  This paper develops a Bayesian network-based method for the calibration of
multi-physics models, integrating various sources of uncertainty with
information from computational models and experimental data. We adopt the
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.
Challenging aspects of Bayesian calibration for multi-physics models are
investigated, 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, which enables efficient use of data especially when the
experimental resources are limited. A first-order Taylor series expansion-based
method is proposed to determine which model parameters are identifiable.
Following the KOH framework, a probabilistic discrepancy function is estimated
and added to the prediction of the calibrated model, attempting to account for
model uncertainty. This discrepancy function 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 are 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.
