A Top-Down Method For Uncertainty Quantification And Predictive Accuracy Assessment

Analytical models are used in engineering science to simulate a host of physical phenomena ranging from the constitutive behavior of materials to manufacturing processes to the static and dynamic performance of components and systems under a variety of environmental conditions. Numerical simulations are increasingly used to replace prototype testing in the development of new products, and must be relied upon when testing is impractical or impossible. The predictive accuracy of a model has been defined as the accuracy of model simulations, or predictions, under conditions for which the model has not been subjected to direct experimental verification. This paper addresses a "top-down" method for predictive accuracy assessment based on the statistical analysis of direct comparisons between physical observations and corresponding model predictions for generically similar sets of analysis-test data. Unlike traditional "bottom-up" methods based on the propagation of only parametric uncertainty through a model, this approach captures all sources of uncertainty represented in the generic database, i.e., "total uncertainty." This generic uncertainty model will include experimental uncertainty to the extent that it has not been separately quantified on the basis of replicate tests and removed from the estimate of total uncertainty, and model form uncertainty to the extent that various models are included in the database. The generic uncertainty model can be propagated by various means through a particular model belonging to the same generic category, whether or not the model has been included in the generic database, to assess the predictive accuracy of the model based on past experience. In this way, the predictive accuracy of future models, e.g. future models of systems not yet built or tested, may be assessed. A practical example is given.