改进的Hilbert-Huang变换方法及其应用
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摘要
针对Hilbert-Huang变换(HHT)方法出现的端点效应问题,提出了添加极值点与支持向量回归机相结合的延拓方法对其进行抑制。首先利用支持向量回归机预测信号极值点的幅值,然后用添加极值点法确定所预测极值点的位置。该改进方法解决了镜像延拓法对端点不是极值点的短数据序列处理效果不佳问题。通过仿真对比分析,用传统的镜像延拓和支持向量回归机延拓后得到的能量误差分别为0.007 4和0.023 8,而用改进方法延拓后得到的能量误差为0.003 0,表明改进方法对HHT端点效应的抑制效果要好于两种传统的方法。最后,将改进方法应用到电机转子不平衡故障特征提取上,验证了其可行性和准确性。
In order to solve the endpoint effect in the Hilbert-Huang transform( HHT),an improved method is proposed by combining the adding extreme points with the support vector regression. The improved method uses the support vector regression method to predict extreme points on both ends of the original signal,and then uses the adding extreme point method to determine the position of the predicted extreme points. The improved method can solve the problem which the boundary of the short time sequence is not the extreme point by using the mirror extension method. Through comparison analysis of simulation signal,the energy error obtained by using the mirror extension and the support vector regression is 0. 0074 and 0. 0238 respectively,while the energy error is 0. 0030 by using the improved method. It indicates that the improved method can inhibit the endpoint effect of the HHT,and it is better than those two traditional methods. Finally,the improved method is used to extract the feature frequency of the motor rotor imbalance fault. The result shows that the improved method is feasible and accurate.
In order to solve the endpoint effect in the Hilbert-Huang transform( HHT),an improved method is proposed by combining the adding extreme points with the support vector regression. The improved method uses the support vector regression method to predict extreme points on both ends of the original signal,and then uses the adding extreme point method to determine the position of the predicted extreme points. The improved method can solve the problem which the boundary of the short time sequence is not the extreme point by using the mirror extension method. Through comparison analysis of simulation signal,the energy error obtained by using the mirror extension and the support vector regression is 0. 0074 and 0. 0238 respectively,while the energy error is 0. 0030 by using the improved method. It indicates that the improved method can inhibit the endpoint effect of the HHT,and it is better than those two traditional methods. Finally,the improved method is used to extract the feature frequency of the motor rotor imbalance fault. The result shows that the improved method is feasible and accurate.
引文
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[13]宁静,诸昌钤,高品贤,等.EMD分解中端点数据的延长方法问题研究[J].计算机工程与应用,2011,47(3):125-128.NING J,ZHU CH L,GAO P X,et al.Research on extending end data in empirical mode decomposition[J].Computer Engineering and Applications,2011,47(3):125-128.
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[15]李建,刘伟,郭晓婷.基于EMD分解的端点延拓新方法[J].电源技术,2012,36(10):1573-1575.LI J,LIU W,GUO X T.A new method of end continuations based on EMD[J].Chinese Journal of Power Sources,2012,36(10):1573-1575.
[16]耿萌,石林锁.基于虚拟仪器的转子不平衡故障模拟及故障分析[J].机床与液压,2008,36(2):188-190.GENG M,SHI L S.Simulation and analyses on rotor imbalance fault based on virtual instrument[J].Machine Tool&Hydraulics,2008,36(2):188-190.
[2]李舜酩,郭海东,李殿荣.振动信号处理方法综述[J].仪器仪表学报,2013,34(8):1907-1915.LI SH M,GUO H D,LI D R.Review of vibration signal processing methods[J].Journal of Scientific Instrument,2013,34(8):1907-1915.
[3]HUANG N E.The empirical mode decomposition and the Hilbert sepctrum for nonlinear and non-stationary time series analysis[J].Proceeding of the Royal Society of London,1998:454:903-995.
[4]HUANG N E.A confidence limit for the empirical mode decomposition and Hilbert spectra analysis[J].Proceeding of the Royal Society of London,2003(459):2317-2345.
[5]VINCENT H T,HU S L J,HOU Z.Damage detection using empirical mode decomposition method and a comparison with wavelet analysis[C].Proceeding of the Second International Workshop on Structural Health Monitoring,Stanford,1999:891-900.
[6]刘俊,王占林,付永领,等.基于改进HHT的一体化电液作动器故障诊断[J].北京航空航天大学学报,2013,39(1):62-66.LIU J,WANG ZH L,FU Y L,et al.Fault diagnosis of EHA-VPVM based on improved HHT[J].Journal of Beijing University of Aeronautics and Astronautics,2013,39(1):62-66.
[7]蔡艳平,李艾华,张玮,等.HHT端点效应的最大Lyapunov指数边界延拓方法[J].仪器仪表学报,2011,32(6):1330-1336.CAI Y P,LI AI H,ZHANG W,et al.HHT end effect processing method based on maximum Lyapunov index boundary extension model[J].Journal of Scientific Instrument,2011,32(6):1330-1336.
[8]孙华刚,冯广斌,曹登庆,等.经验模态分解端点波形延拓改进方法研究[J].电子测量与仪器学报,2010,24(4):319-326.SUN H G,FENG G B,CAO D Q,et al.Research on the improved method of the endpoint wave extension of empirical mode decomposition[J].Journal of Electronic Measurement and Instrument,2010,24(4):319-326.
[9]杜爱明,王彬,杨润海.Hilbert-Huang变换中的一种端点处理方法[J].地震研究,2007,30(1):55-58.DU AI M,WANG B,YANG R H.A boundary processing method in Hilbert-Huang transform[J].Journal ofSeismological Research,2007,30(1):55-58.
[10]王巍,赵宏,梁朝辉,等.基于EMD和SVR的混合智能预测模型及实证研究[J].计算机工程与应用,2012,48(4):225-227.WANG W,ZHAO H,LIANG CH H,et al.Hybrid intelligent prediction method based on EMD and SVR and its application[J].Computer Engineering and Applications,2012,48(4):225-227.
[11]陈自然,彭东林,刘小康,等.基于支持向量机时栅数控转台时序预测研究[J].仪器仪表学报,2012,33(8):1793-1799.CHEN Z R,PENG D L,LIU X K,et al.Research on forecast method for time grating CNC rotary table based on SVR and time series[J].Journal of Scientific Instrument,2012,33(8):1793-1799.
[12]韩建平,钱炯,董小军.采用镜像延拓和RBF神经网络处理EMD中端点效应[J].振动、测试与诊断,2010,30(4):414-417.HAN J P,QIAN J,DONG X J.Suppression of endeffect in empirical mode decomposition by mirror extension and radial basis function neural network prediction[J].Journal of Vibration,Measurement&Diagnosis,2010,30(4):414-417.
[13]宁静,诸昌钤,高品贤,等.EMD分解中端点数据的延长方法问题研究[J].计算机工程与应用,2011,47(3):125-128.NING J,ZHU CH L,GAO P X,et al.Research on extending end data in empirical mode decomposition[J].Computer Engineering and Applications,2011,47(3):125-128.
[14]黎洪生,吴小娟,葛源.EMD信号分析方法端点问题的处理[J].电力自动化设备,2005,25(9):47-49.LI H SH,WU X J,GE Y.Dealing with end issue of EMD method[J].Electric Power Automation Equipment,2005,25(9):47-49.
[15]李建,刘伟,郭晓婷.基于EMD分解的端点延拓新方法[J].电源技术,2012,36(10):1573-1575.LI J,LIU W,GUO X T.A new method of end continuations based on EMD[J].Chinese Journal of Power Sources,2012,36(10):1573-1575.
[16]耿萌,石林锁.基于虚拟仪器的转子不平衡故障模拟及故障分析[J].机床与液压,2008,36(2):188-190.GENG M,SHI L S.Simulation and analyses on rotor imbalance fault based on virtual instrument[J].Machine Tool&Hydraulics,2008,36(2):188-190.
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