采用增广乘子法和模拟退火法的结构可靠性分析

Structure Reliability Analysis by Combining Augmented Multiplier Method and Simulated Annealing Algorithm

为避免一次二阶矩法的雅可比矩阵计算和罚函数法的罚因子选取,提出了一种采用增广乘子法和模拟退火法的结构可靠性分析方法。利用优化理论,以可靠指标最小为目标函数,以极限状态方程为等式约束条件,建立结构可靠性分析数学模型。采用增广乘子法将上述有约束优化模型变换为无约束优化模型,并用模拟退火法求解,从而避免了雅可比矩阵的计算以及初始罚因子的选取。采用一次二阶矩法、本文方法、蒙特卡罗模拟法分别对数值算例及悬臂梁工程算例进行了可靠性分析,结果表明:较一次二阶矩法,本文方法更接近于蒙特卡罗模拟法的结果,更精确;较蒙特卡罗模拟法,本文方法迭代次数较少,效率较高。

To simultaneously avoid calculation of Jacobian matrix of the first order second moment (FOSM) method and selection of the initial value regarding the penalty factor of the penalty function method,a structural reliability analysis method by combining augmented multiplier method with simulated annealing algorithm is proposed.Following optimization theory,the mathematical model is established,where the minimum reliability index is taken as objective function and the limit state equation as equality constraints.The constrained optimization problem is converted to unconstrained optimization problem with augmented multiplier method,and solved it by the simulated annealing algorithm,thus the calculation of Jacobian matrix and selection of the initial value of the penalty factor are meanwhile omitted.The proposed method,the FOSM method,and the Monte Carlo simulation (MCS) method are simultaneously applied to calculating the reliability index of a numerical example and a cantilever beam structure respectively.The result indicates that: the computational result of the proposed method is closer to that of MCS method,so it is more accurate than the FOSM;the iterations of the proposed method are fewer,so it is more effective than MCS method.