New Bayesian Updating Methodology for Model Validation and Robust Predictions Based on Data from Hierarchical Subsystem Tests
2008
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.
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