2013 4 31 2 Journal of Northwestern Polytechnical University Apr. Vol. 31 2013 No. 2 1 1 2 1 1. 710072 2. 412002 EMD PCA DSS EMD PCA EMD-PCA- DSS EMD IMF IMF BSS PCA DSS TN911 A 1000-2758 2013 02-0272-05 empirical Denoising source separation DSS component analysis PCA EMD-PCA-DSS EMD IMF PCA DSS FABIAN 1 1 SHOKO 2 3 1. 1 DSS Farid M. N. 3 DSS S REL 7 A DSS 4 s = w T X 1 5 EMD s + = f s 2 w + = Xs +T 3 6 w + w new = 4 w + 2012-04-15 mode decomposition EMD principal 10902084 11272257 2011JQ1011 20112108001 JC201242 1983
2 273 1 W 4 DSS 2 s + DSS 3 4 BSS DSS 2 1. 2 EMD 2. 1 EMD 8 EMD 3 s 1 t s 2 t s 3 t EMD IMF 2 1 s 3 t = 1 + 0. 5sin 30t sin 1500t s 1 t = sin 120t 1 2 s EMD 2 t = 2sin 20t cos 500t 1 1 000 Hz 1 000 1 IMF 2 1 IMF IMF n IMF n IMF 1. 3 PCA PCA 9 X M N X = UΣV T U V Σ = diag σ 1 σ 2 σ M σ i σ i 0 i = 1 2 M XX T R xx R xx = XX T = UΛU T 5 Λ = diag λ 1 λ 2 λ M λ i λ i 0 i = 1 2 M U u 1 u 1 X u M P p 1 p 2 p M = U u 1 u 2 u M T X 6 P X p i i = 1 2 M i 1 1. 4 EMD-PCA-DSS 1 EMD x = As 2 2 IMF 2 3 PCA 1
274 31 BSS 3 3 BSS IMF 4 PCA 1 1 PCA λ 1 λ 2 λ 3 509. 054 5 292. 674 1 197. 222 8 λ 4 λ 5 λ 6 1. 048 7 2. 241 10 13 2. 01 10 13 1 3 1 5 EMD-PCA-DSS 3 DSS EMD 4
2 275 5 3 EMD-PCA-DSS 25. 5 Hz 3 80. 2 Hz 4 101. 4 1 530 r /min Hz 8 3 4 512 Hz 16 384 6 EMD-PCA-DSS 7 8 7 6 7 8 4 DSS EMD EMD-PCA- DSS EMD- PCA-DSS
276 31 EMD-PCA-DSS 1 Fabian J T Carlos G P Elmar W L. Median-Based Clustering for Under-Determined Blind Signal Processing. IEEE Signal Processing Letter 2006 13 2 96-99 2 Shoko Araki Hiroshi Sawada Ryo Mukai Shoji Makino. Under-Determined Blind Sparse Source Separation for Arbitrarily Arranged Multiple Sensors. Signal Processing 2007 87 1833-1847 3 Farid Movahedi Naini G. Hosein Mohimani Massoud Babaie-Zadeh Christian Jutten. Estimating the Mixing Matrix in Sparse Component Analysis SCA Based on Partial K-Dimensional Subspace Clustering. Neurocomputing 2008 71 2330-2343 4.. 2009 45 8 64-70 Shen Yongjun Yang Shaopu Kong Deshun. New Method of Blind Source Separation in Under-Determined Mixtures Based on Singular Value Decomposition and Application. Journal of Mechanical Engineering 2009 45 8 64-70 in Chinese 5.. 2011 47 4 12-16 Wu Wenfeng Chen Xiaohu Su Xunjia. Blind Source Separation of Single-Channel Mechanical Signal Based on Empirical Mode Decomposition. Journal of Mechanical Engineering 2011 47 4 12-16 in Chinese 6.. 2011 47 7 97-102 Li Zhinong Liu Weibing Yi Xiaobing. Underdetermined Blind Source Separation Method of Machine Faults Based on Local Mean Decomposition. Journal of Mechanical Engineering 2011 47 7 97-102 in Chinese 7 S REL J VALPOLA H. Denoising Source Separation. Journal of Machine Learning Research 2005 6 233-272 8. EMD. 2008 57 10 6139-6144 Yang Yongfeng Ren Xingmin Qin Weiyang et al. Prediction of Chaotic Time Series Based on EMD Method. Acta Physica Sinica 2008 57 10 6139-6144 in Chinese 9 Perlibakas V. Distance Measures for PCA-Based Recognition. Pattern Recognition Letters 2004 25 711-724 An Efficient Denoising Source Separation DSS of Rotating Machine Fault Signals Based on Empirical Mode Decomposition EMD Wang Yuansheng 1 Ren Xingmin 1 Yang Yongfeng 1 Deng Wangqun 2 ( ) 1. Department of Engineering mechanics Northwestern Polytechnical University Xi'an 710072 China 2. China Aviation Dynamical Machinery Research Institute Zhuzhou 412002 China Abstract Combining the features of EMD principal component analysis PCA and DSS we propose an underdetermined DSS method based on EMD and PCA which we believe is efficient. This method is used to deal with the blind source separation BSS problem of rotating machinery in the case of the number of observed mixtures being less than that of contributing sources. The observed signals are decomposed into some intrinsic mode functions IMFs with the EMD method. These IMFs and original observations were composed into new observations. Then the PCA is used to estimate the number of the types of observed signals and the mixed sources are separated by DSS algorithm. It is verified that the new method yields a correct estimate of source number in the simulation tests. Applying EMD-PCA-DSS method to the rotor fault detection we have diagnosed the unbalance phenomenon through the measured fault signals of the rotor. The simulation results experimental results and their analysis show preliminarily that the EMD-PCA-DSS method is indeed efficient in analyzing the fault diagnosis and it has an important engineering significance for condition monitoring and fault detection of rotating machines. Key words blind source separation diagnosis experiments fault detection modal analysis principal component analysis rotating machinery signal processing denoising source separation DSS empirical mode decomposition EMD