IGSA-PNN-based Methods for Power Transformer Fault Diagnosis

To enhance the precision of power transformer fault diagnosis, it is necessary to make improvements. Aiming at the shortcomings of Probabilistic Neural Network (PNN) network experience selection smoothing factor and avoiding the shortcomings of traditional Gravitational Search Algorithm (GSA) easy 0to fall into local optimum and convergence speed slow, a Probabilistic Neural Network (PNN) model using chaos sequence to improved GSA for power transformer fault diagnosis is proposed. Firstly, chaos sequence is used to increase the diversity of gravitational particles to avoid falling into local optimum during the training process. Then, the improved GSA algorithm is used to optimize the parameters of the PNN model itself to improve the prediction accuracy of the model. Finally, the prediction results are compared with the prediction results of other traditional diagnostic models. The results show that IGSA-PNN fault diagnosis model performs better in generalization ability and classification accuracy.


Introduction
Power transformers are one of the important electrical equipment, which undertake the important tasks of power transmission and voltage transformation.With the continuous expansion of the power system, the transformer failure rate is increasing, and monitoring the transformer status and fault diagnosis to ensure uninterrupted power supply is extremely important [1].The application of fault diagnosis technology for early identification of transformer faults, so as to take effective measures, can reduce the probability of accidents.
Dissolved Gases Analysis (DGA) is the mainstream method for transformer fault diagnosis, and the traditional methods such as IEC ratio method and graphic method, which are widely used in practical transformer fault diagnosis [2][3][4].However, these methods have some disadvantages, such as strict application conditions and fuzzy judgment.With the emergence of a large number of intelligent algorithms, most scholars combine DGA diagnosis results with intelligent diagnosis methods to achieve accurate transformer fault prediction.Such as Extreme Learning Machine (ELM), Support Vector Machine (SVM) and BP neural network [5][6][7].
In summary, this paper proposes that a new model for power transformer fault diagnosis, namely the PNN optimized by the improved gravitational search algorithm.Firstly, the traditional GSA algorithm is improved by using chaotic sequences to achieve the purpose of maintaining the diversity of the initial position of the chaotic group particles.Then, the improved GSA algorithm is used to train the smooth factor set of the PNN neural network to enhance the accuracy of power transformer fault where represents the total number of classes, .z refers to the -th centre r of the sample of class .
refers to the dimension of the data space.The sum layer weights the output of the same class of neurons in the pattern layer, as shown in equation (2).
where represents class output.The number of neurons in the summation layer is equal to the number of classes .represents the number of class neurons.The output layer outputs the maximum value in the summation layer, as shown in equation (3).arg max( ) The radial basis function accepts the result of multiplying the vector of the output layer with the weighting coefficient and calculates it, as shown in equation (4).
If both and are normalized, the radial basis operation is performed as shown in equation ( 5).
When the PNN neural network is trained, the same value is taken according to the set of empirical smoothing factors 12 ( , , , ) However, the expression of spatial probability characteristics of training samples cannot be expressed normally.Therefore, the key to PNN network training is to determine the appropriate smoothing factor set 12 ( , , , ) , so it is particularly important to find a suitable training algorithm to optimize the smoothing factor of PNN.

Traditional Gravity Search Algorithm
Gravitational Search Algorithm (GSA) is an intelligent optimization algorithm, which derived from the law of gravitation and Newton's Second Law [9].The feasible solution of the problem to be optimized is represented by the coordinates of each particle, and the mass of the particle represents the fitness.There are N particles in the population, and particle p is represented by equation (7).
where {1, 2, , } pN  and n are the dimensions to be solved, and u p x are the coordinates of particle p in the u -dimensional space.
In the v iteration, the gravitational force of particle q on particles in the u -dimensional space can be expressed as equation ( 8), (9).
where () Gv is the gravitational constant of the v iteration.0 G is the gravitational constant at the initial time, whose value is .  is the constant, whose value is 15 in this paper; T is the maximum number of iterations, whose value can be set. () Rv is the distance between particle p and q at the v iteration;  is a very small constant, whose value is 0.01 in this paper.() Mv is the mass of particle p , whose value can be obtained according to formulas (10) and (11).
where () fv is the fitness of particle p at the v iteration; () bv is the worst fitness function value among all individuals at the v iteration, and ()  wv is the best fitness function value among all individuals at the v iteration. () Mv is the mass of the v iteration of particle p .
Combined with the problem solved in the paper.At the iteration, the worst fitness function value x among all individuals is shown in equation ( 12).The optimal fitness function value y is defined as shown in equation (13).
After the v iteration, the resultant force on particle p in the x-dimensional space can be expressed as equation ( 14). , () where is any value in [0,1] .b k is the first k individuals whose individual mass is in descending order, and the value of k decreases linearly with the number of iterations.
Under the action of gravitation, according to Newton's second law, the acceleration of particle p in the u -dimensional space can be obtained as shown in equation ( 15).The strategy for updating the position of particles is shown in equation ( 16). ( where () wv is the velocity of particle p in the u dimensional space; u p s is the position of particle p in dimension u .

Improvement Strategy
Traditional GSA algorithm convergence speed is slow, the ability of global optimization is poor, so it will lead to the final prediction accuracy is low.Considering the randomness and regularity of chaotic sequence, this paper uses chaotic sequence to improve the GSA algorithm, and uses the ergodic property of chaotic sequence to achieve the purpose of initializing group particles, so that the initial individuals are evenly distributed in the entire solution space as far possible, so as to improve the quality of the initial solution and effectively avoid the local optimal situation.It can also improve the precision of optimization while maintaining the diversity of the group.
The Logistic equation [10] shown in equation ( 17), which is widely used at present, is used to construct a chaotic sequence to enhance the algorithm's capability for global optimization.
where  is the control parameter of chaotic state, and the value in this paper is 4; 1 x − is a 1 t −dimensional chaotic gravitational particle.The specific steps of chaotic initialization of group particle position are as follows: Stop1: Randomly generate set of t -dimensional sequences as initial chaotic gravitational particle 0 x ; Stop2: Substitute 0 x into equation (17) and iterate until the maximum number of iterations t is reached, k chaotic particles are generated and their adaptation values are calculated respectively; Stop3: From the k chaotic particles generated in step 2, the optimal particles are selected to form a set, which is used as the initial group particles of the GSA algorithm.

Optimized PNN Model Based on IGSA
The flow of IGSA algorithm to optimize PNN is shown in figure 1.The steps are as follows.
Stop1 The maximum number of iterations, the total number of particles in the population and the number and dimension to be solved are set; Stop2 The chaotic sequence is used to initialize the gravitational population particles; Stop3 Check the particle crossing condition and calculate the fitness value of each particle; Stop4 Calculate the gravitational attraction and mass of each particle; Stop5 Calculate the total gravity of each particle, update the particle acceleration and position; Stop6 Check whether the requirements for termination are met.

Fault Diagnosis of Power Transformer
The PNN neural network based on IGSA optimization selects 5 main characteristic gases in oil chromatography data of oil-immersed transformer: 2 H , CH 26 CH , 22 CH , 24 CH as the input characteristic quantity of PNN network.Seven transformer fault types are taken as output characteristic quantities of PNN network.The specific types and corresponding codes are shown that; normal (1), low-temperature overheating (2), Medium temperature overheating (3), high temperature overheating (4), Partial discharge (5), Low energy discharge (6), High energy discharge (7).
When the smoothing factor set 12 ( , , , ) of PNN neural network takes a unified value of 0.1, the identification effect validation sample is the best.In the test, the PNN neural network chooses the topology of 5-80-7-7, the volume fraction of dissolved gas in 5 kinds of oil as the input of the network, the number of neurons in the network mode layer is 80.The number of neurons in the mode layer is Gaussian function as the activation function, and the number of neurons in the summing layer is 7(number of fault types).A set of oil chromatographic data was collected from the transformer research data, and 174 sets of oil chromatographic analysis data of power transformer fault including 7 fault types were collected.Among them, 132 sets of training data and 36 sets of prediction data were used for IGSA-PNN models.The distribution of training data and prediction data is shown in table 1.Combined with the above simulation results, the following analysis can be made: As can be seen from table 3, when optimizing the smoothing factor set of PNN neural network, the empirical value method needs to combine the theoretical basis of fault characteristics and manual experience, and after repeated testing, the appropriate factor can be found.PSO optimization solves the problem of optimal value matching of smooth factor set to some extent, but the optimization algorithm has some

Conclusion
In this paper, the traditional GSA algorithm is improved by using chaotic sequence, which increases the diversity of group particles and makes the global optimization ability stronger.Then IGSA algorithm is used in PNN model to optimize its own parameters and improve the accuracy of model diagnosis and prediction.Finally, the model proposed in this paper is compared with the simulation prediction results of PNN and PSO-PNN models.Finally, it is found that the prediction accuracy of the IGSA-PNN model proposed is higher, which can better ensure the accuracy of transformer fault diagnosis, and provide a certain reference for power maintenance personnel to find internal latent faults in time.

Figure 1 .
Figure 1.The details of IGSA-PNN-based methods for transformer fault diagnosis.
The PNN model optimized by IGSA is used to predict and diagnose the fault properties of power transformers, and the predicted results are compared with those predicted by PSO-PNN models.The simulation prediction of these three situations is carried out, and the final classification prediction results of each model are shown in figures 2-3.The summary of the final classification accuracy of each model is shown in table3.
2023 4th International Conference on Mechanical Engineering and Materials Journal of Physics: Conference Series 2694 (2024) 012082 IOP Publishing doi:10.1088/1742-6596/2694/1/0120827 disadvantages such as low search accuracy in the early stage, precocious convergence and low iteration efficiency in the later stage.The fault sample recognition rate of IGSA optimization reaches 95.2%, which is higher than the empirical value and PSO optimization.

Table 1 .
The distribution of samples.Firstly, the PNN model optimized by IGSA algorithm is used to predict the selected training samples.The prediction results of the fault types are shown in table 2.

Table 2 .
Prediction results of training sample.As can be seen from table 2, the PNN model optimized by IGSA algorithm can maintain a high accuracy in predicting the training data, once again verifying the feasibility of the IGSA algorithm in the PNN model.

Table 3 .
Comparison table of classification accuracy of different methods.