# A Data-Driven Model of Cable Insulation Defect Based on Convolutional Neural Networks
## 3 Modeling Method of Data-Driven Model
### Data-Driven Model Implementation Based on CNN  
The convolutional neural network is a neural network algorithm based on convolutional operations with a parameter sharing mechanism and a deep structure. The essence of a CNN is a mathematical model that maps the original input to a new feature representation through multiple layers of data transformation and dimensionality reduction. The number of layers, the size of the convolutional kernel, the non-linear activation function and the pooling method are some of the main aspects that affect the prediction accuracy of a convolutional neural network model. \begin{table}
\begin{tabular}{c c} \hline
**Number** & **Input Feature Quantity** \\ \hline
1 & Cable core radius \\ \hline
2 & Thickness of insulation layer \\ \hline
3 & Cable operating voltage \\ \hline
4 & Number of impurities \\ \hline
5 & Relative electric permittivity of impurities \\ \hline
6 & Electrical conductivity of impurities \\ \hline
7 & Relative electric permittivity of the insulation layer \\ \hline
8 & Electrical conductivity of the insulation layer \\ \hline
9 & X coordinate of the fetching point \\ \hline
10 & Y coordinate of the fetching point \\ \hline
11 & Cable operating frequency \\ \hline \end{tabular}
\end{table} 
Table 2: Input feature quantities. Before building a data-driven model, the first step is to choose the algorithm for training the model. The basic structure of a convolutional neural network consists of an input layer, a convolutional layer, a pooling layer, a fully connected layer and an output layer. Several convolutional and pooling layers are generally taken, using an alternating setup of convolutional and pooling layers, i.e., one convolutional layer is connected to a pooling layer, another convolutional layer is connected after the pooling layer, and so on. The convolutional layer adopts a weight-sharing technique, using a series of convolutional kernels to map local features at low levels to global features at high levels, which can significantly reduce the network parameters and improve the computational efficiency, avoiding the overfitting phenomenon. The pooling layer is usually used immediately after a convolutional layer, whose purpose is to reduce the feature dimension and highlight the main features. The specific convolution calculation formula is as follows [20]. \[h[i,j,\tau]=\sum_{m}\sum_{n}X[i+m,j+n,\tau]K[m,n,\tau]+b_{\tau}=X\otimes K+b_{\tau} \tag{8}\]  
In the above equation, the length \(m\), width \(n\) and depth \(\tau\) of the convolution kernel are first selected. \(\tau\) is also the number of convolution kernels. Then the input data is converted into the input matrix \(X\) and substituted into the convolution calculation formula. The output matrix \(h\) is obtained, where \(i,j\) and \(\tau\) represent the three dimensions of the output matrix respectively. \(b_{\tau}\) is the threshold of the \(\tau\)th convolution kernel. \(\otimes\) denotes the product of the corresponding elements of the matrix multiplied together. Like neural networks with conventional structures, the optimization objective of convolutional neural networks is to minimize the loss function to find the optimal parameters. In this paper, we use the mean square error (MSE) loss function as the objective function. the MSE function is represented by Equation (9)  
\[L_{ossmse}=\frac{1}{N}\sum_{i=1}^{N}(y_{i}-f(x_{i}))^{2} \tag{9}\]  
In the above equation: \(N\) is the number of samples; \(y_{i}\) and \(f(x_{i})\) are the expected and actual outputs of the model, where they represent the actual and predicted values of power, respectively. The essence of convolutional neural networks is that each convolutional layer contains a certain number of eigenfaces or convolutional kernels.