﻿ 基于相关性分析的结构可靠性加严试验方法<sup>*</sup>
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Hardened test method of structural reliability based on correlation analysis
MA Xiaobing, ZHANG Jianchun, ZHAO Yu
School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2016-05-19; Accepted: 2016-07-22; Published online: 2016-08-25 08:33
Foundation item: National Natural Science Foundation of China (61473014, 61471385)
Corresponding author. MA Xiaobing, E-mail: maxiaobing@buaa.edu.cn
Abstract: The traditional test verification of structural reliability is generally based on the independence assumption between loading stress and structural strength. Stating with the correlation analysis of stress and strength, we propose a hardened test method of structural reliability verification based on the stress-strength interference model with Copula correlation when loading and strength both follow the normal distribution. The method combines Copula functions with stress-strength interference model to achieve the transformation of the original reliability index and reliability index under the hardened condition, and the reliability is estimated by the traditional binomial distribution test under the condition of small sample. Compared with the independence assumption, the results show that the negative correlation between stress and strength leads to the increase of sample size and the sample size decreases with the decrease of negative correlation; the positive correlation leads to the decrease of sample size and the sample size decreases with the increase of positive correlation.
Key words: stress-strength interference model     hardened test     Copula function     test sample size     structural reliability

1 基于Copula的相关性分析

1.1 Copula相关应力-强度干涉模型

 (1)

 (2)

1.2 数据相关性分析和Copula模型选择

Copula函数的进一步选择可先通过参数估计得到Copula函数的具体表达式，再通过计算Copula函数和经验分布函数的的平方欧氏距离选择合适的Copula函数，距离越小，Copula函数的拟合程度越好。

2 考虑相关性的加严试验评定模型

2.1 模型系数定义

1) 加严系数

 (3)

2) 变差系数

 (4)

3) 生存系数

 (5)
2.2 恒加严条件下的评定模型

Clayton Copula函数的形式为

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)
2.3 变加严条件下的评定模型

 (13)

 (14)

 (15)

 (16)

3 案例分析

3.1 相关条件下加严试验样本量的确定方法

1) 恒加严条件

 图 1 不同θ下可靠度-生存系数变化 Fig. 1 Variation of reliability-survival coefficient with different θ

2) 变加严条件

3.2 应力强度的相关性对加严试验样本量的影响

 k RL=0.998 RL=0.996 RL=0.994 相关 独立 相关 独立 相关 独立 1.2 97 64 57 39 41 29 1.3 39 24 24 16 18 13 1.4 19 11 13 8 10 7 1.5 10 6 7 5 6 4

 图 2 试验样本量与相关程度参数的关系 Fig. 2 Relationship between test sample size and correlation coefficient

4 结论

1) 本文建立了可描述应力与强度相关性的加严可靠性验证试验条件与试验样本量确定方法，可通过Copula函数的选择及参数的求解来判定和度量应力与强度间的相关特性及大小。

2) 当应力与强度呈负相关时，试验样本量多于相同加严条件下独立时的试验样本量，且随着负相关程度的减弱，试验样本量逐渐减少。

3) 当应力与强度呈正相关时，试验样本量少于相同加严条件下独立时的试验样本量，且随着正相关程度的增强，试验样本量逐渐减少。

 [1] 温玉全, 洪东跑, 王玮. 基于试验熵的火工品可靠性评估理论与方法研究[J]. 爆炸与冲击, 2007, 27(6): 553–556. WEN Y Q, HONG D P, WANG W. Study on theory and method of reliability assessment of explosive initiator based on testing entropy[J]. Explosion and Shock Waves, 2007, 27(6): 553–556. DOI:10.11883/1001-1455(2007)06-0553-04(in Chinese) [2] 荣吉利, 白美, 刘志权. 加严条件下火工机构可靠性评估方法[J]. 北京理工大学学报, 2004, 24(2): 117–120. RONG J L, BAI M, LIU Z Q. Reliability assessment of pyrotechnical devices under rigorous conditions[J]. Transactions of Beijing Institute of Technology, 2004, 24(2): 117–120. (in Chinese) [3] 刘智洋, 刘鲁, 黄敏. 可靠性增长的单调约束模型[J]. 北京航空航天大学学报, 2009, 35(9): 1104–1107. LIU Z Y, LIU L, HUANG M. Monotone restriction model of reliability growth evaluation[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(9): 1104–1107. (in Chinese) [4] SCHICK G J, DRNAS T M.Bayesian reliability dmonstration[M]//HENKE M, JAEGER A, WARTMANN R, et al.Proceedings in operations research.Heidelberg:Physica-Verlag HD, 1972:92-102. [5] 卓洛托夫А А, 季托夫М И. 空间运载器的可靠性保证[M]. 王廼斌, 译. 北京: 宇航出版社, 1996: 17-24. 3ОЛОТОВ А А, ТИТОВ М И.Reliability ensures for the space vehicles[M].WANG N B, translated.Beijing:China Astronautic Publishing House, 1996:17-24(in Chinese). [6] 荣吉利, 张涛. 航天火工机构可靠性的强化试验验证方法[J]. 宇航学报, 2013, 30(6): 2426–2430. RONG J L, ZHANG T. Reliability validation on spacecraft pyrotechnical devices using the hardened test method[J]. Journal of Astronautics, 2013, 30(6): 2426–2430. (in Chinese) [7] 马斌捷, 张俊华. 已知强度和载荷变差系数的结构可靠性分析[J]. 机械强度, 1994, 16(1): 1–6. MA B J, ZHANG J H. The structural reliability analysis for known variation coefficients of strength and load[J]. Journal of Mechanical Strength, 1994, 16(1): 1–6. (in Chinese) [8] 荣吉利, 宋乾强. 正态应力-正态强度下可靠度精确置信下限[J]. 兵工学报, 2015, 36(2): 332–336. RONG J L, SONG Q Q. The exact lower confidence limit of reliability for normal stress and normal strength[J]. Acta Armamentarii, 2015, 36(2): 332–336. (in Chinese) [9] SUN Y, MA L, MORRIS J. A practical approach for reliability prediction of pipeline systems[J]. European Journal of Operational Research, 2009, 198(1): 210–214. DOI:10.1016/j.ejor.2008.07.040 [10] 唐家银, 何平, 陈崇双. 相关性失效机械系统的可靠性分析方法[M].北京: 国防工业出版社, 2014: 15-48. TANG J Y, HE P, CHEN C S. The reliability analysis method for mechanical system with relational failure[M].Beijing: National Defence Industry Press, 2014: 15-48. (in Chinese) [11] 唐小松, 李典庆, 周创兵, 等. 联合分布函数构造的Copula函数方法及结构可靠度分析[J]. 工程力学, 2013, 30(12): 8–17. TANG X S, LI D Q, ZHOU C B, et al. Modeling bivariate distribution using Copulas and its application to component reliability analysis[J]. Engineering Mechanics, 2013, 30(12): 8–17. (in Chinese) [12] WU X Z. Modelling dependence structures of soil shear strength data with bivariate copulas and applications to geotechnical reliability analysis[J]. Soils and Foundations, 2015, 55(5): 1243–1258. DOI:10.1016/j.sandf.2015.09.023 [13] MICHIELS F, DE SCHEPPER A. A new graphical tool for copula selection[J]. Journal of Computational and Graphical Statistics, 2013, 22(2): 471–493. DOI:10.1080/10618600.2012.672080 [14] NELSEN R B. An introduction to copulas[M].Berlin: Springer, 2010: 157-222. [15] 王鹏, 杜志明. 变加严系数的加严试验方法[J]. 质量与可靠性, 2007, 130(4): 24–28. WANG P, DU Z M. The hardened test method considering the changing hardened cofficient[J]. Quality and Reliability, 2007, 130(4): 24–28. (in Chinese)

#### 文章信息

MA Xiaobing, ZHANG Jianchun, ZHAO Yu

Hardened test method of structural reliability based on correlation analysis

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(6): 1080-1084
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0420