596 m 2.0 m 2.5 m

0.051 m

0.051 m

0.44938 m

0.44938 m

2.0 m 2.5 m

Top View

Side View

0.051 m

0.051 m

0.051 m

0.051 m

0.054 m

1.596 m

1.00076 m

Figure 1. Description of the long span bridge (all dimensions in m).

Table 1. Material properties of the bridge.

Youngs Density PoissonsMaterial modulus (GPa) (kg m3) ratio

Concrete andasphalt 22.1 2400 0.2Steel 200.0 7850 0.3

comparing modal parameters from different times in the life

of the structure. In the comparison process, the objectives

are to amplify the differences and make judgements on the

nature and extent of the damage in the structure. Farrar

et al [3] have done an extensive literature review on

damage identification and health monitoring from changes

in the vibration characteristics. These changes in the

modal characteristics form the basis for the various damage

detection schemes. In this study an algorithm called thedamage index method (DIM) [4] has been utilized for

damage detection. The reason for selecting this technique

over other methods was based on the observations of Farrar

and Jauregui [5] in an earlier report and the experimental

data that the authors of this current article obtained from the

model bridge. The authors obtained experimental modal

data from the model bridge before and after the damage

and compared the data using four different techniques:

(1) damage index method (Stubbs et al [4]), (2) mode

shape curvature method (Pandey et al [6]), (3) change in

flexibility method (Pandey and Biswas [7]), (4) change in

stiffness method (Zhang and Aktan [8]). Only the results

obtained from the DIM has been reported because this

method produced the closest match between the predicted

damage location and the actual damage location that was

introduced in the structure.

2. FE modeling in the structural system

In the proposed monitoring scheme, a finite element

analysis of the structure is the first step. It is recommended

that the FE analysis be performed prior to the experimental

modal analysis to aid in the selection of instrumentation

locations and to obtain an approximate dynamic response

of the structure. In the authors experience, only the first

six modes or so are worth identifying at this stage (thisis an approximate analysis). With this logic in mind the

authors generated a finite element model of the model

bridge (figure 1) with generic material properties as shown

in table 1. All calculations including mesh generation and

post-processing were performed with I-DEAS (SDRC) v3.0

(I-DEAS User Manual 1995) on a SUN Sparc 20 computer.

The webs of the W beams were modeled with 174 thin

shell elements. The top concrete plate was made up of

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M L Wang et al

WT2x6.5 Floor Beams

Main W4x13 Beams

WT2x6.5 Beam

Concrete Plate

Figure 2. Meshes of the bridge with 2154 degrees of freedom.

Table 2. Comparison of resonant frequencies (Hz) betweenanalytical and experimental test for a long span bridge.

Experimental results

Analytical resultsMode # Freq. (Hz) Freq. (Hz) Dam. (%)

Mode 1 11.160 8.440 0.200Mode 2 21.140 22.290 0.130Mode 3 28.660 29.000 0.510Mode 4 51.760 51.440 3.260Mode 5 57.340 55.170 4.550Mode 6 71.480 67.070 2.750

180 thin shell elements. The flanges of the W beams were

modeled with 174 beam elements. A total of 528 elements

with 2154 degrees of freedom were used to mesh the entire

bridge structure as shown in figure 2. Depending on the size

and complexity of the structure, simplifying assumptionsmay have to be made to develop the approximate model.

Since the model structure was fairly simple, the authors

went ahead and developed a detailed finite element model

as a first step.

The numerical stimulation was done by using a normal

mode dynamics solver routine in I-DEAS to obtain modal

shapes and frequencies. Since the SDRC I-DEAS code used

was incapable of modeling structural damping, damping

ratios could not be obtained. To verify the accuracy of

the finite element model, the model had to be validated

against actual test data obtained from an experimental

modal analysis of the model bridge. The structure was

instrumented with 24 Dytran 3187B1 accelerometers andexcited with a Kistler 9728A20000 series modal testing

hammer. The accelerometers were arranged in three rows

at a center to center distance of 85 cm (figure 1). Thus the

sensors were placed along the main supporting beams of

the superstructure to produce a uniform geometric mesh.

The data acquisition system consisted of a 32 channel

Zonic PC7000 system. The response from the sensors

were measured in the form of FRFs (frequency response

functions) [9, 10]. The FRF data were then imported

into MEScope (Vibrant Technology) for modal parameter

extraction and mode shape animation. The experimental

FRF data were curve fitted by using a method of residuesto obtain the modal frequency, damping ratio and mode

shapes. The results from the experimental modal analysis

are summarized and compared with the FE results in

figure 3 and table 2. A comparison of the frequencies

indicates minor discrepancies between the simulation and

test results. A significant difference in frequency is

however observed in the first mode. In a situation where

differences between simulation and experimental results

are observed through all the modes, the difference can

be attributed to inappropriate assumptions of material and

geometrical properties. The most plausible explanation for

the difference in the first mode may lie in the modeling

of the boundary conditions. The actual support conditions

may have been more flexible than it was assumed atthe modeling stage. The issue of adjusting the support

flexibility through model updating will be dealt with in a

future article.

While a cursory comparison of the modal frequencies

may provide some initial information, it is rather

insufficient by itself. A more objective way of comparing

the numerical results to the experimental results involves

the comparison of the mode shapes obtained by each

method. A tool called the modal assurance criteria (MAC)

is an effective way of comparing two sets of structural

dynamic data and devising a correlation measure which

is also sometimes referred to as the modal correlation

coefficient and is defined as [9]

MAC(i, j) =|n

j=1(a)j (

e)j |2

(n

j=1(e)j (e)

j (n

j=1(a)j (a)

j )

(1)

where a means analytical data and e means experimental

data, is the mode shape and indicates a complex

conjugate. MAC is calculated to quantify the correlation

between measured mode shapes during the different tests

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Figure 3. Comparison of mode shapes of a long span bridge.

Table 3. Comparison of mode shape (MAC) for analyticaland experimental results for a numerically simulated longspan bridge.

Mode 1 2 3 4 5 6

1 0.990 0.000 0.000 0.000 0.010 0.0102 0.000 0.980 0.000 0.010 0.000 0.0003 0.000 0.000 0.980 0.000 0.010 0.0504 0.000 0.000 0.000 0.900 0.100 0.0605 0.010 0.000 0.000 0.010 0.780 0.1106 0.000 0.170 0.000 0.000 0.000 0.20

and to check the orthogonality of measured mode shapes

during a particular test. MAC uses the orthogonality

properties of the mode shapes to compare either two modes

from the same test or two modes from different tests. Ifthe modes are identical, a scalar value of one is obtained

from the MAC calculations. If the modes are orthogonal,

a value of zero is calculated. Ewins [9] points out that

correlated modes will yield a value greater than 0.9 and

uncorrelated modes will yield a value less than 0.005.

MAC is not affected by a scalar multiple. The results of

these MAC calculations as shown in table 3 and figure 4

provide a comparison between the FE mode shapes and the

experimental mode shapes.

As can be seen, the FEM analysis of the model

bridge provides a fairly good estimate of the actual

modal parameters of the bridge. The experimental results

indicated that the modes beyond the first four modes are

characterized by very high damping ratios, making it harder

to experimentally identify the higher modes.

3. Optimal transducer placement

Structural dynamics based detection and monitoring have

been used for health monitoring with some degree of

success [1115]. The primary transducer input for such

a monitoring system consists of an array of accelerometers.

However, in order to make the system cost effective it is

necessary to develop a transducer optimization techniquefor each and every structure. In this section, the authors

have introduced an optimization technique based on the

maximization of the modal kinetic energy picked up by the

transducer set.

EIM by Kammer [2] optimizes and selects a set of

target modes for identification of the structure based on FE

analysis. An initial candidate set of transducer locations

is selected and these locations are ranked, based on their

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M L Wang et al

MAC

ModeMode

Figure 4. Comparison of mode shapes (MAC) between analytical and experimental results.

contribution to the linear independence of corresponding

FEM target mode partitions. Locations that do not

contribute are removed from the candidate set. The

energy optimization technique algorithm described is a

modification of the EIM and is designed to improve the

modal information and to maximize the measured kinetic

energy of the structural system. The spatial independence

of the identified mode shapes is satisfied by the sensing

configuration obtained with the EOT algorithm. The

distribution of kinetic energy in the system is defined as:

KE = TM (2)

where is the measured mode shape vector. After

decomposition of the mass matrix, M, into upper and

lower triangular Cholesky factors, the kinetic matrix can

be derived as:

KE = T (3)

where = U and M = LU. The matrices L

and U denote the lower and upper triangular Cholesky

factors. The projection of the mode shapes on the reduced

configuration is denoted by

= projection () and = projection (). (4)

Similarly, the energy measured by a reduced set of

transducers is obtained from the initial energy by removing

the contribution of all transducers which have been

eliminated.

KE = T

. (5)

The objective of the transducer placement is to find

a reduced configuration which maximizes the measure of

the kinetic energy of the structure. It is desirable to stop

eliminating the transducers if it results in a rank deficiency

of the energy matrix. Assuming that the mass matrix is

non-singular, the rank N of the quantity KE is equal to the

number of linearly independent projected vectors in matrix

. The problem is solved iteratively by the following

procedure. The eigenvalues and eigenvectors of the

energy matrix are extracted from

KE = . (6)

Computing the eigenpairs at each iteration of the EOT

procedure does not significantly increase the computational

cost because the matrix KE is a square, symmetric, and

positive-definite matrix of size N. Then, using an approach

similar to EIM by Kammer [2], the fractional contributions

of each remaining transducers are assembled into the EOT

vector:

EOT =

i=1...m

1/2

2. (7)

The transducer location with minimal contribution in

the EOT vector is then selected for removal. Subsequently,

the contribution of the removed transducer to the kineticenergy matrix is deleted and the new matrix is checked

for rank deficiency. If the removal of the transducer

produces a rank deficiency it implies that the transducer

location in question cannot be removed. If removal of

the transducer did not produce a rank deficiency then

the transducer location is removed from the candidate

set and the process repeated until one arrives at the

required number of transducers. The quantity between

brackets in equation (7) represents a linear combination of

the measured mode shapes which is designed to achieve

orthonormality, since it can be verified that

1/2T

1/2= I. (8)

Furthermore, each EOT of the vector is a heuristic

measure of the contribution of each transducer to the total

measured energy. The normalization factor 1/2 prevents

the contribution of high frequency modes from dominating

those of the low modes. In theory, the number of remaining

transducers is equal to the size of the target modal set.

However, the apparent rank is often increased due to noise

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Iteration

0 10 20 30 40 50 60 70 800

20

40

60

80

100

Determinant(%)

Fisher Information Matrix

Energy

Figure 5. Determinant of Fisher information matrix and kinetic energy.

Table 4. Comparison of modal frequencies between EIM and EOT.

EIM exp. test EOT exp. testAnal.

Mode Freq. (Hz) Freq. (Hz) Damping (%) Freq. (Hz) Damping (%)

1 11.167 8.251 0.009 8.265 0.0092 21.14 22.047 0.0236 22.11 0.0383 28.66 28.534 0.149 28.58 0.1464 51.76 50.497 1.482 50.814 1.4815 57.34 55.334 3.002 55.084 1.8556 71.48 67.535 0.412 66.768 0.529

in the experimental data, and more than N transducers are

required to identify N independent modes.

To determine the relative efficiencies of the energy

technique and the EIM, a bench mark test was carried out

on the model of the long span bridge. The initial candidate

set consisted of 87 transducer locations that were positioned

to identify six eigenmodes and eigenvectors. Transducerswere eliminated with the EIM and the EOT until a rank

deficiency was created in the Fisher information matrix and

the energy matrix. A plot of the relative performance of

EIM and EOT as a function of the number of transducer

locations deleted is shown in figure 5. Both the methods

started out with the same number of transducers, and after

each iteration the value of the determinant of the Fisher

information matrix and the energy matrix was computed.

This new value of the determinant was then compared to

the old value and presented in the form of a percentage and

has been plotted on the y axis as a function of the number

of iterations. As seen in figure 5, both the methods are very

stable, but the EOT appears to have a distinct advantage asthe number of removed transducers increases.

The above comparison was based on a numerical

simulation only. In order to further investigate the

efficiencies of the two methods, an experimental modal

analysis was performed on the long span bridge model.

Transducer locations based on the EIM and the EOT were

identified for the first six modes for a set of 15 transducers

as shown in figure 6. The above transducer locations were

used to obtain the response of the structure to a forced

excitation. The results from each of the data sets were then

compared to the FE results (table 2).

A comparison of the modal frequencies and damping

ratios for the FE analysis, the EIM and the EOT are shown

in table 4. Both the EIM and the EOT results are inclose agreement. However, as noted earlier there are some

discrepancies between the FE results and the experimental

results which had been attributed to inaccurate modeling of

the support rigidity. The results from the MAC analysis

(between experimental and FE mode shapes) are shown in

tables 5 and 6, and figures 7 and 8. The MAC calculations

for the EIM show a very high correlation between the first

four modes with the correlation dropping off for the fifth

and sixth modes. In comparison, the EOT shows a very

high correlation between the first four modes, with the

correlation dropping off for the fifth and sixth modes also.

However, the correlation coefficients for the fifth and sixthmodes of the EOT is much higher than the fifth and sixth

modes of the EIM. The EOT technique however appears to

be picking up off-diagonal terms, but this can be attributed

to the similarity of the second and sixth mode shapes.

Based on the results obtained from both the numerical

simulation and the experimental data it can be inferred that

the EOT has some distinct advantages over the EIM.

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M L Wang et al

Indicates Sensor Locations

(a)

Indicates Sensor Locations

(b)

Figure 6. Optical transducer locations for the first six modes: (a) 15 transducer locations for the first six modes based onEIM; (b) 15 transducer locations for the first six modes based on EOT.

Table 5. Comparison of mode shape (MAC) for EIM.

Mode 1 2 3 4 5 6

1 0.990 0.002 0.003 0.009 0.002 0.008

2 0.001 0.993 0.005 0.004 0.070 0.1713 0.005 0.011 0.992 0.000 0.006 0.0304 0.008 0.002 0.000 0.984 0.417 0.0135 0.042 0.002 0.005 0.046 0.334 0.2256 0.005 0.179 0.012 0.005 0.096 0.582

4. Damage identification

There are many nondestructive techniques using different

tools such as vision, optical radiography, ultrasonic,

acoustic emission, dynamic properties, magnetic particles,

eddy current, microwave, thermal and so on [1618].

Visual inspection is the oldest and most relied upon methodfor bridge inspection. However, in recent years, researchers

have developed a number of successful programs for

nondestructive bridge evaluation designed to address the

problems facing bridge inspection. Current popular

nondestructive inspection methods employed for bridge

inspection are ultrasonic, radiographic, magnetic particle,

strain measurement and structural dynamic property

measurement methods. Structural dynamic methods [19]

Table 6. Comparison of mode shape (MAC) for EOT.

Mode 1 2 3 4 5 6

1 0.988 0.013 0.007 0.002 0.002 0.011

2 0.019 0.990 0.004 0.002 0.113 0.6213 0.007 0.001 0.971 0.041 0.078 0.0564 0.007 0.010 0.054 0.961 0.3 0.0435 0.007 0.008 0.001 0.007 0.561 0.0276 0.000 0.404 0.008 0.002 0.121 0.788

show a lot of promise in global health monitoring,

because damage that is significant to the bridge will

result in a reduction in stiffness, which in turn alters the

structural dynamic response. Although natural frequencies

of the structure may be the easiest to monitor they are

not necessarily the best indicator of structural damage.

Several other techniques utilizing mode shape data havedemonstrated the ability to indicate and locate damage [20

23]. In this analysis the authors have used the damage

index method, which is one of these many methods that

are available. The procedure is based on the measurement

of the dynamic response of the candidate bridges and

subsequent evaluation of the response.

The damage index method was developed by Stubbs

et al [4] to detect, locate and estimate the severity of

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MAC

Mode Mode

Figure 7. Comparison of mode shapes (MAC) for EIM.

ModeMode

MAC

Figure 8. Comparison of mode shapes (MAC) for EOT.

damage in structures based on a few of their characteristic

mode shapes. For a structure that can be represented as

a beam, a damage index, ij , can be defined for the j th

element based on changes in the curvature of the ith mode

as

ij =(b

a[

i (x)]2 dx/

L0

[

i (x)]2 dx) + 1

(

ba [i (x)]2dx/

L

0 [i (x)]2 dx) + 1(9)

and

j =

N

i=1

ij

where i (x) and

i (x) are the second derivatives of

the ith mode shape corresponding to the undamaged and

damaged structures, respectively. L is the length of the

beam, and a and b are the limits of the j th segment of the

beam where damage is being evaluated. Statistical methods

are then used to examine changes in this index and associate

these changes with possible damage locations. Assuming

that the collection of damage indices, j , represents

a sample population of a normally distributed random

variable, a normalized damage localization indicator isobtained as follows

j =j j

j(10)

where j and j represent the mean and standard deviation

of the damage indices, respectively. The disadvantage of

the method is that it may now show the clear location and

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M L Wang et al

10.8 cm5.4 cm

Figure 9. Damage introduced on the middle of the bridge.

Damage Location

Node1

Element 1E70

N71

. . . .

. . . .

70 @8.571 cm = 600 cm

Figure 10. Schematic damage detection models of thebridge.

magnitude of the damage of the structural system when

there are multiple damage locations with the same severityof the damage because j in equation (10) increases.

In the present study a controlled damage scenario

was introduced in the midspan of one of the supporting

beams by cutting the flange and web with a blowtorch

(figure 9). The damaged structure was instrumented

with 24 accelerometers as described in section 2. A

sensor optimization scheme was not utilized for the

damage identification tests that were carried out. The

main reason for not using an optimization scheme is

the fact that the mode shape based damage identification

methods are dependent on the ability to generate a mode

Mode 3 Mode 1

Mode 2

-0.200

-0.150

-0.100

-0.050

0.000

0.050

0.100

0.150

0.200

ModalAmplitude

1 2 3 4 5 6 7 8 9

Sensor Number

Figure 11. Interpolated modal shapes of the model bridge; BC 1 before damage.

shape. However, the optimization schemes typically

produce a sensor arrangement which when looked at in

isolation may not represent the geometrical shape of the

structure (figure 6(a) and (b)). This poses a serious

problem in reconstructing the mode shape for the structure.

The authors are therefore of the opinion that a sensor

optimization may not work hand in glove with a mode

shape based method like the DIM. It is in view of this

problem that the authors chose to generate a uniform mesh

of 24 accelerometers for the damaged structure.

During modal animation the structure had been

represented as a 2D structure. To make this amenable forDIM analysis the structure was simplified as three rows

of beams. It was assumed that the mode shape of each of

these beams could be obtained from the actual modal vector

consisting of 24 nodes by selecting the modal displacement

data corresponding to the eight sensors in a row that

represented each of the beams. It can be considered that

for damage analysis the structure was reduced to a set of

three 1D beam elements (figure 10). From the FRF data the

modal vectors, modal frequencies and damping ratios were

extracted. Subsequently, the mode shapes were interpolated

between nodes using cubic natural spline functions shown

in figure 11. Subsequent computations were carried out as

shown in equation (10).

The result of this analysis is shown in figure 12. The

figure indicates that the damage localization indicator, j ,

has the highest value between sensor positions 4 and 5,

within which segment the midpoint of the beam where the

damage was introduced did lie. The maximum value is

however attained where the x-axis takes on a value of

4.8 whereas the theoretical midpoint of the beam is at

4.5. Thus it can be inferred that the damage location had

not been identified exactly but it did identify the correct

element. The inability to pinpoint the exact location can

be ascribed to the fact that the DIM tends to identify the

element in which the damage has occurred and not the exact

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0 1 2 3 4 5 6 7 8 9

Number of Elements

-5.0

-3.0

-1.0

1.0

3.0

5.0

DamageLocalizationIndicator

Figure 12. Damage localization indicator for BC 1; mode shapes are interpolated with cubic spline function.

location. If this view is taken into consideration, the DIM

has performed its task perfectly.

5. Conclusion

A structural dynamic based health monitoring system has

been proposed. It has highlighted the different steps that

are involved in such a process and successfully appliedit to a model bridge with a simplified damage scenario.

The sensor location optimization is a vital part of the

entire process and the development of efficient optimization

algorithms is important. Although the EOT techniquethat has been proposed in this article has been derived

from Kammers EIM technique the new method appears

to provide better results as the number of sensors arereduced. Finally, although the DIM has established itself as

a very reliable technique in the benchmark test, the methodis not an ultimate panacea for the problem of structural

dynamics based damage detection and identification. Whilethe method has provided excellent results in the presence

of a single simulated damage, the performance is likely

to deteriorate in a multiple damage scenario. The othershortcoming of this technique is based on the fact that this

technique is not amenable to a sensor optimization scheme,

which means that although the method may be technically

competent, it may not be economically feasible. Thus thesearch for an efficient damage identification method is far

from over.

Acknowledgments

This project was supported by NSF grant 9622576. Dr S

C Liu is the program manager.

References

[1] Nazarim S and Olson L D 1995 Nondestructive Evaluationof Aging Structures and Dams SPIE vol 2457(Bellingham, WA: SPIE)

[2] Kammer D C 1992 Effect of model error on sensorplacement for on-orbit modal identification of largespace structures J. Guidance Control Dyn. 15

[3] Farrar C R, Michael B P, Scott W D and Daniel W S 1995Damage identification and health monitoring of structuraland mechanical systems from changes in their vibrationcharacteristics: a literature review LANL Report

[4] Stubbs N, Kim Jeong Tae and Farrar C R 1995 Fieldverification of a nondestructive damage location andseverity estimation algorithm Proc. 13th Int. ModalAnalysis Conf. (1995)

[5] Farrar C and Jauregui D 1996 Damage detectionalgorithms applied to experimental and numerical modaldata from the I-40 bridge LANL Report LA-13074-MS

[6] Pandey A K, Biswas M and Samman M 1991 Damagedetection from changes in curvature mode shapes J.Sound Vib. 145 32132

[7] Pandey A K and Biswas M 1995 Damage detection instructures using changes in flexibility J. Sound Vib. 169317

[8] Zhang Z and Aktan A E 1995 The damage indices for theconstructed facilities Proc. 13th Int. Modal AnalysisConf. vol 2, pp 15209

[9] Ewins D J 1994 Modal Testing: Theory and Practice(Research StudiesWiley)

[10] Cook R D, Malkus D S and Plesha M E 1989 Conceptsand Applications of Finite Element Analysis 3rd edn(New York: Wiley)

[11] Kiremidjian A S, Meng T H and Law K H 1995 AnAutomated Damage Monitoring System for CivilStructures NSF95-41

[12] Abdel-Ghaffar A M 1991 Cable-stayed bridges underseismic action Cable-Stayed Bridges RecentDevelopments and Their Future, Proc. Semin.(Yokohama, 1991)

[13] Ceravolo R et al 1995 Damage location in structures

through a connectivistic use of FEM modal analysisModal Anal. Int. J. Anal. Exp. Modal Anal. 10 17886

[14] Doebling S W, Hemez F M, Barlow M S, Peterson L Dand Farhat C 1993 Damage detection in a suspendedscale model truss via model update Proc. 11th Int.Modal Analysis Conf.

[15] Kaouk M and Zimmerman D C 1995 Reducing therequired number of modes for structural damageassessment AIAA-95-1094-CP

[16] Bray D F and McBride D 1992 Nondestructive Testing

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Health Monitoring System Large Structural Systems 1998