Bayesian Probabilistic PCA Approach for Model Validation of Dynamic Systems

In the automobile industry, the reliability and predictive capabilities of computer models for a dynamic system need to be assessed quantitatively. Quantitative validation allows engineers to assess and improve model reliability and quality objectively and ultimately lead to potential reduction in the number of prototypes built and tests. A good metric, which is essential in model validation, requires considering uncertainties in both testing and computer modeling. In addition, it needs to be able to compare multiple responses simultaneously, as multiple quantities are often encountered at different spatial and temporal points of a dynamic system. In this paper, a state-of-the-art validation technology is developed for multivariate complex dynamic systems by exploiting a probabilistic principal component analysis method and Bayesian statistics approach. The probabilistic principal component analysis approach is developed to address multivariate correlation, data uncertainty, and dimensionality reduction. The multivariate Bayesian hypothesis testing method is exploited to quantitatively assess the quality of the computer models for dynamic systems. The proposed method is illustrated with a rear seat child restraint system example with a Hybrid III 3-year old child dummy model, consisting of sixteen sets of test data each having nine response variables.