Global sensitivity analysis for multivariate outputs using polynomial chaos-based surrogate models

We propose an efficient global sensitivity analysis method for multivariate outputs that applies polynomial chaos-based surrogate models to vector projection-based sensitivity indices. These projection-based sensitivity indices, which are powerful measures of the comprehensive effects of model inputs on multiple outputs, are conventionally estimated by the Monte Carlo simulations that incur prohibitive computational costs for many practical problems. Here, the projection-based sensitivity indices are efficiently estimated via two polynomial chaos-based surrogates: polynomial chaos expansion and a proper orthogonal decomposition-based polynomial chaos expansion. Several numerical examples with various types of outputs are tested to validate the proposed method; the results demonstrate that the polynomial chaos-based surrogates are more efficient than Monte Carlo simulations at estimating the sensitivity indices, even for models with a large number of outputs. Furthermore, for models with only a few outputs, polynomial chaos expansion alone is preferable, whereas for models with a large number of outputs, implementation with proper orthogonal decomposition is the best approach.