贝叶斯方法在基于风险的检验中的应用
摘要
基于风险的检测方法简称为RBI方法,是一种对风险进行优化的方法,广泛应用在石油化工领域。RBI方法主要针对静设备,比如输油管道和化工容器等,通过量化具体每个设备的风险,将具有相似的失效频率和失效后果的设备进行分类,以此有针对的制定维护流程和检修计划。RBI方法力图做到在提高生产设备可靠性的同时,尽量减少企业用于设备维护的成本,降低停机检修的次数。通过实施RBI项目,企业可以将设备的安全管理和生产管理实现有效的结合,提高对整个系统的管理水平。
我国的多个石化企业都初步实施了RBI项目,但是由于历史原因和特殊的国情,RBI方法在实施中遇到设备数据不足、历史数据缺失的问题,同时RBI方法无法提供动态的风险评估,这些不足影响了项目的实施效果。
本论文中采用分析历史数据建立设备的寿命模型的方法,实现风险的动态评估,采用二参数威布尔分布作为设备的寿命模型；对于数据不足和数据缺失的问题,抽象为统计模型小子样模型和随机截尾模型,尝试多种算法对数据进行处理。算法中主要选择的是EM算法和属于贝叶斯方法中的MCMC算法,对于EM算法,提出基于EM算法的随机截尾寿命数据模型参数估计的通用算法,针对计算疲劳寿命常用的二参数威布尔分布,通过严格的理论推导,给出基于EM算法的寿命数据拟合方法,对于样本属于小子样情况采用结合Bootstrap法的EM算法,对于复杂分布模型,采用EM算法与Monte Carlo法相结合。对于MCMC算法,也给出对于服从威布尔分布的随机截尾数据的通用算法。接着通过使用Monte Carlo法模拟不完全疲劳寿命数据,验证EM算法和MCMC算法的效果,并对两种算法的结果使用使用紧邻算法、支持向量机等分类算法做进一步的分析,得出这两种算法的最佳适用范围,并使用现实中的轴承寿命数据作为演示,计算其可靠性。
Risk based inspection, shorter from RBI, is an optimization method of risk, RBI is widely used in the Oil and Gas industries. RBI mainly approach to the static equipments, such as pipelines and chemical containers, after quantifying the risk of equipments, RBI will classify the equipments by their failure frequency and consequence, so as to develop for the maintenance plan. While improving the reliability, RBI achieves to save costs for the maintenance. The factory will integrate the security management with other business management by RBI, at last upgrades the whole management level.
A number of petrochemical enterprises in China have implemented the RBI project, but due to historical reasons and national conditions, RBI encountered the loss of equipments data historical data, and RBI cannot provide dynamic risk assessment, these problems reduce the effect of the RBI project.
.The equipment life model based on historical data is used in the paper to assess risk dynamically. Two parameter Weibull distribution model is referred as the life model, while the small sample and random censored data are used to describe the real data in RBI project. The two main algorithms chose in the paper are EM algorithm and Bayesian method. A general method based on the EM algorithm is proposed to deal with random censoring model with various distributions. The parameter estimation method for the 2-Parameter Weibull distribution is developed.When the random censoring model is not justified, a bootstrap method is performed before using EM-algorithm, while an extension of the EM algorithm is combined with the Monte Carlo algorithm to address the intractable distribution models. The MCMC algorithm is chose in kinds of Bayesian methods to deal with random censoring model with various distributions. Then the mimic random censoring data simulated by Monte Carlo algorithm is utilized to assess the performance of two methods proposed in the paper. The result is analyzed by classification algorithms, such as KNN and SVM algorithms. Finally the reliability of real bearing is calculated based on the above conclusions
我国的多个石化企业都初步实施了RBI项目,但是由于历史原因和特殊的国情,RBI方法在实施中遇到设备数据不足、历史数据缺失的问题,同时RBI方法无法提供动态的风险评估,这些不足影响了项目的实施效果。
本论文中采用分析历史数据建立设备的寿命模型的方法,实现风险的动态评估,采用二参数威布尔分布作为设备的寿命模型；对于数据不足和数据缺失的问题,抽象为统计模型小子样模型和随机截尾模型,尝试多种算法对数据进行处理。算法中主要选择的是EM算法和属于贝叶斯方法中的MCMC算法,对于EM算法,提出基于EM算法的随机截尾寿命数据模型参数估计的通用算法,针对计算疲劳寿命常用的二参数威布尔分布,通过严格的理论推导,给出基于EM算法的寿命数据拟合方法,对于样本属于小子样情况采用结合Bootstrap法的EM算法,对于复杂分布模型,采用EM算法与Monte Carlo法相结合。对于MCMC算法,也给出对于服从威布尔分布的随机截尾数据的通用算法。接着通过使用Monte Carlo法模拟不完全疲劳寿命数据,验证EM算法和MCMC算法的效果,并对两种算法的结果使用使用紧邻算法、支持向量机等分类算法做进一步的分析,得出这两种算法的最佳适用范围,并使用现实中的轴承寿命数据作为演示,计算其可靠性。
Risk based inspection, shorter from RBI, is an optimization method of risk, RBI is widely used in the Oil and Gas industries. RBI mainly approach to the static equipments, such as pipelines and chemical containers, after quantifying the risk of equipments, RBI will classify the equipments by their failure frequency and consequence, so as to develop for the maintenance plan. While improving the reliability, RBI achieves to save costs for the maintenance. The factory will integrate the security management with other business management by RBI, at last upgrades the whole management level.
A number of petrochemical enterprises in China have implemented the RBI project, but due to historical reasons and national conditions, RBI encountered the loss of equipments data historical data, and RBI cannot provide dynamic risk assessment, these problems reduce the effect of the RBI project.
.The equipment life model based on historical data is used in the paper to assess risk dynamically. Two parameter Weibull distribution model is referred as the life model, while the small sample and random censored data are used to describe the real data in RBI project. The two main algorithms chose in the paper are EM algorithm and Bayesian method. A general method based on the EM algorithm is proposed to deal with random censoring model with various distributions. The parameter estimation method for the 2-Parameter Weibull distribution is developed.When the random censoring model is not justified, a bootstrap method is performed before using EM-algorithm, while an extension of the EM algorithm is combined with the Monte Carlo algorithm to address the intractable distribution models. The MCMC algorithm is chose in kinds of Bayesian methods to deal with random censoring model with various distributions. Then the mimic random censoring data simulated by Monte Carlo algorithm is utilized to assess the performance of two methods proposed in the paper. The result is analyzed by classification algorithms, such as KNN and SVM algorithms. Finally the reliability of real bearing is calculated based on the above conclusions
引文
[1]API Recommended Practice 580, Risk-Based Inspection, First Edition[S]. American Petroleum Institute,2002.5
[2]API Recommended Publication 581, Risk-Based Inspection Base Resource Document[S]. American Petroleum Institute,2000.5
[3]钱成文,牛国赞.基于风险分析的管道检测(RBI)与评价[J].油气储运.2000.19(8)：5-10
[4]黄贤滨,李延渊,兰正贵.新一代设备管理技术——基于风险的检验[J].化工设备与防腐蚀.2004.7(3)：73-77
[5]兰正贵,李奇,佟晓慧.基于风险的检测—-API RP580介绍(上)[J].安全.健康和环境.2004.4(4)：32-35
[6]杨林娟,沈士明.工业风险分析与评价方法综述(二)[J].压力容器.2005.22(8)：35-39
[7]陈登丰.在役承压设备基于风险的检验和工程适用性评估技术的发展[J].中国特种设备安全.2006.22(11)：4-12
[8]陈学东,王冰,杨铁成等.基于风险的检测(RBI)在中国石化企业的实践及若干问题讨论[J].压力容器.2004.21(8)：39-45
[9]陈学东,杨铁成,艾志斌等.基于风险的检测(RBI)在实践中若干问题讨论[J].压力容器.2005.22(7)：36-44
[10]何承厚.国家质检总局决定在中国石化特种设备试点应用RBI检验技术[J].石油化工设备技术.2006.27(5)：65
[11]孙新文.风险评估(RBI)在石化特种设备管理中的应用展望[J].石油化工设备技术.2006.27(3)：33-35
[12]张颖,戴光,张莹等.储油罐区基于风险检验(RBI)技术的应用[J].化工机械.2006.33(3)：174-177
[13]杨振林.RBI技术在特种设备检验中的应用[J].中国质量技术监督.2007(12)：48-49
[14]任世科,孟凡薇,陈德昌.基于风险的检验(RBI)技术在兰州石化公司碳四抽提装置的应用[J].甘肃科技.2008.24(23)：77-80
[15]邵建雄.RBI在炼化企业的应用与思考[J].石油化工设备技术.2008.29(3)：44-47
[16]戴树和.风险分析技术(一)—风险分析的原理和方法[J].压力容器.2002.19(2)：1-9
[17]戴树和.风险分析技术(二)——典型装置上的工程应用[J].压力容器.2002.19(3)：1-6
[18]赵永韬,赵常就,等.工业腐蚀监测的发展及其仪器的智能化[J].全国煤气化技术通讯.2001.9(1)：25-27
[19]王广兵.炼油设备的在线腐蚀监测[J].四川化工.2004.7(6)：33-34
[20]周玉波,邵丽艳,李言涛等.腐蚀监测技术现状及发展趋势[J].海洋科学.2005.29(7)：77-80
[21]曾彦华.腐蚀监测技术在炼油装置上的应用[J].石油化工腐蚀与防护.2005.22(1)：56-59
[22]吕瑞典,薛有祥.油气田腐蚀监测技术综述[J].石油化工腐蚀与防护.2009.26(1)：4-7
[23]肖向辉.腐蚀监测管线厚度查询系统[J].腐蚀与防护.2005.26(11)：500-502
[24]熊峻江,武哲,高镇同.不完全疲劳寿命数据可靠性分析的秩统计方法及其应用[J].航空学报,1998,19(2)：216-219.
[25]熊峻江,刘宝成,邹尚武,尚大晶.不完全疲劳寿命置信度分析方法[J].北京航空航天大学学报.2000,26(4)：420-423.
[26]Elisa T.Lee, John Wenyuwang. Statistical Methods for Survival Data Analysis [M]. John Wiley & Sons, Inc.2003.
[27]李庆华.随机右截尾情况下威布尔分布可靠度的置信下限[D].西北大学,2006
[28]李凌.逐步增加截尾样本下寿命数据的统计分析[D].西北工业大学,2007
[29]姜仁娜.一类双截尾模型的MCMC算法及证券的长记忆性分析[D].清华大学,2004
[30]Horst Rinne. The Weibull Distribution A Handbook[M]. Taylor & Francis Group, LLC,2009
[31]高镇同,熊俊江.疲劳可靠性[M].北京北京航空航天大学出版社.2000.
[32]Dempster, A.P, Laird, N.M, Rubin, D.B. Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B (Methodological).1977,39(1): 1-38.
[33]Jan B, Oostenbrink, Maiwenn J.Al. The analysis of incomplete costdata due to dropout[J]. Health Economics.2005,14:763-776.
[34]Bradley Efron. The Jackknife, the Bootstrap, and Other Resampling Plans[M]. Society for Industrial Mathematics.1987.
[35]梁冯珍,宋占杰,张玉环.应用概率统计[M].天津大学出版社.2004.
[36]A.Clifford Cohen.Maximum Likelihood Estimation in the Weibull Distribution Based On Complete and On Censored Samples[J]. Technometrics.1965,7(4):579-588.
[37]Peter Neal. Monte-Carlo EM algorithm[EB/OL].2008. http://www.maths.manchester.ac.uk/-pneal/CIS/EM_student_2008.pdf.
[38]M.I. Ageel. A novel means of estimating quantiles for 2-parameter Weibull distribution under the right random censoring model[J]. Journal of Computational and Applied Mathematics.2002,149: 373-380.
[39]H Saranga, J Knezevic. Reliability prediction for condition based maintained systems[J]. Reliability Engineering and System Safety.2001,71:219-224.
[40]Chib Wei Hsu, Chih Chung Chang. A Practical Guide to Support Vector Classification[EB/OL]. 2008. http://www.csie.ntu.edu.tw/-cjlin.
[41]M Hamada, H F Martz. Finding Near Optimal Bayesian Experimental Designs via Genetic Algorithms[J]. The American Statistician.2001,55(3).
[42]Xujie Zhao, Chao Yu. A Bayesian Approach to Weibull Survival Model for Clinical Randomized Censoring Trial Based on MCMC Simulation[C]. IEEE.2008.
[43]Ranganath Kothnamsu, Samuel H Huang.System health monitoring and prognostics a review of current paradigms and practices[J]. Int J Adv Manuf Technol.2006,28:1012-1024.
[44]Andrew K S Jardine, Daming Lin. A review on machinery diagnostics and prognostics implementing condition based maintenance[J]. Mechanical Systems and Signal Processing. 2006(20):1483-1510.
[45]Dempster A P, Gerfand A E. Maximum likelihood from incomplete data via the EM algorithm[J]. J.Roy.Stat.Sac.C.1977(39):1-38.
[46]Hasting W. Monte Carlo Sampling Methods Using Markov Chains and Their Applications[J]. Biometrika.1970(57):97-109.
[47]Metropolis N, Rosenbluth A, Roseubluth M. Equations of State Calculations by fast Computing Machine[J]. Journal of Chemical Plysics.1953(21):1087-1092.
[48]Peskun P. Optimum Monte Carlo sampling using Markov Chains[J]. Biometrika. 1973(60):607-612.
[2]API Recommended Publication 581, Risk-Based Inspection Base Resource Document[S]. American Petroleum Institute,2000.5
[3]钱成文,牛国赞.基于风险分析的管道检测(RBI)与评价[J].油气储运.2000.19(8)：5-10
[4]黄贤滨,李延渊,兰正贵.新一代设备管理技术——基于风险的检验[J].化工设备与防腐蚀.2004.7(3)：73-77
[5]兰正贵,李奇,佟晓慧.基于风险的检测—-API RP580介绍(上)[J].安全.健康和环境.2004.4(4)：32-35
[6]杨林娟,沈士明.工业风险分析与评价方法综述(二)[J].压力容器.2005.22(8)：35-39
[7]陈登丰.在役承压设备基于风险的检验和工程适用性评估技术的发展[J].中国特种设备安全.2006.22(11)：4-12
[8]陈学东,王冰,杨铁成等.基于风险的检测(RBI)在中国石化企业的实践及若干问题讨论[J].压力容器.2004.21(8)：39-45
[9]陈学东,杨铁成,艾志斌等.基于风险的检测(RBI)在实践中若干问题讨论[J].压力容器.2005.22(7)：36-44
[10]何承厚.国家质检总局决定在中国石化特种设备试点应用RBI检验技术[J].石油化工设备技术.2006.27(5)：65
[11]孙新文.风险评估(RBI)在石化特种设备管理中的应用展望[J].石油化工设备技术.2006.27(3)：33-35
[12]张颖,戴光,张莹等.储油罐区基于风险检验(RBI)技术的应用[J].化工机械.2006.33(3)：174-177
[13]杨振林.RBI技术在特种设备检验中的应用[J].中国质量技术监督.2007(12)：48-49
[14]任世科,孟凡薇,陈德昌.基于风险的检验(RBI)技术在兰州石化公司碳四抽提装置的应用[J].甘肃科技.2008.24(23)：77-80
[15]邵建雄.RBI在炼化企业的应用与思考[J].石油化工设备技术.2008.29(3)：44-47
[16]戴树和.风险分析技术(一)—风险分析的原理和方法[J].压力容器.2002.19(2)：1-9
[17]戴树和.风险分析技术(二)——典型装置上的工程应用[J].压力容器.2002.19(3)：1-6
[18]赵永韬,赵常就,等.工业腐蚀监测的发展及其仪器的智能化[J].全国煤气化技术通讯.2001.9(1)：25-27
[19]王广兵.炼油设备的在线腐蚀监测[J].四川化工.2004.7(6)：33-34
[20]周玉波,邵丽艳,李言涛等.腐蚀监测技术现状及发展趋势[J].海洋科学.2005.29(7)：77-80
[21]曾彦华.腐蚀监测技术在炼油装置上的应用[J].石油化工腐蚀与防护.2005.22(1)：56-59
[22]吕瑞典,薛有祥.油气田腐蚀监测技术综述[J].石油化工腐蚀与防护.2009.26(1)：4-7
[23]肖向辉.腐蚀监测管线厚度查询系统[J].腐蚀与防护.2005.26(11)：500-502
[24]熊峻江,武哲,高镇同.不完全疲劳寿命数据可靠性分析的秩统计方法及其应用[J].航空学报,1998,19(2)：216-219.
[25]熊峻江,刘宝成,邹尚武,尚大晶.不完全疲劳寿命置信度分析方法[J].北京航空航天大学学报.2000,26(4)：420-423.
[26]Elisa T.Lee, John Wenyuwang. Statistical Methods for Survival Data Analysis [M]. John Wiley & Sons, Inc.2003.
[27]李庆华.随机右截尾情况下威布尔分布可靠度的置信下限[D].西北大学,2006
[28]李凌.逐步增加截尾样本下寿命数据的统计分析[D].西北工业大学,2007
[29]姜仁娜.一类双截尾模型的MCMC算法及证券的长记忆性分析[D].清华大学,2004
[30]Horst Rinne. The Weibull Distribution A Handbook[M]. Taylor & Francis Group, LLC,2009
[31]高镇同,熊俊江.疲劳可靠性[M].北京北京航空航天大学出版社.2000.
[32]Dempster, A.P, Laird, N.M, Rubin, D.B. Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B (Methodological).1977,39(1): 1-38.
[33]Jan B, Oostenbrink, Maiwenn J.Al. The analysis of incomplete costdata due to dropout[J]. Health Economics.2005,14:763-776.
[34]Bradley Efron. The Jackknife, the Bootstrap, and Other Resampling Plans[M]. Society for Industrial Mathematics.1987.
[35]梁冯珍,宋占杰,张玉环.应用概率统计[M].天津大学出版社.2004.
[36]A.Clifford Cohen.Maximum Likelihood Estimation in the Weibull Distribution Based On Complete and On Censored Samples[J]. Technometrics.1965,7(4):579-588.
[37]Peter Neal. Monte-Carlo EM algorithm[EB/OL].2008. http://www.maths.manchester.ac.uk/-pneal/CIS/EM_student_2008.pdf.
[38]M.I. Ageel. A novel means of estimating quantiles for 2-parameter Weibull distribution under the right random censoring model[J]. Journal of Computational and Applied Mathematics.2002,149: 373-380.
[39]H Saranga, J Knezevic. Reliability prediction for condition based maintained systems[J]. Reliability Engineering and System Safety.2001,71:219-224.
[40]Chib Wei Hsu, Chih Chung Chang. A Practical Guide to Support Vector Classification[EB/OL]. 2008. http://www.csie.ntu.edu.tw/-cjlin.
[41]M Hamada, H F Martz. Finding Near Optimal Bayesian Experimental Designs via Genetic Algorithms[J]. The American Statistician.2001,55(3).
[42]Xujie Zhao, Chao Yu. A Bayesian Approach to Weibull Survival Model for Clinical Randomized Censoring Trial Based on MCMC Simulation[C]. IEEE.2008.
[43]Ranganath Kothnamsu, Samuel H Huang.System health monitoring and prognostics a review of current paradigms and practices[J]. Int J Adv Manuf Technol.2006,28:1012-1024.
[44]Andrew K S Jardine, Daming Lin. A review on machinery diagnostics and prognostics implementing condition based maintenance[J]. Mechanical Systems and Signal Processing. 2006(20):1483-1510.
[45]Dempster A P, Gerfand A E. Maximum likelihood from incomplete data via the EM algorithm[J]. J.Roy.Stat.Sac.C.1977(39):1-38.
[46]Hasting W. Monte Carlo Sampling Methods Using Markov Chains and Their Applications[J]. Biometrika.1970(57):97-109.
[47]Metropolis N, Rosenbluth A, Roseubluth M. Equations of State Calculations by fast Computing Machine[J]. Journal of Chemical Plysics.1953(21):1087-1092.
[48]Peskun P. Optimum Monte Carlo sampling using Markov Chains[J]. Biometrika. 1973(60):607-612.