Shen, Z., Chen, X., He, Q., and Zang, C., "Study on Area Metric Based upon Multiple Correlated System Response Quantities," SAE Technical Paper 2015-01-0454, 2015, doi:10.4271/2015-01-0454.
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. As a result, it not only makes SRQs uncorrelated, and also greatly decreases computational cost. Furthermore, numerical examples and an example with engineering background are performed to illustrate the validity and reasonability of the method proposed in this paper.