# Deep Learning Method for Fault Detection of Wind Turbine Converter
## 3 Deep Learning Network Principles
### Oct-ResNet50 Convolutional Neural Network
 \tag{1}\]  
where, \(f(X;W)\) represents the convolution with the parameter, \(W\); \(pool(X,k)\) represents the average pooling operation with the kernel size \(k\times k\) and the step size, \(k\); and \(upsample(X,k)\) is the upsampling operation with the factor \(k\) through the nearest interpolation. The four parallel lines in Figure 4 correspond to the four terms in Equation (1). The two green paths, namely, the first and the fourth, correspond to the information update of the high-frequency and low-frequency feature maps, respectively; the two red paths play the role of information exchange between the two frequency domains. 3. OctConv Operation  
The number of feature map channels \(c_{in}\) is divided into high frequency \((1-a_{in})\)\(c_{in}\) and low frequency \(a_{in}c_{in}\) according to the preset coefficient, \(a_{in}\). The width and height of the low frequency part are reduced to half of the original. OctConv performs the following operations:  
1. The high frequency part is directly convolved through \(f\big{(}X^{H}\big{)}\), that is, high frequency to high frequency convolution; the number of output channels is \((1-a_{out})\)\(c_{out}\). 2. The high-frequency part is first downsampled and then convolved. The downsampling is by \(pool\big{(}X^{H},2\big{)}\) and then \(f\big{(}pool\big{(}X^{H},2\big{)}\big{)}\), that is, the convolution from high-frequency to low-frequency, and the number of output channels is \(a_{out}c_{out}\). Figure 6: OctConv convolution schematic [60]. 3. The low frequency part is directly convolved and then upsampled, \(f\big{(}X^{L}\big{)}\) is the convolution from low frequency to high frequency and the number of output channels is \((1-a_{out})\)\(c_{out}\). 4. The low frequency part directly convolves in \(f\big{(}X^{L}\big{)}\), that is, the low frequency to the low frequency convolution; the number of output channels is \(a_{out}c_{out}\). The above operations are followed by the information aggregation process, i.e., the results from the first and third path are added by bit, and it is the same for the output results from the second and fourth path; see Figure 6.  
4 Analysis of Principles of Improved Convolutional Neural Network Based on Frequency Domain Features  
OctConv is suitable for the majority of existing trunk network structures, such as ResNet and MobileNet, which can bring performance improvement while reducing the amount of computation of existing models and is validated in ImageNet Classification tasks. However, this paper finds that there are two deficiencies in the OctConv structure. The first is the asymmetry of information caused by the asymmetry of the upper- and lower-sampling methods; the second is that OctConv adopts the way that the two frequency domain features are directly added together to ensure the information interaction between the high- and low-frequency domains; however, it is likely to destroy the original characteristics of the features at the high frequency domain and the low frequency domain. Therefore, this paper makes improvement to the OCtConv structure to overcome the above two deficiencies, and proposes the structure of Attention Octave Convolution.