Auxiliary Bayesian updating of embankment settlement based on finite element model and response surface method

Abstract

Geotechnical observational method (OM) that aims to improve predictions of geotechnical structure responses (e.g., embankment settlement) based on the monitoring data can be rigorously formulated under a Bayesian updating framework. However, Bayesian analysis often faces a computational challenge when sophisticated numerical models (e.g., finite element model, FEM) are involved due to a significant number of model evaluations. Although response surface models (RSMs) provide cost-efficient alternatives to alleviate the computational burden, they are criticized for the problem-dependent accuracy. First, RSM is frequently established using the prior distribution, and its applicability in posterior space might degenerate, leading to inconsistent posterior predictions. Second, RSM-based Bayesian analysis can only provide updated responses for which RSMs are constructed. The updated information of other responses, for which the corresponding RSMs are not constructed, is missed. This paper presents an auxiliary Bayesian approach that combines a simple RSM (e.g., lower order polynomials) and FEM to update the embankment settlement based on monitoring data. The proposed approach improves the consistency of RSM-based Bayesian updating at the expense of FEM evaluations with acceptable computational costs. It avoids the blind confidence in applicability of RSMs constructed using prior samples to different posterior space, and provides information on updated predictions of responses without RSMs constructed using prior samples. An embankment example is investigated to illustrate the proposed approach and to explore its performance of the proposed approach.