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A novel hybrid cubature formula with Pearson system for efficient moment-based uncertainty propagation analysis

机译：基于Pearson系统的新型混合培养公式，用于基于矩的有效不确定性传播分析

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摘要

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.
机译：在本文中，提出了一种新颖的混合培养公式，用于基于矩的不确定性传播分析。首先，进行贡献度分析以将响应函数的输入随机向量分类为两个单独的部分，即，较重要的部分和较不重要的部分。在这方面，响应函数的统计矩是多维高斯加权积分，因此可以分解为一个低维高斯加权积分和几个一维高斯加权积分。然后，可以建立用于响应函数的前四个统计矩评估的混合孵化公式，从而使用混合度孵化公式来评估低维积分，并采用五点高斯-赫尔姆特积分获得一维积分。通过这样做，可以确保用于统计矩评估的准确性和效率之间的权衡。最后，采用Pearson系统重建响应函数的概率密度函数。研究了五个数值示例，以证明所提出的方法用于不确定性传播分析的性能，其中还进行了相关的蒙特卡洛模拟以进行比较。结果表明，所提出的方法能够高效地评估响应函数的前四个中心矩及其概率密度函数的整体分布。

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