Global sensitivity analysis for multivariate outputs using generalized RBF-PCE metamodel enhanced by variance-based sequential sampling

Abstract

The mathematical and computational models in engineering applications commonly have multiple outputs, so it is critical to develop global sensitivity analysis (GSA) for multivariate outputs, which can be used to explore the effect of input parameters on output responses. Amongst the existing sensitivity analysis, the covariance-based method is one of the most widely used methods due to its understandability and validity. However, traditional GSA is calculated by Monte Carlo Simulation (MCS), leading to huge computational cost and large sample demand. In this study, the generalized hybrid metamodel using radial basis function (RBF) and sparse polynomial chaos expansion (PCE) is applied for covariance-based GSA. To improve the efficiency and performance of RBF-PCE in mult-models, an efficient sequential sampling method is proposed based on the local variance density of sample points. Three analytical functions and two engineering problems are employed to demonstrate the accuracy and validity of the proposed method. The results indicate that the proposed method has a significant improvement in accuracy and efficiency compared with the existing GSA methods, and the sample demand is reduced by three orders of magnitude compared with MCS-based Sobol' indices.