New Bayesian Updating Methodology for Model Validation and Robust Predictions Based on Data from Hierarchical Subsystem Tests

Abstract

In many engineering applications, it is a formidable task to construct a mathematical model that is expected to produce accurate predictions of the behavior of a system of interest. During the construction of such predictive models, errors due to imperfect modeling and uncertainties due to incomplete information about the system and its input always exist and can be accounted for appropriately by using probability logic. Often one has to decide which proposed candidate models are acceptable for prediction of the target system behavior. In recent years, the problem of developing an effective model validation methodology has attracted attention in many different fields of engineering and applied science. Here, we consider the problem where a series of experiments are conducted that involve collecting data from successively more complex subsystems and these data are to be used to predict the response of a related more complex system. A novel methodology based on Bayesian updating of hierarchical stochastic system model classes using such experimental data is proposed for uncertainty quantification and propagation, model validation, and robust prediction of the response of the target system. After each test stage, we use all the available data to calculate the posterior probability of each stochastic system model along with the quality of its robust prediction. The proposed methodology is applied to the 2006 Sandia static-frame validation challenge problem to illustrate our approach for model validation and robust prediction of the system response. Recently-developed stochastic simulation methods are used to solve the computational problems involved.