结构模糊非概率混合可靠性分析方法

许孟辉; 邱志平

结构模糊非概率混合可靠性分析方法

北京航空航天大学固体力学研究所, 北京 100191

基金项目: 国防基础科研计划资助项目（A2120110001，B2120110011）；国家自然科学基金资助项目（10872017，90816024，10876100）；“111”计划资助项目（B07009）

详细信息

中图分类号: TB121;TB21
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出版历程
- 收稿日期: 2013-04-12
- 网络出版日期: 2014-02-20

Reliability analysis of structures with fuzzy and non-probabilistic hybrid variables

Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics,Beijing 100191, China

摘要

摘要: 针对模糊非概率混合不确定性下结构可靠性分析问题，基于模糊数学分解原理将混合可靠性分析模型转化为[0，1]内连续分布隶属度水平下的非概率可靠性分析模型；针对非概率可靠度计算复杂性，基于逐维策略将结构功能函数最值的计算转化为最值点向量的逐维计算，提出一种确定结构功能函数界限的算法；通过在[0，1]内遍历隶属度值确定结构可靠度的隶属度函数实现结构可靠度模糊性的定量化.算例表明该方法的合理性，计算精度高和计算量小的特点为复杂工程结构可靠度分析及优化设计提供了可行途径.
- 模糊变量 /
- 区间变量 /
- 非概率可靠性 /
- 混合可靠性 /
- 隶属度函数
Abstract: For the reliability analysis of structures in the case of coexistence of fuzzy and non-probabilistic uncertainties, the hybrid analysis model was transformed into non-probabilistic analysis models at different membership values distributed in the interval [0,1] continuously based on the decomposition principle of fuzzy mathematics theories. An algorithm for determining the minimum/maximum of the structural performance function was presented to overcome the complexity in calculating the non-probabilistic reliability based on the optimization strategy dimension by dimension, by which the determination of the extreme values was converted to that of the extreme point vectors of the performance function. The quantification of the fuzziness in structural reliability was accomplished with the membership function of the structural reliability obtained by traversing the membership value in the interval[0,1]. The reasonability of the presented method was proved by two engineering applications and the merits of high accuracy and efficiency suggest a feasible way for the reliability analysis and optimization of complicated engineering structures.
- fuzzy variable /
- interval variable /
- non-probabilistic reliability /
- hybrid reliability /
- membership function

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参考文献(18)

[1]	Cheng Gengdong, Xu Lin, Jiang Lei.A sequential approximate programming strategy for reliability-based structural optimization[J].Computers Structures, 2006, 84(21): 1353-1367
[2]	Ben-Haim Y, Elishakoff I.Convex of uncertainty in applied mechanics[M].Amsterdam: Elsevier Science, 1990
[3]	黄洪钟, 孙占全, 郭东明, 等.随机应力模糊强度时模糊可靠性的计算理论[J].机械强度, 2001, 23(3): 305-307 Huang Hongzhong, Sun Zhanquan, Guo Dongming, et al.Fuzzy reliability analysis in the case of random stress and fuzzy strength[J].Journal of Mechanical Strength, 2001, 23(3): 305-307(in Chinese)
[4]	Huang Hongzhong.Calculation of fuzzy reliability in the case of random stress and fuzzy fatigue strength[J].Chinese Journal of Mechanical Engineering:English Edition, 2000, 13(3): 197- 200, 223
[5]	Dong Yuge, Wang Ainan.A fuzzy reliability analysis based on the transformation between discrete fuzzy variables and discrete random variables[J].International Journal of Reliability, Quality and Safety Engineering, 2006, 13(1): 25-35
[6]	Cai K Y, Wei C Y, Zhang M L.Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context[J].Fuzzy Sets and Systems, 1991, 42(2): 145-172
[7]	Cai K Y, Wei C Y, Zhang M L.Fuzzy states as a basis for a theory of fuzzy reliability[J].Microelectronics and Reliability, 1993, 33(15): 2253-2263
[8]	郭书祥, 吕震宙.基于可能性理论的结构模糊可靠性方法[J].计算力学学报, 2002, 19(1): 89-93 Guo Shuxiang, Lü Zhenzhou.A fuzzy reliability approach for structures in the possibility context[J].Chinese Journal of Com putational Mechanics, 2002, 19(1): 89-93(in Chinese)
[9]	郭书祥, 吕震宙.结构可靠性分析的概率和非概率混合模型[J].机械强度, 2002, 24(4):524-526 Guo Shuxiang, Lü Zhenzhou.Hybrid probabilistic and non-probabilistic model of structural reliability[J].Journal of Mechanical Strength, 2002, 24(4):524-526(in Chinese)
[10]	Qiu Zhiping, Wang Jun.The interval estimation of reliability for probabilistic and non-probabilistic hybrid structural system[J].Engineering Failure Analysis, 2010, 17(5): 1142-1154
[11]	Luo Yangjun, Kang Zhan, Li Alex.Structural reliability assessment based on probability and convex set mixed model[J].Computers and Structures, 2009, 87(21/22): 1408-1415
[12]	姜潮, 刘丽新, 汤一飞.一种带区间变量混合模型的结构可靠性分析方法[J].汽车工程, 2012, 34(8): 727-732 Jiang Chao, Liu Lixin, Tang Yifei.A structural reliability analysis method for hybrid model with interval variables[J].Automotive Engineering, 2012, 34(8): 727-732(in Chinese)
[13]	乔心州, 仇原鹰, 盛英.含模糊变量和区间变量的结构可靠性优化设计方法[J].计算力学学报, 2010, 27(3): 537-541 Qiao Xinzhou, Qiu Yuanying, Sheng Ying.Reliability-based optimization of structures with fuzzy and interval variables[J].Chinese Journal of Computational Mechanics, 2010, 27(3): 537-541(in Chinese)
[14]	李昆锋, 杨自春, 孙文彩.结构非概率-模糊混合可靠性分析方法[J].华中科技大学学报:自然科学版, 2012, 40(8): 67- 71 Li Kunfeng, Yang Zichun, Sun Wencai.Analyzing hybrid non-probabilistic and fuzzy reliability of structures[J].Journal of Huazhong University of Science and Technology:Natural Science Edition, 2012, 40(8): 67-71 (in Chinese)
[15]	Zimmermann H J.Fuzzy set theory and its applications[M].Boston: Kluwer Academic Publishers, 1991
[16]	郭书祥, 吕震宙, 冯元生.基于区间分析的结构非概率可靠性模型[J].计算力学学报, 2001, 18(1): 56-60 Guo Shuxiang, Lü Zhenzhou, Feng Yuansheng.A non-probabilistic model of structural reliability based on interval analysis[J].Chinese Journal of Computational Mechanics, 2001, 18(1): 56-60 (in Chinese)
[17]	颜庆津.数值分析[M].北京:北京航空航天大学出版社, 2010 Yan Qingjin.Numerical analysis[M].Beijing: Beihang University Press, 2010
[18]	姜潮, 张哲, 韩旭.一种基于证据理论的结构可靠性分析方法[J].力学学报, 2013, 45(1): 103-115 Jiang Chao, Zhang Zhe, Han Xu.An evidence-theory-based reliability analysis method for uncertain structures[J].Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 103-115 (in Chinese)