Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems
This work addresses computational challenges in Bayesian inference for non-smooth engineering systems, offering a domain-specific incremental improvement.
The paper tackles the computational burden of Bayesian parameter inference for highly nonlinear engineering models by proposing a multielement Polynomial Chaos Expansion-based Kriging metamodel that uses domain partitioning to handle non-smooth responses, achieving efficiency and accuracy validated through case studies including an analytical benchmark and a numerical simulation of hydrogen diffusion.
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.