Markov Chain Monte Carlo-based Bayesian method for nonlinear stochastic model updating

This paper proposes a Markov Chain Monte Carlo (MCMC)-based Bayesian method for nonlinear stochastic model updating by using the instantaneous characteristics of the structural dynamic responses. According to the discrete analytical mode decomposed method and Hilbert transform, the instantaneous characteristics of the mono-components are firstly extracted from the structural dynamic response and applied to the calculation of likelihood function. Then, the posterior probability density function associated with Bayesian theorem is derived under the assumption of Gaussian prior distribution by using instantaneous characteristics. Afterwards, to calculate the posterior probability density function and improve the sampling efficiency, the delayed rejection adaptive Metropolis-Hastings (DRAM) algorithm is implemented with the advantages of strong adaptive and fast convergence. In the process of Bayesian inference, the posterior samples generated by DRAM require vast quantities of finite element analysis to guarantee the accuracy. For reducing the computational cost, the response surface model is constructed to establish the mathematical regression model between the structural parameters and the theoretical dynamic responses. To validate the effectiveness and applicability of the proposed method, the numerical cases on a three-story nonlinear structure under earthquake excitation considering various noise level effects and an Iwan beam model with two types of excitations are simulated. In addition, an experimental validation on a 1/4 scale, 3-story steel frame structure subjected to a series of earthquake excitations in the laboratory is also performed to further verify the proposed method. Both the numerical and experimental results demonstrate that the DRAM-based Bayesian method can be effectively used to update nonlinear stochastic models with a high accuracy.