Feature Frequency Extraction Based on Principal Component Analysis and Its Application in Axis Orbit

Shock and Vibration, Jul 2018

Vibration-based diagnosis has been employed as a powerful tool in maintaining the operating efficiency and safety for large rotating machinery. However, the extraction of malfunction features is not accurate enough by using traditional vibration signal processing techniques, owing to their intrinsic shortcomings. In this paper, the relationship between effective eigenvalues and frequency components was investigated, and a new characteristic frequency separation method based on PCA (CFSM-PCA) was proposed. Certain feature frequency could be purified by reconstructing the specified eigenvalues. Furthermore, three significant perspectives were studied via the distribution of effective eigenvalues, and theoretical derivations were subsequently illustrated. More importantly, this proposed scheme could also be used to synthesize axis orbits of larger machines. Purified curves were so explicit and the CFSM-PCA exhibited higher efficiency than harmonic wavelet and wavelet packet.

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Feature Frequency Extraction Based on Principal Component Analysis and Its Application in Axis Orbit

Feature Frequency Extraction Based on Principal Component Analysis and Its Application in Axis Orbit Zhen Li, Weiguang Li, and Xuezhi Zhao School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China Correspondence should be addressed to Weiguang Li; nc.ude.tucs@ilgnaugw and Xuezhi Zhao; nc.ude.tucs@zxoahzem Received 14 March 2018; Accepted 15 May 2018; Published 12 July 2018 Academic Editor: Jean-Jacques Sinou Copyright © 2018 Zhen Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Vibration-based diagnosis has been employed as a powerful tool in maintaining the operating efficiency and safety for large rotating machinery. However, the extraction of malfunction features is not accurate enough by using traditional vibration signal processing techniques, owing to their intrinsic shortcomings. In this paper, the relationship between effective eigenvalues and frequency components was investigated, and a new characteristic frequency separation method based on PCA (CFSM-PCA) was proposed. Certain feature frequency could be purified by reconstructing the specified eigenvalues. Furthermore, three significant perspectives were studied via the distribution of effective eigenvalues, and theoretical derivations were subsequently illustrated. More importantly, this proposed scheme could also be used to synthesize axis orbits of larger machines. Purified curves were so explicit and the CFSM-PCA exhibited higher efficiency than harmonic wavelet and wavelet packet. 1. Introduction Principal component analysis (PCA), which can reduce the dimensionality of data set but retain most of original variables [1–3], has been widely used in fields of image processing, fault diagnosis, pattern recognition, neural network, data compression, wavelet transform, and so on. For example, Kirby et al. [4] employed PCA algorithm to compress image and extract main features. Moreover, the combination of PCA and Back Propagation (BP) neural network could also be applied in reorganization of facial image. Xi et al. [5] and Malhi et al. [6] individually applied PCA approach to reduce the dimension of data and extract the feature variables. Additionally, neural network was further used as a classifier to categorize the bearing faults. To investigate the fault diagnosis of impeller in centrifugal compressor, PCA was also adopted to decrease the dimensionality of multiple time series by Jiang’s group [7]. Sun et al. [8] analyzed the defects of conventional fault diagnosis methods and introduced the data mining technology into fault diagnosis. After that, a new scheme used to reduce data features was proposed based on C4.5 decision tree and PCA algorithm. Generally, when PCA is used to denoise or for data compression, the number of effective eigenvalues is determined by the cumulative contribution rate and its deformation [9–14], expressed aswhere and are eigenvalues of covariance matrix, respectively; is the number of eigenvalues of covariance matrices; is the number of effective eigenvalues. When cumulative contribution rate is greater than a certain value (80%-95%), could be decided [2]. Although impressive progress in signal denoising and dimensionality reduction fields has been achieved, the studies on extraction or elimination of specific characteristic spectrum (single frequency) via this classical PCA method have always been ignored. However, precise extraction of the fundamental frequency (1X), the second-harmonic (2X), or the other feature frequencies of raw signal is of significance to the purifications of axial orbit, notch filter [15], speech recognition [16], fault diagnosis of rolling bearing [17], and so forth. Over the past decade, many signal processing tools for the extraction of certain frequency have been developed, such as wavelet packet transform, harmonic wavelet, ensemble empirical mode decomposition (EEMD), and sparse decomposition [18]. For instance, references [19–21] adopted multilevel division technique of wavelet packet to select certain frequency band for the extraction of specific frequency, from which axis orbit could be manufactured. References [22, 23] subdivided random frequency band infinity via harmonic wavelet to extract interesting frequency; the refinement of rotor center’s orbit from one or more interesting frequency bands could be realized subsequently. Nevertheless, wavelet packet and harmonic packet algorithm are subject to the Heisenberg uncertainty principle and resolutions of time domain and frequency domain could not be randomly high simultaneously, i.e., . In addition, in EEMD method, signals are adaptively decomposed into several sums of intrinsic mode functions (IMFs), whose instantaneous frequencies have physical meanings. In practice, the IMF is alw (...truncated)


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Zhen Li, Weiguang Li, Xuezhi Zhao. Feature Frequency Extraction Based on Principal Component Analysis and Its Application in Axis Orbit, Shock and Vibration, 2018, 2018, DOI: 10.1155/2018/2530248