液压设备故障诊断的分形方法研究
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摘要
分形是一门新的学科，它特别适用于分析非线性系统，而将分形用于机械设备故障诊断则是近年来发展的新动向。可以采用分形方法分析机械系统的非线性信号，从中提取出特征信息，并与其它的分析方法相结合，共同实现机械设备的故障模式识别与故障诊断。
本文首先探讨了分形用于机械系统故障诊断的理论基础。在介绍了分形和分形理论中的自相似性、无标度性、分形维数等概念后，讨论了分形与复杂机械系统的关系。分形中的关联维数反映了复杂机械系统运动过程中的吸引子的动态特性，因而可以采用分形的方法来分析复杂机械系统信号。在此基础上，提出了基于分形的机械系统故障诊断的方法与流程。
本文以轧机液压系统中的液压泵为研究对象，制定了运用分形方法对其进行故障诊断的试验方案，包括数据的获取、数据的采集方案、特征参数的提取和故障诊断方法等。在特征参数的提取中采用关联维数作为系统的特征参数，讨论了关联维数的计算方法和计算参数的选择。
在液压泵故障分形分析与诊断实例部分，对不同工作(故障)状态下的液压泵外壁振动速度信号的关联维数进行了分析，并与频谱分析进行了对比，结果表明，关联维数对设备故障比较敏感，能够反映复杂系统的动态特性，同时它也解释了频谱分析方法无法确定的非线性特征产生的原因，给出了定性和定量的结果。
为了课题研究的方便，单独开发了基于分形的数据分析系统，并对其作了简单的介绍。最后对课题的研究作了总结和展望。
Fractal is a new subject and it is especially fit for researching nonlinear system. Recently signal processing methods based on fractal have been applied to mechanical system fault diagnosis. The objective of the proposed research is to develop a method based on fractal theory for analyzing the nonlinear signals of mechanical system. This method will provide further useful information about the underlying dynamics. It is possible to implement mechanical system fault diagnosis by using this method combined with other signals analysis methods.
The basic theory of mechanical system fault diagnosis based on fractal is firstly introduced. The correlation dimension reflects the attractor characteristic of complex mechanical system, so the signal processing methods based on fractal may be used to analyze complex mechanical system. In this research, the flow of mechanical system fault diagnosis is provided and the judgment principle of fractal characteristic of signals is also given.
Hydraulic pumps are the important part of rolling mill and they are also the researched objects of this paper, hi this research, The experimentation project of fault diagnosis of hydraulic pump is established, including data sampling, obtaining character parameters, fault diagnosis method and so on. The correlation dimension is adopted as the character parameter of hydraulic pump dynamical system. The calculating method of correlation dimension and the principle of selecting parameters such as time delay and embedding dimension are discussed in this paper.
In the application of hydraulic pump fault diagnosis by fractal method, this paper analyzes the correlation dimensions of vibration speed signals of hydraulic pump under different working states. The result shows that the correlation dimension is sensitive to hydraulic pump faults and it reflects the dynamic characteristic of dynamics system. The qualitative and quantitative conclusion can be gained by correlation dimension.
The data analysis system based on fractal theory is developed during the research and it is introduced. At last, the research is summered and prospected in this paper.
本文首先探讨了分形用于机械系统故障诊断的理论基础。在介绍了分形和分形理论中的自相似性、无标度性、分形维数等概念后，讨论了分形与复杂机械系统的关系。分形中的关联维数反映了复杂机械系统运动过程中的吸引子的动态特性，因而可以采用分形的方法来分析复杂机械系统信号。在此基础上，提出了基于分形的机械系统故障诊断的方法与流程。
本文以轧机液压系统中的液压泵为研究对象，制定了运用分形方法对其进行故障诊断的试验方案，包括数据的获取、数据的采集方案、特征参数的提取和故障诊断方法等。在特征参数的提取中采用关联维数作为系统的特征参数，讨论了关联维数的计算方法和计算参数的选择。
在液压泵故障分形分析与诊断实例部分，对不同工作(故障)状态下的液压泵外壁振动速度信号的关联维数进行了分析，并与频谱分析进行了对比，结果表明，关联维数对设备故障比较敏感，能够反映复杂系统的动态特性，同时它也解释了频谱分析方法无法确定的非线性特征产生的原因，给出了定性和定量的结果。
为了课题研究的方便，单独开发了基于分形的数据分析系统，并对其作了简单的介绍。最后对课题的研究作了总结和展望。
Fractal is a new subject and it is especially fit for researching nonlinear system. Recently signal processing methods based on fractal have been applied to mechanical system fault diagnosis. The objective of the proposed research is to develop a method based on fractal theory for analyzing the nonlinear signals of mechanical system. This method will provide further useful information about the underlying dynamics. It is possible to implement mechanical system fault diagnosis by using this method combined with other signals analysis methods.
The basic theory of mechanical system fault diagnosis based on fractal is firstly introduced. The correlation dimension reflects the attractor characteristic of complex mechanical system, so the signal processing methods based on fractal may be used to analyze complex mechanical system. In this research, the flow of mechanical system fault diagnosis is provided and the judgment principle of fractal characteristic of signals is also given.
Hydraulic pumps are the important part of rolling mill and they are also the researched objects of this paper, hi this research, The experimentation project of fault diagnosis of hydraulic pump is established, including data sampling, obtaining character parameters, fault diagnosis method and so on. The correlation dimension is adopted as the character parameter of hydraulic pump dynamical system. The calculating method of correlation dimension and the principle of selecting parameters such as time delay and embedding dimension are discussed in this paper.
In the application of hydraulic pump fault diagnosis by fractal method, this paper analyzes the correlation dimensions of vibration speed signals of hydraulic pump under different working states. The result shows that the correlation dimension is sensitive to hydraulic pump faults and it reflects the dynamic characteristic of dynamics system. The qualitative and quantitative conclusion can be gained by correlation dimension.
The data analysis system based on fractal theory is developed during the research and it is introduced. At last, the research is summered and prospected in this paper.
引文
[1] “广州市重点攻关项目——全自动大型薄板连轧机组远程智能监测系统”项目材料．广州：珠江钢铁有限责任公司，2001．5～6
[2] 吴百海．高效重载多机构液压同步系统研究资料．广州：广东工业大学科研处，1997
[3] 黄志坚、吴百海、毛宁．轧机液压故障的智能诊断探讨．机械开发，2000年增刊：48～50
[4] 石博强、申炎华．机械故障诊断的分形方法——理论与实践．北京：冶金工业出版社，2001
[5] D.Logan. Using the Correlation Dimension for Vibration Fault Diagnosis of Rolling Element Bearing—1.Basic Concepts. Mechanical Systems and Signal Processing, 1996, 10(3):241～245
[6] 谢继深．彩色与分形理论在大型轧钢系统中的应用．广州：广东工业大学机电液工程智能控制研究所，2001．53～62
[7] T.B. Krik. Computer Image Analysis of Wear debris for Machine Condition Monitoring and Fault Diagnosis. Wear, 1995, Vol.181:717～722
[8] Mandelbrot K J. Fractal Geometry-Mathematical Foundations and Applications. John and Sons, 1990
[9] 曾文曲、刘世耀．分形几何——数学基础及其应用．沈阳：东北大学出版社，1991．P11
[10] 谭芳．分形漫步，http：//www.bjkp.gov.cn／dxskpwk／k21142-01.htm
[11] Turcotte D L．流体力学中的分形．力学进展，1988，18：511～517
[12] 李后强．分形与分维．成都：四川教育出版社，1990
[13] 董连科．分形理论及应用．沈阳：辽宁科学技术出版社，1991
[14] D.Beule, H.Herzel, E.Uhlmann, et al. Detecting nonlinearities in time series of machining processes. American Control Conference, 1999, 1:694～698
[15] Michael Peter Kennedy. Three Steps to Chaos. IEEE Transactions on circuits and
system-1: Fundamental theory and applications, 1993.10, Vol.40:659～660
[16] T.Y.Li and J.A.Yorke. Period Three Implies Chaos. Amer. Math. Monthly, 1975, 82:985～992
[17] 王东升、曹磊．混沌、分形及其应用．合肥：中国科技大学出版社，1995
[18] 腾丽娜．基于分形的信号处理技术在设备故障诊断中的应用研究．上海交通大学博士学位论文，2002
[19] 姜建东．机械测试信号的分形评估．西安交通大学博士学位论文，1997
[20] 黄志坚．液压设备故障分析与技术改造．武汉：华中理工大学出版社，1999．71～72
[21] Packard N H, Crutchiefield J P, Farmer J D, et al. Geometry from a time series[J].Phys Rev Lett, 1980, 45(6):712～716
[22] Gasdagli M, Eubank S, Farmer J D, et al. State space reconstruction in the presence of nosie[J]. Phys D, 1991, 51(1):52-98
[23] Buzug T, Pfister G. Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavior of strange attractors. Phy. Rev. A45, 1992:7073-7084
[24] Kember G, Fowler A C. A correlation function for choosing time delays in phase portrait reconstructions. Phy. Lett. A 179, 1993:72-80
[25] Rosenstein M T, Collins J J, Luca C.Reconstruction expansion as a geometry-based framework for choosing proper delay time. Physica D73, 1994:82-89
[26] Takens F, Mane. Detecting strange attractors in fluid turbulence[A]. In: Rand D A,Young L S, Eds. Dynamical Systems and Turbulence[C]. Vol.898 of Lecture Notes in Mathematics, Berlin: Springer, 1986, 366
[27] 刘延柱、陈立群．非线性动力学．上海：上海交通大学出版社，2002
[28] 徐京华、吴祥宝，以复杂度测度刻画人脑皮层上的信息传输．中国科学，Vol.24，No.1，1994
[29] 汪慰军、杨世锡．转子——轴承系统油膜失稳的Hopf分岔机理．中国机械工程．1999，3
[30] 廖明．分形在柴油机燃油系统故障诊断中的应用．北京科技大学学报．1998，5
[2] 吴百海．高效重载多机构液压同步系统研究资料．广州：广东工业大学科研处，1997
[3] 黄志坚、吴百海、毛宁．轧机液压故障的智能诊断探讨．机械开发，2000年增刊：48～50
[4] 石博强、申炎华．机械故障诊断的分形方法——理论与实践．北京：冶金工业出版社，2001
[5] D.Logan. Using the Correlation Dimension for Vibration Fault Diagnosis of Rolling Element Bearing—1.Basic Concepts. Mechanical Systems and Signal Processing, 1996, 10(3):241～245
[6] 谢继深．彩色与分形理论在大型轧钢系统中的应用．广州：广东工业大学机电液工程智能控制研究所，2001．53～62
[7] T.B. Krik. Computer Image Analysis of Wear debris for Machine Condition Monitoring and Fault Diagnosis. Wear, 1995, Vol.181:717～722
[8] Mandelbrot K J. Fractal Geometry-Mathematical Foundations and Applications. John and Sons, 1990
[9] 曾文曲、刘世耀．分形几何——数学基础及其应用．沈阳：东北大学出版社，1991．P11
[10] 谭芳．分形漫步，http：//www.bjkp.gov.cn／dxskpwk／k21142-01.htm
[11] Turcotte D L．流体力学中的分形．力学进展，1988，18：511～517
[12] 李后强．分形与分维．成都：四川教育出版社，1990
[13] 董连科．分形理论及应用．沈阳：辽宁科学技术出版社，1991
[14] D.Beule, H.Herzel, E.Uhlmann, et al. Detecting nonlinearities in time series of machining processes. American Control Conference, 1999, 1:694～698
[15] Michael Peter Kennedy. Three Steps to Chaos. IEEE Transactions on circuits and
system-1: Fundamental theory and applications, 1993.10, Vol.40:659～660
[16] T.Y.Li and J.A.Yorke. Period Three Implies Chaos. Amer. Math. Monthly, 1975, 82:985～992
[17] 王东升、曹磊．混沌、分形及其应用．合肥：中国科技大学出版社，1995
[18] 腾丽娜．基于分形的信号处理技术在设备故障诊断中的应用研究．上海交通大学博士学位论文，2002
[19] 姜建东．机械测试信号的分形评估．西安交通大学博士学位论文，1997
[20] 黄志坚．液压设备故障分析与技术改造．武汉：华中理工大学出版社，1999．71～72
[21] Packard N H, Crutchiefield J P, Farmer J D, et al. Geometry from a time series[J].Phys Rev Lett, 1980, 45(6):712～716
[22] Gasdagli M, Eubank S, Farmer J D, et al. State space reconstruction in the presence of nosie[J]. Phys D, 1991, 51(1):52-98
[23] Buzug T, Pfister G. Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavior of strange attractors. Phy. Rev. A45, 1992:7073-7084
[24] Kember G, Fowler A C. A correlation function for choosing time delays in phase portrait reconstructions. Phy. Lett. A 179, 1993:72-80
[25] Rosenstein M T, Collins J J, Luca C.Reconstruction expansion as a geometry-based framework for choosing proper delay time. Physica D73, 1994:82-89
[26] Takens F, Mane. Detecting strange attractors in fluid turbulence[A]. In: Rand D A,Young L S, Eds. Dynamical Systems and Turbulence[C]. Vol.898 of Lecture Notes in Mathematics, Berlin: Springer, 1986, 366
[27] 刘延柱、陈立群．非线性动力学．上海：上海交通大学出版社，2002
[28] 徐京华、吴祥宝，以复杂度测度刻画人脑皮层上的信息传输．中国科学，Vol.24，No.1，1994
[29] 汪慰军、杨世锡．转子——轴承系统油膜失稳的Hopf分岔机理．中国机械工程．1999，3
[30] 廖明．分形在柴油机燃油系统故障诊断中的应用．北京科技大学学报．1998，5