Optimal design of experiments for optimization-based model calibration using Fisher information matrix

Highlights: • A framework is developed to find the optimal design of experiments (DoE) in statistical model calibration. • Both aleatory uncertainty and epistemic uncertainty are taken into account. • Hessian matrix of loglikelihood for kernel density estimation (KDE) is derived. • Observed Fisher information is exploited to quantify the epistemic uncertainty of estimation. • DoE optimization is formulated as integer programming using expected Fisher information for each experimental design. Statistical model calibration to infer unknown model parameters and model bias has been widely developed through comparison between simulation response and experimental data. Bayesian-based model calibration typically represented as Kennedy and O'Hagan (KOH) framework and optimization-based model calibration have been proposed, but efforts on optimization of experimental design to reduce the epistemic uncertainty minimizing experimental resources are still limited. Furthermore, when an unknown model parameter has natural and uncontrollable variability, the estimation may be much more difficult since both aleatory and epistemic uncertainties exist. In this paper, we have developed a framework to find the optimal design of experiments (DoE) satisfying the target information gain for inference of unknown model parameters based on optimization-based model calibration. The expected Fisher information matrix is approximated to quantify the expected information gain for the maximum likelihood estimation (MLE). Namely, the necessary number of experiments at each experimental design can be obtained to attain desired precision on estimators while minimizing the overall experimental cost. The numerical study verifies the feasibility of the proposed framework, which means that there is certainly a dominant DoE that gives more information to the inference on specific model parameters.