Adaptive Bayesian filter with data-driven sparse state space model for seismic response estimation

The present work proposes a seismic response estimation framework for post-earthquake structural condition assessment via acceleration measurements. An augmented sparse state space model is first derived to represent the underlying governing equations of the system of interest with hysteresis nonlinearity. A Bayesian filter is then utilized to provide the displacement estimate under an earthquake excitation by fusing the identified sparse state space model with the measured system acceleration. To avoid subjective assumptions on the process and observation noises in the Bayesian filter, a double-loop process is proposed, where the inner loop is an online Bayesian filtering by the unscented Kalman filter with Robbins-Monro algorithm, while the outer loop is an offline Bayesian updating by the transitional Markov chain Monte Carlo method. The feasibility of the framework is demonstrated on a simple illustrative example and a followed engineering application to the state estimation of a bridge pier finite element model. The results indicate the capability of the framework to properly infer the system displacement, including its residual components.