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Damage Detection in Structures using Artificial Neural Networks

Shilei Zhang, Huanding Wang, Wei Wang School of Civil Engineering

Harbin Institute of Technology Harbin, China

e-mail: lei202202@yahoo.com.cn, Hdwhrb@hit.edu.cn and wwang@hope.hit.edu.cn

Shaofeng Chen School of Transportation Science and Engineering

Harbin Institute of Technology Harbin, China

e-mail: Chensf@hit.edu.cn

AbstractIn order to select a sensitive input parameter for artificial neural networks in damage detection and construct an efficient and robust back propagation algorithm for damage assessment, the application of neural networks to damage detection in structures is summarized and analyzed in this paper. By discussing the use of natural frequency as a diagnostic parameter, natural frequency can rationally reflect damage location but not provide enough information about damage degree. Mode shape and transfer function include abundance information about damage degree compared with natural frequency but have a large measurement error. And three improved back propagation algorithms that are adaptive variable step-size algorithm, Levenberg-Marquart algorithm and homogeneous algorithm are introduced. The result shows that Levenberg-Marquart algorithm harmonizes Gauss- Newton method with steepest descent method and tunes gradually to Gauss-Newton method when the result can not converge to the minimum. Thus choosing complete vibration modal parameters and using Levenberg-Marquart algorithm, structural damage can be effectively detected.

Keywords-artificial neural networks; damage detection; input parameter; Levenberg-Marquart algorithm

I. INTRODUCTION Based on the characteristics of human brains, the

artificial neural network is a parallel distributed processing system by cell bodies. The artificial neural network is also called the connectionism mode, which can achieve the function of a nonlinear dynamical system. Now, many researches based on model updating and singnal processing are carried out in the field of the structural dynamical damage. But there are some problems for above researches such as easily influnce by the environment, the strong model dependence and the poor tolerance to the fault of the system and so on. However, in the field of structural damage detection, the artificial neural network is used widely due to its good nonlinear mapping ability, the ability of solving inverse problems and the strong robustness.

The realizing way to identify damage by artificial neural networks[1] is showed as follow. Firstly, based on the analysis of the finite element method, the learning sample of artificial neural networks is constructed by the structural dynamic characteristics on different damage states. Then, the artificial neural network is trained by the learning sample.

And the mapping between input parameters and damage states is established. At last, the artificial neural network is inputed by the parameter of the structural dynamic characteristics, which is obtained by measuring the damage structure. And damage is detected by the output of the artificial neural network.

Many scholars devote to study on the aspect. Kirkegaard and Rytter[2] use the back propagation algorithm to determine the damage location and degree of a steel beam by frequency variations before and after damage.Wu, Ghaboussi and Garrett[3] use the back propagation algorithm to identify the damage of a three layer frame by a response spectra. Anantha and Johnson[4] carry out the damage assessment of composite materials by a fuzzy neural network. Kaminski[5] compares the effectiveness among natural frequency, frequency variance and the ratio of regular frequency variances. Elkordy, Chang and Lee[6] use the variance of mode shapes to identify the damage of a five layer frame. Rhim and Lee[7] input the transfer function to detect the damage of a cantilever beam by a multilayer perceptron model. Pandy and Barai[8] use a multilayer perceptron model and the displacement under static loads to identify the damage of a steel truss bridge. Mitsuru Nakamura[9] chooses the relative displacement of interlayers as the input and the restoring force of interlayers as the output. And the valicity of the method is studied by the result of a seven layer steel structure before and after the Hanshin-Awaji-daishinsai earthquake in 1995. Using the acceleration of a steel truss, Chen and Kim train the neural network to identify the damage degree[10]. And the fuzzy neural network is combined to judge the damage of a beam[11]. Above results show that artificial neural networks have received increasing attention in damage detection. However, above researchers do not point out what kinds of input parameters is sensitive and which algorithm may lead to false or unreliable output results from such networks. In this paper, the application of artificial neural networks to damage detection will be summarized and analyzed. How to select input parameters for neural networks and some efficient and robust algorithm will be studied.

II. PARAMETRIC STUDY The selection of input parameters is very important to the

application of neural networks on damage detection. The damage should be reflected sensitively by input parameters.

2010 International Conference on Artificial Intelligence and Computational Intelligence

978-0-7695-4225-6/10 $26.00 2010 IEEEDOI 10.1109/AICI.2010.50

207

2010 International Conference on Artificial Intelligence and Computational Intelligence

978-0-7695-4225-6/10 $26.00 2010 IEEEDOI 10.1109/AICI.2010.50

207

In the past, mode data and static responses are choosed as input parameters. And they can be divided into several kinds as follow.

A. Two order frequency variation ratio Frequency is a sensitive parameter on damage detection.

And frequency has a good measuring accuracy. But frequency can not be used to identify the damage of symmetric positions on a symmetrical structure.

Cawleys research shows that two order frequency variation ratio is only related to the damage location[12]. Based on the characteristics of structures,

( ),f K r = , (1) where r represents the damage location.

To expand (1) and ignore the higher order term,

( ) ( )( )0,

0,f r

f r KK

= +

(2)

can be obtained. Because ( )0, 0f r =

( )( ) ( )

0,i

f rK Kg r

K

= =

(3)

can be deduced. Assuming that the variation of the stiffness is

independent to frequency, ( ) ( ) ( )/ /i j i jg r g r h r = = (4)

can be obtained. So, according to (4), two order frequency variation ratio

is only the function of the damage location.

B. The square of the frequency variation The square of the frequency variation is related to the

damage location and the damage degree. However, the ratio of the frequency variation square is only related to the damage location [13].

The characteristic equation of the structural motion is ( )2 0K M = . (5)

The perturbation equation of (5) is ( ) ( )( )( )( )2 2 0K K M M + + + + = . (6)

Let M equal to zero.To expand (6) and ignore the quadratic term,

( ) ( )2 /T TK M = (7) can be gotten.

The overall stiffness matrix can be decomposed to the element stiffness matrix. And the element deformation is related to the structural mode shape. And

( ) ( )m f = . (8) For the ith mode, there are

( ) ( )1

MT Ti i m i m m i

mK k

= = , (9)

where M is the amount of elements. To take (9) into (7),

( ) ( ) ( )21

/J

T Ti j i j j i

jk M

=

=

(10)

can be deduced, where J represents the amount of damage elements.

For the Nth damage element, ( ) ( ) ( )2 /T Ti N i N N i i ik M = (11)

can be obtained by (10). Assuming that N N Nk k = ,

( ) ( ) ( )2 /T Ti N N i N N i i ik M = (12) can be deduced.

The square of the frequency variation is related to the damage degree and location of the element. If the ith frequency and the jth frequency are used,

( ) ( ) ( ) ( )22 /

TTN j N N jN i N N ii

T Tj i i j j

kkM M

=

(13)

can be gotten. It shows as in (13) that the ratio of the frequency

variation square is the function of damage locations, when damage degrees are near.

C. Frequency variation ratio Kaminski compares the effectiveness among the natural

frequency, the frequency variation and the regular frequency variation ratio to damage detection[5]. The result shows that the ratio of the frequency variation

( ) /iFC ui di ui

F f f f= (14) is related to the damage degree and the damage location, but the regular frequency variation ratio

1

/i i j

p

FCR FC FCj

N F F=

=

(15)

is only related to the damage location.

D. Mode shape, mode curvature and transfer function According to the relationship between displacements and

strains, each displacement mode shape is corresponding to a strain mode shape. When the damage happens, there is a prominent stress redistribution nearby the damage location. That will cause a significant change of the strain mode shape. The damage can be located by comparison with every order strain mode shape before and after the damage. According to the theoretical analysis as in [14], high order mode shapes are easier to identify the structural damage t

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