PCA A

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1 Journal of Northwestern Polytechnical University Apr. Vol No EMD PCA DSS EMD PCA EMD-PCA- DSS EMD IMF IMF BSS PCA DSS TN911 A empirical Denoising source separation DSS component analysis PCA EMD-PCA-DSS EMD IMF PCA DSS FABIAN 1 1 SHOKO 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 mode decomposition EMD principal JQ JC

2 W 4 DSS 2 s + DSS 3 4 BSS DSS EMD 2. 1 EMD 8 EMD 3 s 1 t s 2 t s 3 t EMD IMF 2 1 s 3 t = sin 30t sin 1500t s 1 t = sin 120t 1 2 s EMD 2 t = 2sin 20t cos 500t Hz 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 EMD-PCA-DSS 1 EMD x = As 2 2 IMF 2 3 PCA 1

3 BSS 3 3 BSS IMF 4 PCA 1 1 PCA λ 1 λ 2 λ λ 4 λ 5 λ EMD-PCA-DSS 3 DSS EMD 4

4 EMD-PCA-DSS Hz Hz r /min Hz Hz EMD-PCA-DSS DSS EMD EMD-PCA- DSS EMD- PCA-DSS

5 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 Shoko Araki Hiroshi Sawada Ryo Mukai Shoji Makino. Under-Determined Blind Sparse Source Separation for Arbitrarily Arranged Multiple Sensors. Signal Processing 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 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 in Chinese Wu Wenfeng Chen Xiaohu Su Xunjia. Blind Source Separation of Single-Channel Mechanical Signal Based on Empirical Mode Decomposition. Journal of Mechanical Engineering in Chinese Li Zhinong Liu Weibing Yi Xiaobing. Underdetermined Blind Source Separation Method of Machine Faults Based on Local Mean Decomposition. Journal of Mechanical Engineering in Chinese 7 S REL J VALPOLA H. Denoising Source Separation. Journal of Machine Learning Research EMD Yang Yongfeng Ren Xingmin Qin Weiyang et al. Prediction of Chaotic Time Series Based on EMD Method. Acta Physica Sinica in Chinese 9 Perlibakas V. Distance Measures for PCA-Based Recognition. Pattern Recognition Letters 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 China 2. China Aviation Dynamical Machinery Research Institute Zhuzhou 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