Optimization of support vector machine for transformer core and winding looseness fault diagnosis based on improved grey wolf algorithm

To diagnose transformer core and winding looseness faults more timely and effectively, a complementary ensemble empirical mode decomposition (CEEMD) and improved grey wolf optimization-based support vector machine (IGWO-SVM) method for transformer core and winding looseness fault diagnosis are proposed. Firstly, the vibration signal is decomposed into multiple intrinsic mode functions (IMFs) through CEEMD. Secondly, the energy entropy of different IMFs is calculated, and the energy entropy of different states is formed into a feature dataset. Then, the improved GWO-optimized SVM model is used to classify and recognize the feature dataset. Finally, we establish an experimental platform for experimental verification. The results show that the proposed method can accurately and effectively diagnose transformer core and winding looseness faults, and has a high diagnostic accuracy, which is at least 3.5% higher than the existing optimal diagnostic models. The proposed method provides a theoretical reference for the development of transformer fault diagnosis strategies.


Introduction
The transformer is the core equipment in the power system.Potential faults will cause major safety accidents and economic losses [1].As China's electrical system continues to upgrade, higher requirements are put forward for transformers [2].Because the main structure of the transformer is complex, and the transformer operates in the electromagnetic and thermal complex environment for a long time, its internal mechanical components will deteriorate, which may lead to the occurrence of transformer failure [3].Therefore, it is of vital importance for the chronic steady operation of electrical power systems to establish effective transformer fault diagnosis technology and fully grasp the operation state of the transformer [4].
The vibration method has become a rapidly developing and reliable transformer fault diagnosis technology in recent years with the advantages of flexible installation, accuracy, and no electrical connection.To better obtain representative information about transformers, it is necessary to extract features from the vibration signals of transformers.In [5], empirical mode decomposition (EMD) and spectral kurtosis methods were used for feature extraction of transformer vibration signals.Although EMD can effectively reduce signal noise, there are modal aliasing and endpoint effects.In [6], ensemble empirical mode decomposition (EEMD) was used to extract vibration signal energy and 2norm for transformer winding mixed fault identification.Although EEMD effectively suppresses modal aliasing, there are still issues with high computational complexity.CEEMD is an improvement on EEMD, which can effectively reduce computational complexity and better extract signal features compared to EEMD.
Based on these analyses, this study proposes a transformer core and winding looseness fault diagnosis method that combines CEEMD and IGWO-SVM.The original vibration signal is first decomposed by using CEEMD to obtain multiple IMF components, and the energy entropy of each IMF is calculated to constitute the eigenvalue.Secondly, we use IGWO to optimize the penalty function c and kernel function radius g of the SVM in a diagnostic model of transformer fault classification.The trained IGWO-SVM model is used to diagnose and classify transformer core and winding looseness faults.Finally, the experimental results with samples of different degrees of looseness in the core and windings validate the effectiveness of the proposed method.

The CEEMD principle
CEEMD improves based on EMD and EEMD.The final IMF component calculation formula obtained from the CEEMD calculation process in [7] is as follows: ,, where 1 () * ct and 1 () , ct are the signals after the first addition of white noise to the original signal, and k is the number of IMF components.

Energy entropy
Energy entropy is a kind of information entropy that represents the distribution of energy in a signal and has the advantages of simple calculation and strong noise resistance [8].In transformer fault diagnosis, the looseness of the transformer core and winding is often accompanied by specific fault frequencies, due to CEEMD decomposing transformer vibration signals into a series of sparse and bandwidth-limited IMF components.Therefore, in this paper, the energy entropy of each IMF constitutes a set of characteristic quantities to represent the state of the transformer windings.The process of calculating energy entropy is described in detail in [8], which will not be elaborated in this article.

GWO algorithm
The Grey Wolf Optimizer (GWO) has the characteristics of a simple structure and fewer regulating parameters, which is easy to achieve [9].This algorithm divides the entire hunting process into stages of surrounding, hunting, and attacking, ultimately capturing prey to acquire the global best solution.The algorithm steps of GWO are detailed in [9], and will not be elaborated in this article.

IGWO algorithm
The GWO suffers from defects such as a slow rate of convergence and a tendency to sink into a local optimum, so the GWO needs to be enhanced.To address this problem, this paper proposes an improved Grey Wolf Algorithm (IGWO) by using a nonlinear convergence factor and a dynamic weighting strategy.The specific improvement methods are as follows: 1) Introduction of the nonlinear convergence factor.The changing position of individual grey wolves during prey encirclement and the convergence factor a in the position change shows a linear trend, namely: However, considering that the convergence process is not linear, to make the convergence factor a fully show the optimization process of GWO, this study uses the nonlinear convergence approach to reduce a , and the improved a is as follows: where e is the base of the natural logarithm; t stands for the current number of iterations; max T represents the current number of iterations.
2) Adoption of a dynamic weight strategy.
In GWO, when the hunting object is determined,  leads α and χ to launch the chase.During the chase, the gray wolf's position changes in response to the location of escaped prey.The updated formula of the gray wolf position is:  in GWO algorithm is not the best solution necessarily.During the iteration process, as ϖ continues to approach  , α , and χ , it may lose the global optimal position.Therefore, this paper evaluates the position of wolves, introduces dynamic proportional weight, further adjusts the position of gray wolves, and finally accurately preys on prey.The calculation formula of position weight is as follows: The improved gray wolf position update formula is: where ϖ is the dynamic proportional weight; () fX is the fitness function.

Optimization of IGWO-SVM parameters
SVM maps the linear inseparable data set to the high-dimensional space to construct the optimal partition hyperplane to realize classification [10].When constructing a linear inseparable SVM model, the penalty function c and kernel function g will significantly affect the classification effect.Therefore, this article uses the above IGWO to optimize the c and g arguments of SVM to improve the fault recognition rate and speed of SVM.The specific parameter optimization process is as follows: Step 1: Wolves are randomly generated and the position vector of individual wolves is set as [,] cg .We set its optimization upper limit b u and lower limit b l , initialize the number of gray wolf groups N , and set the number of solution iterations to max T .
Step 2: Model diagnostic accuracy is used as a function of fitness.We calculate fitness values for individual gray wolves, and the wolf pack is divided into  , α , and χ wolf packs.The best individual is the one with the greatest fitness, and its location is also the current optimal location.
Step 3: We update the position and fitness of each wolf.
Step 4: We return to perform Steps 3 and 4 until the number of iterations is maximized.
Step 5: We output the optimal individual position and obtain the optimal parameters c and g .

Transformer core and winding looseness fault diagnosis model based on CEEMD and IGWO-SVM
The transformer core and winding looseness fault diagnosis model in this paper combines the characteristics of CEEMD decomposition of fault vibration signal and energy entropy, which can effectively reflect the difference of energy distribution implied in non-stationary time series.The specific implementation steps of the model are as follows: Step 1: The acceleration signal data of the transformer in different states are collected through the vibration signal test points arranged on the surface of the transformer.
Step 2: The collected original vibration signals are divided into multiple groups and decomposed by CEEMD to obtain IMF components in three states.
Step 3: The energy entropy of the six IMFs obtained from the decomposition is computed and utilized to form a multidimensional eigenvector, and multiple sets of feature measures are divided into training and test sets.
Step 4: The IGWO is used to optimize the c and g parameters of SVM with the training set to obtain the optimized SVM model.
Step 5: We use the test set divided in Step 3 to test and classify the trained IGWO-SVM model.This paper mainly studies the loose fault diagnosis medium of transformer winding and iron core, so the test fault mode is set to adjust the nut preload of internal fault phase winding of the transformer, and three experimental conditions are set for analysis.The windings are in a normal state, which is defined as State 1.The second is the fault state in which the winding preload decreases by 35%, which is defined as State 2. The third is the fault state in which the winding preload decreases by 70%, which is defined as State 3.

Test validation and analysis
In this study, the raw vibration signals of the transformer in each state are processed, and the collected data samples of the three states are divided into 90 groups, with 30 sample sets in each operating state.The sampling time of each sample set is 0.2 S, including 4, 000 original data points.70% of each state is taken as the training specimen, and the remaining 30% is used for testing.The operating states are represented by data numbers, of which sample numbers 1, 2, and 3 correspond to the three states of the normal transformer, 35% reduction of preload of iron core and winding, and 70% reduction of preload of iron core and winding, respectively.The time domain waveform of the three collected states is shown in Figure 2. Since the CEEMD method has the effect of principal component analysis and the main fault information is concentrated in the first IMF, the IMF decomposition level is set to six, and the decomposition results of CEEMD for the sample set of three states of the transformer are shown in Figure 3.As shown in Figure 3, CEEMD decomposes the transformer vibration signal into six IMFs components, which can effectively describe the original vibration signal of the transformer.We calculate the energy entropy of six IMFs in each sample set under each state and get the energy entropy of each IMF in different states, as shown in Table 1.Based on obtaining CEEMD and IGWO-SVM-based classification models, to verify the superiority of IGWO-SVM for transformer core and winding fault diagnosis, we compared with traditional SVM, grey wolf optimized support vector machine (GWO-SVM), and particle swarm optimization support vector machine (PSO-SVM) models.In the PSO-SVM model, the population size is 20 and the termination algebra is 200.The same sample training set and testing set are input into the above model, and the diagnosis results of GWO-SVM, PSO-SVM, and traditional SVM models are shown in Figure 5. From Figure 5, under the same input sample set, the IGWO-SVM model has an accuracy of at least 3.5% higher than the comparative model, proving the effectiveness of the IGWO-SVM model in diagnosing transformer core and winding looseness faults.

Conclusions
This paper presents a fault diagnosis method combining CEEMD and IGWO-SVM, which can accurately realize the diagnosis and classification of transformer core and winding looseness faults in different degrees.Aiming at the complexity of transformer vibration signals, the CEEMD eigenmodal component extraction method that can reduce the computational complexity is proposed to achieve the effective extraction of transformer vibration signals.Further, the energy entropy is used to characterize the deep characteristics of the transformer vibration signal, and the energy entropy of different states is used as the input of the IGWO-SVM model.The experimental outcomes indicate that the accuracy of the proposed improved GWO-optimized SVM model can reach 96.29% for different degrees of transformer core and winding looseness fault diagnosis.Compared with GWO-SVM and PSO-SVM, SVM model diagnosis accuracy is higher.The next stage will focus on the practical application of the proposed method and improve its diagnostic ability in application scenarios through improvement.
This paper builds a 10 kV transformer simulation fault test platform, and the sensor used for the test is an IEPE piezoelectric acceleration sensor with Model 1A212E.The model of the acquisition system was DHDAS and the sampling frequency was set to 20 kHz in the test.The vibration signals collected on the walls of the transformer case are mainly axial vibration signals of the windings propagated through the solids of the transformer's structural elements.Therefore, three measuring points are set on the top of the transformer, and each measuring point is equipped with a vibration acceleration sensor.Multiple groups of vibration signals were collected to verify the feasibility of the proposed method.The experimental principle is shown in Figure 1.

3 Figure 2 .
Figure 2. Time domain waveforms of three transformer states.

3 Figure 3 .
Figure 3. CEEMD exploded view of three states of the transformer.

Figure 5 .
Figure 5. Diagnostic results of several comparative models.(a) Diagnostic results of GWO-SVM; (b) Diagnostic results of PSO-SVM; (c) Diagnostic results of SVM

Table 1 .
Energy entropy of IMF in different states.It can be seen fromTable1 that the energy entropy of each IMF of State 2 and State 3 fluctuates greatly compared with that of State 1, and the energy distribution of the vibration signal of State 1 is more concentrated than that of State 2 and State 3, with better discrimination.The energy entropy of six IMFs of each fault type can form a fault characteristic matrix of 90 ≥ 6, which can be input into the IGWO-SVM model which sets the optimization range from c to g to [0.0001, 200] .The diagnosis results are shown in Figure 4.