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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.

Area metric provides a quantitative measure which characterizes the disagreement of numerical predictions and experimental observations. It is defined as the area between the prediction distribution and the data distribution as a kind of global measure of the mismatch between them. U-pooling method, which obtains area metric based upon multiple System Response Quantities (SRQs), is adopted to increase the credibility of metrics. However, the multiple SRQs are required to be independent in u-pooling method, which usually cannot be satisfied in practice. If the area metric is obtained in directly u-pooling method without considering the correlation of the SRQs in engineering applications, the metric would not factually express the disagreement of numerical simulation and experimental observation and it may be unreliable. In this paper, principle component analysis is introduced to remove the correlation of SRQs firstly, and then u-pooling method is applied to get the area metric.