SOBOL’ MAIN EFFECT SENSITIVITY ANALYSIS BASED ON ACTIVE SUBSPACE

Numerous uncertainties exist in practical engineering problems. Quantifying the sensitivity of system responses to various uncertain factors is of great significance for guiding design optimization. Variance decomposition-based sensitivity analysis is a widely used global sensitivity analysis method in engineering. Nevertheless, the calculation of Sobol’ main effect indices frequently suffers from the “curse of dimensionality”. For instance, the computational cost of the conventional single-loop Monte Carlo (MC) method is linearly correlated with the dimensionality of input variables. Recently, the authors proposed the dimension-independent single-loop MC method, which can drastically reduce the number of deterministic model evaluations. However, for high-dimensional and strongly nonlinear cases, the estimation results are highly dependent on samples, and a large sample size is generally required to mitigate results’ variability. This paper first reviews the theory of variance decomposition-based sensitivity analysis, as well as the conventional single-loop MC method and the dimension-independent single-loop MC method for calculating Sobol’ main effect indices. On this basis, a novel method combining the active subspace and k-nearest neighbor (KNN) algorithm is proposed to compute Sobol’ main effect indices. In this method, a small number of samples are first adopted to calculate the gradient covariance matrix for extracting the active subspace. Based on retaining the fastest variation of the gradient of system responses with respect to uncertain inputs, the high-dimensional input space is projected onto a low-dimensional manifold. Subsequently, the KNN algorithm is employed to enrich sample points within regions on the low-dimensional manifold, enabling the estimation of Sobol’ main effect indices with a small sample size. Four numerical examples are utilized to verify the computational efficiency and accuracy of the proposed method, including the classical Sobol’ nonlinear function, water flow model through the borehole, detonation pressure calibration uncertainty model and Golinski gear reducer model. The results demonstrate that the proposed method can effectively improve the computational efficiency of global sensitivity analysis for nonlinear systems while maintaining acceptable accuracy.