Bayesian updating of model parameters using adaptive Gaussian process regression and particle filter

Bayesian model updating provides a powerful framework for updating and uncertainty quantification of models by making use of observations, following probability rules in the treatment of uncertainty. Particle filter (PF) and Bayesian Updating with Structural Reliability method (BUS) have been developed by researchers as promising computational tools for this purpose. However, reducing computational cost in the updating process, especially for complex models, remains one of the key challenges. Surrogate model approach achieves this by appropriately replacing, possibly adaptively, the evaluation of the original computationally costly models with approximate ones that are much less costly. This study proposes an efficient method to estimate the posterior probability density function (PDF) of model parameters by using a surrogate model constructed using adaptive Gaussian Process Regression and PF. Of critical importance is the development of 'learning function', which finds the location of large values of posterior PDF and avoids those that have been visited. The proposed methodology is illustrated using a single-variable example and compared with PF and BUS. Its application is illustrated through an example of structural dynamics and another one on settlement prediction by soil-water coupled FEM with Cam-clay model.