结构可靠性分析的自适应共轭非线性近似方法  

Self-adaptive Conjugate Nonlinear Approximation Method for Structural Reliability Analysis

作　　者：邱继伟 罗海胜[1] QIU Jiwei;LUO Haisheng(China Ordnance Industrial Standardization Research Institute, Beijing 100089, China)

机构地区：[1]中国兵器工业标准化研究所,北京100089

出　　处：《兵工学报》2021年第3期648-654,共7页Acta Armamentarii

摘　　要：经典的1阶可靠性方法在求解非线性结构可靠性问题时,由于仅利用当前迭代设计点的局部信息,致使求解精度及效率无法满足要求,为此提出了一种自适应共轭非线性近似方法。基于两点自适应非线性近似方法,使用当前及上一迭代设计点的极限状态函数值及梯度值信息,构建真实极限状态函数的非线性近似模型;在两点自适应非线性近似方法的基础上,利用前两步迭代设计点的极限状态函数值及梯度值信息,在当前迭代设计点处构建共轭搜索方向。随着迭代过程的进行,基于自适应调整模型中的非线性指数及搜索方向,在提高模型的近似精度的同时可避免迭代过程出现振荡,提高计算的稳定性。通过3个案例说明了所提方法的适用性。When the classical first-order reliability methods are used to solve the reliability problem of nonlinear structure,the accuracy and efficiency of the solution cannot meet the requirements because the calculation process stability is reduced by using the local information of current iterative design point merely.A self-adaptive conjugate aonlinear approximation method is proposed in this work.Firstly,based on the two-point adaptive nonlinear approximation method,a nonlinear approximation model of real limit state function is constructed by using the limit state function value and gradient value of the current and previous iteration design points.Furthermore,on the basis of two-point adaptive nonlinear approximation method,the conjugate search direction is constructed at the current iteration design point by using the limit state function value and gradient value information of the previous two iteration design points.With the development of the iterative process,the nonlinear exponential and the search direction in the model can be adjusted adaptively to improve the approximate accuracy of the model and alleviate the oscillation in the iterative process,then improving the stability of the calculation.Finally,three examples are given to illustrate the applicability of the proposed method.

关 键 词：结构可靠性 两点非线性近似 共轭搜索方向 自适应迭代 1阶可靠性方法 

分 类 号：TB114.33[理学—概率论与数理统计]