超椭球凸集合可靠性综合指标定义及求解方法

doi:CNKI:11-1929/V.20110726.1649.001

固体力学与飞行器总体设计

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超椭球凸集合可靠性综合指标定义及求解方法

周凌¹, 安伟光², 贾宏光¹

1. 中国科学院长春光学精密机械与物理研究所, 吉林长春 130033;
2. 哈尔滨工程大学航天与建筑工程学院, 黑龙江哈尔滨 150001

收稿日期:2011-03-15 修回日期:2011-04-14 出版日期:2011-11-25 发布日期:2011-11-24
通讯作者: 周凌 E-mail:hszl007@163.com
作者简介:周凌(1984- ) 男,博士,助理研究员。主要研究方向:结构非概率可靠性指标及算法。 Tel: 0431-86708827 E-mail: hszl007@163.com安伟光(1943- ) 男,教授,博士生导师。主要研究方向:结构系统可靠性与优化。 E-mail: anweiguang@hrbeu.edu.cn贾宏光(1971- ) 男,博士,研究员,博士生导师。主要研究方向:光机电微小型化与精确制导技术研究。 E-mail: jiahg@ciomp.ac.cn

Definition and Solution of Reliability Comprehensive Index of Super-ellipsoid Convex Set

ZHOU Ling¹, AN Weiguang², JIA Hongguang¹

1. Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China;
2. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China

Received:2011-03-15 Revised:2011-04-14 Online:2011-11-25 Published:2011-11-24

摘要/Abstract

摘要： 针对失效域与超椭球凸集合发生干涉与不发生干涉两种情况下,超椭球凸集合非概率可靠性与非概率可靠度两种指标各自存在的不足,将两指标相结合提出多个超椭球凸集合描述时的可靠性综合指标定义,并提出将改进的有限步长迭代法(MLSA)与Monte-Carlo法结合来求解综合指标的方法。MLSA是在有限步长迭代法的基础上提出的,根据增广拉格朗日函数的极值条件构造了一个新的评价函数,并引入黄金分割法对步长进行一维搜索得到最优步长从而加速收敛。数值算例表明,用MLSA求解多个超椭球凸集合描述时的非概率可靠性指标的结果正确,并具有很好的收敛性,用超椭球凸集合可靠性综合指标评价超空泡射弹屈曲非概率可靠性程度更加合理。

关键词: 超椭球凸集合, 可靠性综合指标, 改进的有限步长迭代法, Monte-Carlo法, 评价函数, 超空泡射弹, 屈曲可靠性

Abstract: Both for the cases when a failure field and a super-ellipsoid convex set interfere or don't interfere with each other, there exists insufficiency of both the super-ellipsoid convex sets non-probabilistic reliability index and non-probabilistic reliability degree index. In view of this, this paper presents a definition of reliability comprehensive index based on multi-ellipsoid convex sets by combining the above two definition indexes. The comprehensive index is calculated by the combined method of modified limit step iteration algorithm (MLSA) and the Monte-Carlo method. The modified limit step length iteration algorithm is presented based on the limit step length iteration algorithm. A new merit function is proposed based on the extreme value condition of the extensive Lagrange function. Golden section method is introduced for one dimension search of the step length and convergence is accelerated. Numerical examples show the validity of the iteration results of the multi-ellipsoid convex sets non-probabilistic reliability index obtained by MLSA, and the algorithm also exhibits better convergence. The structural buckling non-probabilistic reliability degree of a supercavitating projectile is evaluated by the super-ellipsoid convex sets reliability comprehensive index with more satisfactory results.

Key words: super-ellipsoid convex set, reliability comprehensive index, modified limit step length iteration algorithm, Monte-Carlo method, merit function, supercavitating projectile, buckling reliability

中图分类号:

周凌, 安伟光, 贾宏光. 超椭球凸集合可靠性综合指标定义及求解方法[J]. 航空学报, 2011, 32(11): 2025-2035.

ZHOU Ling, AN Weiguang, JIA Hongguang. Definition and Solution of Reliability Comprehensive Index of Super-ellipsoid Convex Set[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011, 32(11): 2025-2035.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

超椭球凸集合可靠性综合指标定义及求解方法

Definition and Solution of Reliability Comprehensive Index of Super-ellipsoid Convex Set

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