参数可靠性全局灵敏度高效分析的代理模型法
收稿日期: 2022-06-22
修回日期: 2022-07-14
录用日期: 2022-07-28
网络出版日期: 2022-08-17
基金资助
国家自然科学基金(12002237);重庆市自然科学基金(CSTB2022NSCQ-MSX0861);广东省基础与应用基础研究基金(2022A1515011515);中央高校基本科研业务费专项资金(D5000211035)
An efficient surrogate method for analyzing parameter global reliability sensitivity
Received date: 2022-06-22
Revised date: 2022-07-14
Accepted date: 2022-07-28
Online published: 2022-08-17
Supported by
National Natural Science Foundation of China(12002237);Natural Science Foundation of Chongqing(CSTB2022NSCQ-MSX0861);Guangdong Basic and Applied Basic Research Foundation(2022A1515011515);Fundamental Research Funds for the Central University(D5000211035)
针对分布参数和输入变量双重随机性下，输入变量分布参数可靠性全局灵敏度分析涉及的复杂耦合3层计算制约参数可靠性全局灵敏度的应用，从单层重要抽样结合自适应Kriging代理模型的角度，建立了参数可靠性全局灵敏度分析的高效算法。首先，利用贝叶斯理论、Metropolis-Hastings准则和Edgeworth级数建立基于重要抽样的参数可靠性全局灵敏度的单层分析公式，统一可靠性与参数可靠性全局灵敏度分析，将参数可靠性全局灵敏度分析的关键问题转化为无条件重要抽样样本安全和失效状态的识别问题，实现重复利用1组无条件重要抽样样本计算得到所有不确定性分布参数对可靠性的影响；其次，利用Kriging代理模型自适应构造近似最优重要抽样概率密度函数（PDF），实现重要抽样样本的产生；最后，在重要抽样样本池内继续更新构造最优重要抽样概率密度函数的Kriging代理模型，直到重要抽样样本安全或失效状态被Kriging代理模型准确识别，利用更新结束后的Kriging代理模型替代真实功能函数识别重要抽样样本安全或失效状态，完成参数可靠性全局灵敏度分析。数值算例和导弹弹翼算例分析验证了本文所提方法的高效性和准确性。
关键词： 参数可靠性全局灵敏度分析; 贝叶斯理论; 代理模型; Metropolis-Hastings准则; 重要抽样法; Edgeworth级数
员婉莹 , 吕震宙 . 参数可靠性全局灵敏度高效分析的代理模型法[J]. 航空学报, 2023 , 44(12) : 227670 -227670 . DOI: 10.7527/S1000-6893.2022.27670
To give an efficient analysis of parameter reliability global sensitivity， this paper proposes a method by integrating the single-loop importance sampling technique and the adaptive Kriging model. First， a single-loop importance sampling algorithm for estimating the parameter reliability global sensitivity is constructed based on the Bayes theorem， Metropolis-Hastings algorithm and Edgeworth expansion， which unifies the analyses of reliability and parameter reliability global sensitivity. Based on the proposed single-loop importance sampling algorithm， the estimation of the parameter reliability global sensitivity is converted into the identification of states （failure or safety） of all unconditional importance sampling samples， so that each parameter reliability global sensitivity can be evaluated by repeatedly using the unconditional importance sampling samples. Secondly， the Kriging model surrogating the performance function is adaptively constructed to approximate the optimal importance sampling Probability Density Function （PDF） and then generate the corresponding importance samples. Finally， the Kriging model used to construct the approximately optimal importance sampling PDF is continuously updated among the candidate sampling pool of the generated importance samples until the states of all importance samples are accurately identified by the Kriging model. Based on the accurately identified states of all importance samples， parameter global reliability sensitivity of each uncertain distribution parameter is assessed.Results of a numerical example and a missile wing structure verify the efficiency and accuracy of the proposed method.
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