Global sensitivity analysis with a hierarchical sparse metamodeling method

To meet the numerical challenges of polynomial chaos expansion for global sensitivity analysis in high stochastic dimensions, this paper proposes a new metamodeling method named hierarchical sparse partial least squares regression-polynomial chaos expansion (HSPLSR-PCE). Firstly, to avoid large data sets, the polynomials are divided into groups according to their nonlinearity degrees and interaction intensities (number of inputs). Then, to circumvent the multicollinearity, latent variables are extracted from each group by using partial least squares regression. Next, the optimal latent variables are automatically selected with the penalized matrix decomposition scheme. Finally, the Sobol sensitivity indices are straightforwardly derived from the expansion coefficients. Results of three examples demonstrate that the proposed method is superior to the traditional counterpart in terms of computational efficiency and accuracy.