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Computer programs and models are playing an increasing role in simulating vehicle crashworthiness, dynamic, and fuel efficiency. To maximize the effectiveness of these models, the validity and predictive capabilities of these models need to be assessed quantitatively. For a successful implementation of Computer Aided Engineering (CAE) models as an integrated part of the current vehicle development process, it is necessary to develop objective validation metric that has the desirable metric properties to quantify the discrepancy between multiple tests and simulation results. However, most of the outputs of dynamic systems are multiple functional responses, such as time history series. This calls for the development of an objective metric that can evaluate the differences of the multiple time histories as well as the key features under uncertainty.

To date, model validation metric is prominently designed for non-dynamic model responses. Though metrics for dynamic responses are also available, they are specifically designed for the vehicle impact application and uncertainties are not considered in the metric. This paper proposes the validation metric for general dynamic system responses under uncertainty. The metric makes use of the popular U-pooling approach and extends it for dynamic responses. Furthermore, shape deviation metric was proposed to be included in the validation metric with the capability of considering multiple dynamic test data. One vehicle impact model is presented to demonstrate the proposed validation metric.