A two-step weighting regularization method for stochastic excitation identification under multi-source uncertainties based on response superposition-decomposition principle. (1st January 2023) - Liu, Yaru; Wang, Lei
Abstract: Excitation identification has received considerable attention because of its importance in safety assessment and structural design. This paper proposed a power spectral density (PSD) identification method for stationary stochastic excitations considering multi-source uncertainties in load fluctuations, material dispersions and measurement noises. Based on the traditional inverse pseudo-excitation method, a two-step weighting regularization strategy is creatively developed to reduce the amplification effects of the uncertainties in the transfer matrix and measurements on reconstructed results near natural frequencies. Especially, to enhance the generalizability of regularization operations, a weighting matrix is defined based on the interval-quantized deviation analysis of pseudo excitations and then an improved Tikhonov regularizing operator is defined given the features of the weighting transfer matrix and pseudo responses. Next, the response superposition-decomposition principle is performed to determine the boundaries of excitation PSD and two uncertainty propagation methods are developed. To guarantee the accuracy and efficiency of uncertainty analysis, the adaptive reduced-dimension Chebyshev model is adopted to characterize the nonlinear response-parameter relationships, and the first-order Taylor series approximation is used to describe the linear response-excitation relationships. Eventually, two numerical examples and one experimental example are discussed to demonstrate the feasibility of the developed approach. The results suggest its promising applications in complicated structures and loading conditions.