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On the use of the maximum entropy method for reliability evaluation involving stochastic process modeling
Structural Safety ( IF 5.8 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.strusafe.2020.102028
Fan Wang , Heng Li

Abstract From a probabilistic perspective, a stochastic process (or random field) is completely specified by its joint probability distribution, which can be further decomposed into marginal distributions and a multivariate copula function. This paper proposes a non-parametric approach based on the maximum entropy theory to build the two parts of the distribution of stochastic processes. The specification of a stochastic process is interpreted as moment constraints and classified into two categories. The first category describes the uncertainty of the random quantity at an arbitrary point. The second category defines the dependence between the random quantities at any two points. The marginal distribution and copula function are then developed by maximizing the entropy under two classes of constraints, which are formulated as two optimization problems. The proposed method is applied to two reliability problems: a beam reliability evaluation considering time-dependent corrosion, and a tunnel reliability evaluation considering soil spatial variability. The first example illustrates the method when only partial information (marginal distribution and autocorrelation function) is available, while the second example shows the development of a random field model based on data. The comparison of the non-parametric approach with typical parametric models indicates the flexibility of the proposed method in capturing the variation of random quantities in time or space.

中文翻译:

最大熵法在涉及随机过程建模的可靠性评估中的应用

摘要 从概率的角度来看,一个随机过程(或随机场)完全由其联合概率分布指定,可以进一步分解为边际分布和多元copula函数。本文提出了一种基于最大熵理论的非参数方法来构建随机过程分布的两部分。随机过程的规范被解释为矩约束并分为两类。第一类描述了随机量在任意点的不确定性。第二类定义了任意两点的随机量之间的相关性。然后通过在两类约束下最大化熵来开发边际分布和 copula 函数,它们被表述为两个优化问题。所提出的方法应用于两个可靠性问题:考虑时间相关腐蚀的梁可靠性评估和考虑土壤空间变异性的隧道可靠性评估。第一个示例说明了只有部分信息(边际分布和自相关函数)可用时的方法,而第二个示例显示了基于数据的随机场模型的开发。非参数方法与典型参数模型的比较表明所提出的方法在捕捉时间或空间随机量变化方面的灵活性。考虑土壤空间变异性的隧道可靠性评估。第一个示例说明了只有部分信息(边际分布和自相关函数)可用时的方法,而第二个示例显示了基于数据的随机场模型的开发。非参数方法与典型参数模型的比较表明所提出的方法在捕捉时间或空间随机量变化方面的灵活性。考虑土壤空间变异性的隧道可靠性评估。第一个示例说明了只有部分信息(边际分布和自相关函数)可用时的方法,而第二个示例显示了基于数据的随机场模型的开发。非参数方法与典型参数模型的比较表明所提出的方法在捕捉时间或空间随机量变化方面的灵活性。
更新日期:2021-01-01
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