Identification Method of Dynamic Loads for Stochastic Structures Based on Matrix Perturbation Theory

Abstract

Based on the matrix perturbation theory and regularization method, an analysis method is proposed to identify the dynamic loads for stochastic structures. The dynamic loads are expressed as functions of time and random parameters in time domain and the forward model for dynamic load identification is established through the convolution integral of loads and the corresponding unit-pulse response functions of system. Through the discretization of convolution integral, the first-order matrix perturbation on the basis of Taylor expansion is used to transform the problem of load identification for stochastic structures into two kinds of certain inverse problems, namely the dynamic load identification on the mean value of structures' random parameters and the sensitivity identification of dynamic loads to each random parameter. With the measured responses containing noise, the modified regularization operator and L-curve method are adopted to overcome ill-posedness of load reconstruction and to obtain stable and approximate solutions of certain inverse problems and valid assessments of statistics of identified loads. Numerical simulations demonstrate that aimed at stochastic structures, the identification and assessment of dynamic loads are achieved stably and effectively by the presented method.