基于功能度量法的概率优化设计的收敛控制

CONVERGENCE CONTROL OF PROBABILISTIC STRUCTURAL DESIGN OPTIMIZATION BASED ON PERFORMANCE MEASURE APPROACH

概率结构优化设计(PSDO)中概率约束的评定可以采用最近提出的、被认为更高效、稳定的功能度量法(PMA).改进均值(AMV)迭代格式经常在PMA中使用,但它对一些非线性功能函数或非正态随机变量,搜索最小功能目标点时可能陷入周期振荡或混沌解,从而使PSDO的两层次算法或序列近似规划算法优化计算失败.利用混沌反馈控制的稳定转换法对功能度量法的AMV迭代格式实施了收敛控制,使嵌入周期和混沌轨道的不稳定不动点稳定化,获得稳定收敛解,从而使概率约束的评定能正常进行;再由两层次算法或序列近似规划算法进行结构优化设计.算例结果表明了稳定转换法实施收敛控制的有效性,以及序列近似规划算法相对高效的优点.

The evaluation of probabilistic constraints in Probabilistic Structural Design Optimization （PSDO） can be carried out using the recently proposed performance measure approach （PMA）. The advanced mean-value （AMV） method is well suitable for PMA due to its simplicity and efficiency. However, when the AMV iterative scheme is applied to search for the minimum performance target point for some nonlinear performance functions, the iterative sequences could fall into the periodic oscillation and even chaos. Then both PMA Two-level and PMA with sequential approximate programming （SAP）, which are based on this evaluation of probabilistic constraints, could yield convergent failure. In the present paper, the convergence control of AMV iterative procedure is first implemented by using the stability transformation method of chaos feedback control. The unstable fixed points embedded in the periodic and chaotic orbit are stabilized and the expected stable convergent solutions are obtained. Once the evaluation of probabilistic constraints can be carried out successfully, the design optimization is performed by PMA Two-level or PMA with SAP. The numerical results demonstrate that the convergence control using the stability transformation method is effective and PMA with SAP is more efficient.