Bayesian State Estimation Method for Nonlinear Systems and Its Application to Recorded Seismic Response

The focus of this paper is to demonstrate the application of a recently developed Bayesian state estimation method to the recorded seismic response of a building and to discuss the issue of model selection. The method, known as the particle filter, is based on stochastic simulation. Unlike the well-known extended Kalman filter, it is applicable to highly nonlinear systems with non-Gaussian uncertainties. The particle filter is applied to strong motion data recorded in the 1994 Northridge earthquake in a seven-story hotel whose structural system consists of nonductile reinforced-concrete moment frames, two of which were severely damaged during the earthquake. We address the issue of model selection. Two identification models are proposed: a time-varying linear model and a simplified time-varying nonlinear degradation model. The latter is derived from a nonlinear finite-element model of the building previously developed at Caltech. For the former model, the resulting performance is poor since the parameters need to vary significantly with time in order to capture the structural degradation of the building during the earthquake. The latter model performs better because it is able to characterize this degradation to a certain extent even with its parameters fixed. For this case study, the particle filter provides consistent state and parameter estimates, in contrast to the extended Kalman filter, which provides inconsistent estimates. It is concluded that for a state estimation procedure to be successful, at least two factors are essential: an appropriate estimation algorithm and a suitable identification model.