Statistical model calibration of correlated unknown model variables through identifiability improvement

A statistical model calibration problem is known to have unstable or non-unique optimal solutions due to its ill-posed inverse nature, which is further complicated by limited test data availability due to time and cost constraints. To overcome these challenges and improve the identifiability of calibration parameters, this study proposes a novel statistical model calibration framework. The proposed method integrates input test data for unknown model variables and output test data for a system response, employing a bivariate form of copula function to model the probability distribution while accounting for the correlations between unknown model variables. Furthermore, a sample-averaged log-likelihood is used as a calibration metric, assuming conditional independence to reflect input and output test data evenly in a single metric. Optimization-based model calibration (OBMC) is performed to identify the probability models that maximize the calibration metric for a given set of input and output test data, among candidates of marginal probability distributions and copula functions. Consequently, this proposed method enhances the identifiability of calibration parameters and overcomes insufficient data issues by taking observations of unknown model variables into account in the statistical model calibration procedure. The proposed framework is validated using numerical examples.