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

Abstract

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.

Damage Identification in Bridges by Processing Dynamic Responses to Moving Loads: Features and Evaluation

“…Based on the foregoing study, Gökdağ [132] used the multiresolution property of the DWT to enhance the damage detection capacity of PSO for the identification of small cracks. To enhance the performance of the PSO method, the measured reference displacements (RDs) in Equation (34) were added in a sequence of random numbers to simulate the effect of experimental noise arising from instrumentation, environmental conditions, numerical errors, and so forth [132]:truey¯false(z,tfalse)noisy=truey¯false(z,tfalse)+Np⋅G⋅σ, where truey¯false(z,tfalse) is the calculated RD, which is free of noise, z is the point on the damaged beam. Np, G, σ denote the noise percentage, Gaussian distribution with zero mean and unit standard deviation, and the standard deviation of truey¯false(z,tfalse), respectively.…”

“…To alleviate noise, the multiresolution property of the DWT was exploited. Then, the objective function in Equation (35) could be revised as [132]: F2false(normalxfalse)=true∑n=1Nmptrue∫0T|y(zn,t)−ytrue¯M(zn,t)|max(|ytrue¯M(zn,t)|)dt, where truey¯M denotes the approximation function of truey¯ at the Mth decomposition level in the DWT. On this basis, the modified method could detect small cracks with a depth ratio of 0.1 despite 5% noise interference; moreover, it could identify small damage in bridges with much more accuracy than the traditional CWT coefficients method [68,83].…”