A novel hybrid cubature formula with Pearson system for efficient moment-based uncertainty propagation analysis. (June 2020) - Xu, Jun; Zhang, Yu; Dang, Chao
Highlights: A hybrid cubature formula is proposed for efficient statistical moments assessment. Contribution-degree analysis is performed to detect the significant variables. The original integral can be decomposed as lower-dimensional integrals. Lower-dimensional integrals are separately evaluated by different schemes. Numerical examples demonstrates the accuracy and efficiency of the proposed method. Abstract: In this paper, a novel hybrid cubature formula is proposed for moment-based uncertainty propagation analysis. First, the contribution-degree analysis is performed to classify the input random vector of the response function into two separate parts, i.e. the more important one and less important one. In this regard, the statistical moment of the response function, which is a multi-dimensional Gaussian-weighted integral, can be decomposed into one lower-dimensional Gaussian-weighted integral and several one-dimensional Gaussian-weighted integrals, accordingly. Then, the hybrid cubature formula can be established for the first-four statistical moments assessment of the response function such that a mixed-degree cubature formula is employed to evaluate the lower-dimensional integral and the five-point Gauss-Hermite quadrature is adopted for obtaining the one-dimensional integrals. By doing so, the trade-off of accuracy and efficiency for statistical moments assessment can be ensured. Finally, the Pearson system is employed to reconstruct the probability density function of the response function. Five numerical examples are investigated to demonstrate the performance of the proposed method for uncertainty propagation analysis, where pertinent Monte Carlo simulations are also conducted for comparisons. It is found that the proposed method can achieve a good accuracy for evaluating the first-four central moments of the response function as well as its entire distribution of the probability density function with high efficiency.