直升机传动系统行星轮系损伤建模与故障预测理论及方法研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
直升机被广泛应用于抗灾救援、科学研究和反恐维稳等诸多领域,在国民经济发展和国家安全中发挥着重要作用。作为直升机的重要组成部分,传动系统的运行环境恶劣多变,导致其关键部件容易产生故障,又因为传动系统的机械部件一般为无冗余设计,一旦出现故障往往引发严重事故。
     故障预测对于监测、预报直升机传动系统关键部件的运行状态、保障其安全运行具有重要意义。在直升机传动系统关键部件的故障预测中,常常存在故障机理不明确、故障演化数据难以获取、早期损伤检测困难、预测特征难以量化选择等问题。为此,本文以直升机传动系统中的核心部件——行星轮系为研究对象,开展了损伤建模与故障预测理论及方法的研究工作。开展的主要研究包括:
     1.系统地研究了行星轮系典型损伤的建模方法,以深入分析典型损伤对行星轮系动态特性的影响。
     (1)研究了基于集中参数动力学理论的典型损伤建模方法。通过分析行星轮系典型损伤的机理及其对时变啮合刚度的影响,建立了行星轮系太阳轮齿根疲劳裂纹、点蚀、胶合和缺齿等常见损伤模式的集中参数动力学模型。
     (2)提出了基于多体动力学模型的行星轮系典型损伤建模方法。通过分析行星轮系典型损伤的接触函数,建立了行星轮系太阳轮点蚀和缺齿等典型损伤模式的多体动力学模型。对比研究表明,上述动力学模型有效刻画了太阳轮常见典型损伤对行星轮系动态特性的影响。
     2.基于损伤模型和统计分析,深入研究了行星轮系典型损伤的特征提取方法;在此基础上,研究了基于灰色关联分析的早期损伤检测与模式识别方法。
     (1)基于行星轮系典型损伤模型的仿真数据分析,提出了基于多种变换域信息的特征生成方法,提出了基于统计算法的特征敏感度和稳定度的评估方法和特征权重方法。
     (2)基于所提取的特征向量,将灰色关联分析应用于行星轮系的早期损伤检测与识别。
     实验数据验证表明,基于损伤模型的特征生成、选择与权重方法可有效提取行星轮系太阳轮典型损伤的特征,特征的敏感度和稳定度优于常用特征指标;基于灰色关联分析的检测和模式识别方法可有效检测和识别行星轮系早期损伤。
     3.针对行星轮系的退化状态识别和故障预测,提出了基于典型损伤演化信息的预测特征提取和选择方法。在此基础上,将灰色关联分析和特征权值向量相结合,提出了基于灰色概率关联分析的行星轮系退化状态识别方法。
     研究表明,上述方法可建立预测特征提取和选择的量化标准,所提取的预测特征适于行星轮系典型损伤的退化状态识别。实验验证结果证实了基于灰色概率关联分析的方法对行星轮系太阳轮齿根裂纹退化状态识别的有效性。
     4.针对行星轮系太阳轮齿根疲劳裂纹的故障预测问题,研究了基于损伤演化机理的剩余使用寿命预测方法,提出了基于改进灰色模型的剩余使用寿命预测方法。
     (1)研究了基于Paris公式的行星轮系太阳轮齿根疲劳裂纹的演化机理模型,研究了基于机理模型的剩余使用寿命预测方法和预测结果准确度的评价方法。
     (2)将损伤演化信息与灰色模型相结合,提出了灰色模型的改进方法,并将改进灰色模型应用于行星轮系太阳轮齿根疲劳裂纹的剩余使用寿命预测。研究表明,通过对损伤演化数据和运行剖面数据的修正,有效提高了基于机理模型预测方法的准确度。同时,与传统灰色模型相比,基于改进灰色模型的预测方法具有更高的准确度。
     5.分析了面向直升机传动系统的故障预测与健康管理系统体系结构,开发了相关的硬件系统和软件系统,并在实验室环境下对该系统进行了验证。
     验证结果表明,直升机传动系统故障预测与健康管理原型系统具有数据采集与状态实时监控、信号回放与特征选择、早期损伤检测与模式识别、故障趋势预测与剩余使用寿命预测和数据、信息、知识管理等基本功能。
As a type of low-flying craft, helicopter is widely used and plays a significant role in many areas of national economy. Due to its non-redundancy structure and severse operation condition, the faults in the parts of transmission system of helicopter are common, which always cause catastrophic accident.
     The development of Prognostics technology promotes the security of helicopter transmission system. There exist some problems such as the fault mechanics is undefinited, run-to-failure data is hard to obtain, incipient damage is difficult to detect, prognosis feature selection is not quantitative etc. After that, the key component named as planetary gear set in helicopter transmission system is selected, and the corresponding theories and methods of damage modeling and failure prognosis are researched. The detailed contents and innovative work can be summarized as follows.
     1. The modeling methods of normal damages in planetary gear set are researched systematically, in order to analyze the impact of normal damages to the dynamical characteristics of planetary gear set.
     (1) The lumped parameter dynamical models of the normal damages in planetary gear set are investigated. By the analysis of damage mechanics and time-varying meshing stiffness, the common damages such as root fatigue crack, pitting, scuffing and tooth breakage in the sun gear of planetary gear set, are developed.
     (2) The multi-body dynamical modeling methods of common damages in planetary gear set are presented. Based on contact function analysis, the multi-body dynamical models of the damages such as pitting and tooth breakage are built.
     The research shows that the models above represent dynamically the response of planetary gear set with common damages, which are the basis of incipient damage detection, degradation state recognition and failure prognosis.
     2. Feature extraction method based on simulation data and statistical algorithm is presented. And then, a grey relational analysis (GRA) based method is proposed for incipient damage detection and pattern recognition.
     (1) Multiple domain information based feature generation method is researched based on simulation data of the models above. And the feature evaluation and weighting approach is processed utilizing the sensitivity analysis and stability analysis. .
     (2) Based on the features extracted above, GRA is utilized into incipient damage detection and pattern recognition for planetary gear set.
     The above research shows the features extracted above are effective for sun gear damages in planetary gear set, which have the merits of sensitivity and stability compared to the traditional indicators. The effectiveness of the detection and recognition approach based on GRA is validated by damage seeded test data.
     3. A prognosis feature extraction and selection method based on the simulation information of damage propagation is derived, in order for degradation state recognition and failure prognosis. On the basis of the prognosis feature extracted above, GRA and feature weighting vector are united to recognize the degradation states of planetary gear set.
     The research shows that a quantitative criterion is set to extract and select prognosis feature, which is suitable for degradation state recognition. The test results validate that the approach based on grey probability relational analysis is effective in degradation state recognition for sun gear root crack of planetary gear set.
     4. To resolve the problems of failure prognosis for sun gear tooth crack in planetary gear set, the residual useful life (RUL) prediction approach based on damage evolution mechanics is researched, and then the RUL prediction approach based on a modified grey model is presented firstly.
     (1) A damage evolution mechanics model of sun gear root fatigue crack of planetary gear set based on Paris equation is researched. After that, the RUL prediction approach based on mechanics model is researched. And then the accuracy of prognosis result is evaluated.
     (2) The grey model is modified and utilized to predict the RUL of planetary gear set with sun gear root fatigue crack for the first time.
     The research shows that the damage evolution mechanics model need modification by run-to-failure data and operation profile data. And the RUL prediction method based on mechanics model holds high accuracy. Compared to the traditional grey model, RUL prediction method based on modified grey model has merit on the accuracy of prediction results.
     5. Aiming at the helicopter transmission, the architecture of PHM system is analyzed. After that the corresponding hardware system and software system are developed. After all, the system is tested in experiment condition.
     The research shows that the PHM prototype system of helicopter transmission system has five main functions, which are composed of data acquisition and real-time condition monitoring, signal playback and feature selection, incipient damage detection and pattern recognition, conditon trend prognosis and RUL prediction, and data & information & knowledge management.
引文
[1] Ashok K, Zhou X, Fuleki D, Gauthier D, Wallace W. Importance of Physics-Based Prognosis for Improving Turbine Reliability (Part 1– A Turbine Blade Case Study) [C]. 16th Symposium on Industrial Application of Gas Turbines (IAGT). Banff, Alberta, Canada, October 12~14, 2005
    [2] Kacprzynski G, Roemer M, Modgil G, Palladino A. Enhancement of Physics-of-Failure Prognostic Models with System Level Features [R]. 2002 IEEE: 0-7803-7231-X/01
    [3] Gregory J. Kacprzynski, Michael Gumina, Michael J. Roemer. A Prognostic Modeling Approach for Predicting Recurring Maintenance for Shipboard Propulsion Systems [C]. Proceedings of ASME Turbo Expo 2001. 4-7 June 2001, New Orleans, LA USA
    [4] Roemer M, Kacprzynski G, Orsagh R. Assessment of Data and Knowledge Fusion Strategies for Prognostics and Health Management [R]. 2001 IEEE: 0-7803-6599-2/01
    [5] Pecht M. Prognostics and Health Management of Electronics [M]. John Wiley & Sons. Inc., Hoboken, New Jersey, 2008.
    [6] Johnson S. Introduction to System Health Engineering and Management in Aerospace [C]. First Internaltional Forum on Integrated System Health Engineering and Management in Aerospace. Napa, California, USA, November 7-10, 2005.
    [7] Hess A. Joint Strike Fighter– Real Prognostics– Challenges, Issues, and Lessons Learned: Chasing the Big“P”[C]. First Internaltional Forum on Integrated System Health Engineering and Management in Aerospace. Napa, California, USA, November 7-10, 2005.
    [8]张宝珍.国外综合诊断、预测与健康管理技术的发展及应用[J].计算机测量与控制,2008,16(5):591~594.
    [9] Fiorucci T, Lakin D, Reynolds T. Advanced engine health management Applications of the SSME real-time vibration monitoring system [R]. AIAA-2000-3622, 2000.
    [10] Dvidson M, Stephens J. Advanced health management system for the space shuttle main engine [R]. AIAA-2004-3912, 2004.
    [11] Powrie H, Novis A. Gas path debris monitoring for F-35 Joint Strike Fighter propulsion system PHM [C]. Aerospace conference, 2006 IEEE.
    [12] Hess A, Fila L. The joint strike fighter (JSF) PHM concept: potential impact on aging aircraft problems [C]. Aerospace Conference Proceedings, 2002-06:3021~3026.
    [13] Augustin M, Bradley S. Achieving HUMS benefits in the military environment– HUMS developments on the CH-146 griffon fleet [C]. Proceedings of the American Helicopter Society 60th Annual Forum, Baltimore, Maryland, May 2004: 7~10.
    [14] Wright R. New IMD HUMS technology improves helicopter lifecycle [C]. Pentagon Brief, Septemper, 2004.
    [15] Byington C, et al. Metrics evaluation and tool development for health and usage monitoring system technology [C]. The American Helicopter Society 59th Annual Forum, Phoenix, Arizona, 2003.
    [16] Clark G, Vian J, West M, et al. Multi-platform airplane health management [C]. Aerospace conference, IEEE, 2007: 1~13.
    [17] Yu, Harris. A New Stress-Based Fatigue Life Model for Ball Bearings [J]. Tribology Transactions, 2001, 44: 11~18.
    [18] Sines and Ohgi. Fatigue Criteria Under Combined Stresses or Strains [J], ASME Journal of Eng. Materials and Tech., 1981, 103: 82~90. 1981.
    [19] Lewis F, Optimal Estimation: With an Introduction to Stochastic Control Theory [M], John Wiley and Sons, New York, April 1986.
    [20] Hess A, Calvello G, Dabney T. PHM a Key Enabler for the JSF Autonomic Logistics Support Concept [C]. 2004 IEEE Aerospace Conference Proceedings. 0-7803-8155-6/04 2004 IEEE.
    [21] Malley M. A Methodology for Simulation the Joint Strike Fighter’s (JSF) Prognostics and Health Management System [R]. GOR/ENS/01M-11. Mar, 2001.
    [22] Krichene A,Kacprzynski G, Hess A. Auto-generating model-based reasoners through dynamic simulation [C]. IEEE Aerospace Conference, 2005: 1~7.
    [23] Smyth P. Hidden Markov models for fault detection in dynamic systems [J]. Pattern Recognition, 1994, 27(1): 149~164.
    [24] Miao Q, Makis V. Condition monitoring and classification of rotating machinery using wavelets and hidden Markov models [J]. Mechanical System and Signal Processing, 2007, 21: 840~855.
    [25] Zhang X, Xu R, Kwan C, et al. An integrated approach to bearing fault diagnostics and prognostics [C]. Proceeding of the 2005 American Contral Conference, 2005, 4: 2750~2755.
    [26] Dong M, He D. A segmental hidden semi-Markov model (HSMM)–based diagnostics and prognostics framework and methodology [J]. Mechanical System and Signal Processing, 2007, 21(5): 2248~2266.
    [27]胡茑庆,邱忠,谢光军,胡雷.涡轮泵故障检测的频段能量比SOM算法.国防科技大学学报[J],2005,27(6):93~96.
    [28] Worden K, Manson G, Allman D. Experimental validation of a structural health monitoring methodology. Part I. Novelty detection on a laboratory structure [J]. Journal of Sound and Vibration, 2003, 259: 323~343.
    [29] Worden K, Manson G.The application of machine learning to structural health monitoring. Part III Damage location on an aircraft wing [J]. Journal of sound and vibration, 2003, 259(2): 365~385.
    [30] Engel, S.J., Gilmartin, B.J., et al. Prognostics, the real issues involved with predicting life remaining. Aerospace Conference Proceedings, 2000 IEEE, 6: 457~469
    [31] Worden K, Manson G, Denoeux T. An evidence-based approach to damage location on an aircraft structure [J]. Mechanical systems and signal processing, 2009, 23: 1792~1804.
    [32] Timusk M, Lipsett M, Chris K. Mechefske. Fault detection using transient machine signals [J]. Mechanical Systems and Signal Processing, 2008, 22: 1724~1749.
    [33]边肇祺,张学工.模式识别[M].北京:清华大学出版社,1999.
    [34]温熙森.模式识别与状态监控[M].北京:科学出版社,2007.
    [35] Willsky A. A survey of design methods for failure detection in dynamic systems [J]. Automatica, 1976, 12: 601~611.
    [36] Shetty V, Das D, Pecht M, et al. Remaining Life Assessment of Shuttle Remote Manipulator System End Effecter [C]. Proceedings of the 22nd Space Simulation Conference, Ellicott City, MD, October 21-23, 2002.
    [37] Kacprzynski G, Liberson A, Palladino A, et al. Metrics and development tools for prognostic algorithms [C]. IEEE Aerospace Conference Proceedings, 2004, 6: 3809~3815.
    [38]陈玉祥,张汉亚.预测技术与应用[M].北京:机械工业出版社,1985.
    [39]孙明玺.现代预测学[M].杭州:浙江教育出版社,1998.
    [40] Ohring M. Reliability and failure of electronic materials and devices [M]. Academic Press, 1998.
    [41] Ioannides, Harris. A New Fatigue Life Model for Rolling Bearings [J]. Journal of Tribology, 1985, 107: 367~378.
    [42]夏鲁瑞,胡茑庆,秦国军.转速波动状态下涡轮泵典型故障诊断方法[J].推进技术,2009,30(3):342~346.
    [43] Hine A, Hindson W, Sanderfer D, Deb S, Domagala C. A Model-based Health Monitoring and Diagnostic System for the UH-60 Helicopter [C]. The Americal Helicopter Society 57th Annual Forum, Washington, DC, May 9-11, 2001.
    [44] Patrick R, Smith M, Zhang B, Byington C, Vachtsevanos G, Rosario R.Diagnostic Enhancements for Air Vehicle HUMS to Increase Prognostic System Effectiveness [C]. 2009 IEEE Aerospace Conference Proceedings, 2009
    [45] Aldaco R. A Model Based Framework for Fault Diagnosis and Prognosis of Dynamical Systems with an Application to Helicopter Transmissions [D]. Georgia Institute of Technology, August 2007.
    [46] Patrick R, Orchard M, Zhang B, Koelemay M, Kacprzynski G, Ferri A, Vachtsevanos G. An Integrated Approach to Helicopter Planetary [C]. Proceedings of Autotest Conference, 2007.
    [47] Swansson N. Application of vibration signal analysis techniques to signal monitoring [C]. Conference on Friction and Wear in Engineering, 1980: 262~267.
    [48] Kacpnynski G, Sadashliar A, Roemer M, Lamirand B, Hess A and Hardman B. Predicting Remaining Life: Better Prognostics through Fusion of Physics of Failure Modeling and Diagnostics [J]. Journal of Materials, 2004, 3: 29~35.
    [49] Kacpnynski G, Sadashliar A, Roemer M, Lamirand B, Hess A and Hardman B. Calibration of Failure Mechanism-Based Prognosis with Vibratory State Awareness Applied to the H-60 Gearbox [C]. 2003 IEEE Aerospace Conference Proceedings. 2003.
    [50] Mathew S, Das D, Rossenberger R and Pecht M. Failure Mechanisms Based Prognostics [C]. 2008 International Conference on Prognostics and Health Management, 2008.
    [51] Gu J, Pecht M. Prognostics and Health Management Using Physics-of-Failure [C]. Proceedings of the 2008 Annual Reliability and Maintainability Symposium, 2008.
    [52] Kacprzynski G, Sarlashkar A, Roemer M, Hess A and Hardman W. Predicting Remaining Life by Fusing the Physics of Failure Modeling with Diagnostics [J]. Journal of Materials, 2004, 3: 29~35.
    [53] Kacprzynski G, Roemer M, Maynard K. Enhancement of Physics-of-Failure Prognostic Models with System Level Features[C]. 2002 IEEE Aerospace Conference Proceedings. March 6-9, 2002.
    [54] Enright M, Hudak S and McClung R. Application of Probabilistic Fracture Mechanics to Prognosis of Aircraft Engine Components [J]. AIAA JOURNAL, 2006, 44(2): 311~316.
    [55]袁菲,徐颖强.考虑齿间载荷分布的齿轮弯曲疲劳寿命估算[J].机械设计, 2006, 23(4): 35~37.
    [56]张景柱,徐诚,胡良明,范钦满.基于ADAMS的操纵摩擦件寿命仿真预测方法[J].机械科学与技术, 2007, 26(6): 767~769.
    [57]张景柱,徐诚,高效生,李峰.基于虚拟样机技术的装备操纵摩擦元件寿命预测[J].火炮发射与控制学报, 2006, 2: 43~46.
    [58] Byington C, Roemer M, Galie T. Prognostic Enhancements to Diagnostic Systems for Improved Condition-Based Maintenance [C]. IEEE 0-7803-7231-X/01, 2002.
    [59] Brotherton T, Jahns G, Jacobs J, et al. Prognosis of faults in gas turbine engines [C]. Aerospace Conference Proceedings, IEEE, 2000, 6: 163~171
    [60] Roemer M, Byington C, Kacprzynski G, Vachtsevanos G. An Overview of Selected Prognostic Technologies with Reference to an Integrated PHM Architecture. Proceedings of the IEEE Aerospace Conference, 2005.
    [61]曾声奎,故障预测与健康管理(PHM)技术的现状与发展[J],航空学报,Vol.26 No.5,Sept,2005:626~632.
    [62] Hess A, Calvello G, Frith P. Challenges, Issues, and Lessons Learned Chasing the“Big P”: Real Predictive Prognostics Part 1 [C]. IEEE Aerospace Conference, 2005, 10: 1~10
    [63] Hess A, Calvello G, Frith P. Challenges, Issues, and Lessons Learned Chasing the“Big P”: Real Predictive Prognostics Part 2 [C]. IEEE Aerospace Conference, 2006, 3: 1~10.
    [64] Engel S, Gilmartin B, et al. Prognostics, the real issues involved with predicting life remaining [C]. Aerospace Conference Proceedings, IEEE, 2000, 6: 457~469.
    [65] Jardine A, Lin D, Banjevic D. A review on machinery diagnostics and prognostics implementing condition-based maintenance [J]. Mechanical Systems and Signal Processing, 2006, 20: 1483~1510.
    [66] Ramakrishnan A, Pecht M. A Life Consumption Monitoring Methodology for Electronic Systems [J]. IEEE Transactions on Components and Packaging Technologies, 2003, 26(3): 625~634.
    [67] Brotherton T, Grabill P. A testbed for data fusion for engine diagnostics and prognostics [C]. IEEE Aerospace Conference, 2002: 3029~3042.
    [68] Romer M, Dzakowic J, et al. Validation and verification of prognostic and health management technologies [C]. IEEE Aerospace Conference, 2004.
    [69] Hess A, Prognositics & Health Management– A Thirty year Retrospective, Prognostics and Health Management Lead, Joint Strike Fighter Program Office [C]. NASA ISHEM Conference, Octorber, 2005.
    [70] Marotta S. Predictive Reliability of Tactical Missiles Using Health Monitoring Data & Probabilistic Engineering Analysis [C]. NASA ISHEM Conference,NAPA, Valley , Nov, 2005.
    [71]张宝珍,国外综合诊断、预测与健康管理的发展历程[C],国防科技工业试验与测试技术高层论坛,2007,9:36~42.
    [72] Ann H, Gordon A. A Review of Diagnostic Techniques for ISHM Applications [C]. NASA ISHEM Conference,NAPA, Valley , Nov, 2005.
    [73]秦俊奇,曹立军,王兴贵.集成模糊推理与定量仿真的故障预测系统研究[J].系统仿真学报,2005,17(9):2154~2158.
    [74]钟群鹏,傅国如,张峥.机电装备失效研究的内涵及其科学问题探讨[J].机械工程学报,2003,39(10):13~20.
    [75] Hess A, Fila L. Prognostics, from the Need to Reality - from the Fleet Users and PHM System Designer/Developers Perspectives [C]. Aerospace Conference Proceedings, 2002 IEEE, 6: 2791–2797.
    [76] Lin D, Makis V. Recursive filters for a partially observable system subject to random failure [J]. Advances in Applied Probability, 2003, 35: 207–227.
    [77] Wang W. A model to predict the residual life of rolling element bearings given monitored condition information to date [J]. IMA Journal of Management Mathematics, 2002, 13: 3–16.
    [78] Luu A, Santi L, et al. Real-time simulation for verification and validation of diagnostic and prognostic algorithms [R]. AIAA-2005-3717, 2005.
    [79] Roemer M, Nwadiogbu E, Bloor G. Development of diagnostic and prognostic technologies for aerospace health management applications [C]. Aerospace Conference Proceedings, 2001 IEEE, 6: 3139~3147.
    [80] Hess A. The prognostic requirement for advanced sensors and non-traditional detection technologies [C]. DARPA/DSO Prognosis Bidder's Conference, 2002, 9: 26~27.
    [81]徐萍,康锐.预测与状态管理系统(PHM)技术研究[J].测控技术. 2004, 23(12): 58~60.
    [82] Valentin R., M. Osterman, Bob Newman. Remaining Life Assessment of Aging Electronics in Avionic Applications. The Annual Reliability and Maintainability, 2003 Proceedings, Tampa Florida, January 27-30, 2003: 313~318.
    [83] Cheng Z, Hu N, Qin G. A New Feature for Monitoring of Planetary Gear Sets Based on Physical Model. Proceedings of the 23rd International Congress on Condition Monitoring and Diagnostic Engineering Management, June 28-July 2, 2010, Nara, Japan: 289~296.
    [84]程哲,胡茑庆,冯占辉,高经纬.基于动力学仿真的行星轮系损伤检测[J].振动、测试与诊断, 2010, 30(4): 379~383.
    [85]成大先.机械设计手册——机械传动[M].北京:化学工业出版社,2004.
    [86] Ambarisha V, Parker R. Suppression of planet mode response in planetarygear dynamics through mesh phasing. Journal of Vibration and Acoustics [J]. Transactions of the ASME 2006. 128(2): 133~142.
    [87] Mi B, Michaels J, Michaels T. An ultrasonic method for dynamic monitoring of fatigue crack initiation and growth [J]. Journal of the Acoustical Society of America, 2006, 119(1): 74~85.
    [88] Botman M, Epicyclic gear vibrations [J]. Journal of engineering for industry, 1976:811~815.
    [89] Bahgat B M , et al. On the Dynamic Gear Tooth Loading of Planetary Gearing as A ffected by Bearing Clearances in High Speed M achinery [J]. Journal of Mechanisms, Transmissions and Automation in Design, T ransaction of the ASME, 1985, 107: 430~436.
    [90] August A , Kasuba R. TorsionalV ibration and Dynam icLoads in a Basic Planetary Gear System [J]. Journal of A coustics, Stress, and Reliability in Design. T ransaction of the A SM E 1986, 108: 348~ 253.
    [91] Parker R G. A Physical Exp lanation for the Effectiveness of Planet Phasing to Supp ress Planetary Gear V ibration [J]. Journal of Sound and V ibration, 2000, 236(4): 561~ 573.
    [92] Parker R G. Mesh Phasing for Epicyclic Gear Vibration [C]. Proceedings of the International Conference on Mechanical Transmissiom, Chongqing, P. R. China, 2001, 4: 53 ~57.
    [93] Kahraman A. Load Sharing Characteristics of Planetary T ransmission [J]. Mech., Mach., Theory., 1994, 29 (8): 1151~ 1165.
    [94] Kahraman A, Planetary gear train dynamics [J]. Journal of mechanical design, 1994, 116: 713~720.
    [95] Kahraman A, Natural modes of planetary gear trains [J]. Journal of Sound and Vibration, 1994, 173(1):125~130.
    [96] Lin J, Parker R, Analytical characterization of the unique properties of planetary gear free vibration [J]. Journal of vibration and acoustics, 1999, 121: 316~321.
    [97] Lin J, Parker R, Sensitivity of planetary gear natural frequencies and vibration modes to model parameters [J]. Journal of Sound and Vibration, 1999, 228: 109~128.
    [98] Lin J, Parker R, Structured vibration characteristics of planetary gears with unequally spaced planets [J]. Journal of Sound and Vibration, 2000, 233:921~928.
    [99] Kahraman A, Blankenship G, Experiments an nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters [J]. Journal of applied mechanical, 1997, 64: 217~226.
    [100] Parker R, A physical explanation for the effectiveness of planet phasing tosuppress planetary gear vibration [J]. Journal of Sound and Vibration, 2000, 236:561~573.
    [101] Kahraman A, Kharazi A, Umrani M, A deformable body dynamic analysis of planetary gears with thin rims [J]. Journal of Sound and Vibration, 2003, 262:752~768.
    [102] Inalpolat M, Kahraman A, A theoretical and experimental investigation of modulation sidebands of planetary gear sets [J]. Journal of Sound and Vibration, 2009, 323:677~696.
    [103] Mark W, Hines J, Stationary transducer response to planetary-gear vibration excitation with non-uniform planet loading [J]. Mechanical Systems and Signal Processing, 2009, 23: 1366–1381.
    [104] Mark W, Stationary transducer response to planetary-gear vibration excitation II: Effects of torque modulations [J]. Mechanical Systems and Signal Processing, 2009, 23: 2253~2259.
    [105] Chaari F, Hbaeib R, Fakhfakh T, Dynamic response simulation of planetary gears by the iterative spectral method [J]. International journal of simulation model. 2005, 4 (1): 35~45.
    [106] Eritenel T, Parker R, Modal properties of three-dimensional helical planetary gears [J]. Journal of Sound and Vibration, 2009, 325: 397~420.
    [107] Sun T, Hu H. Nonlinear dynamics of a planetary gear system with multiple clearances [J]. Mechanism and Machine Theory, 2003, 38: 1371~1390.
    [108]杨通强,宋轶民,张策,王世宇,斜齿行星齿轮系统自由振动特性分析[J].机械工程学报,2005,41(7):50~55.
    [109]王世宇,张策,宋轶民,杨通强,行星齿轮传动固有频率的统计特性分析[J].机械科学与技术,2005,24(6):705~709.
    [110]孙玉杰.三轴式内齿行星齿轮减速器的动力特性分析[D].陕西科技大学硕士学位论文,2005.
    [111]张江峰.三轴式内齿行星齿轮减速器动力学特性的研究[D].陕西科技大学硕士学位论文,2007.
    [112]张锁怀,张江峰,李磊.三轴式内齿行星齿轮减速器动力学特性的研究[D].中国机械工程,2007, 18(21) :2532~2534.
    [113]杨通强,斜齿行星传动动力学研究[D].天津大学博士学位论文,2003.
    [114]孙涛,行星齿轮系统非线性动力学研究[D].西北工业大学博士学位论文,2000.
    [115]孙智民,功率分流齿轮传动系统非线性动力学研究[D].西北工业大学博士学位论文,2001.
    [116]孙智民,沈允文,李素有.封闭行星齿轮传动系统的动态特性研究[J].机械工程学报,2002, 38 (2): 44~52.
    [117]孙涛,沈允文,孙智民,刘继岩.行星齿轮传动非线性动力学模型与方程[J].机械工程学报,2002, 38 (3): 6~10.
    [118]孙涛,沈允文,孙智民,刘继岩.行星齿轮传动非线性动力学方程求解与动态特性分析[J].机械工程学报, 2002, 38 (3): 11~15.
    [119]孙智民,沈允文,李素有.封闭行星齿轮传动系统的扭振特性研究[J].航空动力学报,2001, 16 (2): 163~166.
    [120]孙涛,胡海岩.基于离散傅里叶变换与谐波平衡法的行星齿轮系统非线性动力学分析[J].机械工程学报,2002, 38 (11): 58~61.
    [121]孙智民,季林红,沈允文. 2K-H行星齿轮传动非线性动力学[J].清华大学学报(自然科学版),2003, 43 (5): 636~639.
    [122]魏大盛,王延荣.行星轮系动态特性分析[J].航空动力学报,2003,18 (3):450~453.
    [123]万凯宇.行星齿轮传动系统动力学分析研究[D].南京航空航天大学硕士学位论文,2004.
    [124]李斌.行星齿轮传动系统均载分析方法的研究[D].南京航空航天大学硕士学位论文,2005.
    [125]王建军.计入内齿圈弹性的直齿行星传动动力学研究[D].天津大学硕士学位论文,2006.
    [126]赵玉香,孙首群,朱卫光.行星齿轮传动机构动力学分析[J].机械传动,2008,32 (4):69~71.
    [127]袁敏,李润方,林建德.行星齿轮系统的运动分析及动力学仿真[J].机械传动,2006,30(5): 17~19.
    [128]王世宇.基于相位调谐的直齿行星齿轮传动动力学理论与实验研究[D].天津大学博士学位论文,2005.
    [129]沈允文,邵长健.利用行星架附加阻尼的行星齿轮系统减振研究[J].机械传动,1999,23(4): 29~31.
    [130]林超.双速卷扬机多流传动系统动力学建模及动态性能分析[D].重庆大学博士学位论文,2001.
    [131]李振平,凌云,范凤明,康忠.行星齿轮传动的动特性优化研究[J].车辆与动力技术,2009, 1: 21~24.
    [132]郭飚,段福海,胡青春.塑料行星齿轮系统振动与噪声特性的研究[J].机械设计,2009,26(4): 8~10.
    [133]杨建明.机构及机械传动系统的非线性动力学研究综述[J].桂林电子工业学院学报,2001,21(2): 42~46.
    [134]王建军,李其汉,李润方.齿轮系统非线性振动研究进展[J].力学进展,2005,35(1):37~51.
    [135]胡世炎.机械失效分析手册[M].成都:四川科学与技术出版社,1989.
    [136]钟秉林,黄仁.机械故障诊断学(第3版)[M].北京:机械工业出版社,2006.
    [137]丁玉兰,石来德.机械设备故障诊断技术[M].上海:上海科学技术文献出版社,1994.
    [138]陈进.机械设备振动监测与故障诊断[M].上海:上海交通大学出版社,1999.
    [139] Velex P, Maatar M. A mathematical model for analyzing the influence of shape deviations and mounting errors on gear dynamic behaviour [J]. Journal of Sound and Vibration, 1996, 191(5): 629~660.
    [140] Park D, Kahraman A. A surface wear model for hypoid gear pairs [J]. Wear, 2009, 267: 1595~1604.
    [141] Yuksel C, Kahraman A. Dynamic tooth loads of planetary gear sets having tooth profile wear [J], Mechanism and Machine Theory, 2004, 39:695~715.
    [142] Ding H and Kahraman A. Interactions between nonlinear spur gear dynamics and surface wear [J]. Journal of Sound and Vibration, 2007, 307: 662~679.
    [143] Chaari F, Fakhfakh T and Haddar M. Dynamic Analysis of a Planetary Gear Failure Caused by Tooth Pitting and Cracking [J]. Journal of Failure Analysis and Prevention, 2006, 6(2): 73~78.
    [144] Chaari F, Fakhfakh T and Haddar M. Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness [J]. European Journal of Mechanics - A/Solids, 2009, 28(3): 461~468.
    [145] Chaari F, Baccar W, Abbs M and Haddar M. Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission [J]. European Journal of Mechanics - A/Solids, 2008, 27(4): 691~705.
    [146] Fakhfakh T, Chaari F and Haddar M. Numerical and experimental analysis of a gear system with teeth defects [J]. International Journal of Manufacture Technology, 2005, 25: 542~550.
    [147] Zouari S, Maatar M, Fakhfak T and Haddar M. Three-Dimensional Analyses by Finite Element Method of a Spur Gear: Effect of Cracks in the Teeth Foot on the Mesh Stiffness [J]. Journal of Failure Analysis and Prevention, 2007, 7: 475~481.
    [148] Mosher M, Huff E and Zakrajsek J. Modeling of vibration measurements for gear fault and damage detection on aircraft[C]. Conference on Joint Army Navy NASA Air Force, Colorado Springs, Co, 2003.
    [149] Badaoui M, Cahouet V, Guillet F. Modeling and detection of localized tooth detects in geared systems [J]. Transactions of the ASME, 2001, 123: 422~430.
    [150] Choy F, Polyshchuk V, Zakrajsek J. Analysis of the effects of surface pitting and wear on the vibration of a gear transmission system[J]. Tribology International, 1996, 29(1): 77~83.
    [151] Litak G and Friswell M. Dynamics of a gear system with faults in meshing stiffness [J]. Nonlinear Dynamics, 2005, 41: 415~421.
    [152] K. Mao. Gear tooth contact analysis and its application in the reduction of fatigue wear [J]. Wear, 2007, 262: 1281~1288.
    [153] Kuang J and Lin A. The effect of tooth wear on the vibration spectrum of a spur gear pair [J]. Journal of Vibration and Acoustics, 2001, 123: 311~317.
    [154]明廷涛,张永祥.齿轮裂纹故障仿真计算与诊断[J].机械设计与制造, 2005, 6: 140~142.
    [155]邵忍平,郭万林,刘梦军.裂纹齿轮动力特性分析与模拟[J].机械科学与技术, 2003, 22(5): 788~791.
    [156] Howard I, Jia S, Wang J. The dynamic modelling of a spur gear in mesh including friction and a crack [J], Mechanical Systems and Signal Processing, 2001, (15): 831~838.
    [157]田竹友,冯荣坦.渐开线行星齿轮减速器虚拟样机[J].北京机械工业学院学报,2005,20(1):21~24.
    [158]胡建正,彭金涛,巫士晶.基于虚拟样机技术的行星变速器设计仿真[J].起重运输机械,2004, 8:39~42.
    [159]巫士晶,王晓笋,胡建正等.车辆行星传动系统虚拟样机技术研究与实践[J].中国机械工程,2005, 16(6):550~553.
    [160]王秀山,杨建国,郭前建等.双级圆柱齿轮减速器虚拟样机建造研究[J].南京航空航天大学学报,2005, 37(S):130~133.
    [161]洪清泉.基于虚拟样机技术的动力传动系统建模与仿真[D].北京理工大学,2003.
    [162]赵世宜,刘子建,王辉.虚拟样机技术在汽车变速箱设计中的应用[J].计算机仿真,2006,23(2):200~203.
    [163]张兴霞,王兴贵,杜秀菊等.基于虚拟样机技术的行星轮系的动力学仿真研究[J].机械传动,2006,30(4):4~7.
    [164]龙凯,程颖.齿轮啮合力仿真计算的参数选取研究[J].计算机仿真,2002,19(6):87~88.
    [165]李金玉,勾志践,李媛.基于ADAMS的齿轮啮合过程中齿轮力的动态仿真[J].设计与研究,2005(3):15~17.
    [166]崔新涛.基于虚拟样机技术的变速器动力学仿真研究[D].天津:天津大学,2004.
    [167]毕长飞.采煤机截割部齿轮传动系统的动态特性的研究[D].沈阳:辽宁工程技术大学,2006.
    [168]刘欣.基于虚拟样机技术的直齿行星传动动力学研究[D].天津:天津大学,2007.
    [169] Hsieh W. An experimental study on cam-controlled planetary gear trains [J]. Mechanism and Machine Theory, 2007, 42: 513–525.
    [170]郑凯,胡仁喜,陈鹿民.ADAMS 2005机械设计——高级应用实例[M].北京:机械工业出版社,2006.
    [171]周青龙.故障诊断与监控[M].北京:兵器工业出版社,1992.
    [172]温熙森.模式识别与状态监控[M].北京:科学出版社,2007.
    [173] Wu B, Saxena A, Patrick R and Vachtsevanos G. Vibration Monitoring for Fault Diagnosis of Helicopter Planetary Gears [C]. Proceedings of the 16th IFAC World Congress on Disc, July 4-8, Prague, Cesko, 2005.
    [174] Wu B, Saxena A. An Approach to Fault Diagnosis of Helicopter Planetary Gears [C]. 2004 IEEE Autotestcon, 2004, 20-23, September: 475~481.
    [175] Barszcz T, Randall R. Application of Spectral Kurtosis for Detection of a Tooth Crack in the Planetary Gear of a Wind Turbine [J]. Mechanical Systems and Signal Processing, 2009, 23: 1352~1365.
    [176] Antoni J, Randall R. The Spectral Kurtosis: Application to the Vibratory Surveillance and Diagnostics of Rotating Machines [J]. Mechanical Systems and Signal Processing, 2006, 20: 308~331.
    [177] Sparis P, Vachtsevanos G. A Helicopter Planetary Gear Carrier Plate Crack Analysis and Feature Extraction based on Ground and Aircraft Tests [C]. Proceedings of the 2005 IEEE International Symposium on Intelligent Control, June 27-29, Limassol, Lyprus, 2005: 646~651.
    [178] Tumer I, Huff E. Using Triaxial Accelerometer Data for VibrationMonitoring of Helicopter Gearboxes [C]. Proceedings of DETC’01 2001 ASME Design Engineering Technical Conferences, Pittsburgh, Pennsylvania, USA, September 9-12, 2001: 1~11.
    [179]杨江天,岳维亮.灰色模型在机械故障预测中的应用[J].机械强度, 2001, 23(3): 277~279.
    [180] Blunt D, Keller J. Detection of a fatigue crack in a UH-60A planet gear carrier using vibration analysis [J]. Mechanical System and Signal Processing, 20, 2006: 2095~2111.
    [181] Samuel P, Pines D. Classifying helicopter gearbox faults using a normalized energy metric [J]. Smart Material and Structure, 10, 2001: 145~153.
    [182]关惠玲,韩捷.行星轮系转矩大幅波动故障特征及诊断方法[J].机械强度, 28(1), 2006: 29~33.
    [183] Keller J, Grabill P. Vibration Monitoring of UH-60A Main Transmission Planetary Carrier Fault [C]. The American Helicopter Society 59thAnnual Forum, Phoenix, Arizona, May 6–8, 2003.
    [184] Bartelmus W, Zimroz R. Vibration condition monitoring of planetary gear box under varying External load [J]. Mechanical System and Signal Processing, 23, 2009: 246~257.
    [185]陈仲生,杨拥民,沈国际.独立分量分析在直升机齿轮箱故障早期诊断中的应用[J].机械科学与技术,2004, 23(4): 481~483.
    [186] Samuel P, Pines D. Helicopter Transmission Diagnostics using Constrained Adaptive Lifting [C]. The American Helicopter Society 59th Annual Forum, Phoenix, AZ, May 6-8, 2003.
    [187] Saxena A, Wu B, Vachtsevanos G. A Methodology for Analyzing Vibration Data from Planetary Gear Systems using Complex Morlet Wavelets [C]. American Control Conference, Portland, OR, USA, June 8-10, 2005: 4730~4735.
    [188]肖志松,唐力伟,王虹.行星齿轮箱中齿轮故障模式判别[J].振动与冲击, 24(3), 2005: 125~127.
    [189] Salgado D, Castillo J. A method for detecting degenerate structures in planetary gear trains [J]. Mechanism and Machine Theory, 40, 2005: 948~962.
    [190]胡雷,胡茑庆,秦国军.双阈值单类支持向量机在线故障检测算法及应用[J].机械工程学报, 2009, 45(3): 169~173.
    [191]沈庆根,郑水英.设备故障诊断[M].北京:化学工业出版社,2006.
    [192]杨国安.机械设备故障诊断实用技术[M].北京:中国石化出版社,2007.
    [193]严新平.机械系统工况监测与故障诊断[M].武汉:武汉理工大学出版社,2009.
    [194]王江萍.机械设备故障诊断技术及应用[M].西安:西北工业大学出版社,2001.
    [195]何正嘉,訾艳阳等.机械设备非平稳信号的故障诊断原理及应用[M].北京:高等教育出版社,2001.
    [196]杨志伊.设备状态监测与故障诊断[M].北京:中国计划出版社,2006.
    [197] Dempsey P, Lewicki D, Le D, Investigation of Current M ethods to Identify Helicopter Gear Health [C]. In: 2007 IEEE Aerospace Conference, Big Sky, Montana, March 3-10, 2007.
    [198] Samuel P, Pines D. A Review of Vibration-based Techniques for Helicopter Transmission Diagnostics [J]. Journal of Sound and Vibration, 2005, 282: 475~508.
    [199] Yang B, Kim K. Application of Dempster-Shafer Theory in Fault Diagnosis of Induction Motors Using Vibration and Current Signals [J]. Mechanical Systems and Signal Processing, 2006, 20: 403~420.
    [200] Zakrajsek J, Townsend D, Decker H. An Analysis of Gear Fault Detection Methods as Applied to Pitting Fatigue Failure Data [R]. NASA TM 105950, AVSCOM TR 92-C-035, April 1993.
    [201] Huang N, Shen Z, Long S. The mechanism for frequency downshift in nonlinear wave evolution [J]. Advances in Applied Mechanics, 1996, 32: 59~71.
    [202] Huang N, Shen Z, Long S. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis [J]. Proceeding of Royal Society London, 1998, A(454): 903~995.
    [203] Deng J. Control Problems of grey system [J]. System Control Letter, 1982, 5: 285~294.
    [204] Lin S and Wu S. An Intelligent Web-based GRA/Cointegration Analysis for Systematic Risk [J]. International Journal of Computers, 2010, 4(4): 223~234.
    [205] Deng J. Properties of relational space for grey system [M]. Beijing: China Ocean Press, 1988.
    [206] Deng J. Introduction to grey system theory [J]. The Journal of Grey System, 1989, 1: 1–24.
    [207] Kayacan E, Ulutas B, Kaynak O. Grey system theory-based models in time series prediction [J]. Expert Systems with Applications, 2010, 37: 1784~1789.
    [208] Peng Z and Kirk T. Wear particle classification in a fuzzy grey system [J]. Wear, 1999, 225: 1238~1247.
    [209] Wang Y. Predicting stock price using fuzzy grey prediction system [J]. Expert Systems with Applications, 2002, 22: 33~39.
    [210]翟军,盛建明. MGM (1, n)灰色模型及应用[J].系统工程理论与实践, 1997, 17(5): 109~113.
    [211]靳春梅,樊灵,邱阳等.灰色理论在旋转机械故障诊断与预报中的应用[J],应用力学学报,2000,17(3):74~79.
    [212]段志善,闻邦椿.灰色理论在设备故障诊断中的应用[J],兵工学报,1990,18:231~238.
    [213]程哲,胡茑庆,高经纬.基于物理模型的行星轮系特征提取与评估方法[J].国防科技大学学报, 2010, 32(6): 122~129.
    [214] Loparo K, Falah A, Adams M. Model-based fault detection and diagnosis in rotating machinery [C]. Proceedings of the Tenth International Congress on Sound and Vibration, Stockholm, Sweden, 2003: 1299~1306.
    [215] Sekhar A. Model-based identification of two cracks in a rotor system [J]. Mechanical Systems and Signal Processing, 2004, 18: 977~983.
    [216] Vania A, Pennacchi P. Experimental and theoretical application of fault identification measures of accuracy in rotating machine diagnostics [J]. Mechanical Systems and Signal Processing, 2004, 18: 329~352.
    [217] David M, Jonathan A. Detection of a fatigue crack in a UH-60A planet gear carrier using vibration analysis [J]. Mechanical Systems and Signal Processing, 2006, 20: 2095–2111.
    [218] Keller J, Grabill P. Vibration Monitoring of a UH-60A Main Transmission Planetary Carrier Fault [C]. The American Helicopter Society 59th Annual Forum, Phoenix, AZ, May 6-8, 2003.
    [219] Romano P, A Model Based Framework for Fault Diagnosis and Progress of Dynamical System with an Application to Helicopter Transmissions [D]. Georgia: Georgia Institute of Technology, 2007.
    [220] Byington C, Watson M, Roemer M, Galic T, McGroarty J. Prognostic Enhancements to Gas Turbine Diagnostic Systems [C]. 2003 Aerospace Conference, IEEE Proceedings, 2003, 7: 3247~3255.
    [221] Choi S, Li C. Estimation of Gear Tooth Transverse Crack Size from Vibration by Fusing Selected Gear Condition Indices [J]. Measurement Science and Technology, 2006, 17: 2395~2400.
    [222] Lei Y, Zuo M. Gear Crack Level Identification Based on Weighted K Nearest Neighbor Classification Algorithm [J]. Mechanical Systems and Signal Processing, 2009, 23(6): 1535~1547.
    [223] Coppe A, and etc. A Statistical Model for Estimating Probability of Crack Detection [C]. 2008 International conference on PHM, CA, USA, Oct. 2008.
    [224] Ma J, Li C. Gear Defect Detection through Model-Based Wideband Demodulation of Vibrations [J]. Mechanical Systems and Signal Processing, 1996, 10(5): 653~665.
    [225] Camci F, Chinnam R. Health-State Estimation and Diagnostics in Machining Systems using Hidden Markov Model Committees [C]. The Proceedings of the 15th International Conference on Flexible Automation & Intelligent Manufacturing, Bilbao, Spain, 18-20 July 2005.
    [226] Miao Q, Makis V. Extraction of Machinery Health Index in CBM Based on Wavelet Modulus Maxima [C]. Flexible Automation and Intelligent Manufacturing FAIM2004, Toronto, Canada, 2004: 959~965.
    [227] Zheng J, Li Y, Huang Y. Fractal Feature Extraction of Drilling Force For Drill Wear Monitoring Based on Wavelet Reconstruction [C]. The 3rd International Symposium on Instrumentation Science and technology, 2004, 8: 499~505.
    [228] Alexej A. Condition Assessment and Life Predition of Rolling Element Bearings-Part 1 [J]. Journal of Sound and Vibration, 1995, 29(6): 10~17.
    [229] Qiu H, Liao H, Lee J. Degradation Assessment for Machinery Prognostics Using Hidden Markov Models [C]. Proceedings of the ASME International Design Engineering Technical Conferences and Computer sand Information in Engineering Conference (DETC2005). 2005: 531~537.
    [230] Qiu H, Lee J. Feature Fusion and Degradation Detection Using Self-Organizing Map [C]. Proceedings of the 2004 International Conference on Machine Learning and Application, 2004, 4: 107~114.
    [231] Qiu H, Lee J, Lin J. Robust Performance Degradation Assessment Methods for Enhanced Rolling Element Bearing Prognostics [J]. Advanced Engineering Informatics, 2003, 17: 127~140.
    [232] Zeng Q, Qiu J, Liu G. Application of Hidden Semi-Markov Models Based on Wavelet Correlation Feature Scale Entropy in Equipment Degradation State Recognition [C]. The 7th World Congress on Intelligent Control and Automation, 2008, 6.
    [233]曾庆虎,邱静,刘冠军.基于小波相关特征尺度熵的HSMM设备退化状态识别与故障预测方法研究[J].仪器仪表学报,2008,29(12):2559~2564.
    [234]曾庆虎,刘冠军,邱静.基于小波相关特征尺度熵预测特征信息提取方法研究[J].中国机械工程,2008,19(10):1193~1196.
    [235]印欣运,何永勇,彭志科等.小波熵及其在状态趋势分析中的应用[J].振动工程学报, 2004, 17(2): 165~169.
    [236] Knott J, Withey P. Fracture Mechanics: Worked Examples [M]. The Instituteof Materials, 1993.
    [237] Smith R. Fatigue Crack Growth 30Years of Progress [M]. Pergamon Press, 1986.
    [238] Oppenheimer C, Loparo K. Physically based diagnosis and prognosis of cracked rotor shafts [J]. Component and Systems Diagnostics, Prognostics, and Health Management II, 2002, 33: 122~132.
    [239]刘守道,张来斌,王朝晖,等.滚动轴承故障的灰色GM模型预测[J].润滑与密封, 2000, 2: 38~39.
    [240]王弘宇,马放,杨开.灰色新陈代谢GM(1,1)模型在中长期城市需水量预测中的应用研究.武汉大学学报, 2004, 37(6): 32~35.
    [241]谢乃明,刘思峰.离散GM (1, 1)模型与灰色预测模型建模机理[J].系统工程理论与实践, 2005, 25(1): 93~99.
    [242]戴文战,李俊峰.非等间距GM ( 1, 1)模型建模研究[J].系统工程理论与实践, 2005, 25(9): 89~93.
    [243]陈士玮,李柱国.灰色理论在柴油机油液检测中的应用研究[J].内燃机学报, 2005, 23(5): 475~479.
    [244]夏学文.一类新的时序预报模型[J].系统工程理论与实践, 2000, 20(8): 87~90.
    [245]王清晓,陈家锭.灰色马尔可夫链方法在设备故障预测中的应用初探[J].机械科学与技术, 1997, 16(3): 491~495.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700