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

摘要

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