不确定性信息条件下系统可靠性分析
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摘要
在系统可靠性分析中,参数不确定性的正确表达是评价系统稳定与否的先决条件。然而,在实际情况中,影响系统可靠性的参数分布往往缺乏严格的规律性,即便参数大体符合某种分布,也存在漂移现象,采用传统方法处理这类不确定性,存在信息丢失问题。为此引入概率盒理论,提出一种新的不确定性信息条件下系统可靠性分析方法。首先对各个不确定参数进行概率盒建模;其次,将各参数概率盒等信度离散,结合系统可靠性方程计算笛卡尔积,进而得到系统可靠性概率盒模型;最后,以零点为边界划分出风险区和稳定区,并通过积分计算面积定量地分析系统的可靠性。实验以悬臂梁系统为分析对象,与传统方法进行对比分析,实验结果表明,该方法不仅有效而且提高了准确性。
In system stability analysis,a correct expression of the uncertain parameters is a prerequisite for stability evaluation. However,the parameter distribution that affects system reliability often lacks strict regularity in engineering. Even the parameters generally obey a certain distribution,they always drift. Information-loss is another concern when traditional methods are used to deal with such uncertainties. Therefore,a new method to conduct system reliability analysis under uncertain information is proposed by introducing probability-box theory. Firstly,the probability-box is used to model uncertain parameters. Secondly,the probability-box model of system reliability is obtained by discretizing each parameter into equally confidence levels and calculating Cartesian product with the system reliability equation. Finally,the risk zone and the stable zone are divided with zero as boundary,and the system reliability is quantitatively analyzed by integral calculating the area of probability-box. The cantilever beam system is analyzed in the experiments.Experimental results demonstrate that the proposed method is effective,and can also improve the accuracy compared with other related approaches.
In system stability analysis,a correct expression of the uncertain parameters is a prerequisite for stability evaluation. However,the parameter distribution that affects system reliability often lacks strict regularity in engineering. Even the parameters generally obey a certain distribution,they always drift. Information-loss is another concern when traditional methods are used to deal with such uncertainties. Therefore,a new method to conduct system reliability analysis under uncertain information is proposed by introducing probability-box theory. Firstly,the probability-box is used to model uncertain parameters. Secondly,the probability-box model of system reliability is obtained by discretizing each parameter into equally confidence levels and calculating Cartesian product with the system reliability equation. Finally,the risk zone and the stable zone are divided with zero as boundary,and the system reliability is quantitatively analyzed by integral calculating the area of probability-box. The cantilever beam system is analyzed in the experiments.Experimental results demonstrate that the proposed method is effective,and can also improve the accuracy compared with other related approaches.
引文
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[18] FERSON S,KREINOVICH V,GINZBURG L,et al.Constructing probability boxes and Dempster Shafer structures[R]. SAND2003-4015,Albuquerque,NM:Sandia National Laboratories,2003.
[2]常振.滚动轴承性能稳定性及可靠性分析[J].仪器仪表学报,2017,38(6):1421-1431.CHANG ZH. Stability and reliability analysis of rolling bearing performance[J]. Chinese Journal of Scientific Instrument,2017,38(6):1421-1431.
[3] MI J H,LI Y F,PENG W W,et al. Reliability modeling and analysis of complex multi-state system based on interval fuzzy Bayesian network[J]. Scientia Sinica,2018,48(1):014604
[4] MUSCOLINO G,SOFI A. Analysis of structures with random axial stiffness described by imprecise probability density functions[J]. Computers&Structures,2017(184):1-13.
[5] PARK I,AMARCHINTA H K,GRANDHI R V. A Bayesian approach for quantification of model uncertainty[J]. Reliability Engineering&System Safety,2017,95(7):777-785.
[6]刘海波,姜潮,郑静,等.含概率与区间混合不确定性的系统可靠性分析方法[J].力学学报,2017,49(2):225-235.LIU H B, JIANG CH, ZHENG J, et al. A system reliability analysis method for structures with probability and interval mixed uncertainty[J]. Chinese Journal of Theoretical and Applied Mechanics,2017,49(2):225-235.
[7]时光,陈忠华,郭凤仪,等.基于模糊反演法的参数不确定弓网接触载荷控制[J].仪器仪表学报,2017,38(2):471-479.SHI G,CHEN ZH H,GUO F Y. Control of pantographcatenary contact load with parameter uncertainties based on fuzzy backstepping[J]. Chinese Journal of Scientific Instrument,2017,38(2):471-479.
[8]姜潮,张旺,韩旭.基于Copula函数的证据理论相关性分析模型及结构可靠性计算方法[J].机械工程学报,2017,53(16):199-209.JIANG CH,ZHANG W,HAN X,A Copula function based evidence theory model for correlation analysis and corresponding structural reliability method[J]. Journal of Mechanical Engineering,2017,53(16):199-209.
[9]宋玉杰,彭惠芬,夏晔.再制造抽油杆纵向共振模糊可靠性分析[J].石油学报,2017,38(4):468-474.SONG Y J,PENG H F,XIA Y. A fuzzy reliability analysis on the longitudinal vibration of remanufacturing sucker rod[J]. Acta Petrolei Sinica,2017,38(4):468-474.
[10] CHEN D N,LI H SH,YAO CH Y,et al. Reliability analysis based on evidence theory and Bayesian network for hydraulic drive system[J]. Chinese Hydraulics&Pneumatics,2017(4):8-14.
[11]李贵杰,吕震宙,葛山增,等.用非概率理论分析混合不确定性结构的可靠性[J].国防科技大学学报,2014(5):21-25.LI G J,LV ZH ZH,GE SH Z,et al. A reliability approach based on non-probabilistic theory for structures with hybrid uncertainties[J]. Journal of National University of Defense Technology,2014(5):21-25.
[12]姜潮,张哲,韩旭,等.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 CH,ZHANG ZH,HAN X,et al. A structural reliability analysis method based on evidence theory[J].Chinese Journal of Theoretical and Applied Mechanics,2013,45(1):103-115.
[13]周月阁,叶雪荣,翟国富.基于性能退化和MonteCarlo仿真的系统性能可靠性评估[J].仪器仪表学报,2014,35(5):1185-1191.ZHOU Y G,YE X R,ZHAI G F. System performance reliability assessment based on performance degradation and Monte-Carlo simulation[J]. Chinese Journal of Scientific Instrument,2014,35(5):1185-1191.
[14] SHAYANFAR M A, BARKHORDARI M A,BARKHORI M,et al. An adaptive line sampling method for reliability analysis[J]. Iranian Journal of Science&Technology Transactions of Civil Engineering, 2017,41(3):275-282.
[15] FENG Z,DENG W,HUA N,et al. Reliability analysis of bleed air anti-icing system based on subset simulation method[J]. Applied Thermal Engineering, 2017,115(25):17-21.
[16] PATOWARY A N,HAZARIKA J,SRIWASTAV G L.Reliability estimation of multi-component cascade system through Monte-Carlo simulation[J]. International Journal of System Assurance Engineering&Management,2018,9(6):1279-1286.
[17] PRADLWARTER H J,SCHUELLER G I. Local domain Monte Carlo simulation[J]. Structural Safety, 2010,32(5):275-280.
[18] FERSON S,KREINOVICH V,GINZBURG L,et al.Constructing probability boxes and Dempster Shafer structures[R]. SAND2003-4015,Albuquerque,NM:Sandia National Laboratories,2003.