Vibration Analysis for Fault Diagnosis in Induction Motors Using One-Dimensional Dilated Convolutional Neural Networks

Abstract

Motor faults not only damage the motor body but also affect the entire production system. When the motor runs in a steady state, the characteristic frequency of the fault current is close to the fundamental frequency, so it is difficult to effectively extract the fault current components, such as the broken rotor bar. In this paper, according to the characteristics of electromagnetic force and vibration, when the rotor eccentricity and the broken bar occur, the vibration signal is used to analyze and diagnose the fault. Firstly, the frequency, order, and amplitude characteristics of electromagnetic force under rotor eccentricity and broken bar fault are analyzed. Then, the fault vibration acceleration value collected by a one-dimensional dilated convolution pair is extracted, and the SeLU activation function and residual connection are introduced to solve the problem of gradient disappearance and network degradation, and the fault motor model is established by combining average ensemble learning and SoftMax multi-classifier. Finally, experiments of normal rotor eccentricity and broken bar faults are carried out on 4-pole asynchronous motors. The experimental results show that the accuracy of the proposed method for motor fault detection can reach 99%, which meets the requirements of fault motor detection and is helpful for further application.

1. Introduction

Induction motors are widely used in industrial applications, and their faults directly affect the safe operation of equipment, resulting in serious safety accidents and significant economic losses [1]. Rotor bar fracture and eccentricity error are common failures in winding cage induction motors. Accurate fault diagnosis and detection of rotor bar faults and eccentricity faults is essential to improve the stability of the motor and reduce economic losses of system operation.

The traditional frequency domain analysis method of rotor broken bar fault diagnosis mainly uses Fourier transform to analyze the stationary signal of motor current. However, due to the inherent limitations of Fourier spectrum analysis, the fault characteristic frequency f_b is very close to the power supply frequency f in the spectrum in the case of low slip frequency. Therefore, the signal must be long enough to obtain high-frequency resolution to perform Fourier transform analysis [2]. In order to overcome the defects of the traditional motor current signal analysis method at low slip frequency, scholars have proposed some solutions: ① The fault frequency is converted by mathematical transformation to frequencies, such as 2sf and (1 ± s)2f, that are far from the fundamental frequency. Such methods include motor current square signal analysis, motor current mode signal analysis, Park’s vector square modulus, Park’s vector product method, and so on [3,4]. ② In order to highlight the fault frequency component, the fundamental frequency component is filtered out directly by signal processing or transformed into DC and then filtered out. Such methods include the extended Kalman filter, Hilbert transform, Park’s vector modulus analysis, and so on [5,6]. These methods can avoid the risk that the fault characteristic frequency is submerged by the fundamental frequency, but the spectrum leakage problem still cannot be solved. In order to solve the spectrum leakage problem further, multiple signal classification and estimation of signal parameters via rotation invariance technique (ESPRIT) are introduced to make up for the shortcomings of high-frequency resolution spectrum estimation technique in computational efficiency and estimation accuracy [7]. Moreover, the vibration signal is commonly used to study fault frequencies in fault induction motors [8].

Aiming at the rotor eccentricity fault diagnosis in induction motors, some researchers have conducted extensive work [9]. Joksimović et al. [10] found that when a motor has a mixed eccentricity fault, the low-frequency characteristic frequency of the current fault can be expressed as f₀ ± f_r (where f₀ is the power frequency, f_r is the transfer frequency, f_r = (1 − s)/p), where s denotes slip, and p is the motor pole pairs. [6] proposes to diagnose motor air-gap eccentricity faults based on characteristic harmonic components in stator current and vibration signal spectra and realize multi-signal monitoring of motor air-gap eccentricity faults. Based on the convolution theorem, the diagnosis model with space harmonics and time harmonics stator currents of rotor eccentricity of induction motor is constructed in [11]. A modified Prony’s method for rotor-eccentricity fault detection in induction motors is proposed in [12] based on the time-domain technique. A model-based fault diagnosis technique for the rotor-eccentricity fault of the induction motor is proposed in [13]. In [14], it presents a novel motor current signature analysis method to diagnose the static eccentricity fault in induction motors.

Based on Fourier transform, it may bring spectrum aliasing, spectrum leakage, fence effect, spectrum interference, and other effects, so an intelligent neural network algorithm is also used for fault diagnosis and recognition [15]. A multi-scale convolutional neural network is presented to diagnose and classify features of gearbox vibration signals [16]. In [17], a square pool architecture Convolutional Neural Network (CNN) is adopted to acquire the high-level features, and the Extreme Learning Machine classifier is applied to classify the fault signals. The one-dimensional CNN is used to process the vibration signals for fault detection in [18] and to decrease the high-frequency noise in bearing signals. The one-dimensional CNN with a wide convolutional layer is proposed in [19,20]. In traditional CNNS, multi-layer convolutions are required to process long sequence data, resulting in large models. The model size can be reduced by superimposing pooling layers, but the important characteristic information of fault may be lost by adding pooling layers.

To solve the above problems, a fault diagnosis method based on a One-Dimensional Dilated Convolutional Neural Network (1D-DCNN) for induction motors is proposed in this paper. The dilated convolution can solve the problem of feature accuracy and feature information loss caused by convolution and pooling, and it can parallelize the computation for easy training. The dilated convolution is applied in fault detection in the one-dimensional vibration signal of an induction motor, and this paper is organized as follow: Section 2 analyzes the electromagnetic force that excites the vibration in different rotor fault condition. Section 3 introduces the 1D-DCNN model. Section 4 includes the fault experiments of the induction motor and the fault diagnosis validations. Section 5 presents the discussion and future work.

2. Electromagnetic Force Analysis under Fault

The vibration signals are used to identify motor faults, so the electromagnetic force under normal working conditions, rotor eccentricity, and rotor broken bar are analyzed in detail.

2.1. Normal

The electromagnetic radial force generated by the air-gap magnetic field of the motor, which is applied to the inner surface of the stator core, is proportional to the square of the magnetic flux density according to the Maxwell stress tensor method, and it can be determined by:

$$p_n(\theta ,t)=\frac{b^2(\theta ,t)}{2{\mu }_0},$$

(1)

where $b(\theta ,t)$ is the air gap magnetic flux density, and ${\mu }_0=4\pi \times {10}^{-7}$ H/m is the air permeability.

According to the electromagnetic theory of asynchronous motors, the air gap magnetic field of asynchronous motors can be written as [21]:

$$\begin{array}{ll}b(\theta ,t)=& B_1\cos (p\theta -{\omega }_{1}t-{\phi }_1)+{\displaystyle \sum _{v_z}{B}_{v_z}}\cos (v_z\theta -{\omega }_{1}t-{\phi }_{v_z})\\ & +{\displaystyle \sum _{{\mu }_z}{B}_{{\mu }_z}}\cos ({\mu }_z\theta -{\omega }_{\mu }t-{\phi }_{{\mu }_z})\end{array},$$

(2)

where

$${\omega }_{\mu }=[1+k_2\frac{Z_2}{p}(1-s)]{\omega }_1,$$

(3)

$$v_z=p(6k_1+1), {\mu }_z=k_2{Z}_2+p.$$

(4)

B₁, $B_{{\mathsf{\nu }}_{\mathrm{z}}}$ and $B_{{\mu }_z}$ are the magnitude of the fundamental, the stator harmonic ${\nu }_z$, and the rotor harmonic ${\mu }_z$ magnetic flux density, respectively. p is the pole pairs, $\theta$ is the stator position angle, ${\omega }_1$ is the fundamental angular velocity, t is time, ${\nu }_z$ is the stator slot spatial harmonics, ${\mu }_z$ is the rotor slot spatial harmonics, ${\phi }_1$, ${\phi }_{{\nu }_z}$, ${\phi }_{{\mu }_z}$ are the phase angles of different harmonic magnetic fields, Z₂ is the rotor slot number, s is the slip, and $k_1,k_2=\pm 2,\pm 1$, …

By substituting (2) into (1), the radial force wave generated by the air gap magnetic field is [21]:

$$\begin{array}{ll}{p}_n& =\frac{b^2}{2{\mu }_0}=\frac{1}{2{\mu }_0}[B_1\cos (p\theta -{\omega }_{1}t-{\phi }_1) +{\displaystyle \sum _{v_z}{B}_{v_z}}\cos (v_z\theta -{\omega }_{1}t-{\phi }_{v_z})\\ & +{\displaystyle \sum _{{\mu }_z}{B}_{{\mu }_z}}\cos ({\mu }_z\theta -{\omega }_{\mu }t-{\phi }_{{\mu }_z}){]}^2 ={\displaystyle \sum _r{p}_r}\cos (r\theta -{\omega }_{r}t-{\phi }_r)\end{array},$$

(5)

where p_r is the amplitude of the rth-order radial force, r is the spatial order, ${\omega }_r$ is the angular velocity, ${\phi }_r$ is the phase angle.

Table 1. The air gap force density in induction motor [21].

Type	Order r	Frequency ${\mathit{\omega }}_{\mathit{r}}$	Amplitude pr
Fundamental wave force	2p	2${\omega }_1$	$B_1^2/4{\mu }_0$
Product of fundamental and stator harmonics	$v_z+p$	2${\omega }_1$	$B_1{\displaystyle \sum _{v_z}{B}_{v_z}}/2{\mu }_0$
	$v_z-p$	0
Product of fundamental and rotor slot harmonics	${\mu }_z\pm p$	${\omega }_{\mu }\pm {\omega }_1$	$B_1{\displaystyle \sum _{{\mu }_z}{B}_{{\mu }_z}}/2{\mu }_0$
Product of stator harmonics and rotor harmonics	$v_z\pm {\mu }_z$	${\omega }_{\mu }\pm {\omega }_1$	$B_{v_z}{B}_{{\mu }_z}/2{\mu }_0$

summarizes the characteristics of the air gap electromagnetic force in the induction motor.

The first part is the interaction force between the fundamental magnetic field generated by the fundamental current, which will produce vibration with twice the frequency of the power supply. It is one of the main vibration components in the motor, and it is inevitable. Parts 2 and 3 are the electromagnetic force generated by the interaction between the fundamental magnetic field and the harmonic magnetic field. In the no-load condition, the amplitude of these two terms is smaller.

Part 4 is the force wave caused by the interaction of the stator and rotor teeth harmonic magnetic field, which is generally the main component of electromagnetic noise, and the distributed frequency is within the range of the human ear.

2.2. Static Eccentricity

Due to manufacturing errors and mechanical wear, the motor’s eccentric fault occurs, and a common fault is a static eccentricity; that is, the center of the fixed rotor is offset, but the eccentric position is unchanged when the rotor is rotating. Then, the air gap can be expressed as:

$$\delta ={\delta }_0-{\delta }_{\epsilon }\cos (\theta ),$$

(6)

where ${\delta }_0$ is a uniform air gap, ${\delta }_{\epsilon }$ is eccentric.

Without considering the force wave component with high order and small amplitude and ignoring the constant component, the additional electromagnetic force can be written as:

$$\begin{array}{c}{f}_{re}(\theta ,t)=\frac{B_1^2{\epsilon }^{\prime }}{4{\mu }_0}\cos [(p\pm (p\pm 1))\theta -({\omega }_1\pm {\omega }_1)t-{\varphi }_{0r}]+\\ {\displaystyle \sum _{v_Z}{\displaystyle \sum _{{\mu }_Z}\frac{B_v{B}_{\mu }{\epsilon }^{\prime }}{2{\mu }_0}\cos [(v\pm (\mu \pm 1))\theta -({\omega }_1\pm ({\omega }_{\mu }\pm 1))t-({\varphi }_{vr}-{\varphi }_{\mu r})]}}\end{array},$$

(7)

It can be seen from the formula that when the additional $p\pm 1$-order magnetic field interacts with the main magnetic field, the first-order low-frequency electromagnetic force may be generated by

$$r=p\pm 1-p=1,$$

(8)

The frequency of this force is:

$$\omega ={\omega }_1\pm {\omega }_1,$$

(9)

That is, when the static eccentricity of the rotor occurs, the frequency of the force may be 0.

Table 2. Additional electromagnetic force characteristics due to static eccentricity [21].

Type	Order	Frequency	Amplitude
The electromagnetic wave is generated by the interaction between the $p\pm 1$ additional magnetic field generated by the stator eccentricity and the fundamental magnetic field.	$2p\pm 1$	$2\omega$	$\frac{B_1^2{\epsilon }^{\prime }}{4{\mu }_0}$
	$\pm 1$	0
The ${\mu }_z\pm$ 1 additional magnetic fields generated by the rotor’s static eccentricity interact with the stator harmonics to generate force waves.	${\mu }_z\pm 1+v_z$	$\frac{k_2{Z}_2}{p(1-s){\omega }_1+2{\omega }_1}$	$\frac{B_{{\mu }_z}{B}_{v_z}{\epsilon }^{\prime }}{2{\mu }_0}$
	${\mu }_z\pm 1-v_z$	$\frac{k_2{Z}_2}{p(1-s){\omega }_1-2{\omega }_1}$
The ${\nu }_z\pm$ 1 additional magnetic fields generated by the rotor’s static eccentricity interact with the rotor harmonics to generate force waves.	$v_z\pm 1+{\mu }_z$	$\frac{k_2{Z}_2}{p(1-s){\omega }_1}$

shows the basic characteristics and parameters of the additional main electromagnetic force in the motor due to static eccentricity.

As can be seen from Table 2, when the ${\mu }_z\pm$1 magnetic field due to the static eccentricity interacts with the stator harmonics, the radial force with order ${\mu }_z\pm 1\pm {\nu }_z$, frequency $k_2{Z}_2 ∕p(1-s){\omega }_1+2{\omega }_1$ or $k_2{Z}_2 ∕p(1-s){\omega }_1$ and amplitude $B_{{\mu }_z}{B}_{{\nu }_z}{\epsilon }^{\prime }∕2{\mu }_0$ can be generated. When the ${\nu }_z\pm 1$ magnetic field interacts with rotor harmonics, the radial force with order ${\nu }_z\pm 1\pm {\mu }_z$, frequency $k_2{Z}_2 ∕p(1-s){\omega }_1+2{\omega }_1$ or $k_2{Z}_2 ∕p(1-s){\omega }_1$ and amplitude $B_{{\mu }_z}{B}_{{\nu }_z}{\epsilon }^{\prime }∕2{\mu }_0$ can be generated. Compared with the radial force in normal working conditions, as shown in Table 1, the frequency of the additional radial forces will not change, but the order will be different.

2.3. Rotor Broken Bar Fault

When the rotor bar of the squirrel-cage induction motor is broken, an additional magnetic field superimposed on the main magnetic field will be generated in the air gap, which is expressed as:

$$\begin{array}{c}{b}_r(\theta ,t)=B_r\cos \{r\theta -[(1-s)r/p+s]{\omega }_{1}t\}\\ r=\pm 1,\pm 2,\pm 3,\dots \end{array},$$

(10)

where r is the order number of additional magnetic fields, B_r is the amplitude of the additional magnetic field, p is the pole-pairs, s is the slip, ${\omega }_1$ is the current frequency.

Generally, the skewed rotor is adopted to reduce the harmonic magnetic field of the rotor teeth in the motor. The electromagnetic force wave is the interaction of each harmonic magnetic density in the air gap. Therefore, the interaction between the additional magnetic field and the stator tooth harmonic magnetic field is mainly considered when calculating the additional radial force wave. The stator harmonic magnetic field is expressed as follows:

$$b_v(\theta ,t)=B_v\cos (v\theta -{\omega }_{1}t),$$

(11)

where $B_{\nu }$ is the stator’s v-th harmonic magnetic field amplitude.

Additional electromagnetic force waves can be written as:

$$\begin{array}{ll}{f}_r=& \frac{b_r{b}_v}{2{\mu }_0}=\frac{B_r{B}_v}{4{\mu }_0}\cos \{(r+v)\theta +[s+1+(1-s)r/p]{\omega }_{1}t\}+\\ & \frac{B_r{B}_v}{4{\mu }_0}\cos \{(r-v)\theta -[s-1+(1-s)r/p]{\omega }_{1}t\}\end{array},$$

(12)

It can be seen from the formula that when the rotor bar is broken, additional electromagnetic force with order $r\pm \mathsf{\nu }$ and frequency $[s\pm 1+(1-s)r∕p]{\omega }_1$ is generated in the air gap. The order and frequency of the added electromagnetic force are different from that under normal working conditions.

2.4. Electromagnetic Force Simulation Verification

The simulation methods are used to analyze the air gap radial force of the motor under rotor eccentric and broken bar faults by using the Ansys simulation software. The simulated motor parameters are shown in

Table 3. The Parameters of the induction motor model.

Parameter	Value	Parameter	Value
Stator outer radius Ro/mm	65	Stator slot number	24
Stator inner radius Ri/mm	40	Rotor slot number	22
Stator length le/mm	75	Poles number	4

. The working conditions are set as follows: a three-phase sine voltage source with a frequency of 50 Hz and an amplitude of 220 V is applied, the rotor speed is 1410 rpm, the slip is s = 0.06, the eccentricity of the motor with rotor eccentricity fault is 20%, and the number of broken bars in the motor with rotor broken bar fault is 1.

Figure 1 shows the current waveform under different operating conditions. According to Figure 1, the amplitude of the fundamental current decreases when the rotor eccentric fault occurs. When a rotor bar fault occurs, a component with a frequency of (1–2s)f is induced in the stator current, which is very close to the fundamental frequency of the stator current. Under the modulation effect of this component 2sf, the stator current undergoes periodic fluctuations.

Figure 2 shows the electromagnetic torque under different working conditions. It can be seen that a rotor eccentricity fault can cause a decrease in average torque, and a broken bar fault can also cause a decrease in electromagnetic torque, and torque ripple will increase.

The radial force density under different operating conditions can be seen in Figure 3. It shows that due to the rotor eccentricity, additional odd-order forces appear, and these will cause significant distortion in the spatial distribution of the radial force density. When a broken bar fault occurs, significant odd-order force waves with larger amplitudes will be induced in the radial force density.

The stator tooth concentrated force of asynchronous motors under different faults can be shown in Figure 4. Compared with the radial force under normal working conditions, the radial force under broken bar faults exhibits rich harmonics, including components related to mechanical frequency and slip.

3. The 1D Dilated Convolutional Network Model

From the above analysis, it can be seen that the electromagnetic force of the induction motor in different motor faults has different characteristics, but the amplitudes in characteristic frequency are relatively weak, and simply relying on manual extraction of the vibration of the faulty motors for detection has limitations, which is easy to cause fault misjudgment. Therefore, using a deep learning model to extract motor vibration features, the extracted abstract features are more robust, have better generalization ability, and can accurately identify faults.

3.1. Dilated Convolution Theory

Two-Dimensional Convolutional Neural Networks (2D-CNN) have achieved unprecedented success in the field of computer vision, while One-Dimensional Convolutional Neural Networks (1D-CNN) are often applied to sequential tasks. In order to enlarge the receptive field and reduce the computation amount, the CNN model will add a pooling layer, thus losing the original input detail features and edge information. For this purpose, Dilated Convolution is introduced to obtain the same receptive field with fewer convolutional layers while maintaining the original input detail features and edge information. For vibration sequence data (x₁,x₂,…x_n), a one-dimensional dilated convolution operation is required, as shown in Figure 5. Dilated convolution introduces the dilation rate hyper-parameter, which defines the spacing values when the convolution kernel processes the sequence data. When dilation rate = 1, dilated convolution is equivalent to standard convolution, and the convolution kernel processes the input signal in a continuous manner. When the dilation rate = 2, the original convolution kernel inserts a 0 between each element to process the input signal in a jumping manner.

The one-dimensional dilated convolution output of the L-layer t position is calculated as follows:

$$O_t={\displaystyle \sum _{k=0}^{k-1}{w}_k^{(l)}{x}_{t+(k-\frac{k-1}{2})\cdot d_l}},$$

(13)

where k is the convolution kernel size, $w_k^{(l)}$ is convolution kernel parameter, d_l is expansion rate.

3.2. Model Building

The structure of the detection model in this paper includes an input layer, the 1D-DCNN module, an integrated learning classification layer, and an output layer. The 1D-DCNN module is a residual module composed of a convolution kernel size $3\times 1$ convolution and a Scaled Exponential Linear Unit (SeLU) activation function. Traditional neural networks usually adopt zero filling to prevent the input edge information from being lost, which will cause blind spots in the boundary effect and make the model sensitive to absolute position information. Therefore, the cyclic filling method is used in this paper to mitigate the boundary effect; that is, the convolutional layer convolved the beginning of the input signal and the end of the signal together, making the model more robust to data displacement. In this paper, the SeLU is adopted, namely [22]:

$$SeLU(x)=\lambda \{\begin{array}{cc}x& x>0.\\ \mathsf{\alpha }{e}^x-\mathsf{\alpha }& x\le 0.\end{array},$$

(14)

where $\mathsf{\alpha }$ and $\lambda$ are activation function parameters, and $\mathsf{\alpha }\approx 1.6733$ and $\lambda \approx 1.0507$ are calculated by Klambauer, the SeLU function introduces neural network self-normalization properties to prevent gradient disappearance and explosion problems. In order to reduce the size of the model, the expansion rate, which increases exponentially with the increase in network depth, is used; that is, the expansion rate of the first layer is $\mathrm{d}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}=2^1-1$. The model uses $l=\left[{\log }_2\raisebox{1ex}{$n$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right]$ layer void convolution to realize that each point output from the last convolution layer can obtain the complete sequence information of length n. Finally, simple mean ensemble learning and SoftMax is combined to make classification decisions. In this paper, residual connection [23] is introduced to solve problems such as model overfitting and network degradation in convolutional neural networks with the deepening of layers. Finally, the structure of the 1D-DCNN fault detection model constructed is shown in Figure 6.

4. Detection of Motor Faults Based on 1D-DCNN

4.1. Fault Data Set Construction

A fault motor test platform is built to simulate rotor eccentricity and broken bar faults, as shown in Figure 7. The platform is composed of a normal induction motor, a broken bar rotor, a GD300 controller produced by INVT, a load motor, a load resistor, a Yokogawa oscilloscope with model DLM2024, the acceleration sensor with model CA-YD-1182 and an acquisition system with model YE6231 produced by SINOCERA. The five kinds of motor fault experiments are conducted: no fault, rotor eccentricity 0.1 mm, rotor eccentricity 0.3 mm, rotor broken bar, and rotor broken bar with eccentricity 0.1 mm.

The sampling rate of the signal collector is set to 500 k times/second, and the vibration acceleration data within two seconds is recorded by 2 s. The motors under the five working conditions are numbered, as shown in

Table 4. Fault types and codes.

Number	Fault Type	Motor Speed/r/min
1	broken bars	1500 (load 8.5 Ω)
2	Rotor eccentricity 0.1 mm	1500 (load 8.5 Ω)
3	Normal machine	1500 (load 8.5 Ω)
4	Rotor eccentricity 0.3 mm	1500 (load 8.5 Ω)
5	Rotor broken bar with eccentricity 0.1 mm	1500 (load 8.5 Ω)

. Under the same speed and resistance load, the motor vibration test is carried out for each working condition.

The collected acceleration sequence contains vibration information varying with time. The change in vibration amplitude will increase the difficulty of detection model identification, so it is necessary to normalize the vibration sequence [−1,1]. Through the normalization function mapminmax in MATLAB software on the vibration sequence, $\mathrm{I}=[x_1,x_2,x_3\cdots ,x_{5000}]$ is normalized, and the normalization function mapminmax is shown in the equation

$$y=\frac{(y_{\max }-y_{\min })\times (x-x_{\min })}{x_{\max }-x_{\min }}+y_{\min },$$

(15)

By substituting $y_{\max }=1$ and $y_{\min }=-1$ into the normalization function, we can obtain

$$x_{n,i}=2\times \frac{x_i-x_{\min }}{x_{\max }-x_{\min }}-1,$$

(16)

where $x_{n,i}$ denotes the normalized acceleration, and $x_{\mathrm{i}}$ is the original acceleration value. The vibration sequence [−1, 1] is normalized, the vibration sequence under different working conditions is fixed to the same dimension, and the positive and negative change relationship of the vibration sequence is maintained. The vibration data under normal and fault state of the motor under experimental conditions are analyzed, as shown in Figure 8.

The vibration sequence of each working condition is divided into one cycle; each sample contains 5000 vibration sampling points, and the fault motor database is built. According to the principle of random sampling, the split data set of each working condition is divided into a training set, a verification set, and a test set, and the division ratio is set to 8:1:1. The results are shown in

Table 5. The constructed Database.

Fault Type	1	2	3	4	5
Training Data	320	320	320	320	320
Validation Data	40	40	40	40	40
Test Data	40	40	40	40	40

. In this case, the training set is 320 samples, the verification set is 40 samples, and the test set is 40 samples.

4.2. Model Training

The 1D-DCNN fault detection model is trained using the cross entropy loss function and the Adam optimizer. The Adam parameter is set as the learning rate l_r = 0.001, the exponential decay rate of the first-order moment estimate is 0.9, the exponential decay rate of the second-order moment estimate is 0.999, and the Epoch of training rounds is 100. In order to achieve fast model convergence, the training set and validation set are divided into batches, and the batch size is set to 64. The model accuracy is verified with the validation set when each time Epoch is trained, and the model parameters with the highest validation accuracy are saved. Then, its performance is evaluated with the test set. The parameters of the instantiated 1D-DCNN fault detection model are shown in

Table 6. Parameters of The Model.

Layer Class	Input Size	Output Size	Convolution Kernel Size
Input	(64,5000,1)	(64,1,5000)	—
1D-DCNN Module	(64,32,5000)	(64,32,5000)	3 × 1
Linear	(64,32,5000)	(64,12,5000)	1 × 1
Mean-pooling	(64,12,5000)	(64,12)	—
Output	(64,12)	(64,1)	—

.

In the model training process, the accuracy and loss curves of the training set and verification set change with the number of training iterations, as shown in Figure 9.

As can be seen from Figure 9, the accuracy of the training set increases rapidly at the beginning of the training, and at the 66th iteration, the accuracy reaches over 99% and tends to be stable. The loss value decreases from 1.22 to 0.011 and tends to 0. The accuracy of the validation set oscillates slightly, and by the 81st iteration, the accuracy of the validation set reaches more than 99% and tends to be stable. The loss value drops from 0.57 to 0.017 and tends to 0. The accuracy curve of training samples and verification samples no longer fluctuates greatly, which indicates that the model has high stability. The accuracy of the verification set reaches 99.67% in the 99th iteration, and the model parameters after the 99th training are saved. In the training process, there is no overfitting phenomenon, and the training results are good.

4.3. Model Performance Evaluation

The 200 samples of the test set in Table 3 are used to evaluate the performance of the model with the highest accuracy of the verification set, and the test set samples do not include the training set and the verification set samples. The verification results are shown in Figure 10. It can be seen from Figure 10 that among the 200 data samples, 198 data samples can be identified with fault categories, the number of wrong identification samples is 2, and the fault diagnosis rate is up to 99%. It can be seen that the accuracy of this method meets the diagnostic requirements of industrial equipment. The data of samples 30 and 39 of the first type of fault are misjudged as the fifth type of fault, and the electromagnetic vibration data of samples 30 and 39 are shown in Figure 11.

Moreover, a Comparative Analysis between the proposed method and the conventional one-dimensional CNN is conducted. The structure of the one-dimensional CNN model is shown in Figure 12. The CNN model is mainly composed of a feature extraction layer, a fully connected layer, and a SoftMax output layer. The feature extraction layer is composed of a convolutional layer and a pooling layer. First, the vibration signal serves as the input of the first convolutional layer. The convolutional layer has 64 filters, which are mainly used to initially extract the features of the vibration signal. Then, the output reaching threshold is mapped to another space using the ReLU activation function, and a maximum pooled layer for reducing the sampling rate simplifies the computational complexity and control overfitting. Next, three convolutional layers and two maximum pooling layers are used to extract deeper features in the vibration signals, and the global average pooling layer is used to average the inputs, stack them together, and reduce the computational cost. Finally, the overfitting degree can be reduced by Dropout, and the fault type can be classified by the Softmax classifier. The fault diagnostic results are presented in Figure 13, and the fault types can be seen in Table 4. It can be concluded that the accuracy of the conventional method for identifying faults is 95%, which is lower than the fault accuracy of the proposed method. Moreover, the samples with fault types 2, 3, and 4 in the proposed method have been successfully identified, but it is not effective in the conventional method. Therefore, it illustrates the advantages of the proposed method in feature extraction.

5. Conclusions

In this paper, the electromagnetic force characteristics of rotor eccentricity and broken bar faults in induction motors are analyzed. Aiming at the problem that rotor eccentricity and broken bar fault are not easy to detect, a fault detection model based on a one-dimensional dilated convolutional neural network is proposed to diagnose the motor fault. The proposed dilated CNN model provides an expert, efficient, intelligent solution for fault detection in induction motors. The dilated convolution facilitates faster training, accuracy, and improved convergence speed than other CNN models. The motor fault experiment platform is built, and the vibration signals of the motor under normal working conditions and two fault states are collected. Then, the fault database with one period as the sample is established. The model learns features independently from motor vibration acceleration data without manual feature extraction, and it can identify fault types at the same time. The performance of the model is verified by the test set, and the results show that the proposed model has a fault classification accuracy of 99%, which can meet the accuracy requirement of motor fault detection. In future work, multiple faults, including bearing faults and short-circuit winding faults, will be included in the data set.