Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems

TL;DR

This paper introduces a multielement Polynomial Chaos Kriging surrogate model for efficient Bayesian inference in highly nonlinear, non-smooth systems, reducing computational costs while maintaining accuracy.

Contribution

It proposes a novel piecewise surrogate model combining local Polynomial Chaos Kriging metamodels for non-smooth system response approximation.

Findings

Effective in capturing non-smooth responses with minimal computational effort

Validated through analytical and numerical case studies

Achieves high accuracy in Bayesian parameter inference

Abstract

This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian inference applications, a multielement Polynomial Chaos Expansion based Kriging metamodel is proposed. The developed surrogate model combines in a piecewise function an array of local Polynomial Chaos based Kriging metamodels constructed on a finite set of non-overlapping subdomains of the stochastic input space. Therewith, the presence of non-smoothness in the response of the forward model (e.g.~ nonlinearities and sparseness) can be reproduced by the proposed metamodel with minimum computational costs owing to its local adaptation capabilities. The model parameter inference is conducted through a Markov chain Monte Carlo approach comprising adaptive exploration and delayed rejection. The efficiency and accuracy of the proposed approach are validated through two case studies, including an analytical benchmark and a numerical case study. The latter relates the partial differential equation governing the hydrogen diffusion phenomenon of metallic materials in Thermal Desorption Spectroscopy tests.