面向概率-区间混合可靠性分析的自适应共轭控制方法与应用  

Adaptive conjugate control method for probability-interval hybrid reliability analysis and its engineering application

作　　者：孟增[1] 汪栋梁 郝鹏[2] MENG Zeng;WANG Dongliang;HAO Peng(School of Civil and Hydraulic Engineering,Hefei University of Technology,230009 Hefei,China;Department of Engineering Mechanics,Dalian University of Technology,116024 Dalian,China)

机构地区：[1]合肥工业大学土木与水利工程学院,合肥230009 [2]大连理工大学工程力学系,大连116024

出　　处：《应用力学学报》2022年第6期1076-1085,共10页Chinese Journal of Applied Mechanics

基　　金：国家自然基金面上资助项目(No.11972143)。

摘　　要：复杂工程结构中往往包含多源不确定性,而概率-区间混合不确定性理论是处理这些不确定性因素的有效手段。但是,经典的概率-区间混合可靠性计算模型由双层优化循环嵌套组成,对于复杂工程问题存在计算成本过高和鲁棒性不足的问题。为了改进算法性能,提出了面向概率-区间混合可靠性分析的自适应共轭控制方法,该方法将前两次迭代方向与当前迭代点处的负梯度方向组合,同时加入控制因子对组合后的方向进行修正,改善其迭代点的下降方向,提高相应收敛速度,并通过可行下降方向的定义证明了修正后方向仍为优化问题的下降方向。此外,为防止迭代过程中产生数值振荡,进一步引入了Wolfe-Powell准则,保证控制因子自适应更新的同时增强了算法的鲁棒性。为了获得随机参数的上下界,基于超参数凸模型构造了相应的显式迭代公式。计算结果表明,该方法在解决高非线性问题时能有效地避免迭代过程中出现的振荡现象,与传统方法相比,不仅能满足精度需求,而且可以高效、稳定地求解可靠度指标。Complex engineering structures often contain multi-source uncertainties,while probability-interval hybrid uncertainty theory is an effective tool to deal with these uncertain parameters.However,the classical probability-interval hybrid reliability calculation model is composed of double nested optimization loops,which has the problems of expensive calculation cost and insufficient robustness for complex engineering problems.In order to improve the performance,this study proposes an adaptive conjugate control method for probability-interval hybrid reliability analysis.This method combines the decrease directions of previous two iteration steps with the negative gradient direction at the current iteration step.A control factor is also added to further modify the combined direction,aiming to improve the descent direction and convergence speed.Besides,it is proved that the revised direction is still the descent direction of the optimization problem according to the definition of the feasible descent direction.Moreover,in order to prevent the numerical oscillation in the iterative process,the Wolfe-Powell criterion is introduced to enhance the robustness of the algorithm by adaptive update of control factor.To obtain the upper and lower bounds of random parameters,the corresponding explicit iterative formulas are constructed based on the super parametric convex model.The results show that the proposed method can effectively avoid the oscillation phenomenon in the iteration process when highly nonlinear problems are solved.Compared with the traditional method,the proposed method not only meets the requirement for accuracy,but also solves the reliability index efficiently and stably.

关 键 词：结构可靠度 概率-区间混合不确定性分析 一次二阶矩 共轭方向法 自适应共轭控制 

分 类 号：TB114.3[理学—概率论与数理统计]