MODEL VALIDATION FOR SIMULATIONS OF VEHICLE SYSTEMS

This paper deals with model validation of dynamic systems (with vehicle systems being of particular interest) that have multiple time-dependent output. First, we review several validation methodologies that have been reported in the literature: graphical comparison, feature-based techniques, PDF/CDF based techniques, Bayesian posterior estimation, classical hypothesis testing and Bayesian hypothesis testing. We discuss their advantages and disadvantages in terms of several attributes: applicability to different types of models, need for assumptions, computational cost, subjectivity, propensity to type-I or II errors, and others. We then proceed with the most important attribute: can the validation method provide a quantitative measure of the goodness of the model? We conclude that Bayesian-based model validation frameworks answer this question positively. A bootstrap method is presented that obviates the need to assume a statistical distribution model. The features of the Bayesian validation framework are illustrated using a thermal benchmark problem developed by Sandia National Laboratories and a battery model developed in the Automotive Research Center, a US Army Center of Excellence for modeling and simulation of ground vehicle systems.