Transformer fault diagnosis based on Chaotic Particle Swarm Optimization RBF Neural Network

This article uses logistic chaotic mapping to improve the particle swarm algorithm parameters and construct the chaotic particle swarm optimization (CPSO) algorithm. Then, the CPSO algorithm is used to optimize the width, weight, and center values of the Radial Basis Function Neural Networks (RBFNN) to improve the RBFNN model used to diagnose transformer fault types. Results show that the CPSO-RBFNN model has a small mean square error and high accuracy in diagnosing transformer faults.


INTRODUCTION
As the size of the power grid continues to increase, the power system is facing increasingly serious challenges.The safety of the transformer, as equipment for transmitting electrical energy, is closely related to people's life.The transformer failure can cause a breakdown of the power system, which makes transformer fault diagnosis a hot research topic.The traditional methods for diagnosing transformer faults include the three-ratio [1] method and the four-ratio [2] method.However, ratio methods often have problems such as incomplete coding, which can lead to diagnosis failures.To solve these problems, many artificial intelligence methods have been proposed, such as expert systems [3] , fuzzy logic [4] , and artificial neural network [5][6] .These techniques can help to make the diagnosis of power transformer faults more accurate and provide an effective solution.
While these artificial intelligence methods help to solve the problem of fault diagnosis in power transformers, they still have some disadvantages.For example, expert systems may have weak reasoning abilities and inflexible diagnosis strategies, and fuzzy logic has insufficient learning ability.Artificial neural networks have strong self-learning abilities, but their convergence speed may slow down when dealing with large-scale data, and they are prone to quickly get stuck in local minima during the convergence process.Therefore, when developing fault diagnosis techniques for power transformers, there is a need to explore in depth the strengths and weaknesses of different methods to develop a more comprehensive solution.
Swarm intelligence algorithms and neural networks are popular technologies in artificial intelligence.The combination of the two can further improve algorithm performance and efficiency.In recent years, combining swarm intelligence algorithms with neural networks has become a hot research direction.For example, using particle swarm to optimize the initial weights and biases in a neural network by quickly searching for them and iteratively optimizing these parameters can not only improve the speed of convergence of the network but also the classification results.Various methods that combine swarm intelligence algorithms with neural networks are introduced and have been successfully applied to the diagnosis of faults [7][8][9][10] .These methods have brought many benefits to the power industry by improving the accuracy and efficiency of diagnostics.
In this paper, an RBFNN model with CPSO is constructed for diagnosing transformer faults using historical transformer fault data.The model uses chaotic mapping to optimize the PSO and further optimizes the parameters of the RBFNN, including centroids, widths, and weights.
In the paper, Section 1 introduces the current status of research on transformer fault diagnosis.Section 2 describes the specific steps of CPSO-RBFNN.Section 3 utilizes CPSO-RBFNN to construct a transformer fault diagnosis model and obtains the corresponding diagnosis results.Section 4 concludes the article.

RBF Neural Network
For RBFNN with multiple inputs and a single output., the output is where q denotes the number of hidden layer nodes, ||  || denotes the Euclidean distance,  represents the width of the Gaussian kernel, and  represents the weight value of neuron connection.

Particle Swarm Optimization( PSO)
PSO is based on the idea that each particle constantly adjusts its position and velocity in the search space to search for the best solution.
Assuming a particle number of n and a search space of d, the particle update approach is described in ( 2) and (3).
where  1, … … ,  ,  1, … … ,  ,  denotes particle position,  denotes the flight speed,  denotes the weight,  and  denotes learning factors,  is the extreme individual value of the particle,  denotes the global optimal value, and  / are random numbers taking values in the range [0,1], increasing particle flight's randomness.

Chaos Particle Swarm Optimization (CPSO)
Logistic chaos mapping is a type of nonlinear dynamical system that can be used to generate pseudorandom number sequences, which can be described as where  is a parameter that controls the growth rate; when  4, the system is in chaos.
In CPSO, chaotic sequences are used to optimize the parameters in the particle velocity and position update formulas, which helps to explore the search space more thoroughly and avoid local optimization.The parameters of a chaotic optimization particle swarm can be described as

RBF Neural Network based on CPSO
RBF neural networks are widely used in information processing, fault diagnosis, image processing, pattern recognition, and other fields.However, when RBF neural network is trained and learned, it is slightly insufficient in selecting parameters such as weight, width, and center value, which is not conducive to transformer fault diagnosis.Therefore, this article uses CPSO to optimize the parameters of RBFNN.The steps are as follows.
Step 1: Initialize RBFNN: determine the number of neurons and choose suitable radial basis functions.
Step 2: Initialize the PSO parameters, including the number of particles N, search space dimension D, learning factor  / , inertia weight  / , random number  / , and the maximum number of iterations  .
Step 3: Initialize the CPSO, assigning each particle a random position   and velocity   .
Step 4: Calculate RBFNN mean square error and use it as the particle fitness, save individual extremum  and global optimal value  .
Step 5: Updating the particle positions and velocities according to Equations ( 2) to (7).
Step 6: Determine if to reach the maximum iteration number  is reached, if so, stop iterating; otherwise, return to Step 3 to continue iterating.
Step 7: Decode the global optimal position vector into the optimal structural control parameters of the RBF.
Step 8: Train RBF with input data, adjust network parameters based on output results, and iterate to obtain an optimal network model.

Determination of Diagnostic System
The primary method of diagnosing faults on power transformers involves the composition of the characteristic gases, including H 2 , CH 4 , C 2 H 4 , C 2 H 6 , and C 2 H 2 .Therefore, these five gases are used as inputs to the network.Since the input sample has significant fluctuations, normalization of the sample data is necessary.Formula (9) normalizes the data and maps the value to [0,1].
where  denotes the standardized data,  denotes original data,   ,  ,  ,  ,  , and  is the content of characteristic gas.Table 1 shows the content of characteristic gases and their respective values.According to the analysis, the RBF neural network topology of 5-11-1 is constructed as shown in Figure 1.

Analysis of Actual Prediction Effect
In this study, 330 sets of transformer fault data were collected, and 264 were selected as training samples and 66 as test samples.These data were used to train, learn, and predict transformer fault diagnosis with the CPSO-RBFNN.These data were also used for the RBFNN and the PSO-RBFNN.Table 3 presents the diagnostic results of the three methods.

CONCLUSION
In the diagnosis of transformer faults, the selection of parameters for RBF neural networks is complex, resulting in problems such as slow convergence speed and low accuracy.This article chooses a CPSO to optimize the RBFNN parameters, which enhances the diagnostic accuracy of transformer faults and provides an even more reliable solution.

Table 1 .
Content Of Characteristic Gases./Thefault types of power transformers include no-fault, low-energy discharge, high-energy discharge, low-temperature overheating, medium-temperature overheating, and high-temperature overheating, represented by values between 1-6.Table2shows the output coding values corresponding to the six fault types.

Table 3 .
Comparison Of Three Algorithms Test Diagnosis Results.