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An inequality unscented transformation for estimating the statistical moments

机译：用于估计统计矩的不等式无味变换

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摘要

Point estimate method (PEM) is convenient for estimating statistical moments. This paper focuses on discussing the existing PEMs and presenting a new PEM for the efficient and accurate estimation of statistical moments. Firstly, a classification method of PEMs is proposed based on the strategy of choosing sigma points. Secondly, the minimum number of sigma points and the error of inverse Nataf transformation are derived corresponding to certain order and dimensionality of PEMs. Then the inequality unscented transformation (IUT) is presented to estimate the statistical moments. The proposed IUT permits the existing of limited errors in the matching of the first several order moments to decrease the number of sigma points, it opens new strategy of PEMs. The proposed method has two advantages. The first advantage is overcoming the growth of the number of sigma points with dimensionality since it parameterizes the number of sigma points and accuracy order. The second advantage is the wide applicability, for it has the ability to handle correlated and asymmetric random input variables and to match cross moments. Numerical and engineering results show the good accuracy and efficiency of the proposed IUT.
机译：点估计方法（PEM）方便用于估计统计矩。本文着重讨论现有的PEM，并提出一种新的PEM，以高效，准确地估计统计矩。首先，基于选择西格玛点的策略，提出了一种PEM的分类方法。其次，根据PEM的一定阶次和维数，推导了最小的sigma点数和Nataf逆变换的误差。然后，提出不等式无味变换（IUT）以估计统计矩。提出的IUT允许在前几个阶矩的匹配中存在有限的误差，以减少sigma点的数量，这为PEM开辟了新的策略。所提出的方法具有两个优点。第一个优点是克服了sigma点数量随维数的增长，因为它参数化了sigma点数量和精度顺序。第二个优点是广泛的适用性，因为它具有处理相关和非对称随机输入变量并匹配交叉矩的能力。数值和工程结果表明，所提出的IUT具有良好的精度和效率。

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