Journal of Sensors

Volume 2015 (2015), Article ID 246480, 6 pages

http://dx.doi.org/10.1155/2015/246480

## A Practical Method for Grid Structures Damage Location

^{1}Transportation Equipment and Marine Engineering College, Dalian Maritime University, Dalian, Liaoning 116026, China^{2}Dalian University of Technology, Linggong Road No. 2, Integrated Building 4, 219-B, Dalian, Liaoning 116024, China

Received 29 September 2014; Revised 29 January 2015; Accepted 9 February 2015

Academic Editor: Christos Riziotis

Copyright © 2015 Zhefu Yu and Linsheng Huo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A damage location method based on cross correlation function, wavelet packet decomposition, and support vector machine was proposed for grid structure. The approximate damage positions in grid structures could be determined through the peak abrupt changes of the cross correlation function that was produced by two vibration responses of adjacent measuring points. The vibration response was decomposed into eight bands by wavelet packet in order to accurately locate damage rods. The energy distribution in eight bands was used as a feature vector. SVM is trained to locate damaged bar elements in grid structures. Numerical analysis results showed that this method had good accuracy.

#### 1. Introduction

Grid structures suffer from all kinds of damage during service, due to environmental effects, natural disasters, and human factors. For the maintenance of grid structures, accurately locating damage position is very critical.

The traditional methods of damage location are based in displacement measurement and strain measurement, but they are damaging to the structures [1]. According to the theory of structural dynamics, structural damage can affect the dynamic characteristics of structures. Therefore, damage location methods based on vibration analysis have attracted much attention in the past twenty years [2]. The modes of structural damage could be identified by analyzing modal parameters. The modal parameters include natural frequencies [3], vibration modes [4, 5], and other parameters [6, 7]. For a complex structure, the high natural frequencies are difficult to be measured. Precise measurement of vibration modes requires more measuring sensors [8]. The modal parameters are affected easily by signal noise, structure characteristics, and human factors. The damage location methods based on modal parameters cannot reach the expected result.

Despite the fact that the damage detection methods integrated signal processing [9], pattern recognition and artificial intelligence [10, 11] are the developing direction in recent years; such methods were only applied to some of simple structures. Because the number of bar element in grid structure is huge, and the number of damage mode is enormous, to get the damage location of grid structure, a larger number of damage mode samples are required to train classifier, which will bring huge workload for building samples with finite element methods.

This paper proposed a damage location method which integrated the cross correlation function of the random vibration, wavelet packet decomposition, and SVM. The proposed method includes two steps. The first step is the approximate damage location. The damaged basic units were found through the peak abrupt changes of the cross correlation function [12]. In the second step, wavelet packet and support vector machines are used in determining the damaged bars in the basic units.

#### 2. Cross Correlation Function, Wavelet Packet Decomposition, and SVM

##### 2.1. The Conception of Cross Correlation Function

Cross correlation function can reflect the correlation between two random vibration signals. The correlation changes with the time interval of the two signals. If a structure is subjected to a random excitation, the response of two adjacent measuring points can be regarded as two stationary random processes and . The cross correlation function is shown as where is the cross correlation function; is the time interval; means the expecting value; denotes joint probability distribution function.

If the random vibration responses are ergodic, the cross correlation function can be derived through the time-history of one random process. It is shown as

In the numerical analysis, the vibration response in each measuring point is a discrete time series. The integral of cross correlation function can not be acquired by (2). It can be replaced by the summation formula as shown in where is the number of sampling points.

In a cross correlation function, the largest amplitude as shown in (4) is defined as peak in this paper:

According to the characteristics of grid structures, measuring points are arranged on the bottom nodes uniformly. Cross correlation functions can be acquired by adjacent measuring points. Every cross correlation function has a peak. Thence, a peak matrix for the entire grid structure can be derived [12]. By introducing the peak matrix, the influence of noise pollution in measurement signals can be reduced [13, 14]. In case of one damage mode of a grid structure, the peak matrixes obtained from same spectrum vibrations are highly similar. After normalizing treatment, they are almost identical. Different damage modes produce different peak matrixes. By comparing the peak matrix of the damaged structure with the peak matrix of the intact structure, the approximate damage position would be determined.

##### 2.2. Wavelet Packet Decomposition

Wavelet packet decomposition is derived from the wavelet analysis, which is a tool for multilevel band analysis and signal reconstruction. Wavelet packet decomposition can decompose the high-frequency portion of a signal more narrowly than the wavelet analysis. The different bands of a signal have different energy. The energy distribution of the vibration responses in grid structure may reflect the damage position.

##### 2.3. SVM

SVM proposed by Vapnik is a machine learning algorithm based on statistical learning theory [15]. It minimizes actual risk through seeking minimal structural risk. It can get a good learning result in the case of small sample size. Since the SVM algorithm is a quadratic optimization problem, the resulting solution is globally optimal.

The explanation of SVM starts with a set of training data , where is an* n*-dimension vector and is the class label of the th sample. The optimal hyperplane divides the training data into two classes. The basic idea of SVM is to maximize the margin between the positive samples and the negative samples. Figure 1 shows that the training examples can be linearly separated into two classes. In general, it is not necessary to separate training examples into each class without error. The variable is introduced for misclassification errors; is a constant. Then, this optimization problem is defined as follows:In (5), the first term specifies the size of the margin, and the second term represents the cost of the misclassification. The decision function can be written aswhere are Lagrange multipliers. corresponds to the th sample. When the maximal margin hyperplane is found in feature space, the corresponding to the points close to the hyperplane are greater than zero, and these points are called the support vectors. The corresponding to other points are equal to zero, which means that the representation of the hyperplane is solely given by the support vectors.