An Efficient Statistical Inference Approach for Model Calibration Using Griddy Gibbs Sampling

Abstract

Model calibration is a critical step in many fields to ensure that decisions are made based on models that best capture the behavior of the physical system. Typically, an estimation of the uncertainty of the model is also needed to aid decision makers and to assess risks. Traditional statistical methods have met this need but come at a high computational expense, and thus they may be impractical in industries that desire rapid innovation and decision-making. Optimization and machine learning (ML) approaches offer computationally efficient algorithms for model calibration but do not provide a quantification of model uncertainty. This work proposes a statistical inference approach for model calibration, leveraging griddy Gibbs sampling to efficiently and flexibly calibrate models and provide an estimation of the posterior distribution for the calibrated variables. Using this approach, decision makers would gain a sense of the model uncertainty so that risk can appropriately be accounted for in decisions based upon the model results. The model is benchmarked against traditional Bayesian inference using a piston thermal model with unknown backside heat transfer boundary conditions as the benchmark model. When a sufficient number of simulations and sensor data points are used, the griddy Gibbs calibration provided nearly identical calibrations and 95% credible intervals (CI) on the calibrated variables to the traditional Bayesian calibration at a fraction of the computation cost.