Feature Ranking and Differential Evolution for Feature Selection in Brushless DC Motor Fault Diagnosis

Abstract

A fault diagnosis system with the ability to recognize many different faults obviously has a certain complexity. Therefore, improving the performance of similar systems has attracted much research interest. This article proposes a system of feature ranking and differential evolution for feature selection in BLDC fault diagnosis. First, this study used the Hilbert–Huang transform (HHT) to extract the features of four different types of brushless DC motor Hall signal. When there is a fault, the symmetry of the Hall signal will be influenced. Second, we used feature selection based on a distance discriminant (FSDD) to calculate the feature factors which base on the category separability of features to select the features which have a positive correlation with the types. The features were entered sequentially into the two supervised classifiers: backpropagation neural network (BPNN) and linear discriminant analysis (LDA), and the identification results were then evaluated. The feature input for the classifier was derived from the FSDD, and then we optimized the feature rank using differential evolution (DE). Finally, the results were verified from the BLDC motor’s operating environment simulation with the same features by adding appropriate signal-to-noise ratio magnitudes. The identification system obtained an accuracy rate of 96% when there were 14 features. Additionally, the experimental results show that the proposed system has a robust anti-noise ability, and the accuracy rate is 92.04%, even when 20 dB of white Gaussian noise is added to the signal. Moreover, compared with the systems established from the discrete wavelet transform (DWT) and a variety of classifiers, our proposed system has a higher accuracy with fewer features.

1. Introduction

In response to global environmental issues, environmental awareness and carbon emissions issues have received much attention. The demand for hybrid electric vehicles (HEVs) and electric vehicles (EVs) has gradually increased [1]. Attempts have been made to use HEVs and EVs instead of traditional vehicles, in order to reduce carbon emissions. The following topics need to be paid attention: the brushless DC motor (BLDC) that acts as a core piece of equipment in EVs [2], the range anxiety issue [3] and energy storage systems [4,5]. As time passes by, and with more research and development invested in EVs, such as sensitivity analysis of a rolling stock hydrogen hybrid powertrain [6], and a battery thermal management system [4,5], the work in this article constructed a system to identify the BLDC fault types. In order to detect the operation status of the BLDC, Hall sensors or sensorless algorithms based on back electromotive force are commonly used [7]. The three Hall sensors are installed into the BLDC motor with 120-degree phase differ-ences, so the Hall signals are 120 electrical degree phase differences in normal. When there is a fault, the symmetry of the Hall signal will be affected. A Hall sensor has the obvious advantages of a low cost and simple structure [8]. Additionally, DC motors using Hall sensors have been widely used in commercial and industrial applications [9]. Therefore, this article uses the Hall signal, which is an electrical technology, to establish an identification system. The motor may suffer from different failures, including stator failure [10,11,12], rotor failure [13,14], bearing failure [15,16], eccentricity fault [17] and inverter fault [18]. Stator failure accounts for 30% to 40% of the total failures in motors; rotor failure accounts for 5% to 10% of the total failures; and bearing failure accounts for 40% to 50% of total failures [19]. If the motor is running in a fault condition for a long time, it may cause operation economic losses due to poor performance, which may affect driving safety.

The comprehensive description of the proposed fault diagnosis system includes signal analysis, feature selection, optimization and classifiers. Signal analysis has been developed for decades, and the Hilbert–Huang transform (HHT) is based on the intrinsic mode functions (IMFs) of the original signal to calculate the instantaneous frequency, and then perform spectrum analysis [20]. It is necessary to calculate the IMF before fault diagnosis. When adding more IMFs, the calculation cost will be increased. If the IMF is insufficient, the representative information may be neglected [21]. However, since there is no need to choose the mother wavelet, it is not affected by the resolution of the time domain and frequency domain, and this can more accurately decompose the signal in the high-frequency domain. This technique is commonly used for fault detection in the fields of biomedical applications, structural testing and rotating machinery [22].

After signal analysis, the original signal can provide features with a good identification rate through feature selection. Feature selection can be divided into filter, wrapper, hybrid approach and embedded feature selection [23]. The filter type is based on the relationship between features as the criterion [24], and the wrapper type is based on the relationship between features and the target variable as the criterion [25]. The embedded type is usually used for high-dimensional data features [26,27]. The wrapper and hybrid approach types can obtain better results [28], but the filter type is usually used when considering the computational cost and a large number of features [26,27]. Therefore, this study used the filter feature selection to calculate feature weights, such as the FSDD, belonging to a clustering algorithm [29].

The FSDD calculates the distance discriminant factor of features that are based on the variance distance between feature clusters and within clusters. Due to the low computational complexity of the FSDD, it is suitable for high-dimensional problems or online feature selection [30]. The feature cannot obtain high numerical factors if they have good separation features, but there is a large distance within clusters. The features were obtained through signal analysis in this study, and then the factors of each feature were obtained from the FSDD. The features were entered into the classifier in the order of factors, and then the types of motor failures were identified by the classifier.

This article combines DE with feature factors after feature selection to optimize the feature ranking. DE is an effective and simple global optimization algorithm. The convergence speed and robustness of common benchmark functions and practical problems are better than those of many algorithms [31]. Finally, the recognition results of the BPNN were compared with the result of LDA. An artificial neural network (ANN) is a common nonlinear function processor that imitates the structure and pattern of the human brain [32]. The performance of the learning process of the neural network depends on the weights of the neural network in the training phase. A BPNN [33] is a supervised machine learning technique that adjusts its weights to minimize the error of the calculated output [33], and it is suitable for identifying nonlinear relationships [34]. In a feedforward ANN, the data flow has no feedback paths [35]. A BPNN is used in the fault diagnosis problem of NPC inverters [36], high-impedance faults [37] and virtual speed sensors for DC motors [38], while LDA is often used for supervised feature extraction and can also maximize the variance between classes based on linear projections, minimize the intra-class variance and finally obtain the largest separation between the feature sets in each class [39]. LDA can be used as a supervised classifier, through different types of data to maximize separation [40].

Based on the above-mentioned related literature, this research proposes a fault identification system for a BLDC established by Hall signals, which includes signal analysis selection, feature selection and classifiers.

2. Experimental Setup and Hardware Design

2.1. Experimental Design

This section introduces the experimental equipment, experimental architecture and signal samples in this research and studies the healthy and three different types of faults in a BLDC to build a fault classification system. A total of 750 samples of Hall signal data records for each motor and the measured signals were analyzed by the HHT in Matlab. After the analysis, the extracted features that can reflect the motor conditions were normalized so that the feature values of the 4 motor types were between 0 and 1, which avoids the gradient explosion problem in the classifier. Additionally, we will discuss the signals of the four conditions to grasp the operating conditions of the motor.

The BLDC (420 W/3020 rpm/DC 24 V/60 Hz) had the following three fault conditions in this experiment: bearing fault, stator winding fault and rotor fault. The data acquisition system (NI PXIe-1073) was used to acquire the Hall signal of the DC brushless motor, and the sampling rate was 1000 Hz, and the measurement time was 1500 s. There was a total of 1500 s of measurement records for BLDC motors in each condition, and the 1500-s data were divided into 750 samples of data, every sample having 2000 points. The load was simulated by an AC servo motor (11 kW/2000 rpm/69 Hz). Through the above equipment, the measurement data of the BLDC Hall signal can be obtained.

2.2. Experimental Architecture

The process of this research is that the servo motor of the dynamometer generates the opposite torque to the BLDC as the load, and then the BLDC motor drives the operation. The BLDCM rated voltage was 24 V, and the motor rate speed was configured as 3020 RPM. The BLDCM parameters are listed in

Table 1. BLDC parameters.

Type	Rated Current	Rated Torque	Rated Speed	Rated Output Power	Rated Efficiency
BL5K35030D	22.07 A	13.5 Kg-cm	3020 RPM	418.7 W	81.2%

. A total of four BLDCs were tested in this experiment. One motor was normal, whereas the other three motors were faulty. The faulty types included bearing damage in the inner raceway, winding short circuit and rotor damage. The bearing inner raceway had a 1 mm physical crack. The winding short circuit was set by exfoliating a part of the 2-coil insulation. The rotor damage was set by digging a hole. The NI PXIe-1073 was used to capture the Hall signal during operation. The data from the measurement were analyzed by Matlab for signal analysis, and then feature selection was used to calculate the factor of the features. The rank of features was optimized by DE after the features were ranked in descending order by the feature factors. Finally, the results of the fault type identification from classifiers were returned. The experimental process and configuration are shown in Figure 1.

3. Proposed Method

3.1. Signal Analysis and Feature Extraction

The signal can be expressed in the time and frequency domains. In some cases, the frequency domain of the signal can be presented in a clearer way than the time domain [41]. Additionally, the signals are usually significantly different elements. These scores cannot be expressed in the same base function, meaning two or more base functions are required to analyze the signal separately [42].

Dr. Norden E. Huang proposed the HHT in 1998, and it has since been widely used in speech analysis and nonlinear and unstable signal analysis [43]. Empirical mode decomposition is the basic theory of the HHT. IMFs through the Hilbert transform can be used to obtain the Hilbert spectrum of the analysis data.

The original function of the input is represented by x(t), which can be decomposed into n IMFs and trend functions through EMD. EMD is modeled as

$$x(t)={\displaystyle \sum _{l=1}^n{h}_l(t)+r_n(t)}$$

(1)

Then, IMFs are brought into the Hilbert transform (HT) to obtain the instantaneous amplitude and instantaneous frequency of the signals. The HT is modeled as

$$H_l(t)=\frac{1}{\pi }Pv{\displaystyle \underset{-\infty }{\overset{\infty }{\int }}\frac{h_l\left(\tau \right)}{t-\tau }}d\tau$$

(2)

where Pv is the caution principal value, which is to avoid the singularity of $\tau =t$ and $\tau =\pm \infty$. The Hilbert spectrum is formulated as

$$Z_l(t)=h_l(t)+j{H}_l(t)=a_l(t)e^{j{\theta }_l\left(t\right)}$$

(3)

where $h_l\left(t\right)$ represents the IMF, and $H_l\left(t\right)$ can be obtained through Hilbert transformation. Among them, $a_l\left(t\right)$ is the instantaneous amplitude, and ${\theta }_l\left(t\right)$is the instantaneous phase angle.

The four types of motor Hall signals were decomposed through empirical mode decomposition, which separates the signal from the first to eighth layers (IMF1 to IMF8), and the instantaneous amplitude and instantaneous frequency of each layer were obtained through the Hilbert–Huang transform. Additionally, we then captured the maximum (Tmax), average (Tmean), mean square error (Tmse), standard deviation (Tstd), maximum/mean (Tmax/Tmean) and maximum/root mean square (Tmax/Trms) of the time domain, and the maximum (Fmax), average (Fmean), mean square error (Fmse), standard deviation (Fstd), maximum/average (Fmax/Fmean) and maximum/root mean square (Fmax/Frms) of the frequency domain. Each IMF took 12 features and normalized them so that the feature values of the 4 motor types were distributed between 0 and 1. This step obtained a total of 96 features, as shown in

Table 2. Feature extraction of the HHT.

		Max	Mean	Mse	Std	Max/Mean	Max/Rms
Time domain	IMF1	F1	F2	F3	F4	F5	F6
	IMF2	F7	F8	F9	F10	F11	F12
	IMF3	F13	F14	F15	F16	F17	F18
	IMF4	F19	F20	F21	F22	F23	F24
	IMF5	F25	F26	F27	F28	F29	F30
	IMF6	F31	F32	F33	F34	F35	F36
	IMF7	F37	F38	F39	F40	F41	F42
	IMF8	F43	F44	F45	F46	F47	F48
Frequency domain	IMF1	F49	F50	F51	F52	F53	F54
	IMF2	F55	F56	F57	F58	F59	F60
	IMF3	F61	F62	F63	F64	F65	F66
	IMF4	F67	F68	F69	F70	F71	F72
	IMF5	F73	F74	F75	F76	F77	F78
	IMF6	F79	F80	F81	F82	F83	F84
	IMF7	F85	F86	F87	F88	F89	F90
	IMF8	F91	F92	F93	F94	F95	F96

.

The normal BLDC Hall signal was decomposed by the empirical mode, and it generated the IMF waveform, as shown in Figure 2a. The transform first extracted a signal of a high frequency, and the subsequent layers of the IMF were low-frequency waveforms.

The feature map is a schematic of the features from 3000 pieces of data, and the feature map was drawn by Matlab. The vertical axis of the feature map is the number of features, and the horizontal axis is the number of data. As it is shown in Figure 2b, the features from the four types of motors are highly similar, and there is no obvious difference.

3.2. Feature Selection

The system includes feature selection in order to pick out the few critical features from the signal. The feature selection was implemented using the FSDD of the clustering algorithm to calculate the category separability of features. The high value of the factor represents an important feature. Additionally, the features were ranked in descending order by feature factors after feature selection. The features of the Hall signal extracted after signal analysis can reduce the recognition rate of the classifier or not affect the recognition result by feature selection and deletion, which can save the cost of the calculation of the recognition system.

The feature distance discriminant factor ${\lambda }^m$ is based on the Euclidean distance between the features of the same category $d_w^m$ and the Euclidean distance between the features of different classes $d_b^m$. The flow chart of the FSDD is shown in Figure 3. The Euclidean distance of the feature was calculated by the center of the category feature $g_c^m$and the center of the sample feature $g_i^m$, where C, m and i are the category number, feature number and sample number. $q_i^m$ is the feature of the sample. The compensation factor ${\eta }^m$ was calculated by the distance variance $u_b^m$ and $v_w^m$. The calculation procedure is as follows:

Step 1.

Calculate the variance and average of all the samples in the mth feature.

$${\sigma }_m^2=\frac{1}{N}{\displaystyle \sum _{i=1}^N{\left(q_i^m-\overline{q^m}\right)}^2}$$

(4)

$$\overline{q^m}=\frac{1}{N}{\displaystyle \sum _{i=1}^N{q}_i^m}$$

(5)

Step 2.

Calculate the variance and the average of the sample of class C in the mth feature.

$${\sigma }_{m(C)}^2=\frac{1}{N_C}{\displaystyle \sum _{i=1}^{N_C}{\left(q_i^m-\overline{q_C^m}\right)}^2}$$

(6)

$$\overline{q_C{}^m}=\frac{1}{N_C}{\displaystyle \sum _{i=1}^{N_C}{q}_i^m}$$

(7)

Step 3.

Calculate the weighted variance of the class center $g_C$ at the mth feature.

$${{\sigma }^{″}}_m^2={\displaystyle \sum _{C=1}^C{\rho }_C{\left(g_C^m-g^m\right)}^2}$$

(8)

$$g^m={\displaystyle \sum _{C=1}^C{\rho }_C{g}_C^m}$$

(9)

Step 4.

Calculate the inter-class distance $d_b$ of the mth feature and the intra-class distance $d_w$ of the mth feature.

$$d_b^m=\frac{{{\sigma }^{″}}_m^2}{{\sigma }_m^2}$$

(10)

$$d_w^m=2\frac{{\displaystyle \sum _{C=1}^C{\rho }_C{\sigma }_m^2\left(C\right)}}{{\sigma }_m^2}$$

(11)

$${\rho }_C=\frac{N_C}{{\displaystyle \sum _{C=1}{N}_C}}$$

(12)

Step 5.

Calculate the variance factor $v_b^m$ of $d_b^m$ in the mth feature and the variance factor $v_w^m$ of $d_w^m$ in the mth feature.

$$v_b^m=\frac{max\Vert \overline{g_i^m}-\overline{g_C^m}\Vert }{min\Vert \overline{g_i^m}-\overline{g_C^m}\Vert }$$

(13)

$$\Vert \overline{g_i^m}-\overline{g_C^m}\Vert =\frac{\overline{g_i^m}-\overline{g_C^m}}{{\sigma }_m^2}$$

(14)

$$v_w^m=\frac{max\left(d_w^m\right)}{min\left(d_w^m\right)}$$

(15)

Step 6.

Calculate the compensation factor of the mth feature.

$${\eta }^m=\frac{1}{v_w^m}+\frac{1}{v_b^m}$$

(16)

Step 7.

Calculate the distance discrimination factor of the mth feature.

$${\lambda }^m=d_b^m-{\eta }_m{d}_w^m$$

(17)

Step 8.

Normalize the distance discriminant factor.

$${\lambda }^{m^{\prime }}=\frac{{\lambda }^m-min\left({\lambda }^m\right)}{max\left({\lambda }^m\right)-min\left({\lambda }^m\right)}$$

(18)

3.3. Differential Evolution

The differential evolution proposed by Storn and Price is an optimization technology used to solve various complex problems [31]. The calculation principle is similar to the genetic algorithm (GA), including three mechanisms of mutation, crossover and selection. The offspring are derived from random parental parameter mutations, as shown in Figure 4. At the same time, this algorithm refers to particle swarm optimization (PSO) to make the evolution direction approach the best particle. DE is a random search algorithm, and the randomness used in this algorithm prevents the algorithm from falling into the local optimum. Therefore, it can be used for many important problems that need to be optimized, including neural network training, and Bayesian network inference [44]. The algorithms are combined with the DE algorithm to improve the computational efficiency or improve the recognition rate [45,46]. In this article, the identification result was set as the fitness value, the input was the feature rank and the output was the new feature ranking, and the feature ranking order was optimized by DE after features were ranked to improve the identification. The calculation procedure of the differential evolution algorithm is as follows:

Step 1.

Initially, set the parameters including the number of particles and the number of iterations j. $G_{1,0}$ is the first generation input of the first particle of the particle group initially.

Step 2.

Calculate the fitness value of the first generation of the first particle.

Step 3.

Randomly select the parameters in the offspring $G_{1,j}$, $G_{2,j}$ and $G_{3,j}$ to produce mutations.

$$V_{r,j+1}=G_{1,j}+F\left(G_{2,j}-G_{3,j}\right)$$

(19)

Step 4.

The step of crossover is a random operation that bases on rand and CR. If CR is smaller, it means vectors U and G are more similar.

$$U_{r,j+1}=\left\{\begin{array}{cc}{V}_{r,j+1}& if\hspace{1em}rand\le CR\\ G_{r,j+1}& if\hspace{1em}rand>CR\end{array}\right\}$$

(20)

Step 5.

The step of elimination obtains a better fitness value through the greedy algorithm.

$$U_{r,j+1}=\left\{\begin{array}{cc}{U}_{r,j+1}& if\hspace{1em}{U}_{r,j+1}\le G_{r,j}\\ G_{r,j}& \end{array}\right\}$$

(21)

Step 6.

The stopping rule is whether the fitness value has converged, meaning the optimal value. The fitness value is one minus the accuracy rate (1-ACC). If the number of calculations reaches the iterations j, it stops. Otherwise, repeat steps 3 to 5.

Step 7.

Finally, all particles converge to obtain the best global solution. After the optimization, a set of solutions can be obtained as the best particle coordinate $G_{\mathrm{best}}$which is the optimized importance of the feature.

3.4. Classifier

The feature rank is obtained by feature selection, which is conducive to the classifier of the neural network model. The nonlinear classifier BPNN will be compared with the linear projection classifier LDA. The classifier randomly selects 70% of the data from the motor samples, and the features are brought into the classifier for training, and the remaining 30% of data are used as test samples.

3.4.1. Backpropagation Neural Network

A BPNN imitates the capabilities of neural system resource processing data and discriminant analysis by simulating the structure of biological data processing. Among them, neurons are used for message transmission and backpropagation to correct errors in order to achieve the best identification result. A BPNN has three structures that are composed of an input layer, a hidden layer and an output layer. The model structure is shown in Figure 5. By entering the input value ${X=(X}_1{,X}_2{\dots X}_n)$ and weights ${W=(W}_1{,W}_2{\dots W}_n)$ in the input layer, the expected output result ${Y=(Y}_1{,Y}_2{,Y}_3{,Y}_4$) will be obtained after the hidden layer ${H=(H}_1{,H}_2{,H}_3{\dots H}_k)$. Then, the error will be corrected by backpropagation, and the new weight will be brought into the forward propagation to obtain the output result ${O=(O}_1{,O}_2{,O}_3{,O}_4)$.

3.4.2. Linear Discriminant Analysis

LDA is used to obtain the new coordinate position of the best distance between the classes and minimize the distance within the class through the projection coordinate axis, which is used to judge different classes. First, one must calculate the intra-class distance matrix $S_w$ and the inter-category distance matrix $S_b$ as

$$S_w=\frac{1}{N}{\displaystyle \sum _{c=1}^C{\displaystyle \sum _{x\in X_N}^N\left(x-{\mu }_c\right){\left(x-{\mu }_c\right)}^T}}$$

(22)

$$S_b=\frac{1}{C}{\displaystyle \sum _{c=1}^C\left({\mu }_c-\mu \right){\left({\mu }_c-\mu \right)}^T}$$

(23)

Secondly, the projection matrix ${W=S}_w^{-1}{S}_b$ must be calculated by $S_w$ and $S_b$, where the maximum W is the final projection matrix, and the sample features and projection matrix should be converted into new sample features for classification.

4. Method Efficiency and Robustness

4.1. Dataset Results

We unified the UCI dataset identification results when the initial factor was the same [47]. Then, the feature rank of the dataset was optimized so the features were sequentially entered into the classifier. From

Table 3. The accuracy rate of the different recognition systems.

Dataset	Optimize	Classifier	Number of Feature	Accuracy (%)
segmentation	–	BPNN	19	85.62
	DE	BPNN		91.77
	–	LDA		78.35
	DE	LDA		78.42
sonar	–	BPNN	60	84.66
	DE	BPNN		87.21
	–	LDA		71.20
	DE	LDA		72.24
wine	–	BPNN	13	77.96
	DE	BPNN		89.81
	–	LDA		98.30
	DE	LDA		98.90
vowel	–	BPNN	10	44.52
	DE	BPNN		49.61
	–	LDA		58.10
	DE	LDA		60.60
WDBC	–	BPNN	30	62.74
	DE	BPNN		66.98
	–	LDA		95.30
	DE	LDA		95.63

, it can be observed that the identification rate of the BPNN can be significantly improved when the factors are optimized by DE.

4.2. Identification System Validation Results

The work in this article built a system, and an original signal was brought into the system. In the classifier part of the system, the signal was separately brought into the BPNN and LDA to compare different classifiers which can obtain better results in BLDC fault diagnosis. The features from 2100 samples of data were brought into the classifier for training, whilst the features from the remaining 900 samples of data were used as test samples, and this was repeated 100 times to calculate the average accuracy rate in order to know the resolution of the degree of the type of motor failure. Initially, the input was 96 features, and then the number of inputs decreased after the feature selection. The data matrix was 96 × 3000, which means 96 features and 3000 samples from four types of motor.

The signal was directly recognized by the classifier after the feature analysis by the HHT. Although the number of features was the largest, there may be more features that cannot clearly distinguish the fault, which led to an accuracy rate for the BPNN of 95.70%, and an accuracy rate for LDA of 74.89%. Feature selection can reduce computational costs by determining the features of less influence and redundancy.

In Figure 6, the accuracy rate is 93.96% when the FSDD selects 14 features. When the data are brought into the linear classifier LDA, the best accuracy rate is 74.57% in the FSDD feature selection, as shown in Figure 6. Of the two methods, the BPNN can obtain a higher recognition rate and smooth accuracy rate, as when the number of features is 14 in the BPNN, the accuracy rate is 93.96%, as shown in

Table 4. The accuracy rate of the better recognition results in two systems.

Signal Analysis	Feature Selection	Classifier	Number of Features	Accuracy (%)
HHT	FSDD	BPNN	14	93.96
HHT	FSDD	LDA	56	74.57

. From Table 3, it can be observed that the identification rate of the BPNN can be significantly improved when the factors are optimized by DE. However, the result of LDA would not obviously improve. Therefore, it is concluded that the BPNN is a better classifier in this identification system.

In Figure 6, we know that the accuracy rate starts to stabilize when the number of features is 14. From this finding, the work in this article used a differential evolution to optimize the factor of the first 14 important features. The first 14 features are F36, F33, F81, F18, F61, F57, F87, F94, F62, F93, F59, F12, F37 and F28.

This research used DE to optimize the factor of the first 14 features that were introduced into the BPNN and LDA. The accuracy rate was increased from 93.96% to 96.00%, and the recognition rate was improved by 3%, as shown in

Table 5. The accuracy rate of the different recognition systems.

Signal Analysis	Feature Selection	Optimizer	Classifier	Number of Features	Accuracy (%)
HHT	–	–	BPNN	96	95.70
HHT	FSDD	–	BPNN	14	93.96
HHT	FSDD	DE	BPNN	14	96.00

. The factor of features selected by the FSDD that were optimized by DE can effectively increase the recognition rate and reduce the number of features by 85%.

The systems conducted signal analysis by the DWT, and the features that were brought into the various classifiers [48] compare with those of the identification system presented in this article. The result of the initial system that just has the HHT and the BPNN was 95.70%, already better than the other systems. The result of the systems established from a variety of classifiers with the DWT were not higher than 90%, and the result of the identification system proposed in this article was 96.00%, as shown in

Table 6. The accuracy rate of the different recognition systems.

Signal Analysis	Feature Selection	Optimizer	Classifier	Number of Features	Accuracy (%)
HHT	–	–	BPNN	96	95.70
HHT	FSDD	DE	BPNN	14	96.00
DWT	–	–	Fine Gaussian SVM [48]	112	74.40
DWT	–	–	Fine KNN [48]	112	76.30
DWT	–	–	Bagged Trees [48]	112	89.90
DWT	–	–	Subspace KNN [48]	112	76.30

.

The Hall signal was analyzed by the HHT, and then the FSDD was used for feature selection, which was combined with DE to optimize the importance of features. Finally, features were brought into the BPNN to obtain the identification result. In

Table 7. The accuracy rate in the different SNRs.

Signal Analysis	Feature Selection	Optimizer	Classifier	Number of Features	∞ dB	30 dB	25 dB	20 dB
HHT	–	–	BPNN	14	93.96	92.66	92.13	90.84
HHT	FSDD	DE	BPNN		96.00	94.28	92.42	92.04

, the original signal is added with different proportions of white noise. After the feature importance was optimized, the noise-free accuracy rate was 96.00%, which is better than the non-optimized accuracy rate of 93.96%. The accuracy rate was 92.04% when the SNR was 20 dB, which is still better than the non-optimized accuracy rate of 90.84% when the SNR was 20 dB. It is confirmed that this method has a robust anti-noise ability.

5. Conclusions

In fault types, bearing damage, stator winding failure and rotor damage make up the majority. The complexity of fault detection is reduced through this system in executing the preliminary diagnosis. This article presented a fault classification system for BLDCs. This system includes four subsystems which are signal analysis, feature selection, ranking optimization and classifiers. In this article, the proposed system reduced the number of features to 14, which significantly eliminated 85% of the redundant features, and the final accuracy rate reached 96.00%, which is higher than the result of the identification of 96 features. In terms of the anti-noise ability, the original signal was added with different white Gaussian noise SNRs = 20 dB. The accuracy rate was 92.04% in the same 14 features; thus, the identification system has a robust anti-noise ability.