改进Kriging的热结构耦合梁共振非概率可靠性分析

摘要

Since the implicit limit state function for thermal⁃structural coupling of a beam is difficult to determine, a non⁃probabilistic resonance reliability method for the thermal⁃structural coupling of a beam is presented. The method is based on the theories of resonance reliability analysis, the improved Kriging model and finite element analysis techniques. In the proposed method, the approximation model for the reliability function of the beam structure is established by Kriging method, and the improved Kriging approximate model becomes more close to the limit state function by using the active learning method to improve the selecting method of new sample points. Then considering the uncertainty of structure parameters, the parameters of beam structure are described by interval variables, so that the approximation model for the non⁃probabilistic resonance reliability of the beam structure including ellipsoidal convex sets can be established. Finally, the non⁃probabilistic resonance reliability index of the beam structure is calculated by the optimization method. The calculation results show that the proposed method is of rationality and high accuracy, and can provide a feasible way for the non⁃probabilistic resonance reliability analysis of thermal⁃structural coupling of the beam structure.%针对梁结构在热结构耦合作用时其极限状态函数为隐式形式且难以求解的问题，基于振动可靠性理论，将改进的Kriging模型与有限元方法相结合，提出了热结构耦合梁共振非概率可靠性分析方法。首先利用Kriging法构建热结构耦合梁可靠性功能函数的近似模型，并利用主动学习法改进了选取新增样本点的方式，使得改进后的Kriging近似模型更加逼近于真实极限状态函数。在此基础上，考虑结构参数的不确定性，对梁结构的不确定变量用区间变量进行描述，建立了含有超椭球凸集的梁结构共振非概率可靠性模型，最后结合优化方法求解出梁结构共振非概率可靠性指标。算例结果表明了该方法的合理性以及计算精度高的特点，为热结构耦合梁的共振非概率可靠性分析提供了可行的途径。