# Weak Fault Feature Extraction and Enhancement of Wind Turbine Bearing Based on OCYCBD and SVDD
## 2 Optimized Cyclostationary Blind Deconvolution
### Optimal Parameter Selection Strategy Guided by FWEE Indicator  
In Section 2.2, the influences of filter length and cyclic frequency have been investigated through the simulated fault signal. And the obtained CYCBD result will be unsatisfactory if these two parameters are selected unreasonably. Thus, the important problem of applying CYCBD to bearing fault feature extraction is how to choose the key influencing parameters appropriately for the best performance. We have known that the cyclic frequency parameter is closely related to the fault feature frequency. In terms of this parameter selection, if it is directly confirmed by referring to the theoretical fault characteristic frequency, then desired result will be difficult to obtain. The reason is because the actual feature frequency is often inconsistent with the theoretical calculating value due to the inevitable random slippage of roller during bearing operation. As for filter length selection, there is not any reference. If this key parameter is artificially chosen only through the operator's experiences, then the performance of CYCBD may be weakened. In order to essentially overcome the inherent deficiency of influencing parameters selection and automatically acquire the optimal deconvolution result, the OCYCBD method is put forward here. In this method, firstly, the cyclic frequency \(a\) is precisely confirmed by the fast spectral coherence and the equal step size search strategy, then the filter length \(L\) is further reasonably selected to highlight the superiority of CYCBD on the basis of satisfying the prime requirement of \(a\). The detailed implementation steps are as follows:  
1. Confirm the search center of cyclic frequency. It is a great challenge to determinate the cyclic frequency parameter with a high precision owing to the wide search scope. Thus, for the purpose of improving the search efficiency and easing the computational burden, the search center of cyclic frequency needs to be confirmed firstly, and the whole search process is carried out around this center. Spectral coherence provides a new interpretation of periodic flows of energy across the analysis frequency band and the cyclic frequency band [27]. With the help of its excellent ability in revealing the presence of modulation and describing the cyclostationarity, the fast spectral coherence is applied to accurately estimate the search center, and the relevance theory of fast spectral coherence can refer to literature [28]. The cyclic frequency location corresponding to the maximum energy distribution in the fast spectral coherence is regarded as the search center \(a^{M}\). In order to avoid the interference as far as possible, only the regions \([f-df,\)\(f+df]\)\((f\in[fi,fo,fe,fc])\) around the theoretical defect feature frequencies are analyzed, where \(fi\), \(fo\), \(fe\) and \(fc\) respectively represent the theoretical defect feature frequencies of inner ring, outer ring, roller, and cage. In this paper, the analysis region interval \(df\) is set to 5 Hz. However, the precise cyclic frequency parameter is still difficult to determinate due to the influence of cyclic frequency resolution. Then more precise search process around the search center \(a^{M}\) is performed in the following steps. 2. Determinate the search scope and search step size. The search scope of cyclic frequency parameter is initialized as \([a^{I},\)\(a^{E}]\) = [floor(\(a^{M}-\Delta f\)), ceil(\(a^{M}+\Delta f\))] with search step size of 0.05 Hz. Where \(a^{E}\) and \(a^{I}\) are the upper boundary and the lower boundary of search scope, \(\Delta f\) denotes the cyclic frequency resolution of spectral coherence, floor \((\cdot)\) and ceil \((\cdot)\) respectively refer to the round down operation and the round up operation. As for the filter length \(L\), the deconvolution signal will be distorted if it is too large, while the treatment efficiency will be  
Figure 5: The histogram of FWEE indicators corresponding to different SNRs. inconspicuous if this parameter is too small.