Mechanical Fault Diagnosis of a Disconnector Operating Mechanism Based on Vibration and the Motor Current

Abstract

The mechanical fault diagnosis of a disconnector operating mechanism using a single signal is not sufficiently accurate and reliable. To address this problem, this paper proposes a new fault diagnosis method based on the vibration signal and the motor current signal. First, based on the analysis of the motor stator current signal envelope, segmented envelope RMS values are extracted. Then, the vibration signal of the operating mechanism is processed with VMD (Variational Mode Decomposition). In this paper, the number of modal decompositions K is selected according to the envelope entropy. Second, the effective value of the current segment envelope is fused with the energy entropy value of each IMF component to construct the feature parameters for fault identification. Finally, a fusion weighting algorithm using AdaBoost is proposed to train an SVM as a strong classifier to improve the correct fault diagnosis rate. In this paper, the proposed new diagnosis method is applied to a 220 kV disconnector operating mechanism. The algorithm can effectively identify three operating states of a disconnector operating mechanism.

1. Introduction

As important power equipment, disconnectors are widely used in power systems. Their operating state directly affects the safety and stability of a power system [1]. A high−voltage disconnector operation mechanism lacks housing and is open to the air. Exposure to wind and sunlight over a long time can easily lead to rust and pollution, resulting in a series of mechanical and electrical faults, such as a stuck transmission mechanism [2]. Studies show that the mechanical fault of a disconnector operating mechanism is the main source of faults [3]. At present, there is little research on online monitoring technology for high−voltage disconnectors. To maintain the stability and safety of power systems, it is necessary to conduct research on online monitoring technology for disconnector operating mechanisms.

At present, the efficiency of manual patrolling is low, and the accuracy is poor. To quickly diagnose a fault and discover the hidden dangers to the equipment in time, the analysis and technology for state monitoring are based on various equipment signals, such as the stator current of a motor, the operating torque, the temperature rise of the equipment and the mechanical vibration, have been carried out [4]. Real−time and efficient control of the operating state of disconnectors has gradually become a research hotspot in academia.

The motor current signal of a disconnector operation mechanism will change with the change in operating torque under different disconnector operating states. Fault characteristics can be extracted using real−time monitoring and analysis of the stator current signal. Using fault characteristics as indicators, machine learning is used to evaluate the operating status and find faults. This allows the equipment to be shut down for maintenance in the shortest time and reduces economic losses [5]. It can be used to represent the mechanical characteristics of a disconnector operation mechanism by monitoring the characteristics of the stator current [6]. The monitoring system for mechanical properties developed with this characteristic can effectively represent the operating state of the mechanical structure.

Vibration signals on the operating mechanism surface of a high−voltage disconnector operating mechanism contain the working state information of each component of the operating mechanism. The fault characteristics of the disconnector operating mechanism can be extracted by analysing the vibration signals on its surface. Taking the fault characteristics as indicators, a machine learning algorithm can be used to evaluate its operating status and realize disconnector operating mechanism fault diagnosis [7,8]. A vibration sensor can be installed in the operating mechanism box of the disconnector and on a fixed device. It can collect vibration signals instantly and does not affect the mechanical characteristics of the disconnector. Therefore, it can realize the online monitoring of the disconnector operating mechanism and has good engineering value [9].

At present, there is no mature analytical method for stable signals such as the stator current of motors. Parameters such as the extreme value, root−mean−square value, and variance of the stator current can be extracted directly for characteristic analysis. In addition, after taking the fast Fourier transform, the required frequency in the spectrum of the time−domain signal can be observed. The change in device state can be determined by analysing the change in frequency [10]. Bispectrum analysis was used to analyse the stator current signal, which improved the monitoring ability of weak signals and successfully diagnosed a variety of gear faults [11]. Reference [12] used a time−shift method to process the stator current signal. The processed signal was input into a deep neural network for fault identification of gears and nondestructive detection.

For the decomposition of unstable signals such as vibration signals, the commonly used methods include dynamic time warping (DTW), empirical mode decomposition (EMD), and variational mode decomposition (VMD) [13,14,15]. DTW takes the dynamic time warping distance between the nominal and abnormal states of the disconnector as a characteristic parameter to judge the state of the disconnector. However, the selection of the benchmark signal of this algorithm lacks a mature method, and the algorithm lacks stability in practical applications [16]. EMD decomposes unsteady vibration signals into a series of stable intrinsic mode functions (IMFs) by generating basis functions. The extracted IMF features are used to replace the characteristic parameters of the source signal for analysis. However, modal aliasing often occurs when EMD decomposes signals without white noise. Therefore, the signals cannot be decomposed reliably [17]. VMD, as a completely nonrecursive signal analysis method, is an overall optimization of EMD. It can achieve effective separation of IMFs and obtain effective decomposed components of a given signal. It successfully solves the problem of mode aliasing in EMD [18]. An improved VMD based on double threshold filtering is used to decompose the partial discharge signal of a transformer [19]. Then, the characteristic parameters in the IMFs are extracted according to the marginal spectrum for fault classification.

To realize the fault diagnosis of a high−voltage disconnector operating mechanism, it is first necessary to analyse the current signal of the motor stator and the vibration signal on the surface. Then, characteristic parameters are extracted, which reflect the operating state of the disconnector operating mechanism. Meanwhile, a machine learning method is used to classify the extracted characteristic parameters. The classification results are the results of the evaluation of the operating mechanism status, which can be directly diagnosed when the operating mechanism is in a faulty state. At present, in terms of fault diagnosis methods, a neural network algorithm and support vector machine has been widely used in fault diagnosis [20]. A neural network obtains the mapping relationship between samples through training and then classifies the samples adaptively. However, the training of a neural network requires a large number of samples, and the number of disconnector vibration and current signal samples is small. Therefore, a trained neural network has a poor recognition effect [21]. For this kind of classification of small samples, a support vector machine (SVM) is often used for classification and recognition. A diagnostic algorithm with an integrated SVM under AM−Relief feature selection is proposed to diagnose mechanical faults of high−voltage circuit breakers with an accuracy of 98% in [22]. This proves the effectiveness of the SVM algorithm. However, a traditional SVM algorithm lacks the ability of multiclassification and cannot be directly used to classify various operating states. Boosting originated from the transformation of weak learning algorithms to strong learning algorithms. AdaBoost was developed to solve the online assignment problem in boosting. It can improve the performance of weak classification algorithms through the fusion weighting of multiple weak classification algorithms. It is an excellent ensemble learning algorithm and is widely used in the design and optimization of learning algorithms [23]. A transformer fault diagnosis method based on an improved AdaBoost was proposed to solve the problems of fuzzy and random samples in transformer fault diagnosis in [24]. The experimental results show that the method can improve the accuracy of a diagnostic model.

At present, there are many kinds of signals used for the fault diagnosis of disconnectors. The stator current is used as the source signal to realize the fault diagnosis of a disconnector in [25]. Faults of the disconnector are diagnosed based on multichannel vibration signals [26]. Reference [27] carries out an intelligent diagnosis of mechanical disconnector defects based on operating torque. However, the signals used for fault diagnosis are relatively singular and lack reliability. To solve the problem that a single signal is not reliable enough, a multisignal monitoring method of a high−voltage disconnector’s operating mechanism is proposed based on the vibration and stator current signals. Envelope entropy is used to select the modal decomposition number K of the VMD algorithm to improve the decomposition effect of the vibration signals of the operating mechanism. After analysing the stator current signal, its characteristic parameters are extracted. Then, the characteristic parameters of the current signal and vibration signal are fused for diagnosis. To improve the classification performance of the SVM, it is used as a weak classifier in the AdaBoost model. The strong classifier AdaBoost−SVM is obtained through the weighted iteration of the model. It realizes the identification of different operating states of the operating mechanism and improves the fault diagnosis ability. A 220 kV disconnector operating mechanism box of CJTKA was selected for experiments to verify the effectiveness of the proposed method.

2. Fault Diagnosis Principle of the Disconnector Operating Mechanism

The operating mechanism of a high−voltage disconnector is mostly driven by an asynchronous motor. The air−gap torque of the asynchronous motor can reflect the state change of the operating mechanism. Through the induction of the stator flux, the stator current contains abundant information about the state of the operating mechanism. The stator current signal of a high−voltage disconnector asynchronous motor is directly related to the operating torque required by the disconnector. When the operating mechanism fails, the operating torque changes, and the stator current of the motor also changes. The relation between the operating torque and motor current is as follows [28]:

$$T_1\approx \frac{30m_0}{\pi n_0}\left(U_1{I}_1-I_1^2{R}_1\right)$$

(1)

where $T_1$ is the operating torque of the motor, $m_0$ is the number of stator phases of the motor, $n_0$ is the synchronous speed, $U_1$ is the input voltage of the motor, $I_1$ is the stator current of the motor and $R_1$ is the phase resistance of the stator winding.

There is a quadratic function relationship between the operating torque $T_1$ and the stator current $I_1$. Therefore, when the operating mechanism of the disconnector fails, the change in the operating torque will inevitably cause a change in the stator current. The state of the operating mechanism of the disconnector can be reflected by analysing and extracting the characteristic parameters of the stator current.

A large number of vibration signals will be generated during the opening and closing process of the disconnector. These vibration signals contain the state information of each part of the disconnector operating mechanism. The operating mechanism of the disconnector has a fixed travel when it opens or closes. For example, in a single opening action, the operating motor first receives a starting current signal, and the operating mechanism drives the main switch to start opening after the travel switch is opened. In the opening process, the auxiliary switch will be opened to assist the rotation of the main shaft in the operating mechanism box. When the last switch is retracted, the travel switch closes once, and the opening action ends. In the opening and closing action, the vibration signal on the surface of the operating mechanism corresponds to the state of travel of the operating mechanism. When the auxiliary switch screw is loosened and the transmission mechanism is jammed, the time and intensity of the action of the corresponding travel will also change due to the change in the mechanical characteristics of the operating mechanism. These changes are reflected in the vibration signal on the surface of the operating mechanism. Therefore, the vibration signals on the surface of the mechanism should be analysed, and the characteristic parameters can be extracted to reflect the state of the disconnector operating mechanism.

According to the characteristics of the operating mechanism when the disconnector is running, this study analyses whether the operating state of the operating mechanism can be monitored using the stator current and vibration signals. Thereby, a nonintrusive and real−time mechanical fault diagnosis of the operating mechanism is realized.

3. Research on the Processing Method of the Stator Current Signal

In this study, the stator current signals of the operating motor were collected for the classification of three operating conditions. The waveforms of the fundamental current of the operating motor stator under different operating conditions are shown in Figure 1. The motor starts at approximately 1.5 s and shuts down at approximately 14.57 s, and the whole process of opening is approximately 13.07 s. The motor current was maximum at the beginning of the opening. At this time, the operating mechanism was in a static state, and the static friction force was large. Therefore, the motor needed a large operating torque to drive the start of the disconnector. As the friction changed from static to sliding, the force of friction decreased. The operating torque and current required are reduced, so the curve drops. A small amount of static friction is generated at the end of the opening, so more working torque and current are needed and the curve will go up. When the transmission mechanism is jammed, the above phenomenon will be more obvious, and the rise in the curve will be more significant due to the additional friction.

To distinguish the motor current under the three operating conditions more intuitively, the current is enveloped. The upper current envelope diagrams of the three operating conditions from the start of opening to the end are shown in Figure 2.

The current envelopes present different states under the three operating conditions. When the transmission mechanism is jammed, the current envelope value is generally higher than that of the other two conditions. However, there is a lack of a prominent event for horizontal comparison. Therefore, feature extraction and analysis are carried out on the current envelope of each operating condition to distinguish the three operating states.

The effective value is also called the root−mean−square value, which can be used to characterize the effective energy of the signal. The variation in the amplitude of the current under the three operating conditions is different, and the effective value contained in it is also different. The mathematical expression of the effective value of the current is:

$$I_{rms}=\sqrt{\frac{1}{T}{\displaystyle {\int }_0^T{i}^2\left(t\right)dt}}$$

(2)

where $I_{rms}$ is the effective value of the current, $T$ is the period of the AC signal, for which the power frequency is generally 50 Hz, and $i\left(t\right)$ is the instantaneous value of the current. After discretization, the discrete version can be obtained as follows:

$$I_{rms}=\sqrt{\frac{1}{N}{\displaystyle \sum _{n=1}^N{i}_n^2}}$$

(3)

where $i_n$ is the current sampling value at the $n_{th}$ point and $N$ is the sampling point in each cycle.

To more accurately characterize the difference in the effective value of the current under different operating conditions, we take 100 points in the current envelope of the motor from start to finish under the three operating conditions to calculate the effective value of the current envelope. The effective values of the fundamental current of the motor stator under the three conditions are shown in

Table 1. Effective values of the stator fundamental current—time data.

	Time/s	2.8	4.1	5.4	6.7	8	9.3	10.6	11.9	13.2	14.57
Condition
Nominal condition		0.202	0.177	0.176	0.178	0.174	0.170	0.174	0.170	0.172	0.171
Screw−loosened condition		0.201	0.174	0.176	0.175	0.177	0.172	0.171	0.174	0.173	0.173
Transmission mechanism−jammed condition		0.203	0.187	0.183	0.184	0.185	0.186	0.186	0.181	0.183	0.186

. When the screw is loosened, the sliding friction of the operating mechanism also changes irregularly due to irregular shaking. The RMS under the screw−loosened condition fluctuates irregularly compared with the nominal condition. When the transmission mechanism is jammed, the effective values of the jammed transmission mechanism are greater than those under nominal and loosen−screw conditions due to the general increase in sliding friction. Therefore, the effective values of the segments of the current envelope can be used to distinguish the above three operating conditions. It is reasonable to take the effective values of the segments of the current envelope as the characteristic parameters.

4. Research on the Processing Method of the Vibration Signal

4.1. Principle of the Improved VMD Algorithm

This study uses VMD to decompose and process unstable vibration signals. To achieve the optimal effect of signal decomposition, the number of modal decompositions K of the VMD was selected using the envelope entropy.

VMD determines the centre frequency and bandwidth of each component by iteratively searching for the optimal solution of the variational model. It can realize frequency subdivision and adaptive separation of the signal [29].

The variational model is as follows:

$$\{\begin{array}{l}\underset{\left\{u_k\right\} ,\left\{{\omega }_k\right\}}{{\displaystyle \min }}\left\{{{\displaystyle \sum _{k=1}^K\Vert {\partial }_t\left[\left(\delta \left(t\right)+\frac{j}{\pi t}\right)\ast u_k\left(t\right)\right]e^{-j{\omega }_{k}t}\Vert }}_2^2\right\}\\ s.t. {\displaystyle \sum _{k=1}^K{u}_k=f}\end{array}$$

(4)

where $f$ is the input signal, $\left\{u_k\right\}=\{u_1,u_2,\dots ,u_k\}=X$ is the K intrinsic mode functions, $\left\{{\omega }_k\right\}=\{{\omega }_1,{\omega }_2,\dots ,{\omega }_k\}$ is the frequency centre of each IMF, $\delta \left(t\right)$ is the impulse function, and ${\partial }_t$ is the partial derivative operation.

An augmented function is constructed to solve the optimal solution of the variational model, and its expression is as follows [30]:

$$\begin{array}{l}L\left(\left\{u_k\right\},\left\{{\omega }_k\right\},\lambda \right)=\\ \alpha {{\displaystyle \sum _{k=1}^K\Vert {\partial }_t\left[\left(\delta \left(t\right)+\frac{j}{\pi t}\right)\ast u_k\left(t\right)\right]e^{-j{\omega }_{k}t}\Vert }}_2^2+\\ {\Vert f\left(t\right)-{\displaystyle \sum _{k=1}^K{u}_k\left(t\right)}\Vert }_2^2+\langle \lambda \left(t\right),f\left(t\right)-{\displaystyle \sum _{k=1}^K{u}_k\left(t\right)}\rangle \end{array}$$

(5)

where $\lambda$ is the Lagrange operator and $\alpha$ is the quadratic penalty factor. $\omega$ is replaced by $\omega -{\omega }_k$ in the frequency domain to write the original formula in the integral form. Finally, an expression of each modal component is obtained:

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

(6)

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

(7)

In Formula (6), ${\widehat{u}}_k^{n+1}\left(\omega \right)$ is equivalent to Wiener filtering of $\widehat{f}\left(\omega \right)-{\displaystyle \sum _{i\ne k}{\widehat{u}}_i\left(\omega \right)}$, and ${\omega }_k^{n+1}$ is the centre of the power spectrum of the modal function. The modal component IMF can be obtained by the inverse Fourier transform of $\left\{{\widehat{u}}_i\left(\omega \right)\right\}$.

The most important parameter that affects the decomposition effect of VMD is the number of modal decompositions K. If K is too small, the signal mutation is not obvious enough and cannot be completely decomposed. If K is too large, it will produce redundant components and increase useless computation. The mechanical vibration signal of a disconnector is random. Therefore, it is difficult to find an appropriate number for modal decomposition.

The entropy of the envelope is the entropy value of the envelope signal calculated in the form of information entropy using the Hilbert transformation of each modal function. The larger the value is, the sparser the modal function is and the less information it contains. The smaller the value is, the sparser the modal function is and the more information it contains. The value of the envelope entropy is used to reflect the sparse feature of the modal function, that is, the decomposition effect of VMD. The envelope entropy can be obtained as follows:

$$\{\begin{array}{l}{p}_i=\raisebox{1ex}{$h\left(i\right)$}\!\left/ \!\raisebox{-1ex}{${\displaystyle \sum _{i=1}^{N}h\left(i\right)}$}\right.\\ E_p=-{\displaystyle \sum _{i=1}^N{p}_i\lg \left(p_i\right)}\end{array}$$

(8)

where $h\left(i\right)$ is the envelope signal after the Hilbert transformation of the modal function, $p_i$ is the normalized value, $E_p$ is the envelope entropy, and $i=1,2,\dots ,N$, where $N$ are the points of the envelope signal graph.

In this study, the optimal number of modal decompositions K is determined by calculating the envelope entropy of each modal component of the vibration signal at the auxiliary switch screw under nominal operating conditions at different VMD decomposition layers. The smaller the envelope entropy is, the better the VMD decomposition effect of the corresponding layers is. This study calculates the envelope entropy value of each modal component after VMD decomposition step by step from K = 2. After calculation, it was found that the envelope entropy value of each mode component will gradually decrease. Therefore, when the envelope entropy value of a certain mode component suddenly increases, the optimal decomposition layer number is the current decomposition layer number minus one. After repeated calculation, it was found that when K = 7, the envelope entropy of each IMF is (IMF_1~7): 4.577, 2.929, 2.924, 2.91, 2.847, 2.824, 2.937, respectively. The envelope entropy value curve is shown in Figure 3. It can be seen that the envelope entropy of the first six modal components decreases gradually. However, the envelope entropy of the seventh layer suddenly increases. Therefore, the number of modal decomposition layers is selected as 6 in this study.

4.2. Feature Parameter Extraction

Figure 4 shows the opening vibration signal at nominal condition, screw−loosened condition, and transmission mechanism−jammed condition. There are three obvious actions of the disconnector in one opening process. Under the three states, the disconnector starts to open when the motor receives the starting current signal at approximately 1.5 s. At this time, the travel switch is opened, causing an obvious vibration signal. After that, the operating mechanism drives the main switch to start opening. At this point, the vibration amplitude of the screw−loosened state is basically the same as that of the nominal state. When the transmission mechanism is jammed, the torque required to start the opening increases due to the sticking of the mechanism, resulting in a stronger vibration signal. The amplitude of the vibration signal here is 1.83 times bigger than that of the other two operating states. Under the nominal condition, the auxiliary switch is turned on, and the main shaft in the operating mechanism box rotates at approximately 10.73 s. The amplitude of this action is the largest, and the vibration signal is the most obvious. When the screw is loosened, the loosening of the screw leads to a slow action in the first half of the opening. The sensitivity of the vibration sensor here also decreases. Therefore, under this event, the auxiliary switch action time will be delayed, and the vibration quantity collected will be less. The event occurred at 11.17 s, and the vibration amplitude was 25% of the nominal condition. When the transmission mechanism is jammed, the action of the first half of the opening is slower, and the action of the auxiliary switch is also slowed due to the jam. Therefore, the auxiliary switch action time under this event will be further delayed, and the vibration signal here will be smaller due to the slow action of the auxiliary switch. The event occurred at 13.22 s, and the vibration amplitude was 45% of the nominal condition. Under the three operating conditions, at approximately 14.57 s, the travel switch is closed, and there is an obvious vibration signal. Under this event, the vibration amplitude under the nominal and screw−loosened conditions are almost the same. However, when the device is jammed, a stronger vibration signal is generated due to the stiffness of the mechanism. At this time, the amplitude of the vibration signal is 1.36 times bigger than that of the other two conditions. This is the end of an opening action, and the process took approximately 13 s. From the analysis of the time−domain signals in the above three cases, it can be found that the time nodes and vibration amplitudes of the event when the auxiliary switch turns on in the three states are different. In this study, the auxiliary switch action events are selected as the key events for analysis. The vibration signal of the auxiliary switch under nominal conditions is shown in Figure 5.

Figure 6 shows the frequency domain diagram of each modal component obtained after VMD processing of the signal in Figure 5. Figure 6 shows that the centre frequencies of the IMF obtained by VMD processing are independent of each other, and most of the signals are near the central frequency. There is no spectrum overlap between modal components. The maximum frequency of each mode is 10,000 Hz. This means that the mechanical vibration signal of the disconnector contains a certain high−frequency component.

The energy entropy represents the uniformity of the energy distribution in space. The energy distribution of the disconnector operating mechanism is different in different states. Using the energy entropy as a characteristic parameter can correctly distinguish different operating states of the disconnector [31]. In this study, VMD is used to process the vibration signal to calculate the energy entropy of each IMF. The energy entropy is used as the characteristic parameter to construct a matrix of the characteristic parameters of the vibration of the operating mechanism.

To obtain the energy entropy of each IMF, it is necessary to first divide the signal evenly. The energy entropy of each IMF segment is calculated as follows:

$$Q\left(i\right)={\displaystyle {\int }_{t_{i-1}}^{t_i}{\left|A_n\left(t\right)\right|}^2{d}_t}$$

(9)

where $A_n\left(t\right)$ represents the envelope of IMF $n$, where $i=1,2,3,\dots ,R$, $t_{i-1}$, and $t_i$ represent the beginning and end moments of paragraph $i$. After referring to [32] and a large number of experimental analyses, the IMFs are divided into 10 sections, and the energy entropy is calculated. After normalization, $Q\left(i\right)$ was written as $\delta \left(i\right)$. The expression is as follows:

$$\delta \left(i\right)=\frac{Q\left(i\right)}{{\displaystyle \sum _{i=1}^{R}Q\left(i\right)}}$$

(10)

$\delta \left(i\right)$ is substituted into the energy entropy formula to complete the calculation. The energy entropy is expressed as follows:

$$H=-{\displaystyle \sum _{i=1}^R\delta \left(i\right)lg\delta \left(i\right)}$$

(11)

Three groups of nominal signals, signals of loosen fault, and signals of jamming fault were randomly selected to form small data samples. After VMD decomposition, the mean value of energy entropy contained in each IMF under the three conditions was calculated according to Formulas (9)–(11).

Table 2. Average energy entropy of three groups of random signals of the disconnector in the three operating conditions.

Disconnector Status	Energy Entropy
	H1	H2	H3	H4	H5	H6
Nominal	0.9514	0.3851	0.4456	0.7495	0.5986	0.8320
Nominal	0.9436	0.3947	0.4410	0.7566	0.5418	0.8349
Nominal	0.9546	0.4122	0.4506	0.7487	0.5914	0.8279
Screw−loosened	0.9469	0.3722	0.3556	0.6579	0.4145	0.8255
Screw−loosened	0.9327	0.3701	0.3422	0.6487	0.4325	0.8107
Screw−loosened	0.9417	0.3694	0.3326	0.6079	0.4301	0.8311
Transmission mechanism−jammed	0.8197	0.2622	0.2462	0.5253	0.4808	0.7340
Transmission mechanism−jammed	0.8024	0.2581	0.2395	0.5309	0.4862	0.7217
Transmission mechanism−jammed	0.8122	0.2720	0.2438	0.5217	0.4783	0.7401

gathers the calculation results of the average energy entropy of 30 groups of the nominal, loosen fault, and jamming fault conditions.

Table 2 shows that the energy entropy difference of the disconnector in the same state is very small, and the difference in energy entropy in different states is obvious. The entropy value reflects the uniformity of the signal. The disconnector signal is relatively stable under the nominal condition, while the signal will fluctuate to different degrees under the other conditions. Therefore, under the nominal operating condition, the energy entropy is generally higher than that under the other conditions. The energy entropy of the measured signals conforms to the above theory.

5. Fault Diagnosis

5.1. Methods for Classifying Faults Based on AdaBoost−SVM

The AdaBoost method can improve the performance of a weak classification algorithm through weighted fusion. First, all samples are supplemented with a weight (usually the initial weight is set as a uniform distribution), and a classifier is trained on this sample. After classifying the samples, the error rate of the classifier is obtained. The larger the error is, the smaller the weight assigned to the classifier. The weight of the misclassified samples is increased, and the weight is recalculated according to the error rate. In this way, the weighted fusion of multiple weak classifiers is finally obtained through successive iterations [33].

The AdaBoost−SVM classifier is a strong classifier that uses an SVM as a basic weak classifier and is formed by automatic weighted fusion. N labelled samples $\left\{\left(x_1,y_1\right),\left(x_2,y_2\right),\dots ,\left(x_n,y_n\right)\right\}$ are given, where $x_i$ is the characteristics of the sample vector, $y_i\left(y_i\in \left\{+1,-1\right\}\right)$ is the corresponding label, $\omega \left(i\right)$ is the weight of $n$ samples, the initial weight is $\omega \left(i\right)=1/n$ and the number of iterations is $m$. The algorithm’s steps are as follows:

• Input initial characteristic parameters into the SVM to obtain multiple initial weak classifiers $R_j$:

  $$R_j=p\left(x,y,\omega \right)$$

  (12)
• Calculate the classification error $E_{err}$ of each weak classifier $R_j$:

  $$E_{err}={\displaystyle \sum _{i=1}^n\left[R_j\left(x_i\right)\ne y_i\right]}{\omega }_i$$

  (13)
• Adjust the coefficient of weight ${\omega }_j$ of each sample according to its classification error:

  $${\omega }_j=\left(1/2\right)\ln \left[\left(1-E_{err}\right)/E_{err}\right]$$

  (14)
• Redistribute the weight of each sample and adjust the sample distribution according to the weight coefficient:

  $${\omega }_{j+1}\left(i\right)=\frac{{\omega }_j\left(i\right)}{C_j}\times \{\begin{array}{l}{e}^{{\omega }_j}\left(R_j\left(x_i\right)\ne y_i\right)\\ e^{-{\omega }_j}\left(R_j\left(x_i\right)=y_i\right)\end{array}$$

  (15)

  where $C_j$ is the comprehensive coefficient. If a sample’s distribution is the same as that of the last time, the cycle will exit; otherwise, the cycle will continue.
• Obtain a combinatorial strong classifier:

  $$H\left(x\right)=sign\left[{\displaystyle \sum _{j=1}^T{\omega }_j{R}_j\left(x\right)}\right]$$

  (16)

  where weak classifier $R_j=\left(r_1,r_2,\dots ,r_T\right)$ and the weight ${\omega }_j=\left({\omega }_1,{\omega }_2,\dots ,{\omega }_T\right)$.

The kernel function and corresponding parameters of the SVM should be determined in advance when it is used for classification. Commonly used kernel functions include radial basis kernel functions, polynomial kernel functions, and Gaussian kernel functions. Compared with other kernel functions, radial basis kernel functions require fewer parameters. According to [34], a radial basis kernel function was selected as the kernel function in this study, the penalty parameter C was set to 2.4093 and the kernel function parameter g was set to 5.7777. In this study, ten initial weak classifiers are set up. After nine AdaBoost iterations of Formulas (12)–(15) are weighted, the conditions for exiting the loop are satisfied, and the combined strong classifier is obtained.

5.2. Algorithm Flow of Fault Diagnosis

In the field measurement, a jammed transmission mechanism of disconnectors fault is simulated by placing a wood piece between the main transmission shaft and the casing. In this study, a Screw−loosened fault is simulated by loosening an auxiliary switch screw. The vibration signal under various conditions is collected by a vibration sensor. The motor current signal under each operating condition is collected by a current clamp. Improved VMD is used to decompose the vibration signal and extract the energy entropy as the characteristic parameter. After the current signal is enveloped, the effective value of the segmented envelope of the current signal is extracted. The effective value of the envelope and energy entropy is used to construct syncretic characteristic parameters and input them into AdaBoost−SVM for state recognition. Finally, we complete the fault diagnosis of the disconnector.

The troubleshooting procedures are as follows:

• Two channels of signals were collected in one experiment. The first channel is the a−phase current signal at the output end of the motor stator, which is collected using a single−phase current clamp. After the host computer receives the motor current signal, it starts the acquisition of the second channel. The second channel is responsible for collecting mechanical vibration signals at the auxiliary switch screw with a magnetic suction vibration sensor. The sampling frequency is set to 50 kHz, and the sampling time is set to 15 s. Finally, 30 groups of nominal disconnector signals, 30 groups of jamming fault signals, and 30 groups of loosen fault signals were collected.
• The energy entropy of the six IMFs of the disconnector under different operating conditions was calculated after the improved VMD decomposition. After processing the current signal, the RMS of the envelope signal is calculated. The RMS of the envelope of the current signal and the energy entropy of the vibration signal is fused to construct the matrix of characteristic parameters.
• The matrix of fused characteristic parameters generated by each set of data in step 2 is input into the enhanced AdaBoost−SVM to judge the operating state of the disconnector.

A flow chart of fault diagnosis is shown in Figure 7. Experimental site images are shown in Figure 8.

5.3. Results of Fault Diagnosis

The fault sample obtained in this study is a sample of small data composed of 30 groups of nominal signals, 30 groups of loosen fault signals, and 30 groups of jamming fault signals. In this study, AdaBoost is adopted to take an SVM as a weak classifier and obtain a strong classifier with higher accuracy after weighted fusion.

The fusion feature parameters of the vibration signal and current signal were input into the AdaBoost−SVM classifier. There are 90 groups of feature parameters, of which 1–30 groups are in the nominal state, 31–60 groups are in the screw loose state, and 61–90 groups are in the jam fault state. The nominal, screw loose, and jam fault labels of the disconnector are marked as 1, 2, and 3 respectively. Sixty groups (20 groups of nominal data, 20 groups of screw−loosened data, and 20 groups of jamming fault data) were selected from the 90 groups of characteristic data for training. The remaining 30 groups were used for testing. The test set number of samples is shown in

Table 3. Sample test set.

Disconnector Status	Serial Number	Label
Nominal operating condition	1–30	1
Screw−loosened condition	31–60	2
Transmission mechanism−jammed	61–90	3

.

According to the AdaBoost−SVM algorithm steps, 30 sets of test samples are input into 10 initial weak classifier SVMs. The initial weight of each sample is 0.033. After classification, according to Formula (13), the classification error $E_{err}$ of each classifier is calculated to be 0.167, 0.2, 0.167, 0.133, 0.1, 0.167, 0.133, 0.133, 0.2, and 0.167. Then, according to Formula (14), the weight coefficients ${\omega }_j$ of each classifier are 0.84, 0.693, 0.84, 0.937, 1.1, 0.84, 0.937, 0.937, 0.639, and 0.84. Then, we calculate the new sample weight ${\omega }_{j+1}\left(i\right)$ according to Formula (15), where the generalized coefficient $C_j$ is 10. Due to limited space, this paper presents the new distribution of the weights of the sample of the first initial classifier for samples under nominal conditions (group 3 and group 7 are incorrectly classified, others are correctly classified): 0.036, 0.036, 0.195, 0.036, 0.036, 0.036, 0.036, 0.195, 0.036, 0.036, 0.036. Formulas (12)–(15) are repeated nine times to obtain each sample’s distribution ${\omega }_{j+1}\left(i\right)$ as the eighth. We can then output the enhanced classifier $H\left(x\right)$. Finally, the test samples are input into the enhanced classifier. According to the classification results of each initial classifier, the final classification result of the tests is output after weighted fusion.

The test results are shown in Figure 9.

Figure 9 shows that the ten groups of nominal operating signals and the ten groups of loosened fault signals are classified correctly. One misjudgement occurred in the ten groups of jamming fault signals. Overall, the diagnostic accuracy rate was above 96%. We have achieved satisfactory diagnostic results.

6. Conclusions

• A new method for fault diagnosis is adopted in this paper, which solves the problems of inconvenient and unreliable fault diagnosis of a disconnector operating mechanism. The source signals contain the vibration signal on the surface of the operating mechanism and the current signal of the motor stator. The effective value of the segmented envelope is extracted as the characteristic parameter of the current signal. The envelope entropy is used to select K, and then VMD is used to decompose the vibration signal and extract its energy entropy. The syncretic characteristic parameters are input into AdaBoost−SVM to achieve a good classification effect.
• The method of fault diagnosis proposed in this paper is of certain universality. Vibration and motor current signals can be collected and analysed for a large number of mechanical faults of disconnector operating mechanisms in power systems. Furthermore, it is possible to select suitable feature signals and extract feature parameters to achieve a more effective fusion diagnosis according to the characteristics of other power devices. This method has certain practical significance and can be popularized.