LAUSR

Abstract Variance-based sensitivity analysis (SA) has been frequently applied to dynamic models with multivariate output. The generalized sensitivity indices are defined by combining principal components analysis with analysis of variance to synthesize the influence of each input on the whole dynamic output. In order to efficiently perform global SA on dynamic models, two efficient algorithms based on cubature formula are proposed in this paper to estimate these generalized variance-based sensitivity indices. The new algorithms are double-loop nested cubature formula (DLCF) and single loop cubature formula (SLCF). The DLCF method estimates the sensitivity indices by decreasing the dimensionality of the input variables procedurally, while SLCF method performs SA through extending the dimensionality of the inputs. Both of them can make full use of the advantages of the cubature formula, and provide efficient estimates for the generalized variance-based sensitivity indices. The numerical and engineering examples demonstrate that both the proposed algorithms can avoid the expensive computational cost associated with the sampling methods, and improve the SA of the dynamic models significantly.