Diagnosis of Power Transformer On-Load Tap Changer Mechanical Faults Based on SABO-Optimized TVFEMD and TCN-GRU Hybrid Network

Abstract

Accurate mechanical fault diagnosis of On-Load Tap Changers (OLTCs) remains crucial for power system reliability yet faces challenges from vibration signals’ non-stationary characteristics and limitations of conventional methods. This paper develops a hybrid framework combining metaheuristic-optimized decomposition with hierarchical temporal learning. The methodology employs a Subtraction-Average-Based Optimizer (SABO) to adaptively configure Time-Varying Filtered Empirical Mode Decomposition (TVFEMD), effectively resolving mode mixing through optimized parameter selection. The decomposed components undergo dual-stage temporal processing: A Temporal Convolutional Network (TCN) extracts multi-scale dependencies via dilated convolution architecture, followed by Gated Recurrent Unit (GRU) layers capturing dynamic temporal patterns. An experimental platform was established using a KM-type OLTC to acquire vibration signals under typical mechanical faults, subsequently constructing the dataset. Experimental validation demonstrates superior classification accuracy compared to conventional decomposition–classification approaches in distinguishing complex mechanical anomalies, achieving a classification accuracy of 96.38%. The framework achieves significant accuracy improvement over baseline methods while maintaining computational efficiency, validated through comprehensive mechanical fault simulations. This parameter-adaptive methodology demonstrates enhanced stability in signal decomposition and improved temporal feature discernment, proving particularly effective in handling non-stationary vibration signals under real operational conditions. The results establish practical viability for industrial condition monitoring applications through robust feature extraction and reliable fault pattern recognition.

1. Introduction

As a critical infrastructure of modern society, the stable and reliable operation of power systems plays a pivotal role in ensuring industrial production, residential life, and the steady development of the socioeconomic framework [1] The On-Load Tap Changer (OLTC), a vital component of power transformers, adjusts the winding turns ratio to regulate output voltage while the transformer is under load. This functionality ensures voltage stability, enhances power quality, and optimizes the efficiency of power system operations [2]. With the increasing demands for higher voltage and larger capacity in power systems, the operating conditions of power transformers have become more complex and stringent, leading to a significant rise in OLTC switching frequency. Prolonged and frequent operation exposes OLTC components, such as contacts, drive mechanisms, and insulating materials, to various combined stresses, including electrical, thermal, and mechanical. These stresses inevitably result in wear, fatigue, overheating, and discharge failures [3,4]. If OLTC failures are not promptly detected and addressed, they may cause transformer malfunctions or outages, leading to widespread power outages, compromising power system reliability and safety, and causing significant economic and social impacts [5,6].

In recent years, vibration signal analysis has been extensively studied and applied in mechanical fault diagnosis. During OLTC operations, the mechanical motion of internal components and electrical switching inevitably generate vibrations, which encapsulate abundant information closely related to the equipment’s operational state. Bengtsson et al. first proposed an online OLTC mechanical condition monitoring method based on vibration signals, which garnered significant attention for its simplicity and accuracy [7]. By collecting, processing, and analyzing vibration signals, it is possible to achieve early fault detection, localization, and severity assessment. Vibration-based OLTC fault diagnosis is noninvasive, supports online monitoring, and is sensitive to early faults, making it an effective technique for OLTC condition monitoring and fault diagnosis [8,9]. To efficiently extract weak fault features from vibration signals, particularly given their nonstationary and nonlinear nature, various signal processing methods have been developed. Empirical Mode Decomposition (EMD) and its derivatives have shown potential in handling nonstationary and nonlinear vibration signals. For instance, Ensemble Empirical Mode Decomposition (EEMD) partially mitigates mode mixing but suffers from residual noise. Variational Mode Decomposition (VMD), a novel adaptive signal decomposition method, demonstrates improved decomposition accuracy and noise resistance by resolving a variational problem to decompose signals into mode components with specific bandwidths [10,11]. However, existing methods like EMD, EEMD, and VMD struggle with OLTC vibration signals characterized by strong background noise, multimodal coupling, and complex time-varying properties, limiting their ability to extract subtle fault features or distinguish complex fault modes [12,13,14]. Wang et al. introduced Time-Varying Filtering Empirical Mode Decomposition (TVFEMD), which alleviates mode mixing and cumulative decomposition errors by incorporating time-varying filters, effectively preserving time-varying characteristics without enforcing symmetric envelopes [15]. However, the performance of TVFEMD heavily depends on two key parameters: bandwidth threshold, which affects modal separation, and B-spline order, which impacts filtering performance. Given the efficiency of the Subtraction-Average-Based Optimizer (SABO) in optimization tasks, this study employs an SABO to adaptively optimize TVFEMD parameters [16,17].

Traditional fault diagnosis methods often rely on expert experience and predefined rules, which struggle to handle complex multimodal signals and nonlinear fault modes effectively. The rapid development of machine learning and deep learning has introduced new paradigms for fault diagnosis. Deep learning excels at extracting features and modeling from large-scale data, enabling efficient recognition of complex patterns for precise classification. While traditional machine learning algorithms like SVM, ELM, and XGBoost achieve fault classification, they require handcrafted features and involve complex computations. Deep learning approaches, including Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM) networks, and transformer models, are widely used in fault diagnosis. The CNN excels in extracting spatial features but struggles with long-range dependencies in time series data. LSTM is adept at capturing temporal dynamics but is computationally intensive, particularly for large datasets. Transformers excel in modeling long-range dependencies but require substantial data and computational resources [18,19]. In contrast, Temporal Convolutional Networks (TCNs) have emerged as a popular choice for time-series analysis due to their ability to capture long-range dependencies and parallelize computations effectively [20]. Gated Recurrent Units (GRUs), a simplified variant of recurrent neural networks, offer reduced computational complexity and excellent performance for dynamic time-series data [21,22]. This study combines a TCN and GRU to develop a fault diagnosis model, leveraging the TCN’s parallel processing capabilities and GRU’s dynamic memory properties to efficiently model and classify complex time-series signals. Hyperparameter optimization further enhances model performance, providing a novel solution for fault diagnosis under complex operating conditions.

This study addresses the key challenges in the fault diagnosis of OLTC vibration signals by integrating vibration signal processing techniques with machine learning algorithms. A hybrid optimization method based on TVFEMD and a GRU is proposed. The SABO algorithm is introduced to adaptively optimize the parameter settings of TVFEMD, preserving time-varying characteristics and reducing mode mixing, thereby achieving precise decomposition of vibration signals. Additionally, features extracted via the TCN neural network are fed into the GRU for fault classification and recognition, further enhancing diagnostic performance. This method fully considers the nonstationary and complex nature of vibration signals, overcoming the limitations of traditional diagnostic methods in handling complex fault modes. It provides a more precise, reliable, and intelligent fault diagnosis solution for the reliable operation of OLTC in power systems.

The structure of this paper is organized as follows: Section 2 introduces the theoretical foundations of SABO-TVFEMD and TCN-GRU. Section 3 describes the experimental setup for simulating typical OLTC mechanical faults and presents an initial analysis of the collected vibration signals. Section 4 details the application of the proposed method to experimental data, including feature extraction, diagnostic results, and comparisons with commonly used methods. Finally, Section 5 summarizes the main findings of this study and discusses future research directions.

2. Theoretical Foundation

The key to mechanical fault diagnosis lies in efficiently extracting critical features from signals and accurately classifying them [23]. This study combines signal decomposition techniques with deep learning models to propose a fault diagnosis method based on SABO-TVFEMD-TCN-GRU. The method centers on the optimized TVFEMD, utilizing the SABO algorithm to adaptively adjust decomposition parameters. This overcomes the mode mixing and parameter dependency issues encountered by traditional signal decomposition techniques when processing nonstationary signals. Additionally, the TCN-GRU model is employed to capture the time-frequency characteristics of signals, enabling accurate classification of vibration signals. The theoretical foundation section elaborates on the signal decomposition principles of TVFEMD, the design of the SABO optimization algorithm, and the advantages of the TCN and GRU in extracting temporal features, providing a theoretical basis for constructing the fault diagnosis model.

2.1. Time-Varying Filtered Empirical Mode Decomposition

Time-Varying Filtered Empirical Mode Decomposition (TVFEMD) essentially employs a low-pass filter with a time-varying cutoff frequency to perform iterative mean removal during the EMD process. Local narrowband signals replace intrinsic mode functions (IMFs) as the iterative stopping criterion, effectively addressing intermittency and mode mixing when handling nonlinear and nonstationary signals. The TVFEMD process is divided into two main stages: local cutoff frequency rearrangement and time-varying filtering-based sifting [15,24,25].

(1)

Local Cutoff Frequency Rearrangement to Eliminate Mode Mixing.

Step 1: According to Hilbert decomposition theory, any real-valued signal $x(t)$ can be transformed into an analytic signal $z\left(t\right)$ through the Hilbert transform:

$$z(t)=x(t)+j\hat{x}\left(t\right)=A(t)e^{j\phi (t)}=a_1\left(t\right)e^{j{\phi }_1(t)}+a_2\left(t\right)e^{j{\phi }_2(t)}$$

(1)

$$A^2\left(t\right)=a_1^2(t)+a_2^2(t)+2a_1(t)a_2(t)\cos [{\phi }_1(t)-{\phi }_2(t)]$$

(2)

where $A(t)$, $a(t)$ represents the amplitude, and $\phi \left(t\right)$ represents the phase.

Step 2: When $\cos [{\phi }_1(t)-{\phi }_2(t)]=1$, $A(t)$ represents a local maximum; when $\cos [{\phi }_1(t)-{\phi }_2(t)]=-1$, $A(t)$ represents a local minimum. For all the local maxima points $\left\{t_{\max },A\left(t_{\max }\right)\right\}$ and local minima points $\left\{t_{\min },A\left(t_{\min }\right)\right\}$ of $A(t)$, interpolation is performed to obtain the curves ${\beta }_1(t)$ and ${\beta }_2(t)$, respectively. As a result, the following expression can be derived:

$$\begin{array}{l}{a}_1\left(t\right)=\left[{\beta }_1(t)+{\beta }_2(t)\right]/2\\ a_2\left(t\right)=\left[{\beta }_2(t)-{\beta }_1(t)\right]/2\end{array}$$

(3)

Step 3: For all the local maxima points $\left\{t_{\max },A^2\left(t_{\max }\right)\right\}$ and local minima points $\left\{t_{\min },A^2\left(t_{\min }\right)\right\}$ of $A^2(t)$, interpolate to obtain ${\eta }_1(t)$, ${\eta }_2(t)$ and define the following:

$$\begin{array}{l}{\eta }_1(t)={{\phi }^{\prime }}_1\left(t\right)\left[a_1^2\left(t\right)-a_1\left(t\right)a_2\left(t\right)\right]+{{\phi }^{\prime }}_2\left(t\right)\left[a_2^2\left(t\right)-a_1\left(t\right)a_2\left(t\right)\right]\\ {\eta }_2(t)={{\phi }^{\prime }}_1\left(t\right)\left[a_1^2\left(t\right)+a_1\left(t\right)a_2\left(t\right)\right]+{{\phi }^{\prime }}_2\left(t\right)\left[a_2^2\left(t\right)+a_1\left(t\right)a_2\left(t\right)\right]\end{array}$$

(4)

where ${{\phi }^{\prime }}_1\left(t\right)$ and ${{\phi }^{\prime }}_2\left(t\right)$ are the derivatives of ${\phi }_1(t)$ and ${\phi }_2(t)$, respectively, and the local cutoff frequency ${{\phi }^{\prime }}_{bis}(t)$ is defined as follows:

$${{\phi }^{\prime }}_{bis}(t)={\displaystyle \frac{\left[{{\phi }^{\prime }}_1(t)+{{\phi }^{\prime }}_2(t)\right]}{2}}={\displaystyle \frac{{\eta }_2\left(t\right)-{\eta }_1\left(t\right)}{4a_1(t)a_2(t)}}$$

(5)

Step 4: Define the time sequence of the local maxima points of the signal $x(t)$ as $u_i,i=1,2,3\dots$. if

$${\displaystyle \frac{\max \left[{{\phi }^{\prime }}_{bis}(u_i:u_{i+1})\right]-\min \left[{{\phi }^{\prime }}_{bis}(u_i:u_{i+1})\right]}{\min \left[{{\phi }^{\prime }}_{bis}(u_i:u_{i+1})\right]}}>\rho$$

(6)

If the above condition holds (with $\rho$ = 0.25 in this study), then $u_i$ is considered a discontinuity point, and $e_j=u_i,j=1,2,3\dots$, $e_j$ represents the discontinuity point sequence. If ${{\phi }^{\prime }}_{bis}(u_{i+1})-{{\phi }^{\prime }}_{bis}(u_i)>0$, $e_j$ is considered the rising edge of ${{\phi }^{\prime }}_{bis}(t)$, and ${{\phi }^{\prime }}_{bis}(e_{j-1}:e_j)$ is regarded as the minimum value; if ${{\phi }^{\prime }}_{bis}(u_{i+1})-{{\phi }^{\prime }}_{bis}(u_i)<0$, $e_j$ is considered the falling edge of ${{\phi }^{\prime }}_{bis}(t)$, and ${{\phi }^{\prime }}_{bis}(e_{j-1}:e_j)$ is regarded as the minimum value. The remaining part of ${{\phi }^{\prime }}_{bis}(t)$ is considered the peak value.

Step 5: Perform interpolation between all peak values to obtain the rearranged local cutoff frequency ${{\phi }^{\prime }}_{bis}(t)$.

(2)

Filtering Stage Based on Time-Varying Filters.

Step 1: Reconstruct the signal based on the rearranged cutoff frequency:

$$h(t)=\cos \left[{\displaystyle \int {{\phi }^{\prime }}_{bis}(t)dt}\right]$$

(7)

Use the extrema of $h(t)$ as nodes, and divide $h(t)$ into n segments, each with a step size of m. Here, n is referred to as the order of the B-spline function. Perform B-spline interpolation between the extrema, and the result is denoted as $m(t)$, representing the local mean curve.

Step 2: Check whether the residual signal $\theta \left(t\right)$ satisfies the stopping criterion $\theta \left(t\right)<\xi$, where $\xi$ is the given bandwidth threshold. If it does, then $x\left(t\right)$ is the IMF; otherwise, set $x\left(t\right)=x\left(t\right)-m(t)$, and repeat all previous steps until the stopping criterion is met. The formulas for Loughlin’s instantaneous bandwidth and the weighted average instantaneous frequency are given in Equations (9) and (10).

$$\theta (t)={\displaystyle \frac{B_{Loughlin}(t)}{{\phi }_{avg}(t)}}$$

(8)

$$B_{Loughlin}(t)=\sqrt{{\displaystyle \frac{{a^{\prime }}_1^2(t)+{a^{\prime }}_2^2(t)}{a_1^2(t)+a_2^2(t)}}+{\displaystyle \frac{a_1^2(t)a_2^2(t){\left({{\phi }^{\prime }}_1\left(t\right)-{{\phi }^{\prime }}_2\left(t\right)\right)}^2}{{\left(a_1^2(t)+a_2^2(t)\right)}^2}}}$$

(9)

$${\phi }_{avg}(t)={\displaystyle \frac{a_1^2(t){{\phi }^{\prime }}_1\left(t\right)+a_2^2(t){{\phi }^{\prime }}_2\left(t\right)}{a_1^2(t)+a_2^2(t)}}$$

(10)

2.2. Subtraction-Average-Based Optimizer

The TVFEMD process requires a predefined bandwidth threshold $\xi$ and B-spline order n, introducing subjectivity and uncertainty. The Subtraction-Average-Based Optimizer (SABO), a metaheuristic optimization algorithm, is employed to optimize these parameters. Its basic principle is to update each agent’s position using the subtraction-average operation of all agents in the search space, iteratively converging toward the optimal solution. The SABO algorithm follows these steps [26,27]:

First, define the operator “${-}_v$” as

$$A{-}_{v}B=sign\left(F\left(A\right)-F\left(B\right)\right)\left(A-\overline{v}\ast B\right)$$

(11)

A and B are different individuals, and sign is the sign function. F(A) and F(B) represent the fitness values of A and B, respectively. $\overline{v}$ is a vector with the same dimension as the search space. Each of its components is a random number generated from the set {1, 2}; $\ast$ represents the Hadamard product of two vectors.

Randomly initialize the population in the optimization space:

$$x_{i,j}=l_{bj}+r\cdot (u_{bj}-l_{bj})$$

(12)

where $x_{i,j}$ represents an individual. $u_{bj}$ represents the upper boundary of the optimization problem, while $l_{bj}$ is the lower bound for optimization and is a randomly generated value within the range [0, 1]. In the SABO, the displacement of any search agent $x_i$ in the search space is calculated through the arithmetic mean of the “${-}_v$” of each search agent $x_j$. The new position of each search agent is calculated as follows:

$$X_i^{new}=x_i+{\overrightarrow{r}}_i\ast {\displaystyle \frac{1}{N}}{\displaystyle \sum _{j=1}^N\left(X_i-v{X}_j\right)},\hspace{1em}i=1,2,\dots N$$

(13)

where ${\overrightarrow{r}}_i$ is a vector with the same dimension as the search space, consisting of random numbers between [0, 1]. N is the total number of individuals. $X_i^{new}$ is the latest calculated position of the i-th individual. If the new position is better, it replaces the previous position; otherwise, the following rule holds:

$$X_i=\left\{\begin{array}{l}{X}_i^{new}, F_i^{new}<F_i\\ X_i, else\end{array}\right.$$

(14)

$F_i^{new}$ and $F_i$ represent the objective function values of the search agent $X_i^{new}$ and $X_i$, respectively.

To validate the optimization performance of the SABO algorithm, the CEC2005 optimization benchmark function set was selected for testing. Single-peak functions F1 and F2 were chosen to evaluate the optimization accuracy and speed of the algorithm, while multi-peak functions F9 and F10 were used to test the algorithm’s global optimization capability and its ability to escape local optima. The expressions and search spaces of the test functions are shown in

Table 1. Test function expressions and search spaces.

Function	Expression	Search Space
F1	${\displaystyle \sum _{i=1}^n{x}_i^2}$	[−100,100]
F2	${\displaystyle \sum _{i=1}^n\left|x_i\right|}+{\displaystyle \prod _{i=1}^n\left|x_i\right|}$	[−10,10]
F9	$10n+{\displaystyle \sum _{i=1}^n[x_i^2-10\cos (2\pi x_i)]}$	[−5.12,5.12]
F10	$-20\exp \left(-0.2\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{x}_i^2}}\right)-\exp \left({\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\cos (2\pi x_i)}\right)+20+e$	[−32,32]

[28,29].

The functions listed in Table 1 were used to evaluate and compare the optimization performance of the SABO algorithm, Particle Swarm Optimization (PSO) algorithm, and Grey Wolf Optimization (GWO) algorithm [30,31]. The experiments were configured with 1000 iterations and a population size of 100. Figure 1a–d display the 3D representations of the four test functions along with the convergence curves for each algorithm. The results shown in the figures indicate that the SABO algorithm consistently achieves the optimal value first across all test functions. This demonstrates its significant advantages in terms of global optimization capability and convergence speed, as well as its strong ability to escape local optima.

2.3. Temporal Convolutional Network

The Temporal Convolutional Network (TCN) is a deep learning architecture specifically designed for modeling sequential data. With its capability to efficiently capture long-range dependencies in time-series signals and its advantages in parallel computation, the TCN has become a popular method in the field of sequence analysis [32]. Theoretically, it significantly enhances model prediction accuracy.

Compared with traditional methods like the CNN and RNN, the TCN leverages techniques such as dilated convolutions, long-range dependency modeling, and residual connections to better extract features from sequential data, offering superior modeling capacity and flexibility. Its strengths include strong capabilities for modeling long-term dependencies, efficient handling of variable-length sequences, and translation invariance. These make theTCN highly performant and scalable for time-series data processing while avoiding issues like vanishing or exploding gradients [33]. The specific structure of the TCN model is shown in Figure 2 [34]. The TCN network structure includes the following [31]:

(1)

Residual Block: To mitigate gradient vanishing and exploding problems in deep networks, the TCN employs residual connections to enhance stability and training efficiency while maintaining model complexity. As shown in Figure 2a,b, the TCN module is primarily composed of multiple residual blocks, each consisting of four main parts: the dilated causal convolution layer (Dilated Causal Conv), normalization layer (WeightNorm), activation function layer (ReLU), regularization layer (Dropout).

(2)

Dilated Causal Convolution: This is the core operation of the TCN, combining the temporal dependence of causal convolution with the long-range modeling capability of dilated convolution. It allows the TCN to efficiently handle long-range dependencies in time-series data. Its structure is depicted in Figure 2c. Unlike recurrent neural networks (e.g., LSTM and GRUs) that process sequential data step-by-step, dilated causal convolution achieves parallel computation through convolution operations, improving computational efficiency. This method ensures causality in time-series modeling, extends the receptive field, captures richer temporal features with a shallower network, and supports efficient parallel computation.

2.4. Gated Recurrent Unit

The Gated Recurrent Unit (GRU) is a variant of the Recurrent Neural Network (RNN). It was designed to address the gradient vanishing and exploding problems that traditional RNNs encounter when processing long sequence data, enabling more effective modeling of sequential data [35]. Compared with Long Short-Term Memory (LSTM) networks, the GRU simplifies the structure by merging the input gate and forget gate into a single update gate, which plays a critical role in controlling the retention of information. Additionally, the GRU replaces the output gate in LSTM with a reset gate, which flexibly adjusts how the current state interacts with previous information. The structure of a GRU is shown in Figure 3, and its mathematical representation is described in Equation (15) [36,37]:

$$\left\{\begin{array}{l}{z}_t=\sigma \left(w_{(x,z)}^T{x}_t+w_{(h,z)}^T{h}_{t-1}\right)\\ r_t=\sigma \left(w_{(x,r)}^T{x}_t+w_{(h,r)}^T{h}_{t-1}\right)\\ g_t=\tanh [w_{(x,g)}^T{x}_t+w_{(h,g)}^T(r\otimes h_{t-1})]\\ h_t=(-z_t)\otimes h_{t-1}+z_t\otimes g_t\end{array}\right.$$

(15)

where $x_t$ is the input at time t, $h_t$ is the output or state at time t, $h_{t-1}$ is the state at time $t-1$, w is the weight, $\sigma$ is the sigmoid activation function, and $\tanh$ is the hyperbolic tangent activation function.

2.5. Fault Diagnosis Model Based on SABO-TVFEMD-TCN-GRU

Based on the advantages of the SABO algorithm, this paper applies an SABO to optimize TVFEMD in order to search for the optimal bandwidth threshold $\xi$ and B-spline order $n$. The minimum information entropy is selected as the fitness function, as shown in Equation (16). In the equation, the normalized energy of the i-th component is typically represented as follows:

$$H(x)=-{\displaystyle \sum _{i=1}^n{p}_i\log {}_{2}p_i}$$

(16)

Through SABO-TVFEMD, different IMF components with different time-frequency characteristics are obtained. These IMFs are then input into the TCN-GRU model for fault classification and diagnosis. The TCN-GRU model combines the advantages of the TCN in capturing long-sequence global dependency features and the GRU’s efficiency in capturing dynamic temporal changes, enabling more accurate processing of non-stationary signals for precise fault feature classification and diagnosis [38,39]. The flowchart of the proposed method is shown in Figure 4. The fault diagnosis process is described as follows:

Step 1: Simulate typical mechanical faults of OLTC through experiments and collect the vibration signals generated during the process.

Step 2: Divide the data into a training set and a validation set to prepare for subsequent model training and testing.

Step 3: Use the SABO algorithm to search and optimize two key parameters of TVFEMD (bandwidth threshold $\xi$ and B-spline order $n$), return the parameter combinations, and use TVFEMD to decompose the signal, evaluating the quality of each parameter set using minimum information entropy $H(x)$ as the fitness function.

Step 4: Update the search agents and continually adjust the bandwidth threshold $\xi$ and B-spline order $n$ until the termination condition is met.

Step 5: Use the best parameter combination obtained from optimization, apply TVFEMD to decompose the vibration signal, and generate IMF components.

Step 6: Input the decomposed IMF components into the TCN-GRU classification model for training and classification.

Step 7: Output the fault diagnosis results.

3. OLTC Mechanical Fault Simulation Experiment

This study uses a certain KM-type combined OLTC as the experimental object and sets up an experimental platform as shown in Figure 5a. Figure 5b depicts the experimental OLTC, while Figure 5c shows the sensor layout. To provide data support for the fault diagnosis model, vibration signals were collected by simulating typical mechanical faults of the OLTC. To analyze the vibration characteristics of the OLTC under different fault conditions, three typical mechanical faults were designed, as presented in the schematic diagram in Figure 6: (a) transmission shaft gear jamming, simulated by inserting wood chips into the gear box of the switch drive mechanism; (b) transmission shaft screw loosening, achieved by loosening the screws at the connection of the transmission rod; and (c) arcing plate loosening, realized by loosening the screws fixing the arcing plate. In this experiment, a voltage output accelerometer with a sensitivity of 50 V/g was installed at the flange of the OLTC top. Given that the vibration signals generated during the switching action of the OLTC feature impact characteristics and have a frequency range of approximately 50 Hz to 10 kHz, the signal sampling rate was set to 25 kHz.

Multiple tests at the same gear position and multiple groups of tests at multiple gear positions were carried out, respectively, under normal working conditions and the set fault working conditions. Figure 7 shows the vibration signal waveforms during the operation period of the switching switch when switching from the 3rd gear position to the 4th gear position under four working conditions. During the operation stage of the switching switch, the overall amplitude of the vibration data reached its peak value. The information content in this stage is the richest, which is the key basis for judging the mechanical faults of the OLTC [40].

As illustrated in Figure 7, a distinct pattern can be observed during the switching action phase, wherein the vibration waveform exhibits four prominent peaks, each closely corresponding to the sequential operations of the OLTC contacts. A comparative analysis of the vibration waveforms under various operating conditions reveals notable differences in amplitude. Under normal conditions, the peak vibration amplitude is recorded at 3.614 g. In contrast, this value increases significantly under fault conditions: 7.069 g for the transmission shaft gear jamming fault, 5.100 g for the transmission shaft screw loosening fault, and 5.610 g for the arcing plate loosening fault. These results clearly indicate that the peak vibration amplitudes associated with fault conditions are substantially higher than those observed during normal operation, with the gear jamming and arcing plate loosening faults exhibiting particularly prominent peak values.

This substantial variation indicates that changes in operating conditions have a profound impact on vibration characteristics. However, relying solely on time-domain waveform analysis falls short of fully uncovering the intrinsic characteristics of vibration signals and potential fault modes. Therefore, further decomposition and feature extraction of vibration signals are essential to extract key fault diagnosis information.

4. Data Analysis

4.1. Signal Decomposition Results Based on SABO-TVFEMD

According to the previously described method and steps, the search range for the SABO and the optimal TVFEMD parameter results for each operating condition are presented in

Table 2. SABO search range and optimal TVFEMD parameter results.

Parameter	Search Range	Search Results
		Normal	Fault 1	Fault 2	Fault 3
$\xi$	[0.1,0.15,0.2,0.25,0.3]	0.2	0.25	0.25	0.2
n	[10,15,20,25,30]	25	20	20	15

. Specifically, Faults 1–3 correspond to the following mechanical fault conditions: transmission shaft gear jamming, transmission shaft screw loosening, and arcing plate loosening.

Figure 8a presents the SABO-TVFEMD results of vibration signals under normal operating conditions, while Figure 8b illustrates the spectral plots of each IMF.

Table 3. Distribution table of energy ratios and peak frequencies of IMFs depicted in Figure 8.

IMFs	Energy Ratios	Peak Frequencies	IMFs	Energy Ratios	Peak Frequencies
IMF1	8.01%	2139.43 Hz	IMF6	0.92%	239.94 Hz
IMF2	45.08%	1766.20 Hz	IMF7	0.04%	59.98 Hz
IMF3	27.70%	726.47 Hz	IMF8	0.03%	26.66 Hz
IMF4	10.65%	499.87 Hz	IMF9	0.06%	13.33 Hz
IMF5	7.44%	339.91 Hz	IMF10	0.07%	0.51 Hz

systematically summarizes the energy ratios and peak frequencies of every IMF shown in Figure 8. Analysis shows that IMF1 to IMF5 capture 98.88% of the total energy, with no mode mixing observed in any IMF. This confirms the effectiveness of the decomposition, indicating that the primary vibration components are concentrated in these five IMFs, while the others mainly represent noise. Therefore, the subsequent analysis focuses on IMF1 to IMF5.

Figure 9a–c respectively show the time-domain waveforms and frequency spectra of IMF1-IMF5 after SABO-TVFEMD decomposition under three fault operating conditions. The results indicate that IMF1 to IMF5 display distinct fluctuations in the time domain, and their frequency spectra clearly delineate the main frequency ranges of these components. The lack of frequency aliasing further validates the high quality of the decomposition. By comparing the decomposition results of different conditions, significant disparities in both time-domain and frequency-domain characteristics can be observed. These findings lay a solid data foundation for subsequent research and development.

4.2. Fault Diagnosis Based on the TCN-GRU

In the OLTC mechanical fault simulation experiment, 200 sets of vibration data were collected for each operating condition. The data were partitioned into a training set and a test set at a ratio of 8:2. Specifically, the training set consists of 160 sets of signals for each operating condition, amounting to 640 sets in total. The test set is composed of 40 sets of signals for each operating condition, totaling 160 sets. Each signal sample was preprocessed using the SABO-TVFEMD method, and IMF1-IMF5 derived from the decomposition was used as input for the TCN-GRU model. The grid search algorithm was applied to optimize the selected parameters of the TCN-GRU model. The final parameter settings are presented in

Table 4. Parameters of the TCN-GRU model.

Parameters	Optimization Range	Optimal Parameters
Kernel size	{2, 3, 4, 5}	3
Number of filters	{32, 64, 128}	64
Dilation factors	/	[1, 2, 4]
Residual blocks	{2, 3, 4, 5}	3
Conv1D_filters	/	128
Conv1D_kenel size	/	1 × 1
Conv1D_activation	/	ReLU
GRU hidden units	{32, 64, 128}	64
Dropout Rate	{0.1, 0.2, 0.3, 0.5}	0.2
Optimizer	/	Adam
Learning Rate	{0.001, 0.0001, 0.00001}	0.001
Batch Size	/	32
Epochs	/	200

. “/” indicates that no optimization was performed, and a fixed value was adopted.

During the model training process, loss and accuracy are crucial metrics for evaluating model performance. Figure 10 depicts the Loss–accuracy curves of the TCN-GRU model on the training set and the test set. Figure 10a shows the training loss and test loss curves. At the beginning of training, the model’s ability to fit the data was poor, with both training loss and test loss at high levels, approximately 1.77 and 1.75, respectively. As training progressed, both curves declined significantly, and the model’s fitting effect on the data continuously improved. In the later stages of training, the training loss dropped to approximately 0.05, and the test loss dropped to approximately 0.11. Moreover, the curves stabilized, indicating that the model achieved good fitting on both the training set and the test set. Figure 10b presents the training accuracy and test accuracy curves. At the start of training, the training accuracy and test accuracy were approximately 28.3% and 24.9%, respectively. As the number of training rounds increased, the training accuracy climbed rapidly, reaching approximately 99.3% in the later stages of training, demonstrating a substantial improvement in the model’s recognition ability on the training set. The test accuracy also exhibited an upward trend and eventually stabilized at approximately 96.3%, fully demonstrating that the model possesses excellent generalization ability on the test set.

4.3. Ablation and Comparison Experiments

First, to verify the effectiveness of the SABO-TVFEMD decomposition method adopted in this paper, we trained models with different decomposition methods using the same training set and evaluated their performance on the test set. To rule out the contingency of the experimental results, without using pre-trained weights, we carried out 10 independent training sessions for each model in

Table 5. Average classification of four decomposition methods.

Model	Average Accuracy
SABO-TVFEMD-TCN-GRU	96.38%
TVFEMD-TCN-GRU	91.62%
VMD-TCN-GRU	88.12%
EMD-TCN-GRU	84.62%

. Table 5 presents the average classification accuracy of each model in 10 experiments. Figure 11 shows the classification accuracy of each model over 10 experiments. Figure 12 shows the confusion matrix of the classification results of each model in Table 5 for one of the experiments. Faults 1–3 correspond to the following mechanical fault conditions: transmission shaft gear jamming, transmission shaft screw loosening, and arcing plate loosening.

Table 5 presents the average classification accuracy of five different decomposition methods integrated with the TCN-GRU model. The SABO-TVFEMD-TCN-GRU model attains an average accuracy of 96.38%, the highest among all models. The TVFEMD-TCN-GRU model follows with an average accuracy of 91.62%. The VMD-TCN-GRU model records an average accuracy of 88.12%, while the EMD-TCN-GRU model has an average accuracy of 84.62%. Evidently, the SABO-TVFEMD-TCN-GRU model outperforms the other models. This indicates that compared to TVFEMD, VMD, and EMD decomposition methods, the SABO-TVFEMD decomposition method significantly improves the classification accuracy in fault diagnosis.

Subsequently, to verify the improvement effect of the TCN-GRU model on the accuracy of fault diagnosis, we trained models based on the SABO-TVFEMD decomposition method and composed of TCN-GRU, TCN, GRU, and LSTM, respectively, using the same training set.

Table 6. Average classification accuracy of four models.

Model	Average Accuracy
SABO-TVFEMD-TCN-GRU	96.38%
SABO-TVFEMD-TCN	91.88%
SABO-TVFEMD-GRU	87.25%
SABO-TVFEMD-LSTM	82.75%

shows the average classification accuracy of each model on the test set. Figure 13 illustrates the classification accuracy of each model in Table 6 over 10 experiments, and Figure 14 presents the confusion matrix of one of the experiments.

Table 6 presents the average classification accuracy of each model on the test set, offering a clear comparison of their performance in the fault diagnosis task. Among the four models evaluated, the SABO-TVFEMD-TCN-GRU model achieved the highest average accuracy of 96.38%, demonstrating the effectiveness of integrating the TCN-GRU architecture with the SABO-TVFEMD decomposition method in enhancing diagnostic performance. The SABO-TVFEMD-GRU and SABO-TVFEMD-LSTM models attained lower average accuracies of 87.25% and 82.75%, respectively. The SABO-TVFEMD-TCN model performed better than both, reaching an average accuracy of 91.88%. Nevertheless, its performance still lagged behind that of the SABO-TVFEMD-TCN-GRU model. These results suggest that while the LSTM, GRU, and TCN architectures individually offer certain advantages, they may be limited in fully capturing the complex features of fault data. In contrast, the combined TCN-GRU structure demonstrates superior capability in extracting temporal dependencies and handling the nonlinear characteristics of the signal, thereby leading to improved fault classification accuracy.

To further validate the performance of the proposed model, we conducted a comparative study with several representative state-of-the-art diagnostic methods. All models were trained using the same training dataset and evaluated on the same testing set to ensure fairness and consistency.

Table 7. Comparison with existing methods.

Model	Average Accuracy
SABO-TVFEMD-TCN-GRU	96.38%
MFEMD-LIM [11]	91.88%
TA-CNN-SVM [41]	91.24%
Multi-Feature Fusion-PSO-LSSVM [42]	87.25%
VMD-RVM [14]	85.50%
VMD-SA-ELM [43]	81.37%

presents the average diagnostic accuracy obtained over 10 independent runs for each method.

The results demonstrate that our proposed model outperforms existing approaches in terms of diagnostic accuracy, which highlights its superior feature extraction capability and classification effectiveness. This improvement can be attributed to the adaptive signal decomposition achieved by SABO-TVFEMD and the powerful temporal modeling of the TCN-GRU architecture.

5. Conclusions

In the operation of power systems, the stable operation of the On-Load Tap Changer is crucial for the reliable power supply of the power grid. This study proposes a new method for diagnosing mechanical faults of the On-Load Tap Changer based on SABO-TVFEMD-TCN-GRU. By conducting a multi-level analysis on the vibration signals of the On-Load Tap Changer, this method achieves precise feature extraction and thus enables efficient and accurate fault diagnosis.

In the experimental phase, three typical mechanical faults were simulated: transmission shaft gear jamming, transmission shaft screw loosening, and arcing plate loosening. Through the analysis of vibration signals, the differences in vibration characteristics under different fault conditions were deeply explored. Meanwhile, the SABO algorithm was used to optimize the bandwidth threshold $\xi$ and B-spline order n of TVFEMD, significantly improving the extraction effect of the intrinsic mode components of the signals and providing rich feature information for subsequent fault classification.

Verified by multiple groups of comparative experiments, the SABO-TVFEMD-TCN-GRU model proposed in this study shows significant advantages in the fault diagnosis task. Compared with other signal decomposition methods and classification models, the fault diagnosis accuracy of this model reaches 96.38%, outperforming traditional methods. When facing complex and changeable operating environments, this model exhibits stronger robustness. Especially in multi-fault mode recognition, it shows higher accuracy and stability.

In conclusion, the SABO-TVFEMD-TCN-GRU model provides an innovative and efficient solution for the mechanical fault diagnosis of the On-Load Tap Changer. It not only improves the accuracy of fault diagnosis but also can effectively adapt to signal changes in complex environments. It has important application value for the online monitoring and fault early warning of smart grid equipment and is expected to promote the further development of power equipment condition monitoring technology.

Currently, most intelligent OLTC monitoring systems are in pilot or semi-industrial application phases, typically implemented in substations with high reliability requirements. Existing commercial solutions often rely on single-source signal processing and threshold-based evaluation approaches. While the proposed framework has not yet been fully deployed in real-world scenarios, its modular design and data-driven modeling make it well suited for future field applications. Further work will focus on real-time implementation via embedded systems and edge computing platforms, with the aim of enabling adaptive and scalable diagnosis under compound fault conditions in actual power grid environments.