粒子群算法在结构非概率可靠性优化中的应用

摘要

In order to solve the reliability optimization problem of uncertainty structures in actual engineering, an optimization model was established to minimize the structure mass with the constraints of its non-probabilistic reliability index and cross-sectional area. The non-probabilistic reliability index was derived using the convex model method for the probability set theory, and a method for structural non-probabilistic reliability optimization was proposed based on particle swarm optimization ( PSO ). The results of an application example show that the structure mass relative error between the uncertainty optimization method and the deterministic optimization method is barely 0. 009% , when deterministic optimization parameters take average value and the expected non-probabilistic reliability index is zero. The cross-sectional area and mass of the truss structure increase with an increase in the expected non-probabilistic reliability index. When the expected non-probabilistic reliability index is 1.5, the structure mass obtained by the proposed optimization method is decreased by 0. 323% compared with that by the gradient projection method.%为了解决实际工程中不确定性结构的可靠性优化问题,建立了以结构非概率可靠性指标和横截面积为约束条件、最小化结构质量为目标的优化模型.利用非概率集合理论中的凸模型方法,求出可靠性指标,提出了基于粒子群算法的结构非概率可靠性优化方法.算例分析结果表明:与参数取平均值时的结构确定性优化方法相比,容许非概率可靠性指标为零时的结构非确定性优化方法得到的结构质量误差仅为0.009％.随着容许非概率可靠性指标的增大,桁架结构横截面积及质量也相应增大；当容许非概率可靠性指标为1.5时,与梯度投影法优化结果相比,利用该方法优化后的结构质量减少了0.323％.