Model Validation Methods for Multiple Correlated Responses via Covariance-Overlap Based Distance

Model validation methods have been widely used in engineering design to provide a quantified assessment of the agreement between simulation predictions and experimental observations. For the validation of simulation models with multiple correlated outputs, not only the uncertainty of the responses but also the correlation between them needs to be considered. Most of the existing validation methods for multiple correlated responses focus on the area metric, which only compares the overall area difference between the two cumulative probability distribution curves. The differences in the distributions of the data sets are not fully utilized. In this paper, two covariance-overlap based model validation (COMV) methods are proposed for the validation of multiple correlated responses. The COMV method is used for a single validation site, while the covariance-overlap pooling based model validation (COPMV) method can pool the evidence from different validation sites into a scalar measure to give a global evaluation about the candidate model. The effectiveness and merits of the proposed methods are demonstrated by comparing with three different existing validation methods on three numerical examples and a practical engineering problem of a turbine blade validation example. The influence of sample size and the number of partitions in the proposed methods are also discussed. Results show that the proposed method shows better performance on the uncertainty estimation of different computational models, which is useful for practical engineering design problems with multiple correlated responses.