# A Comparative Study of Four Nonlinear Dynamic Characteristics in Feature Extraction of Bearing Fault Diagnosis

Authors: Yuxing Li; Shuai Zhang; Lili Liang
Journal: Journal of Sensors
 (2022)

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## Abstract

To effectively extract the fault features of bearing signals in complex environments, four common nonlinear dynamic characteristics are used to analyze and compare the simulated signals and measured bearing fault signals in this paper, including Lempel-Ziv complexity (LZC), dispersion entropy (DE), Lyapunov exponent (LE), and fractal dimension (FD). Three groups of simulation experiments were carried out, and the simulation results show that all nonlinear dynamic characteristics can reflect the complexity change trend of MIX signal; compared with LZC and LE, DE and FD can better reflect the frequency change of amplitude modulated trend of chirped signal; only DE can reflect the amplitude change trend of amplitude modulated chirped signal. The experiments of feature extraction and classification are carried out for bearing fault signals. It concluded that compared with LZC, LE, and DE, FD has better stability and classification performance with the minimum standard deviation and the highest recognition rate.


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## Body

## 1. Introduction

As the technology improves, mechanical equipment is widely used, and its scale and complexity are also increasing. As an important part of mechanical equipment, the performance of bearings has a great impact on the operation of mechanical equipment. Therefore, to ensure the reliability of mechanical equipment, it is necessary to carry out fault diagnosis of bearings [1].The current bearing fault diagnosis technology is mainly based on vibration signals; the vibration signal of bearing is usually nonlinear and nonstationary signals [2]. Traditional feature extraction methods are mainly applicable to the analysis of linear stationary signals, but it is difficult to analyze nonlinear and nonstationary signals. The feature extraction method based on nonlinear dynamics can better analyze the bearing signal and realize the bearing fault diagnosis [3]. Common nonlinear dynamic characteristics include Lempel-Ziv complexity (LZC), dispersion entropy (DE), fractal dimension (FD), and Lyapunov exponent (LE).LZC is widely used in nonlinear scientific research [4]. Its physical significance is that it can reflect the rate of the emergence of new patterns in time series with the increase of length. Due to its limitations, some improved LZC are proposed to improve its performance. Normalized LZC (NLZC) and weight LZC (WLZC) were proposed and applied to the analysis of biosequence and piecewise smooth systems of switching converters in 2009 and 2012 [5, 6]. By introducing the permutation mode of permutation entropy and the mapping mode of DE, permutation LZC (PLZC) and dispersion LZC (DLZC) were proposed in 2015 and 2020 [7–10]. In 2022, dispersion entropy-based LZC (DELZC) was presented by introducing the dispersion mode of dispersion entropy [11].DE is an index based on Shannon entropy to express the complexity and irregularity of time series [12], which has better performance than permutation entropy [13]. Fluctuation-based DE (FDE) and reverse DE (RDE) were proposed by introducing fluctuation information and amplitude information in 2018 and 2019 [14–16]. In 2021, fluctuation-based reverse DE (FEDE) was presented by combining the fluctuation and distance information of FDE and RDE. In addition, with the development of entropy theory, some new complexity indicators have been proposed and applied to the field of fault diagnosis and underwater acoustics, such as bubble entropy (BE), slope entropy (SE), and their improved versions [17–22].In this paper, LZC, DE, FD, and LE are used to analyze the feature extraction performance of bearing fault signals. The structure of the rest of this paper is as follows: the second part introduces the algorithm principle of LZC and DE; in the third part, we carried out simulation experiments; in the fourth part, the experiments of feature extraction and classification recognition for measured bearing signals are carried out; finally, the conclusion of this paper is given in the fifth part.


## 2. Theory

In this paper, we selected four common nonlinear dynamic characteristics; LZC, DE, FD, and LE are used, and the latest two nonlinear dynamic parameters LZC and DE are mainly introduced. There is no need to set parameters for FD; for LE, we take the embedding dimensionm=3, the delay time τ=1, and category quantity c=6.


### 2.1. Lempel-Ziv Complexity

LZC is a parameter to evaluate the irregularity of finite symbolic sequences. If LZC is larger, it means that the new mode of time series is more likely to appear, and the change of time series tends to be disordered and vice versa. The principle of LZC is as follows:(1)
Convert time seriesX=Xi,i=1,2,⋯,N with length of N into binary symbol sequence Y=Yj,j=1,2,⋯,N; Yj can be expressed as(1)Yi=0ifXi<X¯,1otherwise,where X¯ is the average value of X(2)
Algorithm initialization: setS1=Y1, Q1=, C1=1, and i=1; define Ci is the complexity of the first i characters. The main calculation steps of binary symbol sequence Y complexity CN are as follows:Step 1:i=i+1.Step 2: makeSi=Si−1Yi and Qi=Qi−1Yi.Step 3: determine whetherQi belongs to Si−1. If Qi belongs to Si−1, let Ci=Ci−1; otherwise, Qi=, and Ci=Ci−1+1.Step 4: decide whetheri is greater than N. If i is greater than N, the operation is completed, and CN is obtained; otherwise, return to Step 1.The above is the calculation flow ofCN. The calculation flow chart of CN is shown in Figure 1(3)
Obtain the normalizedLZCN, which can be expressed as(2)LZCN=CNLN,(3)LN=limN⟶∞CN≈NlogkN,where k is the number of categories of the symbol sequence. Since the symbol sequence Y is a binary symbol sequence, k=2. When N⟶∞, as the data length increases, the normalized complexity tends to 1.Figure 1
The calculation flow chart ofCN.


### 2.2. Dispersion Entropy

DE is a parameter that describes the degree of irregularity of time series. Compared with the sample entropy and permutation entropy, the calculation speed of DE is faster, and the relationship between amplitudes is considered. The calculation process of DE is as follows:(1)
Use the normal cumulative distribution function to map the given time seriesX=Xj,j=1,2,⋯,N to Y=Yj,j=1,2,⋯,N, and Yj can be expressed as(4)Yj=∫−∞Xje−t−μ2/2σ2dt(2)
MapYj to Zjc using linear transformation, and Zjc can be expressed as(5)Zjc=roundc∗Yj+0.5,where round is the integral function, c is the number of categories, Zjc is a positive integer, and its value range is 1,c. A new time series Zc is obtained, and Zc can be expressed as Z1C,Z2C,⋯ZNC(3)
Reconstruct the phase space ofZc, and calculate the embedded vector Zjm,c:(6)Zjm,c=Zjc+Zj+τc,.⋯,Zj+m−1τc,where j=1,2,⋯,N−m−1τ, m is the embedding dimension, and τ is the delay time
(4)
MakeZjc=v0, Zj+τc=v1,..., Zj+m−1τc=vm−1, and get the dispersion mode πv0v1⋯vm−1 corresponding to Zjm,c. Since the value of v in πv0v1⋯vm−1 is a positive integer and its value range is 1,c, there are cm possibilities for the dispersion mode. The probability Pπv0v1⋯vm−1 of πv0v1⋯vm−1 for each dispersion mode can be expressed as(7)Pπv0v1⋯vm−1=Numberπv0v1⋯vm−1N−m−1τ,where Numberπv0v1⋯vm−1 is the number of πv0v1⋯vm−1(5)
According to Shannon entropy theorem, the definition of DE is(8)DEX,m,c,τ=−∑π=1cmPπv0v1⋯vm−1lnPπv0v1⋯vm−1(6)
When the probabilities of all dispersion modes are equal, the maximum value of DElncm is obtained; on the contrary, if only one mode occurs, the minimum value of 0 is obtained. Therefore, normalized DE can be expressed as(9)De=DEX,m,c,τlncm.In this paper, we takem=3, τ=1, and c=6.


## 2.1. Lempel-Ziv Complexity

LZC is a parameter to evaluate the irregularity of finite symbolic sequences. If LZC is larger, it means that the new mode of time series is more likely to appear, and the change of time series tends to be disordered and vice versa. The principle of LZC is as follows:(1)
Convert time seriesX=Xi,i=1,2,⋯,N with length of N into binary symbol sequence Y=Yj,j=1,2,⋯,N; Yj can be expressed as(1)Yi=0ifXi<X¯,1otherwise,where X¯ is the average value of X(2)
Algorithm initialization: setS1=Y1, Q1=, C1=1, and i=1; define Ci is the complexity of the first i characters. The main calculation steps of binary symbol sequence Y complexity CN are as follows:Step 1:i=i+1.Step 2: makeSi=Si−1Yi and Qi=Qi−1Yi.Step 3: determine whetherQi belongs to Si−1. If Qi belongs to Si−1, let Ci=Ci−1; otherwise, Qi=, and Ci=Ci−1+1.Step 4: decide whetheri is greater than N. If i is greater than N, the operation is completed, and CN is obtained; otherwise, return to Step 1.The above is the calculation flow ofCN. The calculation flow chart of CN is shown in Figure 1(3)
Obtain the normalizedLZCN, which can be expressed as(2)LZCN=CNLN,(3)LN=limN⟶∞CN≈NlogkN,where k is the number of categories of the symbol sequence. Since the symbol sequence Y is a binary symbol sequence, k=2. When N⟶∞, as the data length increases, the normalized complexity tends to 1.Figure 1
The calculation flow chart ofCN.


## 2.2. Dispersion Entropy

DE is a parameter that describes the degree of irregularity of time series. Compared with the sample entropy and permutation entropy, the calculation speed of DE is faster, and the relationship between amplitudes is considered. The calculation process of DE is as follows:(1)
Use the normal cumulative distribution function to map the given time seriesX=Xj,j=1,2,⋯,N to Y=Yj,j=1,2,⋯,N, and Yj can be expressed as(4)Yj=∫−∞Xje−t−μ2/2σ2dt(2)
MapYj to Zjc using linear transformation, and Zjc can be expressed as(5)Zjc=roundc∗Yj+0.5,where round is the integral function, c is the number of categories, Zjc is a positive integer, and its value range is 1,c. A new time series Zc is obtained, and Zc can be expressed as Z1C,Z2C,⋯ZNC(3)
Reconstruct the phase space ofZc, and calculate the embedded vector Zjm,c:(6)Zjm,c=Zjc+Zj+τc,.⋯,Zj+m−1τc,where j=1,2,⋯,N−m−1τ, m is the embedding dimension, and τ is the delay time
(4)
MakeZjc=v0, Zj+τc=v1,..., Zj+m−1τc=vm−1, and get the dispersion mode πv0v1⋯vm−1 corresponding to Zjm,c. Since the value of v in πv0v1⋯vm−1 is a positive integer and its value range is 1,c, there are cm possibilities for the dispersion mode. The probability Pπv0v1⋯vm−1 of πv0v1⋯vm−1 for each dispersion mode can be expressed as(7)Pπv0v1⋯vm−1=Numberπv0v1⋯vm−1N−m−1τ,where Numberπv0v1⋯vm−1 is the number of πv0v1⋯vm−1(5)
According to Shannon entropy theorem, the definition of DE is(8)DEX,m,c,τ=−∑π=1cmPπv0v1⋯vm−1lnPπv0v1⋯vm−1(6)
When the probabilities of all dispersion modes are equal, the maximum value of DElncm is obtained; on the contrary, if only one mode occurs, the minimum value of 0 is obtained. Therefore, normalized DE can be expressed as(9)De=DEX,m,c,τlncm.In this paper, we takem=3, τ=1, and c=6.


## 3. Simulation Experiment

### 3.1. MIX Signal

To verify the effectiveness of four nonlinear dynamic characteristics, we use MIX signal synthesized by periodic signal and random signal for simulation experiment. MIX signal can be expressed as(10)MIXt=1−Z×Xt+Z×Yt,(11)Xt=2sin2πt12,where Yt is a random signal with an interval between −3,3, Z is a proportional coefficient gradually decreasing from 1 to 0, and Xt is a periodic signal. The time domain waveform of MIX signal is shown in Figure 2. It can be obtained from Figure 2 that the number of sampling points for MIX signal is 30000; MIX signal gradually changes from regularity to complexity with the increase of sampling points.Figure 2
Time domain waveform of MIX signal.We take the length of the sliding window as 1000 sampling points and slide backward from the first sampling point with 80% overlap to obtain 145 samples. LZC, DE, FD, and LE for MIX signal of each sample are calculated. The four nonlinear dynamic characteristic curves of MIX signal are shown in Figure3.Figure 3
Nonlinear dynamic characteristics of MIX signal.As can be observed from Figure3, the four nonlinear dynamic characteristics show a downward trend; compared with LZC and LE, the curve of DE and FD is smoother; for LE, compared with LZC, DE, and FD, the second half of its curve fluctuates more violently. The experimental results show that DE and FD can better reflect the change trend of MIX signal complexity.


### 3.2. Amplitude Modulated Chirped Signal

Amplitude modulated chirped signal is based on the chirped signal and adds the periodic change of amplitude. To study the influence of the change of signal frequency and amplitude on four nonlinear dynamic characteristics, we use amplitude modulated chirped signal to carry out simulation experiments. The amplitude modulated chirped signal can be expressed as(12)xt=1+cos2×t÷2ej2πf0t+1/2kt2,where f0 is the initiation frequency, taking 10 Hz, and k is the modulation frequency, taking 1.5; when the amplitude modulated chirped signal lasts 20 seconds (20000 sampling points) with a sampling frequency of 1000 Hz, we can get that the frequency increases from 10 Hz to 40 Hz. The amplitude modulated chirped signal waveform is shown in Figure 4. It can be found from Figure 5 that the waveform of the amplitude modulated chirped signal gradually becomes denser and the amplitude changes periodically as the sampling point increases.Figure 4
Time domain waveform of four kinds of bearing fault signals.
(a)
N-100(b)
IR-108(c)
B-121(d)
OR-133Figure 5
Time domain waveform of amplitude modulated chirped signal.We take the length of the sliding window as 1000 sampling points and slide backward from the first sampling point with 90% overlap to obtain 190 samples. LZC, DE, FD, and LE for amplitude modulated chirped signal of each sample are calculated. The four nonlinear dynamic characteristic curves of amplitude modulated chirped signal are shown in Figure6.Figure 6
Nonlinear dynamic characteristic curves of amplitude modulated chirped signal.It can be observed from Figure6 that compared with LZC and LE, the rising trend of DE and FD curves is more obvious, which can better reflect the frequency change of amplitude modulated chirped signal; the amplitude change of DE curve is consistent with that of amplitude modulated chirped signal, which can reflect the amplitude change of amplitude modulated chirped signal. Compared with LZC and LE, DE and FD can reflect the frequency change of amplitude modulated chirped signal, and only DE can reflect the amplitude change of amplitude modulated chirped signal.


## 3.1. MIX Signal

To verify the effectiveness of four nonlinear dynamic characteristics, we use MIX signal synthesized by periodic signal and random signal for simulation experiment. MIX signal can be expressed as(10)MIXt=1−Z×Xt+Z×Yt,(11)Xt=2sin2πt12,where Yt is a random signal with an interval between −3,3, Z is a proportional coefficient gradually decreasing from 1 to 0, and Xt is a periodic signal. The time domain waveform of MIX signal is shown in Figure 2. It can be obtained from Figure 2 that the number of sampling points for MIX signal is 30000; MIX signal gradually changes from regularity to complexity with the increase of sampling points.Figure 2
Time domain waveform of MIX signal.We take the length of the sliding window as 1000 sampling points and slide backward from the first sampling point with 80% overlap to obtain 145 samples. LZC, DE, FD, and LE for MIX signal of each sample are calculated. The four nonlinear dynamic characteristic curves of MIX signal are shown in Figure3.Figure 3
Nonlinear dynamic characteristics of MIX signal.As can be observed from Figure3, the four nonlinear dynamic characteristics show a downward trend; compared with LZC and LE, the curve of DE and FD is smoother; for LE, compared with LZC, DE, and FD, the second half of its curve fluctuates more violently. The experimental results show that DE and FD can better reflect the change trend of MIX signal complexity.


## 3.2. Amplitude Modulated Chirped Signal

Amplitude modulated chirped signal is based on the chirped signal and adds the periodic change of amplitude. To study the influence of the change of signal frequency and amplitude on four nonlinear dynamic characteristics, we use amplitude modulated chirped signal to carry out simulation experiments. The amplitude modulated chirped signal can be expressed as(12)xt=1+cos2×t÷2ej2πf0t+1/2kt2,where f0 is the initiation frequency, taking 10 Hz, and k is the modulation frequency, taking 1.5; when the amplitude modulated chirped signal lasts 20 seconds (20000 sampling points) with a sampling frequency of 1000 Hz, we can get that the frequency increases from 10 Hz to 40 Hz. The amplitude modulated chirped signal waveform is shown in Figure 4. It can be found from Figure 5 that the waveform of the amplitude modulated chirped signal gradually becomes denser and the amplitude changes periodically as the sampling point increases.Figure 4
Time domain waveform of four kinds of bearing fault signals.
(a)
N-100(b)
IR-108(c)
B-121(d)
OR-133Figure 5
Time domain waveform of amplitude modulated chirped signal.We take the length of the sliding window as 1000 sampling points and slide backward from the first sampling point with 90% overlap to obtain 190 samples. LZC, DE, FD, and LE for amplitude modulated chirped signal of each sample are calculated. The four nonlinear dynamic characteristic curves of amplitude modulated chirped signal are shown in Figure6.Figure 6
Nonlinear dynamic characteristic curves of amplitude modulated chirped signal.It can be observed from Figure6 that compared with LZC and LE, the rising trend of DE and FD curves is more obvious, which can better reflect the frequency change of amplitude modulated chirped signal; the amplitude change of DE curve is consistent with that of amplitude modulated chirped signal, which can reflect the amplitude change of amplitude modulated chirped signal. Compared with LZC and LE, DE and FD can reflect the frequency change of amplitude modulated chirped signal, and only DE can reflect the amplitude change of amplitude modulated chirped signal.


## 4. Bearing Fault Diagnosis Based on Nonlinear Dynamic Characteristics

### 4.1. Measured Bearing Fault Signal

The research object of this paper is bearing signal. We randomly selected four bearing signals with different faults in the same working state, which came from the website [23]; data files are in MATLAB format. Each signal data includes drive end accelerometer data, fan end accelerometer data, and motor rotational speed; the drive end accelerometer data is used by us for research. We name the normal bearing signal, inner ring fault bearing signal, rolling element fault bearing signal, and outer ring fault bearing signal as N-100, IR-108, B-121, and OR-133, respectively. 100000 sampling points are taken for each bearing signal, and time domain waveform of four kinds of bearing fault signals is shown in Figure 4.


### 4.2. Feature Extraction

We take 2000 sampling points as the sliding window length. The sliding window slides backward from the first sampling point, and 50 samples are obtained. LZC, DE, FD, and LE of each sample are calculated. Figure7 shows the nonlinear dynamic characteristic curves of four types of bearing signals.Figure 7
Nonlinear dynamic characteristic curves of four types of bearing signals.
(a)
LZC(b)
DE(c)
FD(d)
LEIt can be found from Figure7 that the FD curves of the four bearing signals do not overlap; the DE curves of two bearing signals overlap; the LZC curves of three bearing signals overlap; the LE curves of the four bearing signals are all overlapped; for the B-121, except for the FD curve, the other three feature curves have overlapping parts. In conclusion, compared with LZC and LE, DE and FD have better performance in feature extraction.To more intuitively compare the feature extraction effects of four kinds of nonlinear dynamics on four kinds of bearing signals, we calculate their mean and standard deviation, respectively. Table1 shows the mean value and standard deviation of the nonlinear dynamic characteristics for the four types of bearing signals.Table 1
Mean value and standard deviation of the nonlinear dynamic characteristics for four bearing signals.
CharacteristicParameterFault typeN-100B-121IR-108OR-133LZCMean value0.69040.69420.87310.7293Standard deviation0.02300.02850.02040.0185DEMean value0.79890.91840.92520.7752Standard deviation0.00540.00480.00410.0067FDMean value1.37621.47201.42111.4047Standard deviation0.00520.00700.00270.0037LEMean value0.39150.30210.23460.1405Standard deviation0.07000.05980.05360.0447It can be seen from Table1 that for nonlinear dynamic characteristics of the four types of bearing signals, the mean value difference of each nonlinear dynamic characteristic is not obvious; the mean value of FD is the largest, and the mean value of LE is the smallest for the four types of bearing signals; compared with LZC and LE, the standard deviation of DE and FD is significantly smaller, indicating that DE and FD are more stable for nonlinear dynamic feature extraction. Compared with LZC and LE, DE and FD have better effect on feature extraction of four types of bearing signals.


### 4.3. Classification

In this paper, k-Nearest Neighbor (KNN) algorithm is introduced to classify and recognize for four different bearing signals. For each nonlinear dynamic characteristic, the same 25 samples of each type of bearing signal are selected as the training samples for classification training, and then, the remaining 25 samples of each type are used as the test set for classification and recognition. Figure8 shows the classification and recognition results of four types of bearing signals.Figure 8
Classification and recognition results of four types of bearing signals.
(a)
LZC(b)
DE(c)
FD(d)
LEIt can be seen from Figure8 that FD only has one wrong recognition result for four types of bearing signals, and the number of samples with recognition errors is the least; there are few wrong recognition results of four types of bearing signals by DE; LZC and LE have many wrong recognition results for different types of bearing signals, and their classification and recognition ability is poor. The following results are obtained: compared with LZC and LE, FD and DE have better classification and recognition performance for different types of bearing signals.To compare the classification and recognition results of each nonlinear dynamic feature on four bearing signals more conveniently, we calculate the average recognition rate (ARR) of each kind of signal under each nonlinear dynamic characteristic. Table2 shows the recognition rates of four bearing signals based on KNN for each nonlinear dynamic characteristic.Table 2
Recognition rates of four bearing signals based on KNN for each nonlinear dynamic characteristic.
CharacteristicN-100B-121IR-108OR-108ARRLZC84%23%100%18%55%DE88%72%76%100%84%FD100%100%100%96%99%LE68%28%36%60%48%It can be observed from Table2 that FD has the ARR for four types of bearing signals; the ARR of DE for different types of bearing signals is higher, and the ARR reaches 84%; the ARR of LZC and LE is lower, reaching 55% and 48%; the recognition rate of FD for three types of bearing signals has reached 100%; for any bearing signal, the recognition rate of LE has not reached 100%. Compared with LZC and LE, DE and FD have highest classification and recognition rate for different types of bearing signals.


## 4.1. Measured Bearing Fault Signal

The research object of this paper is bearing signal. We randomly selected four bearing signals with different faults in the same working state, which came from the website [23]; data files are in MATLAB format. Each signal data includes drive end accelerometer data, fan end accelerometer data, and motor rotational speed; the drive end accelerometer data is used by us for research. We name the normal bearing signal, inner ring fault bearing signal, rolling element fault bearing signal, and outer ring fault bearing signal as N-100, IR-108, B-121, and OR-133, respectively. 100000 sampling points are taken for each bearing signal, and time domain waveform of four kinds of bearing fault signals is shown in Figure 4.


## 4.2. Feature Extraction

We take 2000 sampling points as the sliding window length. The sliding window slides backward from the first sampling point, and 50 samples are obtained. LZC, DE, FD, and LE of each sample are calculated. Figure7 shows the nonlinear dynamic characteristic curves of four types of bearing signals.Figure 7
Nonlinear dynamic characteristic curves of four types of bearing signals.
(a)
LZC(b)
DE(c)
FD(d)
LEIt can be found from Figure7 that the FD curves of the four bearing signals do not overlap; the DE curves of two bearing signals overlap; the LZC curves of three bearing signals overlap; the LE curves of the four bearing signals are all overlapped; for the B-121, except for the FD curve, the other three feature curves have overlapping parts. In conclusion, compared with LZC and LE, DE and FD have better performance in feature extraction.To more intuitively compare the feature extraction effects of four kinds of nonlinear dynamics on four kinds of bearing signals, we calculate their mean and standard deviation, respectively. Table1 shows the mean value and standard deviation of the nonlinear dynamic characteristics for the four types of bearing signals.Table 1
Mean value and standard deviation of the nonlinear dynamic characteristics for four bearing signals.
CharacteristicParameterFault typeN-100B-121IR-108OR-133LZCMean value0.69040.69420.87310.7293Standard deviation0.02300.02850.02040.0185DEMean value0.79890.91840.92520.7752Standard deviation0.00540.00480.00410.0067FDMean value1.37621.47201.42111.4047Standard deviation0.00520.00700.00270.0037LEMean value0.39150.30210.23460.1405Standard deviation0.07000.05980.05360.0447It can be seen from Table1 that for nonlinear dynamic characteristics of the four types of bearing signals, the mean value difference of each nonlinear dynamic characteristic is not obvious; the mean value of FD is the largest, and the mean value of LE is the smallest for the four types of bearing signals; compared with LZC and LE, the standard deviation of DE and FD is significantly smaller, indicating that DE and FD are more stable for nonlinear dynamic feature extraction. Compared with LZC and LE, DE and FD have better effect on feature extraction of four types of bearing signals.


## 4.3. Classification

In this paper, k-Nearest Neighbor (KNN) algorithm is introduced to classify and recognize for four different bearing signals. For each nonlinear dynamic characteristic, the same 25 samples of each type of bearing signal are selected as the training samples for classification training, and then, the remaining 25 samples of each type are used as the test set for classification and recognition. Figure8 shows the classification and recognition results of four types of bearing signals.Figure 8
Classification and recognition results of four types of bearing signals.
(a)
LZC(b)
DE(c)
FD(d)
LEIt can be seen from Figure8 that FD only has one wrong recognition result for four types of bearing signals, and the number of samples with recognition errors is the least; there are few wrong recognition results of four types of bearing signals by DE; LZC and LE have many wrong recognition results for different types of bearing signals, and their classification and recognition ability is poor. The following results are obtained: compared with LZC and LE, FD and DE have better classification and recognition performance for different types of bearing signals.To compare the classification and recognition results of each nonlinear dynamic feature on four bearing signals more conveniently, we calculate the average recognition rate (ARR) of each kind of signal under each nonlinear dynamic characteristic. Table2 shows the recognition rates of four bearing signals based on KNN for each nonlinear dynamic characteristic.Table 2
Recognition rates of four bearing signals based on KNN for each nonlinear dynamic characteristic.
CharacteristicN-100B-121IR-108OR-108ARRLZC84%23%100%18%55%DE88%72%76%100%84%FD100%100%100%96%99%LE68%28%36%60%48%It can be observed from Table2 that FD has the ARR for four types of bearing signals; the ARR of DE for different types of bearing signals is higher, and the ARR reaches 84%; the ARR of LZC and LE is lower, reaching 55% and 48%; the recognition rate of FD for three types of bearing signals has reached 100%; for any bearing signal, the recognition rate of LE has not reached 100%. Compared with LZC and LE, DE and FD have highest classification and recognition rate for different types of bearing signals.


## 5. Conclusions

To effectively extract the fault characteristics of bearing signals in complex situations, four kinds of nonlinear dynamic characteristic are used to analyze and compare the simulated signals and the measured bearing fault signals. The following conclusions are obtained:(1)
The validity of four nonlinear dynamic characteristics was verified by the MIX signal; compared with LZC and LE, FD and DE can better reflect the frequency variation trend of amplitude modulated chirped signal, and DE can also reflect the change trend of simulation signal amplitude(2)
Through the feature extraction and classification recognition of the measured bearing signals, it is concluded that compared with LZC and LE, the feature extraction effect of DE and FD is better; FD has the highest classification recognition rate, and the average recognition rate of FD is 99%



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*Source: 9405082-2022-09-15.xml*