截断相关正态变量情况下可靠性模型及其求解的自适应超球抽样法

Reliability Models Involving Truncated Correlated Normal Variables and its Solution by an Adaptive Radial Based Sampling

针对工程中含截断相关正态变量的问题,建立了其可靠性和可靠性灵敏度的分析模型,并采用自适应超球抽样对分析模型进行了求解。在所建分析模型中,利用截断相关正态变量密度函数与非截断相关正态变量密度函数的关系,并通过将变量的截断区域当作一种失效模式来处理,进而可以将原截断相关正态变量情况下的可靠性和灵敏度分析问题转化为一般的相关正态变量情况下的可靠性和灵敏度问题。由于超球抽样算法具有高效和稳健的优点,它被用来求解原问题的可靠性和可靠性灵敏度。文中的超球抽样采用的是一种自适应寻找超球半径的策略,可以进一步地提高算法的稳健性。在详细给出建模原理和模型的求解步骤后,算例被用来说明模型的合理性和算法的可行高效性。

For the engineering problem involving truncated correlated normal variables（CNV） ,reliability and reliability sensitivity（RS） models are established,and an adaptive radial based sampling is employed to analyze the reliability and the RS. In the established models,the truncated CNV is transformed into the general CNV without truncation,and the intervals of the truncated CNV are treated as multiple failure modes,on which the reliability and the RS with the truncated CNV are transformed into those only with general CNV. Since the radial based sampling is efficient and robust,it is used to analyze the transformed reliability and RS from the original problem with the truncated CNV. An adaptive strategy is employed to search for the optimal radial in the sampling,by which the robustness of the method is improved furthermore. After the model concepts and the detailed implementation are given,several examples are presented to demonstrate the feasibility of the model and the efficiency of the solutions.