# A Data-Driven Model of Cable Insulation Defect Based on Convolutional Neural Networks
## 1 Introduction  
With the continuous development of power grid technology, the use of power cables is rapidly increasing and their coverage is becoming larger and larger. The operation and then reliability of power cables directly affects the safe and stable operation of the power system. Small defects in the cable during manufacture or installation can be excited by over-voltage ageing, temperature, microorganisms and other factors. If the cable is not de-contaminated and treated in a timely manner, it will lead to cable failure and bring great losses to production and life [1]. The traditional study of cable insulation impurity conditions consists of two main methods: physical experiments [2] and theoretical calculations [3]. Most physical experiments on cable insulation are preventive tests, i.e., measuring insulation resistance [4], DC withstand voltage [5] and leakage current [6], which do not allow for the assessment of the insulation condition during cable operation. Currently, finite element modelling calculations are also used in some studies to assess the state of cable insulation in the presence of impurities [7]. In the literature [8], the electric field distribution of cables during normal operation was calculated by modelling with the finite element method. Reference [9] calculated the electric field distribution in the case of cable defects (including impurities) by using finite element calculation software. The method of finite element modelling calculations has significant advantages in terms of cost and cycle time of the study. The accuracy and reproducibility of the results are good [10], which is of practical interest for observing the electric field distribution of cable insulation under different operating conditions. However, there are still limitations to the finite element calculation method. Due to the complexity of cable operating conditions, finite element models of cables are often complex and take relatively long to calculate [11]. Therefore, it is difficult to study the electric field in the case of impurities in the cable insulation using the finite element method alone. Convolutional neural networks (CNN) evolved from the structure of the biological visual system to obtain specific features and recognize the corresponding patterns in graphic images [12]. Convolutional neural networks are widely used because of their characteristics of local perception and weight sharing, which greatly reduces the number of training parameters and improves the computational efficiency of complex networks [13]. Compared to other deep learning methods, CNN algorithms are much less complex and challenging to train, reducing the risk of overfitting [14]. It is relatively easy to build networks with deep structure using CNN algorithms. Machine learning has been successfully applied in many fields and is increasingly being used in the power industry [15]. The literature [16] uses neural networks to evaluate the insulation conditions of 11 kV paper cables. The literature [17] identifies cable partial discharge defects by means of different neural network models and the literature [18] uses fuzzy neural networks to evaluate cable insulation. The literature [19] identifies the partial discharge signals of cables by means of a data-driven model. These studies all classify and identify cable faults and the results of the data are generally one-dimensional. In this paper, the data-driven model is used to achieve the prediction of the electric field distribution of the cable operating condition, presenting a two-dimensional distribution cloud of the cable electric field. Finite element calculations provide the underlying data, which is then learned through artificial intelligence methods to construct a data-driven model of the electric field in the case of cable defects. The research in this paper is based on this idea. The electric field data of the cable is obtained through finite element calculations, and a CNN-based data-driven model is constructed from the multidimensional input feature quantities of the cable.