隐式极限状态方程的非概率可靠性分析  

NON-PROBABILISTIC RELIABILITY ANALYSIS METHOD FOR IMPLICIT LIMIT STATE FUNCTION

作　　者：马超[1] 吕震宙[1] 

机构地区：[1]西北工业大学航空学院,西安710072

出　　处：《机械强度》2009年第1期45-50,共6页Journal of Mechanical Strength

基　　金：国家自然科学基金(10572117);航空科学基金(2007ZA53012);新世纪优秀人才支持计划(NCET-05-0868);863计划课题(2007AA04Z401)资助项目~~

摘　　要：针对凸集模型比例因子的非概率可靠度指标相对隐式极限状态方程难以求解问题,提出一种基于支持向量机回归的非概率可靠度指标分析方法。所提方法用支持向量机回归拟合极限状态方程,通过优化算法获得可靠度指标和设计点,用设计点更新支持向量机训练样本的抽样中心,并重复计算过程直至收敛。由于构造合适的迭代格式可以有效地近似结构的真实失效域边界,故求解精度好,又由于使用极限状态方程的代理措施,使得计算效率高。文中用四个数值算例证明方法的精度和效率,并将文中方法用于实际的飞机机翼可靠性分析中。Since the non-probabilistic reliability index based on convex model scale factor is difficult to be solved for implicit limit state function, a support vector machine （SVM） regression is proposed. The proposed method employs SVM regression to fit the actual limit state function, and an optimization problem is constructed to obtain the index and design point. The design point is used to update the sampling center in the SVM training procedure. The full procedure is repeated until the given convergence criterion is satisfied. The special iteration guarantees the actual limit state function can be well approximated, hence the precision of the proposed method is high. Simultaneously, since the limit state function surrogate is adopted, the efficiency of the proposed method is high. Four numerical examples demonstrate the excellent behavior of the proposed method. An application of the proposed method in a wing reliability analysis also shows its value in engineering.

关 键 词：可靠性 非概率 支持向量机 隐式极限状态方程 凸模型 

分 类 号：TB114.3[理学—概率论与数理统计]