Fault Feature Extraction Based on Variational Modal Decomposition and Lifting Wavelet Transform: Application in Gear of Mine Scraper Conveyor Gearbox

Abstract

Vibration-based fault diagnosis of chain conveyor gearboxes is challenging under high load and strong shock conditions. This paper applies motor current characteristic analysis technology to scraper conveyor gearbox fault diagnosis and proposes a fault feature extraction method. Firstly, a variational mode decomposition algorithm combined with a genetic algorithm is used to divide the original current signal into several sub-bands with different frequency modulation information, and irrelevant information is preliminarily eliminated. Secondly, an intrinsic mode function (IMF) sub-band fault information extraction method based on lifting wavelet transform is proposed. The minimum entropy value is used to set the sensitive parameters involved in lifting wavelet transform, and the power supply current frequency and noise interference information of a scraper conveyor are removed from the current signal. Finally, it is proved that variational mode decomposition combined with lifting wavelet transform can effectively diagnose the fault of a scraper conveyor by comparative experiments.

1. Introduction

Intelligent technology of coal mines is the core of improving coal mining efficiency, ensuring coal mine production safety and realizing the high-quality development of the coal industry, and the intelligence of coal machine equipment is the key to the intelligent construction of coal mines [1,2]. A scraper conveyor is one of the key pieces of coal equipment in intelligent fully mechanized mining faces, which transports coal out of fully mechanized mining faces. In the process of coal transportation, the gear box of the scraper conveyor bears a complex load, high load intensity and strong impact load, which makes the use environment of the gear box of the scraper conveyor complex and harsh, and the probability of equipment failure is high, even leading to major mine accidents in serious cases [3,4,5]. Therefore, in order to realize the intelligent mining of coal in a fully mechanized mining face, it is necessary to solve the problem of fault self-diagnosis of the scraper conveyor. However, the fault diagnosis of the scraper conveyor contains many key technologies, and the fault diagnosis of the gearbox of the scraper conveyor is one of the difficult problems to be solved urgently.

The majority of scientific and technological workers have carried out a lot of research on gearbox fault diagnosis [6,7]. Fault diagnosis of the gearbox based on vibration signal analysis is a common method [8]. However, the sensitivity of vibration signals is very easily affected by the fixing mode and installation environment of the sensor. The gearbox of the scraper conveyor receives the impact of coal and rock, and the vibration sensor is easily damaged. In addition, the reduction gear box of the scraper conveyor will also vibrate due to the impact load during coal transportation, resulting in complex information components of the vibration signal of the reduction gear box, and the fault information is covered up by many noise components, which increases the difficulty of fault diagnosis. Therefore, the fault diagnosis method based on vibration signal analysis is not suitable for the reduction gearbox of scraper conveyors. In addition, the fault diagnosis method of the gearbox based on current characteristic analysis (MCSA) is another popular and practical method [9,10]. The principle of the MCSA method is that when the gear fails, the stator current of the motor will change, and the health state of the reducer gear of the scraper conveyor is analyzed by decomposing the current signal [11,12,13]. This method can effectively make up for the deficiency of fault diagnosis of the reduction gearbox of the scraper conveyor based on vibration signal monitoring.

MCSA is a non-invasive detection method, which has the advantages of easy acquisition of the current signal without interference to the original system, strong anti-interference and small attenuation of the current signal, and has been widely examined in recent years. Izaz R et al. present a method of fault diagnosis for a rotating vector (RV) reducer by using an embedded current system. By analyzing the characteristics of the motor current, this method establishes a fault classification system based on ML [14,15]. However, in the actual production process of an underground coal mine, the operation of the scraper conveyor gearbox will inevitably be affected by uncertain factors such as impact load, which will interfere with the torque information of the gearbox gear and even lead to the inability to effectively extract the characteristic information of the faulty gear from the current signal [16]. In view of this problem, a large number of scholars have conducted theoretical and laboratory research. Li et al. used the time-shift method to remove power frequency interference, corrected prominent fault characteristic signals by the exponent and finally realized gearbox fault diagnosis by using a deep neural network [17]. Gueltekin O et al. put forward a novel data fusion method based on a convolutional neural network, which uses signals measured from multiple additional sensors to intelligently detect ATV tools [18]. Chen et al. analyzed and modeled the current signal of an induction motor in the presence of air gap eccentricity and adopted adaptive iterative generalized demodulation, finally realizing the health state detection of gears [19]. In addition, Cheng considered wind turbines with variable gears caused by wind speed and wind direction interference. By using Hilbert transform to obtain the envelope of the current signal and converting the current envelope signal with a constant time interval into a resampling current envelope signal with a constant phase angle interval, it is difficult to extract the fault feature of the gearbox of a fan under the interference of the operating environment [20]. For low-speed and heavy-duty scraper conveyors, the MCSA is used to diagnose the gearbox fault. The load changes with the change in time and space. The change in load leads to a change in motor current. The fault of the motor electrical system of the scraper conveyor and the current signal interference caused by the sudden change in load make it difficult for the simple current signal analysis method to accurately identify the fault characteristics of the gearbox of the scraper conveyor.

So as to effectively extract the fault characteristics of the gearbox under load impact disturbance, existing scholars use time–frequency analysis methods to extract the fault feature data of the gearbox. Variational mode decomposition (VMD) is the most commonly used one [21]. VMD decomposes the original current signal containing various information into a modal signal (IMF) reflecting the dynamic mechanism of the mechanical system, and then realizes the fault diagnosis of equipment. Mahgoun et al. analyzed the specific performance of gear failure under unsteady load and variable speed and extracted the fault sub-band information through VMD to obtain its spectrum diagram and kurtosis value [22]. The experimental results show that the kurtosis value calculated from the original signal cannot give any information about the existence of faults, but the kurtosis value calculated after VMD of the original signal can be used as an index to distinguish different faults. Fan et al. constructed a dynamic model of a heavy-duty gearbox and obtained the vibration frequency of the gear root crack [23]. Zhang et al. realized gear fault diagnosis by using sample entropy and the grasshopper optimization algorithm [24]. In addition, the signal is decomposed by VMD, and then the approximate entropy of each mode is calculated, and the approximate entropy threshold is reconstructed by using the approximate entropy threshold. Irrelevant interference information entry Row elimination is carried out, so as to highlight the fault characteristics [25]. Liu et al. use VMD and SVD to extract global fault features directly, and combine them with a convolution neural network to obtain a final total recognition rate of 100% [26]. Li et al. put forward a fault diagnosis method for rolling bearings based on deep learning. This method helps the deep network to locate useful data segments, extract input discriminant features, visualize the learned diagnosis knowledge and verify the effectiveness of the method [27]. Recent studies have shown that these methods mainly eliminate the interference information by removing some irrelevant components defined by the criteria or calculating the statistical parameters of each IMF, so as to highlight the feature information and achieve the ultimate goal of fault diagnosis. However, VMD retains the function of a Wiener filter to some extent, which cannot remove irrelevant interference noise in fault sub-bands, especially non-stationary signals.

In order to effectively extract the gear feature information under impact conditions, a method combining variational mode decomposition with lifting wavelet transform is proposed in this paper. Firstly, the influence mechanism of load impact on the current signal of a scraper conveyor is analyzed by modeling, and the frequency characteristic information of the fault gear under load impact is explained. Then, the scraper conveyor current signal is decomposed into band-limited signals modulated by different scales by VMD, in which the decomposition levels and penalty factors are determined by a genetic algorithm (GA), and then lifting wavelet transform (LWT) is performed on the sub-band signals representing faults. According to the different entropy between the fault gear signal and random load shock signal, the local entropy is used as the fitness function of the GA, and the wavelet bases and decomposition layers involved in LWT are determined. Finally, the power frequency and load shock information in the IMF component signal representing fault are eliminated, and the fault feature information is extracted. The method proposed in this study is shown in Figure 1.

2. Materials and Methods

2.1. Current Signal Characteristics of Scraper Conveyor Under Load Impact

When the scraper conveyor transports coal, the traction mechanism of the scraper conveyor is a stepless closed scraper chain which bypasses the head sprocket and the tail sprocket for circulating movement, starts the motor, drives the scraper chain to run continuously through the hydraulic coupler, reducer and transmission sprocket and trans-ports the coal installed on the middle groove from the tail to the head for transportation [28,29]. This is shown in Figure 2.

During the operation of a three-phase asynchronous motor, the motor system bears time-varying torque disturbance, which mainly includes a coal flow load and friction load produced by the scraper conveyor running in a chute. In addition, it will be subjected to a random impact load caused by lump coal and a stuck chain. These load disturbances will cause torque fluctuation on the asynchronous motor shaft. In order to balance the load torque fluctuation, the induction motor will produce the corresponding electromagnetic torque, which will eventually cause a change in motor current information, and the transmission system state information will be modulated into the current signal.

Firstly, for the coal flow load impact and the friction load of the scraper chain running in the chute, the total load moment is assumed for clarity and simplicity to be T_A. The firing frequency is $f_{cfAi}$. Torsional vibration occurs, because the coal flow load impact and friction force are not fixed, so the equation is established to meet the dynamic balance [30], that is

$$T_A=T_{cfA0}+{\sum }_i{T}_{cfAi}cos\left(2\pi f_{cfAi}t+{\phi }_{cfAi}\right)$$

(1)

Here, $T_A$ is the load torque, $T_{cfA0}$ is the average load torque value of coal load and friction caused by the scraper running in the chute and ${\phi }_{cfAi}$ is the corresponding phase information. $f_{cfAi}$ is the frequency under the corresponding load amplitude.

For the asynchronous motor drive system, the following dynamic formula is satisfied:

$$T_e=T_A+J{\displaystyle \frac{d{\omega }_{mc}}{dt}}+{\displaystyle \frac{B}{{\omega }_{mc}}}$$

(2)

Here, $T_e$ is the electromagnetic torque of the motor, $J$ is the inertia of the system, ${\omega }_{mc}$ is the motor speed, $B$ is the motor power, and the load torque is $T_A$. When there is periodic fluctuation, the electromagnetic torque of the existing motor is

$$T_e=T_{e0}+{\sum }_i{T}_{ei}cos\left(2\pi f_{i}t+{\phi }_{ei}\right)$$

(3)

Then, the electromagnetic torque and load fluctuation need to meet the following conditions:

$$\left\{\begin{array}{c}{T}_{e0}-T_{cfA0}=2\pi B{f}_e\\ {\sum }_i{T}_{ei}cos\left(2\pi f_{i}t+{\phi }_{ei}\right)-{\sum }_i{T}_{cfAi}cos\left(2\pi f_{cfAi}t+{\phi }_{cfAi}\right)=J{\displaystyle \frac{d{\omega }_{mosc}}{dt}}+B{\omega }_{mosc}\end{array}\right.$$

(4)

Here, $f_e$ is the fundamental frequency of the stator current of a synchronous motor and ${\omega }_{mosc}$ is the periodic fluctuation of rotational speed. Then, the motor speed under load torque interference is as follows:

$${\omega }_{mc}={\displaystyle \frac{1}{B}}\left(T_{e0}-T_{cfA0}\right)+{\sum }_i{\omega }_{mci}cos\left(2\pi f_{i}t+{\phi }_{mi}\right)$$

(5)

The three-phase output current is expressed as a vector by using $i_d=0$, and the torque is $T_e.$ There are the following forms:

$$T_e=\mathsf{\Gamma }{i}_q$$

(6)

Here, $\mathsf{\Gamma }$ is a constant; from (3) and (6), for $T_e$ it can be seen that $i_q$ will also superimpose the cosine component of the corresponding frequency component on the basis of the DC component

$$i_q=i_{q0}+{\sum }_i{i}_{qi}cos\left(2\pi f_{i}t+{\phi }_{qi}\right)$$

(7)

where $i_{q0}$ is the average of q-axis currents, $i_{qi}$ is the frequency of q-axis fluctuation, $f_i$ is the component amplitude, ${\phi }_{qi}$ is the corresponding phase. The current in the dq coordinate system is transformed into an abc three-phase coordinate system (8) by inverse matrix transformation of the amplitude watch constant principle [31].

$$\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]=\left[\begin{array}{cc}\begin{array}{c}cos\left(\theta \right)\\ cos\left(\theta -{\displaystyle \frac{2}{3}}\pi \right)\\ cos\left(\theta +{\displaystyle \frac{2}{3}}\pi \right)\end{array}& \begin{array}{c}-sin\left(\theta \right)\\ -sin\left(\theta -{\displaystyle \frac{2}{3}}\pi \right)\\ -sin\left(\theta +{\displaystyle \frac{2}{3}}\pi \right)\end{array}\end{array}\right]\left[\begin{array}{c}0\\ i_q\end{array}\right]$$

(8)

And the rotor position information is

$$\theta ={\theta }_0+\int p{\omega }_{mc}dt={\theta }_0+{\displaystyle \frac{1}{B}}\left(T_e-T_{cfA0}\right)pt+{\displaystyle \frac{p}{2\pi }}{\sum }_i{\displaystyle \frac{{\omega }_{mci}}{f_i}}sin\left(2\pi f_{i}t+{\phi }_{mi}\right)$$

(9)

where ${\theta }_0$ is the initial position information of the rotor; $P$ is the pole logarithm; and ${\theta }_{tz}$ is a modulation component corresponding to the angular velocity fluctuation.

Substituting $i_{q0}$ and ${\theta }_0$ into the phase current Formula (8) yields

$$i_a=i_{q0}cos\left(2\pi f_{e}t+{\theta }_0+{\theta }_{tz}+{\displaystyle \frac{\pi }{2}}\right)+{\displaystyle \frac{1}{2}}{\sum }_i{i}_{qi}\left[cos\left(2\pi \left(f_e+f_{cfAi}\right)t+{\phi }_{qi}+{\theta }_0+{\theta }_{tz}+{\displaystyle \frac{\pi }{2}}\right)\right.\left.cos\left(2\pi \left(f_e-f_{cfAi}\right)t-{\phi }_{qi}+{\theta }_0+{\theta }_{tz}+{\displaystyle \frac{\pi }{2}}\right)\right]$$

(10)

Then, the torque fluctuation caused by load and friction appears in the stator current spectrum when the amplitude information of the current signal changes, and the impact of load impact on the current signal of the scraper conveyor appears on both sides of the power frequency $\left|f_e\pm f_{cfAi}\right|$, which is the frequency component.

From the above modeling based on the relationship between torque information and current signal, torque load information can be clearly reflected in the current signal. The load torque of the motor when the gear is in a normal state $T_A$ is made up of constant torque $T_L$, and when the frequency $T_{cfAi}$ is, respectively, $f_{r1}$, $f_{r2}$, $f_{r3}$ and $f_{r4}$, the corresponding phase is ${\phi }_{r1}$, ${\phi }_{r2}$, ${\phi }_{r3}$ and ${\phi }_{r4}$, where $i=\mathrm{1,2},3\cdots n$, which is

$$T_A=T_{L0}+T_{cfA0}+T_{L1}cos\left(2\pi f_{r1}t+{\phi }_{r1}\right)+T_{L2}cos\left(2\pi f_{r2}t+{\phi }_{r2}\right)+T_{L3}cos\left(2\pi f_{m1}t+{\phi }_{r3}\right)+{\sum }_i{T}_{cfAi}cos\left(2\pi f_{cfAi}t+{\phi }_{cfAi}\right)$$

(11)

where $f_{r1}$ is the frequency rotation of the driving gear; $f_{r2}$ is the frequency rotation of the driven gear; $f_{m1}$, the frequency of the teeth meshing of the wheels, is the frequency information raised by the load. The analysis shows that it will appear in the motor current spectrum $\left|f_e\pm f_{cfAi}\right|$, $\left|f_e\pm f_{r1}\right|$, $\left|f_e\pm f_{r2}\right|$, $\left|f_e\pm f_{m1}\right|$. When the gear box teeth are broken, the motor current of the scraper conveyor will contain this fault signal, and its frequency is an $f_r$ pulse signal. The pulse signal is expanded into a Fourier series:

$$f_o={\displaystyle \frac{x_0}{2}}+{\sum }_{n=1}^{\infty }{A}_{n}cos\left(2\pi n{f}_{r}t+{\phi }_n\right)$$

(12)

where ${\displaystyle \raisebox{1ex}{$x_0$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ is the DC component. The signal is generated by Fourier transform or a frequency doubling component. Therefore, local faults of gears will lead to the occurrence of the current spectrum $\left|f_e\pm {nf}_r\right|$ [32]. When the gear produces distributed faults, such as wear, the fault frequency of the gear is the meshing frequency of the gear $f_m$. In the same way, it can be seen that the current spectrum will appear at this time with a magnitude of $\left|f_s\pm {nf}_m\right|$ [33].

2.2. VMD-Related Theories

2.2.1. Construction of Variational Problems

The characteristics of the faulty gear of the scraper conveyor have been changing in the motor stator current signal due to its load fluctuation. The VMD algorithm decomposes the collected current signals by constructing a variational model, and uses the decomposed IMFs components to carry out Hilbert transform to obtain modal analytical signals. Then, the exponential term is added to adjust the estimated center frequency. The bandwidth of each modal component can be estimated by calculating the square norm of the analytic signal gradient, and then the variational problem becomes finding K modal components ${\mathcal{u}}_k$ and the problem of minimizing the bandwidth of modal component estimation; finally, a constrained variational model can be obtained:

$$\left\{\begin{array}{c}{min}_{\left\{u_x\right\}\left\{{\omega }_x\right\}}\left\{{\sum }_k{‖{\partial }_t\left[\left(\delta \left(t\right)+{\displaystyle \frac{j}{\pi t}}\right)\ast u_k\left(t\right)\right]e^{-j{\omega }_{k}t}‖}^2\right.\\ s.t{\sum }_k{u}_k=i_{ia}\end{array}\right.$$

(13)

where $\delta \left(t\right)$ is the pulse signal, ${\mathcal{u}}_k$ is the decomposed K modal components; and ${\omega }_k$ represents the center frequency of the bandwidth.

2.2.2. Solution of Variational Problems

This process can accurately decompose the signal. Constrained variation is converted into unconstrained variation by Equation (14):

$$L\left(\left\{u_k\right\},\left\{{\omega }_k\right\},\lambda \left(t\right)\right)=\alpha {\sum }_k{‖{\partial }_t\left[\left(\delta \left(t\right)+{\displaystyle \frac{j}{\pi t}}\right)\ast u_k\left(t\right)\right]e^{-j{\omega }_{k}t}‖}_2^2+{‖f\left(t\right)-{\sum }_k{u}_k\left(t\right)‖}_2^2+〈\lambda \left(t\right),f\left(t\right)-{\sum }_k{u}_k\left(t\right)〉$$

(14)

where $\alpha$ is a quadratic penalty factor and $\lambda \left(t\right)$ is the Lagrange multiplication operator.

The VMD algorithm is very simple [26]. First, each mode is continuously updated in the frequency domain directly, and finally it is transformed into the time domain by inverse Fourier transform; secondly, the center frequency is re-estimated and updated cyclically. The VMD filtering principle is shown in Figure 3 [34].

2.3. Optimization of VMD Parameters by Genetic Algorithm

Through the above analysis, VMD faces the problem of parameter selection. The determination of parameters α and K can effectively extract sub-band signals representing faults [35].

The genetic algorithm (GA) is a global random search method proposed by Professor Holland according to the evolutionary mechanism of natural species. By simulating the crossover and mutation of natural genes by using the probability optimization method, it realizes the automatic adjustment of search direction and search space and has wide applicability and strong global optimization search ability [36,37]. The algorithm flow is shown in Figure 4.

2.4. Fault Feature Extraction Strategy Based on VMD and LWT

After processing by the VMD algorithm, the characteristic waveform of the current signal induced by gear fault will be retained in the time domain signal of the IMF sub-band, and lifting wavelet is constructed according to data characteristics. Therefore, after VMD operation, lifting wavelet operation can realize the steps of prediction and updating on the IMF sub-band dominated by fault to eliminate information redundancy and extract deep features of the faulty gear. LWT is based on traditional Laurent polynomials and the Euclidean algorithm. By improving the wavelet and scale functions with known features, a set of new wavelet and scale functions with specific desired features are obtained [38]. The detailed steps are as follows:

LWT divides wavelet transform into three steps: segmentation, prediction and update and decomposition and reconstruction [39], as shown in Figure 5.

Splitting: the original sequence ${imf}_{si}=\left\{x\left(k\right),k\in Z\right\}$, according to parity, is divided into two disjoint sub-sequences, including even sequence samples and odd sequence samples, namely

$$\left\{\begin{array}{c}{s}_i=e_{i-1}\cup o_{i-1}\\ e_{i-1}\cap o_{i-1}=\varnothing \end{array}\right.$$

(15)

Prediction: using the actual value of the odd sequence $o_{i-1}$ and the prediction operator $P(\ast )$ dual sequence $e_{i-1}$ after interpolation, the signal can be defined as wavelet detail coefficients $d_{i-1}$, namely

$$d_{i-1}=o_{i-1}-P\left(e_{i-1}\right)$$

(16)

Update: the predicted sub-sequence $d_{i-1}$ undergoes update splitting to obtain the even sequence $e_{i-1}$ so that the even sequences have some of the global characteristics of the original sequence, namely

$$S_{i-1}=e_{i-1}+U\left(d_{i-1}\right)$$

(17)

where $S_{i-1}$ for $S_i$ is the low-frequency part ; $U(\ast )$ is the update operator.

The whole VMD-LWT process is shown in Figure 6, assuming that when the fault sub-band is in the ${imf}_2$ and when the number of predictor coefficients is 2 and the number of updater coefficients is 4, the reconstruction process of lifting wavelet transform is the inverse transform of the decomposition process, where $X_e[\ast ]$ and $X_o[\ast ]$ are, respectively, ${imf}_2$ after inert decomposition, $p$ represents the prediction function coefficient, while $d[\ast ]$ is the detail coefficient after prediction, which is the high-frequency part, $u$ is the update function coefficient, $s[\ast ]$ is the low-frequency part after update, and Result is the Result after VMD-LWT transformation.

Therefore, the adaptive construction of wavelet bases is carried out by the VMD algorithm combined with lifting wavelet; when matching the best adaptive wavelet basis and decomposition layers, the load fluctuation information and power frequency information will be weakened, and finally the fault information of scraper conveyor gears will be extracted.

2.5. Determination Criterion of Sensitive Parameters of VMD-LWT Based on Entropy

Taking information entropy as the fitness function of the genetic algorithm, the decomposition levels and penalty factors of VMD are determined. The wavelet basis function and decomposition level of LWT can also be finally determined. The irregularity and complexity of the signal are effectively characterized by the method of local envelope entropy. The smaller the information entropy, the smaller the uncertainty, and vice versa [40]. The envelope signal is decomposed into a sequence p_i, and its entropy value represents the sparsity of the original signal. The zero-mean signal is changed $x\left(j\right)(j=\mathrm{1,2},\cdots ,N)$ and the envelope entropy of $E_P$ indicates

$$\left\{\begin{array}{c}{E}_p=-{\sum }_{j=1}^N{p}_{j}lg{p}_j\\ e_j=a\left(j\right)∕{\sum }_{j=1}^{N}a\left(j\right)\end{array}\right.$$

(18)

where $P_i$ is the normalized form of $a_i$ and $a_i$ is the envelope signal of demodulation signal $x_j$.

2.6. The Proposed Method

Aiming at the difficulty of fault feature extraction of the reduction gear of a scraper conveyor in an actual coal mine environment, a feature extraction method based on VMD and LWT is proposed. The method consists of three parts: data acquisition, fault feature information extraction by the VMD method and LWT method and parameter optimization based on entropy. The overall flow is shown in Figure 1.

3. Experimental Validation

3.1. Current Data Acquisition

This paper studies the gear of the mine scraper conveyor model HB-KPL-75(Halbach&braun, Hattingen, Germany). The stator current signals of induction motor corresponding to four different fault gears are collected under load shock conditions. Under the condition of low speed and heavy load, the motor current of the scraper conveyor is very large, so it is necessary to use a current transformer to collect current signals. The acquisition process of the motor current signal of the scraper conveyor is shown in Figure 7, and the sampling frequency is determined to be 10 KHz [40].

HB-KPL-75 adopts a planetary gear reduction system, which is mainly composed of a spiral bevel gear, helical cylindrical gear and planetary gear transmission. The specific parameters are shown in

Table 1. HB-KPL-75 transmission-related parameters.

Gear Name	Number of Teeth	Rotation Frequency (Hz)	Gear Mesh Frequency (Hz)
Bevel gear	36	$f_{r1}$23.3	$f_{m1}840$
Bevel gear	70	$f_{r2}12$
Helical gear	36	$f_{r3}12$	$f_{m2}456$
Helical gear	83	$f_{r4}5.5$
Sun wheel	17	$f_{r5}5.2$	$f_{m3}89$
Planetary gear	21	$f_{r6}2.7$
Internal gear ring	71	$f_{r7}1.1$

[41].

The data collected are four different states of gear running under load interference, namely, broken teeth, pitting, wear and normal state.

3.2. Frequency Band Division Based on VMD-GA

The motor current of scraper conveyor fluctuates obviously, as the load increases gradually, as shown in Figure 8. The four fault characteristic signals are seriously disturbed by the load information. Therefore, it is difficult to distinguish gear fault types by time domain signals [41].

Firstly, the frequency band is divided by VMD, and the local envelope entropy is used as the fitness function by the GA. Through many experiments, the range of decomposition levels is selected as 3–8, because too small decomposition levels may lead to insufficient VMD, and similarly too large decomposition levels may lead to excessive decomposition, resulting in irrelevant single-mode component information. The GA optimizes VMD parameters and retains the decomposition levels and penalty coefficients after optimization. Specific GA parameter settings are shown in

Table 2. Parameter setting of genetic algorithm.

Parameter	Setting
Penalty factor	1000–4500
Decomposition layers	3–8
Generations	10
Population size	20
Mutation probability	0.18
Crossover probability	0.7

[41].

The genetic algorithm can determine the optimal combination of parameters. When the broken teeth are iterated for the fourth time, the normal teeth are iterated for the fifth time, the wear is iterated for the sixth time and the pitting is iterated for the first time, the best fitness is achieved, respectively, as shown in Figure 9 [41].

Combined with the gear parameters of the HB-KPL-75 gearbox, the fault characteristic frequency is calculated, and the fault sub-band position is preliminarily determined; then, the normal position of the broken teeth and gear is IMF1, and the position of pitting and wear is IMF2.The IMF1 and IMF2 corresponding to the fault are reserved, and the rest of the IMF component information is regarded as irrelevant interference information in order to initially eliminate the load and scraper chain impact interference. And the fault positions of IMF1 and IMF2 are extracted separately, Through the frequency spectrum, it can be observed that the overall frequency modulation characteristics of the current signal are relatively simple, the characteristic frequency range of broken teeth and normal teeth is 0–500 Hz and the frequency range of pitting and wear is 500–1200 Hz. The broken teeth and normal working conditions are less affected by the power frequency, but seriously affected by irrelevant impact load. For pitting and wear conditions, the characteristic frequency of the gear is seriously disturbed by the power frequency signal, and appears on both power frequency sides $\left|f_e\pm f_{cfAi}\right|$, frequency components caused by irrelevant load interference. This is shown in Figure 10.

So, using VMD(Variational Mode Decomposition) to combine the best decomposition layers and penalty factors will lead to inaccurate signal decomposition. The extracted fault frequency band may be mixed with the impact load signal. The power frequency signal will seriously interfere with the expression of pitting corrosion and wear characteristics.

3.3. Feature Enhancement Based on VMD-LWT Algorithm

Lifting wavelet transform adaptive signal decomposition is carried out by using the characteristics of the signal itself. Next, lifting wavelet transform is performed on the remaining IMF1 and IMF2 sub-band signals, and Shannon wavelet entropy is combined to describe the similarity between the fault characteristic waveform and fault gear waveform. The current signal of the gear box of a scraper conveyor under abnormal working conditions is usually a pulsating impact signal in the time domain. Therefore, when the impulse signal is transformed by lifting wavelet transform, the closer the wavelet basis function is to the impulse signal, the easier it is to extract the fault features. Among the orthogonal or biorthogonal wavelets related to the lifting scheme, the Daubechies wavelet function has the greatest similarity with the impact signal caused by the faulty gear among the common wavelets [42]. It should be noted that the more layers of wavelet decomposition and reconstruction, the better. More levels of decomposition will lose some details. However, fewer levels of decomposition layers will not be able to extract features effectively. Therefore, in this article the maximum number of decomposition layers is selected to be four layers [43,44]. The result is shown in Figure 11.

As shown in Figure 11, when the gear is broken, pitted and worn, respectively, the wavelet bases (Db6, 2), (Db7, 4), (Db8, 3) and (Db7, 3) and the number of decomposition layers are combined with each other. The Shannon wavelet entropy reaches the minimum value. Under this combination, the signal sparsity expressed is the best, and the wavelet bases associated with the lifting scheme and the fault characteristic waveform reach the maximum similarity. The VL operation results under the best matching wavelet basis and decomposition level are shown in Figure 12.

The experimental results show that four kinds of fault features can be extracted perfectly in the frequency domain by using the VL data preprocessing method under load interference. For broken teeth and normal working conditions, the irrelevant characteristic frequencies between 0 and 100 Hz are well suppressed, and the fault characteristic information is enhanced, which also shows the rationality of using Shannon wavelet entropy to describe the similarity between fault gear characteristic waveforms. And for pitting and wear conditions, the power frequency information is eliminated to the maximum extent, which also proves the effectiveness of the fusion VL algorithm in removing power frequency signals.

4. Comparative Test Under Load Interference

By comparing empirical mode decomposition with the EWT algorithm, the effectiveness of the VMD-LWT algorithm proposed in this paper is verified, and the operation results are shown in Figure 13.

The experimental results show that the EWT and EMD methods cannot extract all the characteristic information of broken teeth and normal working conditions under the condition of load impact interference, and certain load interference information is introduced. Specifically, the number of EMD decomposition layers is difficult to control in the case of broken teeth, so the EMD decomposition layers are not extracted in the case of broken teeth $f_e-2f_{r1}$ as well as the $f_e-f_{r1}$ characteristic frequency information . Because EWT has better adaptive time–frequency signal analysis ability, it can be extracted in the presence of serious load fluctuation interference $f_e-f_{r1}$ fault characteristic frequency information. In the case of a normal gear, EMD and EWT both extract serious power frequency information, while EMD extracts serious power frequency information $f_e+f_{r2}$ as well as $f_e+f_{r1}$ fault characteristic frequency information. And under pitting and wear conditions, both EMD and EWT can extract irrelevant frequency information caused by load fluctuation near the power frequency. In addition, the amplitude of fault feature spectrum extracted by EWT is obviously higher than that of the EMD method. However, for pitting conditions, EWT extracts too many false components.

5. Conclusions

In this paper, a fault diagnosis model of the reducer gear of a scraper conveyor based on VMD-LWT current signal feature extraction is established, which solves the problem that it is difficult to diagnose the fault of a scraper conveyor by vibration signal. The VMD-LWT gear fault feature extraction algorithm can effectively solve the problem of fault feature extraction of equipment under a low speed and heavy load and load shock, and provides a new means for fault diagnosis of equipment under bad working conditions by using current signals. The specific conclusions are as follows: (1) A low-speed and heavy-duty scraper conveyor current signal is characterized by simple overall frequency modulation, and the main component is power frequency information. In addition, the impact of load shock on the current signal is mainly on both sides of the power frequency signal. (2) The VMD-LWT gear fault feature extraction algorithm is proposed, which can effectively deal with the problem of difficult fault feature extraction of a scraper conveyor gearbox under load impact. The experimental results show that after the original current data are decomposed by VMD, the fault characteristic information is seriously affected by the impact of load under the condition of broken teeth and a normal gear. The characteristic information of gear failure caused by pitting and wear is affected by the working current frequency of the scraper conveyor. The progressive implementation of LWT for a VMD sub-band can suppress the irrelevant interference information in the sub-band signal.

However, the current research focuses on a single data set of the health status of the reducer gear of the scraper conveyor, and future work will focus on the detection of the more complex fault of the broken chain of the scraper conveyor, so that not only the broken chain fault can be detected, but also the position of the broken chain can be located.