大型矿井通风网络可靠度模型的近似算法
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摘要
针对目前风量分布中依靠经验认识全部近似认为是正态分布的情况,利用概率图分析法给出了判断风量分布的严格定义,且给出了基于对数正态分布的风量分布模型,证明了并非所有风量分布均服从正态分布.为避开失效模式的NP难题,提出网络可靠度的近似算法.该方法以递推分解算法为基础,引入多维正态变量积分公式,计算多失效模型的联合概率,进而计算风网系统的可靠度,大大降低了计算复杂性.对于特别复杂的风网,也可以采用上下界逼近的方法得出近似值,并通过实例分析,验证了本方法的高精度和高效率.
Current understanding of air flows assumes a normal distribution to the flows.A probabilistic graphical analysis is used to show the actual distribution to be more accurately given by a log normal distribution.Some air flows are quite decidedly not normally distributed.An approximation algorithm of air network reliability is proposed to avoid the NP failure mode.The method is based on recursive decomposition.A multidimensional,normal variable,integral is introduced for calculation of the joint probability of multiple failures.Reliability of the ventilation network is calculated and the complexity of the computations is greatly reduced.Complex networks may benefit from the method of approximation bounds.A practical example analysis is presented showing the high efficiency and accuracy of the method.
Current understanding of air flows assumes a normal distribution to the flows.A probabilistic graphical analysis is used to show the actual distribution to be more accurately given by a log normal distribution.Some air flows are quite decidedly not normally distributed.An approximation algorithm of air network reliability is proposed to avoid the NP failure mode.The method is based on recursive decomposition.A multidimensional,normal variable,integral is introduced for calculation of the joint probability of multiple failures.Reliability of the ventilation network is calculated and the complexity of the computations is greatly reduced.Complex networks may benefit from the method of approximation bounds.A practical example analysis is presented showing the high efficiency and accuracy of the method.
引文
[1]贾进章.矿井火灾时期通风系统可靠性[M].北京:煤炭工业出版社,2005:23-35.
[2]王洪德,刘贞堂.矿井通风网络可靠性的定量分析与评价[J].中国矿业大学学报,2007,36(3):371-375.WANG Hong-de,LIU Zhen-tang.Quantitative anal-ysis and evaluation on reliability of mine ventilationnetwork[J].Journal of China University of Mining&Technology,2007,36(3):371-375.
[3]贾进章,刘剑,姜克寒.风路可靠度确定数学模型[J].辽宁工程技术大学学报,2005,24(6):801-804.JIA Jin-zhang,LIU Jian,JIANG Ke-han.Mathe-matical model for determination of airway reliability[J].Journal of Liaoning Technical University,2005,24(6):801-804.
[4]FONG C C,BUZACOTT J A.An algorithm for sy-mbolic reliability computation with path-sets or cut-sets[J].IEEE Transactions on Reliability,1987,R-36(1):34-37.
[5]LOCKS M O.A minizing algrithms for sum of dis-joint products[J].IEEE Transactions on Reliability,1987,R-36(4):445-453.
[6]HARIRI S,RAGHAVENDRA C S.A symbolic re-liability algorithm based on path and cut set methods[J].IEEE Transactions on Reliability,1987,C-36(10):1224-1232.
[7]金星,洪延姬.工程系统可靠性数值分析方法[M].北京:国防工业出版社,2002.
[8]曹晋华,程侃.可靠性数学引论:修订版[M].北京:高等教育出版社,2006.
[9]卢明银,徐人平.系统可靠性[M].北京:机械工业出版社,2008.
[10]王国富,王志忠.应用统计[M].长沙:中南大学出版社,2003.
[11]张志国,曹洋,孙平.对数正态分布参数的精确估计及其应用[J].辽宁科技大学学报,2008,31(3):269-272.ZHANG Zhi-guo,CAO Yang,SUN Ping.Preciseestimation and application of log-normal distributionparameters[J].Journal of University of Science andTechnology Liaoning,2008,31(3):269-272.
[12]顾益明.分组型数据的产品可靠性的近似极大似然估计[J].上海师范大学学报:自然科学版,2001,30(2):28-33.GU Yi-ming.The approximate likelihood estimateof multicomponent data[J].Journal of ShanghaiTeachers University:Natural Sciences,2001,30(2):28-33.
[13]郑明,杨艺.基于分组数据的对数正态分布的参数估计[J].系统工程理论方法应用,2004,13(6):553-556.ZHENG Ming,YANG Yi.Estimating parameter inlognormal distribution from grouped data[J].Sys-tems Engineering-Theory Methodology Applica-tions,2004,13(6):553-556.
[14]李杰,刘威,钱摇琨.网络可靠度分析的最小割集递推分解算法[J].地震工程与工程振动,2007,27(5):33-39.LI Jie,LIU Wei,QIAN Yao-kun.Minimal cut-based recursive decomposition algorithm for networkreliability analysis[J].Journal of Earthquake Engi-neering and Engineering Vibration,2007,27(5):33-39.
[15]刘威,李杰.网络可靠度分析的最小路算法和最小割算法研究[J].地震工程与工程振动,2008,28(3):33-38.LIU Wei,LI Jie.Comparison between path-basedand cut-based algorithms for reliability analysis ofnetworks[J].Journal of Earthquake Engineeringand Engineering Vibration,2008,28(3):33-38.
[16]何军,李杰.大型相关失效工程网络系统可靠度的近似算法[J].计算力学学报,2003,20(3):261-266.HE Jun,LI Jie.Approximate method for large en-gineering network system with correlation failure[J].Journal of Chinese Journal of ComputationalMechanics,2003,20(3):261-266.
[17]TERADA S,TAKAHASHI T.Failure-conditionedreliability index[J].Journal of Structural Engineer-ing,ASCE,1988,1143(4):943-952.
[18]PANDEY M D.An effective approximation to eval-uate multinormal integrals[J].Journal of StructuralSafety,ASCE,1998(20):56-67.
[19]周利华.矿井通风网络最小路集不交化可靠度的计算[J].系统工程理论与实践,2004(3):134-138.ZHOU Li-hua.Calculation of system reliability formine ventilation network based on boolean manipu-lation and minimization algorithm in the independ-ence minimal path sets[J].Systems Engineering-Theory&Practice,2004(3):134-138.
[20]周利华.矿井通风网络最小割集不交和可靠度的计算[J].湘潭矿业学院学报,2003,18(1):10-12.ZHOU Li-hua.Calculation of system reliability formine ventilation network based on boolean manipu-lation and minimization algorithm in the minimal cutsets[J].J Xiangtan Min Inst,2003,18(1):10-12.
[21]陈开岩,傅清国.矿井通风系统安全可靠性评价软件设计及应用[J].中国矿业大学学报,2003,32(4):343-348.CHEN Kai-yan,FU Qing-guo.Design and applica-tion of estimation software for safety reliability ofmine ventilation system[J].Journal of China Uni-versity of Mining&Technology,2003,32(4):343-348.
[22]李江,陈开岩,林柏泉.遗传算法在矿井通风网络优化中的应用[J].中国矿业大学学报,2007,36(6):789-793.LI Jiang,CHEN Kai-yan,LIN Bai-quan.Geneticalgorithm for the optimization of mine ventilationnetwork[J].Journal of China University of Mining&Technology,2007,36(6):789-793.
[2]王洪德,刘贞堂.矿井通风网络可靠性的定量分析与评价[J].中国矿业大学学报,2007,36(3):371-375.WANG Hong-de,LIU Zhen-tang.Quantitative anal-ysis and evaluation on reliability of mine ventilationnetwork[J].Journal of China University of Mining&Technology,2007,36(3):371-375.
[3]贾进章,刘剑,姜克寒.风路可靠度确定数学模型[J].辽宁工程技术大学学报,2005,24(6):801-804.JIA Jin-zhang,LIU Jian,JIANG Ke-han.Mathe-matical model for determination of airway reliability[J].Journal of Liaoning Technical University,2005,24(6):801-804.
[4]FONG C C,BUZACOTT J A.An algorithm for sy-mbolic reliability computation with path-sets or cut-sets[J].IEEE Transactions on Reliability,1987,R-36(1):34-37.
[5]LOCKS M O.A minizing algrithms for sum of dis-joint products[J].IEEE Transactions on Reliability,1987,R-36(4):445-453.
[6]HARIRI S,RAGHAVENDRA C S.A symbolic re-liability algorithm based on path and cut set methods[J].IEEE Transactions on Reliability,1987,C-36(10):1224-1232.
[7]金星,洪延姬.工程系统可靠性数值分析方法[M].北京:国防工业出版社,2002.
[8]曹晋华,程侃.可靠性数学引论:修订版[M].北京:高等教育出版社,2006.
[9]卢明银,徐人平.系统可靠性[M].北京:机械工业出版社,2008.
[10]王国富,王志忠.应用统计[M].长沙:中南大学出版社,2003.
[11]张志国,曹洋,孙平.对数正态分布参数的精确估计及其应用[J].辽宁科技大学学报,2008,31(3):269-272.ZHANG Zhi-guo,CAO Yang,SUN Ping.Preciseestimation and application of log-normal distributionparameters[J].Journal of University of Science andTechnology Liaoning,2008,31(3):269-272.
[12]顾益明.分组型数据的产品可靠性的近似极大似然估计[J].上海师范大学学报:自然科学版,2001,30(2):28-33.GU Yi-ming.The approximate likelihood estimateof multicomponent data[J].Journal of ShanghaiTeachers University:Natural Sciences,2001,30(2):28-33.
[13]郑明,杨艺.基于分组数据的对数正态分布的参数估计[J].系统工程理论方法应用,2004,13(6):553-556.ZHENG Ming,YANG Yi.Estimating parameter inlognormal distribution from grouped data[J].Sys-tems Engineering-Theory Methodology Applica-tions,2004,13(6):553-556.
[14]李杰,刘威,钱摇琨.网络可靠度分析的最小割集递推分解算法[J].地震工程与工程振动,2007,27(5):33-39.LI Jie,LIU Wei,QIAN Yao-kun.Minimal cut-based recursive decomposition algorithm for networkreliability analysis[J].Journal of Earthquake Engi-neering and Engineering Vibration,2007,27(5):33-39.
[15]刘威,李杰.网络可靠度分析的最小路算法和最小割算法研究[J].地震工程与工程振动,2008,28(3):33-38.LIU Wei,LI Jie.Comparison between path-basedand cut-based algorithms for reliability analysis ofnetworks[J].Journal of Earthquake Engineeringand Engineering Vibration,2008,28(3):33-38.
[16]何军,李杰.大型相关失效工程网络系统可靠度的近似算法[J].计算力学学报,2003,20(3):261-266.HE Jun,LI Jie.Approximate method for large en-gineering network system with correlation failure[J].Journal of Chinese Journal of ComputationalMechanics,2003,20(3):261-266.
[17]TERADA S,TAKAHASHI T.Failure-conditionedreliability index[J].Journal of Structural Engineer-ing,ASCE,1988,1143(4):943-952.
[18]PANDEY M D.An effective approximation to eval-uate multinormal integrals[J].Journal of StructuralSafety,ASCE,1998(20):56-67.
[19]周利华.矿井通风网络最小路集不交化可靠度的计算[J].系统工程理论与实践,2004(3):134-138.ZHOU Li-hua.Calculation of system reliability formine ventilation network based on boolean manipu-lation and minimization algorithm in the independ-ence minimal path sets[J].Systems Engineering-Theory&Practice,2004(3):134-138.
[20]周利华.矿井通风网络最小割集不交和可靠度的计算[J].湘潭矿业学院学报,2003,18(1):10-12.ZHOU Li-hua.Calculation of system reliability formine ventilation network based on boolean manipu-lation and minimization algorithm in the minimal cutsets[J].J Xiangtan Min Inst,2003,18(1):10-12.
[21]陈开岩,傅清国.矿井通风系统安全可靠性评价软件设计及应用[J].中国矿业大学学报,2003,32(4):343-348.CHEN Kai-yan,FU Qing-guo.Design and applica-tion of estimation software for safety reliability ofmine ventilation system[J].Journal of China Uni-versity of Mining&Technology,2003,32(4):343-348.
[22]李江,陈开岩,林柏泉.遗传算法在矿井通风网络优化中的应用[J].中国矿业大学学报,2007,36(6):789-793.LI Jiang,CHEN Kai-yan,LIN Bai-quan.Geneticalgorithm for the optimization of mine ventilationnetwork[J].Journal of China University of Mining&Technology,2007,36(6):789-793.
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