民航发动机性能评估方法与视情维修决策模型研究
|
摘要
价值高昂、结构复杂的航空发动机构成了飞机的心脏。为了有效地保障其规定的高可靠性、安全性和经济性,国内、外航空公司已普遍采用经济、合理的视情维修(Condition-based maintenance, CBM)策略。然而,由于民航发动机各单元体/子系统之间的复杂性、运行监控信息的不确定性以及维修阈值的模糊性,航空公司当前在发动机运行管理与CBM决策过程中还存在着一些亟待解决的问题。本文基于这一工程背景,结合民航总局重点基金项目“民航发动机性能预测与维修成本控制研究”,利用多元参数建模思想,对发动机随机劣化过程中存在的性能综合评估、随机失效过程建模、换发优化决策及送修等级决策等CBM决策方面的关键和核心问题进行了深入的研究,并经相关航空公司的实证分析,表明所提出的理论建模方法是有效、合理的,具有很大的实用价值。主要研究内容如下:
(1)鉴于目前工程实践中所用的单参数评估方法存在的诸多不足,根据客观赋权法的思想,采用粗糙集与模糊数学理论相结合的模糊信息熵权法研究了基于多参数的发动机性能综合评估问题,拓展了传统的综合评估方法;在工程实例计算中通过将模糊信息熵权法与单参数评估法、主成分分析法等传统评估方法加以对比,表明该方法勿需任何先验知识、决策过程中损失的客观信息较少,因此通过该方法对发动机性能的综合评估,可以更加准确地把握发动机机队的运营状况。该方法目前已在国内航空公司得到初步应用,发动机维护工程师经过多个工程实例验证了该方法的有效性。
(2)性能衰退是导致民航发动机换发的重要原因,但是在实际中该衰退过程的随机性增加了实际维修决策的难度。因此,针对发动机随机失效过程的维修决策建模问题,首次提出了将发动机性能衰退导致换发的在翼时间视为寿命数据进行生存分析的建模思想。文中分析了数据的截尾机制、协变量相关性及筛选基本原则等问题;进而研究了生存分析中广泛应用的比例强度模型(Proportional intensity model,PIM)的构成特点;在此基础上,综合考虑状态参数、维修历史等协变量对系统的影响效应,提出了应用于复杂系统的扩展型PIM(Gerenalized PIM,GPIM),并详细推导了该模型在全参数和半参数两类情形下的参数估计的求解过程。
(3)民航发动机运行过程中执行CBM策略的核心内容是换发决策,优化目标是在满足规定可靠性的前提下实现维修成本的最小化。首先研究了状态、维修等协变量对发动机系统劣化的影响效应,并采用GPIM求解出系统的失效强度函数和可靠性函数;其次,以长期的平均维修成本为目标函数进行维修阈值的优化,以CF6型发动机的历史故障数据为例,得到了相应的发动机换发决策控制限曲线,从而为航空公司实际维修决策提供了准确的量化指标。该类建模方法还可以推广应用到其他型号发动机的维修决策中,因此具有重要的实用价值。
(4)当在翼发动机整机性能衰退、需要立即换发送修时,对送修等级的决策是航空公司目前面临的一个难题。基于民航发动机的状态监控信息,提出了采用变精度粗糙集(Variable Precision Rough Set,VPRS)理论方法来挖掘反映送修等级和状态参数之间内在关联性的决策规则。其中,针对连续型条件属性数据的离散化问题,本文利用自组织神经网络和不相容评估相结合的方法来处理连续数据的离散化问题。通过实例验证表明:由该方法所获取的知识规则为发动机维护工程师制定合理的送修等级提供了积极的辅助作用,因而具有较大的参考价值。
Aero-engine, a valuable and complex systems in aviation industry, is the heart of an aircraft. In order to ensure the better reliability, safety and economy of aero-engine, condition-based maintenance (CBM) policy is populated for airlines in the world. However, for the complexity among the modules or subsystems in the engine, the uncertainty of operation monitoring information, and the fuzziness of maintenance threshold, there are some problems needed to be solved between the engine operation management and maintenance decision-making. Based on this engineering background, combining the key fund project“Study on predicting performance and optimalizing maintenance cost of aeroengine”of civil aviation administration, the thesis deeply discussed the key problem of synthetic performance estimation, modeling of stochastic failure, decision-making of engine removal and forecasting of maintenance levels, which were appeared in the engine stochastic deterioration process, based on the theory of multi-parameters modeling. And these models and methods were proved to be very effective, reasonable, and valuable by some practical examples in airlines. The main contents of this dissertation are as follow:
(1) According to the various shortages of previous single-parameter assessment method for engines, the feasibility of applying fuzzy information entropy weights method, which combines rough theory and fuzzy math theory, was studied in the thesis, based on the subjectively weighted method and multi-status parameters. In the example, after comparing with the traditional ways of single-parameter assessment and principle component analysis, fuzzy information entropy weights method showed satisfied result, which needed no prior knowledge with less lose of objective information. After estimating the engine performance synthetically, people can accurately know the health of the whole engine fleet. And this method, which extended the traditional synthetic estimation theory, has been initially applied in airlines, and is proved to be very effective by some engineering examples.
(2) Performance deterioration is an important reason of engine removals. But since the randomness of performance deterioration increases the difficulty of maintenance decision-making, it’s significative to study the modeling of maintenance decision-making considering engine stochastic failure process. According to the difference between classical hypothesis and practice conditions in modeling of CBM decision-making, the engine times on wing (TOW) due to performance deterioration were looked as life data creatively. And the coherent censoring theory, the correlation of covariats, and basic screening principle were analysed. Furthermore, the characteristics of proportional intensity model (PIM) were studied, which was populated in survival data analysis. Based on thought of PIM, a generalized PIM was put forward, which considered the affects of condition monitoring parameters, maintenance history, etc, and could be applied in complex systems. The resolve process of parameters estimation in this model was detailedly deduced too.
(3) The key part of CBM policy during commercial aero-engine operation is engine removal decision-making, whose optimization object is to minimize the maintenance cost under some reliability requirements. Firstly, in the case of fleet’s history failure data of CF6 type engine, the generalized PIM was established, which studied the affects of covariates such as condition parameters, maintenance effect, and so on. Then the maintenance threshold was optimized under the object function of long-term average maintenance cost, and the engine removal decision-making control curve was created, which could be an accurate factor of engine maintenance decision-making in airlines. This modeling theory can be generalized to the maintenance decision-making of other type engines, and has important practising value.
(4) When the engine on wing is deteriorating greatly and need to remove immediately, the estimation of maintenance levels is very important for airlines. Based on the engine condition monitoring information, a method about variable precision rough Set (VPRS), was introduced to mine the relevance and decision-making rules between maintenance levels and condition parameters. According to the problem of discretization for continuous condition attributes, a discretization method combining self-organization maps(SOM)neural network algorithm and incompatibility estimation was designed. And the certification of some examples showed that this method had obvious dominance, could control the maintenance cost effectively, and had good value for practice.
(1)鉴于目前工程实践中所用的单参数评估方法存在的诸多不足,根据客观赋权法的思想,采用粗糙集与模糊数学理论相结合的模糊信息熵权法研究了基于多参数的发动机性能综合评估问题,拓展了传统的综合评估方法;在工程实例计算中通过将模糊信息熵权法与单参数评估法、主成分分析法等传统评估方法加以对比,表明该方法勿需任何先验知识、决策过程中损失的客观信息较少,因此通过该方法对发动机性能的综合评估,可以更加准确地把握发动机机队的运营状况。该方法目前已在国内航空公司得到初步应用,发动机维护工程师经过多个工程实例验证了该方法的有效性。
(2)性能衰退是导致民航发动机换发的重要原因,但是在实际中该衰退过程的随机性增加了实际维修决策的难度。因此,针对发动机随机失效过程的维修决策建模问题,首次提出了将发动机性能衰退导致换发的在翼时间视为寿命数据进行生存分析的建模思想。文中分析了数据的截尾机制、协变量相关性及筛选基本原则等问题;进而研究了生存分析中广泛应用的比例强度模型(Proportional intensity model,PIM)的构成特点;在此基础上,综合考虑状态参数、维修历史等协变量对系统的影响效应,提出了应用于复杂系统的扩展型PIM(Gerenalized PIM,GPIM),并详细推导了该模型在全参数和半参数两类情形下的参数估计的求解过程。
(3)民航发动机运行过程中执行CBM策略的核心内容是换发决策,优化目标是在满足规定可靠性的前提下实现维修成本的最小化。首先研究了状态、维修等协变量对发动机系统劣化的影响效应,并采用GPIM求解出系统的失效强度函数和可靠性函数;其次,以长期的平均维修成本为目标函数进行维修阈值的优化,以CF6型发动机的历史故障数据为例,得到了相应的发动机换发决策控制限曲线,从而为航空公司实际维修决策提供了准确的量化指标。该类建模方法还可以推广应用到其他型号发动机的维修决策中,因此具有重要的实用价值。
(4)当在翼发动机整机性能衰退、需要立即换发送修时,对送修等级的决策是航空公司目前面临的一个难题。基于民航发动机的状态监控信息,提出了采用变精度粗糙集(Variable Precision Rough Set,VPRS)理论方法来挖掘反映送修等级和状态参数之间内在关联性的决策规则。其中,针对连续型条件属性数据的离散化问题,本文利用自组织神经网络和不相容评估相结合的方法来处理连续数据的离散化问题。通过实例验证表明:由该方法所获取的知识规则为发动机维护工程师制定合理的送修等级提供了积极的辅助作用,因而具有较大的参考价值。
Aero-engine, a valuable and complex systems in aviation industry, is the heart of an aircraft. In order to ensure the better reliability, safety and economy of aero-engine, condition-based maintenance (CBM) policy is populated for airlines in the world. However, for the complexity among the modules or subsystems in the engine, the uncertainty of operation monitoring information, and the fuzziness of maintenance threshold, there are some problems needed to be solved between the engine operation management and maintenance decision-making. Based on this engineering background, combining the key fund project“Study on predicting performance and optimalizing maintenance cost of aeroengine”of civil aviation administration, the thesis deeply discussed the key problem of synthetic performance estimation, modeling of stochastic failure, decision-making of engine removal and forecasting of maintenance levels, which were appeared in the engine stochastic deterioration process, based on the theory of multi-parameters modeling. And these models and methods were proved to be very effective, reasonable, and valuable by some practical examples in airlines. The main contents of this dissertation are as follow:
(1) According to the various shortages of previous single-parameter assessment method for engines, the feasibility of applying fuzzy information entropy weights method, which combines rough theory and fuzzy math theory, was studied in the thesis, based on the subjectively weighted method and multi-status parameters. In the example, after comparing with the traditional ways of single-parameter assessment and principle component analysis, fuzzy information entropy weights method showed satisfied result, which needed no prior knowledge with less lose of objective information. After estimating the engine performance synthetically, people can accurately know the health of the whole engine fleet. And this method, which extended the traditional synthetic estimation theory, has been initially applied in airlines, and is proved to be very effective by some engineering examples.
(2) Performance deterioration is an important reason of engine removals. But since the randomness of performance deterioration increases the difficulty of maintenance decision-making, it’s significative to study the modeling of maintenance decision-making considering engine stochastic failure process. According to the difference between classical hypothesis and practice conditions in modeling of CBM decision-making, the engine times on wing (TOW) due to performance deterioration were looked as life data creatively. And the coherent censoring theory, the correlation of covariats, and basic screening principle were analysed. Furthermore, the characteristics of proportional intensity model (PIM) were studied, which was populated in survival data analysis. Based on thought of PIM, a generalized PIM was put forward, which considered the affects of condition monitoring parameters, maintenance history, etc, and could be applied in complex systems. The resolve process of parameters estimation in this model was detailedly deduced too.
(3) The key part of CBM policy during commercial aero-engine operation is engine removal decision-making, whose optimization object is to minimize the maintenance cost under some reliability requirements. Firstly, in the case of fleet’s history failure data of CF6 type engine, the generalized PIM was established, which studied the affects of covariates such as condition parameters, maintenance effect, and so on. Then the maintenance threshold was optimized under the object function of long-term average maintenance cost, and the engine removal decision-making control curve was created, which could be an accurate factor of engine maintenance decision-making in airlines. This modeling theory can be generalized to the maintenance decision-making of other type engines, and has important practising value.
(4) When the engine on wing is deteriorating greatly and need to remove immediately, the estimation of maintenance levels is very important for airlines. Based on the engine condition monitoring information, a method about variable precision rough Set (VPRS), was introduced to mine the relevance and decision-making rules between maintenance levels and condition parameters. According to the problem of discretization for continuous condition attributes, a discretization method combining self-organization maps(SOM)neural network algorithm and incompatibility estimation was designed. And the certification of some examples showed that this method had obvious dominance, could control the maintenance cost effectively, and had good value for practice.
引文
[1]左洪福.发动机磨损状态监测与故障诊断技术.北京:航空工业出版社, 1996, 10.
[2]国际航空运输协会(IATA).国际航空运输2002年度行业报告.北京:国际航空运输协会, 2002.
[3] Erwin V. Zaretsky, Robert C. Hendricks, Sherry Soditus. Weibull-Based Design Methodology for Rotating Aircraft Engine Structures, NASA/TM—2002-211348.
[4]徐民筑.航空维修成本管理及控制.南京:南京航空航天大学民航学院机务维修高级研修班资料, 2001.
[5]И.В.凯巴.航空燃气涡轮发动机技术诊断.北京:航空工业出版社, 1990, 6.
[6] R. A. Cottis, P. J. Laycock, P. A. Scarf. Extrapolation of Exreme Pit Depth in Space and Time. J. Electrochem. Soc., 1990, 137: 64-69.
[7]朱建东.飞机发动机的监控技术及其发展趋势.飞机设计, 2003, 1: 58-61.
[8] S. O. T. Ogaji, S. Sampath, R. Singh, et. al. Parameter selection for diagnosing a gas-turbine’s performance-deterioration. Applied Energy, 2002, 73: 25-46.
[9]陈大光,韩凤学,唐耿林.多状态气路分析法诊断发动机故障的分析.航空动力学报, 1994, V9(4): 349-352.
[10] Marcus Bengtsson, Erik Olsson, Peter Funk, et. al. Technical Design of Condition Based Maintenance System - A Case Study using Sound analysis and Case-Based Reasoning. Proceedings of the 8th Maintenance and Reliability Conference, 2004,5.
[11]张海军,左洪福,梁剑.航空发动机多指标模糊信息熵的性能排序研究.应用科学学报, 2006, V24(3): 288-292.
[12] Xiaozhan Xu. A note on the subjective and objective integrated approach to determine attribute weights. European Journal of Operational Research, 2004, 156: 530-532.
[13] A. Jessop. Entropy in multiattribute problems. Journal of Multi-Criteria Decision Analysis, 1999, 8: 61-70.
[14] Q. Zhang, Z. X. Han, F. S. Wen. New Approach for Fault Diagnosis in Power Systems Based on Rough Set Theory. Proceedings of APSCOM'97 in Hong Kong, 1997: 55-59.
[15]刘思峰,郭天榜,党耀国.灰色系统理论及其应用.北京:科学出版社, 1999.
[16]张恒喜,董彦非,郭基联.灰色关联度分析在变量筛选应用中的误区.系统工程理论与实践, 2002, V22(11): 126-128.
[17]陆明生.多目标决策中的权系数.系统工程理论与实践, 1986, V6(4): 77-78.
[18] K. Sugihara, H. Tanaka. Interval Evaluations in the Analytic Hierarchy Process by Possibility Analysis. Computational intelligence, 2001, V17(3): 567-579.
[19]镇常青.多目标决策中的权重调查确定方法.系统工程理论与实践, 1987, V7(2): 16-24.
[20]王应明,傅国伟.主成分分析法在有限方案多目标决策中的应用.系统工程理论方法应用, 1993, V2(2): 43-48.
[21]范作民.发动机故障诊断主因子模型模型故障相关性准测的研究.中国民航学院学报, 1997, V15(4): 1-8.
[22]宋春雳,冉伦,李金林.熵权双基点法在武器装备研制风险评估中的应用.北京理工大学学报,2003, V5(5): 77-79.
[23]王明涛.多指标综合评价中权系数确定的一种综合分析方法.系统工程, 1999, V17(2): 56-61
[24]樊治平.多属性决策的一种新方法.系统工程, 1994, V12(1): 25-28..
[25] R. A. Ribeiro. Fuzzy multiple attribute decision making: A review and new preference elicitation techniques. Fuzzy Sets and Systems, 1996, 78: 155-181.
[26]李玉兰,周彦红,尹国举.模糊综合评判在战斗损伤评估中的应用.军械工程学院学报, 2005, V17(2): 42-45.
[27]朱绍强,王卓健.基于TOPSIS法的飞机维修方案的决策.航空计算技术, 2004, V34(3): 10-12.
[28]郭显光.改进的熵值法及其在经济效益评价中的应用.系统工程理论与实践,1998, 12: 98-102.
[29]黄定轩.基于客观信息熵的多因素权重分配方法.系统工程理论方法应用, 2003, V12(4): 321~324.
[30]徐泽水.不确定多属性决策方法及应用.北京:清华大学出版社, 2004, 8.
[31] Robert A., Halsmer. Smoothing CFM56 engine removal rate at USAir. AIAA the 17th aerospace ground testing conference, Nashville, 1992, 7: 6-8.
[32] P&W Corporation. PW4000 type engine ranking reports, 2001, 3: 3-28.
[33]刘燕. RB211-535E4发动机性能趋势变化分析.航空工程与维修, 2000, 3: 27-28.
[34]黄粤,韦桂兰,高朝阳.状态分析技术在发动机管理中的应用.适航与维修, 2000, 6: 11-14.
[35]王帅,康力平.航空发动机综合权值排队系统的建立与应用.中国民航学院学报, 2004, V22(6): 157-160.
[36]侯胜利,胡金海,李应红.基于混沌变量的航空发动机性能监控与故障诊断.航空动力学报, 2005, V20(2): 314-317.
[37]胡金海,谢寿生,胡剑锋等.基于粗糙集的航空发动机性能评估分析.系统工程与电子技术, 2006, V28(5): 102-105.
[38] (英) J.莫布雷著.以可靠性为中心的维修.北京:机械工业出版社, 1995, 12.
[39]常士基.现代民用航空维修工程管理.山西:山西科学技术出版社, 2002, 6.
[40] A. H. Christer, W. Wang. A simple condition monitoring model for a direct monitoring process. European Journal of Operational Research, 1995, 82: 258-269.
[41] M. Kijima. Hazard Rate and Reversed Hazard Rate Monotoncities in Continuous-Time Markov Chains. Journal of Applied Probability, 1998, 35: 545-556.
[42] Tumer, A Bajwa. A survey of aircraft engine health monitoring systems. AIAA/ ASME/ SAE/ASEE Joint Propulsion Conference and Exhibit, 1999, AIAA-99-2528.
[43] R. E. Barlow, L. C. Hunter. Optimum Preventive Maintenance Policies. Operations Research, 1960, 8: 90-100.
[44] I. D. Cho, M. Parlar. A survey of maintenance models for multi-unit systems. European Journal of Operational Research, 1991, 51: 1-23.
[45] R. Dekker, R. E. Wildeman, F. Van Der Duyn schouten. A review of multicomponent maintenance models with economic dependence. Mathematical Methods of Operational Research, 1997, V45(3): 411-435.
[46] H. Wang. A survey of maintenance policies of deteriorating systems. European Journal of Operational Research, 2002, V139(3): 469-189.
[47] H. E. Ascher, K. A. H. Kobbacy. Modelling Preventive Maintenance for Deterirating Repairable System. IMA Journal of Mathematics Applied in Business & Industry, 1995, 6: 85-99.
[48] W. Wang, P. A. Scard, M. A. J. Smith. On the application of a model of condition-based maintenance. Journal of Operational Research Society, 2000, 51: 1218-1227.
[49] Terje Aven. Condition based replacement policies: a counting process approach. Reliability Engineering and System Safety, 1996, 51: 275-281.
[50] E. L. Kaplan, P. Meier. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 1958, 53: 457-481.
[51] D. R. Cox. Regression models and life tables. J. Roy. Statist. Soc., 1972, V34(2): 187-220.
[52] R. Howard. Dynamic programming and markove decision process. Cambrideg: MIT Press, 1960.
[53] Y. Jia, W. Wang. A development of a condition based maintenance model and itsprototype software. in the 5th International Conference on Reliability. Maintainability and Safety, Dalian, 2001.
[54] J. H. Chiang, J. Yuan. Optimal maintenance policy for a Markovian system under periodic inspection. Reliability Engineering & System Safety, 2001, V71(2): 165-172.
[55] Chengbin Chu, Jean-Marie Proth, Philippe Wolff. Predictive maintenance: The one-unit replacement model. International Journal of Production Economics, 1998, V53(3): 285-295.
[56] A. Grall, C. Bérenguer, L. Dieulle. A condition based maintenance policy for stochastically deteriorating system. Reliability Engineering and System Safety, 2002, 76: 167-180. [ 57 ] Wolfgang Stadje, Dror Zuckerman. A generalized maintenance model for stochastically deteriorating equipment. European Journal of Operational Research, 1996, V89(2): 285-301.
[58] L. Dieulle, C. Berenguer, A. Grall, et. al. Sequential condition based maintenance scheduling for a deteriorating system. European journal of operational research, 2003, 150: 451-461.
[59] H. M. Taylor. Optimal replacement under additive damage and other failure models. Naval Research Logistics, 1975, 22: 1-18.
[60] R. M. Feldman. Optimal replacement with semi-markov shock models using discounted costs. Maths. Opns. Res., 1977, 2: 78-90.
[61] T. Aven, A counting process approach to replacement models. Opt., 1987, 18: 285-296.
[62] A. H. Christer, W. M. Waller. Delay time model of industrial inspection maintenance problems. J. Opl. Res. Soc., 1984, 35: 401-406.
[63] P. A. Scarf. On the Application of Mathematical Models in Maintenance. European Journal of Operational Research, 1997, V99(3): 493-506.
[64] R. D. Baker, P. A. Scarf, W. Wang. A delay-time model for repairable machinery: maximum likelihood estimation of optimum inspection intervals. Journal of Mathematics Applied in Business and Industry, 1997, V8(1): 83-92.
[65] F. P. A. Coolen, P. Coolen-Schrijner, K. J. Yan. Noparametric Predictive Inference in Reliability. Reliability Engineering and System Safety, 2002, V78(2): 185-193.
[66] Jan A. M. Hontelez, Helen H. Burger, Diederik J. D. Wijnmalen. Optimum condition-based maintenance policies for deteriorating systems with partial information. Reliability Engineering and System Safety, 1996, 51: 267-274.
[67] C. G. Vassiliadis, E. N. Pistikopoulos. Maintenance scheduling and process optimization under uncertainty. Computers & Chemical Engineering, 2001, 25: 217-236.
[68] R. Howard. Semi-markovian decision processed. Proc. Internat. Statist. Ottawa,Canada, 1963.
[69] W. S. Jewell. Markov-renewas programming 1: formulation, finite-return models. 2: infinite return models, examples. Opens Res., 1963, 11: 938-971.
[70] C. M. Adolfo, S. H. Antonio. Models for maintenance optimization: a study for repairable systems and finite time periods. Reliability Engineering & System Safety, 2002, V75(3): 367-377.
[71] G.. F. Beadle, S. Come, C. Henderson, et. al. The Effect of Adjuvant Chemotherapy on the Cosmetic Results after Primary Radiation Treatment for Early Stage Breast Cancer. International Journal of Radiation Oncology. Biology and Physics, 1984, 10: 2131-2137.
[72] P. Aaby, J. Bukh. Kronborg, et, al. Delayed Excess Mortality after Exposure to Measles During the First Six Months of Life. American Journal of Epidemiology, 1990, 132: 211-219.
[73] R. Guo, H. Ascher, E. Love. Towards Practical and Synthetical Modelling of Repairable Systems, Economic Quality Control, 2001, V16(2): 147-181.
[74] A. K. S. Jardine, P. M. Anderson, D. S. Mann. Application of the Weibull proportional hazards model to aircraft and marine engine failure data. Quality and Reliability Engineering International, 1987, 3: 77-82.
[75] E. Arjas. A Graphical Method for Assessing Goodness of Fit in Cox’s Proporional Hazards Model. American Statistical Association , 1988, 83: 204-212.
[76] V. Makis, A.K.S. Jardine. Optimal replacement in the proportional hazards model. INFOR, 1991, 30: 172-183.
[77] C. E. Love, R. Guo. Using Proportional Hazard Modelling in Plant Maintenance. Quality and Reliability Engineering International, 1991, 7: 7-17.
[78] M. Newby. Perspective on Weibull proportional hazards models. IEEE Reliability Trans., 1994, 43: 217-223.
[79] D. Kumar, B. Klefsjo. Proportional Hazards Model: A Review. Reliability Engineering and System Safety, 1994, 44: 177-188.
[80] R. Guo, C. E. Love. Simulating Nonhomogeneous Poisson Processes with Proportional Intensities. Naval Research Logistics, 1994, 41: 507-522.
[81] H. E. Ascher, K. A. H. Kobbacy, Modelling preventive maintenance for deteriorating repairable systems. Journal of Mathematics Applied in Business and Industry, 1995, 6: 85-100.
[82] D. F. Percy, K. A. H. Kobbacy, H. E. Ascher. Using Proportional-Intensities Models to Schedule Preventive-Maintenance Intervals. IMA Journal of Mathematics Applied in Business & Industry, 1998, 9: 289-302.
[83] B. Rao, L. S. P. Semimartingales and Their Statistical Inference. Chapman & Hall/CRC, 1999.
[84] Pieter-Jan Vlok, Maciej wnek, Maciej Zygmunt. Utilising statistical residual life estimates of bearings to quantify the influence of preventive maintenance actions. Mechanical systems and signal processing, 2004, 18: 833-847.
[85] Yong Sun, Lin Ma, Joseph Mathew, et. al. Mechanical systems hazard estimation using condition monitoring. Mechanical Systems and Signal Processing, 2004: 1-13.
[86] DAVID F. PERCY, M. BABAKALLI ALKALI. Generalized proportional intensities models for repairable systems. IMA Journal of Management Mathematics, 2005, 7: 1-15.
[87] Shwu-Tzy Jiang, Thomas L. Landers, Teri Reed Rhoads. Assessment of Repairable-System Reliability Using Proportional IntensityModels: A Review. IEEE Transactions on Reliability, 2006, V55(2): 328-336.
[88]顾磊,钱正芳,范英,等.舰船装备视情维修间隔模型研究.华中科技大学学报(自然科学版), 2003, V31(6): 61-66.
[89]张恒喜.小样本寿命数据多元回归分析.西安:西北工业大学出版社, 2003, 6.
[90]范作民等.航空发动机故障诊断导论.航空工业出版社, 2004, 6.
[91]甘茂治,康建设,高琦.军用装备维修工程学.北京:国防工业出版社, 1999.
[92]陶凤和,甘茂治,于永利.机械系统与设备维修性模型的建立.中国机械工程, 1999, V10(12): 1404-1406.
[93] S. Vittal, P. Hajela, A. Joshi. Review of Approaches to gas turbine life management. The 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2004, 9.
[94] Y. A. Nozhnitsky, R. A. Doulnev, I. V. Egorov. Evolution of aviation engine life management in CIS. CIAM, 2000: 1-25.
[95]徐可君,江龙平.军用航空发动机可靠性和寿命管理.中国工程科学, 2003, V5(1): 82-88.
[96]张宝珍,曾天翔.先进的故障预测与状态管理技术.测控技术, 2003, V22(11): 4-6.
[97] H. C. Pusey, M. J. Roemer. Assessment of turbomachinery condition monitoring and failure prognosis technology, Shock and Vibration Digest, 1999, 31: 365-371.
[98] J. J. Gill. Lessons learned from rotary- and fixed-wing HUMS applications, Proceedings of the IEEE Aerospace Conference, 2000.
[99] Barry L. Ferrell. Air Vehicle Prognostics & Health Management. Proceedings of the IEEE Aerospace Conference, 2000.
[100] L. C. Jaw, R. Friend. ICEMS: A platform for advanced condition-based health management, Proceedings of the IEEE Aerospace Conference, 2001.
[101] C. E. Fisher. Gas Path Debris Monitoring– A 21st Century PHM Tool. Proceedings of the IEEE Aerospace Conference, 2000.
[102] E. L. Suarez, M. J. Duffy, R. N. Gamache, et. al. Jet engine life prediction systems integrated with prognostics health management. Proceedings of the IEEE Aerospace Conference, 2004.
[103]陈光.航空发动机设计手册(第3册):可靠性与维修性.北京:航空工业出版社, 2000, 6.
[104] http://www.ge-china.com.
[105] http://www.pratt-whitney.com.
[106] A. K. S. Jardine, T. Joseph, Banjevic. Optimization of Condition-Based Maintenance Decisions for Equipment Subject to Vibration Monitoring, Journal of Quality in Maintenance Engineering, 1999, V5(3): 192-202.
[107] http://www.mece.ualberta.ca/staff/zuo/research.htm
[108] http://www.arl.psu.edu/areas/soa/conditionmaint.html
[109]贾云献.基于多状态信息的CBM建模研究及原型软件开发.中国兵工学会首届维修专业学术年会论文集, 2003, 1: 102-106.
[110]张秀斌,王广伟,郭波.视情维修决策软件的设计实现.计算机应用研究, 2002, V106(5): 89-91.
[111]梁剑等.基于成本优化的航空发动机视情维修决策研究.南京:南京航空航天大学博士学位论文, 2004, 9.
[112]左洪福,张海军,戎翔.基于比例风险模型的航空发动机视情维修决策.航空动力学报, 2006, 4: 56-60.
[114]于秀林,任雪松.多元统计分析.北京:中国统计出版社, 1999, 8.
[115] Jose M. Pena, Sylvain Letourneau, Fazel Famili. Application of Rough Sets Algorithms to Prediction of Aircraft Component Failure. Proceedings of the Third International Symposium on Intelligent Data Analysis, 1999, 8: 1-13.
[116]郭显光.改进的熵值法及其在经济效益评价中的应用.系统工程理论与实践, 1998, 12: 98-102.
[117] G. R. Weckman, R. L. Shell, J. H. Marvel. Modeling the reliability of repairable systems in the aviation industry. Computers and industrial engineering, 2001, 40: 51-63.
[118] H. E. Ascher, H. Feingold. Repairable Systems Reliability: Modelling, Inference Misconceptions and their Causes. Mar-cel Dekker, 1984.
[119] S. Jiang, T. L. Landers, T. R. Rhoads. Semi-parametric proportional intensity models robustness for right-censored recurrent failure data. Reliability Engineering and System Safety, 2005, V90(1): 91-98.
[120] D. Kumar, B. Klefsjo. Proportional Hazards Model: A Review. Reliability Engineering and System Safety, 1994, 44: 177-188.
[121] H. Wang, H. Pham. A quasi-renewal process and application in imperfect maintenance. Int. J. Syst. Sci., 1996, 27: 1055-1062.
[122] S. Vithala. Robustness of Semi-Parametric Proportional Intensity Model for the Case of a Log-Linear Nonhomogeneous Poisson Process. MS thesis of the University of Arkansas, 1994, 12.
[123] (加拿大) J. F. Lawless.寿命数据中的统计模型与方法.北京:中国统计出版社, 1983, 3.
[124]陈家鼎.生存分析与可靠性引论.安徽:安徽教育出版社, 1993, 1.
[125]王惠文.偏最小二乘回归方法及其应用.北京:国防工业出版社, 1999, 4.
[126]张恒喜,朱家元,郭基联等.军用飞机型号发展工程导论.北京:国防工业出版社, 2004, 4.
[127] Waloddi Weibull. A Statistical Distribution of Wide Applicability. Journal of Applied Mechanics, 1951, 18: 293-297.
[128] Huairui Guo, Wenbiao Zhao, Adamantios Mettas. Practical Methods for Modeling Repairable Systems with Time Trends and Repair Effects. Proceedings Annual Reliability and Maintainability Symposium, Newport Beach, California, USA, 2006 , 1: 23-26.
[129] http://www.clockwork-solutions.com
[130] Shwu-Tzy Jiang. Assessment of semi-parametric proportional intensity models applied to recurrent failure data with multiple failure types for repairable-system reliability. A dissertation for university of Oklahoma, 2004, 3.
[131]常继百,左洪福.民航发动机性能监控和预测方法研究.南京:南京航空航天大学, 2004.
[132] B. Alain. Calculating maintenance reserves. Engine Yearbook, 2004: 36-41. [ 133 ] G. Kleinert. The economics of high thrust turbofan maintenance. Aircraft Maintenance World, 1990, 9.
[134] V. Makis, A. K. S. Jardine. A Note on Optimal Replacement Policy under General Repair. European Journal of Operational Research, 1993, 69: 75-82.
[135] G. R. Weclman, R. L. Shell, J. H. Marvel. Modeling the reliability of repairable systems in the aviation industry. Computers & Industrial Engineering, 2001, 40: 51-63.
[136] P. V. N. Prasad, K. R. M. Rao. Failure Analysis and Replacement Strategies of Distribution Transformers Using Proportional Hazard Modeling. IEEE Proceedings Annual Reliability and Maintainability Symposium, 2003: 523-527.
[137] H. Yo-Ping, C. Hung-Chi. Practical Consideration for Grey Modeling and Its Application to Image Processing. The Journal of Grey System, 1996, V8(3): 217-233.
[138] R. C. Luo, T. M. Chen, K. L. Su. Target Tracking Using hierarchical Grey-Fuzzy Motion Decision-making method. IEEE Trans. Syst. Man cyb. Part-A, 2001, V31(3): 179-186.
[139] I. C. Hsu. Applying the Grey Prediction Model to the Global Integrated Circuit Industry. Technological Forecasting & Social Change, 2003, V70(6): 563-574.
[140]王国胤. Rough集理论与知识获取.西安:西安交通大学出版社, 2001, 5.
[141] M. Jose, L. Sylvain, Fazel Famili. Application of rough sets algorithms to prediction of aircraft component failure. Proceedings of the third international symposium on intelligent data analysis, 1999.
[142] Z. Pawlak. Rough sets and intelligent data analysis. International Journal of Information Sciences, 2002, 147: 1-12.
[143]曾黄麟.粗集理论及其应用.重庆:重庆大学出版社, 1998.
[144]张文修,吴伟志,梁吉业等.粗糙集理论与方法.北京:科学出版社, 2003, 1.
[145] W. Ziarko. Variable Precision Rough Set Model. Jouranl of Computer and System Sciences, 1993, 46: 39-59.
[146] J. Rissanen. Modeling By the Shortest Data Description. Automatic, 1978, 14: 465-471.
[147] R. Susmaga. Analyzing discretizations of continuous attributes given a monotonic discrimination function . Intelligent Data Analysis, 1997, V1(4): 157-159.
[148] Huang Jin-Jie, Li Shi-Yong. A GA-based approach to rough data model. Proceedings of the 5th World Congress on Intelligent Control and Automation, HangZhou, 2004: 1880~1884.
[149]谢宏,程浩忠,牛东晓.基于信息熵的粗糙集连续属性离散化算法.计算机学报, 2005, V28(9): 1570-1574.
[150] A. Roy, S. K. Pal. Fuzzy discretization of feature space for a rough set classier . Pattern Recognition Letters, 2003, V24(6): 895~902.
[151] T. Kohonen. The self-organizing map. Neurocomputing, 1998, 21: 1-6.
[152] Richard J. Roiger, Michael W. Geatz,翁敬农译.数据挖掘教程.北京:清华大学出版社, 2003.
[153]曹存根.面向专家的知识获取.北京:科学出版社, 1998.
[154] T. Kohonen. The self-organizing map. Neurocomputing, 1998, 21: 1-6.
[155] Z. Pawlak. Rough Sets Present State and Further Prospects in Proc. of the 2nd Int. Workshop on Rough Sets and Soft Computing, 1994.
[156] I. Duntsch, G. Gediga. Uncertainty measures of rough set prediction. Articicial Intelligence, 1998, 106: 109-137.
[157]梁吉业,孟晓伟.信息熵在粗糙集理论中的应用.山西大学学报, 2002, V25(3): 281-284.
[158] Mi. Ju-Sheng, Wu Wei-Zhi, Zhang Wen-Xiu. Approaches to knowledge reduction based on variable precision rough set model. Information Sciences, 2004, 159: 255-272.
[159]刘家学,沈建辉. WP27发动机性能故障的信息熵综合模糊诊断法.模糊系统与数学, 1999, 1: 61-65.
[160] GE Transportation, CF6-80C2A5 Workscope Planning Guide. General Electric Company, 2001.
[2]国际航空运输协会(IATA).国际航空运输2002年度行业报告.北京:国际航空运输协会, 2002.
[3] Erwin V. Zaretsky, Robert C. Hendricks, Sherry Soditus. Weibull-Based Design Methodology for Rotating Aircraft Engine Structures, NASA/TM—2002-211348.
[4]徐民筑.航空维修成本管理及控制.南京:南京航空航天大学民航学院机务维修高级研修班资料, 2001.
[5]И.В.凯巴.航空燃气涡轮发动机技术诊断.北京:航空工业出版社, 1990, 6.
[6] R. A. Cottis, P. J. Laycock, P. A. Scarf. Extrapolation of Exreme Pit Depth in Space and Time. J. Electrochem. Soc., 1990, 137: 64-69.
[7]朱建东.飞机发动机的监控技术及其发展趋势.飞机设计, 2003, 1: 58-61.
[8] S. O. T. Ogaji, S. Sampath, R. Singh, et. al. Parameter selection for diagnosing a gas-turbine’s performance-deterioration. Applied Energy, 2002, 73: 25-46.
[9]陈大光,韩凤学,唐耿林.多状态气路分析法诊断发动机故障的分析.航空动力学报, 1994, V9(4): 349-352.
[10] Marcus Bengtsson, Erik Olsson, Peter Funk, et. al. Technical Design of Condition Based Maintenance System - A Case Study using Sound analysis and Case-Based Reasoning. Proceedings of the 8th Maintenance and Reliability Conference, 2004,5.
[11]张海军,左洪福,梁剑.航空发动机多指标模糊信息熵的性能排序研究.应用科学学报, 2006, V24(3): 288-292.
[12] Xiaozhan Xu. A note on the subjective and objective integrated approach to determine attribute weights. European Journal of Operational Research, 2004, 156: 530-532.
[13] A. Jessop. Entropy in multiattribute problems. Journal of Multi-Criteria Decision Analysis, 1999, 8: 61-70.
[14] Q. Zhang, Z. X. Han, F. S. Wen. New Approach for Fault Diagnosis in Power Systems Based on Rough Set Theory. Proceedings of APSCOM'97 in Hong Kong, 1997: 55-59.
[15]刘思峰,郭天榜,党耀国.灰色系统理论及其应用.北京:科学出版社, 1999.
[16]张恒喜,董彦非,郭基联.灰色关联度分析在变量筛选应用中的误区.系统工程理论与实践, 2002, V22(11): 126-128.
[17]陆明生.多目标决策中的权系数.系统工程理论与实践, 1986, V6(4): 77-78.
[18] K. Sugihara, H. Tanaka. Interval Evaluations in the Analytic Hierarchy Process by Possibility Analysis. Computational intelligence, 2001, V17(3): 567-579.
[19]镇常青.多目标决策中的权重调查确定方法.系统工程理论与实践, 1987, V7(2): 16-24.
[20]王应明,傅国伟.主成分分析法在有限方案多目标决策中的应用.系统工程理论方法应用, 1993, V2(2): 43-48.
[21]范作民.发动机故障诊断主因子模型模型故障相关性准测的研究.中国民航学院学报, 1997, V15(4): 1-8.
[22]宋春雳,冉伦,李金林.熵权双基点法在武器装备研制风险评估中的应用.北京理工大学学报,2003, V5(5): 77-79.
[23]王明涛.多指标综合评价中权系数确定的一种综合分析方法.系统工程, 1999, V17(2): 56-61
[24]樊治平.多属性决策的一种新方法.系统工程, 1994, V12(1): 25-28..
[25] R. A. Ribeiro. Fuzzy multiple attribute decision making: A review and new preference elicitation techniques. Fuzzy Sets and Systems, 1996, 78: 155-181.
[26]李玉兰,周彦红,尹国举.模糊综合评判在战斗损伤评估中的应用.军械工程学院学报, 2005, V17(2): 42-45.
[27]朱绍强,王卓健.基于TOPSIS法的飞机维修方案的决策.航空计算技术, 2004, V34(3): 10-12.
[28]郭显光.改进的熵值法及其在经济效益评价中的应用.系统工程理论与实践,1998, 12: 98-102.
[29]黄定轩.基于客观信息熵的多因素权重分配方法.系统工程理论方法应用, 2003, V12(4): 321~324.
[30]徐泽水.不确定多属性决策方法及应用.北京:清华大学出版社, 2004, 8.
[31] Robert A., Halsmer. Smoothing CFM56 engine removal rate at USAir. AIAA the 17th aerospace ground testing conference, Nashville, 1992, 7: 6-8.
[32] P&W Corporation. PW4000 type engine ranking reports, 2001, 3: 3-28.
[33]刘燕. RB211-535E4发动机性能趋势变化分析.航空工程与维修, 2000, 3: 27-28.
[34]黄粤,韦桂兰,高朝阳.状态分析技术在发动机管理中的应用.适航与维修, 2000, 6: 11-14.
[35]王帅,康力平.航空发动机综合权值排队系统的建立与应用.中国民航学院学报, 2004, V22(6): 157-160.
[36]侯胜利,胡金海,李应红.基于混沌变量的航空发动机性能监控与故障诊断.航空动力学报, 2005, V20(2): 314-317.
[37]胡金海,谢寿生,胡剑锋等.基于粗糙集的航空发动机性能评估分析.系统工程与电子技术, 2006, V28(5): 102-105.
[38] (英) J.莫布雷著.以可靠性为中心的维修.北京:机械工业出版社, 1995, 12.
[39]常士基.现代民用航空维修工程管理.山西:山西科学技术出版社, 2002, 6.
[40] A. H. Christer, W. Wang. A simple condition monitoring model for a direct monitoring process. European Journal of Operational Research, 1995, 82: 258-269.
[41] M. Kijima. Hazard Rate and Reversed Hazard Rate Monotoncities in Continuous-Time Markov Chains. Journal of Applied Probability, 1998, 35: 545-556.
[42] Tumer, A Bajwa. A survey of aircraft engine health monitoring systems. AIAA/ ASME/ SAE/ASEE Joint Propulsion Conference and Exhibit, 1999, AIAA-99-2528.
[43] R. E. Barlow, L. C. Hunter. Optimum Preventive Maintenance Policies. Operations Research, 1960, 8: 90-100.
[44] I. D. Cho, M. Parlar. A survey of maintenance models for multi-unit systems. European Journal of Operational Research, 1991, 51: 1-23.
[45] R. Dekker, R. E. Wildeman, F. Van Der Duyn schouten. A review of multicomponent maintenance models with economic dependence. Mathematical Methods of Operational Research, 1997, V45(3): 411-435.
[46] H. Wang. A survey of maintenance policies of deteriorating systems. European Journal of Operational Research, 2002, V139(3): 469-189.
[47] H. E. Ascher, K. A. H. Kobbacy. Modelling Preventive Maintenance for Deterirating Repairable System. IMA Journal of Mathematics Applied in Business & Industry, 1995, 6: 85-99.
[48] W. Wang, P. A. Scard, M. A. J. Smith. On the application of a model of condition-based maintenance. Journal of Operational Research Society, 2000, 51: 1218-1227.
[49] Terje Aven. Condition based replacement policies: a counting process approach. Reliability Engineering and System Safety, 1996, 51: 275-281.
[50] E. L. Kaplan, P. Meier. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 1958, 53: 457-481.
[51] D. R. Cox. Regression models and life tables. J. Roy. Statist. Soc., 1972, V34(2): 187-220.
[52] R. Howard. Dynamic programming and markove decision process. Cambrideg: MIT Press, 1960.
[53] Y. Jia, W. Wang. A development of a condition based maintenance model and itsprototype software. in the 5th International Conference on Reliability. Maintainability and Safety, Dalian, 2001.
[54] J. H. Chiang, J. Yuan. Optimal maintenance policy for a Markovian system under periodic inspection. Reliability Engineering & System Safety, 2001, V71(2): 165-172.
[55] Chengbin Chu, Jean-Marie Proth, Philippe Wolff. Predictive maintenance: The one-unit replacement model. International Journal of Production Economics, 1998, V53(3): 285-295.
[56] A. Grall, C. Bérenguer, L. Dieulle. A condition based maintenance policy for stochastically deteriorating system. Reliability Engineering and System Safety, 2002, 76: 167-180. [ 57 ] Wolfgang Stadje, Dror Zuckerman. A generalized maintenance model for stochastically deteriorating equipment. European Journal of Operational Research, 1996, V89(2): 285-301.
[58] L. Dieulle, C. Berenguer, A. Grall, et. al. Sequential condition based maintenance scheduling for a deteriorating system. European journal of operational research, 2003, 150: 451-461.
[59] H. M. Taylor. Optimal replacement under additive damage and other failure models. Naval Research Logistics, 1975, 22: 1-18.
[60] R. M. Feldman. Optimal replacement with semi-markov shock models using discounted costs. Maths. Opns. Res., 1977, 2: 78-90.
[61] T. Aven, A counting process approach to replacement models. Opt., 1987, 18: 285-296.
[62] A. H. Christer, W. M. Waller. Delay time model of industrial inspection maintenance problems. J. Opl. Res. Soc., 1984, 35: 401-406.
[63] P. A. Scarf. On the Application of Mathematical Models in Maintenance. European Journal of Operational Research, 1997, V99(3): 493-506.
[64] R. D. Baker, P. A. Scarf, W. Wang. A delay-time model for repairable machinery: maximum likelihood estimation of optimum inspection intervals. Journal of Mathematics Applied in Business and Industry, 1997, V8(1): 83-92.
[65] F. P. A. Coolen, P. Coolen-Schrijner, K. J. Yan. Noparametric Predictive Inference in Reliability. Reliability Engineering and System Safety, 2002, V78(2): 185-193.
[66] Jan A. M. Hontelez, Helen H. Burger, Diederik J. D. Wijnmalen. Optimum condition-based maintenance policies for deteriorating systems with partial information. Reliability Engineering and System Safety, 1996, 51: 267-274.
[67] C. G. Vassiliadis, E. N. Pistikopoulos. Maintenance scheduling and process optimization under uncertainty. Computers & Chemical Engineering, 2001, 25: 217-236.
[68] R. Howard. Semi-markovian decision processed. Proc. Internat. Statist. Ottawa,Canada, 1963.
[69] W. S. Jewell. Markov-renewas programming 1: formulation, finite-return models. 2: infinite return models, examples. Opens Res., 1963, 11: 938-971.
[70] C. M. Adolfo, S. H. Antonio. Models for maintenance optimization: a study for repairable systems and finite time periods. Reliability Engineering & System Safety, 2002, V75(3): 367-377.
[71] G.. F. Beadle, S. Come, C. Henderson, et. al. The Effect of Adjuvant Chemotherapy on the Cosmetic Results after Primary Radiation Treatment for Early Stage Breast Cancer. International Journal of Radiation Oncology. Biology and Physics, 1984, 10: 2131-2137.
[72] P. Aaby, J. Bukh. Kronborg, et, al. Delayed Excess Mortality after Exposure to Measles During the First Six Months of Life. American Journal of Epidemiology, 1990, 132: 211-219.
[73] R. Guo, H. Ascher, E. Love. Towards Practical and Synthetical Modelling of Repairable Systems, Economic Quality Control, 2001, V16(2): 147-181.
[74] A. K. S. Jardine, P. M. Anderson, D. S. Mann. Application of the Weibull proportional hazards model to aircraft and marine engine failure data. Quality and Reliability Engineering International, 1987, 3: 77-82.
[75] E. Arjas. A Graphical Method for Assessing Goodness of Fit in Cox’s Proporional Hazards Model. American Statistical Association , 1988, 83: 204-212.
[76] V. Makis, A.K.S. Jardine. Optimal replacement in the proportional hazards model. INFOR, 1991, 30: 172-183.
[77] C. E. Love, R. Guo. Using Proportional Hazard Modelling in Plant Maintenance. Quality and Reliability Engineering International, 1991, 7: 7-17.
[78] M. Newby. Perspective on Weibull proportional hazards models. IEEE Reliability Trans., 1994, 43: 217-223.
[79] D. Kumar, B. Klefsjo. Proportional Hazards Model: A Review. Reliability Engineering and System Safety, 1994, 44: 177-188.
[80] R. Guo, C. E. Love. Simulating Nonhomogeneous Poisson Processes with Proportional Intensities. Naval Research Logistics, 1994, 41: 507-522.
[81] H. E. Ascher, K. A. H. Kobbacy, Modelling preventive maintenance for deteriorating repairable systems. Journal of Mathematics Applied in Business and Industry, 1995, 6: 85-100.
[82] D. F. Percy, K. A. H. Kobbacy, H. E. Ascher. Using Proportional-Intensities Models to Schedule Preventive-Maintenance Intervals. IMA Journal of Mathematics Applied in Business & Industry, 1998, 9: 289-302.
[83] B. Rao, L. S. P. Semimartingales and Their Statistical Inference. Chapman & Hall/CRC, 1999.
[84] Pieter-Jan Vlok, Maciej wnek, Maciej Zygmunt. Utilising statistical residual life estimates of bearings to quantify the influence of preventive maintenance actions. Mechanical systems and signal processing, 2004, 18: 833-847.
[85] Yong Sun, Lin Ma, Joseph Mathew, et. al. Mechanical systems hazard estimation using condition monitoring. Mechanical Systems and Signal Processing, 2004: 1-13.
[86] DAVID F. PERCY, M. BABAKALLI ALKALI. Generalized proportional intensities models for repairable systems. IMA Journal of Management Mathematics, 2005, 7: 1-15.
[87] Shwu-Tzy Jiang, Thomas L. Landers, Teri Reed Rhoads. Assessment of Repairable-System Reliability Using Proportional IntensityModels: A Review. IEEE Transactions on Reliability, 2006, V55(2): 328-336.
[88]顾磊,钱正芳,范英,等.舰船装备视情维修间隔模型研究.华中科技大学学报(自然科学版), 2003, V31(6): 61-66.
[89]张恒喜.小样本寿命数据多元回归分析.西安:西北工业大学出版社, 2003, 6.
[90]范作民等.航空发动机故障诊断导论.航空工业出版社, 2004, 6.
[91]甘茂治,康建设,高琦.军用装备维修工程学.北京:国防工业出版社, 1999.
[92]陶凤和,甘茂治,于永利.机械系统与设备维修性模型的建立.中国机械工程, 1999, V10(12): 1404-1406.
[93] S. Vittal, P. Hajela, A. Joshi. Review of Approaches to gas turbine life management. The 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2004, 9.
[94] Y. A. Nozhnitsky, R. A. Doulnev, I. V. Egorov. Evolution of aviation engine life management in CIS. CIAM, 2000: 1-25.
[95]徐可君,江龙平.军用航空发动机可靠性和寿命管理.中国工程科学, 2003, V5(1): 82-88.
[96]张宝珍,曾天翔.先进的故障预测与状态管理技术.测控技术, 2003, V22(11): 4-6.
[97] H. C. Pusey, M. J. Roemer. Assessment of turbomachinery condition monitoring and failure prognosis technology, Shock and Vibration Digest, 1999, 31: 365-371.
[98] J. J. Gill. Lessons learned from rotary- and fixed-wing HUMS applications, Proceedings of the IEEE Aerospace Conference, 2000.
[99] Barry L. Ferrell. Air Vehicle Prognostics & Health Management. Proceedings of the IEEE Aerospace Conference, 2000.
[100] L. C. Jaw, R. Friend. ICEMS: A platform for advanced condition-based health management, Proceedings of the IEEE Aerospace Conference, 2001.
[101] C. E. Fisher. Gas Path Debris Monitoring– A 21st Century PHM Tool. Proceedings of the IEEE Aerospace Conference, 2000.
[102] E. L. Suarez, M. J. Duffy, R. N. Gamache, et. al. Jet engine life prediction systems integrated with prognostics health management. Proceedings of the IEEE Aerospace Conference, 2004.
[103]陈光.航空发动机设计手册(第3册):可靠性与维修性.北京:航空工业出版社, 2000, 6.
[104] http://www.ge-china.com.
[105] http://www.pratt-whitney.com.
[106] A. K. S. Jardine, T. Joseph, Banjevic. Optimization of Condition-Based Maintenance Decisions for Equipment Subject to Vibration Monitoring, Journal of Quality in Maintenance Engineering, 1999, V5(3): 192-202.
[107] http://www.mece.ualberta.ca/staff/zuo/research.htm
[108] http://www.arl.psu.edu/areas/soa/conditionmaint.html
[109]贾云献.基于多状态信息的CBM建模研究及原型软件开发.中国兵工学会首届维修专业学术年会论文集, 2003, 1: 102-106.
[110]张秀斌,王广伟,郭波.视情维修决策软件的设计实现.计算机应用研究, 2002, V106(5): 89-91.
[111]梁剑等.基于成本优化的航空发动机视情维修决策研究.南京:南京航空航天大学博士学位论文, 2004, 9.
[112]左洪福,张海军,戎翔.基于比例风险模型的航空发动机视情维修决策.航空动力学报, 2006, 4: 56-60.
[114]于秀林,任雪松.多元统计分析.北京:中国统计出版社, 1999, 8.
[115] Jose M. Pena, Sylvain Letourneau, Fazel Famili. Application of Rough Sets Algorithms to Prediction of Aircraft Component Failure. Proceedings of the Third International Symposium on Intelligent Data Analysis, 1999, 8: 1-13.
[116]郭显光.改进的熵值法及其在经济效益评价中的应用.系统工程理论与实践, 1998, 12: 98-102.
[117] G. R. Weckman, R. L. Shell, J. H. Marvel. Modeling the reliability of repairable systems in the aviation industry. Computers and industrial engineering, 2001, 40: 51-63.
[118] H. E. Ascher, H. Feingold. Repairable Systems Reliability: Modelling, Inference Misconceptions and their Causes. Mar-cel Dekker, 1984.
[119] S. Jiang, T. L. Landers, T. R. Rhoads. Semi-parametric proportional intensity models robustness for right-censored recurrent failure data. Reliability Engineering and System Safety, 2005, V90(1): 91-98.
[120] D. Kumar, B. Klefsjo. Proportional Hazards Model: A Review. Reliability Engineering and System Safety, 1994, 44: 177-188.
[121] H. Wang, H. Pham. A quasi-renewal process and application in imperfect maintenance. Int. J. Syst. Sci., 1996, 27: 1055-1062.
[122] S. Vithala. Robustness of Semi-Parametric Proportional Intensity Model for the Case of a Log-Linear Nonhomogeneous Poisson Process. MS thesis of the University of Arkansas, 1994, 12.
[123] (加拿大) J. F. Lawless.寿命数据中的统计模型与方法.北京:中国统计出版社, 1983, 3.
[124]陈家鼎.生存分析与可靠性引论.安徽:安徽教育出版社, 1993, 1.
[125]王惠文.偏最小二乘回归方法及其应用.北京:国防工业出版社, 1999, 4.
[126]张恒喜,朱家元,郭基联等.军用飞机型号发展工程导论.北京:国防工业出版社, 2004, 4.
[127] Waloddi Weibull. A Statistical Distribution of Wide Applicability. Journal of Applied Mechanics, 1951, 18: 293-297.
[128] Huairui Guo, Wenbiao Zhao, Adamantios Mettas. Practical Methods for Modeling Repairable Systems with Time Trends and Repair Effects. Proceedings Annual Reliability and Maintainability Symposium, Newport Beach, California, USA, 2006 , 1: 23-26.
[129] http://www.clockwork-solutions.com
[130] Shwu-Tzy Jiang. Assessment of semi-parametric proportional intensity models applied to recurrent failure data with multiple failure types for repairable-system reliability. A dissertation for university of Oklahoma, 2004, 3.
[131]常继百,左洪福.民航发动机性能监控和预测方法研究.南京:南京航空航天大学, 2004.
[132] B. Alain. Calculating maintenance reserves. Engine Yearbook, 2004: 36-41. [ 133 ] G. Kleinert. The economics of high thrust turbofan maintenance. Aircraft Maintenance World, 1990, 9.
[134] V. Makis, A. K. S. Jardine. A Note on Optimal Replacement Policy under General Repair. European Journal of Operational Research, 1993, 69: 75-82.
[135] G. R. Weclman, R. L. Shell, J. H. Marvel. Modeling the reliability of repairable systems in the aviation industry. Computers & Industrial Engineering, 2001, 40: 51-63.
[136] P. V. N. Prasad, K. R. M. Rao. Failure Analysis and Replacement Strategies of Distribution Transformers Using Proportional Hazard Modeling. IEEE Proceedings Annual Reliability and Maintainability Symposium, 2003: 523-527.
[137] H. Yo-Ping, C. Hung-Chi. Practical Consideration for Grey Modeling and Its Application to Image Processing. The Journal of Grey System, 1996, V8(3): 217-233.
[138] R. C. Luo, T. M. Chen, K. L. Su. Target Tracking Using hierarchical Grey-Fuzzy Motion Decision-making method. IEEE Trans. Syst. Man cyb. Part-A, 2001, V31(3): 179-186.
[139] I. C. Hsu. Applying the Grey Prediction Model to the Global Integrated Circuit Industry. Technological Forecasting & Social Change, 2003, V70(6): 563-574.
[140]王国胤. Rough集理论与知识获取.西安:西安交通大学出版社, 2001, 5.
[141] M. Jose, L. Sylvain, Fazel Famili. Application of rough sets algorithms to prediction of aircraft component failure. Proceedings of the third international symposium on intelligent data analysis, 1999.
[142] Z. Pawlak. Rough sets and intelligent data analysis. International Journal of Information Sciences, 2002, 147: 1-12.
[143]曾黄麟.粗集理论及其应用.重庆:重庆大学出版社, 1998.
[144]张文修,吴伟志,梁吉业等.粗糙集理论与方法.北京:科学出版社, 2003, 1.
[145] W. Ziarko. Variable Precision Rough Set Model. Jouranl of Computer and System Sciences, 1993, 46: 39-59.
[146] J. Rissanen. Modeling By the Shortest Data Description. Automatic, 1978, 14: 465-471.
[147] R. Susmaga. Analyzing discretizations of continuous attributes given a monotonic discrimination function . Intelligent Data Analysis, 1997, V1(4): 157-159.
[148] Huang Jin-Jie, Li Shi-Yong. A GA-based approach to rough data model. Proceedings of the 5th World Congress on Intelligent Control and Automation, HangZhou, 2004: 1880~1884.
[149]谢宏,程浩忠,牛东晓.基于信息熵的粗糙集连续属性离散化算法.计算机学报, 2005, V28(9): 1570-1574.
[150] A. Roy, S. K. Pal. Fuzzy discretization of feature space for a rough set classier . Pattern Recognition Letters, 2003, V24(6): 895~902.
[151] T. Kohonen. The self-organizing map. Neurocomputing, 1998, 21: 1-6.
[152] Richard J. Roiger, Michael W. Geatz,翁敬农译.数据挖掘教程.北京:清华大学出版社, 2003.
[153]曹存根.面向专家的知识获取.北京:科学出版社, 1998.
[154] T. Kohonen. The self-organizing map. Neurocomputing, 1998, 21: 1-6.
[155] Z. Pawlak. Rough Sets Present State and Further Prospects in Proc. of the 2nd Int. Workshop on Rough Sets and Soft Computing, 1994.
[156] I. Duntsch, G. Gediga. Uncertainty measures of rough set prediction. Articicial Intelligence, 1998, 106: 109-137.
[157]梁吉业,孟晓伟.信息熵在粗糙集理论中的应用.山西大学学报, 2002, V25(3): 281-284.
[158] Mi. Ju-Sheng, Wu Wei-Zhi, Zhang Wen-Xiu. Approaches to knowledge reduction based on variable precision rough set model. Information Sciences, 2004, 159: 255-272.
[159]刘家学,沈建辉. WP27发动机性能故障的信息熵综合模糊诊断法.模糊系统与数学, 1999, 1: 61-65.
[160] GE Transportation, CF6-80C2A5 Workscope Planning Guide. General Electric Company, 2001.