The focus of this report is real-time Bayesian state estimation using nonlinear models. A recently developed method, the particle filter, is studied that is based on Monte Carlo simulation. Unlike the well-known extended Kalman filter, it is applicable to highly nonlinear systems with non-Gaussian uncertainties. Recently developed techniques that improve the convergence of the particle filter simulations are also introduced and discussed. Comparisons between the particle filter and the extended Kalman filter are made using several numerical examples of nonlinear systems. The results indicate that the particle filter provides consistent state and parameter estimates for highly nonlinear systems, while the extended Kalman filter does not.
The particle filter is applied to a real-data case study: a 7-story hotel whose structural system consists of non-ductile reinforced-concrete moment frames, one of which was severely damaged during the 1994 Northridge earthquake. Two identification models are proposed: a timevarying 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. Once again, the particle filter provides consistent state and parameter estimates, in contrast to the extended Kalman filter. 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. Finally, recorded motions from the 1994 Northridge earthquake are used to illustrate how to do real-time performance evaluation by computing estimates of the repair costs and probability of component damage for the hotel
