# Monitoring of Industrial Machine Using a Novel Blind Feature Extraction Approach
## 3 Proposed Signal Processing Methodology
### Feature Extraction Algorithms  
Faults in rotating machinery such as bearings, tend to produce weak vibration signatures in the data. These weak signatures can tend to create cyclo-stationary random components as shown in Figure 5. These signals are hidden inside the raw data with other signal components. Other vibration components include input shaft frequencies and higher-order harmonics due to load fluctuations. The aim of the blind feature extraction technique proposed in this study is to extract these weak signatures from the signals. These weak signatures are non-stationary components in the signal and can excite resonance frequencies of the bearing because of the cyclic behaviour. SK Based Blind Feature Extraction Algorithm  
Spectral Kurtosis (SK) is a technique that can be used to extract non-stationary frequency components concealed in time-series signal. It is capable of realising the non-stationary characteristic of a signal while suppressing Gaussian noise and stationary components utilising its Kurtosis statistical parameter. Researchers have showed interests in using this technique due to its performance in detecting non-stationary components generated by the defect. For instance, most of the applications are focused on damage detection of rotating machines in respect to bearing faults [22,23]. SK was initially used as a supplementary tool to PSD for detecting arbitrary frequency in a signal which cannot be displayed by Fourier Transform. However, it was rarely been used due to the lack of theoretical proof. [PERSON] was one of the first to publish the mathematical approach to assemble the missing theory background of SK. It is also validated with applications in vibration-based condition monitoring [11]. SK can be estimated using the signal-to-noise (SNR) ratio of the detected transients buried in noisy  
Figure 4: PSD estimate of before and after denoising using Stationary Wavelet Transform. Figure 5: **(Left)** Bearing configuration with rolling elements (**left**) [21]. (**Right**) Signal expected due to bearing fault. signals. Consider a vibration signal, \(x(t)\), SK can be calculated using Equation (1) based on the second (\(S_{2,x}\)) and fourth (\(S_{4,x}\)) spectral moments of the signal. \[SKx(f)\triangleq\frac{S_{4,x}}{S_{2,x}}-2 \tag{1}\]  
The spectral moment can be estimated according to Equation (2),  
\[SK_{n,x}(f)=\langle|PS(f)|^{n}\rangle \tag{2}\]  
where \(PS(f)\) is Fourier power spectrum of the signal, \(x(t)\). An SK-based Wiener filter is derived using the processed SK estimates with a statistical threshold. This adaptive threshold is selected using the maximum value of the SK estimates in order to ease the need of baseline data. In this study at a 20% threshold on the maximum value of the SK, the estimate is considered. The approach is demonstrated and validated here. The methodology is presented in Figure 6.  
The pre-processed data shown in Figure 3, demonstrates how the pattern buried inside the raw vibration data can be extracted. It is used as input to the SK based filtering function which computes the spectral kurtosis of the data. The spectral kurtosis can either be estimated using a Fast Fourier Transform (FFT) Algorithm or by using time-frequency techniques such as the Short-Time Fourier Transform (STFT). The advantage offered by STFT based SK estimate is that this approach can address non-stationary signals better than FFT, i.e., by considering windows. The SK estimate is presented in Figure 7. Two signals from the healthy and defect data sets are used to realise this diagram, later the feature estimate of all 2156 signals is presented. Figure 6: Spectral Kurtosis Feature extraction and filtering methodology, steps 1 is described in Section 3.2. Figure 7: Spectral Kurtosis Estimate for signal 10 and 2100, healthy and defect. The SK based Weiner filter extracted by threshold filter is presented in Figure 8. It is evident from this plot that the Weiner filter for healthy bearing has no significant peak which corresponds to the non-stationary behaviour in the signal.