A new method for model validation with multivariate output

Traditional methods for model validation assessment mainly focus on validating a single response. However, for many applications joint predictions of the multiple responses are needed. It is thereby not sufficient to validate the individual responses separately, which ignores correlation among multiple responses. Validation assessment for multiple responses involves comparison with multiple experimental measurements, which makes it much more complicated than that for single response. With considering both the uncertainty and correlation of multiple responses, this paper presents a new method for validation assessment of models with multivariate output. The new method is based on principal component analysis and the concept of area metric. The method is innovative in that it can eliminate the redundant part of multiple responses while reserving their main variability information in the assessment process. This avoids directly comparing the joint distributions of computational and experimental responses. It not only can be used for validating multiple responses at a single validation site, but also is capable of dealing with the case where observations of multiple responses are collected at multiple validation sites. The new method is examined and compared with the existing u-pooling and t-pooling methods through numerical and engineering examples to illustrate its validity and potential benefits.