基于HLS-SVDR和SPPCS的CEEMD的滚动轴承微故障特征提取
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摘要
针对互补集总经验模态分解(complementary ensemble empirical mode decomposition,简称CEEMD)在处理非平稳随机信号时能够有效地消除模态混叠,却仍然存在包络拟合过冲/欠冲和端点效应问题,提出了同伦-最小二乘支持向量双回归(homotopy least squares-support vector double regression,简称HLS-SVDR)的保形分段三次样条(shape-preserving piecewise cubic spline,简称SPPCS)的完备CEEMD改进方法。首先,使用SPPCS插值法消除在构造上、下包络曲线过程中产生的拟合过冲/欠冲问题,获得有效的包络线;其次,使用HLS-SVDR对各层信号极值点的包络均值曲线两端进行左、右预测覆盖以抑制端点效应;最后,将该方法用于滚动轴承的微故障特征提取的实例分析中。实验结果表明,该方法能够更有效地提取滚动轴承微故障特征,实现了一种既保持CEEMD原有特性,同时又能够抑制过冲/欠冲和端点效应的完备CEEMD算法。
Complementary ensemble empirical mode decomposition(CEEMD)can deal with non-stationary random signals very well,but there are still some shortcomings,such as the fitting overshoot/undershoot and end effects problems.A new method for solving the exiting problem that is shape-preserving piecewise cubic spline(SPPCS)CEEMD based on homotopy least squares-support vector double regression(HLSSVDR)is proposed in this paper,and to achieve correct and efficient EMD decomposition of signals.Firstly,the SPPCS is used to eliminate the fitting overshoot/undershoot problem in the process of structuring the upper and lower envelope curve,and valid envelope curve can be obtained.Then,the HLS-SVDR is introduced to predict and replace the left and right values at both ends of the mean values of the upper and lower envelopes of extreme points of each layer signals for restraining the end effects.Lastly,the proposed method is applied to analyze the case of the feature extraction of rolling bearing′s slight fault.The experimental results indicate that the proposed method can effectively and accurately extract the rolling bearing′s slight fault feature.A complete CEEMD algorithm can keep the original characteristics of CEEMD,and also effectively restrain the fitting overshoot/undershoot and end effects problems.
Complementary ensemble empirical mode decomposition(CEEMD)can deal with non-stationary random signals very well,but there are still some shortcomings,such as the fitting overshoot/undershoot and end effects problems.A new method for solving the exiting problem that is shape-preserving piecewise cubic spline(SPPCS)CEEMD based on homotopy least squares-support vector double regression(HLSSVDR)is proposed in this paper,and to achieve correct and efficient EMD decomposition of signals.Firstly,the SPPCS is used to eliminate the fitting overshoot/undershoot problem in the process of structuring the upper and lower envelope curve,and valid envelope curve can be obtained.Then,the HLS-SVDR is introduced to predict and replace the left and right values at both ends of the mean values of the upper and lower envelopes of extreme points of each layer signals for restraining the end effects.Lastly,the proposed method is applied to analyze the case of the feature extraction of rolling bearing′s slight fault.The experimental results indicate that the proposed method can effectively and accurately extract the rolling bearing′s slight fault feature.A complete CEEMD algorithm can keep the original characteristics of CEEMD,and also effectively restrain the fitting overshoot/undershoot and end effects problems.
引文
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[11]王传菲,安钢,王凯,等.基于镜像延拓和神经网络的EMD端点效应改进方法[J].装甲兵工程学院学报,2010,24(2):62-63.Wang Chuanfei,An Gang,Wang Kai,et al.Improved method for end effects of EMD based on mirror extension and neural network[J].Journal of Academy of Armored Force Engineering,2010,24(2):62-63.(in Chinese)
[12]高强,段晨东,赵艳青,等.基于最大相关波形延拓的经验模式分解端点效应抑制方法[J].振动与冲击,2013,32(2):62-66.Gao Qiang,Duan Chendong,Zhao Yanqing,et al.Amaximal correlation waveforill extension method for end effects reduction of empirical mode decomposition[J].Journal of Vibration and Shock,2013,32(2):62-66.(in Chinese)
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[14]方琨,王渝,马利兵,等.基于RO-SBM的HilbertHuang变换端点效应抑制方法[J].振动、测试与诊断,2013,33(2):319-324.Fang Kun,Wang Yu,Ma Libin,et al.The end effect suppressing method based on the Hilbert-Huang transform of RO-SBM[J].Journal of Vibration,Measurement&Diagnosis,2013,33(2):319-324.(in Chinese)
[15]尹爱军,王璇.PDE信号修补方法及在EMD端点效应处理中的应用[J].振动与冲击,2012,31(2):6-9.Yin Aijun,Wang Xuan.Signal restoring based on PDE and its application in end effect processing of EMD[J].Journal of Vibration and Shock,2012,31(2):6-9.(in Chinese)
[16]李钊,周晓军,徐云,等.基于均生函数周期叠加外推法的EMD端点问题的研究[J].振动与冲击,2013,32(15):138-143.Li Zhao,Zhou Xiaojun,Xu Yun,et al.End effect treatment for EMD based on the period superposition extrapolation of mean generating function[J].Journal of Vibration and Shock,2013,32(15):138-143.(in Chinese)
[17]杨庆,陈桂明,薛冬林,等.基于最小平方距离相关的EMD改进算法及应用[J].振动与冲击,2011,30(6):62-66.Yang Qing,Chen Guiming,Xue Donglin,et al.Improved method for empirical mode decomposition based on SSDA and its application[J].Journal of Vibration and Shock,2011,30(6):62-66.(in Chinese)
[18]Qi Keyll,He Zllerlgjia,Zi Yanyallg,et al.Cosine window-based boundary processing method for EMDand its application in rubbing fault diagnosis[J].Mechanical Systems and Signal Processing,2007,21(7):2750-2760.
[19]马文朋,张俊红,马梁,等.改进的经验模式分解在机械故障诊断中的应用[J].振动、测试与诊断,2015,35(4):637-644.Ma Wenpeng,Zhang Junhong,Ma Liang,et al.Improved empirical mode decomposition in mechanical fault diagnosis application[J].Journal of Vibration,Measurement&Diagnosis,2015,35(4):637-644.(in Chinese)
[20]白春华,周宣赤,林大超,等.消除EMD端点效应的PSO-SVM方法研究[J].系统工程理论与实践,2013,33(5):1298-1306.Bai Chunhua,Zhou Xuanchi,Lin Dachao,et al.PSO-SVM method based on elimination of end effects in EMD[J].Systems Engineering-Theory&Practice,2013,33(5):1298-1306.(in Chinese)
[21]赵军,李林峰,郭天太,等.优化HHT端点效应的新方法[J].计量学报,2016,37(5):509-514.Zhao Jun,Li Linfeng,Guo Tiantai,et al.A new method to optimize endpoint effect in HHT[J].Acta Metrologica Sinica,2016,37(5):509-514.(in Chinese)
[22]窦东阳,赵英凯.利用ARIMA改进HHT端点效应的方法[J].振动、测试与诊断,2010,30(3):249-253.Dou Dongyang,Zhao Yinkai.Using ARIMA method to improve end effect of HHT[J].Journal of Vibration,Measurement&Diagnosis,2010,30(3):249-253.(in Chinese)
[23]龙思胜,张铁宝,龙峰,等.希尔伯特-黄变换拟合过冲和端点飞翼的原因及解决办法[J].地震学报,2005,27(5):561-568.Long Sisheng,Zhang Tiebao,Long Feng,et al.Causes and solutions of overshoot and undershoot and end swing in Hilbert-Hung transform[J].Acta Seismologica Sinica,2005,27(5):561-568.(in Chinese)
[24]Suykens J A K,Vandewalle J.Least squares support vector machine classifiers[J].Neural Processing Letters,1999(9):293-300.
[25]Dou Yixin,Fu Jiahua.Homotopy perturbation sparsity regularization method with application[J].Acta A-nalysis Functions Application,2016,18(1):76-83.
[26]Zhang Jianguang,Han Yahong.Tucker decomposition based tensor learning for human action recognition[J].Multimedia Systems,2016,22(3):343-353.
[27]Guo Weiwei,Kotsia I,Patras I.Tensor learning for regression[J].IEEE Transactions on Image Processing,2012,21(2):816-827.
[2]胡爱军,孙敬敬,向玲,等.经验模态分解中的模态混叠问题[J].振动、测试与诊断,2011,31(4):429-434.Hu Aijun,Sun Jinjin,Xiang Ling,et al.The mode mixing problem in the empirical model decomposition[J].Journal of Vibration,Measurement&Diagnosis,2011,31(4):429-434.(in Chinese)
[3]曹莹,段玉波,刘继承,等.Hilbert-Huang变换中的模态混叠问题[J].振动、测试与诊断,2016,36(3):518-524.Cao Ying,Duan Yubo,Liu Jicheng,et al.The mode mixing problem in the hilbert-huang transform[J].Journal of Vibration,Measurement&Diagnosis,2016,36(3):518-524.(in Chinese)
[4]汤宝平,董绍江,马靖华,等.基于独立分量分析的EMD模态混叠消除方法研究[J].仪器仪表学报,2012,33(7):1477-1482.Tang Baoping,Dong Shaojiang,Ma Jinghua,et al.Study on the method for eliminating mode mixing of empirical mode decomposition based on independent component analysis[J].Chinese Journal of Scientific Instrument,2012,33(7):1477-1482.(in Chinese)
[5]Yeh J R,Shieh J S,Huang N E.Complementary ensemble empirical mode decomposition:a novel noise enhanced data analysis method[J].Advances in Adaptive Data Analysis,2010,2(2):135-156.
[6]Chen Q,Huang N,Riemenschneider S,et al.A B-spline approach for empirical mode decompositions[J].Advances in Computational Mathematics(S1019-7168),2006,24(1):171-195.
[7]时培明,王敬,温江涛,等.基于包络线算法改进EMD的旋转机械故障诊断方法研究[J].计量学报,2016,37(1):62-66.Shi Peiming,Wang Jing,Wen Jiangtao,et al.Study on rotating machinery fault diagnosis method based on envelopes fitting algorithms EMD[J].Acta Metrologica Sinica,2016,37(1):62-66.(in Chinese)
[8]Evans T S,Lambiotte R.Line graphs,link partitions,and overlapping communities[J].Physical Review E,2009,80(1):100-105.
[9]吴贤规,王安娜,会国涛,等.经验模态分解中一种改进的包络线拟合算法[J].东北大学学报:自然科学版,2015,36(11):1535-1547.Wu Xiangui,Wang Anna,Hui Guotao,et al.An improved envelope fitting algorithm for the empirical mode decomposition[J].Journal of Northeastern University:Natural Science,2015,36(11):1535-1547.(in Chinese)
[10]蔡艳平,徐光华,李艾华,等.EMD局部积分均值增密插值改进算法及其在转子故障诊断中的应用[J].振动与冲击,2016,35(19):81-87.Cai Yanping,Xu Guanghua,Li Aihua,et al.A improved EMD algorithm based on local integral average constraint cubic spline interpolation by adding dense points and its application in rotary machine fault diagnosis[J].Journal of Vibration and Shock,2016,35(19):81-87.(in Chinese)
[11]王传菲,安钢,王凯,等.基于镜像延拓和神经网络的EMD端点效应改进方法[J].装甲兵工程学院学报,2010,24(2):62-63.Wang Chuanfei,An Gang,Wang Kai,et al.Improved method for end effects of EMD based on mirror extension and neural network[J].Journal of Academy of Armored Force Engineering,2010,24(2):62-63.(in Chinese)
[12]高强,段晨东,赵艳青,等.基于最大相关波形延拓的经验模式分解端点效应抑制方法[J].振动与冲击,2013,32(2):62-66.Gao Qiang,Duan Chendong,Zhao Yanqing,et al.Amaximal correlation waveforill extension method for end effects reduction of empirical mode decomposition[J].Journal of Vibration and Shock,2013,32(2):62-66.(in Chinese)
[13]杨小强,李沛,黄杰,等.基于极值波延拓的端点效应处理方法[J].系统工程与电子技术,2016,38(9):1987-1992.Yang Xiaoqiang,Li Pei,Huang Jie,et al.Method based on extension of extreme wave in dealing with end effect[J].Systems Engineering and Electronics,2016,38(9):1987-1992.(in Chinese)
[14]方琨,王渝,马利兵,等.基于RO-SBM的HilbertHuang变换端点效应抑制方法[J].振动、测试与诊断,2013,33(2):319-324.Fang Kun,Wang Yu,Ma Libin,et al.The end effect suppressing method based on the Hilbert-Huang transform of RO-SBM[J].Journal of Vibration,Measurement&Diagnosis,2013,33(2):319-324.(in Chinese)
[15]尹爱军,王璇.PDE信号修补方法及在EMD端点效应处理中的应用[J].振动与冲击,2012,31(2):6-9.Yin Aijun,Wang Xuan.Signal restoring based on PDE and its application in end effect processing of EMD[J].Journal of Vibration and Shock,2012,31(2):6-9.(in Chinese)
[16]李钊,周晓军,徐云,等.基于均生函数周期叠加外推法的EMD端点问题的研究[J].振动与冲击,2013,32(15):138-143.Li Zhao,Zhou Xiaojun,Xu Yun,et al.End effect treatment for EMD based on the period superposition extrapolation of mean generating function[J].Journal of Vibration and Shock,2013,32(15):138-143.(in Chinese)
[17]杨庆,陈桂明,薛冬林,等.基于最小平方距离相关的EMD改进算法及应用[J].振动与冲击,2011,30(6):62-66.Yang Qing,Chen Guiming,Xue Donglin,et al.Improved method for empirical mode decomposition based on SSDA and its application[J].Journal of Vibration and Shock,2011,30(6):62-66.(in Chinese)
[18]Qi Keyll,He Zllerlgjia,Zi Yanyallg,et al.Cosine window-based boundary processing method for EMDand its application in rubbing fault diagnosis[J].Mechanical Systems and Signal Processing,2007,21(7):2750-2760.
[19]马文朋,张俊红,马梁,等.改进的经验模式分解在机械故障诊断中的应用[J].振动、测试与诊断,2015,35(4):637-644.Ma Wenpeng,Zhang Junhong,Ma Liang,et al.Improved empirical mode decomposition in mechanical fault diagnosis application[J].Journal of Vibration,Measurement&Diagnosis,2015,35(4):637-644.(in Chinese)
[20]白春华,周宣赤,林大超,等.消除EMD端点效应的PSO-SVM方法研究[J].系统工程理论与实践,2013,33(5):1298-1306.Bai Chunhua,Zhou Xuanchi,Lin Dachao,et al.PSO-SVM method based on elimination of end effects in EMD[J].Systems Engineering-Theory&Practice,2013,33(5):1298-1306.(in Chinese)
[21]赵军,李林峰,郭天太,等.优化HHT端点效应的新方法[J].计量学报,2016,37(5):509-514.Zhao Jun,Li Linfeng,Guo Tiantai,et al.A new method to optimize endpoint effect in HHT[J].Acta Metrologica Sinica,2016,37(5):509-514.(in Chinese)
[22]窦东阳,赵英凯.利用ARIMA改进HHT端点效应的方法[J].振动、测试与诊断,2010,30(3):249-253.Dou Dongyang,Zhao Yinkai.Using ARIMA method to improve end effect of HHT[J].Journal of Vibration,Measurement&Diagnosis,2010,30(3):249-253.(in Chinese)
[23]龙思胜,张铁宝,龙峰,等.希尔伯特-黄变换拟合过冲和端点飞翼的原因及解决办法[J].地震学报,2005,27(5):561-568.Long Sisheng,Zhang Tiebao,Long Feng,et al.Causes and solutions of overshoot and undershoot and end swing in Hilbert-Hung transform[J].Acta Seismologica Sinica,2005,27(5):561-568.(in Chinese)
[24]Suykens J A K,Vandewalle J.Least squares support vector machine classifiers[J].Neural Processing Letters,1999(9):293-300.
[25]Dou Yixin,Fu Jiahua.Homotopy perturbation sparsity regularization method with application[J].Acta A-nalysis Functions Application,2016,18(1):76-83.
[26]Zhang Jianguang,Han Yahong.Tucker decomposition based tensor learning for human action recognition[J].Multimedia Systems,2016,22(3):343-353.
[27]Guo Weiwei,Kotsia I,Patras I.Tensor learning for regression[J].IEEE Transactions on Image Processing,2012,21(2):816-827.