Multi-source random excitation identification for stochastic structures based on matrix perturbation and modified regularization method

In view of the characteristic of pseudo excitation and effects of the regularization parameter λ on the residual norm and solution norm, a novel modified regularization method is proposed to solve the ill-posed problem and mitigate the error propagation of random dynamic loads identification. Compared with Moore-Penrose pseudo inverse and Tikhonov regularization methods that are sensitive to the selection of measurement locations, the proposed modified regularization method can always identify the loads accurately and stably regardless of measurement locations. In addition, the identified loads always match the actual ones from low to high frequency domains using the proposed modified regularization method. Furthermore, the matrix perturbation method is combined with the modified regularization method to analyze the multisource loads acting on the uncertain structure. Several practical engineering examples are conducted to demonstrate that the lower and upper bounds of identified forces can be obtained, which clearly validates the effectiveness and feasibility of the proposed methods in the application of complicated structures.