Bayesian Based Model Validation Method for Uncertain Multivariate Dynamic Systems under Virtual Prototype Environment

Abstract

In the virtual prototype environment,validation of computational models with multiple and correlated functional responses under uncertainty requires the consideration of multivariate data correlation,uncertainty quantification and propagation,and objective robust metrics.It presents a Bayesian based model validation method,together with statistic error analysis,probabilistic principal component analysis(PPCA),and subjective matter experts' based threshold definition and transformation,to address these critical issues.The statistic error analysis is used to quantify the errors from the repeated test data and computational simulation results.The PPCA is employed to handle multivariate correlation and to reduce the dimension of the multivariate functional responses.The subjective matter experts' based threshold definition and transformation is used to decide the threshold interval in the reduced data space.The Bayesian interval hypothesis testing is used to quantitatively assess the quality of a multivariate dynamic system.The differences between the average test data and computer simulation results are extracted for dimension reduction,and then Bayesian interval hypothesis testing is performed on the reduced difference data to assess the model validity.In addition,physics-based threshold is defined and transformed to the reduced space for Bayesian interval hypothesis testing.This new approach resolves some critical drawbacks of the previous methods and adds some desirable properties of a model validation metric for uncertain dynamic systems,such as symmetry.A real-world dynamic system with multiple,repeated functional responses is used to demonstrate this new approach,and shows its potential in promoting the continual improvement of virtual prototype testing.