供水管网经济剩余寿命预测
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摘要
供水管道修复/更换过程通常需要花费巨大的预算并消耗大量的时间,寻找一种高效的程序或方法,如对管道经济剩余寿命进行评估,将有利于管网的维护管理。
本文对爆管统计模型进行了详细分析,结合研究区域供水管网的基本信息和管道爆管历史记录,建立了爆管预测EPR模型(进化多项式模型,Evolutionary Polynomial Regression)。EPR模型为分组管道的综合模型,不能直接用来预测单根管道的爆管率,鉴于EPR爆管模型包含综合变量管长和时间因子管龄,建立了单根管道爆管率预测方程。结合管道极限爆管率,求得管道经济最优更换时间。将管道经济最优更换时间作为管道生存时间,选择半参数Cox模型(比例风险模型)对管道进行生存分析,求得了管道生存函数,经分析,管道生存时间符合Weibull分布。采用标准得分残差对模型进行检验,证明管道生存函数符合比例风险假定。管道经济剩余寿命定义为管道从现在算起达到其中位剩余寿命的时间,在此基础上建立了管道经济剩余寿命预测模型,并采用剩余残差对模型进行了检验。最后对管道经济寿命的影响因素进行了分析,确定在本文模型变量的设置情况下,管径和管材为保护因子,管长为危险因子。
研究表明,上述方法可以分析出管道经济寿命的影响因素,并建立管道经济剩余寿命的预测模型,且模型具有较高的拟合精度。
Since rehabilitation and replacement of water pipes usually require immense budget and time, efficient program or methodology, such as evaluating the economic residual life of pipes, is expected to extremely useful in the maintenance of water distribution system.
This paper introduced many statistical models of pipe failure prediction and the EPR (Evolutionary Polynomial Regression) model was developed based on the basic information of water pipes and historic records of pipe breaks in the study area. The EPR model reported here was aggregated, so it cannot be used directly for assessing burst rate at the individual pipe level. But EPR model contained the aggregated variable (pipe length) and the time factor (pipe age), the burst rate forecasting equation of individual pipe was established. The optimal replacement time of a pipe was obtained using the equivalence relationship between burst rate and threshold break rate. The survival analysis based on Cox regression (the proportional hazards model) for pipes were made, which the survival times were defined as the economic optimal replacement times of pipes. Then the survival function was obtained, and the distribution of the survival times of the pipes was considered to have a Weibull distribution. The survival function was proved to obeyed the proportional hazards assumption by analyzing the standardized score residuals. The model for predicting economic residual life of water pipes was constructed based on the definition of economic residual life which calculated as the remaining time until a pipe reached the median survival time from the current time of the analysis. Then the model was test by the deviance residuals. Finally, the main factors affecting the economic life of water pipes were analyzed, the conclusion was that pipe diameter and pipe material were protective factors, pipe length was risk factor in this paper.
It showed that the methodology developed in this paper may help utilities identify important factors related to the economic life, and obtain the model for predicting economic residual life of water pipes which was verified to be of better fitting accuracy.
本文对爆管统计模型进行了详细分析,结合研究区域供水管网的基本信息和管道爆管历史记录,建立了爆管预测EPR模型(进化多项式模型,Evolutionary Polynomial Regression)。EPR模型为分组管道的综合模型,不能直接用来预测单根管道的爆管率,鉴于EPR爆管模型包含综合变量管长和时间因子管龄,建立了单根管道爆管率预测方程。结合管道极限爆管率,求得管道经济最优更换时间。将管道经济最优更换时间作为管道生存时间,选择半参数Cox模型(比例风险模型)对管道进行生存分析,求得了管道生存函数,经分析,管道生存时间符合Weibull分布。采用标准得分残差对模型进行检验,证明管道生存函数符合比例风险假定。管道经济剩余寿命定义为管道从现在算起达到其中位剩余寿命的时间,在此基础上建立了管道经济剩余寿命预测模型,并采用剩余残差对模型进行了检验。最后对管道经济寿命的影响因素进行了分析,确定在本文模型变量的设置情况下,管径和管材为保护因子,管长为危险因子。
研究表明,上述方法可以分析出管道经济寿命的影响因素,并建立管道经济剩余寿命的预测模型,且模型具有较高的拟合精度。
Since rehabilitation and replacement of water pipes usually require immense budget and time, efficient program or methodology, such as evaluating the economic residual life of pipes, is expected to extremely useful in the maintenance of water distribution system.
This paper introduced many statistical models of pipe failure prediction and the EPR (Evolutionary Polynomial Regression) model was developed based on the basic information of water pipes and historic records of pipe breaks in the study area. The EPR model reported here was aggregated, so it cannot be used directly for assessing burst rate at the individual pipe level. But EPR model contained the aggregated variable (pipe length) and the time factor (pipe age), the burst rate forecasting equation of individual pipe was established. The optimal replacement time of a pipe was obtained using the equivalence relationship between burst rate and threshold break rate. The survival analysis based on Cox regression (the proportional hazards model) for pipes were made, which the survival times were defined as the economic optimal replacement times of pipes. Then the survival function was obtained, and the distribution of the survival times of the pipes was considered to have a Weibull distribution. The survival function was proved to obeyed the proportional hazards assumption by analyzing the standardized score residuals. The model for predicting economic residual life of water pipes was constructed based on the definition of economic residual life which calculated as the remaining time until a pipe reached the median survival time from the current time of the analysis. Then the model was test by the deviance residuals. Finally, the main factors affecting the economic life of water pipes were analyzed, the conclusion was that pipe diameter and pipe material were protective factors, pipe length was risk factor in this paper.
It showed that the methodology developed in this paper may help utilities identify important factors related to the economic life, and obtain the model for predicting economic residual life of water pipes which was verified to be of better fitting accuracy.
引文
[1] Gat Y L, Eisenbeis P. Using maintenance records to forecast failures in water networks[J]. Urban Water, 2000, 2(3): 173-181.
[2] Dandy G C, Engelhardt M. Optimal scheduling of water pipe replacement using genetic algorithms[J]. Journal of Water Resources Planning and Management, 2001, 127(4): 214-223.
[3] Loganathan G V, Park S, Sherali H D. Threshold break rate for pipeline replacement in water distribution systems[J]. Journal of Water Resources Planning and Management, 2002, 128(4): 271-279.
[4] Mailhot A, Paulin A, Villeneuve J. Optimal replacement of water pipes[J]. Water Resources Research, 2003, 39(5): 1136-1149.
[5] Watson T. A hierarchical Bayesian model and simulation software for water pipe networks[D]. Auckland: University of Auckland, 2005.
[6] Yousef M, Nassar R. Analysis of accelerated failure times of rehabilitation liners subjected to a constant or variable pressure[J]. Tunneling and Underground Space Technology, 2006, 21(1): 97-105.
[7] Vairavamoorthy K, Yan J, Galgale M, et al. IRA-WDS: A GIS-based risk analysis tool for water distribution systems[J]. Environmental Modeling and Software, 2007, 22(7): 951-965.
[8] Park S, Jun H, Kim B, et al. Modeling of water main failure rates using the log-linear ROCOF and the power law process[J]. Water Resources Management, 2008, 22(9): 1311-1324.
[9] Dridi L, Mailhot A, Parizeau M, et al. Multiobjective approach for pipe replacement based on Bayesian inference of break model parameters[J]. Journal of Water Resources Planning and Management, 2009, 135(5): 344-354.
[10] Christodoulou S, Deligianni A. A neurofuzzy decision framework for the management of water distribution networks[J]. Water Resources Management, 2010, 24(1): 139-156.
[11] Daniel P, Daniel B N, James H G. Detection of patterns in water distribution pipe breakage using spatial scan statistics for point events in a physical network[J]. Journal of Computing in Civil Engineering, 2011, 25(1): 21-30.
[12]何芳.供水管网爆管分析方法与预防技术研究[D].上海:同济大学, 2005.
[13]余承烈,韩自力.对铸铁管爆管现象的认识及预防措施[J].工业用水与废水, 2000, 31(2): 42-44.
[14]朱东海,张土乔,毛根海.城市给水管网爆管点动态定位的神经网络模型研究[J].水利学报, 2000(5): 1-5.
[15]何芳,刘遂庆.供水管网爆管事故分析与对策探讨[J].管道技术与设备, 2004(5): 20-23.
[16]马乐宁,刘文君,徐洪福.供水管道爆漏事故影响因素实例分析[J].给水排水, 2006, 32(9): 86-89.
[17]张玉先,陈欣,张硕.常州市大口径输水钢管爆管原因与对策研究[J].给水排水, 2006, 32(7): 89-93.
[18]于静,蒋白懿,代进.基于极限爆管率的给水管最佳更换时间研究[J].给水排水, 2007, 33(9): 108-110.
[19]方丹霞,陈明.基于GIS的供水管道爆管因素空间分析[J].城市勘测, 2007(2): 30-32.
[20]荣宏伟,张朝升,张立秋,等.城市给水管爆管机理分析[J].广州大学学报(自然科学版), 2008, 17(6): 59-63.
[21]李震,裴亮,田一梅.基于FAHP的供水管道爆管因素权重的确定[J].中国给水排水, 2009, 25(9): 75-78.
[22]王祎,田一梅,单金林,等.供水管网系统爆管预测[J].天津大学学报, 2010, 43(9): 840-843.
[23]张海亚,田一梅,裴亮.基于GIS的供水管网爆管空间分析模型的建立与应用[J].中国给水排水, 2010, 26(19): 71-77.
[24]刘俊,俞国平.基于遗传程序设计的供水管网爆管预测模型[J].同济大学学报(自然科学版), 2011, 39(3): 401-404.
[25]张海亚.基于GIS的城市供水管网爆管空间分析及预测[D].天津:天津大学, 2009.
[26] Kleiner Y, Rajani B. Comprehensive review of structural deterioration of water mains: statistical models[J]. Urban Water, 2001, 3(3): 121-150.
[27] Park S, Jun H, Agbenowosi N, et al. The proportional hazards modeling of water main failure data incorporating the time-dependent effects of covariates[J]. Water Resources Management, 2011, 25(6): 1-19.
[28] Male J W, Walski T M. Analyzing watermain replacement policies[J]. Journal of Water Resources Planning and Management, 1990, 116(3): 363-374.
[29] Shamir U. An analytic approach to scheduling pipe replacement[J]. Journal American Water Works Association, 1979, 71(5): 248-258.
[30] Walski T M, Pelliccia A. Economic analysis of water main breaks[J]. Journal American Water Works Association, 1982, 74(3): 140-147.
[31] Clark R M. Water distribution systems: A spatial and cost evaluation[J]. Journal of Water Resources Planning and Management Division, 1982, 108(3): 243-256.
[32]陈希儒.广义线性模型(一)[J].数理统计与管理, 2002, 21(5): 54-61.
[33] Guikema S D, Davidson R A. Statistical models for the effect of tree trimming on power system outages[J]. IEEE Transactions Power Delivery, 2006, 21(3): 1549-1557.
[34]王济川,郭志刚. Logistic回归模型方法与应用[M].北京:高等教育出版社, 2001.
[35]卢纹岱. SPSS for Windows统计分析(第3版)[M].北京:电子工业出版社, 2003.
[36] Cox D R. Regression models and life tables[J]. Journal of Royal Statistic Society, 1972, 34(B): 187-220.
[37] Marks H D. Predicting water distribution maintenance strategies: A case study of New Haven Connecticut[J]. Advance in Water Resources, 1985, 8(2): 86-95.
[38] Andreou S A, Marks H D. A new Methodology for modeling break failure patterns in deteriorating water distribution systems: Theory[J]. Advance in Water Resources, 1987, 10(1): 2-10.
[39] Andreou S A, Marks H D. A new Methodology for modeling break failure patterns in deteriorating water distribution systems: Applications[J]. Advance in Water Resources, 1987, 10(1): 11-20.
[40] Marks H D, Andreou S A, Jeffrey L, et al. Statistical models for water main failures[J]. Advance in Water Resources, 1987, 12(4): 184-193.
[41] Bremond B. Statistical modeling as help in network renewal decision[J]. Journal of Water Resources Planning and Management, 1997, 123(2): 67-77.
[42] Lei J. Statistical approach for describing lifetimes of water mains-case Trondheim Municipality[J]. SINTEF Civil and Environmental Engineering, 1997, 22(7): 21-26.
[43] Li D, Haimes Y Y. Optimal maintenance-related decision making for deteriorating water distribution systems 1[J]. Water Resources Research, 1992, 28(4): 1053-1061.
[44] Li D, Haimes Y Y. Optimal maintenance-related decision making for deteriorating water distribution systems 2[J]. Water Resources Research, 1992, 28(4): 1063-1070.
[45] Davidson J W, Savic D A, Walters G A. Method for Identi?cation of explicit polynomial formulae for the friction in turbulent pipe ?ow[J]. Journal of Hydroinformatics, 1999, 2(1): 115-126.
[46] Giustolisi O, Laucelli D, Savic D A. Development of rehabilitation plans for water mains replacement considering risk and cost-bene?t assessment[J]. Civil Engineering and Environmental Systems, 2006, 23 (3): 175-190.
[47] Berardi L, Giustolisi O, Kapelan Z, et al. Development of pipe deterioratin models for water distribution systems using EPR[J]. Journal of Hydroinformatics, 2008, 10(2): 113-126.
[48] Giustolisi O, Berardi L. Prioritizing pipe replacement: from multiobjective genetic algorithms to operational decision support[J]. Journal of Water Resources Planning and Management, 2009, 135(6): 484-492.
[49] Xu Q, Chen Q W, Li W F, et al. Pipe break prediction based on evolutionary data-driven methods with brief recorded data[J]. Reliability Engineering and System Safety, 2011, 96(8): 928-942.
[50] Koza J R. Genetic Programming: On the Programming of Computers by Natural Selection[M]. Cambridge: MIT Press, 2006.
[51] Giustolisi O, Savic D A. A symbolic data-driven technique based on volutionary polynomial regression[J]. Journal of Hydroinformatics, 2006, 10(2): 113-126.
[52] Giustolisi O, Doglioni A, Savic D A, et al. A multi-model approach to analysis of environmental phenomena[J]. Environmental Modelling and Software, 2007, 22(5): 674-682.
[53]刘同生,刘茂.国外城市供水管道最佳更换时间预测的经验与借鉴[J].给水排水, 2009, 35(11): 218-221.
[54] Stone S L, Dzuray E J, Meisegeier D. Decision-support tools for predicting the performance of water distribution and wastewater collection systems[M]. Cincinnati: United States Environmental Protection Agency, 2002.
[55]马学文,夏利,程琳.城市供水管道更新时间预测模型[J].沈阳建筑大学学报(自然科学版), 2008, 24(1): 129-131.
[56]黎子良,郑祖康.生存分析[M].杭州:浙江科学技术出版社, 1993.
[57]彭非,王伟.生存分析[M].北京:中国人民大学出版社, 2004.
[58]胡良平,高辉. SAS统计分析教程[M].北京:电子工业出版社, 2010.
[59] Klein J P, Moeschberger M L. Survival analysis: techniques for censored and truncated data[M]. New York: Springer, 2003.
[60] Therneau T M, Grambsch P M, Fleming T R. Martingale-based residuals for survival models[J]. Biometrika, Oxford Journals, 1990, 77(1), 147-160.
[61] Alllison P D. Survival analysis using SAS: a practical guide[M]. Cary, NC: SAS Institute Incorporated, 1996.
[2] Dandy G C, Engelhardt M. Optimal scheduling of water pipe replacement using genetic algorithms[J]. Journal of Water Resources Planning and Management, 2001, 127(4): 214-223.
[3] Loganathan G V, Park S, Sherali H D. Threshold break rate for pipeline replacement in water distribution systems[J]. Journal of Water Resources Planning and Management, 2002, 128(4): 271-279.
[4] Mailhot A, Paulin A, Villeneuve J. Optimal replacement of water pipes[J]. Water Resources Research, 2003, 39(5): 1136-1149.
[5] Watson T. A hierarchical Bayesian model and simulation software for water pipe networks[D]. Auckland: University of Auckland, 2005.
[6] Yousef M, Nassar R. Analysis of accelerated failure times of rehabilitation liners subjected to a constant or variable pressure[J]. Tunneling and Underground Space Technology, 2006, 21(1): 97-105.
[7] Vairavamoorthy K, Yan J, Galgale M, et al. IRA-WDS: A GIS-based risk analysis tool for water distribution systems[J]. Environmental Modeling and Software, 2007, 22(7): 951-965.
[8] Park S, Jun H, Kim B, et al. Modeling of water main failure rates using the log-linear ROCOF and the power law process[J]. Water Resources Management, 2008, 22(9): 1311-1324.
[9] Dridi L, Mailhot A, Parizeau M, et al. Multiobjective approach for pipe replacement based on Bayesian inference of break model parameters[J]. Journal of Water Resources Planning and Management, 2009, 135(5): 344-354.
[10] Christodoulou S, Deligianni A. A neurofuzzy decision framework for the management of water distribution networks[J]. Water Resources Management, 2010, 24(1): 139-156.
[11] Daniel P, Daniel B N, James H G. Detection of patterns in water distribution pipe breakage using spatial scan statistics for point events in a physical network[J]. Journal of Computing in Civil Engineering, 2011, 25(1): 21-30.
[12]何芳.供水管网爆管分析方法与预防技术研究[D].上海:同济大学, 2005.
[13]余承烈,韩自力.对铸铁管爆管现象的认识及预防措施[J].工业用水与废水, 2000, 31(2): 42-44.
[14]朱东海,张土乔,毛根海.城市给水管网爆管点动态定位的神经网络模型研究[J].水利学报, 2000(5): 1-5.
[15]何芳,刘遂庆.供水管网爆管事故分析与对策探讨[J].管道技术与设备, 2004(5): 20-23.
[16]马乐宁,刘文君,徐洪福.供水管道爆漏事故影响因素实例分析[J].给水排水, 2006, 32(9): 86-89.
[17]张玉先,陈欣,张硕.常州市大口径输水钢管爆管原因与对策研究[J].给水排水, 2006, 32(7): 89-93.
[18]于静,蒋白懿,代进.基于极限爆管率的给水管最佳更换时间研究[J].给水排水, 2007, 33(9): 108-110.
[19]方丹霞,陈明.基于GIS的供水管道爆管因素空间分析[J].城市勘测, 2007(2): 30-32.
[20]荣宏伟,张朝升,张立秋,等.城市给水管爆管机理分析[J].广州大学学报(自然科学版), 2008, 17(6): 59-63.
[21]李震,裴亮,田一梅.基于FAHP的供水管道爆管因素权重的确定[J].中国给水排水, 2009, 25(9): 75-78.
[22]王祎,田一梅,单金林,等.供水管网系统爆管预测[J].天津大学学报, 2010, 43(9): 840-843.
[23]张海亚,田一梅,裴亮.基于GIS的供水管网爆管空间分析模型的建立与应用[J].中国给水排水, 2010, 26(19): 71-77.
[24]刘俊,俞国平.基于遗传程序设计的供水管网爆管预测模型[J].同济大学学报(自然科学版), 2011, 39(3): 401-404.
[25]张海亚.基于GIS的城市供水管网爆管空间分析及预测[D].天津:天津大学, 2009.
[26] Kleiner Y, Rajani B. Comprehensive review of structural deterioration of water mains: statistical models[J]. Urban Water, 2001, 3(3): 121-150.
[27] Park S, Jun H, Agbenowosi N, et al. The proportional hazards modeling of water main failure data incorporating the time-dependent effects of covariates[J]. Water Resources Management, 2011, 25(6): 1-19.
[28] Male J W, Walski T M. Analyzing watermain replacement policies[J]. Journal of Water Resources Planning and Management, 1990, 116(3): 363-374.
[29] Shamir U. An analytic approach to scheduling pipe replacement[J]. Journal American Water Works Association, 1979, 71(5): 248-258.
[30] Walski T M, Pelliccia A. Economic analysis of water main breaks[J]. Journal American Water Works Association, 1982, 74(3): 140-147.
[31] Clark R M. Water distribution systems: A spatial and cost evaluation[J]. Journal of Water Resources Planning and Management Division, 1982, 108(3): 243-256.
[32]陈希儒.广义线性模型(一)[J].数理统计与管理, 2002, 21(5): 54-61.
[33] Guikema S D, Davidson R A. Statistical models for the effect of tree trimming on power system outages[J]. IEEE Transactions Power Delivery, 2006, 21(3): 1549-1557.
[34]王济川,郭志刚. Logistic回归模型方法与应用[M].北京:高等教育出版社, 2001.
[35]卢纹岱. SPSS for Windows统计分析(第3版)[M].北京:电子工业出版社, 2003.
[36] Cox D R. Regression models and life tables[J]. Journal of Royal Statistic Society, 1972, 34(B): 187-220.
[37] Marks H D. Predicting water distribution maintenance strategies: A case study of New Haven Connecticut[J]. Advance in Water Resources, 1985, 8(2): 86-95.
[38] Andreou S A, Marks H D. A new Methodology for modeling break failure patterns in deteriorating water distribution systems: Theory[J]. Advance in Water Resources, 1987, 10(1): 2-10.
[39] Andreou S A, Marks H D. A new Methodology for modeling break failure patterns in deteriorating water distribution systems: Applications[J]. Advance in Water Resources, 1987, 10(1): 11-20.
[40] Marks H D, Andreou S A, Jeffrey L, et al. Statistical models for water main failures[J]. Advance in Water Resources, 1987, 12(4): 184-193.
[41] Bremond B. Statistical modeling as help in network renewal decision[J]. Journal of Water Resources Planning and Management, 1997, 123(2): 67-77.
[42] Lei J. Statistical approach for describing lifetimes of water mains-case Trondheim Municipality[J]. SINTEF Civil and Environmental Engineering, 1997, 22(7): 21-26.
[43] Li D, Haimes Y Y. Optimal maintenance-related decision making for deteriorating water distribution systems 1[J]. Water Resources Research, 1992, 28(4): 1053-1061.
[44] Li D, Haimes Y Y. Optimal maintenance-related decision making for deteriorating water distribution systems 2[J]. Water Resources Research, 1992, 28(4): 1063-1070.
[45] Davidson J W, Savic D A, Walters G A. Method for Identi?cation of explicit polynomial formulae for the friction in turbulent pipe ?ow[J]. Journal of Hydroinformatics, 1999, 2(1): 115-126.
[46] Giustolisi O, Laucelli D, Savic D A. Development of rehabilitation plans for water mains replacement considering risk and cost-bene?t assessment[J]. Civil Engineering and Environmental Systems, 2006, 23 (3): 175-190.
[47] Berardi L, Giustolisi O, Kapelan Z, et al. Development of pipe deterioratin models for water distribution systems using EPR[J]. Journal of Hydroinformatics, 2008, 10(2): 113-126.
[48] Giustolisi O, Berardi L. Prioritizing pipe replacement: from multiobjective genetic algorithms to operational decision support[J]. Journal of Water Resources Planning and Management, 2009, 135(6): 484-492.
[49] Xu Q, Chen Q W, Li W F, et al. Pipe break prediction based on evolutionary data-driven methods with brief recorded data[J]. Reliability Engineering and System Safety, 2011, 96(8): 928-942.
[50] Koza J R. Genetic Programming: On the Programming of Computers by Natural Selection[M]. Cambridge: MIT Press, 2006.
[51] Giustolisi O, Savic D A. A symbolic data-driven technique based on volutionary polynomial regression[J]. Journal of Hydroinformatics, 2006, 10(2): 113-126.
[52] Giustolisi O, Doglioni A, Savic D A, et al. A multi-model approach to analysis of environmental phenomena[J]. Environmental Modelling and Software, 2007, 22(5): 674-682.
[53]刘同生,刘茂.国外城市供水管道最佳更换时间预测的经验与借鉴[J].给水排水, 2009, 35(11): 218-221.
[54] Stone S L, Dzuray E J, Meisegeier D. Decision-support tools for predicting the performance of water distribution and wastewater collection systems[M]. Cincinnati: United States Environmental Protection Agency, 2002.
[55]马学文,夏利,程琳.城市供水管道更新时间预测模型[J].沈阳建筑大学学报(自然科学版), 2008, 24(1): 129-131.
[56]黎子良,郑祖康.生存分析[M].杭州:浙江科学技术出版社, 1993.
[57]彭非,王伟.生存分析[M].北京:中国人民大学出版社, 2004.
[58]胡良平,高辉. SAS统计分析教程[M].北京:电子工业出版社, 2010.
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