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首页> 外文期刊>Applied Mathematical Modelling >An improved high order moment-based saddlepoint approximation method for reliability analysis
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An improved high order moment-based saddlepoint approximation method for reliability analysis

机译：改进的基于高阶矩的鞍点逼近方法用于可靠性分析

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摘要

Moment-based methods use only statistical moments of random variables for reliability analysis. The cumulative distribution function (CDF) or probability density function (PDF) of a performance function can be constructed from the perspective of the first few statistical moments, and the failure probability can be evaluated accordingly. However, existing moment-based methods may lead to large errors or instability. As such, the present paper focuses on the high order moment method for higher accuracy of reliability estimation by combining the common saddlepoint approximation technique, and an improved high order moment-based saddlepoint approximation (SPA) method for reliability analysis is presented. The approximated cumulant generating function (CGF) and the CDF of the performance function in terms of its first four statistical-moments are constructed. The developed method can be used for reliability evaluation of uncertain structures follow any types of distribution. Several numerical examples are given to demonstrate the efficacy and accuracy of the proposed method. Comparisons of the new method and several existing high order moment methods are also made on the reliability assessment.
机译：基于矩的方法仅使用随机变量的统计矩进行可靠性分析。可以从前几个统计矩的角度构造性能函数的累积分布函数（CDF）或概率密度函数（PDF），并可以据此评估故障概率。但是，现有的基于矩量的方法可能会导致较大的错误或不稳定。因此，本文重点研究了高阶矩方法，通过结合常用的鞍点逼近技术提高了可靠性，并提出了一种改进的基于高阶矩的鞍点逼近（SPA）方法进行可靠性分析。根据前四个统计矩，构造了近似累积量生成函数（CGF）和性能函数的CDF。所开发的方法可用于不确定结构遵循任何类型分布的可靠性评估。给出了几个数值例子，以证明该方法的有效性和准确性。在可靠性评估上，还对新方法和几种现有的高阶矩方法进行了比较。

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