Statistical prior modeling with radius-uniform distribution for a correlation hyperparameter in bayesian calibration

Model calibration is a process aimed at adjusting unknown parameters to minimize the error between the simulation model output and experimental observations. In computer-aided engineering, uncertainties in physical properties and modeling discrepancies can generate errors. Among various model calibration approaches, Kennedy and O’Hagan (KOH)’s Bayesian model calibration is noted for its ability to consider a variety of sources of uncertainty. However, one of the difficulties in KOH’s Bayesian model calibration is the complexity of determining the prior distributions of hyperparameters, which is often challenging in real-world problems due to insufficient information. Most previous studies have relied on users’ intuition to mitigate this issue. Thus, this study proposes a statistical prior modeling method for the correlation hyperparameter of a model discrepancy, which affects the calibration performance. In this work, a radius-uniform distribution is introduced as a prior distribution of the correlation hyperparameter based on the properties of the Gaussian process. Three case studies are provided, one numerical and two engineering cases, to confirm that the proposed method results in lower error than any other previously proposed distribution without additional computational cost. Further, the proposed method does not require user-dependent knowledge, which is a significant advantage over previous methods.