Comparing Time Histories for Validation of Simulation Models: Error Measures and Metrics

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 measures and a metric to compare time histories obtained from simulation model outputs and experimental tests. The focus of the work is on vehicle safety applications. We restrict attention to 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. Three independent error measures are proposed for vehicle safety applications, associated with three physically meaningful characteristics (phase, magnitude, and slope), which utilize norms, cross-correlation measures, and algorithms such as dynamic time warping to quantify discrepancies. A combined use of these three measures can serve as a metric that encapsulates the important aspects of time history comparison. It is also shown how these measures can be used in conjunction with ratings from subject matter experts to build regression-based validation metrics.