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

[+] Author and Article Information
H. Sarin, M. Kokkolaras, G. Hulbert, P. Papalambros

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-1316

S. Barbat, R.-J. Yang

Passive Safety, Research and Advanced Engineering, Ford Motor Company, Highland Park, MI 48203-3177

J. Dyn. Sys., Meas., Control 132(6), 061401 (Oct 28, 2010) (10 pages) doi:10.1115/1.4002478 History: Received September 15, 2008; Revised May 12, 2010; Published October 28, 2010; Online October 28, 2010

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.

Copyright © 2010 by American Society of Mechanical Engineers
Topics: Errors
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Figure 1

Time history examples

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Figure 2

Failure of S&G metric to quantify error due to magnitude

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Figure 3

DTW results for time histories 1 and 2

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Figure 4

DTW results for time histories 1 and 3

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Figure 5

Example to compare S&G phase measure to cross-correlation

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Figure 6

Illustration of DTW effect on time histories: (top) time histories before DTW and (bottom) time histories after DTW

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Figure 7

Computational results and test data for head impactor displacement (top), head acceleration in the x-direction (middle), and neck force in the x-direction (bottom)

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Figure 8

Sample of results for head impact case

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Figure 9

A typical plot presented to the SMEs

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Figure 10

Regression-based validation metric: data fit and test

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Figure 11

Comparison of EARTH to other metrics




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