Research on Bridge Damage Identification Based on WPE-MDS and HTF-SAPSO

In recent decades, structural damage identification based on the wavelet analysis method has been widely developed, but it is still confronted with many difficulties, such as large decomposition error and complex data. In order to overcome the shortcomings of analysis based on wavelet, the wavelet packet analysis method is adopted to decompose the acceleration data into wavelet packets, and the frequency band energy value after wavelet packet decomposition (WPE) is taken as the different dimensions of the Mahalanobis distance squared (MDS) in this study, where the MDS value of the same element between different samples is calculated, and the mean value of 30 groups of MDS values for each element is processed. The change rate between the MDS value of the element that exceeds the MDS value in the healthy state and the MDS mean value in the healthy state as the objective function. The combination of weight coefficient and hyperbolic tangent function is used to improve the simulated annealing particle swarm optimization (SAPSO) algorithm, and the improved hyperbolic tangent function-simulated annealing particle swarm optimization (HTF-SAPSO) is used to iteratively calculate the damage severity. The numerical simulation and vibration testing of a steel beam are conducted to verify the identification performance of damage location and the analysis of damage severity by this method, respectively. The numerical model of the experimental I-beam is established based on the MATLAB modeling platform, and the different damage cases are utilized to illustrate the correctness of this study. The different proportions of noise effects are adopted to the numerical simulation analysis, where the correlations between noise effects and MDS value and damage severity are analyzed. In the numerical simulation, although the MDS value increases to different degrees with the increase of the noise ratio, the damage identification result of the damaged element remains mostly constant, which indicates that the influence is negligible. In conclusion, it is feasible to construct the damage index via the combination of WPE and MDS values, the damage location can be judged from whether the MDS value of the element exceeds the threshold, and the HTF-SAPSO algorithm is more efficient and accurate to be adopted in the quantification of the damage severity