Transformer Fault Diagnosis Method Based on SCA-VMD and Improved GoogLeNet

Abstract

Aiming at the influence of the fundamental frequency and its harmonics in transformer vibration signals on fault signals, which cause a low fault identification rate and degradation of classification model performance, a new strategy is proposed for fault diagnosis using periodic map spectrum feature maps as input features. In this study, the optimal decomposition parameters were first found adaptively using the VMD improved by the positive cosine optimisation algorithm; then, the transformer vibration signal was modally decomposed, and the periodic map spectrum features were plotted according to the differences in the energy distribution of the different modal components at different frequencies. Finally, the GoogLeNet classification model with the improved attention mechanism assigned different weights to the feature maps in both spatial and channel dimensions to improve the classification accuracy and achieve transformer fault diagnosis. The experimental results verified the validity of the adopted feature map and the proposed model, and the accuracy was significantly improved to 99.04% compared with the traditional GoogLeNet, which is valuable for engineering applications.

1. Introduction

With the significant enhancement in the comprehensive globalisation of the world and the rapid social and economic development, the scale of the power grid is constantly expanding, and the user requirements for the safety and stability of electric power equipment are getting higher and higher [1]. The transformer, as one of the key pivotal pieces of equipment for transforming voltage, regulating power, improving voltage stability and improving power quality, can ensure uninterrupted power supply to end users, as well as the safety and stability of the power system [2,3,4]. Therefore, it is important to set up a perfect and accurate fault early warning mechanism to monitor and diagnose the condition of a power transformer in real time to obtain the internal mechanical status of the power transformer and to prevent accidents in a timely and effective manner [5].

At present, the methods for transformer mechanical fault diagnosis are mainly divided into those based on transformer electrical characteristics and those based on transformer vibration characteristics. Methods based on electrical characteristics mainly include the low-voltage impulse method, frequency response analysis method and short-circuit impedance method [6,7], but they are not widely used because they generally require power outage diagnosis. The transformer vibration method mainly refers to the vibration signal analysis method, which is used to diagnose the winding status online by collecting the vibration signals on the surface of the transformer tank, which has no electrical connection with the transformer; this method is more accurate, easier to operate, safer and more convenient compared with other methods, and is a hot spot of current research [8,9]. The research related to transformer vibration signals began in the 1980s. In the mid-to-late 1990s, refs. [10,11] proposed the use of vibration analysis to analyse the vibration signals on the surface of transformers.

The vibration signal analysis method can identify the electromagnetic force, mechanical movement, structural deformation and other physical phenomena inside the transformer, which can reveal the overall working status of the transformer and possible faults [12,13] and is more intuitive and easier to interpret than other methods. The transformer vibration signal research mainly considers the vibration mechanism via the extraction of vibration signal eigenvalues and real-time calculation of the transformer box surface vibration signal changes [14,15,16], and by using the same transformer historical data or the same type of transformer data for comparison and analysis of the normal operating conditions, you can judge the working state of the transformer under test. So far, related researchers have achieved certain research results in the study of transformer vibration characteristics and fault diagnosis methods based on vibration signals. In [17], by mining the fault information contained in the vibration signals, continuous wavelet transform (CWT) was used for the feature extraction, and the vibration signals were converted into RGB images with a time–frequency relationship; then, an improved convolutional neural network (CNN) model was used to complete the image recognition task of transformer fault diagnosis. In [18], a transformer fault diagnosis method based on the combination of time-shifted multiscale bubble entropy (TSMBE) and stochastic configuration network (SCN) was proposed. The method introduces bubble entropy to overcome the shortcomings of traditional entropy models that rely too much on hyperparameters. Based on the bubble entropy, a TSMBE tool was proposed to measure the signal complexity, and then, the TSMBE of the transformer vibration signal was extracted as the fault feature. Finally, the fault features were input into the random configuration network model to achieve the accurate identification of different transformer state signals. In [19], the vibration signals were converted into different images by combining the simultaneous wavelet transform and the simultaneous generalised S-transform, which effectively expanded the samples and extracted the effective features of the signals. A two-stream densely connected residual contraction network (TSDen2NetRS) was used to achieve high-precision transformer fault diagnosis under different operating conditions. Ref. [20] proposed a new approach based on the improved empirical wavelet transform (IEWT) and sandy bee algorithm (SSA) optimisation learning machine (KELM), which not only efficiently diagnoses fault classes present in the training set, but also identifies unknown fault classes. Ref. [21] combined two parts, namely, a data measurement subsystem and data reception subsystem, to form a monitoring system based on IoT technology, and proposed a new method of transformer fault diagnosis based on an IoT monitoring system and integrated machine learning; the proposed method compensated for the deficiency of individual deep learning methods to extract feature information. However, the above study ignored the fact that during the actual operation of the transformer, the existence of the closed magnetic circuit of the core, the electrical circuit of the windings and the gate ring, and thus, the formation of the closed circuit, resulting in additional electromagnetic force on some structural parts; this produces nonlinear characteristics of the closed magnetic circuit, the electrical circuit and the gate ring, and thus introduces additional harmonic and nonharmonic components, resulting in the accuracy of the vibration-signal-based fault diagnosis. In [22,23,24], by studying the force characteristics and vibration characteristics of the transformer core and windings in a harmonic environment, it was found that the vibration energy distribution was shifted from the low-frequency band to the high-frequency band after the harmonics were injected, but the existing studies did not make use of this feature in the transformer fault diagnosis research.

The above work shows that most of the studies on transformer fault diagnosis based on vibration signals, although significant, ignored the interference caused by harmonic and non-harmonic components of the vibration signals on the signals, thus resulting in a low fault recognition rate and degradation of the performance of the classification model. On this basis, a transformer fault diagnosis method based on SCA-VMD and improved GoogLeNet was proposed to collect and analyse different fault signals of transformers and successfully applied in transformer fault diagnosis experiments. In comparison with existing research, the following main contributions were made: (1) This paper introduces the positive cosine algorithm to adaptively determine the VMD algorithm in the signal processing process, which cannot determine the decomposition parameters K and α of the parameter problem, and defines an adaptive function of the minimum average envelope entropy for the adaptive function to verify the superiority of the performance of this paper’s algorithm (SCA-VMD). The results show that the required number of iterations of this algorithm was significantly fewer than the comparative algorithm, and the operation was more efficient, which greatly improved the modal decomposition quality. The periodic map spectrum of the vibration signals decomposed based on SCA-VMD are summed up according to the modal components, the modal components are used as the horizontal axis, the frequency is used as the vertical axis, and the brightness of each point represents the energy magnitude of the modal component at the corresponding frequency to draw the feature map. (2) Aiming at the problem of the low resolution of the computed periodic map spectrum feature maps and small changes in the value of energy under different fault types, which leads to the poor effect of direct feature map recognition, the spatial channel attention mechanism was used to improve the GoogLeNet classification model to judge the importance of the information in the image and the position in the image to assign different weights to the various parts of the input feature maps and to provide a more effective feature map of the transformer fault types for the subsequent GoogLeNet method. (3) This study built an experimental platform for experimental transformer fault signal acquisition and applied the proposed method to the vibration signals to achieve transformer fault diagnosis and localisation.

The rest of the paper is organised as follows: Section 2 describes the SCA-VMD data processing model and the computation process of periodic map spectrum feature maps. Section 3 describes the improved GoogLeNet fault diagnosis method based on the attention mechanism. Section 4 builds an experimental platform for transformer fault data acquisition and constructs sample data. The feasibility of the transformer fault diagnosis method based on SCA-VMD and improved GoogLeNet is verified. Section 5 discusses the contributions of this paper. Section 6 provides the conclusion of this report.

2. Vibration Signal Data Preprocessing and Feature Extraction Modelling

2.1. Variational Modal Decomposition (VMD)

Variational mode decomposition (VMD) mainly deals with the problem of resolving K amplitude–frequency modulation sub-signals from the original vibration signal [25]. VMD can decompose transformer vibration signal data non-recursively into mode components with a specified number of levels, which not only has good adaptability but also reduces the instability of the original signal sequence. The algorithm uses Wiener filtering to eliminate the high- and low-frequency components of the signal and initialises the related parameters to obtain K estimated center angular frequencies ωk. Finally, the alternating direction method of multipliers is used to update each mode function and its center frequency, and each mode is demodulated to the relevant frequency band to minimise the total estimated bandwidth to achieve optimal mode decomposition. The formula is as follows:

$$\{\begin{array}{c}\underset{\left\{u_k\right\}\left\{w_k\right\}}{min}\left\{{\displaystyle \sum }_k\Vert {\partial }_t\left[\left(\delta \left(t\right)+\frac{j}{\pi t}\right)\ast u_k\left(t\right)\right]e^{-j{\omega }_{k}t}{\Vert }_2^2\right\}\\ s.t.{\displaystyle \sum }_k{u}_k=X\left(t\right)\end{array}$$

(1)

In Equation (1), $\left\{u_k\right\}=\left\{u_1,u_2,\cdots ,u_k\right\}$ and $\left\{{\omega }_k\right\}=\left\{{\omega }_1,{\omega }_2,\cdots ,{\omega }_k\right\}$ are the K modal components and frequency centres obtained from the decomposition, respectively. For problems with restricted variables, to find $u_k$ and ${\omega }_k$ for the optimal solution, updating occurs as follows:

$${\widehat{u}}_k^{n+1}\left(\omega \right)=\frac{\widehat{X}\left(\omega \right)-{{\displaystyle \sum }}_{i\ne k}{\widehat{u}}_i\left(\omega \right)+\widehat{\lambda }\left(\omega \right)/2}{1+2\alpha {(\omega -{\omega }_k)}^2}$$

(2)

$${\omega }_k^{n+1}=\frac{{{\displaystyle \int }}_0^{\infty }\omega \left|{\widehat{u}}_k{(\omega )}^2\right|d\omega }{{{\displaystyle \int }}_0^{\infty }\left|{\widehat{u}}_k{(\omega )}^2\right|d\omega }$$

(3)

where $\lambda$ is the Lagrangian operator and $\alpha$ is the quadratic penalty factor.

The steps to create a VMD model are as follows:

• Initialise $\left\{{\widehat{u}}_k^1\right\}, \left\{{\omega }_k^1\right\}, \left\{{\widehat{\lambda }}^1\right\}$, and n.
• Update $u_k$ and $w_k$ according to Equations (2) and (3).
• Update λ using ${\lambda }^{n+1}\left(\omega \right)\leftarrow {\lambda }^n\left(\omega \right)+\tau \left[\widehat{X}\left(\omega \right)-{\displaystyle \sum }_k{\widehat{u}}_k^{n+1}\left(\omega \right)\right]$.
• Set the judgment accuracy e > 0. If the judgment condition ${\displaystyle \sum }_k\frac{\Vert {\widehat{u}}_k^{n+1}-{\widehat{u}}_k^n{\Vert }_2^2}{\Vert {\widehat{u}}_k^n{\Vert }_2^2}<e$ is not met, then go back to step 2; terminate the iteration if the judgment condition is met. However, the VMD algorithm is somewhat subjective in determining the decomposition parameters K and α during signal processing, which requires a lot of practical experience and repeated attempts. Therefore, this paper introduces the positive cosine algorithm to adaptively determine the above parameters.

2.2. Sine–Cosine Optimisation Algorithm (SCA)

The sine–cosine optimisation algorithm (SCA), as a new stochastic optimisation algorithm based on the population technique, contains two phases, namely, exploration and exploitation, and has the advantages of simple structure, easy implementation and fast convergence [26], which can be used in conjunction with the VMD algorithm to adaptively search for the optimal decomposition parameters K and α.

In the SCA, the following two equations are used for the particle value position update:

$$X_j^{t+1}=X_j^t+{\alpha }_1\times \mathit{sin}({\alpha }_2)\times \left|{\alpha }_3{D}_j^t-X_j^t\right|$$

(4)

$$X_j^{t+1}=X_j^t+{\alpha }_1\times \mathit{cos}({\alpha }_2)\times \left|{\alpha }_3{D}_j^t-X_j^t\right|$$

(5)

where $X_j^t$ is the position of the current solution in the i-th dimension in the t-th iteration; ${\alpha }_1$, ${\alpha }_2$ and ${\alpha }_3$ are random numbers; and $D_j^t$ is the position of the i-th dimension endpoint.

These two equations are usually used in the following combination:

$$X_j^{t+1}=\{\begin{array}{c}{X}_j^t+{\alpha }_1\times \mathit{sin}({\alpha }_2)\times \left|{\alpha }_3{P}_j^t-X_j^t\right|{\alpha }_4<0.5\\ X_j^t+{\alpha }_1\times \mathit{cos}({\alpha }_2)\times \left|{\alpha }_3{P}_j^t-X_j^t\right|{\alpha }_4\ge 0.5\end{array}$$

(6)

where ${\alpha }_4$ is a random number in [0,1].

From Equation (6), SCA has ${\alpha }_1, {\alpha }_2, {\alpha }_3$ and ${\alpha }_4$ main parameters. ${\alpha }_1$ defines the direction of motion, which may or may not lie in the space between the solution and the endpoint; ${\alpha }_2$ determines the distance travelled in the direction of the target or towards the target; ${\alpha }_3$ denotes the stochastic weight of the target; and lastly, the parameter ${\alpha }_4$ toggles between the sine and cosine components in Equation (6).

The search principle of SCA is shown in Figure 1, where the model updates the response location by varying the range of values of the sine and cosine, and the exploration of the search space is guaranteed by determining whether the random location is in space or out of space by determining the defined ${\alpha }_2\in \left[0, 2\pi \right]$. In each iteration, the range of values of the sine and cosine functions in the equations are adaptively adjusted to achieve a balanced exploration and utilisation to find promising regions of the search space, and ultimately, the global optimisation is achieved using Equation (7):

$${\alpha }_1=\nu -t\frac{\nu }{T}$$

(7)

In Equation (7), $\nu$ is a constant, t is the current iteration and T is the maximum number of iterations.

2.3. VMD Based on SCA Parameter Optimisation

In VMD, the sine–cosine algorithm can be used to optimise the parameters K and alpha for optimal decomposition. For this purpose, an adaptive function needs to be defined and the minimum average envelope entropy is defined as the minimum of the average of the envelope entropies of all envelope segments. The performance superiority of the algorithms can be assessed by comparing the MAEE values obtained using the different algorithms since a smaller MAEE value indicates that the algorithm captures the complexity and nonlinear features of the signal better. Therefore, the objective is to find the minimum MAEE value. The minimum mean envelope entropy is the minimum of the average value of the envelope entropy for each segment, i.e.,

$$MAEE=\min \left(\frac{1}{\overline{N}}{{\displaystyle \sum }}_{i=1}^N{H}_i\right)$$

(8)

where N is the number of envelope segments and $H_i$ is the envelope entropy of the i-th envelope segment.

In order to achieve adaptive determination of the optimal decomposition parameters K and alpha for the optimised variational modal decomposition (VMD) based on the sine–cosine algorithm (SCA), the algorithm is designed according to the following steps:

• Initialisation parameters: the initial parameters of the algorithm, including K and alpha, are set using a priori knowledge, experience or random selection.
• Define the fitness function: define the fitness function as shown in Equation (8), i.e., the minimum average envelope entropy.
• SCA optimisation: The sine–cosine algorithm (SCA) is used to optimise the fitness function. In each iteration, the fitness function (MAEE) is minimised by adjusting the parameters K and alpha.
• Iterative process: The parameters K and alpha are progressively optimised over several iterations. In each iteration, the value of the fitness function is calculated, the parameters are updated and the stopping condition is checked to see whether it is met.
• Performance evaluation: During the iteration process, the value of MAEE is monitored. If the MAEE value is found to be small enough and the MAEE no longer changes significantly after the number of iterations is reached, the iteration can be stopped.

In this solution process, the initial population is randomly generated, and each individual represents a set of sine and cosine parameters. For each individual, its sine and cosine parameters are applied to the VMD decomposition, and the calculated envelope entropy is used as the fitness value. The individuals are selected according to their fitness values, and the individual with high fitness is selected as the parent and cross-transformed to generate new individuals. For the newly generated individuals, their sine–cosine parameters are applied to the VMD decomposition, the calculated envelope entropy is used as the fitness value and the newly generated individuals are merged into the current population. According to the iteration number or fitness, determine whether the termination conditions are met; if the termination conditions are not met, continue the selection, crossover, mutation, fitness calculation and population update processes. The optimised VMD decomposition result is finally obtained, and the SCA-VMD algorithm flow is shown in Figure 2.

2.4. Vibration Signal Feature Extraction

Accurate extraction of effective features in transformer vibration signals and the selection of an optimal subset are key aspects of fault identification. A periodic map spectrum, as a widely used tool for analysing the spectral characteristics of signals, can display the energy distribution of signals at different frequencies, which can provide a quick and intuitive understanding of the frequency distribution of signals, and the frequency filtering result, i.e., selecting or excluding certain frequency intervals in order to remove or retain some specific frequency components of the signal, based on the energy occupancy ratios of different frequency intervals [27]. Based on the SCA-VMD decomposition of the measured time-domain signals to obtain the periodic map spectrum, by comparing the periodic map spectrum under different working conditions, it is easier to find out the influence of the faults on the vibration signals, which is conducive to the diagnosis of the cause and location of the faults, and it has a high diagnostic accuracy and robustness.

The following is the flow of generating feature maps after modal decomposition:

• Variational modal decomposition: the signal is decomposed using the VMD algorithm to obtain the kth order mode u_k, where u_k can be expressed as

$$u_k\left(t\right)={{\displaystyle \sum }}_{\omega }{c}_k\left(\omega \right)h_k\left(\omega ,t\right)$$

(9)

where $c_k\left(\omega \right)$ denotes the amplitude of the mode at frequency ω and $h_k\left(\omega ,t\right)$ is a complex amplitude denoting the amplitude of a sinusoidal wave with frequency ω at time t.

2.

Calculate the periodogram: The short-time Fourier transform (STFT) is performed on u_k(t) to obtain the short-time spectrum S_k(ω,t):

$$S_k\left(\omega ,t\right)=\mid {{\displaystyle \sum }}_{T}w\left(\tau \right)u_k\left(t+\tau \right)e^{-j\omega \tau } {\mid }^2$$

(10)

where w(τ) is the window function, which is used to frame the signal. Substituting $u_k\left(t\right)$ into the short-time Fourier transform equation and using Euler’s formula yields

$$S_k\left(\omega ,t\right)=\mid {{\displaystyle \sum }}_{{\omega }^{\prime }}{c}_k\left({\omega }^{\prime }\right){{\displaystyle \sum }}_{\tau }w\left(\tau \right)h_k\left({\omega }^{\prime },t+\tau \right)e^{-j\left({\omega }^{\prime }-\omega \right)\tau } {\mid }^2$$

(11)

Since $h_k\left({\omega }^{\prime },t+\tau \right)$ is an amplitude and can be regarded as a constant, the above equation can be expressed as

$$S_k\left(\omega ,t\right)=\mid {{\displaystyle \sum }}_{{\omega }^{\prime }}{c}_k\left({\omega }^{\prime }\right)H_k\left({\omega }^{\prime },\omega \right)e^{-j{\omega }^{\prime }t} {\mid }^2$$

(12)

$H_k\left({\omega }^{\prime },\omega \right)={{\displaystyle \sum }}_{\tau }w\left(\tau \right)h_k\left({\omega }^{\prime },\tau \right)e^{-j\left({\omega }^{\prime }-\omega \right)\tau }$ can be regarded as the frequency response of the filter and is used to measure the energy of the amplitude of frequency ω’ at frequency ω. Thus, the amplitude energy periodic map spectrum S_k(ω,t) can be derived at moment t with frequency ω.

• Summing by modal components: the total periodic map spectrum S(ω,t) is obtained by summing each modal component.
• Plotting feature maps: After the periodic map spectrum of the vibration signal based on SCA-VMD decomposition is summed up using modal components, the modal components are used as the horizontal axis, the frequency is used as the vertical axis and the brightness of each point represents the energy magnitude of the modal component at the corresponding frequency to plot the feature maps so that we can obtain the energy distributions of the different modal components at different frequencies, which can better reflect the characteristics of the vibration signal faults and the information of the faults.

3. Predictive Models for Data Fusion

3.1. Attention Mechanism

In this study, the periodic map spectrum feature maps obtained based on SCA-VMD are used for fault recognition, but the low resolution of the images and the small change in the value of the energy under different fault types are factors that lead to the poor effect of direct feature map recognition. For this reason, the classification model needs to judge the importance of the information in the image and its position in the image according to the characteristics of the images of different fault characteristics of the transformer to assign different weights to each part of the input feature map and to provide a more effective feature map of transformer fault types for the subsequent GoogLeNet method. In view of this, the above objectives were achieved through the proposed attention mechanism combining the channel attention mechanism and the spatial attention mechanism.

The importance of each feature channel is calculated by reducing the loss function in terms of channel attention computation, and the features with higher correlation are weighted accordingly to improve the representation of the features [28]. This module performs global mean pooling and global maximum pooling on the feature map and derives the mean and maximum values. The resulting features are then fed into a weight-sharing MLP that generates features of the same dimensions as the input and is nonlinearly transformed using the ReLU activation function. Finally, the outputs of the two fully connected layers are summed and the results are normalised to a range between 0 and 1 using a sigmoid function. The resulting values are considered as the weights of each channel, the dot product is taken with the feature map and the weighted feature map based on the channel attention mechanism can be obtained through Equations (13)–(15).

$$T_{channel}=MLP\left(AvgPool\left(F\right)+MaxPool\left(F\right)\right)$$

(13)

$$W_{channel}\left(F\right)=Activation\left(T_{channel}\right)$$

(14)

$$F_{c-weighted}=F·W_{channel}\left(F\right)$$

(15)

F is the input feature; AvgPool(F) and MaxPool(F) denote average and maximum pooling, respectively; and Activation is the sigmoid activation function.

The spatial attention mechanism allows for weighting between the height and width dimensions of the feature map to improve the representation of features [29]. In this module, the input feature map is first compressed in the spatial direction to obtain the mean and maximum values for each spatial location. Then, the two values are spliced and fed into a convolutional layer to obtain the weights for each location. Finally, a dot product is taken between the resulting weights and the input feature maps, and the spatial-attention-mechanism-based weighted feature maps can be obtained using Equations (16)–(18).

$$T_{spatial}=Conv(concat\left(AvgPool\left(F\right),MaxPool\left(F\right)\right)$$

(16)

$$W_{spatial}\left(F\right)=Activation\left(T_{spatial}\right)$$

(17)

$$F_{s-weighted}=F·W_{spatial}\left(F\right)$$

(18)

3.2. GoogLeNet Based on Attention Mechanisms

GoogLeNet model is one of the commonly used convolutional neural network models in the field of image classification and recognition, which has the characteristics of high classification and recognition accuracy and few parameters [30]. Using parallel multiple convolution kernels and pooling layers of different sizes, GoogLeNet effectively captures the features of different scales. It introduces methods such as the Inception structure, depth and width design, parameter efficiency, auxiliary classifier and average pooling, as shown in Figure 3, which makes the network easier to train and optimise. It effectively improves the network expression ability, accuracy and computational efficiency, making it a powerful convolutional neural network model.

An improved GoogLeNet network model based on the attention mechanism is proposed on the basis of the GoogLeNet model to accurately identify different transformer fault types under operating conditions. The attention mechanism enables the network to pay more attention to the more important information for the image classification task by learning the weights of each channel and space, while different fault types correspond to different locations of the key information in the feature map of the periodogram. Therefore, the choice of the attention mechanism allows the network to focus more on the most representative features for the classification task, improves the network’s ability to adapt to the differences between different images, and thus, improves the model’s generalisation ability and recognition accuracy.

The model takes GoogLeNet as the backbone network. Before the input image reaches the first convolutional layer of GoogLeNet, a module based on the spatial attention mechanism is introduced to obtain the weighted feature map based on the spatial attention mechanism, and the weighted feature representations are sent to the first convolutional layer of GoogLeNet and after the last GoogLeNet step for processing. After the Inception module, a module based on the channel attention mechanism is introduced to adaptively adjust the weights of different channels on the feature maps processed by the spatial attention mechanism and the GoogLeNet subject network so that the network pays more attention to the features that are useful for the classification task; this also reduces the influence of redundant features, thus improving the network’s adaptivity. At the same time, this attention mechanism can also reduce the number of parameters in the network and reduce the complexity of the model. The overall architecture of the GoogLeNet model was improved based on the attention mechanism shown in Figure 4.

4. Tests and Analysis of Results

The transformer fault simulation experimental platform was built according to the DL/T industry standard, which mainly includes a transformer, load cabinet, analogue-to-digital converter and host computer. The platform wiring diagram is shown in Figure 5.

The tested transformer is a three-coherent isolated servo SG transformer (see

Table 1. Transformer-related parameters.

Parameter	Value
Input voltage	380 V
Output voltage	220 V
Output voltage accuracy	±1.5%
Rate of change of voltage	≤1.5%
Applicable frequency	50/60 Hz

for related parameters), and the load cabinet is used to adjust the transformer load. The vibration signal was collected using the CT1005LC sensor (see

Table 2. Sensor related parameters.

Parameter	Value
Charge sensitivity (mV/g)	49.7
Frequency range (Hz)	0.5~5000
Operating voltage (VDC)	15~28
Operating current (mA)	2~10
Output amplitude (Vp)	±5

for specific parameters) produced by a company in Shanghai. During the experiment, the vibration signal data of the transformer during normal and fault operation were recorded, and the sampling frequency was set to 2048 Hz.

Using the experimental platform to simulate the four states of the transformer, each subset of the data samples corresponded to an operational state, and the four subsets contained 3200 sets of samples. The four states of the transformer and the state markers are shown in

Table 3. The four operating states of the transformer.

Fault State Type	Fault Simulation Type	Marking
Normal state of operation	Normal operation	0
Loose windings	Reduction in the longitudinal preload of the compression coils (loosening displacement 0.2 cm)	1
Loose core	Loosening bolts and tie bolts for tightening the core (loosening displacement 0.2 cm)	2
Loose base	Loose base reduced base bolt preload (0.2 cm displacement of loose screw)	3

, and the four states were normal, loose winding, loose core and loose base. In the experimental transformer used in this study, the bolts and the fasteners changed their displacement value by 0.2 cm from the time they reached the maximum preload to the time when they just started to be tightened, and beyond 0.2 cm, the reliability and safety of the transformer was in jeopardy and transformer fault identification was required; therefore, a displacement value of 0.2 cm was set to differentiate between these states.

4.1. Comparative Performance Analysis of SCA-VMD Algorithms

The superiority of the performance of this study’s algorithm (SCA-VMD) was verified using the minimum average envelope entropy as a function of fitness. Ten experiments were carried out using the transformer’s normal operating conditions operating data, the average of the 10 experimental data was taken, and the particle swarm optimisation algorithm (PSO-VMD) and genetic algorithms (GA-VMD) were used as comparisons [15]. The comparison of the iteration process of different algorithms is shown in Figure 6. The standard deviation of the average envelope entropy value of the iterative process was sought, and the results are shown in

Table 4. Performance comparison of different algorithms under normal operating conditions.

Methods	Average Iteration Time (s)	Number of Iterations	Minimum Average Envelope Entropy	Standard Deviation
PSO-VMD	19.0	14	7.390	0.176
GA-VMD	26.7	15	7.412	0.128
SCA-VMD	13.5	7	7.323	0.127

: the minimum average envelope entropy of the method proposed in this paper was smaller than that of PSO-VMD and GA-VMD, and the number of iterations was obviously less than that of the comparison algorithms, and the operation efficiency was higher.

4.2. Data Preprocessing and Sample Set Construction

After the initial data sample set was obtained using simulation tests, the data were further preprocessed using SCA-VMD. When performing the periodic map spectrum generation, the Hanning window was selected as the FFT window to ensure the balance of frequency resolution and time resolution.

Figure 7 shows the frequency energy curves and feature maps of each mode of the sample data of transformer fault modes under the four different operating conditions after preprocessing. The following operating conditions were numbered 0–3 in turn. As can be seen from the figure, the periodic pattern spectrum feature map generated using SCA-VMD clearly shows the differences between different types of faults and contains a large number of harmonic components, and the frequency of the harmonic components of each fault state was different, indicating that the selection of periodic pattern spectrum feature map as the basis for transformer fault diagnosis was reasonable and feasible.

4.3. Network Structure and Hyperparameter Settings

During the construction of the experimental model, the input images were first weighted using a spatial-based attention mechanism module. The spatial attention mechanism module was composed of two convolutional layers and sigmoid activation function, where the first convolutional layer had an input channel number of 2, which represented the result after averaging and maximising the input feature maps, and the second convolutional layer had an output channel number of 1, which represented the result after attentional weighting of the input feature maps; in forward propagation, the input feature maps were averaged along the channel dimensions and maximum value, and then spliced together as input; after two convolutional layers and the sigmoid activation function, the attention weight was obtained, and finally, the original feature map was multiplied using the attention weight and fed into the GoogLeNet network. The convolutional layer in the GoogLeNet network used 64 7 × 7 convolutional kernels (step 2, padding 3) and 3 × 3 pooling kernels (step 2, padding 1), the Inception module performed convolutional operations on the inputs using convolutional kernels of different sizes, as shown in Figure 3, and spliced the outputs of multiple different sizes in the channel dimensions, using the LRN layer for local response normalisation, and then performed channel attention weighting on the spliced feature maps, and finally, multiplied the original feature maps by the attention weights and performed dimensionality reduction on the feature maps using global average pooling. The use of two fully connected layers, as well as the use of ReLU and softmax activation functions, had good nonlinearity while the network output a probability distribution.

In the training phase, the loss function was set to the cross-entropy loss, which is most widely used in classification problems. A training mode with a batch size of 64 was used to speed up the network convergence and save computer memory. In the selection of the optimisation algorithms, this study used the gradient-based SGD optimiser method and the learning rate decay strategy, which adjusted the learning rate after every certain epoch. In addition, L2 regularisation and 0.4 dropout were introduced during the training process to avoid the risk of overfitting and enhance the generalisation ability of the model.

4.4. Comparative Analysis of Models

In the experiment, in order to find the optimal division ratio, the model training process sequentially used the ratio parameters 3:1, 4:1 and 5:1 for the same dataset training; in terms of accuracy and running time, the comparison found that the 4:1 division ratio had a higher accuracy and shorter running time. Therefore, in this study, the training set and test set were randomly assigned with a 4:1 ratio. In the process of model evaluation, in order to avoid the influence of random errors, all algorithms were run 75 times, and the average recognition accuracy (including standard deviation) was used as the final evaluation index. Figure 8 shows the trend of loss and recognition accuracy of different models during training.

Table 5. Average test accuracy of different classification models (%).

Model	Average Recognition Accuracy	Standard Deviation
GoogLeNet	97.97	0.65
Spatial Attention–GoogLeNet	98.72	0.57
Channel Attention–GoogLeNet	98.44	0.60
Attention–GoogLeNet	99.04	0.51

gives the average recognition accuracy and standard deviation of different models on the test set.

As shown in Figure 8, although the initial loss values of the four models were not at the same level, the overall trend of the loss changes during the training process was more similar, which was due to the fact that the different models were based on the traditional GoogLeNet as the basic architecture. As the iteration proceeded, the loss values of GoogLeNet improved based on the spatial attention mechanism and GoogLeNet improved based on the channel attention mechanism decrease occurring at a slightly faster rate than the traditional GoogLeNet decrease rate, whereas the GoogLeNet improved based on both the spatial and channel attention mechanisms developed in this study, as seen by the fastest decrease rate of the loss and was the first to reach stabilisation, which was related to the different models of the attention mechanisms introduced. After about 60 epochs, the losses of the different models did not continue to significantly drop but fluctuated within a fairly small range, indicating that the models had converged. In terms of the training accuracy, the overall trend of different models was highly correlated with the trend of the model loss. After convergence, for the training dataset, the recognition accuracies of the different models, except the traditional GoogLeNet, reached high levels, fluctuating above 99.8%.

Although the differences between the different models were not significant on the training set, the differences were more pronounced when dealing with the test set. As shown in Table 5, the average accuracy of the traditional GoogLeNet model on the test set was 97.97%, with a standard deviation of 0.65%, whereas the channel and spatial attention models had accuracies of 98.72% and 98.44%, respectively, with a smaller standard deviation. Compared with the traditional GoogLeNet model and the improved model with different attention mechanisms, the developed GoogLeNet improved with spatial- and channel-based attention mechanisms had the highest average accuracy of 99.04% during testing. This indicates that the introduction of different attention mechanisms could improve the accuracy of the model to some extent. In addition, the experimental results from the test set show that the processing power of the channel-based classification model was more advantageous than the spatial-based classification model.

Figure 9 compares the classification accuracy of four different models on the test set using a confusion matrix. Overall, most of the misdiagnosed samples appeared between 0 and 1 states, and the cause of misdiagnosis may have been a slight difference in the original data, and for most categories, the type of the sample could be fully identified.

4.5. Performance Comparison and Analysis of Different Models

In order to comprehensively evaluate the performances of different models in the fault identification task, a series of comparative experiments were conducted in this study. As shown in Figure 10, this chapter selects representative machine learning SVM, random forest, K-nearest neighbour algorithm and deep learning CNN, GAN and LSTM algorithms as the comparison object, aiming at clarifying the superiority of transformer fault diagnosis model proposed in this paper relative to other models by comparing the recognition accuracy performance indexes of the models, and providing scientific basis for its practical application.

As shown in Figure 10,the fault diagnosis model proposed in this study achieved a high accuracy of 99.04% in the experiment. In contrast, the accuracies of all models under either machine or deep learning were not above 99.00%. The above data show that the periodic map spectrum calculated after mode decomposition by SCA-VMD was used as the feature input. And using the attention mechanism to improve GoogLeNet on the transformer fault diagnosis task showed obvious superiority, and its accuracy was much higher than other models, which provides strong support for its reliability and effectiveness in practical engineering applications.

In order to further verify the classification performance of the proposed scheme, it was compared with methods found in the literature [19,20]. Ref. [19] and this study transformed the transformer vibration signal into different images and extracted the effective features of the signal to achieve high-accuracy fault diagnosis under different operating conditions. Ref. [20] was similar to the initial data processing methods carried out in this study, both of which mined the fault feature information after the adaptive decomposition of the vibration signals and used a two-level diagnostic model based on SSA-KELM for fault diagnosis. Using the dataset collected in this study, the proposed method was compared with the methods used in [19] and [20].

As shown in

Table 6. Comparison of test results of different methods.

Methodologies	Accuracy (%)
Ref. [19]	97.36
Ref. [20]	97.28
Proposed programme	99.04

, upon comparison, it can be found that the accuracy of the proposed scheme applied to dry-type transformers and oil-immersed transformers was higher than that of other methods, which indicates the reasonableness of the proposed SCA-VMD adaptive decomposition to compute the periodogram as a feature after combining the improved GoogLeNet for fault diagnosis.

5. Discussion

In this study, the periodic map spectrum was used as a feature map and combined with GoogLeNet in transformer fault diagnosis, which addressed the influence of traditional diagnostic methods that ignore the additional harmonic and non-harmonic components of transformer vibration signals on fault diagnosis based on vibration signals. The aim of this study was to combine SCA-VMD with improved GoogLeNet to build a diagnostic model for transformer fault diagnosis. The feasibility of the proposed method and the accuracy of fault diagnosis were found through experimental validation. The results show that compared with the traditional diagnostic model, the method had significantly fewer iterations in data processing and fault type identification than the comparative algorithms, and operated more efficiently and with higher identification accuracy.

6. Conclusions

The transformer was accompanied by different amplitude vibration signals under different operating conditions. The accuracy and rapidity of fault classification depended on the accuracy of feature extraction of the vibration signal periodic map spectrum and the optimisation degree of the classification model. In this study, the following conclusions were obtained:

• A method based on SCA-VMD mode decomposition was proposed. SCA was used to adaptively optimise the parameters, that is, the number of modes and penalty factor, to optimise the decomposition effect of VMD and improve the input quality of the prediction model.
• The feature extraction method of the periodic map spectrum generated after the SCA-VMD was used. The periodic map spectrum feature map reflected the difference in the energy distribution of the different mode components at different frequencies to reflect the different fault types of transformers.
• This paper proposes GoogLeNet optimised by an attention mechanism to realise transformer fault diagnosis. The spatial and channel attention mechanisms are combined with different layers of the periodic map spectrum for the corresponding weighting, which improves the accuracy of the GoogLeNet classification model.

The datasets used in the experiments were usually limited and covered a certain number of fault modes, the diagnosis of unknown fault modes may be poor, and obtaining a sufficient number and diversity of fault data may become an expensive and time-consuming task. The research work following this paper will be devoted to introducing more data types to enable the improvement and optimisation of transformer fault diagnosis methods based on SCA-VMD and the improved GoogLeNet.