## 5 Conclusions  
Planetary gearbox bearings diagnostics is not an easy task. In most of the industrial applications, in fact, the data quality is low, as it is very likely to find large amount of external noise, strong rotation frequency, and other information irrelevant to the fault in the training data. In these cases, traditional diagnostic tools cannot give a high-confidence output, and the recognition accuracy will be low. To solve this problem, a novel WSC-CNNs model with data argumentation in enhanced 2D feature space is established to address the weak fault diagnosis of planetary bearings. WSC is used as for pre-processing to extract the characteristic information of one-dimensional data, expanding it to a two-dimensional time-frequency map. Different fault types will show different spatial distribution characteristics in WSC, which increases the distance between healthy and damaged features. Subsequently, a 2D feature space data argumentation strategy based on image segmentation is proposed, and the fault feature concentration area is divided into sub-regions, which can improve the efficiency of the algorithm and enrich the sample set. Additionally, then, the augmented 2D WSC image is fed into a CNN, which can be very efficient for planetary bearing classification. Compared with other traditional benchmark algorithms, the proposed algorithm can improve the recognition ability of the weak fault signal of the planetary  
Figure 10: The learned features of two-dimensional visualization maps by comparison.  
Figure 9: Evaluate classifiers performance by comparison.  
bearing. Compared with the DAE algorithm, the recognition accuracy of the proposed algorithm is improved by 9.57%. Compared with the direct analysis of the original data by the CNN model, the accuracy rate obtained by using WSC pre-processing as the sample set is increased by 19.92%. Further performing 2D image enhancement, the accuracy can be improved by about 4.86%.  
Conceptualization, R.Y. and Z.A.; methodology, Z.A.; software, R.Y.; validation, R.Y. and Z.A.; formal analysis, Z.A.; investigation, W.H. and R.W.; resources, R.Y.; data curation, R.Y.; writing--original draft preparation, R.Y.; writing--review and editing, Z.A. and W.H. and R.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 52005300.  
Not applicable.  
The authors declare no conflict of interest.  
The original signal  
The size of \(x(n)\)  
First-order cyclic statistics  
Averaging operator  
Time  
The period of cyclic statistics  
Time offset  
Second-order cyclic statistic  
The conjugate of \(x\)  
Cyclic autocorrelation function spectrum  
Cyclic frequency  
\(h[n]\)  
Window function  
Sampling period  
The size of \(h[n]\)  
Spectral frequency points  
The number of sub-segment window function scanned  
Cyclic frequency points  
Overlap length  
Activation values of the \(i\)-th neuron in layer \(l\)  
Bias item  
Connection matrix  
S
The number of categories  
Wavelet basis function  
\(a\)  
Scale factor  
Time factor  
\(K\)  
Convolution kernel  
B  
Convolution layer output feature map  
\(r_{1}\)  
The size of sliding convolution window  
Pooling layer output feature  
\(r_{2}\)  
The size of filter and the step length of each movement  
\(f_{r}\)  
Planetary carrier rotation frequency  
\(f_{b}\)  
Planetary bearing inner race fault characteristic frequency  
\(f_{ab}\)  
Planetary bearing outer race fault characteristic frequency  
\(f_{rb}\)  
Planetary bearing rolling elements fault characteristic frequency