基于粒子群算法和增广拉格朗日乘子法的混合可靠性分析

Hybrid Reliability Analysis Based on Particle Swarm Optimization Algorithm and Augmented Lagrange Multiplier Method

本文提出了一种基于粒子群算法和增广拉格朗日乘子法的混合可靠性分析方法.该方法通过引入参数的不确定性和区间变量,得到一种概率-区间混合不确定模型,充分利用增广拉格朗日乘子法将有约束优化问题转化为无约束优化问题,基于此进行求解和结构可靠性分析.数值算例和工程实例验证了该算法在计算结构可靠性问题时对于线性和非线性的功能函数有良好的收敛性和较高的计算效率.

A hybrid reliability analysis method is proposed based on particle swarm optimization and augmented Lagrange multiplier method. By introducing the uncertainty of parameters and interval variables, a probabilistic-interval mixed uncertainty model is obtained. The constrained optimization problem is transformed into unconstrained optimization problem by the augmented Lagrange multiplier method. Based on this method, the solution and structural reliability can be realized. One numerical example and two engineering examples are provided to show that the proposed algorithm has good convergence and high computational efficiency for linear and nonlinear functional functions when calculating structural reliability problems.