A novel adaptive importance sampling algorithm for Bayesian model updating

Abstract

Bayesian model updating has computational capability of reducing uncertainties in engineering models and yielding valuable inferences for model predictions from observed data. Importance sampling (IS) and Markov chain Monte Carlo (MCMC) are the two main techniques among the existing simulation-based methods for Bayesian model updating. Motivated by the fact IS outperforms MCMC in terms of computational efficiency once the proposal importance sampling density (ISD) is appropriately chosen, this paper proposes an innovative adaptive importance sampling (AIS) algorithm using Gaussian mixture to overcome the limitations of conventional IS-based methods. Integrating of the concepts of population Monte Carlo (PMC) and cross entropy (CE) contributes to the major novelty of the proposed algorithm. Consequently, the proposed AIS algorithm can successfully construct the ISD that resembles the sophisticated target posterior density. Moreover, a metric quantifying sampling effectiveness called normalized effective sample size (N-ESS) is also adopted to measure the similarity between the ISD and the target density. One benchmark example of system identification and one case study of chloride-induced concrete corrosion are investigated to demonstrate the accuracy and robustness of the proposed algorithm.