A Generalized Polynomial Chaos-Based Method for Efficient Bayesian Calibration of Uncertain Computational Models

TL;DR

This paper introduces a generalized Polynomial Chaos-based approach for efficient Bayesian calibration of complex dynamic models with uncertain parameters and structures, enabling improved uncertainty quantification and model credibility assessment.

Contribution

It develops a novel spectral representation and projection method combining Karhunen-Loeve expansion with Polynomial Chaos for Bayesian calibration of spatio-temporally varying uncertainties.

Findings

Successfully calibrated a flow simulator through the proposed method.

Demonstrated effective uncertainty quantification in model parameters.

Enhanced model credibility assessment through posterior distribution analysis.

Abstract

This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent stationary Gaussian processes with uncertain hyper-parameters describe uncertainties of the model structure and parameters while Karhunnen-Loeve expansion is adopted to spectrally represent these Gaussian processes. The Karhunnen-Loeve expansion of a prior Gaussian process is projected on a generalized Polynomial Chaos basis, whereas intrusive Galerkin projection is utilized to calculate the associated coefficients of the simulator output. Bayesian inference is used to update the prior probability distribution of the generalized Polynomial Chaos basis, which along with the chaos expansion coefficients represent the posterior probability distribution. Parameters of the posterior distribution are identified that quantify credibility of the simulator model. The proposed method is demonstrated for calibration of a simulator of quasi-one-dimensional flow through a divergent nozzle.