用于结构可靠指标计算的随机梯度算法

提出了一种基于几何原理求解结构可靠指标的高效实用算法,即随机梯度算法.该算法根据随机搜索方向的梯度反馈信息,采取有效的优化策略对随机搜索方向加以调整,缩短搜索路径,使目标的搜索方向更为准确,搜索效率更高.编制了相应程序对该算法的计算过程进行跟踪演示,以便直观形象地了解程序执行运作情况和算法性能,便于进行参数分析.经3个工程算例验证,该算法适用于结构可靠指标计算,计算精度令人满意.

Stochastic Gradient Algorithm for Calculating Structural Reliability Index

An efficient and practical stochastic gradient algorithm for calculating structural reliability index is presented in this paper on basis of geometrical principle of reliability index. Certain effective optimization tactics are adopted to adjust the stochastic search orientation and shorten search trace according to the feedback gradient information, so that the search direction for the target turns more accurate and gains higher efficiency. The simulations and demonstrations make it convenient to visualize and realize the factual performances and properties of the algorithm, to prosecute the detailed and comprehensive parameters analysis. Three experimental examples show that the algorithm is applicable in calculating structural reliability index, and obtaining satisfactory precision as well.