Effective Rotor Fault Diagnosis Model Using Multilayer Signal Analysis and Hybrid Genetic Binary Chicken Swarm Optimization

Abstract

This article proposes an effective rotor fault diagnosis model of an induction motor (IM) based on local mean decomposition (LMD) and wavelet packet decomposition (WPD)-based multilayer signal analysis and hybrid genetic binary chicken swarm optimization (HGBCSO) for feature selection. Based on the multilayer signal analysis, this technique can reduce the dimension of raw data, extract potential features, and remove background noise. To compare the validity of the proposed HGBCSO method, three well-known evolutionary algorithms are adopted, including binary-particle swarm optimization (BPSO), binary-bat algorithm (BBA), and binary-chicken swarm optimization (BCSO). In addition, the robustness of three classifiers including the decision tree (DT), support vector machine (SVM), and naive Bayes (NB) was compared to select the best model to detect the rotor bar fault. The results showed that the proposed HGBCSO algorithm can obtain better global exploration ability and a lower number of selected features than other evolutionary algorithms that are adopted in this research. In conclusion, the proposed model can reduce the dimension of raw data and achieve high robustness.

1. Introduction

Rotating machines are among the most significant devices in the industry field. Many rotating machines that break down usually cause an unexpected operation. In the worst case, rotating machine failures cause tremendous economic losses or serious casualties. One of the most critical components of rotating machines is the rotor. Rotor bar failure will cause speed and torque fluctuations and lead to shaft vibration, which leads to the premature failure of other motor components [1]. Thus, early detection for the rotor fault can also help prevent other types of fault, like bearing or eccentricity [2]. Considering the reliability and performance of rotating machines, the authors have conducted in-depth research and proposed some fault diagnosis models, which have achieved good results. For example, Brkovic et al. proposed a simpler, faster, and accurate bearing early fault detection and diagnosis technique based on scatter matrices and quadratic classifiers [3]. Gligorijevic et al. presented a new online condition monitoring technique for early fault detection and diagnosis to prevent the unexpected faulty operation of bearings [4]. Van et al. used various bearing fault diagnosis models by improved non-local-mean de-noising and empirical mode decomposition (EMD) feature extraction and two-stage feature selection [5]. Helmi et al. proposed a model for the fault detection and diagnosis of rolling bearings structure based on time domain and frequency domain features of the extraction of the vibration signal and the adaptive neuro-fuzzy interface system network. Their experimental results enabled the detection of faults in rotating machines and the categories of faults with high accuracy [6].

The most widely used techniques for fault detection are motor current signature analysis (MCSA), vibration signal analysis, and acoustic sound signals analysis [7]. All these techniques for fault detection have advantages and weaknesses. The MCSA technique has the advantages of being noninvasive and easy to implement. However, under certain conditions, its application is not sensitive enough because it has a low signal-to-noise ratio. Its other disadvantages include its spectral leakage and low-frequency resolution. The downside of acoustic sound signal analysis is its sensitivity to external noise. The technique of acoustic emission, which measures the acoustic signals in the ultrasonic range providing a high signal-to-noise ratio, has the disadvantage of requiring more complex implementation [8]. Vibration signal analysis has high potential for fault detection as it is easy to measure and can extract favorable fault features. Because vibration signals contain noisy, non-linear, and non-stationary components, some time-frequency analysis such as short-time Fourier transform (STFT), Wigner–Ville distribution (WVD), wavelet transform (WT), Hilbert-Huang transform (HHT) and empirical mode decomposition (EMD), have become the most effective techniques in recent years. However, the above techniques have their own limitations. For example, STFT is limited to a fixed length of the window [9]. WVD is limited by cross-terms interference for the non-stationary signals [10]. WT is suitable for non-stationary signal processing with high resolution to solve the above problems from STFT and WVD [11,12]. However, when analyzing the practical signal, the pre-defined wavelet-based parameters may not completely guarantee efficiency for practical signal processing and analysis, which makes WT non-adaptive [13]. For vibration signals, the self-adaptive signal analysis may be more efficient [14]. As proposed by Huang et al. [15], EMD adaptively decomposes the non-stationary signals into a set of intrinsic mode functions (IMFs). However, EMD is limited by end effects and mode mixing [16,17,18].

Similar principles with EMD, local mean decomposition (LMD) is a self-adaptive time-frequency domain analysis method first proposed by J. S. Smith in 2005 that has good results for the analysis of EEG signals [19]. The LMD decomposes the signal into a set of product functions (PFs), each of which is the product of an envelope signal and a frequency modulated signal. LMD has many potential properties. First, LMD directly obtains instantaneous amplitude and instantaneous frequency without Hilbert transform (HT) [19]. Second, LMD solves the over-/undershoot problem by using the moving averaging method to compute the local mean [20]. Third, the end effects and mode mixing problem already alleviate or are not obvious in LMD [21,22]. Fourth, compared with EMD, LMD decomposes the signal into fewer components, and that each component contains more useful information [22]. However, in the practical fault diagnosis of rotating machines, the vibration signals acquisitioned from sensors always contain huge noise, which causes LMD to decompose additional and redundant frequency components. To solve this problem, the wavelets de-noising technique such as wavelet packet decomposition (WPD) has obtained good results to implement signal denoising [23,24,25]. To extract the useful features from the vibration signal and remove noise, the multilayer signal analysis method is applied in three steps as follows. First, the LMD decomposes the original signal into a set of PFs. Then, the PF selection method is used to select effective components. Then, WPD is used to further extract feature information and denoise. Finally, the statistical features are extracted from these components.

In order to build a good model prediction, strongly relevant features should be selected and irrelevant, redundant, or noisy features should be eliminated [26]. The feature selection method is applied to remove uncorrelated features to obtain the optimal feature subset. In recent decades, evolutionary algorithms such as particle swarm optimization (PSO), bat algorithm (BA), and chicken swarm optimization (CSO) have been used for feature selection. However, each algorithm has its own limitations. For example, BA cannot balance between its exploration and exploitation capability [27]. Both BA and PSO are suffer from premature convergence and easily fall into the local optimal when computing high-dimension problems [27,28]. CSO was a new evolutionary algorithm proposed by Meng et al. in 2014 [29], which has good ability in terms convergence rate and convergence accuracy. Nevertheless, like PSO and BA, the basic CSO has the same limitation of premature convergence and easy to fall into local optima [30]. Therefore, the researchers have proposed many improved CSO, which achieved good results [30,31,32]. In this research, combining with basic CSO and genetic algorithm (GA), it is called hybrid genetic binary chicken swarm optimization (HGBCSO). Based on GA, the crossover operation is an effective tool to improve the global search ability and population diversity [33]. Moreover, two positions updating strategies are adopted to improve global exploration abilities. By using these improvements, HGBCSO can balance exploration and exploitation and avoid premature convergence.

The solutions present in evolutionary algorithms for feature selection are binary strings in binary search space [34]. In this research, the above algorithms are applied for feature selection as binary-PSO (BPSO) [35], binary-BA (BBA) [36,37], and binary-CSO (BCSO) [38,39].

The last task of the proposed model is to classify the optimal feature subset. In recent years, neural networks and machine learning algorithms are widely using in the field of machinery fault diagnosis [40,41]. Compared with neural networks, machine learning algorithms have the advantages of higher classification performance [42,43,44,45]. Therefore, three machine learning algorithms, including decision tree (DT), support vector machine (SVM), and naive Bayes (NB) are applied and compared robustness in this research. The DT-based diagnosis models are natural, which may not need the knowledge for researchers and can be easily applied to diagnosis models. However, the DT classifier is suffering from overfitting and low generalization performance which would reduce the diagnosis performance. The NB-based diagnosis models are easy to achieve fault diagnosis with multiple states. However, because of the low ability of data fitting, it is difficult to represent the complicated function relationship. The SVM is a widely used machine learning method for fault diagnosis. The SVM-based diagnosis models can easily obtain the global optimal solution and further obtain the high diagnostic accuracy based on the objective solution of convex quadratic optimization [46]. In conclusion, this article proposes a rotor bar fault diagnosis model, which uses a multilayer signal analysis to extract fault features, and uses HGBCSO for feature selection.

In this article, the main points can be summarized as three points:

• Proposing a multilayer signal analysis method combining two signal processing methods (LMD and WPD) and PF selection. This technique can reduce the dimension of original data, descend background noise, and extract potential features.
• Proposing a feature selection method using the combination with BCSO and GA and two positions update strategies to enhance global exploration capabilities, improve population diversity, and prevent premature convergence.
• Proposing a rotor bar fault diagnosis model based on multilayer signal analysis, feature selection method, and classification.

2. Multilayer Signal Analysis

To extract potential features and descend background noise from the non-stationary signal, the feature extraction process can be accomplished as follows. First, vibration signals are recorded from test motors. Second, the proposed multilayer signal analysis method is used to analyze test signals. Finally, the potential features which contain rotor fault signatures are extracted.

2.1. Local Mean Decomposition

LMD can decompose a multi-component signal into a set of PFs. Each PF component is the product of an envelope signal and a frequency modulated signal. Defining a signal $x\left(t\right)$, $x\left(t\right)$ can decompose into a set of PFs by iterating through the following loop:

Step 1: 

Find all local extrema $n_i$ of the original signal $x\left(t\right)$. Calculate the local mean $m_i$ and local envelope $a_i$ of two successive extrema $n_i$ and $n_{i+1}$ by

$$m_i=\frac{{(n}_i{ + n}_{i+1})}{2}$$

(1)

$$a_i=\frac{\left|n_i {- n}_{i+1}\right|}{2}.$$

(2)

Step 2: 

All the local mean $m_i$ and local envelope $a_i$ can be extended by using straight lines extending between successive extrema.

Step 3: 

Construct local mean function $m_{11}\left(t\right)$ and local envelope function $a_{11}\left(t\right)$ by smoothing the local mean and local envelope using moving averaging method.

Step 4: 

Subtracting the local mean function $m_{11}\left(t\right)$ from the original signal $x\left(t\right)$ to obtain a residue signal $h_{11}\left(t\right)$:

$$h_{11}{\left(t\right)=x\left(t\right) - m}_{11}\left(t\right).$$

(3)

Step 5: 

Then, the frequency modulated signal $s_{11}\left(t\right)$ can be obtained from $h_{11}\left(t\right)$ and $a_{11}\left(t\right)$. $h_{11}\left(t\right)$ can be the amplitude demodulated by dividing it by the envelope function.

Step 6: 

If $s_{11}\left(t\right)$ is a purely frequency modulated signal, then go to Step 7. Otherwise, take $s_{11}\left(t\right)$ as a new signal and repeat Step 1 to 5 until the condition is satisfied.

$$s_{11}\left(t\right)=\frac{h_{11}\left(t\right)}{a_{11}\left(t\right)}.$$

(4)

Step 7: 

Multiply all the smoothed local envelope functions during iteration to obtain the envelope signal $a_1\left(t\right)$ of the first product function ${PF}_1$.

Then, with the envelop function and the final frequency demodulated, the first product function ${PF}_1$ will be generated:

$$a_1(t)=a_{11}(t)a_{12}(t)\dots a_{1n}(t)={\displaystyle \prod _{q=1}^n{a}_{1q}(t)}$$

(5)

$${PF}_1{=a}_1{\left(t\right)s}_{1n}\left(t\right).$$

(6)

Step 8: 

Then, $u_1=x\left(t\right)-{PF}_1\left(t\right)$ treated as the smoothed version of the original data and the procedure is repeated from Step 1 to 7, until $u_i\left(t\right)=u_{i-1}\left(t\right)-{PF}_i\left(t\right)$ is a monotonic function or no more than five oscillations. Finally, $x\left(t\right)$ can be denoted as

$$x(t)={\displaystyle \sum _{i=1}^{p}P{F}_i(t)+u_p(t)}$$

(7)

where $p$ is the number of PFs.

2.2. Product Function Selection

The LMD can decompose a multi-component signal into a set of PFs. However, some components include more fault information than others. Therefore, the second layer is to extract those components that contain most of the fault information of the original signal as a key step in the extraction of features from multiple PF components. Some statistics have been used to select those effective components. The correlation coefficient (CC) [47] is used to evaluate the similarity between the component and the original signal.

Kurtosis [25] and root mean square (RMS) [48] are also used for the PF selection. Kurtosis is a measure of the “tailedness” of signal distribution, or how outlier prone the signal is. Developing faults can increase the number of outliers. Therefore, the value of the kurtosis metric increases.

When the original signal has an early-stage fault, as the weak fault signature is generally buried in the noise. CCs cannot have good performance for selecting the effective PFs. RMS are also not sensitive to an early-stage fault [49]. Kurtosis is sensitive to an early-stage fault. However, Kurtosis could not keep increasing the trend when the fault becomes more serious [48]. Therefore, a single statistic is not effective to select the PFs, because the severity levels of the faults strongly affect its effectiveness. Yu et al. [50] proposed a comprehensive evaluation value (CEV) value for PF selection. The PFs decomposed by LMD are defined as PF₁, PF₂, PF₃,…, PF_n. The CEV-defined $Q_i$ as for each PF component is the mean of the three statistic values as follows:

$$Q_i={\displaystyle \sum _{j=1}^3\frac{H_{i,j}}{{\displaystyle {\sum }_{i=1}^n{H}_{i,j}}}}$$

(8)

where the statistic values including CC, kurtosis, and RMS are defined as $H_{i,1}$, $H_{i,2}$, and $H_{i,3}$ for the ith PF component decomposed by LMD.

2.3. Wavelet Packet Decomposition

Because the selected PFs based on the CEV value remain at a much high frequency noise in the PFs, the final layer uses WPD to further analyze and denoise the selected PFs. WPD is a powerful method for analyzing the time-frequency domain. The main difference between WPD and discrete wavelet transform (DWT) is that WPD can decompose detail coefficients and approximate coefficients at the same time. Thus, WPD has good resolution at both high and low frequencies and is suitable for processing non-stationary signals [51].

In WPD, a wavelet packet function $W_{j,k}^n\left(t\right)$ is defined as follows:

$$W_{j,k}^n(t)=2^{\frac{j}{2}}{W}^n(2^{j}t-k)$$

(9)

where index $n$ is called the modulation parameter or the oscillation parameter, and $j$ and $k$ are the index scale and translation operations, respectively.

The wavelet packet coefficients of a signal $x\left(t\right)$ can be calculated as follows:

$$W_{j,n,k}(t)={\displaystyle \int x(t)W_{j,k}^n(t)dt}$$

(10)

2.4. Feature Extraction Process

This part is explaining the following step for feature extraction:

Step 1: 

Record vibration signals from test machines.

Step 2: 

In the first layer of the multilayer signal analysis, LMD is used to decompose the vibration signals into a set of PFs. Figure 1a illustrates how the LMD decomposes the normal IM vibration signal into four PFs.

Step 3: 

In the second layer of the multilayer signal analysis, PF selection is used to select the effective components. In this paper, we choose the best two CEV values for the selected PFs into the final layer. Figure 1b illustrates the PF selection method selecting the best two PFs.

Step 4: 

In the third layer of the multilayer signal analysis, WPD is used to further analyze and denoise the selected PFs. In this paper, two-level WPD is adopted and decomposition construction consists of four wavelet packet coefficients: ${aa}_2$, ${da}_2$, ${ad}_2$, ${dd}_2$. The two-level WPD decomposes the selected PFs as shown in Figure 1c.

Step 5: 

The eight statistical feature parameters are calculated for each wavelet packet coefficient. A total of 64 (2 × 4 × 8) features are extracted from the output decomposition structure of two selected PFs.

Therefore, the potential fault feature dataset includes 64 features.

Table 1. Eight statistical feature definition.

Feature	Equation
(1) Max value	$x_{max}=max\left(x\right(n\left)\right)$
(2) Min value	$x_{min}=min\left(x\right(n\left)\right)$
(3) Root mean square	$x_{rms}={\left(\frac{{{\displaystyle \sum }}_{n=1}^N\sqrt{\left|x\left(n\right)\right|}}{N}\right)}^2$
(4) Mean square error	$x_{mse}=\frac{1}{N}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\left(x_n - \mu \right)}^2$
(5) Standard deviation	$x_{std}=\sqrt{\frac{{{\displaystyle \sum }}_{n=1}^N{\left(x\right(n) - \mu )}^2}{N - 1}}$
(6) Kurtosis	$x_{kur}=\frac{{{\displaystyle \sum }}_{n=1}^N{\left(x\right(n) - \mu )}^4}{{(N - 1)x}_{std}^4}$
(7) Crest factor	$x_{crest}=\frac{x_{max}}{\sqrt{\frac{1}{N}{{\displaystyle \sum }}_{n=1}^N{x}_n^2}}$
(8) Clearance factor	$x_{clear}=\frac{x_{max}}{{\left(\frac{1}{N}{{\displaystyle \sum }}_{n=1}^N\sqrt{\left|x_n\right|}\right)}^2}$

Note: x(n) is a signal series for $n=1, 2, \dots , N$, where N is the number of data points.

shows the parameters definition of these statistical features.

3. Hybrid Genetic Binary Chicken Swarm Optimization for Feature Selection

This section can separate in four parts. The first part is a brief introduction to the basic BCSO algorithm for feature selection. The second to fourth parts explain each positions update strategy using the proposed HGBCSO method. The operation of these strategies combines with BCSO to search for a potential solution.

3.1. Binary Chicken Swarm Optimization

The basic CSO algorithm mimics the hierarchal order and behaviors of searching food in the chicken swarm. Each chicken is represented by their position in a $D$-dimensional space by $x_{i,j}\left(i\in [1, \dots , N], j\in [1, \dots , D]\right)$. The positions update of the equation of a different type of chickens is as follows:

• Rooster’s position update equation:

  $$x_{i,j}^{t+1}=x_{i,j}^t(1+Randn(0,{\sigma }^2))$$

  (11)

  $${\sigma }^2=\{\begin{array}{c}1\\ exp(\frac{f_k-f_i}{\left|f_i\right|+\epsilon })\end{array}$$

  (12)

  where ${Randn(0, \sigma }^2)$ is a Gaussian distribution with a mean of 0 and standard deviation ${\sigma }^2$, $\epsilon$ is a small constant to prevent the denominator being 0. $k$ is a rooster’s index, which is selected randomly between 1 and the maximum number of roosters except $i$. $f_i$ and $f_k$ are the fitness values of the ith and kth rooster.
• Hen’s position update equation:

  $$x_{i,j}^{t+1}=x_{i,j}^t+S1Rand(x_{r1,j}^t-x_{i,j}^t)+S2Rand(x_{r2,j}^t-x_{i,j}^t)$$

  (13)

  $$S1=exp((f_i-f_{r1})/(abs(f_i)+\epsilon ))$$

  (14)

  $$S2=exp((f_{r2}-f_i))$$

  (15)

  Rand is a uniform random number between 0 and 1, $r1$ is an index of the rooster, which is in the ith hen’s group-mate, $r2$ is an index of the chicken in all roosters and hens, which is randomly chosen from the swarm, and let $r1\ne r2$.
• Chick’s position update equation:

  $$x_{i,j}^{t+1}=x_{i,j}^t+FL(x_{m,j}^t-x_{i,j}^t)$$

  (16)

  where $m$ is an index of the mother hen corresponding to ith chick, FL is a parameter in the range [0.4, 1], which keeps the chick to forage for food around its mother.

For feature selection in the BCSO, each chicken represents a solution in the binary search space (i.e., each feature subset). In contrast to CSO, each chicken is updated by the binary position of a solution which has values “1” and “0”, which means the corresponding feature is selected or unselected. The most widely used transfer function to transfer from the real position to the binary position is the sigmoid function in (17). The binary position of each chicken $b_{i,j}$ is updated as follows:

$$sig(x_{i,j})=\frac{1}{1+e^{-x_{i,j}}}$$

(17)

$$b_{i,j}=\{\begin{array}{c}{1 sig(x}_{i,j})\ge 0.5\\ {0 sig(x}_{i,j})<0.5\end{array}$$

(18)

3.2. Update the Hen’s Position Based on Levy Flight

The disadvantage of basic CSO and other evolutionary algorithms is premature convergence. In basic CSO, hens play an important role in the entire group because there is the largest number of hens. Inspired by this, Liang et al. [30] proposed the levy flight search strategy into hen’s position update equation. In this method, the short-distance and occasional long-distance searching appear alternately, such that it enhances the search performance and avoids the iterations falling into a local optimal. The hen’s position update equation based on levy flight is as follows:

$$\begin{gathered} x_{i,j}^{t+1}=x_{i,j}^t+S1Rand(x_{r1,j}^t-x_{i,j}^t)+S2RandLevy(\lambda ) \\ \otimes (x_{r2,j}^t-x_{i,j}^t) \end{gathered}$$

(19)

where ⊗ is a vector operator representing the point multiplication and the random step value of a levy flight is taken from the levy distribution, which is shown as follows:

$$Levy(\lambda )~u=t^{-\lambda }(1<\lambda <3)$$

(20)

3.3. Update the Chick’s Position Based on Inertia Weight

Based on CSO, the chicks’ do not update the position by themself, and only follow their own mother hen, so when their own mother hen falls into the local optimal, the chicks will also fall into the local optimal. In this research, the linear decreasing inertia weight is used to update the chick’s position, which can let the chicks update the position by themselves, preventing the chicks falling into local optimal. The linear decreasing inertia weight [52] $w$ updates as follows:

$$w=w_{max}-(w_{max}-w_{min})(\frac{t}{ite{r}_{max}})$$

(21)

where $w_{max}$ and $w_{min}$ are the maximum and minimum values of inertia weight,$t$ is the number of iterations and ${iter}_{max}$ is the maximum number of iterations. Then, the chick’s position update equation is defined as follows:

$$x_{i,j}^{t+1}=w{x}_{i,j}^t+FL(x_{m,j}^t-x_{i,j}^t)$$

(22)

3.4. Update the Chicken’s Position Based on Crossover Operation

Based on GA: the crossover operation is a powerful tool for enhancing the exploration and exploitation capability, improving the population diversity, avoiding premature convergence, creating more effective solutions, and improving the average fitness values of the population. In this research, the chicken’s position update operation is based on three-points crossover operation. The operation is described as follows:

Step 1: 

Randomly selected pairs of solutions carry out the three points crossover operation.

Step 2: 

Repeat until the new population is formed.

The three-points crossover operation is illustrated in Figure 2.

3.5. The Proposed HGBCSO Method

The proposed method HGBCSO is combined with the crossover operation and two positions update the strategies, which helps avoid the local optimal and improve the global search performance. Therefore, HGBCSO is the proposed method for feature selection in this research. The k-NN classifier is used to evaluate each chicken. The fitness function is based on the classification accuracy (ACC), which is defined as follows:

$$Fitness=\frac{N_{True}}{N_{True}+N_{False}}\times 100\%$$

(23)

where $N_{True}$ is true positive, $N_{False}$ is false negative. The flowchart of the proposed method to achieve an optimal feature subset is illustrated in Figure 3.

4. Diagnosis Model for Rotor Bar Fault

This section is introducing a fault diagnosis model for a rotor bar based on the vibration signals of the IM. Figure 4 illustrates the proposed model and contains the following three main stages:

Stage 1: 

Measuring the vibration signals from the test IM, which are processed by multilayer signal analysis. The first layer is to use LMD to decompose the vibration signals into a set of PFs. The second layer is to use PF selection to select two effective PFs. The third layer is to use WPD to further analyze and denoise the selected PFs. In this model, the wavelet decomposition level is adopted at level 2. The eight statistical feature parameters are calculated for each wavelet packet coefficient. Finally, 64 features are extracted during Stage 1.

Stage 2: 

Using the proposed method HGBCSO to remove the irrelative features from the feature set, achieving the optimal feature subset. The optimal feature subset will improve the classifier performance of the fault diagnosis model.

Stage 3: 

Three well-known classifiers, including DT, SVM, and NB, are used to classify the optimal feature subset. The ACCs are used to evaluate the robustness of classifiers with rotor bar data to select the best classifier for diagnosing rotor bar faults.

5. Experiment Results

Two experimental case studies are introduced in this section.

Case study 1 shows the results of the HGBCSO method using the UCI machine learning datasets for feature selection. To evaluate the effectiveness of the HGBCSO method, the basic BCSO and two well-known evolutionary algorithms are compared.

Case study 2 uses the experimental dataset from IM, including normal motor and broken rotor bar motors, to evaluate the validity of the proposed model.

5.1. Case Study 1: UCI Machine Learning Datasets

• Describe of Datasets

The feature set used in the motor fault diagnosis model is usually the low-dimensional feature sets [53,54]. Thus, six UCI machine learning repository datasets [55] are applied in this research. The six machine learning datasets are described in

Table 2. Description of 6 UCI machine learning datasets.

Datasets	Features	Instances	Classes
Wine	13	178	3
Leaf	15	340	30
Vehicle Silhouettes	18	94	4
WDBC	30	569	2
Ionosphere	34	351	2
Sonar	60	208	2

.

2.

Parameter Setting

In this research, the high ACC fault diagnosis model is our focus. The k-NN classifier with the number of nearest neighbor k = 1 and 10-folds cross-validation is adopted to evaluate the solutions from HGBCSO and the other three compared evolutionary algorithms.

Table 3. Experimental parameter setting of four evolutionary algorithms.

HGBCSO	BCSO	BPSO	BBA
Number of chickens: 10 Number of iterations: 100 Rooster parameter: 0.2 Hen parameter: 0.7 Mother parameter: 0.1 ωmin = 0.4 ωmax = 0.9	Number of chickens: 10 Number of iterations: 100 Rooster parameter: 0.2 Hen parameter: 0.7 Mother parameter: 0.1	Number of particles: 10 Number of iterations: 100 c1 = c2 = 2.05	Number of bats: 10 Number of iterations: 100 Maximum frequency: 2 Minimum frequency: 0 Loudness: 0.9 Pulse rate: 0.9

shows the parameter setting of four algorithms, including HGBCSO, BCSO, BPSO, and BBA.

3.

Experimental Results for UCI Machine Learning Datasets

This experiment was simulated by Matlab 2017a. The results of three algorithms, including BCSO, BPSO, and BBA are used to assess the validity of the proposed HGBCSO algorithm. In this experiment, two following indicators are using to compare the results of algorithms: (1) Convergence curve of the best solution for each algorithm; (2) Calculate the average ACC and the average number of selected features (Avg No. Fs) for each algorithm in thirty independent runs.

Figure 5 shows the convergence curve of the best solution for each algorithm. The HGBCSO achieves higher ACC than the other compared algorithms on leaf, vehicle silhouettes, WDBC, ionosphere, and sonar. Especially on WDBC and ionosphere, HGBCSO achieves higher ACC than the other compared algorithms of 1.17 and 1.14%.

Table 4. The result of HGBCSO and other evolutionary algorithms.

Datasets	HGBCSO		BCSO		BPSO		BBA
	Avg Fitness Value	Avg No. Fs	Avg Fitness Value	Avg No. Fs	Avg Fitness Value	Avg No. Fs	Avg Fitness Value	Avg No. Fs
Wine	99.53	8.93	99.49	8.60	99.06	8.37	98.29	7.77
Leaf	76.25	10.73	76.07	10.73	75.16	10.43	72.45	9.2
Vehicle Silhouettes	76.60	8.33	75.99	9.17	74.61	9.37	71.21	9.57
WDBC	99.37	16.23	97.81	16.30	97.45	15.60	96.83	15.90
Ionosphere	94.19	13.23	93.76	14.3	93.23	14.77	91.72	15.7
Sonar	94.37	31.07	93.53	31.13	93.33	31.43	90.51	30.43

presents the average fitness value (Avg fitness value) and the Avg No. Fs for each algorithm. In each dataset, the algorithm achieves better results which are in bold in Table 4. The results show that HGBCSO achieves a better average ACC in these six machine learning datasets. Especially on WDBC, the average classification accuracy is significantly better than BCSO with a difference of 1.56%. HGBCSO is most effective on the vehicle silhouettes and the ionosphere dataset achieves a higher Avg fitness value and lower Avg No. Fs. Based on the above results, the proposed HGBCSO method is satisfied with our focus.

5.2. Case Study 2: Rotor Broken Bar Experimental Database

• Experimental Setup

The experimental database for detecting and diagnosing rotor broken bar from the IEEE Dataport [56] was used in this case study. The experimental setup in this database consisted of a three-phase IM (1 hp, 220V/380V, 3.02A/1.75A, 4 poles, 60 Hz, a nominal torque of 4.1 Nm and a rated speed of 1715 rpm) coupled to a DC machine. To simulate the failure on the rotor, five rotors tested healthy for one, two, three, and four broken bars, respectively. In this experiment, 12.5, 50, and 100% of the full load of the experimental datasets were used in the rotor bar fault diagnosis model.

Five axial accelerometers (sensitivity of 10 mV/mm/s and the frequency range of 5 to 2000 Hz) were used to measure the vibration signals in both drive end (DE) and non-drive end (NDE) sides of the motor, axially or radially, in the horizontal or vertical directions. Vibration signals are acquired using a 10 channels data acquisition system with 16 bits A/D converters, type ADS 2000 Lynx Testing, and Measurement Systems. All vibration signals were sampled at the same time for 18 s, the sample rate of the vibration signals was 7.6 kHz, and ten repetitions were performed from the transient to steady state of the induction motor. Figure 6 shows the vibration signals acquisition from the healthy motor and broken bars motor.

2.

Experimental Results for Feature Selection

Section 4 presented the proposed three stages of the rotor bar fault diagnosis model. In stage 1, the potential fault feature dataset that included 64 features was extracted. In stage 2, HGBCSO was applied to the rotor bar datasets, including 12.5, 50, and 100% of full load conditions. In addition, the other three feature selection algorithms (BCSO, BPSO, BBA) are also calculated. The results under three different load conditions are shown from

Table 5. Comparison of the 12.5% load condition rotor bar dataset.

Algorithms	Avg Fitness Value (%)	Avg No. Fs
HGBCSO	95.09	31.73
BCSO	95.05	31.97
BPSO	93.99	32.80
BBA	94.57	32.83

,

Table 6. Comparison of the 50% load condition rotor bar dataset.

Algorithms	Avg Fitness Value (%)	Avg No. Fs
HGBCSO	95.22	28.6
BCSO	95.09	30.27
BPSO	94.64	33.03
BBA	94.22	32.70

and

Table 7. Comparison on the 100% load condition rotor bar dataset.

Algorithms	Avg Fitness Value (%)	Avg No. Fs
HGBCSO	91.86	29.10
BCSO	91.70	30.67
BPSO	90.83	31.50
BBA	89.85	31.57

. Compare with the other algorithms, the proposed algorithm reaches higher average classification accuracy in 30 independent runs. The convergence curves of the best solution under three different load conditions are shown in Figure 6. In Figure 7a, BCSO, BBA converge at the 51st and 75th iteration, respectively. In Figure 7b, BBA, BPSO converge at the 31st and 53rd iteration, respectively. In Figure 7c, BBA, BPSO converge at the 48th and 54th iteration, respectively. The above results show that the weaknesses of BCSO, BPSO, and BBA are its premature convergence and the likelihood of it falling into the local optimal. Meanwhile, in Figure 7a–c, HGBCSO converges at the 87th, 63rd, and 90th iteration, respectively. These results show that the proposed method based on three proposed positions’ update strategies has global exploration ability and preventing premature convergence.

Table 8. Details on the 12.5% load condition rotor bar dataset.

Algorithms	Features	Feature Indicators (F)
HGBCSO	22	2, 3, 5, 9, 10, 12, 14, 15, 16, 17, 18, 19, 20, 22, 29, 30, 41, 44, 47, 49, 51, 55.
BCSO	28	1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 20, 23, 26, 27, 29, 30, 32, 40, 41, 46, 51, 52, 55, 58.
BPSO	31	2, 3, 5, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 25, 26, 27, 28, 29, 30, 31, 32, 33, 38, 41, 45, 46, 50, 51, 63.
BBA	32	2, 3, 4, 8, 9, 11, 12, 13, 14, 15, 16, 18, 19, 20, 22, 24, 26, 27, 30, 32, 33, 35, 36, 38, 40, 41, 42, 44, 45, 49, 54, 63.

,

Table 9. Details on the 50% load condition rotor bar dataset.

Algorithms	Features	Feature Indicators (F)
HGBCSO	27	1, 5, 6, 7, 9, 10, 11, 12, 13, 14, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 36, 39, 40, 42, 48, 53, 61.
BCSO	38	1, 3, 4, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 23, 24, 25, 31, 32, 33, 35, 37, 38, 39, 42, 43, 46, 47, 50, 51, 52, 53, 55, 57, 61, 63.
BPSO	30	1, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 20, 22, 24, 27, 31, 37, 38, 39, 42, 43, 44, 46, 48, 49, 50, 52, 55.
BBA	32	1, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 20, 22, 25, 27, 29, 31, 34, 35, 36, 38, 39, 40, 45, 48, 51, 54, 56, 58, 60.

and

Table 10. Details on the 100% load condition rotor bar dataset.

Algorithms	Features	Feature Indicators (F)
HGBCSO	23	1, 2, 4, 5, 10, 12, 15, 16, 17, 18, 19, 20, 22, 23, 24, 37, 38, 41, 42, 43, 44, 46, 52.
BCSO	33	5, 6, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 27, 32, 33, 37, 40, 41, 43, 44, 45, 49, 51, 52, 53, 56, 61, 63.
BPSO	33	3, 5, 6, 8, 9, 10, 11, 12, 14, 16, 17, 19, 20, 21, 22, 23, 25, 27, 28, 36, 37, 42, 44, 47, 49, 50, 52, 53, 54, 55, 59, 61, 63.
BBA	34	3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 20, 22, 23, 25, 26, 28, 32, 33, 36, 37, 39, 41, 42, 45, 46, 50, 53, 54, 59, 62.

present the best solution for each algorithm. Based on the number of the selected features of the optimal feature subset, HGBCSO has achieved 22 features from the 12.5% of full load condition dataset, 27 features from the 50% of full load condition dataset, and 23 features from the 100% of full-load condition dataset. Compared with the other algorithms, the proposed algorithm reaches the lower number of the selected features in 30 independent runs.

3.

Experimental results for classification

In stage 3, three provided classifiers, including DT, SVM, and NB, were adopted to classify the optimal feature subset.

Table 11. Parameter setting of three classifiers.

DT	SVM	NB
Complex tree Split criterion: Gini’s diversity index Surrogate splits: off Max number of splits: 100	Kernel function: polynomial Polynomial order: 2 Kernel scale: auto Box constraint: 1	Kernel distributions: normal Support regions: unbounded

shows the parameter setting of the three classifiers, including DT, SVM, and NB. Four optimal feature subsets were provided from HGBCSO, BCSO, BPSO, and BBA, respectively. In addition, the original feature set means without doing the feature selection were also used to classify in this experiment. The robustness of these three classifiers was also considered in the noise condition. In this experiment, the original signals were added to different levels of Gaussian white noise to simulate the noisy environment. This experiment was closer to the real condition in industrial production. In this experiment, the signal-to-noise ratio (SNR) value test ranged from −10 to 10 dB. Figure 8 shows the healthy motor signal is added by the Gaussian white noise with SNR = 0 dB. The average ACC is obtained after 30 training times. Figure 9 shows the average ACC using the DT, SVM, and NB of three different load conditions and under different SNR values. Obviously, DT and SVM achieved a better classification performance than NB. The proposed HGBCSO achieved higher ACC than the other three algorithms under different load conditions. As the SNR value decreases, the performance of the three classifiers decreases. However, under a lower SNR value, the robustness of the SVM classifier was more effective compared to DT and NB. Especially in SNR = −8 dB, the ACC of all algorithms and under 12.5, 50, and 100% of full load conditions are higher than 84.61, 75.86, and 75.62% when using the SVM classifier. The accuracy of all algorithms is lower than 82.89, 74.7, and 71.79% when using the DT classifier. The accuracy of all algorithms is lower than 72.6, 66.94, and 62.15% when using the NB classifier. In SNR = −10 dB, the ACC of SVM is still higher than DT and NB. Therefore, the SVM classifier is the suitable classifier with the rotor bar fault diagnosis model. Finally, we compared it with the classification results for different load conditions based on the proposed fault diagnosis model. As the load torque increases, the performance of the proposed model decreases. The classification accuracy of the proposed model under 12.5% of full load condition and under the SNR value ranging from −10 to 10 dB is from 88.64 to 94.17%. The classification accuracy of the proposed model under 50% of full load condition and under the SNR value ranging from −10 to 10 dB is from 78.97 to 93.67%, respectively. The classification accuracy of the proposed model under 100% of full load condition and under the SNR value ranging from −10 to 10 dB is from 75.62 to 88.83%. In conclusion, according to the above analysis, the proposed rotor bar fault diagnosis model in this research is highly effective and achieves high robustness to detecting rotor bar failure.

6. Conclusions

This article presents an effective rotor bar fault diagnosis model. The model contains three main stages to detect rotor bar failure. This research uses multilayer signal analysis for processing signals. In multilayer signal analysis, the vibration signals can be decomposed into the effective product function components which contains most of the fault information of the original signal. The proposed HGBCSO algorithm uses three positions update strategies to improve the basic BCSO algorithm and enhance the ability to select important features. The results show that the HGBCSO algorithm achieved higher ACC. The best fault diagnosis model achieves better robustness by using the SVM classifier. The classifier performance was tested from low load torque to full load torque and under high noise level. The result shows that the proposed model achieves 75.62% classification accuracy under 100% full load condition and SNR = −10 dB. In addition, the proposed HGBCSO algorithm was compared with the UCI machine learning datasets and the results are better than the adopted evolutionary algorithm. However, the proposed model still has some limitations as follows: (1) the feature extract process is highly dependent on the former knowledge for researchers; (2) machine learning has a shallow structure that cannot work well for complex non-linear problems. Therefore, deep learning algorithms and automatic feature extraction for rotor bar fault classification should be considered in the future.