Framework for Validation of Computer Models Applied to a Resistance Spot Weld Model

We view the most important question in evaluation of a computer model to be: Does the computer model provide predictions that are accurate enough for the intended use of the model? The purpose of this presentation is to discuss a systematic six-step model validation process intended to help answer that question. This will be done by presenting a Bayesian statistical strategy for developing error bounds on model predictions with the interpretation that there is a specified confidence (e.g. 80%) that the corresponding true process value will lie within the range of these error bounds. Although seldom done in practice, such error bounds and confidence estimates should be provided whenever model predictions are made. A Caveat: The process of model validation is inherently a hard statistical problem. The statistical problem is so hard that one rarely sees model validation approaches that actually produce error bounds and confidence estimates on computer model predictions. The intent of this presentation is essentially to provide a ‘proof of concept’, that it is possible to provide such bounds and estimates for predictions of computer models, while taking into account all of the uncertainties present in the problem. However, the computations required in the methodology we propose can be intensive, especially when there are large numbers of model inputs, large numbers of unknown parameters, or a large amount of data (model-run or field). The test bed application we consider in this presentation (a resistance spot weld model) is relatively modest in these dimensions. Finally, we call the reader’s attention to the reference, Bayarri et. al. (2002). This reference provides a down-loadable PDF file that contains a technical report presenting all of the technical details associated with our proposed validation strategy as well as practical application of the strategy to the spot weld model described in this presentation as well as to an automobile crash model.