A Crack Identification Method for Bridge Type Structures under Vehicular Load Using Wavelet Transform and Particle Swarm Optimization

In this work a crack identification method is proposed for bridge type structures carrying moving vehicle. The bridge is modeled as an Euler-Bernoulli beam, and open cracks exist on several points of the beam. Half-car model is adopted for the vehicle. Coupled equations of the beam-vehicle system are solved using Newmark-Beta method, and the dynamic responses of the beam are obtained. Using these and the reference displacements, an objective function is derived. Crack locations and depths are determined by solving the optimization problem. To this end, a robust evolutionary algorithm, that is, the particle swarm optimization (PSO), is employed. To enhance the performance of the method, the measured displacements are denoised using multiresolution property of the discrete wavelet transform (DWT). It is observed that by the proposed method it is possible to determine small cracks with depth ratio 0.1 in spite of 5% noise interference. 1. Introduction Structures under vehicular loads have significant applications such as railway tracks, bridges, and roadways. Moving load yields larger deflections and higher stresses than equivalent static loading; thus, dynamics of such structures has received significant attention [1, 2]. If the carrying structure includes crack-like defects, then the impact of moving load becomes more pronounced [3–6]. Various damage detection methods have been developed for such structures using the continuous wavelet transform (CWT) [7–11]. They are based on the fact that CWT coefficients of beam dynamic response demonstrate local peaks at crack locations, and magnitudes of these peaks are proportional to crack depths. The significant deficiency of these methods is that CWT coefficients become insensitive to crack at higher moving load speeds. The reason is that time-dependent structural response becomes smoother at higher vehicle speeds. In this case crack-induced singularities disappear, and CWT coefficients of the response signal fail to extract damage info. Some of the methods in the area of structural damage detection are based on model updating [12]. The basic idea is to update mathematical or finite element model of the structure to match the calculated response to that measured from damaged structure, so that damage parameters are estimated. This is achieved solving an optimization problem. To this end metaheuristic methods are generally preferred, as they do not require gradient info and have less possibility of being trapped by local minima in comparison with the gradient-based methods. The particle swarm optimization (PSO)