Model validation with multivariate responses via factor analysis

Abstract

Computational models have been widely applied to simulate complex physical phenomena because of rapid development of computers’ abilities and inexecutable conditions of the experiments. Validating the effectiveness of computational models is then essential and significant. Existing validation metrics focusing on a single response may cause confusing results when they are applied for multiple responses simultaneously. The target of this work is to validate computational models with multiple responses via the factor analysis method by considering both the uncertainty and correlation of the multiple responses. Factor analysis aims to explain the correlated multi-dimensional variables with fewer common factors and the latter then can describe the main information the former containing. Briefly, factor analysis has a favorable ascendency——dimensionality reduction, which makes multiple responses validation easy to implement. The proposed method is based on the factor analysis and the concept of “area metric” for validating a single response, which avoids comparing the joint distribution of the computational models and that of the experimental observations. It is applicable for validating multiple responses both at a single validation site and at multiple validation sites. Both numerical example and engineering example are employed to demonstrate the rationality and necessity of the proposed methodology.