Enhanced adaptive sequential Monte Carlo method for Bayesian model class selection by quantifying data fit and information gain

Abstract

For complex engineering structures, it is important to systematically select a model class among various choices and search the complicated parameter space, while also quantifying uncertainties. This paper develops an enhanced adaptive sequential Monte Carlo (ASMC) method to solve Bayesian model updating and model class selection in a unified manner. Main contributions are: (1) Analysis of the sequential sampling process reveals difficulties of sampling from complex probability density functions (PDFs), which naturally leads to the PDF approximation using incremental weights of samples, and then the adaptive sampling scheme with this approximation. (2) Following ASMC framework, new formulations are derived to calculate model class evidence; these formulations enable the separate quantification of data fit and information gain of a model class. A simulated and a full-scale structure were used to demonstrate the proposed method. This work lays good foundation for downstream research such as automation in construction and structural health monitoring.