Transformer fault analysis based on rough sets and improved gravity algorithms

Transformer is one of the most important equipment of power grid, in order to ensure the safe and reliable operation of power grid, the correct diagnosis of transformer fault is very important. Rough set theory is a new field of mathematical science, and it is applicable to many fields, including pattern recognition, machine learning, decision support, process control, and predictive models. Considering the incompleteness and complexity of transformer fault diagnosis data, a fault diagnosis method based on rough set theory and improved gravity algorithm is proposed in this paper.


Introduction
A transformer is a vital equipment in the power system, and its health condition directly affects the safety and stable operation of the power network.Therefore, it is of crucial significance to diagnose transformer faults accurately and quickly.In the current power system network, the operating environment of the transformer is relatively harsh.Moreover, the fault information may become inaccurate and incomplete due to the sensor error measurement or the loss of signal transmission.This brings great difficulty to the transformer fault diagnosis.The maintenance decision problem is actually a multi-attribute decision problem, while the rough set theory can effectively solve the multi-attribute decision problem with a preference relationship.Based on this point, this paper proposes an improved search algorithm based on rough set theory to optimize the parameters of support vector machine (SVM).Compared with traditional diagnostic methods, this algorithm has several significant advantages: 1) it can more effectively handle fault information with noise and incomplete data; 2) it shows high fault diagnosis accuracy and robustness in simulation experiments.The results of simulation experiments show that the improved search algorithm significantly improves the accuracy and reliability of transformer fault diagnosis.Therefore, this paper not only provides an efficient and accurate method for transformer fault diagnosis but also provides an effective new way to solve multi-attribute decision problems.

Rough set theory
Rough Set Theory (RS), a new mathematical tool developed by Pawlak Z and his partners in 1982 to solve vague and incorrect problems, provides a range of tools to analyze and explain uncertain and incomplete data. [8]It now finds use in pattern recognition and classification, machine learning, process control, knowledge discovery, and expert systems, as well as in-patient pattern recognition in the medical field.In recent years, it has been applied to evaluate the state of the main equipment in power systems [1] .The rough set theory is a classification set theory for object properties.The most important characteristic is that it only uses information from the data itself without prior knowledge.This theory provides a method for diagnosing transformer experts using fuzzy, non-deterministic data [7] .This section first explains the basic concepts of rough set theory.

Support vector machines in fault diagnosis
Support vector machine (SVM) is a supervised learning algorithm proposed by Vapnik and Chervonenkis et al. in the 1990s, widely used in classification, regression, and anomaly detection tasks.Especially in the field of power systems, SVM is used in a variety of fault diagnosis and status assessment applications due to its excellent performance and robustness.The SVM shows significant advantages in transformer fault diagnosis.For example, Yuan et al. (2015) used SVM to analyze the data of dissolved gas in transformer oil.They successfully diagnosed a variety of different types of faults, including short circuits in winding and discharge in oil.Another example is the study conducted by Wang et al. (2018), which used an SVM combined with a feature selection algorithm to effectively improve the accuracy and reliability of transformer fault diagnosis.However, despite the advantages of SVM in fault diagnosis, it also has several limitations.For example, SVM often requires large amounts of label data for training, which may not be readily accessible in real-world applications.Moreover, the computational complexity of SVM is also high, which can be problematic in large-scale and real-time applications.For this reason, this paper combines rough set theory and SVM.By using coarse set theory for feature selection and data preprocessing, we not only reduce the model complexity but also improve the accuracy and robustness of fault diagnosis.This method shows superior performance over conventional SVM methods in simulation experiments, and it is, therefore, expected to be an effective tool for transformer fault diagnosis.

Related work
In the field of transformer fault diagnosis, various methods have been proposed and studied, including rule-based methods, neural networks, and various statistical models. [3]However, these methods exhibit significant deficiencies in dealing with incomplete or imprecise data. [2]For example, neural networks require a large amount of training data, which is often difficult to obtain in real-world applications. [4]ince the rough set theory was proposed by Pawlak Z in 1982, it has been widely used in many fields, including data analysis and pattern recognition.For SVM, it has been widely used in text classification, bioinformatics, and many other fields.However, it has still not received widespread attention and application in power systems and transformer fault diagnosis.These problems highlight the urgent need for new methods and techniques in the fault diagnosis of transformers. [6]This paper thus proposes a new fault diagnosis method combining rough set theory and SVM.By introducing these two powerful mathematical tools, we aim to address problems existing in traditional methods, such as data incompleteness and high computational complexity.We demonstrate the superiority of the method for fault diagnosis accuracy and reliability in simulation experiments.

Traditional gravitational search algorithm
Gravitational Search Algorithm (GSA) is an intelligent optimization algorithm based on the Law of Universal Gravitation and Newton's Second Law.In traditional GSA, the feasible solution to the problem to be optimized is expressed by the coordinates of each particle, and the mass of the particles represents the degree of suitability.There are N a number of particles in the p set population.Particles are represented by vectors (  ) , where p {1,2,..., N } n are the dimensions to be solved, and v p x are the p coordinates of the particles in the first v dimensional space.In the u second iteration, the particle's q gravitational force on the particle p in v the fourth dimensional space can be expressed as: in the formula, ( ) u G is the u gravitational constant for the second substitution; 0 G is the gravitational constant from the beginning, its value is kg / m N .
; α is a constant, the value in this paper is 20; T is the maximum number ( ) of substitutions; it is the u distance between the particles p and q at the time e of the second change; it is a very small constant, the value in this paper is 0.01; ( ) is the mass of the particle p , obtained from the following formula: in the formula, ( ) is the p degree of suitability of u , the particle at the time of the second transformation ( ) is the u minimum value of the function and the optimal value of a single property in all individuals at the time of the second transition, respectively; it is the ( ) u m p mass of the particle's p second iteration.Because this requirement solves the problem at the lowest level, it will be defined separately using the following formula: ( ) After the u second iteration, the net p force received by the particles in the first v dimensional space can be expressed as: in the formula: rand [0, 1] is between random numbers; kbest is the previous k individual in order of quality, and the value of k decreases with the number of iterations.The acceleration in the first v dimensional space according to Newton's second p law is as follows (8):  (9)   in the formula: v p w is the speed of the particle p in the first v dimensional space; v p s is the position of the particle p in the second v dimension.
Algorithmic GSA still explores the best answers by determining particle gravity, mass acceleration, and particle coordinate improvements. [13]2 Improving strategies Traditional GSA algorithms are flawed in convergence speed, global optimization, and accuracy of final prediction.[5] Considering the arbitrariness of chaotic sequences, the GSA improved optimization algorithm for chaotic sequences derived from regularity characteristics turns to chaotic sequences to initialize the target individuals of the group's own sexual particles as uniformly distributed as much as possible throughout the solution space.For initial quality improvement, the best situation is to effectively avoid and improve accuracy.Chaotic sequences are generated using currently widely used Logistic formulas to improve the overall search capability of the algorithm.This is shown in Formula (10).

Performance comparison
To verify the suitability of the improved GSA algorithm proposed in this paper, a test function sphere with a minimum value of 0 was selected to evaluate the suitability.A comparative analysis was performed with the existing GSA algorithm.The above optimization algorithm tests the function in Matlab.The simulation results obtained are shown in Figure 1.

Rough set improved transformer fault diagnosis of GSA-SVM model
Transformer fault diagnosis can be explained by pattern recognition of the type of problem, so it is appropriate to use RS for treatment.The basic method is to find the minimum reduced set using the fault coefficient as the conditional property and the fault signal as the determining property. [12]Transformers can be diagnosed through rules calculated based on rs that obtain clear knowledge classification rules describing knowledge through diagnosis and can be used as a basic rule in rules-based systems [9] .The RS-based diagnostic model is shown in Figure 2:

Fault diagnosis
Two causes are held accountable for transformer failure: transformer short circuit overheating or partial discharge.According to the changes in the content of various dissolved gases caused by the oil being heated and split after the transformer has failed, the potential failure of the transformer can be analyzed and determined using artificial intelligence calculation methods.There are mainly 5 types of dissolved gases generated by the fault, including H₂, CH4, C2H6, C2H4, and C2H₂.The diffusion coefficient between them and the diffusion coefficient close to the dissolved gas is calculated.Their ratio is calculated to provide a basis for fault diagnosis. [11]CH4/H₂, C2H2/C2H4, and C2H4/C2H are selected.According to the ratio of these three pairs of gas components, the six fault types of the transformer were analyzed and diagnosed.The 6 fault types include low-energy discharge, high-energy discharge, low-temperature overheating, medium-temperature overheating, high-temperature overheating, partial discharge, etc.This method is called the Three Secrets.In the transformer fault diagnosis process, first, the acquisition of nuclear function optimization is determined by simulating training data and test data.An SVM algorithm model mechanism is established.It is predicted that when the transformer fault diagnosis system fails, it is collected because the hardware system is fissile gas.Finally, three pairs of gas component content (CH4/H₂, C2H2/C2H4, C2H4/C2H6) ratio serve as variable data to calculate the types of errors associated with running the SVM model and accurately report the current fault situation [10] .

Confusion matrix
The confusion matrix for the unoptimized SVM model is shown in Figure 3.The results of the SVM model without optimization are not ideal.The most accurate type 4 fault prediction rate is 93.3%, while the accuracy rate of category 5 fault prediction is 90%.Analysis of Figure 3. reveals that different types of abnormal data, such as prediction error 41, prediction error 3, prediction error 4, and 6, account for error rates of 6.7%, 18.8%, and 5.9%, respectively.The predicted results have no practical significance for solving the problem.

Conclusion
Fault diagnosis methods based on rough set theory and improved gravity algorithms can handle missing or erroneous transformer fault signs.Correct troubleshooting results can still be obtained when defective data is present.Therefore, this method is more suitable for fault diagnosis of transformers.An improved SvM parameter optimization model based on rough sets and improved gravitational search algorithms is proposed using a traditional GSA -Svm model to visually analyze the model.Predicting models by optimizing chaotic sequences can effectively break out of a specific level of particle evolution, improve the diagnostic accuracy of analog circuits, reduce classification time, and streamline fault diagnosis.

Figure 4 .
Figure 4. Confusion matrix of the optimized SVM model.