# Weak Fault Feature Extraction and Enhancement of Wind Turbine Bearing Based on OCYCBD and SVDD
## 2 Optimized Cyclostationary Blind Deconvolution
### Research on the Influences of Key Parameters  
As a kind of parametric signal processing method, CYCBD needs to set the cyclic frequency parameter \(a\) and the filter length parameter \(L\) in advance. To research the influences of these two parameters on the deconvolution performance, it is assumed that a local defect occurs on the inner ring of rolling bearing, and a simulated fault signal comprising periodic impact components and Gaussian white noises is constructed as follows [21; 22]:  
\[x(t)=\sum_{i=0}^{M-1}\left[(1+A\cos(2\pi f_{r}t))\delta(t-iT)\right]\otimes \left[e^{-ct}\cos(2\pi f_{n}t)\right]\right]+n(t) \tag{14}\]  
where \(\otimes\) denotes the convolution operation, \(\delta(t)\) represents the Dirac delta function and \(c=700\) rad/s is the structural attenuation factor of bearing system. \(M=60\), \(f_{r}=30\) Hz and \(f_{n}=4000\) Hz respectively represent the number of impact, the rotating frequency and the resonant frequency excited by defect point strike. \(A=0.3\) refers to the impact amplitude fluctuation caused by rotating frequency modulation, and fault feature frequency of inner ring is set to 120 Hz, which is equal to the reciprocal of impact period \(T\). Furthermore, the sample rate and sample length are set to 16,000 Hz and 8192 points,respectively. \(n(t)\) denotes the added noises with standard deviation of 1, and the SNR of simulated signal is -10 dB, which can be calculated by the formula in reference [23]. Figure 1 displays the waveforms as well as the corresponding spectra of simulated fault signal. After adding the Gaussian white noises, the periodic impact components can't be found in the mixed signal. Meanwhile, the feature frequency spectral peak is indistinguishable not only in the frequency spectrum but also in the envelope spectrum. Then this simulated fault signal is applied to research the performance of CYCBD with different parameters on noise interference suppression and fault feature extraction. Firstly, the influence of filter length parameter \(L\) is discussed when cyclic frequency parameter is fixed at \(a=120\) according to the fault feature frequency 120 Hz. The waveforms and envelope spectra of deconvolution signals gained by CYCBD with filter lengths of 50,100,150 and 200 are shown in Figure 2. In order to quantificationally compare the analysis results, the feature energy ratio (FER) index of envelope spectrum used in reference [24] is taken as the criterion in this paper to evaluate the obtained different deconvolution signals, and the FER index is described as:  
\[\text{FER}=\left(\sum_{k=1}^{K}F_{k}/\sum_{i=1}^{N}E_{i}\right)\times 100\% \tag{15}\]  
where \(F_{k}\) and \(K\) respectively denote the amplitude of \(k\)th feature frequency spectral line and the number of spectral line, and we set \(K=4\) here. \(E_{i}\) and \(N\) respectively refer to the amplitude of \(i\)th frequency component and the number of frequency component. Figure 1: (**a**) The waveform of impact signal; (**b**) The waveform of simulated fault signal; (**c**) The frequency spectrum of simulated fault signal; (**d**) The envelope spectrum of simulated fault signal. In Figure 2, the fault feature frequency and its harmonics are all successfully gained by CYCBD with different filter lengths. But the FER indexes of these four envelope spectra are different, which means there exist gaps among the obtained results, and this conclusion also can be drawn by comparing the waveforms and the feature frequency components. Among these results, it is indicated that the extracted features of the third deconvolution signal, whose FER index is the largest value 22.53%, are the most obvious. And the presented features of the second deconvolution signal, whose FER index is the smallest value 7.32%, are the worst. Then the comparison results show the performance of CYCBD isn't proportional to the filter length. Whether the selected filter length parameter is too big or too small, it will not be conducive to fault feature extraction.