可靠性全局灵敏度求解的Meta-IS-AK算法

Meta-IS-AK algorithm for estimating global reliability sensitivity

可靠性全局灵敏度(GRS)可以衡量输入变量对结构系统失效概率的平均影响,但目前仍然缺乏具有广泛适应性的高效算法。针对此问题,本文将在元重要抽样和可靠性全局灵敏度的贝叶斯算法基础上建立一种新的高效算法。所提算法首先利用已有的贝叶斯算法,将可靠性全局灵敏度转换成由无条件失效概率及输入变量失效域条件下的概率密度函数(PDF)表达的形式,然后分3步来完成算法的组织。第1步是利用元重要抽样的迭代策略抽取失效域的重要抽样样本;第2步是在已有的元重要抽样法中嵌入自适应Kriging模型,高效计算出无条件失效概率;第3步是利用Metropolis-Hastings准则,将失效域的重要抽样样本转化成为原始密度函数在失效域的样本点,进而同时求得各个输入变量在失效域中的条件概率密度函数,并最终求得可靠性全局灵敏度。由于所提算法充分利用了已有的可靠性全局灵敏度贝叶斯算法的维度独立性、元重要抽样法对隐式多失效域的适应性以及元重要抽样法中嵌入式Kriging模型的高效性,因此所提算法具有广泛的适用范围和较高的效率,该结论得到了算例结果的充分验证。

Global Reliability Sensitivity(GRS)measures the average impact of input variable on the failure probability of a structural system,but there is still a lack of efficient algorithms with broad adaptability.For this issue,a new efficient algorithm is established based on meta-important sampling and the Bayesian algorithm of GRS.The proposed algorithm firstly utilizes the existing Bayesian method to convert the GRS into a form expressed by the unconditional failure probability and the conditional Probability Density Function(PDF)of the input variable on failure domains,and then the algorithm is organized in three steps.The first step is to extract the importance samples of the failure domain by using the iteration strategy of metaimportant sampling.The second step is to embed the adaptive Kriging model in the existing meta-important sampling method to efficiently estimate the unconditional failure probability.The third step is to use the Metropolis-Hastings criterion to convert the importance samples in the failure domains into the samples of the original density function in the failure domains and simultaneously obtain the conditional PDF of each input variable on the failure domain,and finally the GRS can be obtained.As the proposed algorithm makes full use of the dimensional independence of the existing Bayesian algorithm of GRS,the adaptability of the meta-important sampling method and the efficiency of the embedded Kriging model,the proposed algorithm has wide adaptability and high efficiency.The above conclusions are verified by the results of the examples.