A new calibration metric that considers statistical correlation: Marginal Probability and Correlation Residuals

Computer-aided engineering (CAE) models have been indispensable to virtual testing for designing and evaluating engineered systems to satisfy reliability requirements. However, it is not easy to fully characterize the variability in the model input variables due to limited resources. Statistical model calibration is thus of great importance as a strategy to improve the predictive capability of a CAE model. Optimization-based statistical model calibration is formulated as an unconstrained optimization problem that infers the unknown statistical parameters of input variables associated with a CAE model by maximizing statistical similarity between predicted and observed output responses. A calibration metric is defined as the objective function to be maximized that quantifies statistical similarity. One important challenge in formulating a calibration metric is how to properly consider the statistical correlation in output responses. Thus, this study proposes a new calibration metric: The Marginal Probability and Correlation Residual (MPCR). The foundational idea of the MPCR is to decompose a multivariate joint probability distribution into multiple marginal probability distributions, while considering the statistical correlation between output responses. The MPCR has favorable properties, such as normalization, boundedness, and marginalization. Two mathematical and two engineering examples are presented to demonstrate the effectiveness and potential benefits of the MPCR.