# Deep Learning Method for Fault Detection of Wind Turbine Converter
## 3 Deep Learning Network Principles
### Oct-ResNet50 Convolutional Neural Network  
[PERSON] et al. [60] proposed a novel Octave Convolution (OctConv) operation applied to convolutional neural networks (CNNs). OctConv is designed as a single, generic, plug-and-play convolution unit that can directly replace the original convolution without the need to adjust the network architecture [60]. OctConv is dedicated to reducing the spatial redundancy in CNNs and aims to replace the ordinary convolution operations without adjusting the backbone CNN architecture. It is confirmed that OctConv has superiority over the ordinary convolution methods in improving efficiency and performance of CNN models [60]. 1. Idea for OctConv  
The idea for OctConv is to understand the image from the perspective of the frequency domain. To view an image from the perspective of spatial domain, it can be generally represented by a \(c\times H\times W\) matrix where \(H\) and \(W\) denote the spatial dimensions and \(c\) is the number of feature maps or channels. Each position in the matrix corresponds to a value of [0, 255]. From the perspective of the frequency domain, the image can be decomposed into low spatial frequency components (low frequency domain) that describe smoothly changing structures and high spatial frequency components (high frequency domain) that describe the fast-changing fine details. It can effectively process the corresponding low-frequency and high-frequency components, and can also achieve effective interfrequency communication. OctConv defines the feature map after the \"downsampling\" operation as the \"low frequency domain\", while the original size feature map without downsampling is defined as the \"high frequency domain\". After the above operations, the size of the feature map is reduced due to downsampling, thereby reducing the computation amount of OctConv. In addition, because the network has different scales of information (two frequency domains) and the two scales of the information are aggregated after the convolution is completed, the performance of OctConv is improved. 2. OctConv Principle  
OctConv is a combination of downsampling and upsampling operation, as shown in Figure 6, where the green arrows represent the operation of information updates; the red arrows facilitate information exchange between the two frequencies; and \(X\) and \(Y\) are the input and output tensors, respectively. Between the input and output, it is the convolution process. Figure 5: Structure chart of three-layer bottleneck layer residual unit. The output, \(Y\), is expressed by:  
\[Y=\left\{Y^{H},Y^{L}\right\},\text{ and }Y^{H}=Y^{H\to H}+Y^{L\to H},\ Y^{L}=Y^{L\to L}+Y^{H\to L}\]  
where the format \(Y^{A\to B}\) represents the convolutional update from the feature map group \(A\) to \(B\), \(Y^{H}\) and \(Y^{L}\) denote the high- and low-frequency components of \(Y\), respectively. Specifically, \(Y^{H\to H}\) and \(Y^{L\to L}\) indicate intrafrequency update, and \(Y^{H\to L}\) and \(Y^{L\to H}\) indicate interfrequency communication. In order to obtain the above terms, the convolution kernel \(W\) is divided into \(W=\left[W^{H},W^{L}\right]\) for the convolution with the input feature maps of \(X^{H}\) and \(X^{L}\), respectively. Each component can be further divided into two parts (within frequency part and between frequencies part), namely, \(W^{H}=\left[W^{H\to H},W^{L\to H}\right]\) and \(W^{L}=\left[W^{L\to L},W^{H\to L}\right]\). The main work of OctConv is to split the original convolution operation into four operations, and the input processed by three of these four operations is half the height and width of the original feature map. Therefore, the amount of computation is reduced. Using average pooling for downsampling, the output \(Y=\left\{Y^{H},Y^{L}\right\}\) is:  
\[ \begin{array}{c}Y^{H}=f\big{(}X^{H};W^{H\to H}\big{)}+upsample\big{(}f \big{(}X^{L};W^{L\to H}\big{)},\ 2\big{)}\\ Y^{L}=f\big{(}X^{L};W^{L\to L}\big{)}+f\big{(}pool\big{(}X^{H},\ 2\big{)};\ W^{H\to L}\big{)} \end{array}