Shock and Vibration

Volume 2016 (2016), Article ID 3989743, 12 pages

http://dx.doi.org/10.1155/2016/3989743

## Damage Detection of Structures for Ambient Loading Based on Cross Correlation Function Amplitude and SVM

^{1}Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China^{2}Department of Civil Engineering, National Taiwan University, Taipei, Taiwan

Received 17 November 2015; Accepted 1 March 2016

Academic Editor: Abdollah Shafieezadeh

Copyright © 2016 Lin-sheng Huo et al. 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

An effective method for the damage detection of skeletal structures which combines the cross correlation function amplitude (CCFA) with the support vector machine (SVM) is presented in this paper. The proposed method consists of two stages. Firstly, the data features are extracted from the CCFA, which, calculated from dynamic responses and as a representation of the modal shapes of the structure, changes when damage occurs on the structure. The data features are then input into the SVM with the one-against-one (OAO) algorithm to classify the damage status of the structure. The simulation data of IASC-ASCE benchmark model and a vibration experiment of truss structure are adopted to verify the feasibility of proposed method. The results show that the proposed method is suitable for the damage identification of skeletal structures with the limited sensors subjected to ambient excitation. As the CCFA based data features are sensitive to damage, the proposed method demonstrates its reliability in the diagnosis of structures with damage, especially for those with minor damage. In addition, the proposed method shows better noise robustness and is more suitable for noisy environments.

#### 1. Introduction

Structural damage detection is crucial in reducing catastrophic failures and prolonging the service life of structures. One of the most popular global structural damage detection techniques is the vibration-based damage detection technique, which has received considerable attention in recent years. The vibration-based damage detection methods can be classified as the model-based damage detection method (MBDDM) and non-model-based damage detection method (NMBDDM) [1, 2]. For the model-based method, the structural model is a function of the physical properties of the structure (mass, damping, and stiffness); hence model updating techniques are needed to improve the precision of the parameters describing the structure. As most model updating techniques are complicated and their precisions are limited for complex structures, the non-model-based method, which can avoid the drawbacks of the model-based method, is considered as a better choice in general. It can be easily implemented in online Structural Health Monitoring (SHM) systems for its simple computing process.

For the NMBDDM, a precise analytical model of the structure is not required, and the damage features can be extracted from the modal parameters or dynamic responses [2]. As a huge amount of damage information can be extracted from the modal parameters, some damage features can be detected based on the changes of natural frequencies or mode shapes [3]. However, modal parameters such as the mode shapes cannot be identified precisely for complex structures, which may reduce the accuracy of the NMBDDM. Therefore, some scholars have proposed the extraction of damage features directly from the dynamic response in time domain, frequency domain, or time-frequency domain. In their researches, statistical analysis technologies including the outlier analysis [4] and independent component analysis (ICA) [5] and signal process technologies including the wavelet transform technology (WPT) [6, 7] and Hilbert Huang transform (HHT) [8, 9] have been adopted to extract damage features from the dynamic response.

Almost all of the NMBDDM mentioned above can be used only to identify the presence of damage. Yang and coworkers [2, 10–12] proposed a type of NMBDDM, which can be used to detect and locate damage with the correlation and relative difference between the cross correlative function amplitude vectors obtained from the intact and damaged structures. However, this method seems to have its limitation. Firstly, it is valid only for the case under steady random excitation within the specific frequency spectrum. Further, it requires the number of sensors nearly equal to that of the detectable damage locations of the structure, which means that the method may be impractical due to the high cost of the installation sensors.

It is known that the damage information provided by the damage features of the NMBDDM is generally insufficient and the locations and degree of damage are incapable of identification in full [1, 2]. Some scholars have introduced the intelligence algorithms to the NMBDDM methods, such as the artificial neural network (ANN) [13, 14] for their excellent pattern recognition capability. In this connection, the damage features are used as input data, and the intelligence algorithms are introduced as the analysis tools for matching the damage patterns, detecting the damage locations, and estimating the degree of severity.

The support vector machine (SVM) is another computational method based on the statistical learning theory, of which the classification ability can be applied in damage diagnosis of structures. Compared with ANN, the SVM can be used to achieve the same global optimal solution for a smaller number of samples for its better generalization [15]. The process of damage diagnosis utilizing the SVM consists of two steps: (1) features extraction from the measured dynamic responses and (2) patterns classification based on the input vectors composed of features. The SVM allows us to recognize and classify the structural damage patterns in a way as accurate as possible. The accuracy of the SVM lies mainly in the kernel function and the damage features. Improving the kernel function such as the wavelet packet kernel function [16, 17] can help improve the generalization ability. The selecting of damage features should be such proper as to contain the characteristics of the structure as fully as possible. The desired damage features are sensitive to the damage and independent variables that may not be easily interfered by external factors such as excitation and noise. Previously, the data features have been extracted from the structural modal parameters [18–20], independent component analysis (ICA) [21], envelope spectrum [22, 23], wavelet packet transform (WPT) energy spectrum [24, 25], and other statistical information [26]. Most of these data features have been proposed for the monitoring of mechanical devices, and few of them can be applied to the damage diagnosis of large and complex civil engineering structures.

The objective herein is to propose a new method that integrates the cross correlation function amplitude (CCFA) with the support vector machine (SVM) for the damage identification of skeletal structures. The proposed method can be used to locate damage and identify damage patterns with the limited number of sensors. This paper is organized as follows. Firstly, the cross correlation function amplitude and support vector machine are introduced in Sections 2 and 3, respectively. In Section 4, the damage detection method for civil engineering structures based on the CCFA and SVM is illustrated in detail. In addition, the simulation data of IASC-ASCE benchmark simulation model and a vibration experiment of truss structure are used to illustrate the feasibility of proposed method in Sections 5 and 6.

#### 2. Cross Correlation Function Amplitude (CCFA)

The cross correlation function of two stationary stochastic processes and with a time lag is defined aswhere is the expectation of the stochastic variable.

The equation of motion for degree-of-freedom (DOF) structure with classical damping is where** X**(*t*) is the -dimensional displacement vector, is the excitation vector, and** M**,** C**, and** K** denote, respectively, the mass, damping, and stiffness matrices of the structure with the dimension of . The displacement response can be decomposed into the modal coordinates as in which is the th modal vector and is the corresponding modal coordinate. The th modal response can be separately written asBy Duhamel’s integral, the th modal response at point due to excitation at point is where, , and are the modal mass, modal damping ratio, and natural frequency of the th mode, respectively; and is the damped natural frequency of the th mode. For ambient loading, the exciting points are numerous, and is the accumulation of responses caused by each exciting point as follows:

Based on the natural excitation technique (NExT) [27], the cross correlation function between the th modal responses at the th and* j*th points can be written asIf the ambient vibration source is a white noise random process, thenwhere is a constant representing the one-side autospectral density of the white noise and (*t*) is the Dirac delta function. Substituting (7) and (9) into (8), one can express the cross correlation function of the th modal displacement responses at the th and* j*th point as follows:where is the coefficient depending on th modal parameters, exciting points, and measured response at point and is a phase dependent on the th modal parameters. Since the structural responses under the white noise excitation are stationary stochastic processes, the cross correlation function of the th modal* velocity* responses at the th and* j*th points can be written as Also, the cross correlation function of the th modal acceleration responses at the th and th points can be expressed asConsequently, the cross correlation function amplitudes (CCFAs) of the th modal displacement, velocity, and acceleration responses are whereThe values of and have been listed in Table 1.