Model validation method with multivariate output based on kernel principal component analysis

At present, for the multiple correlated complex computational models with uncertainty, the traditional validation methods still have some problems, such as difficult calculation and poor stability.Aimed at such complex computational models, a new multivariate model validation method is proposed based on kernel principal component analysis (KPCA). By combining the KPCA with the idea of area metric, the proposed method constructs a new model validation metric which is easy to be calculated and has high stability. In proposed method, the correlated multivariate output variables are transformed into uncorrelated kernel principal component by the KPCA, and then for each kernel principal component, the computational model is compared with the experiment. Thus this method avoids the difficulties of solving the joint cumulative distribution function of multivariate output in the traditional methods. Because the KPCA can effectively extract the nonlinear characteristic of the analyzed model, the multivariate output model validation method based on the KPCA is more robust than that based on the principal component analysis (PCA). Under the same experiment sample data, the method based on the KPCA has a lower error rate than that based on PCA. Furthermore, by extracting the kernel principal component, dimensionality reduction of the multivariate output can be implemented; thereby the complexity of the multivariate output validation can also be reduced. The proposed method can be applied not only to the general multivariate output model validation, but also to the model validation with multiple validation sites. Finally, the correctness and effectiveness of the proposed method are demonstrated by the numerical and engineering examples.