# A Data-Driven Model of Cable Insulation Defect Based on Convolutional Neural Networks
## 4 Results and Discussion
### Predicted Electric Field Strength of the Cable  
After applying the convolutional neural network method to learn the data set, a data-driven model of the cable with insulation impurities is created. In this case, the structural parameters of the cable model remain unchanged, and the voltage of the cable operation is changed. At this time, the cable operating voltage is 11 kV, the relative electric permittivity of impurities is 30, the conductivity is 18 S/m, the relative electric permittivity of insulation layer material is 1.5, the conductivity is 0.25 S/m, and the operating frequency is 50 Hz. The electric field intensity at each location of the cable was calculated using the data-driven model, and the electric field distribution clouds were plotted by MATLAB software and compared with those calculated and plotted by COMSOL Multiphysics with MATLAB software, and the results are shown in Figures 4 and 5. Figure 4: Comparison of calculated values of the data-driven model with finite element method for changing impurity conductivity, (**a**) Electric field strength calculated by the data-driven model, (**b**) Electric field strength calculated by finite element. Figure 3: Training results of the convolutional neural network algorithm on the training and test sets, (**a**) Fitting results of single impurity in cable, (**b**) Fitting results of multiple impurities in cable. But in practice, the cable insulation layer at the distribution of many impurities, so in the model, other conditions remain unchanged, for multiple impurities in the case of cable operating voltage changes, the electric field distribution of the cable to learn. At this time, the other parameters of the cable remain unchanged, and only the number of impurities and the cable operating voltage are changed. Using the model to predict the electric field strength at each location of the cable, draw the electric field strength distribution cloud map and finite element calculation for comparison, the results are shown in Figures 6 and 7. The results of the electric field strength calculated by the data-driven model obtained by the convolutional neural network-based algorithm are reliable. Therefore, the cable insulation under the above conditions can be analyzed based on the cloud diagram. From Figures 4-7, it can be seen that the cloud diagram composed of the data obtained by learning and the cloud diagram composed of the actual finite element calculation have  
Figure 5: Local enlargement of the calculated values of the data-driven model for changing the impurity conductivity compared with the calculated values of the finite element method, (**a**) Electric field strength at impurities calculated by data-driven model. (**b**) Electric field strength at impurities calculated by finite element. Figure 6: Comparison of calculated values of the data-driven model with finite element method for changing voltage parameters, (**a**) Electric field strength calculated by data-driven model, (**b**) Electric field strength calculated by finite element. basically the same values at each position of the model, so the calculation results based on the convolutional neural network algorithm can be considered valid, and the electric field strength of impurities at the tip of the cable insulation in both cases is about 3 \(\times\) 10\({}^{6}\) V/m, which is still less than the Breakdown field strength value, so the cable can still operate normally at this time. In the application of the data-driven model, a point near the impurities in the cable model was analyzed to examine the error between the values obtained by algorithmic learning within the training set and outside the training set and the finite element calculated values when the cable core voltage and the impurity conductivity were varied respectively, as shown in Figure 8. In this case, the voltage values of 9-11 kV and the conductivity of 10-30 S/m were set as the training set.