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In the present study, a two-step approach comprised of wavelet transform and model updating method for multiple structural damage localization and quantification in beams is proposed. The first step is commenced with applying wavelet transform to axial components of mode shapes so as to predict where the damages are located. During this step, wavelet transform might mistakenly detect a number of elements as impaired due to both sampling interval and middle support effect. In the next step, by defining a damage sensitive objective function consisting of natural frequencies and mode shapes, damage intensities at predicted locations will be computed via model updating method employing ECBO (Enhanced Colliding Bodies Optimization) algorithm. The problem with mistakenly predicted damaged locations will be addressed by reported damage intensities during the second step. The present study also indicates that this two-step method greatly assists in reducing the number of variables during model updating process leading to more precise results. Three numerical examples with multiple damages and noisy modal data are studied in order to guarantee the efficacy of the method. Moreover, one numerical example is solved with a number of other Meta-Heuristic algorithms including GA (Genetic Algorithm), CSS (Charged System Search), Pattern Search and Cuckoo algorithm whose results are compared to ECBO algorithm with the intention of ensuring the veracity of ECBO results. The results vividly demonstrate that this method is highly efficient even in the presence of noise.

A two-step method composed of wavelet transform and model updating method for multiple damage diagnosis in beams