Zhan, Z., Yang, J., Chen, X., and Shen, Z., "An Integrated Validation Method for Nonlinear Multiple Curve Comparisons," SAE Int. J. Mater. Manf. 9(2):355-360, 2016, doi:10.4271/2016-01-0288.
In automobile industry, computational models built to predict the performances of the prototype vehicles are on the rise. To assess the validity or predictive capability of the model for its intended usage, validation activities are conducted to compare computational model outputs with test measurements. Validation becomes difficult when dealing with dynamic systems which often involve multiple functional responses, and the complex characteristics need to be appropriately considered. Many promising data analysis tools and metrics were previously developed to handle data correlation and evaluate the errors in magnitude, phase shift, and shape. However, these methods show their limitations when dealing with nonlinear multivariate dynamic systems. In this paper, kernel function based projection is employed to transform the nonlinear data into linear space, followed by the regular principal component analysis (PCA) based data processing. The agreement between the reduced test and model outputs are then evaluated based on the validation metric of EEARTH. The proposed strategy helps to better represent the original data after dimension reduction, which improves the credibility of the afterwards multivariate validation. A vehicle design case is employed to demonstrate the effectiveness and advantages of the proposed method.