一种Kriging模型和改进子集模拟的多响应系统可靠性分析方法研究

Analyzing Structural Reliability of Multi-response System based on Kriging Model and Generalized Subset Simulation

在结构可靠性分析中,一个重要的挑战是减少对功能函数的调用。而在实际工程中的失效问题往往是小概率、多响应,并且相关的功能函数通常是隐式的情况,需要复杂的有限元计算,因此减少对功能函数的调用尤为重要。为了构建精准的代理模型,针对系统中的多个响应,分别构建了Kriging代理模型,采用拉丁超立方抽样提高其有效性,采用主动学习方式提升了Kriging模型的精度,同时减少了样本量。为了提升多响应模式下子集模拟的计算效率,采用了改进的子集模拟方法。为了解决小概率失效问题以及减少对功能函数的调用,结合Kriging模型和改进的子集模拟建立了AK-GSS模型。算例分析表明该模型为多响应模式下相关的结构可靠性分析提供新方法。

An important challenge in structural reliability is to reduce the number of calls to the performance function.The failure has the characteristics of small probability and multiple responses in the engineering practice;the complex finite element modeling is indispensable.Therefore,it is particularly important to reduce the number of calls to the performance function.To construct the accurate surrogate model for the performance functions of the multi-response system,active learning is used to improve the accuracy,and the Latin Hypercube Sampling(LHS)is used to enhance the sampling efficiency.The Generalized Subset Simulation(GSS)is employed to enhance the computational efficiency of the GSS in the multiple-response system.An active learning reliability method based on the Kriging model and GSS is proposed to solve the small failure probability problem and reduce the number of calls to the performance function.The numerical simulation results show that the new method can effectively analyze the structural reliability of the multi-response system.