GFD和核主元分析的机械振动特征提取
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摘要
针对旋转机械非线性特征提取的问题,提出了广义分形维数(generalized fractal dimension,简称GFD)和核函数主元分析(kernel principal component analysis,简称KPCA)的旋转机械振动特征提取方法。首先,通过广义分形维数进行初次特征提取,形成高维特征空间;其次,通过核主元分析方法对高维特征空间降维并进行第二次特征提取;最后,利用核主元分析方法和KN近邻(KNN)方法对转子和轴承不同状态下的特征进行了分类。研究表明,GFD-KPCA方法对旋转机械进行了有效的特征提取,对不同状态的数据有高精度的分类,对参数选取有较低的依赖性。轴承微弱振动特征提取结果显示,GFD-KPCA性能优于常规的KPCA特征提取算法,具有更好的精度和适用范围。
For the problem of rotary machine nonlinear feature extraction,a method based on generalized fractal dimension(GFD)and kernel principal component analysis(KPCA)is proposed.Firstly,GFD is used for feature extraction and formed a high dimensions feature space.Secondly,KPCA is used for dimensionality reduction in high dimensions space and feature extraction ulteriorly.Finally,data in different running conditions of a rotor system and faulty bearing are classified using the methods of KPCA and K nearest neighbor(KNN).The result shows that this GFD-KPCA method can effectively extract features,accurately classify data in different conditions,and has a low dependence on selecting parameters.Bearing weak fault vibration feature extraction results show that the performance of GFD-KPCA is better than that of conventional KPCA feature extraction algorithm,which has better accuracy and scope of application.
For the problem of rotary machine nonlinear feature extraction,a method based on generalized fractal dimension(GFD)and kernel principal component analysis(KPCA)is proposed.Firstly,GFD is used for feature extraction and formed a high dimensions feature space.Secondly,KPCA is used for dimensionality reduction in high dimensions space and feature extraction ulteriorly.Finally,data in different running conditions of a rotor system and faulty bearing are classified using the methods of KPCA and K nearest neighbor(KNN).The result shows that this GFD-KPCA method can effectively extract features,accurately classify data in different conditions,and has a low dependence on selecting parameters.Bearing weak fault vibration feature extraction results show that the performance of GFD-KPCA is better than that of conventional KPCA feature extraction algorithm,which has better accuracy and scope of application.
引文
[1]胡茑庆.转子碰磨非线性行为与故障辨识的研究[D].长沙:国防科技大学,2005.
[2]Ibrahim A S.Nonlinear vibration phenomena in aeroengine measurements[J].Dynamics of Coupled Structures,2016,4:241-252.
[3]Huang H F,Song X L,Liu C,et al.A novel fractal method for fault diagnosis and signal measurements[J].Optik,2016,127:6805-6812.
[4]Shi Juanjuan,Liang Ming,Guan Yunpeng.Bearing fault diagnosis under variable rotational speed via the joint application of windowed fractal dimension transform and generalized demodulation:A method free from prefiltering and resampling[J].Mechanical Systems and Signal Processing,2016,68/69:15-33.
[5]Zheng Zhi,Jiang Wanlu,Wang Zhenwei,et al.Gear fault diagnosis method based on local mean decomposition and generalized morphological fractal dimensions[J].Mechanism and Machine Theory,2015,91:151-167.
[6]徐玉秀,钟建军,闻邦椿.旋转机械动态特性的分形特征及故障诊断[J].机械工程学报,2005,41(12):186-189.Xu Yuxiu,Zhong Jianjun,Wen Bangchun.Fractal fault diagnosis and classification to modal characteristic of rotor system[J].Chinese journal of mechanical engineering.2005,41(12):186-189.(in Chinese)
[7]李兵,张培林,米双山,等.齿轮故障信号多重分形维数的形态学计算方法[J].振动、测试与诊断,2011,31(4):450-453.Li Bing,Zhang Peilin,Mi Shuangshan,et al.Morphological calculate method of multi-fractal dimension of gear fault signal[J].Journal of Vibration,Measurement&Diagnosis,2011,31(4):450-453.(in Chinese)
[8]庞茂,吴瑞明,谢明祥.关联维数快速算法及其在机械故障诊断中的应用[J].振动与冲击,2010,29(12):106-109.Pang Mao,Wu Ruiming,Xie Mingxiang.Improved correlation dimension algorithm with its application to mechanical fault diagnosis[J].Journal of Vibration and Shock,2010,29(12):106-109.(in Chinese)
[9]胡金海,谢寿生,侯胜利,等.核函数主元分析及其在故障特征提取中的应用[J].振动、测试与诊断,2007,27(1):48-52.Hu Jinhai,Xie Shousheng,Hou Shengli,et al.Kernal principal component analysis and its application to fault feature extraction[J].Journal of Vibration,Measurement&Diagnosis,2007,27(1):48-52.(in Chinese)
[10]Ines J,Okba T.Mohamed F H,et al.Moving window KPCA with reduced complexity for nonlinear dynamic process monitoring[J].ISA Transactions,2016,64:184-192.
[11]Jean M,Fran9ois.Genernalized fractal dimension:equivalences and basic properties[J].Journal of Mathématiques Pures et Appliquéés,2001,80(10):977-1012.
[12]钟建军.基于分形理论的旋转机械故障诊断的应用研究[D].沈阳:沈阳工业大学.2002.
[13]Bernhard S.Nonlinear component analysis as a Kernal eigenvalue problem[J].Neural Computation,1998,10:1299-1319.
[14]李巍华,廖广兰,史铁林.核函数主元分析及其在齿轮故障诊断中的应用[J].机械工程学报,2003,39(8):65-70.Li Weihua,Liao Guanglan,Shi Tielin.Kernel principal component analysis and its application in gear fault diagnosis[J].Chinese Journal of Mechanical Engineering,2003,39(8):65-70.(in Chinese)
[15]胡金海,谢寿生,陈卫,等.基于核函数主元分析的航空发动机故障检测方法[J].推进技术,2008,29(1):79-83.Hu Jinhai,Xie Shousheng,Chen Wei,et al.An aeroengine fault detection method based on kernel principal component analysis[J].Journal of Propulsion Technology,2008,29(1):79-83.(in Chinese)
[16]Liu Zhiwen,Guo Wei,Hu Jinhai,et.al.A hybrid intelligent multi-fault detection method for rotating machinery based on RSGWPT,KPCA and Twin SVM[J/OL].ISA Transactions,(2016-04-24)[2016-11-03].www.elsevier.com/locate/isatrans
[17]李应红,尉询凯.航空发动机的智能诊断、建模与预测方法[M].北京:科学出版社,2013:200-204.
[18]Case Western Reserve University.Bearing data center seeded fault test data[EB/OL].[2017-01-15].http:∥csegroups.case.edu/bearingdatacenter/home.
[19]Qiu H,Lee J,Lin J,et al.Robust performance degradation assessment methods for enhanced rolling element bearing prognostics[J].Advanced Engineering Informatics,2003(17):127-140.
[20]Qiu H,Lee J,Lin J,et al.Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics[J].Journal of Sound and Vibration,2006(289):1066-1090.
[21]胡世杰,钱宇宁,严加强.基于概率密度空间划分的符号化时间序列分析及其在异常诊断中的应用[J].振动工程学报,2014,27(5):780-784.Hu Shijie,Qian Yuning,Yan Jiaqiang.Anomaly detection using symbolic time series analysis based on probability density space partitioning[J].Journal of Vibration Engineering,2014,27(5):780-784.(in Chinese)
[2]Ibrahim A S.Nonlinear vibration phenomena in aeroengine measurements[J].Dynamics of Coupled Structures,2016,4:241-252.
[3]Huang H F,Song X L,Liu C,et al.A novel fractal method for fault diagnosis and signal measurements[J].Optik,2016,127:6805-6812.
[4]Shi Juanjuan,Liang Ming,Guan Yunpeng.Bearing fault diagnosis under variable rotational speed via the joint application of windowed fractal dimension transform and generalized demodulation:A method free from prefiltering and resampling[J].Mechanical Systems and Signal Processing,2016,68/69:15-33.
[5]Zheng Zhi,Jiang Wanlu,Wang Zhenwei,et al.Gear fault diagnosis method based on local mean decomposition and generalized morphological fractal dimensions[J].Mechanism and Machine Theory,2015,91:151-167.
[6]徐玉秀,钟建军,闻邦椿.旋转机械动态特性的分形特征及故障诊断[J].机械工程学报,2005,41(12):186-189.Xu Yuxiu,Zhong Jianjun,Wen Bangchun.Fractal fault diagnosis and classification to modal characteristic of rotor system[J].Chinese journal of mechanical engineering.2005,41(12):186-189.(in Chinese)
[7]李兵,张培林,米双山,等.齿轮故障信号多重分形维数的形态学计算方法[J].振动、测试与诊断,2011,31(4):450-453.Li Bing,Zhang Peilin,Mi Shuangshan,et al.Morphological calculate method of multi-fractal dimension of gear fault signal[J].Journal of Vibration,Measurement&Diagnosis,2011,31(4):450-453.(in Chinese)
[8]庞茂,吴瑞明,谢明祥.关联维数快速算法及其在机械故障诊断中的应用[J].振动与冲击,2010,29(12):106-109.Pang Mao,Wu Ruiming,Xie Mingxiang.Improved correlation dimension algorithm with its application to mechanical fault diagnosis[J].Journal of Vibration and Shock,2010,29(12):106-109.(in Chinese)
[9]胡金海,谢寿生,侯胜利,等.核函数主元分析及其在故障特征提取中的应用[J].振动、测试与诊断,2007,27(1):48-52.Hu Jinhai,Xie Shousheng,Hou Shengli,et al.Kernal principal component analysis and its application to fault feature extraction[J].Journal of Vibration,Measurement&Diagnosis,2007,27(1):48-52.(in Chinese)
[10]Ines J,Okba T.Mohamed F H,et al.Moving window KPCA with reduced complexity for nonlinear dynamic process monitoring[J].ISA Transactions,2016,64:184-192.
[11]Jean M,Fran9ois.Genernalized fractal dimension:equivalences and basic properties[J].Journal of Mathématiques Pures et Appliquéés,2001,80(10):977-1012.
[12]钟建军.基于分形理论的旋转机械故障诊断的应用研究[D].沈阳:沈阳工业大学.2002.
[13]Bernhard S.Nonlinear component analysis as a Kernal eigenvalue problem[J].Neural Computation,1998,10:1299-1319.
[14]李巍华,廖广兰,史铁林.核函数主元分析及其在齿轮故障诊断中的应用[J].机械工程学报,2003,39(8):65-70.Li Weihua,Liao Guanglan,Shi Tielin.Kernel principal component analysis and its application in gear fault diagnosis[J].Chinese Journal of Mechanical Engineering,2003,39(8):65-70.(in Chinese)
[15]胡金海,谢寿生,陈卫,等.基于核函数主元分析的航空发动机故障检测方法[J].推进技术,2008,29(1):79-83.Hu Jinhai,Xie Shousheng,Chen Wei,et al.An aeroengine fault detection method based on kernel principal component analysis[J].Journal of Propulsion Technology,2008,29(1):79-83.(in Chinese)
[16]Liu Zhiwen,Guo Wei,Hu Jinhai,et.al.A hybrid intelligent multi-fault detection method for rotating machinery based on RSGWPT,KPCA and Twin SVM[J/OL].ISA Transactions,(2016-04-24)[2016-11-03].www.elsevier.com/locate/isatrans
[17]李应红,尉询凯.航空发动机的智能诊断、建模与预测方法[M].北京:科学出版社,2013:200-204.
[18]Case Western Reserve University.Bearing data center seeded fault test data[EB/OL].[2017-01-15].http:∥csegroups.case.edu/bearingdatacenter/home.
[19]Qiu H,Lee J,Lin J,et al.Robust performance degradation assessment methods for enhanced rolling element bearing prognostics[J].Advanced Engineering Informatics,2003(17):127-140.
[20]Qiu H,Lee J,Lin J,et al.Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics[J].Journal of Sound and Vibration,2006(289):1066-1090.
[21]胡世杰,钱宇宁,严加强.基于概率密度空间划分的符号化时间序列分析及其在异常诊断中的应用[J].振动工程学报,2014,27(5):780-784.Hu Shijie,Qian Yuning,Yan Jiaqiang.Anomaly detection using symbolic time series analysis based on probability density space partitioning[J].Journal of Vibration Engineering,2014,27(5):780-784.(in Chinese)
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