Statistical model calibration considering identifiability under insufficient data environment

Abstract

The reliability-based design optimization (RBDO) using computer-aided engineering (CAE) simulations is a significant methodology for solving engineering problems. However, combining reliability analysis and optimization algorithms can lead to cost and time inefficiencies, and also accurate distribution modeling of input variables is necessary beforehand. Since the accuracy of the simulation model depends on the model parameters used, improving the accuracy of the simulation model involves calibrating the model parameters to minimize differences from observed output data. Although statistical model calibration (SMC) methods are being actively studied to overcome the limitations of the existing deterministic approach, these methods can face problems due to a limited amount of data and the problem of identifiability. To address these issues, this dissertation proposes a framework that can use all available input and output data for statistical model calibration to improve identifiability under an insufficient data environment. The proposed framework uses the Bayesian approach, where a prior distribution estimation step is followed by a posterior distribution estimation step. The calibration domain is moved from the existing model parameter domain to the statistical parameter domain of the model parameters to enable conservative estimation. Even in the case of an unidentifiable problem, the input data is reflected in the model calibration process to improve identifiability. Optimization-based model calibration (OBMC) is performed using the sample-averaged log-likelihood as a calibration metric, with the copula function used to characterize the model parameters as a multivariate probability distribution. Finally, the statistical model validation (SMV) of the estimated distribution also includes the concept of leave-p-out cross-validation (LpOCV), which takes into account the lack of data and ensures that the variability of the given data is reflected in the validation results. This approach complements the existing hypothesis testing utilizing the u-pooling metric and enables a quantitative comparison of the performance of the proposed model calibration algorithm. Various numerical examples confirm that the proposed methods effectively estimate the distribution of model parameters, even in a data-insufficient environment, while improving identification.