Challenging issues in Bayesian calibration of multi-physics models

Abstract

This paper investigates several challenging aspects of Bayesian calibration for multiphysics models, including: (1) calibration with different forms of experimental data (e.g., interval data and time series data), (2) determination of the identifiability of model parameters when the analytical expression of model is known or unknown, (3) calibration of multiple physics models sharing common parameters, and (4) efficient use of available data in a multi-model calibration problem especially when the experimental resources are limited. A Bayesian network-based method is developed for the calibration of multi-physics models, integrating various sources of uncertainty with information from computational models and experimental data. We adopt the well-known Kennedy and O’Hagan (KOH) framework for model calibration under uncertainty, and develop extensions to multi-physics models and various scenarios of available data. Both aleatoric uncertainty (due to natural variability) and epistemic uncertainty (due to lack of information, including data uncertainty and model uncertainty) are accounted for in the calibration process.A first-order Taylor series expansion-based method is proposed to determine which model parameters are identifiable, i.e., to find the parameters that can be calibrated with the available data. Following the KOH framework, a probabilistic discrepancy term is estimated and added to the prediction of the calibrated model, attempting to account for model uncertainty. This discrepancy term is modeled as a Gaussian process when sufficient data are available for multiple model input combinations, and is modeled as a random variable when the available data set is small and limited. The overall approach is illustrated using two application examples related to microelectromechanical system (MEMS) devices: (1) calibration of a dielectric charging model with time-series data, and (2) calibration of two physics models (pull-in voltage and creep) using measurements of different physical quantities in different devices.