Bayesian Updating of Model Parameters by Iterative Particle Filter with Importance Sampling

Abstract

Data assimilation with a particle filter (PF) has attracted attention for use in Bayesian updating. However, PFs have a problem known as degeneracy, where weights tend to concentrate into only a few particles after a few iterations (all other particles degenerate), which causes poor computational performance. This study discusses the applicability of a PF to the Bayesian updating of model parameters and probabilistic prediction with the updated model and proposes a method that uses a PF to limit degeneracy. The proposed method, called iterative particle filter with importance sampling (IPFIS), uses iterative observation updating in a PF, a Gaussian mixture model, and importance sampling. Two examples are used to demonstrate the proposed algorithm. In the first example, posterior distributions of the stiffness parameters of a two-degree-of-freedom model are identified. In the second example, IPFIS is applied to a consolidation settlement problem of a soft ground due to embankment loading, and probability distributions of the geotechnical parameters in an elastoplastic finite-element model and the simulated settlement displacements are updated based on time-series observation.