Histogram-based Stress-strength Interference Model and Approach to Reliability Calculation by Using UGF

Abstract

Abstract:

Based on UGF approach and histograms of stress and strength,a method for approximately calculating the component reliability was proposed when the probability density functions of stress and strength can not be determined exactly. For finite experimental data about stress acted on a component and its strength,the histograms of stress and strength were obtained through statistical analysis.The conventional UGF was extended and an interval-valued UGF(IVUGF) was proposed to characterize the interval-valued discrete random variables.The stress and strength characterized by histograms were expressed by using IVUGF,and then a histogram-based stress-strength interference model was proposed.A combination operator of IVUGF was applied to component's limit state function(LSF) and the IVUGF of the LSF was obtained.The weighting coefficient of probability mass was defined.The component reliability was obtained by calculating the weighted sum of all probability mass within the safety margin determined by LSF.Three typical examples were presented and it is showed that the proposed method can achieve satisfactory accuracy of reliability calculation and possesses practical value in engineering.

Key words: stress-strength interference model, histogram, reliability, universal generating function(UGF)

摘要：

为解决应力与强度的精确概率分布密度函数未知时的结构可靠性分析问题，提出了一种基于通用发生函数和直方图的可靠度近似计算方法。对于应力与强度的有限个实验数据，经过统计分析后绘出其直方图。对传统的通用发生函数法进行扩展，提出了一种区间值型的发生函数。用扩展后的发生函数对应力与强度的统计直方图进行数学表征，进而提出了一种基于直方图的应力-强度干涉模型。用区间值型发生函数法对结构的极限状态函数进行组合运算，获得极限状态函数的区间值型发生函数表示。定义了极限状态函数的概率质量加权系数，通过安全域内所有概率质量的加权累加获得结构的可靠度。给出了三个典型的可靠度计算实例。实例表明，所提出的方法具有较高的可靠度计算精度，是一种有效的可靠性分析新方法。

关键词: 应力-强度干涉模型, 直方图, 可靠度, 通用发生函数

CLC Number:

GUO Hui-Cuan, DAI Juan, CHENG Li-Zhi, JIA Zun-Feng. Histogram-based Stress-strength Interference Model and Approach to Reliability Calculation by Using UGF[J]. China Mechanical Engineering, 2013, 24(15): 2041-2047.

郭惠昕, 戴娟, 程立志, 夏尊凤. 应力—强度干涉的直方图模型及可靠度计算的发生函数法[J]. 中国机械工程, 2013, 24(15): 2041-2047.

References

[1]Ushakov I. A Universal Generating Function[J]. Soviet Journal of Computer and Systems Sciences, 1986,24(5) : 118-129.
[2]Levitin G. Universal Generating Function and its Applications[M]. Berlin: Springer, 2005.
[3]Ushakov I. The Method of Generalized Generating Sequences-J3. European Journal of Operational Re- search,2000,125(2) :316-323.
[4]Lisnianski A, Levitin G. Multistate System Reliability Assessment, Optimization and Applications[M]. Singapore: World Scientific, 2003.
[5]Levitin G. The Universal Generating Function in Reliability Analysis and Optimization[M]. London: Springer, 2005.
[6]Ding Y, Lisnianski A. Fuzzy Universal Generating Functions for Multi-state System Reliability As- sessment[J]. Fuzzy Sets and Systems, 2008, 159 (3) :307-324.
[7]周金宇[1],谢里阳[2].结构系统可靠性分析的发生函数法[J].中国科学：技术科学,2010,40(2):177-185.
[8]An Zongwen, Huang Hongzhong, Liu Yu. A Dis- crete Stress-strength Interference Model Based on Universal Generating Function[J]. Reliability Engineering & System Safety,2008,93(10):1485-1490.
[9]An Zongwen, Huang Hongzhong, Wang Zhonglai, et al. Discrete Stress- strength Interference Model of Reliability Analysis under Multi-operating Conditions[J]. Chinese Journal of Mechanical Engineer- ing, 2010,23 (3) : 1-5.
[10]贺国芳许海宝.可靠性数据的收集与分析[M].北京：国防工业出版社,1995.1-24. 8
[11]Jaynes E T. Information Theory and Statistical Mechanics[J]. Physical Review, 1957,106(4) : 620- 630.
[12]胡承毅[1],徐山鹰[2],杨晓光[2].区间算法简介[J].系统工程理论与实践,2003,23(4):59-62. 2
[13]Dong W M,Shah H C. Vertex Method for Computing Functions of Fuzzy Variables[J]. Fuzzy Sets and Systems, 1987,24(1) :65-78.
[14]唐樟春[1],吕震宙[1],吕媛波[1].随机变量概率信息不充分时的可靠性新模型[J].工程力学,2011,28(4):18-22.
[15]谭海涛[1],徐定海[1],王善[1].一种计算结构可靠度的一元分解法[J].哈尔滨工程大学学报,2009,0(8):883-886.