| 易平,谢东赤.概率功能度量求解的共轭梯度步长调节法[J].计算力学学报,2018,35(6):750~756 |
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| 概率功能度量求解的共轭梯度步长调节法 |
| Conjugate gradient step length adjustment method for calculation of probabilistic performance measure |
| 投稿时间：2017-08-31 修订日期：2017-11-29 |
| DOI：10.7511/jslx20170831002 |
| 中文关键词: 功能度量法 共轭梯度 步长调节 |
| 英文关键词:performance measure approach conjugate gradient step length adjustment |
| 基金项目:国家自然科学基金（51479027）资助项目. |
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| 中文摘要: |
| 功能度量法（PMA）由于其稳定高效的特点，适用于概率结构优化设计中概率约束的评定。PMA中改进均值法常用于求解概率功能度量，针对其求解高度非线性功能函数时出现周期振荡和混沌等不收敛现象，提出了一种新的共轭梯度步长调节法（CGS）。该方法基于RMIL共轭搜索方向和自适应步长调节策略提出，新的共轭搜索方向在保证收敛性的前提下加速了迭代进程，而自适应步长调节策略无需了解功能函数凹凸性及非线性程度等先验信息，无需确定步长的合适取值。通过限定步长准则自动选取初始步长，并随迭代过程不断调节，直至最终收敛。多个算例表明，与其他求解方法相比，本文的共轭梯度步长调节法更加高效且稳健。 |
| 英文摘要: |
| The performance measure approach(PMA)is suitable for the assessment of probability constraints in probabilistic structural design optimization(PSDO)due to its stable and efficient characteristics.The advanced mean value(AMV)is often used to solve the probabilistic performance measure in PMA.However,for highly nonlinear performance function the iterative sequence of AMV formulation may yield a non-convergent solution such as periodic oscillation and chaos.In this paper,a new method,conjugate gradient step length adjustment method(CGS),is presented.This method is based on the RMIL conjugate search direction and the self-adaptive step length strategy.The new conjugate search direction accelerates the iterative process under the premise of ensuring the convergence.The self-adaptive step length strategy makes it unnecessary to obtain the prior information such as convexity or concavity and non-linearity of the performance function,and to determine an appropriate value of the step length.The step length is initially automatically selected by step-length-limiting criterion and is constantly adjusted during the iteration process until the final convergence.Several examples show that the proposed CGS method is more efficient and robust than other methods. |
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