A sequential calibration and validation framework for model uncertainty quantification and reduction

Abstract

This paper aims to provide new insights into model calibration, which plays an essential role in improving the validity of Modeling and Simulation (M&S) in engineering design and analysis. Various existing model calibration approaches including the direct Bayesian calibration method, the well-known Kennedy and O’Hagan (KOH) framework and its variants, and the optimization-based calibration method, are first investigated. It is observed that the direct Bayesian calibration and optimization-based calibration may be misled by potentially wrong information if the computer model cannot adequately capture the underlying true physics, while the effectiveness of the KOH framework and its variants is significantly affected by the prior distributions of the unknown model parameters. Based on this observation, a sequential model calibration and validation (SeCAV) framework is proposed to improve the efficacy of both model parameter calibration and bias correction for the purpose of uncertainty quantification and reduction. In the proposed method, the model validation and Bayesian calibration are implemented in a sequential manner, where the former serves as a filter to select the best experimental data for the latter, and provides the latter with a confidence probability as a weight factor for updating the uncertain model parameters. The parameter calibration result is then integrated with model bias correction to improve the prediction accuracy of the M&S. A mathematical example and an engineering example are employed to demonstrate the advantages and disadvantages of different approaches. The results show that the SeCAV framework, in general, performs better than the existing methods.