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基于线抽样的可靠性灵敏度分析方法

Reliability sensitivity algorithm based on line sampling

  • 摘要: 提出了一种基于线抽样的可靠性灵敏度分析方法. 线抽样可靠性分析中,结构失效概率Pf是由每个抽样样本对应的失效概率Pfj 的算术平均值来计算的,由此可知Pf对基本变量分布参数\theta 的灵敏度\partial Pf / \partial \theta可以表示为Pfj 对\theta 的偏导数\partial Pfj / \partial \theta的算术平均值,而\partial Pfj / \partial \theta 则可以很容易地由Pfj与基本变量分布参数\theta 的解析关系求得. \partial Pfj / \partial\theta 和\partial Pf / \partial \theta的计算公式被详细推导. 可靠性灵敏度分析的线抽样方法继承了线抽样法的优点,诸如精度高、收敛快且适用于高维及多模式情况等. 这些优点由算例证实.

     

    Abstract: In this paper, reliability sensitivity algorithm based online sampling is presented. In the line sampling for structural reliabilityanalysis, the failure probability Pf of structure is calculated byaveraging the failure probability Pfj (j=1,...,N) corresponding toeach simulated sample. From Pf in the linesampling, the reliability sensitivity of Pf with respect to thedistribution parameter \theta , i.e. \partial Pf / \partial \theta , canbe calculated by averaging \partial Pfj / \partial \theta , and\partial Pfj / \partial \theta can be obtained by using the analyticalrelationship between Pfj and \theta . The expressions of \partialPfj / \partial \theta and \partial Pf / \partial \theta are derivedin detail. With the use of the line sampling, reliability sensitivity algorithmenjoys the advantages of the line sampling, such as high precision,high efficiency and wide applicability in high dimensions and multiplefailure modes. Examples are used to show the advantages of thepresented reliability sensitivity algorithm.

     

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