STRUCTURAL PHYSICAL PARAMETER IDENTIFICATION USING BAYESIAN ESTIMATION BASED ON MULTI-RESOLUTION ANALYSIS: FORMULATION AND VERIFICATION

With the existence of uncertainties like measurement noise and model error, structural physical parameter identification becomes an indeterminate problem. In this paper, a probabilistic approach capable of dealing with this problem effectively is presented on the basis of Bayesian statistics theory and Markov Chain Monte Carlo (MCMC) methods using measured responses and excitations. By means of wavelet multiresolution analysis, differential equations of motion are used to establish the multiscale dynamic equations of linear structural systems, from which the linear regression models of physical parameters are inferred with the approximations and details of loads and responses obtained from multilevel wavelet decompositions. Based on these models, the posterior joint probability density function (PDF) of physical parameters is obtained using the Bayesian estimation, then MCMC methods are implemented to obtain the marginal PDF and optimal estimate of physical parameters from their posterior joint PDF. The numerical simulations of 4DOF shear building demonstrate the accuracy and validity of the proposed method, and show that this approach can achieve identification accuracy satisfying engineering needs under noise.