Assessment method for 220 kv cable outer sheath damage based on bp neural network

220 kV high-voltage submarine cables find extensive application in offshore wind power transmission systems. Ensuring the safe operation of these cables involves accurately detecting and assessing the extent of damage to the cable sheath. This study begins by constructing a finite element simulation model for the cable based on its actual model. Subsequently, a method for evaluating the cable sheath’s damage state is proposed by using a BP neural network. The network takes ambient temperature, current, and six-point temperatures of the damaged section as input characteristics. Results indicate a correct rate of 94.29% for the BP neural network, demonstrating its effective discrimination of cable sheath damage levels. This approach introduces a novel evaluation method for cable sheath damage.


Introduction
In recent years, offshore wind power has experienced rapid growth, and submarine cables serve as a crucial link between offshore wind farms and the onshore power grid [1].Particularly, 220 kV highvoltage submarine cables play a pivotal role in offshore wind power transmission systems.The outer sheath is a critical component of the cable, serving to protect the metal sheath and insulation.Damages to the outer sheath, whether minor or severe, can lead to increased metal sheath circulation, reducing cable transmission capacity and impeding heat dissipation.In more severe cases, it can result in metal sheath corrosion, posing a threat to the cable's main insulation and potentially causing power failures.Consequently, cable sheath damage has emerged as a significant latent risk to the safety and stability of the power grid [2].Therefore, detecting and evaluating the damage state of high-voltage cable sheaths is of great importance to reduce major cable failures, prolong the service life of cables, and ensure safe and stable long-term operation of cables [3].
At present, most researchers judge whether there is a fault by monitoring partial discharge and AC withstand voltage test of cable [4][5].However, these traditional methods generally require high voltage and strong current test environment, the operation is more complicated, and the above monitoring methods are mostly used to monitor the insulation fault of the cable.The temperature detection method can measure temperatures along the cable, identifying specific abnormal temperature positions without electromagnetic interference.This method is applicable for monitoring outer sheath damage faults in the cable.In [6], it is demonstrated that the feasibility of monitoring and locating heating faults in power cables by using a distributed temperature sensor and detecting instantaneous short circuit faults with distributed optical fiber proves challenging, with detection accuracy significantly dependent on the optical fiber's laying position.In [7], a novel method for detecting insulation faults in XLPE cables is introduced by using optical fiber temperature sensors.This method furnishes a theoretical foundation and a viable approach for the timely detection and evaluation of cable faults, holding substantial significance in the prevention and mitigation of cable faults.Furthermore, the swift progress of artificial intelligence and computer technology has led to the widespread application of artificial intelligence algorithms in online cable fault detection and fault classification [8][9].
When the outer sheath of the cable is damaged, the cable surface temperature undergoes abnormal changes.The accuracy of distributed optical fiber detection is significantly influenced by the optical fiber's laying position.To enhance the precision of sheath fault assessment, this paper introduces a method based on a BP neural network.This method assesses the degree of cable sheath damage by using circumferential temperature data from the damaged position.Ultimately, the proposed approach enables a quick and accurate evaluation of the degree of cable sheath damage, offering a novel perspective for sheath fault assessment.

Cable finite element and model parameters
This paper establishes an electromagnetic thermal simulation model for a 220 kV HV AC cable in a cable trench by using COMSOL Multiphysics.The cable under investigation consists of nine layers arranged as follows: cable core, conductor shield layer, XLPE insulation layer, insulation shield layer, alloy lead sheath, PE sheath, inner cushion layer, armor layer, and outer sheath (from the inside out).The specific construction is depicted in Figure 1, and corresponding geometric parameters for each layer structure are provided in Table 1.Electric field control equation.The heat generated by the cable as it is laid in the trench is first transferred to the outer surface of the cable by conduction, and then from the outer surface of the cable to the air in the trench by natural convection and radiation. , Where  represents a vector differential operator; J represents the current measurement, measured in A/m 3 ; , j Q  represents the current source, measured in A/m 3 ; σ represents the conductivity of the material, measured in S/m; E represents the electric field intensity, measured in V/m; Je represents the external injection current density, measured in A/m 3 ;  represents the potential, measured in V.

Control equation of heat transfer field ()
where ρ represents the material density, measured in kg/m 3 ; CP represents constant pressure heat capacity, measured in J/(kg• K); v is the speed, measured in m/s; T represents the material temperature, measured in K; K represents the thermal conductivity of the material, measured in W/(m• K); Q represents the heating power per unit volume of the heat source, and the unit is W/m 3 .Considering that the semi-conductive layer primarily balances the electric field, it has a relatively thin thickness.In this study, it is treated as an insulating layer during the heat transfer process.

Boundary condition
The complete calculation model must include boundary conditions.The three common boundary conditions for temperature field calculations are as follows.
The first condition is the known boundary temperature, expressed as: The second boundary condition pertains to the known normal heat flux density.The equation can be expressed as: The third boundary condition corresponds to the convective boundary condition.The equation can be formulated as: The cable considered in this paper is installed within a cable trench.The heat flux between the cable surface and the surrounding air is of a convective nature.Typically, the convective heat transfer process is assessed through the formulation of boundary conditions.

Damage assessment process
The BP neural network-based damage state assessment process for the outer sheath of a high-voltage cable is shown in Figure 2.
(1) Database construction.First, different degrees of damage to the outer sheath are set in the COMSOL Multiphysics software, and then the temperature data of the outer surface of the cable is obtained by simulation calculation.To obtain the circumferential temperature distribution of the damaged outer sheath, the surface temperature of the outer sheath is obtained every 60 degrees along the circumference at the center of the damage.The six-point temperature is expressed as θ0, θ60, θ120, θ180, θ270, θ300.The eigenvectors I, θat, θ0, θ60, θ120, θ180, θ240, and θ300 are obtained, where I is the working current of the cable and θat is the ambient temperature.
(3) Training generation and sample test.The data is divided into training and test sets, allocating 90% and 10% of the total samples, respectively.Randomness is ensured by performing a random division from the original dataset.
(4) Training process.The network parameters are iteratively adjusted to attain optimal values, creating a connection between input and output variables. (

BP neural network
The BP neural network consists of an input layer, a hidden layer, and an output layer, depicted in Figure 3.The algorithmic process involves two steps: forward propagation of signals and backward propagation of errors [10].During forward propagation, the input layer value is computed by the weighted sum of the activation function, transmitted to the hidden layer, and subsequently propagated to the output layer by using the same approach.If the predicted output from the output layer does not meet the accuracy criteria, the error signal is retroactively transmitted along the original path.Weight updates are implemented through the gradient descent method, and the next forward propagation is initiated.This iterative process continues, steadily diminishing the error until the desired accuracy is attained.It is assumed that the network has n inputs and m outputs, with S neurons in the hidden layer.The hidden layer produces an output, bj, with a threshold of θj.The output layer has a threshold of θk.The transfer function for the hidden layer is f1, and for the output layer is f2.The weights from the input layer to the hidden layer are wij, and from the hidden layer to the output layer are wjk.The network output, yk, is obtained, with the expected output being tk.
The output of the first neuron in the hidden layer is as follows: The output of the output layer is calculated, namely: () The error function is defined by the actual output of the network, that is: Network training entails iteratively adjusting weights and thresholds to minimize the network error, aiming to reach a predefined minimum or stop at a predetermined training level.Once trained, prediction samples are input into the network to generate prediction results.

Dataset generation
In this document, four levels of damage are established, corresponding to intact, mild damage, moderate damage, and severe damage.In this paper, the network is constructed based on Python 3.6 and the TensorFlow open-source framework.The database is created according to the data obtained by finite element simulation.In each damage type, the value range of ambient temperature is 0~40°C, and one temperature value is taken every 5 degrees.There are 8 groups.The current value range is 400~1800 A, and one current value is taken every 25 A. A total of 56 groups make up 1120 data records.In each group of damage types, the training sample count is 1008 and the test sample count is 112.The specific information on the training library is shown in Table 2.

Data pre-processing
Since there is a large gap in the order of magnitude of the actual data, which will have a great impact on the prediction effect of the neural network, this paper chooses the normalization method and limits the data range to [0,1], as shown in Equation ( 5 In the equation, ymax and ymin represent the maximum and minimum values of the data, respectively.Following normalization, the larger the data value is, the closer it approaches 1, and the smaller the value is, the closer it approaches 0. In this way, the influence of different orders of magnitude is eliminated, and the size relationship between different data is not changed, which not only optimizes the training results but also speeds up the training speed.

Test result
Four groups of outer sheath breakage tests are tested under different simulation experiment conditions without training.In this paper, the confusion matrix visualization tool is used to reflect the classification results.In the confusion matrix, each column represents the predicted category, while each row corresponds to the actual category of the data, as illustrated in Figure 4.It can be clearly seen that the recognition accuracy rate of the BP neural network is 94.29%, there are 57 groups of each label, and a total of 13 samples are misidentified.The correct rate of label "0" and label "3" is 100%, the number of false positives of label "1" and label "2" are 4 and 11 respectively, and the classification accuracy rate is 96.49% and 80.70% respectively.By comparing the expected output with the actual output results of the network, it can be seen that the network can effectively discriminate the damage degree of the cable outer protective layer, which verifies the feasibility of the BP network to evaluate the damage state of the cable outer protective layer.

Conclusions
The detection accuracy of the damage degree of 220 kV cable outer sheath based on the BP neural network is 94.29%.The network can effectively discriminate the damage degree of cable outer sheath.The outer sheath damage assessment method proposed in this paper can be applied to the laying of highvoltage cables in cable trenches, tunnels, and the seabed, which can be used to detect the running state of the cables in real time and locate and evaluate the damage of the outer sheath.

Figure 2 .
Figure 2. Evaluation process of the damage state of high-voltage cable outer sheath based on BP neural network.

Figure 3 .
Figure 3.The topology of the BP neural network.

Figure 4 .
Figure 4. Test results of BP network.

Table 2 .
Network Training Information.