基于Sobol序列的防尘供水管网系统可靠性分析
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摘要
为研究矿山井下防尘供水管网系统的可靠性,综合考虑供水管网系统功能及其结构,引入流可靠度和基于阈级的单元重要度的概念,结合供水管网路径重要度和连通率,将解析法和模拟法相结合,建立矿井防尘供水管网系统可靠性计算模型,并利用Sobol序列替代伪随机数序列的拟蒙特卡罗法对供水管网系统的可靠度进行解算.将求解模型应用于开滦集团某煤矿防尘供水管网系统可靠性分析,计算结果系统可靠度为0.983,889,标准差为1.497×10~(-4).研究结果表明:组件阈级越低,其重要度就越高,对整个供水管网的影响程度越高;在管网系统可靠性求解模拟中,与伪随机数序列相比,Sobol序列的解算结果具有更高的精准度和稳定性,收敛速度更快.
In order to study the reliability of mine underground dust-proof water supply network system,the reliability calculation model of mine dust-proof water supply network system was established,by considering the function and structure of the network system,introducing the concept of flow reliability and unit importance based on threshold level,and integrating the path importance and connectivity of water supply network.The reliability was solved by using Sobol sequence of quasi Monte-Carlo instead of pseudo-random number sequence.The solving model was used to analyze the reliability of a coal mine dust-proof water supply network in Kailuan Group,the calculated result was 0.983,889 and the standard deviation was 1.497×10~(-4).The results showed that the lower the unit threshold level was,and the higher the importance degree was,the greater the impact on the entire pipe network was.The reliability of water supply network system calculated by Sobol sequence had higher accuracy and stability,and the convergence rate was faster than that by pseudo random sequence.
In order to study the reliability of mine underground dust-proof water supply network system,the reliability calculation model of mine dust-proof water supply network system was established,by considering the function and structure of the network system,introducing the concept of flow reliability and unit importance based on threshold level,and integrating the path importance and connectivity of water supply network.The reliability was solved by using Sobol sequence of quasi Monte-Carlo instead of pseudo-random number sequence.The solving model was used to analyze the reliability of a coal mine dust-proof water supply network in Kailuan Group,the calculated result was 0.983,889 and the standard deviation was 1.497×10~(-4).The results showed that the lower the unit threshold level was,and the higher the importance degree was,the greater the impact on the entire pipe network was.The reliability of water supply network system calculated by Sobol sequence had higher accuracy and stability,and the convergence rate was faster than that by pseudo random sequence.
引文
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[14]侯雨伸,王秀丽,刘杰,等.基于拟蒙特卡罗方法的电力系统可靠性评估[J].电网技术,2015,39(3):744-750.Hou Yushen,Wang Xiuli,Liu Jie,et al.A quasiMonte Carlo method based power system reliability evaluation[J].Power System Technology,2015,39(3):744-750(in Chinese).
[15]黄美发,景晖,匡兵,等.基于拟蒙特卡罗方法的测量不确定度评定[J].仪器仪表学报,2009,30(1):120-124.Huang Meifa,Jing Hui,Kuang Bing,et al.Measurement uncertainty evaluation based on quasi Monte-Carlo method[J].Chinese Journal of Scientific Instrument,2009,30(1):120-124(in Chinese).
[16]罗立哲,胡志根,刘全,等.土石围堰边坡稳定的多因素综合风险分析[J].天津大学学报:自然科学与工程技术版,2013,46(7):617-622.Luo Lizhe,Hu Zhigen,Liu Quan,et al.Comprehensive risk analysis of rock-fill cofferdam slope stability considering multiple random factors[J].Journal of Tianjin University:Science and Technology,2013,46(7):617-622(in Chinese).
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[18]Niederreiter H.Low-discrepancy and low-dispersion sequences[J].Journal of Number Theory,1988,30(1):51-70.
[19]Sobol’I M.On the distribution of points in a cube and the approximate evaluation of integrals[J].USSR Computational Mathematics and Mathematical Physics,1967,7(4):784-802.
[20]朱尧辰.点集偏差引论[M].合肥:中国科学技术大学出版社,2011:120-121.Zhu Yaochen.Introduction to Discrepancy of Point Sets[M].Hefei:University of Science and Technology of China Press,2011:120-121(in Chinese).
[21]Antonov I A,Saleev V M.An economic method of computing LPτ-sequences[J].USSR Computational Mathematics&Mathematical Physics,1979,19(1):252-256.
[2]Tanyimboh T T,Setiadi Y.Joint layout,pipe size and hydraulic reliability optimization of water distribution systems[J].Engineering Optimization,2008,40(8):729-747.
[3]何忠华,袁一星.基于剩余能量熵的供水管网可靠性优化设计[J].浙江大学学报:工学版,2014,48(7):1188-1194.He Zhonghua,Yuan Yixing.Reliability optimization design of water distribution system based on surplus energy entropy[J].Journal of Zhejiang University:Engineering Science,2014,48(7):1188-1194(in Chinese).
[4]Raad D N,Sinske A N,van Vuuren J H.Comparison of four reliability surrogate measures for water distribution systems design[J].Water Resources Research,2010,46:W05524-1-W05524-11.
[5]侯晓东,蒋仲安.矿井防尘供水管网失效模糊故障树分析[J].金属矿山,2008,38(6):112-115.Hou Xiaodong,Jiang Zhongan.Fuzzy fault tree analysis of failure of water supply network for mine dust-proofing[J].Metal Mine,2008,38(6):112-115(in Chinese).
[6]赵新华,陈春芳,郑毅.给水管网可靠度的计算[J].中国给水排水,2000,16(1):57-60.Zhao Xinhua,Chen Chunfang,Zheng Yi.Calculation of reliability of water distribution network[J].China Water&Wastewater,2000,16(1):57-60(in Chinese).
[7]Xu C G,Goulter I C,Tickle K S.Assessing the capacity reliability of ageing water distribution systems[J].Civil Engineering and Environmental Systems,2003,20(2):119-133.
[8]章征宝,余云进,徐得潜,等.基于蒙特卡罗法的城市给水管网可靠性分析[J].给水排水,2007,33(7):106-110.Zhang Zhengbao,Yu Yunjin,Xu Deqian,et al.The reliability analysis of urban water distribution network based on Monte-Carlo method[J].Water&Wastewater Engineering,2007,33(7):106-110(in Chinese).
[9]Ciaponi C,Franchioli L,Papiri S.Simplified procedure for water distribution networks reliability assessment[J].Journal of Water Resources Planning and Management,2012,138(4):368-376.
[10]蒋仲安,王佩,施蕾蕾,等.基于QMC的矿井防尘供水管网水力可靠性分析[J].煤炭学报,2013,38(增2):399-404.Jiang Zhongan,Wang Pei,Shi Leilei,et al.Hydraulic reliability analysis of water supply network for mine dust prevention based on QMC[J].Journal of China Coal Society,2013,38(Suppl 2):399-404(in Chinese).
[11]蒋仲安,王佩,施蕾蕾,等.基于低偏差序列的矿井供水管网可靠性[J].中南大学学报:自然科学版,2014,45(5):1686-1691.Jiang Zhongan,Wang Pei,Shi Leilei,et al.Mine water supply network reliability based on low deviation sequence[J].Journal of Central South University:Science and Technology,2014,45(5):1686-1691(in Chinese).
[12]刘震,潘斌.海底油气集输管网可靠性评估[J].海洋工程,2003,21(4):104-109.Liu Zhen,Pan Bin.Reliability evaluation for subsea oilgas pipeline networks[J].The Ocean Engineering,2003,21(4):104-109(in Chinese).
[13]陈思锭,李重剑,陈黎鹏.树枝状输气管网可靠性评估[J].油气储运,2012,31(5):335-339.Chen Siding,Li Zhongjian,Chen Lipeng.Reliability evaluation of dendritic gas pipeline network[J].Oil&Gas Storage and Transportation,2012,31(5):335-339(in Chinese).
[14]侯雨伸,王秀丽,刘杰,等.基于拟蒙特卡罗方法的电力系统可靠性评估[J].电网技术,2015,39(3):744-750.Hou Yushen,Wang Xiuli,Liu Jie,et al.A quasiMonte Carlo method based power system reliability evaluation[J].Power System Technology,2015,39(3):744-750(in Chinese).
[15]黄美发,景晖,匡兵,等.基于拟蒙特卡罗方法的测量不确定度评定[J].仪器仪表学报,2009,30(1):120-124.Huang Meifa,Jing Hui,Kuang Bing,et al.Measurement uncertainty evaluation based on quasi Monte-Carlo method[J].Chinese Journal of Scientific Instrument,2009,30(1):120-124(in Chinese).
[16]罗立哲,胡志根,刘全,等.土石围堰边坡稳定的多因素综合风险分析[J].天津大学学报:自然科学与工程技术版,2013,46(7):617-622.Luo Lizhe,Hu Zhigen,Liu Quan,et al.Comprehensive risk analysis of rock-fill cofferdam slope stability considering multiple random factors[J].Journal of Tianjin University:Science and Technology,2013,46(7):617-622(in Chinese).
[17]Halton J H.On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals[J].Numerische Mathematik,1960,2(1):84-90.
[18]Niederreiter H.Low-discrepancy and low-dispersion sequences[J].Journal of Number Theory,1988,30(1):51-70.
[19]Sobol’I M.On the distribution of points in a cube and the approximate evaluation of integrals[J].USSR Computational Mathematics and Mathematical Physics,1967,7(4):784-802.
[20]朱尧辰.点集偏差引论[M].合肥:中国科学技术大学出版社,2011:120-121.Zhu Yaochen.Introduction to Discrepancy of Point Sets[M].Hefei:University of Science and Technology of China Press,2011:120-121(in Chinese).
[21]Antonov I A,Saleev V M.An economic method of computing LPτ-sequences[J].USSR Computational Mathematics&Mathematical Physics,1979,19(1):252-256.