A Comprehensive Metric for Comparing Time Histories in Validation of Simulation Models With Emphasis on Vehicle Safety Applications

Computer modeling and simulation are the cornerstones of product design and development in the automotive industry. Computer-aided engineering tools have improved to the extent that virtual testing may lead to significant reduction in prototype building and testing of vehicle designs. In order to make this a reality, we need to assess our confidence in the predictive capabilities of simulation models. As a first step in this direction, this paper deals with developing a metric to compare time histories that are outputs of simulation models to time histories from experimental tests with emphasis on vehicle safety applications. We focus on quantifying discrepancy between time histories as the latter constitute the predominant form of responses of interest in vehicle safety considerations. First we evaluate popular measures used to quantify discrepancy between time histories in fields such as statistics, computational mechanics, signal processing, and data mining. Then we propose a structured combination of some of these measures and define a comprehensive metric that encapsulates the important aspects of time history comparison. The new metric classifies error components associated with three physically meaningful characteristics (phase, magnitude and topology), and utilizes norms, cross-correlation measures and algorithms such as dynamic time warping to quantify discrepancies. Two case studies demonstrate that the proposed metric seems to be more consistent than existing metrics. It is also shown how the metric can be used in conjunction with ratings from subject matter experts to build regression-based validation models.