Statistical model calibration and design optimization under aleatory and epistemic uncertainty

Statistical model calibration is a framework for inference on unknown model parameters and modeling discrepancy between simulation and experiment through an inverse method in the presence of uncertainty. Most of the existing approaches cannot treat aleatory uncertainty of model parameters and model discrepancy simultaneously, and thus reliability analysis and design optimization using a calibrated simulation model accounting for uncertainty have been limitedly applied. Therefore, a statistical model calibration using stochastic Kriging accounting for the aleatory uncertainty of model parameters is proposed in this paper. The probability distributions of the model parameters and corresponding discrepancy are quantified and estimated through the maximum likelihood estimation (MLE). Since it may be difficult to secure sufficient experimental data for model calibration due to limited resources, the quantification of epistemic uncertainty on the calibrated model and propagation to reliability are also presented. Then, the design optimization accounting for aleatory and epistemic uncertainty, which is called confidence-based design optimization (CBDO), can yield the conservative optimum to prevent the unexpected failure. In conclusion, the proposed framework facilitates the statistical model calibration and design optimization under aleatory uncertainty of model parameters and model discrepancy and epistemic uncertainty caused by insufficient data.