基于可靠度的结构优化的序列近似规划算法

Sequential approximate programming approach to reliability based structural optimization

基于可靠度的优化的最直观解法是把可靠度和优化的各自算法搭配一起形成嵌套两层次迭代。为改善其收敛性提高计算效率,人们提出了功能测度法、半无限规划法、单层次算法等多种改进方法。本文对传统结构优化界的经典序列近似规划法改造并扩展应用于求解基于可靠度的结构优化问题,构造该问题的序列近似规划模型和求解过程;其核心思想是在每个近似规划子问题中采用近似可靠度指标对设计变量的线性近似,在优化迭代过程中同步更新设计变量和随机空间中的近似验算点坐标,以达到可靠度分析和优化迭代同步收敛的目标。为了算法的实施,还推导出近似可靠度指标的半解析灵敏度计算公式,编制了程序,最终实现与通用软件的连接。论文用算例证实算法的有效性。

The classical bi-level approach to the reliability based optimization problem is not effective. To address the difficulty, an extended sequential approximate programming approach is proposed. In the new approach, optimum design of RBO is obtained by solving a sequence of approximate linear programming. We develop a new linear approximation of the approximate reliability index with respect to the design variables to improve the efficiency, where the Karush-Kuhn-Tucker conditions are used to obtain the approximate reliability index. The derivative of the approximate reliability index is deduced. Program based on Sequential Linear Programming method of RBO has been developed to solve the structural and non-structural reliability based optimization problems. By integrating the algorithm with the existing FEM software we manage to solve a number of reliability based optimization problems. Numerical results show the concurrent convergence of both optimization and reliability calculation and the efficiency of our new approach.