Integrating Bayesian Calibration, Bias Correction, and Machine Learning for the 2014 Sandia Verification and Validation Challenge Problem

Abstract

This paper describes an integrated Bayesian calibration, bias correction, and machine learning approach to the validation challenge problem posed at the Sandia Verification and Validation Challenge Workshop, May 7–9, 2014. Three main challenges are recognized as: I—identification of unknown model parameters; II—quantification of multiple sources of uncertainty; and III—validation assessment when there are no direct experimental measurements associated with one of the quantities of interest (QoIs), i.e., the von Mises stress. This paper addresses these challenges as follows. For challenge I, sensitivity analysis is conducted to select model parameters that have significant impact on the model predictions for the displacement, and then a modular Bayesian approach is performed to calibrate the selected model parameters using experimental displacement data from lab tests under the “pressure only” loading conditions. Challenge II is addressed using a Bayesian model calibration and bias correction approach. For improving predictions of displacement under “pressure plus liquid” loading conditions, a spatial random process (SRP) based model bias correction approach is applied to develop a refined predictive model using experimental displacement data from field tests. For challenge III, the underlying relationship between stress and displacement is identified by training a machine learning model on the simulation data generated from the supplied tank model. Final predictions of stress are made via the machine learning model and using predictions of displacements from the bias-corrected predictive model. The proposed approach not only allows the quantification of multiple sources of uncertainty and errors in the given computer models, but also is able to combine multiple sources of information to improve model performance predictions in untested domains.