Publications Details

Validation of mathematical models using weighted response measures

Paez, Thomas L.; Massad, Jordan M.; Hinnerichs, Terry D.; O'Gorman, Christian C.; Hunter, Patrick H.

Advancements in our capabilities to accurately model physical systems using high resolution finite element models have led to increasing use of models for prediction of physical system responses. Yet models are typically not used without first demonstrating their accuracy or, at least, adequacy. In high consequence applications where model predictions are used to make decisions or control operations involving human life or critical systems, a movement toward accreditation of mathematical model predictions via validation is taking hold. Model validation is the activity wherein the predictions of mathematical models are demonstrated to be accurate or adequate for use within a particular regime. Though many types of predictions can be made with mathematical models, not all predictions have the same impact on the usefulness of a model. For example, predictions where the response of a system is greatest may be most critical to the adequacy of a model. Therefore, a model that makes accurate predictions in some environments and poor predictions in other environments may be perfectly adequate for certain uses. The current investigation develops a general technique for validating mathematical models where the measures of response are weighted in some logical manner. A combined experimental and numerical example that demonstrates the validation of a system using both weighted and non-weighted response measures is presented.