Incipient Fault Feature Extraction of Rolling Bearings Using Autocorrelation Function Impulse Harmonic to Noise Ratio Index Based SVD and Teager Energy Operator  
[PERSON]  
1 School of Advanced Manufacturing Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China; [EMAIL_ADDRESS] (K.Z. ); [EMAIL_ADDRESS] (B.Z. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (J.L.) 2 SMRT-NTU Smart Urban Rail Corporate Laboratory, Nanyang Technological University, Singapore 639798, Singapore; [EMAIL_ADDRESS]  
Correspondence: [EMAIL_ADDRESS]; Tel. : +86-187-1628-5005  
2 September 2017; Accepted: 25 October 2017; Published: 30 October 2017  
[PERSON]  
Many advanced signal decomposition methods have been studied for fault feature extraction in the field of rotary machine diagnosis. The typical multicomponent decomposition methods include short-time Fourier transform [9], wavelet transform [10], Hilbert-Huang transform [11], Empirical Mode Decomposition/Ensemble Empirical Mode Decomposition (EMD/EEMD) [12; 13], and Local Mean Decomposition (LMD) [14]. Among a wide range of de-noising and signal enhancing methods available in the literature, noise elimination algorithms based on singular value decomposition (SVD) are considerably faster and easier to implement [5; 8]. Also, it is a non-parametric signal analysis tool, which can be implemented without pre-defined basis functions. Therefore, the SVD method has been employed for fault detection in much research [15; 16; 17; 18; 19]. In order to extract the impulse fault feature from the vibration signals of the rolling bearing, it is very important to select the effective singular components for reconstructing a new signal when the SVD method is applied. There are many traditional methods such as the median value of singular values, mean value of singular values, and Difference spectrum of singular values (DSSV) based SVD methods [1]. Among them, the well-established traditional median value of singular values based SVD method and the mean value of singular values based SVD method choose the effective singular components with large singular values. It is believed that the larger singular values can contain much more useful fault features when these methods are applied. However, as the literature [1; 20] points out, a larger singular value corresponding to singular components may not contain the informative fault feature. The energy value of the informative fault feature may be very weak. A Difference spectrum of singular values (DSSV) is introduced to capture the abrupt change in the singular values, which reflects the boundary between the signal and the noise, based on the principle that the effective informative singular components can be extracted [20; 21]. The literature [1] proposed a method to capture the abrupt change based on the correlation coefficient singular value decomposition (CCSVD) method. However, these methods are characterized by capturing the abrupt change and may remove the useful signals and retain the noise signals. As a result, they may not be able to extract the weak fault feature effectively. To solve this problem, one study [5] proposed kurtosis to quantify the impulsive feature of the vibration signal, and the simulation and experiment results indicate that the de-noising method is successful in both the frequency domain and time domain for fault identification. Another study [15] proposed a Periodic Modulation Intensity (PMI) index to select fault features with relatively lower energy levels, and it is robust in the presence of heavy noise and strong random interferences. From the above analysis, it can be seen that it is vital to select suitable singular components for extracting mechanical fault features using the SVD method. The crucial step is to find an index to measure the abundance of fault information for the singular components.