# Fault Diagnosis of Axle Box Bearing with Acoustic Signal Based on Chirplet Transform and Support Vector Machine

Authors: Jimin Zhang; Xianting Hu; Xujie Zhong; Hechao Zhou
Journal: Shock and Vibration
 (2022)

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## Abstract

Acoustic fault diagnosis technology equipment is non-contact, and the acoustic signal is easy to access. However, it is difficult to extract the feature information of the acoustic signal with low signal-to-noise ratio (SNR). In this paper, a fault diagnosis model (FDM) of axle box bearing based on Chirplet transform (CT) and support vector machine (SVM) is established to diagnose bearing fault based on acoustic signal. The availability of the model is verified by comparing with the vibration acceleration signal bearing fault diagnosis results, and the correctness of the model is verified by utilizing the open database of Western Reserve University. The acoustic-vibration comprehensive bearing fault diagnosis experiment platform (AVEP) is established to investigate the acoustic signal and acceleration signal diagnosis accuracy. The results suggest that, based on the FDM, the diagnosis accuracy and stability of acoustic signal are not as good as acceleration signal when the number of samples is small under the single condition; the diagnosis accuracy of acoustic signal is similar to that of acceleration signal when the number of samples is enough under the multiple condition, which provides a reference for the application of acoustic fault diagnosis technology in engineering in the future.


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## Body

## 1. Introduction

As one of the important parts of the rail vehicle running gear, axle box bearing plays a key role in supporting the rotary structure and reducing friction loss, which directly affects the safety of the rail vehicle. Under the influence of irregular track and improper assembly, the bearing surface of the vehicle running gear is prone to wear, corrosion, and peeling, which leads to the reduction of bearing rotation accuracy and the increase of vibration noise, thus affecting the safety of the vehicle. Therefore, it is necessary to monitor the running state of the bearing.In order to ensure the safety, the vehicle-carried condition monitoring system which monitors the bearing condition by measuring the bearing temperature and vibration acceleration has been widely used in the field of rail transit in China. However, the trackside acoustic detection system (TADS) is not widely used. It is expensive to introduce the system from abroad, so it is urgent for China to develop products with independent intellectual property rights [1]. Different from the acceleration signal that has formed a complete system after a long period of development, the source of the acoustic signal is complex and the signal-to-noise ratio is low. Therefore, the research on bearing fault diagnosis based on acoustic signal has important practical significance and engineering value.Heng and Nor [2] used statistical analysis method to study the application of acoustic and vibration signal in rolling bearing fault detection and compared the results from different statistical parameters. Naim and Ball [3] used the smoothed pseudo-Wigner–Ville distribution method to analyze the acoustic signal and found it was very effective for identifying the local fault and detecting the early fault of the gearbox. Amanath and Krishna [4] used EMD to deal with the acoustic signal of rolling bearing, which proved its superiority in early fault detection. Yu and Huang [5] designed a diagnosis method of envelope demodulation, autocorrelation and power spectral density based on filtering, kurtosis, and absolute value plus low-pass filtering for rolling bearing fault acoustic signal. Zhou et al. [6] utilized correlation analysis and wavelet transform principle to make the time-frequency analysis of the rolling bearing fault acoustic signal from the perspective of application, and the vagary of the acoustic signal caused by the fault was separated by the multi-scale decomposition and reconstruction. You et al. [7] denoised and enveloped the collected acoustic signal by the envelope analysis based on wavelet transform and then extracted the feature frequency after frequency domain conversion, which was employed as the input vector of linear neural network after conversion to identify the condition of rolling bearing.Machine learning is a data-driven approach. Generally, the application process of machine learning in bearing fault diagnosis is to input the time domain, frequency domain, or time-frequency domain features of data into the classification model to classify different fault types.Samanta and Al balushi [8] extracted root mean square, variance, skewness, kurtosis, and normalized Sixth Central Moment of the time domain feature from bearing vibration signal and used them as the input of artificial neural network for bearing fault diagnosis. Zhang et al. [9] used Morlet wavelet transform and random decrement technique to identify the characteristic parameters of vibration system. Purushotham et al. [10] used discrete wavelet transform of Mel frequency scale to diagnose single fault and multiple faults for rolling bearing and also proposed a new method to improve the diagnosis accuracy by using Mel frequency complex cepstrum coefficient as the input of hidden Markov model classifier.The advantages of acoustic signal compared with acceleration signal are mainly in the following two aspects. One is that the acceleration sensor needs to be firmly installed on the axle box, whose mounting seat or hole needs to be left on the axle box. However, the small and light acoustic sensor can be installed at the bottom of the vehicle body, which has few effects and requirements on the structure. The other is that the condition information of running gear components (wheelset bearing, gearbox, motor bearing, etc.) of the vehicle can be measured by a set of acoustic signals, which means that a set of acoustic signals can analyze the condition of multiple components.Compared with the acceleration signal, the main disadvantage of the acoustic signal is that the data is greatly affected by the noise. Noise from the environment and the vehicle, including wheel rail noise and traction drive system (including transformer, converter, etc.) as well as the noise of some auxiliary equipment, may submerge fault signal.In this study, the characteristics of acoustic signal and acceleration signal from the established acoustic-vibration comprehensive bearing fault diagnosis experiment platform (AVEP) are compared to investigate the feasibility of bearing fault diagnosis based on acoustic signal. The bearing condition monitoring model based on time-frequency parameters is established to propose a feasible and targeted diagnosis method for bearing intelligent operation and maintenance management based on acoustic signal.In this paper, the process of fault diagnosis model (FDM) based on Chirplet transform (CT) and support vector machine (SVM) is described. The experimental scheme, content, and device of AVEP are introduced, as well as the data as the source data to support the verification of the bearing fault diagnosis algorithm. The characteristics of acoustic signal and acceleration signal in bearing fault diagnosis are summarized by comparing the diagnosis results. The introduction should be succinct, with no subheadings. Limited figures may be included only if they are truly introductory and contain no new results.


## 2. Theoretical Background

### 2.1. Chirplet Transform

Suppose a signalst is a frequency modulation (FM) signal, that is, st=Acosϕt+wt, where A denotes the amplitude and ϕt denotes the phase. The analytic signal zt is defined as(1)zt=st+jHst=Acosϕt+jHAcosϕt=Aexpjϕt.The principle of CT [11] is to map the signal st∈L2R to a series of linear Chirplet function spaces ht,ω,ct internal. In the inner product space, it can be expressed as(2)CTst,ω;c=zt,ht,ω,ct,where c denotes the linear frequency modulation (LFM) coefficient, ω denotes the angular frequency, zt denotes the analytic signal of st, as shown in equation (1), and ht,ω,ct denotes the Chirplet base, as shown in(3)ht,e,ct=gστ−texpjωτ−t+c2τ−t2,where gσt denotes a Gaussian window function with a time width of σ, as shown in(4)gσt=12πσexp−t24σ.Then, equation (2) can be written as(5)CTst,ω;c=∫−∞+∞zτgσ∗τ−texp−jωτ−t+c2τ−t2dτ.It can be seen from equation (4) that the Chirplet base is transformed on the basis of Gaussian window function gσt. In the time shift, gσt is transformed into gστ−t, which means that the window function moves to the right t along the time axis. In the frequency shift expjωt, gσt is transformed into gσtexpjωt, and the corresponding time domain grid remains constant while the frequency domain grid shifts. When gσt LFM equals gσtexpjc/2t2, the waveform of window function in time domain changes linearly, and c is utilized to adjust the variation rate of time-frequency grid [12].Consider a time-varying signal whose instantaneous frequency is10+2.5tHz, and the signal expression is as(6)st=sin2π10+2.5tt.Short time Fourier transform (STFT), continuous wavelet transform (CWT), and CT are performed on the signal, respectively, and the results are shown in Figure1. It can be seen from the figure that CT has better time-frequency resolution for time-varying signals whose instantaneous frequency varies linearly.Figure 1
Comparison of time-frequency diagram obtained by different methods. (a) Short time Fourier transform. (b) Continuous wavelet transform. (c) Chirplet transform. (d) Theoretical time-frequency diagram.
(a)(b)(c)(d)


### 2.2. Support Vector Machine Model

SVM algorithm is widely used in the classification field which can be applied to high-dimensional feature space and still effective when the number of dimensions is larger than that of samples. The subset of training points (called support vector) is utilized by SVM in the decision function, which makes SVM take up less memory. In addition, SVM can also specify different kernel functions for decision functions according to the characteristics of data types. Based on SVM, the modeling approach of the FDM will be studied in detail.The main function of linear SVM is to find a hyperplane, which can ensure that all the points in the input training data of different classifications are farthest away from it, and all thex located on both sides of the hyperplane meet the decision function, as shown in(7)fx=ωT⋅x+b=0,where ω denotes the coefficient of the hyperplane and b denotes the constant term of the hyperplane.The equation of boundaryL1 and L2 is ωT⋅x+b=±1. Suppose that the support vector x1 is located on the boundary L1 and the support vector x2 is located on the boundary L2; then there is ωT⋅x1+b=−1,ωT⋅x2+b=+1, and the subtraction of the two equations leads to ωT⋅x2−x1=2, and then equation (8) can be obtained:(8)ωTω⋅x2−x1=2ω.The left side of equation (11) is the sum of the distances from the support vectors x1 and x2 to the hyperplane. Therefore, ω needs to be the minimum to minimize the sum of the distances from x1 and x2 to the hyperplane.Considering that all sample points should be located on the outside of the boundary as far as possible, there isωT⋅xi+b≥1 when yi=1; there is ωT⋅xi+b≤−1 when yi=−1. The result is as(9)yiωT⋅xi+b≥1.The problem of solving hyperplane is transformed into a quadratic convex optimization problem, as shown in(10)min12ω2s.t.yiωT⋅x+b≥1,i=1,2,3,…,n.Lagrange multiplier can be utilized to deal with this optimization problem. The formula is shown in(11)Lpw,b,α=12w2−∑i=1nαiyiw⋅xi+b−1,where αi denotes the Lagrange coefficient and αi>0. According to the Karush–Kuhn–Tucker (KKT) theory, the optimal solution wi∗,bi∗ of the equation can be obtained from(12)∑i=1nαi∗yi∗xi⋅w∗+b∗−1=0.Anyxi satisfying the above equation is the solution of the support vector which is closest to the hyperplane. The classification process function equation can be obtained as follows:(13)fx=sgn∑i=1nαiyi⋅xi⋅xj+b,where αi denotes the Lagrange coefficient and n denotes the number of SVM.


### 2.3. Fault Diagnosis Modeling

CT is utilized to extract the feature of acceleration signal and acoustic signal to obtain the feature vector whose dimension is [(fragment length) (transform scale)]. When the fragment length is 15000 and the transform scale is 100, the vector dimension is [15000 100]. The vector with too high dimension is not conducive to input the machine learning model, so the principal component analysis (PCA) method is used to reduce the dimension. As a data set dimension reduction method, the principal component analysis aims to keep the data relationship displayed in the data set as much as possible. The original interrelated variables are transformed into a series of new uncorrelated variables called principal components, which are ordered, and the most information of the original data is retained in the first principal component. The principal components whose eigenvalues are higher than 2 are usually selected to judge whether their eigenvalues and variance ratio can represent the index of original vector as vector after dimension reduction. In this research, the variance ratio of the first five principal components that have been selected reaches 70%, which proves that the vector obtained after dimension reduction can represent the original vector.After dimension reduction, the time-frequency features obtained by CT are divided into training set and test set according to the ratio of 0.8:0.2. The training set vector is input into the SVM model, RBF is selected as the kernel function of the SVM, and the grid search method is used to adjust the two input parametersC and γ of SVM, where C denotes the regularization parameter and γ defines the influence degree of the single training example. The model with the optimal parameters is regarded as the final FDM, and the test set vector is input into the model to obtain the diagnosis accuracy.The flow diagram of the FDM is shown in Figure2.Figure 2
Flow diagram of the bearing fault diagnosis model.


## 2.1. Chirplet Transform

Suppose a signalst is a frequency modulation (FM) signal, that is, st=Acosϕt+wt, where A denotes the amplitude and ϕt denotes the phase. The analytic signal zt is defined as(1)zt=st+jHst=Acosϕt+jHAcosϕt=Aexpjϕt.The principle of CT [11] is to map the signal st∈L2R to a series of linear Chirplet function spaces ht,ω,ct internal. In the inner product space, it can be expressed as(2)CTst,ω;c=zt,ht,ω,ct,where c denotes the linear frequency modulation (LFM) coefficient, ω denotes the angular frequency, zt denotes the analytic signal of st, as shown in equation (1), and ht,ω,ct denotes the Chirplet base, as shown in(3)ht,e,ct=gστ−texpjωτ−t+c2τ−t2,where gσt denotes a Gaussian window function with a time width of σ, as shown in(4)gσt=12πσexp−t24σ.Then, equation (2) can be written as(5)CTst,ω;c=∫−∞+∞zτgσ∗τ−texp−jωτ−t+c2τ−t2dτ.It can be seen from equation (4) that the Chirplet base is transformed on the basis of Gaussian window function gσt. In the time shift, gσt is transformed into gστ−t, which means that the window function moves to the right t along the time axis. In the frequency shift expjωt, gσt is transformed into gσtexpjωt, and the corresponding time domain grid remains constant while the frequency domain grid shifts. When gσt LFM equals gσtexpjc/2t2, the waveform of window function in time domain changes linearly, and c is utilized to adjust the variation rate of time-frequency grid [12].Consider a time-varying signal whose instantaneous frequency is10+2.5tHz, and the signal expression is as(6)st=sin2π10+2.5tt.Short time Fourier transform (STFT), continuous wavelet transform (CWT), and CT are performed on the signal, respectively, and the results are shown in Figure1. It can be seen from the figure that CT has better time-frequency resolution for time-varying signals whose instantaneous frequency varies linearly.Figure 1
Comparison of time-frequency diagram obtained by different methods. (a) Short time Fourier transform. (b) Continuous wavelet transform. (c) Chirplet transform. (d) Theoretical time-frequency diagram.
(a)(b)(c)(d)


## 2.2. Support Vector Machine Model

SVM algorithm is widely used in the classification field which can be applied to high-dimensional feature space and still effective when the number of dimensions is larger than that of samples. The subset of training points (called support vector) is utilized by SVM in the decision function, which makes SVM take up less memory. In addition, SVM can also specify different kernel functions for decision functions according to the characteristics of data types. Based on SVM, the modeling approach of the FDM will be studied in detail.The main function of linear SVM is to find a hyperplane, which can ensure that all the points in the input training data of different classifications are farthest away from it, and all thex located on both sides of the hyperplane meet the decision function, as shown in(7)fx=ωT⋅x+b=0,where ω denotes the coefficient of the hyperplane and b denotes the constant term of the hyperplane.The equation of boundaryL1 and L2 is ωT⋅x+b=±1. Suppose that the support vector x1 is located on the boundary L1 and the support vector x2 is located on the boundary L2; then there is ωT⋅x1+b=−1,ωT⋅x2+b=+1, and the subtraction of the two equations leads to ωT⋅x2−x1=2, and then equation (8) can be obtained:(8)ωTω⋅x2−x1=2ω.The left side of equation (11) is the sum of the distances from the support vectors x1 and x2 to the hyperplane. Therefore, ω needs to be the minimum to minimize the sum of the distances from x1 and x2 to the hyperplane.Considering that all sample points should be located on the outside of the boundary as far as possible, there isωT⋅xi+b≥1 when yi=1; there is ωT⋅xi+b≤−1 when yi=−1. The result is as(9)yiωT⋅xi+b≥1.The problem of solving hyperplane is transformed into a quadratic convex optimization problem, as shown in(10)min12ω2s.t.yiωT⋅x+b≥1,i=1,2,3,…,n.Lagrange multiplier can be utilized to deal with this optimization problem. The formula is shown in(11)Lpw,b,α=12w2−∑i=1nαiyiw⋅xi+b−1,where αi denotes the Lagrange coefficient and αi>0. According to the Karush–Kuhn–Tucker (KKT) theory, the optimal solution wi∗,bi∗ of the equation can be obtained from(12)∑i=1nαi∗yi∗xi⋅w∗+b∗−1=0.Anyxi satisfying the above equation is the solution of the support vector which is closest to the hyperplane. The classification process function equation can be obtained as follows:(13)fx=sgn∑i=1nαiyi⋅xi⋅xj+b,where αi denotes the Lagrange coefficient and n denotes the number of SVM.


## 2.3. Fault Diagnosis Modeling

CT is utilized to extract the feature of acceleration signal and acoustic signal to obtain the feature vector whose dimension is [(fragment length) (transform scale)]. When the fragment length is 15000 and the transform scale is 100, the vector dimension is [15000 100]. The vector with too high dimension is not conducive to input the machine learning model, so the principal component analysis (PCA) method is used to reduce the dimension. As a data set dimension reduction method, the principal component analysis aims to keep the data relationship displayed in the data set as much as possible. The original interrelated variables are transformed into a series of new uncorrelated variables called principal components, which are ordered, and the most information of the original data is retained in the first principal component. The principal components whose eigenvalues are higher than 2 are usually selected to judge whether their eigenvalues and variance ratio can represent the index of original vector as vector after dimension reduction. In this research, the variance ratio of the first five principal components that have been selected reaches 70%, which proves that the vector obtained after dimension reduction can represent the original vector.After dimension reduction, the time-frequency features obtained by CT are divided into training set and test set according to the ratio of 0.8:0.2. The training set vector is input into the SVM model, RBF is selected as the kernel function of the SVM, and the grid search method is used to adjust the two input parametersC and γ of SVM, where C denotes the regularization parameter and γ defines the influence degree of the single training example. The model with the optimal parameters is regarded as the final FDM, and the test set vector is input into the model to obtain the diagnosis accuracy.The flow diagram of the FDM is shown in Figure2.Figure 2
Flow diagram of the bearing fault diagnosis model.


## 3. Experiment Research

### 3.1. Bearing Fault Diagnosis Experiment Platform of Western Reserve University

The bearing fault experiment platform of Western Reserve University consists of a motor, torque sensor, and dynamometer. The test bearings supporting motor shaft are divided into the bearing supporting motor drive end and the bearing supporting motor fan end. Cross-combination tests of different fault severity (7 mils, 14 mils, 21 mils, 28 mils, and 40 mils), different fault locations (inner-race, outer-race, roller), and different sensor locations (fan end and drive end) are carried out on test bearings.Take the data of bearing fault at drive end and acceleration sensor position at drive end, load 0 hp, and rotating speed 1797 rpm as an example, the slightest bearing fault (7 mils) is selected for comparative analysis. The results of the difference of acceleration signals from different kinds of fault bearings in time domain and frequency domain are shown in Table1.Table 1
Comparison of time domain and frequency domain results of bearings in different conditions.
Bearing conditionTime domain diagramFrequency domain diagramNormalInner-race faultRoller faultOuter-race faultThe time-frequency diagrams of acceleration signals of fault bearings under different types are obtained by CT on the above data, as shown in Figure3. It can be found that the time domain energy of the normal bearing is mainly concentrated below 200 Hz, while the fault bearing is mainly concentrated between 400 Hz and 800 Hz. There is a difficulty to observe clearly the bearing fault characteristic frequency and its multiple frequency (theoretical value is 138.8 Hz for inner-race, 112.8 Hz for roller, and 86.4 Hz for outer-race) under the condition only from the time-frequency diagram. It is very hard to obtain the specific evaluation criteria of the state classification model directly based on the time-frequency analysis method and then determine the fault type and severity of the rolling bearing according to the characteristic frequency. It provides a new approach to solve this problem by inputting time-frequency coefficients into machine learning model (MLM) for classification after dimension reduction.Figure 3
Chirplet time-frequency diagram of bearing in different conditions. (a) Normal bearing. (b) Inner-race fault. (c) Roller fault. (d) Outer-race fault.
(a)(b)(c)(d)


### 3.2. Acoustic-Vibration Comprehensive Bearing Fault Diagnosis Experiment Platform

The experiment environment includes generator noise, air conditioning noise, wind noise, and vehicle driving noise in addition to the test equipment to simulate the realistic noise environment around the vehicle. Figure4 is the physical picture of the experiment platform, which is composed of variable-frequency motor (left) and test bearing (right), two acceleration sensors (brand: CHENG TEC; model: CT1050L; sensitivity: 500 mV/g; range: ≤10 g) are installed on the lateral and vertical direction surfaces of the test bearing, respectively, and four acoustic sensors (brand: CRY Sound; model: CRY331; frequency range: 3.15 Hz∼16 kHz; sensitivity: 40 mV/Pa; linear range: 16∼140 dB) which are placed towards the bearing are arranged at a certain distance from the bearing. The motor shaft and the test bearing main shaft are connected by a coupling, and the motor speed is adjusted by parameters of the variable-frequency controller, and the bottom of the bearing is pressurized by a jack to simulate the load of the bearing.Figure 4
Physical picture of bearing experiment platform.The single row cylindrical rolling bearing NJ(P)3226X1 equipped for Chinese freight trains is used as the test bearing. The specific size and fault frequency of the bearing are shown in Tables2 and 3. In order to simulate the mixed fault of outer-race and roller, WEDM (wire cut electrical discharge machining) is utilized to cause the crack fault with a width of 0.18 mm and a depth of 0.5 mm into the outer-race and roller of the test bearing.Table 2
Bearing size table (unit: mm).
Inner-race diameter (mm)Outer-race diameter (mm)Number of rollersRoller diameter (mm)Pitch diameter (mm)1302501432190Table 3
Characteristic parameters of bearing fault.
Inner-raceOuter-raceCageRoller8.1795.8200.4162.885Note: the fault frequency unit is Hz, which needs to be multiplied by the bearing speed, and the bearing speed unit is r/s.The 8-channel data recorder is utilized to collect vibration signals and acoustic signals under different load and speed conditions which are described in Table4. The acquisition time is more than 20 s under each condition.Table 4
Description of load and speed conditions.
Condition numberLoad (kg)Speed (rpm)Sampling rate (kHz)Condition numberLoad (kg)Speed (rpm)Sampling rate (kHz)2_05500148304_051000148302_10500296304_101000296302_15500444304_151000444302_20500592304_201000592302_25500741304_251000741302_30500888304_301000888302_355001036304_351000103630


### 3.3. Experiment Data Analysis

#### 3.3.1. Time Domain Analysis

Tables5 and 6 are time domain signal comparison diagrams of the normal bearing and the fault bearing. At low speed (148 rpm∼592 rpm), there are obvious periodic pulse signals which correspond to the bearing fault in the lateral acceleration and vertical acceleration signals. Under the high speed (592 rpm∼ 1036 rpm) condition, the severe vibration signals of the experiment platform cover the periodic pulse signals, which cause pulse signals to not be seen clearly in time domain. The normal signal is very stable in time domain, while the fault bearing signal is fluctuating.Table 5
Time domain diagram of vertical acceleration signal.
Speed (rpm)Normal bearingFault bearing4441036Table 6
Time domain diagram of acoustic signal.
Speed (rpm)Normal bearingFault bearing4441036It can be seen from Table6, different from acceleration signals, that there are no obvious periodic pulse signals in high or low speed condition. The acoustic signals of the normal bearing are very stable, while the acoustic signals of the fault bearing fluctuate and often have sharp peaks.


#### 3.3.2. Frequency Domain Analysis

Frequency domain analysis is to get the amplitude of the signal in frequency by Fourier transform, which is the most basic means to understand the signal. When the fault occurs in different positions of the bearing, it will cause different fault characteristic frequencies which is generally below 1000 Hz. The peak signal in the middle and high frequency bands is usually formed by bearing natural frequency modulation. In order to analyze the bearing fault characteristic frequency, the frequency domain diagram of 0∼1000 Hz is selected for preliminary analysis.Tables7 and 8 are frequency domain comparison diagrams of acceleration signal and acoustic signal of normal bearing and fault bearing.Table 7
Frequency domain diagram of vertical acceleration signal.
Speed (rpm)Normal bearingFault bearing4441036Table 8
Frequency domain diagram of acoustic signal.
Speed (rpm)Normal bearingFault bearing4441036It can be seen from the frequency domain diagram of vertical acceleration that the frequency domain energy of the fault bearing is concentrated below 100 Hz, and the larger amplitude (0.05∼0.1) is obtained near 0 Hz, while the energy distribution of the normal bearing is at 1∼100 Hz and 700∼1000 Hz.It is worth noting that, under low-speed operating conditions (444 rpm), there is a phenomenon of fault characteristic frequency and shaft rotation frequency modulation that clearly points to the bearing fault. The fundamental frequency of the modulation is 110 Hz, which corresponds to the fault characteristic frequency of the bearing inner race. In the spectrum, the amplitude decreases at the fault characteristic frequency and each frequency doubling, and modulation lines appear on both sides of each frequency doubling. But at high speed (1036 rpm), the severe vibration of the bearing experiment platform covers the original pulse characteristic frequency signal, and the bearing fault characteristics cannot be well seen in the frequency domain.According to the comparison of the frequency domain diagrams of the acoustic signal in Table8, the characteristic of the acoustic signal is that there is a very large amplitude near 0 Hz, and the energy distribution is relatively uniform in other frequency regions. The energy of fault signal is more concentrated in 0∼100 Hz region than other regions, while the energy of normal signal is more uniform in the whole frequency band. Low frequency vibration is usually caused by local fault of bearing, of which it can be clearly seen that some frequencies are concentrated in the band in the frequency spectrum analysis.


#### 3.3.3. Time-Frequency Analysis

Tables9 and 10 show the time-frequency signal comparison diagrams of the normal bearing and the fault bearing after CT.Table 9
Time-frequency diagram of vertical acceleration signal.
Speed (rpm)Normal bearingFault bearing4441036Table 10
Time-frequency diagram of acoustic signal.
Speed (rpm)Normal bearingFault bearing4441036There is no obvious characteristic spectral line within 0∼1000 Hz in the time domain diagram of the normal bearing and the scattered point distribution is more uniform. However, the signal of the fault bearing is unstable at low frequency (0∼50 Hz), and some energy pulses appear.For the acoustic signal, the normal bearing energy distributes in the range of 0∼1000 Hz, while the time-frequency energy of the fault bearing is mainly concentrated in the low frequency. Because the local fault of the bearing is mainly caused by the low frequency vibration, the frequency spectrum line in the time-frequency diagram is mainly concentrated below 100 Hz. By comparing Tables9 and 10, it can be found that the unstable pulse displaying in the wavelet time-frequency diagram of the acceleration signal of the fault bearing in Table 9 is not reflected in the wavelet time-frequency diagram of the acoustic signal of the fault bearing in Table 10, which indicates that compared with the acceleration signal the ability of describing the local characteristics of the non-stationary signal of the acoustic signal is not strong.


## 3.1. Bearing Fault Diagnosis Experiment Platform of Western Reserve University

The bearing fault experiment platform of Western Reserve University consists of a motor, torque sensor, and dynamometer. The test bearings supporting motor shaft are divided into the bearing supporting motor drive end and the bearing supporting motor fan end. Cross-combination tests of different fault severity (7 mils, 14 mils, 21 mils, 28 mils, and 40 mils), different fault locations (inner-race, outer-race, roller), and different sensor locations (fan end and drive end) are carried out on test bearings.Take the data of bearing fault at drive end and acceleration sensor position at drive end, load 0 hp, and rotating speed 1797 rpm as an example, the slightest bearing fault (7 mils) is selected for comparative analysis. The results of the difference of acceleration signals from different kinds of fault bearings in time domain and frequency domain are shown in Table1.Table 1
Comparison of time domain and frequency domain results of bearings in different conditions.
Bearing conditionTime domain diagramFrequency domain diagramNormalInner-race faultRoller faultOuter-race faultThe time-frequency diagrams of acceleration signals of fault bearings under different types are obtained by CT on the above data, as shown in Figure3. It can be found that the time domain energy of the normal bearing is mainly concentrated below 200 Hz, while the fault bearing is mainly concentrated between 400 Hz and 800 Hz. There is a difficulty to observe clearly the bearing fault characteristic frequency and its multiple frequency (theoretical value is 138.8 Hz for inner-race, 112.8 Hz for roller, and 86.4 Hz for outer-race) under the condition only from the time-frequency diagram. It is very hard to obtain the specific evaluation criteria of the state classification model directly based on the time-frequency analysis method and then determine the fault type and severity of the rolling bearing according to the characteristic frequency. It provides a new approach to solve this problem by inputting time-frequency coefficients into machine learning model (MLM) for classification after dimension reduction.Figure 3
Chirplet time-frequency diagram of bearing in different conditions. (a) Normal bearing. (b) Inner-race fault. (c) Roller fault. (d) Outer-race fault.
(a)(b)(c)(d)


## 3.2. Acoustic-Vibration Comprehensive Bearing Fault Diagnosis Experiment Platform

The experiment environment includes generator noise, air conditioning noise, wind noise, and vehicle driving noise in addition to the test equipment to simulate the realistic noise environment around the vehicle. Figure4 is the physical picture of the experiment platform, which is composed of variable-frequency motor (left) and test bearing (right), two acceleration sensors (brand: CHENG TEC; model: CT1050L; sensitivity: 500 mV/g; range: ≤10 g) are installed on the lateral and vertical direction surfaces of the test bearing, respectively, and four acoustic sensors (brand: CRY Sound; model: CRY331; frequency range: 3.15 Hz∼16 kHz; sensitivity: 40 mV/Pa; linear range: 16∼140 dB) which are placed towards the bearing are arranged at a certain distance from the bearing. The motor shaft and the test bearing main shaft are connected by a coupling, and the motor speed is adjusted by parameters of the variable-frequency controller, and the bottom of the bearing is pressurized by a jack to simulate the load of the bearing.Figure 4
Physical picture of bearing experiment platform.The single row cylindrical rolling bearing NJ(P)3226X1 equipped for Chinese freight trains is used as the test bearing. The specific size and fault frequency of the bearing are shown in Tables2 and 3. In order to simulate the mixed fault of outer-race and roller, WEDM (wire cut electrical discharge machining) is utilized to cause the crack fault with a width of 0.18 mm and a depth of 0.5 mm into the outer-race and roller of the test bearing.Table 2
Bearing size table (unit: mm).
Inner-race diameter (mm)Outer-race diameter (mm)Number of rollersRoller diameter (mm)Pitch diameter (mm)1302501432190Table 3
Characteristic parameters of bearing fault.
Inner-raceOuter-raceCageRoller8.1795.8200.4162.885Note: the fault frequency unit is Hz, which needs to be multiplied by the bearing speed, and the bearing speed unit is r/s.The 8-channel data recorder is utilized to collect vibration signals and acoustic signals under different load and speed conditions which are described in Table4. The acquisition time is more than 20 s under each condition.Table 4
Description of load and speed conditions.
Condition numberLoad (kg)Speed (rpm)Sampling rate (kHz)Condition numberLoad (kg)Speed (rpm)Sampling rate (kHz)2_05500148304_051000148302_10500296304_101000296302_15500444304_151000444302_20500592304_201000592302_25500741304_251000741302_30500888304_301000888302_355001036304_351000103630


## 3.3. Experiment Data Analysis

### 3.3.1. Time Domain Analysis

Tables5 and 6 are time domain signal comparison diagrams of the normal bearing and the fault bearing. At low speed (148 rpm∼592 rpm), there are obvious periodic pulse signals which correspond to the bearing fault in the lateral acceleration and vertical acceleration signals. Under the high speed (592 rpm∼ 1036 rpm) condition, the severe vibration signals of the experiment platform cover the periodic pulse signals, which cause pulse signals to not be seen clearly in time domain. The normal signal is very stable in time domain, while the fault bearing signal is fluctuating.Table 5
Time domain diagram of vertical acceleration signal.
Speed (rpm)Normal bearingFault bearing4441036Table 6
Time domain diagram of acoustic signal.
Speed (rpm)Normal bearingFault bearing4441036It can be seen from Table6, different from acceleration signals, that there are no obvious periodic pulse signals in high or low speed condition. The acoustic signals of the normal bearing are very stable, while the acoustic signals of the fault bearing fluctuate and often have sharp peaks.


### 3.3.2. Frequency Domain Analysis

Frequency domain analysis is to get the amplitude of the signal in frequency by Fourier transform, which is the most basic means to understand the signal. When the fault occurs in different positions of the bearing, it will cause different fault characteristic frequencies which is generally below 1000 Hz. The peak signal in the middle and high frequency bands is usually formed by bearing natural frequency modulation. In order to analyze the bearing fault characteristic frequency, the frequency domain diagram of 0∼1000 Hz is selected for preliminary analysis.Tables7 and 8 are frequency domain comparison diagrams of acceleration signal and acoustic signal of normal bearing and fault bearing.Table 7
Frequency domain diagram of vertical acceleration signal.
Speed (rpm)Normal bearingFault bearing4441036Table 8
Frequency domain diagram of acoustic signal.
Speed (rpm)Normal bearingFault bearing4441036It can be seen from the frequency domain diagram of vertical acceleration that the frequency domain energy of the fault bearing is concentrated below 100 Hz, and the larger amplitude (0.05∼0.1) is obtained near 0 Hz, while the energy distribution of the normal bearing is at 1∼100 Hz and 700∼1000 Hz.It is worth noting that, under low-speed operating conditions (444 rpm), there is a phenomenon of fault characteristic frequency and shaft rotation frequency modulation that clearly points to the bearing fault. The fundamental frequency of the modulation is 110 Hz, which corresponds to the fault characteristic frequency of the bearing inner race. In the spectrum, the amplitude decreases at the fault characteristic frequency and each frequency doubling, and modulation lines appear on both sides of each frequency doubling. But at high speed (1036 rpm), the severe vibration of the bearing experiment platform covers the original pulse characteristic frequency signal, and the bearing fault characteristics cannot be well seen in the frequency domain.According to the comparison of the frequency domain diagrams of the acoustic signal in Table8, the characteristic of the acoustic signal is that there is a very large amplitude near 0 Hz, and the energy distribution is relatively uniform in other frequency regions. The energy of fault signal is more concentrated in 0∼100 Hz region than other regions, while the energy of normal signal is more uniform in the whole frequency band. Low frequency vibration is usually caused by local fault of bearing, of which it can be clearly seen that some frequencies are concentrated in the band in the frequency spectrum analysis.


### 3.3.3. Time-Frequency Analysis

Tables9 and 10 show the time-frequency signal comparison diagrams of the normal bearing and the fault bearing after CT.Table 9
Time-frequency diagram of vertical acceleration signal.
Speed (rpm)Normal bearingFault bearing4441036Table 10
Time-frequency diagram of acoustic signal.
Speed (rpm)Normal bearingFault bearing4441036There is no obvious characteristic spectral line within 0∼1000 Hz in the time domain diagram of the normal bearing and the scattered point distribution is more uniform. However, the signal of the fault bearing is unstable at low frequency (0∼50 Hz), and some energy pulses appear.For the acoustic signal, the normal bearing energy distributes in the range of 0∼1000 Hz, while the time-frequency energy of the fault bearing is mainly concentrated in the low frequency. Because the local fault of the bearing is mainly caused by the low frequency vibration, the frequency spectrum line in the time-frequency diagram is mainly concentrated below 100 Hz. By comparing Tables9 and 10, it can be found that the unstable pulse displaying in the wavelet time-frequency diagram of the acceleration signal of the fault bearing in Table 9 is not reflected in the wavelet time-frequency diagram of the acoustic signal of the fault bearing in Table 10, which indicates that compared with the acceleration signal the ability of describing the local characteristics of the non-stationary signal of the acoustic signal is not strong.


## 3.3.1. Time Domain Analysis

Tables5 and 6 are time domain signal comparison diagrams of the normal bearing and the fault bearing. At low speed (148 rpm∼592 rpm), there are obvious periodic pulse signals which correspond to the bearing fault in the lateral acceleration and vertical acceleration signals. Under the high speed (592 rpm∼ 1036 rpm) condition, the severe vibration signals of the experiment platform cover the periodic pulse signals, which cause pulse signals to not be seen clearly in time domain. The normal signal is very stable in time domain, while the fault bearing signal is fluctuating.Table 5
Time domain diagram of vertical acceleration signal.
Speed (rpm)Normal bearingFault bearing4441036Table 6
Time domain diagram of acoustic signal.
Speed (rpm)Normal bearingFault bearing4441036It can be seen from Table6, different from acceleration signals, that there are no obvious periodic pulse signals in high or low speed condition. The acoustic signals of the normal bearing are very stable, while the acoustic signals of the fault bearing fluctuate and often have sharp peaks.


## 3.3.2. Frequency Domain Analysis

Frequency domain analysis is to get the amplitude of the signal in frequency by Fourier transform, which is the most basic means to understand the signal. When the fault occurs in different positions of the bearing, it will cause different fault characteristic frequencies which is generally below 1000 Hz. The peak signal in the middle and high frequency bands is usually formed by bearing natural frequency modulation. In order to analyze the bearing fault characteristic frequency, the frequency domain diagram of 0∼1000 Hz is selected for preliminary analysis.Tables7 and 8 are frequency domain comparison diagrams of acceleration signal and acoustic signal of normal bearing and fault bearing.Table 7
Frequency domain diagram of vertical acceleration signal.
Speed (rpm)Normal bearingFault bearing4441036Table 8
Frequency domain diagram of acoustic signal.
Speed (rpm)Normal bearingFault bearing4441036It can be seen from the frequency domain diagram of vertical acceleration that the frequency domain energy of the fault bearing is concentrated below 100 Hz, and the larger amplitude (0.05∼0.1) is obtained near 0 Hz, while the energy distribution of the normal bearing is at 1∼100 Hz and 700∼1000 Hz.It is worth noting that, under low-speed operating conditions (444 rpm), there is a phenomenon of fault characteristic frequency and shaft rotation frequency modulation that clearly points to the bearing fault. The fundamental frequency of the modulation is 110 Hz, which corresponds to the fault characteristic frequency of the bearing inner race. In the spectrum, the amplitude decreases at the fault characteristic frequency and each frequency doubling, and modulation lines appear on both sides of each frequency doubling. But at high speed (1036 rpm), the severe vibration of the bearing experiment platform covers the original pulse characteristic frequency signal, and the bearing fault characteristics cannot be well seen in the frequency domain.According to the comparison of the frequency domain diagrams of the acoustic signal in Table8, the characteristic of the acoustic signal is that there is a very large amplitude near 0 Hz, and the energy distribution is relatively uniform in other frequency regions. The energy of fault signal is more concentrated in 0∼100 Hz region than other regions, while the energy of normal signal is more uniform in the whole frequency band. Low frequency vibration is usually caused by local fault of bearing, of which it can be clearly seen that some frequencies are concentrated in the band in the frequency spectrum analysis.


## 3.3.3. Time-Frequency Analysis

Tables9 and 10 show the time-frequency signal comparison diagrams of the normal bearing and the fault bearing after CT.Table 9
Time-frequency diagram of vertical acceleration signal.
Speed (rpm)Normal bearingFault bearing4441036Table 10
Time-frequency diagram of acoustic signal.
Speed (rpm)Normal bearingFault bearing4441036There is no obvious characteristic spectral line within 0∼1000 Hz in the time domain diagram of the normal bearing and the scattered point distribution is more uniform. However, the signal of the fault bearing is unstable at low frequency (0∼50 Hz), and some energy pulses appear.For the acoustic signal, the normal bearing energy distributes in the range of 0∼1000 Hz, while the time-frequency energy of the fault bearing is mainly concentrated in the low frequency. Because the local fault of the bearing is mainly caused by the low frequency vibration, the frequency spectrum line in the time-frequency diagram is mainly concentrated below 100 Hz. By comparing Tables9 and 10, it can be found that the unstable pulse displaying in the wavelet time-frequency diagram of the acceleration signal of the fault bearing in Table 9 is not reflected in the wavelet time-frequency diagram of the acoustic signal of the fault bearing in Table 10, which indicates that compared with the acceleration signal the ability of describing the local characteristics of the non-stationary signal of the acoustic signal is not strong.


## 4. Results and Discussion

### 4.1. Western Reserve University Public Data Set Results

There are 12 working conditions in CRWU bearing data set, corresponding to different sensor positions, loads, and speeds. For each working condition, 10 different bearings labeled as shown in Table11 are for test.Table 11
Fault classification label table.
Fault type and degreeLabelNormal0Inner-race fault, depth of 7 mils1Inner-race fault, depth of 14 mils2Inner-race fault, depth of 20 mils3Roller fault, depth of 7 mils4Roller fault, depth of 14 mils5Roller fault, depth of 20 mils6Outer-race fault, depth of 7 mils7Outer-race fault, depth of 14 mils8Outer-race fault, depth of 20 mils9The data collected from each bearing of each working condition corresponds to a CSV file, and the acquisition length is more than 20 s. The signal in the CSV file is divided into a fragment with 2000 sample points when the sampling frequency equals 12 kHz (i.e., the first eight working conditions), and the signal in the CSV file is divided into a fragment with 4000 sample points when the sampling frequency equals 48 kHz (i.e., the last four working conditions). Each CSV file gets 50 fragments, and a total of 500 fragments can be obtained from 10 kinds of bearings.Table12 shows the classification results of the database of Western Reserve University under each working condition. It can be seen from the results that the method of variable time-frequency wavelet transform combined with SVM has a good classification effect for fault bearings with different types and degrees, which proves the correctness of this method.Table 12
Accuracy results of bearing database of western reserve university under different working conditions.
Fault locationLoad (W)Speed (rpm)Sampling rate (kHz)Acceleration sensor at drive end (%)Acceleration sensor at fan end (%)Drive end0179712100.00100.00Drive end735177212100.00100.00Drive end1470175012100.00100.00Drive end2205173012100.00100.00Fan end0179712100.0099.00Fan end735177212100.00100.00Fan end1470175012100.00100.00Fan end2205173012100.00100.00Drive end0179748100.00100.00Drive end735177248100.00100.00Drive end147017504899.00100.00Drive end2205173048100.00100.00


### 4.2. Database Results of Acoustic-Vibration Comprehensive Bearing Fault Diagnosis

There are 14 kinds of working conditions in the data set of AVEP, corresponding to different loads and speeds (see Table4). For each working condition, two kinds of different bearings are for test, which are normal bearing and roller and outer-race integrated fault bearing, respectively. Label each kind of bearing, as shown in Table 13.Table 13
Fault classification label table.
Fault type and degreeLabelNormal0Roller and outer-race integrated fault1The sampling frequency was 12 kHz. For the single working condition, the number of samples is 160, and the number of samples of each fault type is 80, and each sample contains 15000 sample points. The training set and test set are divided by the ratio of 0.8 : 0.2. For the mixed condition (all single condition samples are mixed together for classification), the number of samples is 2240, and the training set and test set are divided in the same way.Tables14 and 15 are the classification results of the data of the AVEP and the classification accuracy of the lateral acceleration, the vertical acceleration, the four acoustic signals, and the average of the four acoustic signals are studied, respectively. Under the single working condition, the acceleration signal has better classification effect than that of the acoustic, which is reflected in its stronger stability. Because the number of samples under the single working condition is too small to adjust parameters well, some acoustic signal classification effect is not ideal, but the acceleration signal still has good classification accuracy in the case of few samples. But in the mixed condition, the acoustic signal can also achieve good accuracy compared with the acceleration signal. The average accuracy of the four acoustic signals is 99.55%, while the lateral and vertical acceleration sensor signals are 99.78% and 100.00%, respectively. It shows that when the signals of different working conditions are mixed, the acoustic signal also has excellent fault identification ability under multiple working conditions based on the model. In addition, it is found that the classification accuracy of the four acoustic signals after averaging is not significantly improved compared with that of the single sensor.Table 14
Classification accuracy of AVEP data under single working condition.
Working conditionLateral acceleration (%)Vertical acceleration (%)Acoustic sensor mean (%)Acoustic sensor 1 (%)Acoustic sensor 2 (%)Acoustic sensor 3 (%)Acoustic sensor 4 (%)2_05100.00100.0093.7590.62100.0084.3896.882_10100.00100.0096.88100.00100.0084.3896.882_15100.00100.0090.6293.75100.0068.7584.382_20100.00100.0096.8896.88100.00100.0096.882_25100.00100.00100.0090.62100.00100.0090.622_30100.00100.0096.88100.00100.00100.00100.002_35100.00100.00100.00100.00100.00100.00100.004_05100.00100.0096.8887.50100.0093.7578.124_10100.00100.0096.88100.0099.2295.3192.974_15100.00100.00100.00100.00100.0078.1290.624_20100.00100.0093.75100.00100.00100.0096.884_25100.00100.00100.0096.8896.88100.00100.004_30100.00100.0078.12100.00100.00100.00100.004_35100.0096.88100.00100.00100.00100.00100.00Table 15
Classification accuracy of AVEP data under mixed conditions.
Working conditionLateral accelerationVertical accelerationAcoustic sensor meanAcoustic sensor 1Acoustic sensor 2Acoustic sensor 3Acoustic sensor 4Mixed99.78%100.00%99.55%99.78%99.55%98.21%99.33%


## 4.1. Western Reserve University Public Data Set Results

There are 12 working conditions in CRWU bearing data set, corresponding to different sensor positions, loads, and speeds. For each working condition, 10 different bearings labeled as shown in Table11 are for test.Table 11
Fault classification label table.
Fault type and degreeLabelNormal0Inner-race fault, depth of 7 mils1Inner-race fault, depth of 14 mils2Inner-race fault, depth of 20 mils3Roller fault, depth of 7 mils4Roller fault, depth of 14 mils5Roller fault, depth of 20 mils6Outer-race fault, depth of 7 mils7Outer-race fault, depth of 14 mils8Outer-race fault, depth of 20 mils9The data collected from each bearing of each working condition corresponds to a CSV file, and the acquisition length is more than 20 s. The signal in the CSV file is divided into a fragment with 2000 sample points when the sampling frequency equals 12 kHz (i.e., the first eight working conditions), and the signal in the CSV file is divided into a fragment with 4000 sample points when the sampling frequency equals 48 kHz (i.e., the last four working conditions). Each CSV file gets 50 fragments, and a total of 500 fragments can be obtained from 10 kinds of bearings.Table12 shows the classification results of the database of Western Reserve University under each working condition. It can be seen from the results that the method of variable time-frequency wavelet transform combined with SVM has a good classification effect for fault bearings with different types and degrees, which proves the correctness of this method.Table 12
Accuracy results of bearing database of western reserve university under different working conditions.
Fault locationLoad (W)Speed (rpm)Sampling rate (kHz)Acceleration sensor at drive end (%)Acceleration sensor at fan end (%)Drive end0179712100.00100.00Drive end735177212100.00100.00Drive end1470175012100.00100.00Drive end2205173012100.00100.00Fan end0179712100.0099.00Fan end735177212100.00100.00Fan end1470175012100.00100.00Fan end2205173012100.00100.00Drive end0179748100.00100.00Drive end735177248100.00100.00Drive end147017504899.00100.00Drive end2205173048100.00100.00


## 4.2. Database Results of Acoustic-Vibration Comprehensive Bearing Fault Diagnosis

There are 14 kinds of working conditions in the data set of AVEP, corresponding to different loads and speeds (see Table4). For each working condition, two kinds of different bearings are for test, which are normal bearing and roller and outer-race integrated fault bearing, respectively. Label each kind of bearing, as shown in Table 13.Table 13
Fault classification label table.
Fault type and degreeLabelNormal0Roller and outer-race integrated fault1The sampling frequency was 12 kHz. For the single working condition, the number of samples is 160, and the number of samples of each fault type is 80, and each sample contains 15000 sample points. The training set and test set are divided by the ratio of 0.8 : 0.2. For the mixed condition (all single condition samples are mixed together for classification), the number of samples is 2240, and the training set and test set are divided in the same way.Tables14 and 15 are the classification results of the data of the AVEP and the classification accuracy of the lateral acceleration, the vertical acceleration, the four acoustic signals, and the average of the four acoustic signals are studied, respectively. Under the single working condition, the acceleration signal has better classification effect than that of the acoustic, which is reflected in its stronger stability. Because the number of samples under the single working condition is too small to adjust parameters well, some acoustic signal classification effect is not ideal, but the acceleration signal still has good classification accuracy in the case of few samples. But in the mixed condition, the acoustic signal can also achieve good accuracy compared with the acceleration signal. The average accuracy of the four acoustic signals is 99.55%, while the lateral and vertical acceleration sensor signals are 99.78% and 100.00%, respectively. It shows that when the signals of different working conditions are mixed, the acoustic signal also has excellent fault identification ability under multiple working conditions based on the model. In addition, it is found that the classification accuracy of the four acoustic signals after averaging is not significantly improved compared with that of the single sensor.Table 14
Classification accuracy of AVEP data under single working condition.
Working conditionLateral acceleration (%)Vertical acceleration (%)Acoustic sensor mean (%)Acoustic sensor 1 (%)Acoustic sensor 2 (%)Acoustic sensor 3 (%)Acoustic sensor 4 (%)2_05100.00100.0093.7590.62100.0084.3896.882_10100.00100.0096.88100.00100.0084.3896.882_15100.00100.0090.6293.75100.0068.7584.382_20100.00100.0096.8896.88100.00100.0096.882_25100.00100.00100.0090.62100.00100.0090.622_30100.00100.0096.88100.00100.00100.00100.002_35100.00100.00100.00100.00100.00100.00100.004_05100.00100.0096.8887.50100.0093.7578.124_10100.00100.0096.88100.0099.2295.3192.974_15100.00100.00100.00100.00100.0078.1290.624_20100.00100.0093.75100.00100.00100.0096.884_25100.00100.00100.0096.8896.88100.00100.004_30100.00100.0078.12100.00100.00100.00100.004_35100.0096.88100.00100.00100.00100.00100.00Table 15
Classification accuracy of AVEP data under mixed conditions.
Working conditionLateral accelerationVertical accelerationAcoustic sensor meanAcoustic sensor 1Acoustic sensor 2Acoustic sensor 3Acoustic sensor 4Mixed99.78%100.00%99.55%99.78%99.55%98.21%99.33%


## 5. Conclusions

In order to study the feasibility of acoustic signal in bearing fault diagnosis, an acoustic-vibration comprehensive experiment platform was established. The acceleration signal and the acoustic signal were collected simultaneously in the complex background noise environment and were input into the variable time-frequency wavelet transform combined with support vector machine model as the source data. The specific conclusions are as follows:(1)
Compared with continuous wavelet transform, the FDM has better time-frequency resolution in feature extraction step and is more suitable for non-stationary time-varying signals. It has been applied to the open bearing database of Western Reserve University of the United States to complete the experiment verification and has achieved higher diagnosis accuracy.(2)
In the experiment of acoustic-vibration comprehensive experiment platform, comparing the diagnosis results of four acoustic sensors, it is found that the effect of the acoustic sensors 1 and 2 is better than that of the acoustic sensors 3 and 4. It may be because acoustic sensors 3 and 4 are closer to the motor end and are more affected by the motor noise. In the practical application environment, acoustic sensors should be far away from other acoustic components.(3)
In the experiment of acoustic-vibration comprehensive experiment platform, the diagnosis results of the acoustic signal and the acceleration signal at different speeds are compared. The results show that the acceleration signal has good diagnosis results at different speeds, but the diagnosis results of the acoustic signal are better at some speeds and are not good at some speeds. The overall stability of acoustic signal diagnosis results is not as good as acceleration signal. The reason may be that the number of samples in the single working condition is small, which leads to the poor results of the acoustic signal.(4)
In the experiment of acoustic-vibration comprehensive experiment platform, under the working condition mixed multi-speeds, the acoustic signal can obtain the diagnosis accuracy similar to the acceleration signal, which indicates that the acoustic signal can also be used as the approach of bearing fault diagnosis to apply in the scene of non-contact diagnosis when the amount of data is sufficient.



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*Source: 9868999-2022-05-16.xml*