Fault Diagnosis of Wheelset Bearings in High-Speed Trains Using Logarithmic Short-Time Fourier Transform and Modified Self-Calibrated Residual Network

Abstract

Fault diagnosis of wheelset bearings in high-speed trains has attracted constant interest in the scientific community and industrial field. Under the harsh working condition, e.g., time-varying speed and load, most existing methods are hindered by the limited and unknown situations of wheelset bearings. Although the self-calibrated convolution is proven to effectively expand the receptive field with more accurate discriminative regions, its use in fault diagnosis still lacks needed physical interpretation as well as computational efficiency. To this end, this paper presents a novel framework by using the logarithmic short-time Fourier transform and the modified self-calibrated convolution. It first manifests a time-frequency map that has explicit physics meaning while reducing the gap between high energy and detailed characteristics in the masking of interfering signals. To simplify redundant kernels, a Modified Self-calibrated Residual Block is proposed without introducing any more parameters, while preserving an interpretable and simple structure. The effectiveness and robustness of the proposed method are verified by the experimental data collected from an industrial railway axle bearing test rig. Results are found superior to those of five state-of-art methods, which is more practical in terms of accuracy, cost time and model size.

Full text

IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 18, NO. 10, OCTOBER 2022 7285
Fault Diagnosis of Wheelset Bearings in
High-Speed Trains Using Logarithmic
Short-Time Fourier Transform and Modified
Self-Calibrated Residual Network
Ge Xin , Zhe Li , Limin Jia , Qitian Zhong, Honghui Dong , Member, IEEE, Nacer Hamzaoui,
and Jerome Antoni
Abstract—Fault diagnosis of wheelset bearings in high-
speed trains has attracted constant interest in the scientific
community and industrial field. Under the harsh working
condition, e.g., time-varying speed and load, most existing
methods are hindered by the limited and unknown situ-
ations of wheelset bearings. Although the self-calibrated
convolution is proven to effectively expand the receptive
field with more accurate discriminative regions, its use in
fault diagnosis still lacks needed physical interpretation as
well as computational efficiency. To this end, this article
presents a novel framework by using the logarithmic short-
time Fourier transform and the modified self-calibrated con-
volution. It first manifests a time-frequency map that has ex-
plicit physics meaning while reducing the gap between high
energy and detailed characteristics in the masking of in-
terfering signals. To simplify redundant kernels, a modified
self-calibrated residual block is proposed without introduc-
ing any more parameters, while preserving an interpretable
and simple structure. The effectiveness and robustness
of the proposed method are verified by the experimental
data collected from an industrial railway axle bearing test
rig. Results are found superior to those of five state-of-art
methods, which are more practical in terms of accuracy,
cost time, and model size.
Manuscript received October 27, 2021; accepted December 11, 2021.
Date of publication December 17, 2021; date of current version July
11, 2022. This work was supported in part by the National Natural
Science Foundation of China under Grant 51905029 and in part by
the Fundamental Research Funds for the Central Universities under
Grant 2020JBM032 and Grant 2020JBZD011. Paper no. TII-21-4716.
(Corresponding author: Limin Jia.)
Ge Xin is with the School of Traffic and Transportation, Beijing Jiao-
tong University, Beijing 100044, China, and also with the Key Laboratory
of Transport Industry of Big Data Application Technologies for Compre-
hensive Transport, Beijing Jiaotong University, Beijing 100044, China
(e-mail: ge.xin@bjtu.edu.cn).
Zhe Li and Qitian Zhong are with the School of Traffic and Trans-
portation, Beijing Jiaotong University, Beijing 100044, China (e-mail:
20120759@bjtu.edu.cn; 20120968@bjtu.edu.cn).
Limin Jia and Honghui Dong are with the Key Laboratory of Rail Traffic
Control and Safety, Beijing Jiaotong University, Beijing 100044, China
(e-mail: jialm@vip.sina.com; hhdong@bjtu.edu.cn).
Nacer Hamzaoui and Jerome Antoni are with the Labora-
tory of Vibration and Acoustics, University of Lyon, INSA Lyon,
69621 Villeurbanne, France (e-mail: nacer.hamzaoui@insa-lyon.fr;
jerome.antoni@insa-lyon.fr).
Color versions of one or more figures in this article are available at
https://doi.org/10.1109/TII.2021.3136144.
Digital Object Identifier 10.1109/TII.2021.3136144
Index Terms—Logarithmic short-time Fourier trans-
form, modified self-calibrated residual network (MSCRes-
Net), unknown working conditions, wheelset bearing fault
diagnosis.
I. INTRODUCTION
THANKS to the advantage in rapidity, punctuality, comfort,
and convenience, high-speed train (HST) has been tremen-
dously developed in recent decades. With the rapid growth of
HST, condition monitoring technology is of utmost significant
to the safety of railway vehicle operation, which has attracted a
growing interest in the scientific community [1]. The wheelset
bearings play a vital role in running gears of HST and are of great
fragility and vulnerability. Once bearings fail, due to the high
running speed and the crowdedness of passengers, it accelerates
the degradation of running gears while threatening the operation
safety, and even results in the casualty and property loss [2]. It
is, therefore, of great theoretical and engineering demand to
recognize the health state of bearings and further formulate
corresponding maintenance strategies according to the exact
location of bearing damage, i.e., the condition-based predictive
maintenance. The fault diagnosis methods are mainly catego-
rized as follows [3]: physics-based vibration signal processing
method, machine learning (ML) based black box method as well
as a proper combination of them.
The physics-based vibration signal processing method aims to
construct a physical model that reveals the structure and charac-
teristics of the mechanical system. Typical tools include spectral
analysis (time-frequency domain [4], frequency-frequency rep-
resentation [5], etc.), statistics and probability analysis (spec-
tral kurtosis [6], hidden Markov [7], Bayesian estimation [8],
stochastic model [9], etc.), matrix analysis (symplectic geometry
analysis [10], [11], low-rank and sparsity [12], [13], etc.). With
regard to specified problems in practice, most of them match
the fault signature of vibration signal and achieve success to
some degree, yet it also appears challenging to the modeling of
the complex structure. Since the solidification of this modeling
is an indispensable prerequisite, once the application scenario
does not fit the original physical assumptions, parameters of the
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7286 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 18, NO. 10, OCTOBER 2022
model have to be reset, which is not practically applicable to
fault diagnosis under complex variable conditions.
ML has strong adaptability by abstracting different scenarios
into the same problem, and has been widely used in many
classification problems, such as image, semantic and vibration
signal, etc. Based on this, a wide range of intelligent fault diag-
nosis techniques has been published in recent years. Although
various classifiers, such as random forest [14], support vector
machine [15], k-nearest neighbor [16], and extreme learning
machines [17], have been developed for fault detection, their
use asks for features meticulously extracted by expertise of the
researchers. In contrast, Deep-learning based methods directly
use the original signal to achieve the goal, which greatly reduces
the cost in applying manual feature selection and improves
the usability [18]. For example, Lei et al. [18] proposed an
end-to-end long short-term memory (LSTM) network to detect
the fault type from the wind turbine. Zheng et al. [19] combined
a convolutional neural network (CNN) withbidirectional LSTM
to extract local feature and reduce dimension. Li et al. [20] use
LSTM, gate recurrent unit, and one-dimensional CNN to build
an end-to-end diagnosis model. Unfortunately, the end-to-end
models can hardly extrapolate outside the database which has
been used for training, thus their use may be hindered in prac-
tice by the efficiency and robustness under unknown working
conditions.
In short, the physics-based methods are more efficient with
explicit physical meaning but more constrained by physical
assumptions, whereas the ML-based methods enable stronger
adaptability with artificial intelligence but lack interpretabil-
ity and extrapolability. Recently, more and more researchers
attempt to extract interpretable information by utilizing the
physics-based technology as the input of deep learning. As a
result, it not only achieves a clear physical meaning, but also
a better classification performance. Zhang et al. [21] utilize
short-time Fourier transform (STFT) to obtain an input image,
and an improved LeNet5 is used to detect the bearing fault.
According to the second-order cyclostationary characteristics
of the bearing vibration signal, Chen et al. [22] convert the
data into the frequency-frequency representation as feature map
by applying fast spectral correlation. Li et al. [23] extract the
feature from both time domain and frequency domain, and then
a back-propagation neural network is introduced to learn the
multiscale local feature. Li et al. [24] designed a continuous
wavelet convolutional layer so that the model obtains an ex-
planation on physical meaning of the architecture. Other deep
learning methods, such as auto-encoder [25], and deep belief
network [26] are also widely used in bearing fault diagnosis.
As a particular case of complex systems, wheelset bearings
in HST undergo the influence of unknown working conditions.
Since the general methods earlier may not be suitable to deal
with complex fault mechanisms, more effective fault diagnosis
methods are needed [27]. Peng et al. [28] propose multibranch
and multiscale CNN to handle the problems of low signal-to-
noise ratio of the vibration signals and variable load conditions.
Su et al. [1] propose an end-to-end method named residual-
squeeze net which directly utilizes raw data to detect fault. Wang
et al. [29] explore the use of the attention mechanism in deep
Fig. 1. Structure of train running gear.
learning methods to recalibrate features of each layer, which
achieves great diagnosis performance.
Although the prementioned methods have successfully ad-
dressed the issue of bearing fault diagnosis in HST under specific
working condition, it still has two challenges for its engineering
applications as follows:
1) The complex structure of running gear: As shown in
Fig. 1, due to the complex mechanical structure of running
gear, the fault signal is often immerged in high noises
coming from multiple sources, such as components (sus-
pension system, traction drive wheelset, etc.), machine
operation, metal impacts, motion friction, etc. [30], which
will increase the difficulty of bearing fault diagnosis.
2) The variable working conditions: The working environ-
ment of bearings in HST is changing with the time due
to reasons, such as passenger flow, passenger capacity in
different time periods, and stopover stations, which may
cause the fault characteristics to change from time to time.
In consideration of the challenges earlier, the performance
of current methods for wheelset bearing fault diagnosis in
HST is barely satisfactory. There is an urgent demand to pro-
pose a diagnosis method that suppresses noisy signal with
well-generalization ability against variable working conditions.
In this article, a novel model integrated with logarithmic
STFT (log-STFT) and modified self-calibrated residual network
(MSCResNet) is proposed. The main contributions of this article
lie in the following aspects:
1) The STFT is utilized to extract features from raw signal in
order to retain explicit physical meaning of fault signature
as well as the fruitful individual information. In addition,
the logarithmic function enlarges the details of the char-
acteristics among each fault type, whereas reducing the
difficulty of the classification for the network at the same
time.
2) A CNN with modified self-calibrated residual block
(MSCResB) is used to enlarge the receptive field with-
out introducing any more parameters, which enables
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XIN et al.: FAULT DIAGNOSIS OF WHEELSET BEARINGS IN HSTS USING LOGARITHMIC STFT AND MSCRESNET 7287
the model to obtain powerful generalization ability and
diagnose the fault under unknown working conditions
while simultaneously preserving a more interpretable and
simpler structure.
3) A novel framework by using logarithmic STFT and
MSCResNet is proposed to solve the engineering problem
for wheelset bearing fault diagnosis, which is proved to
have strong robustness as well as high accuracy under
unknown working conditions.
The rest of this article is organized as follows. In Section II,
the theoretical basis of logarithmic STFT is provided. The
structure of MSCResB is carried out and the proposed model
is demonstrated in detail in Section III. Section IV gives the
experiment to illustrate the effectiveness and robustness of the
proposed method. Finally, Section V concludes this article.
II. LOGARITHMIC STFT
The measured vibration signal y(t)could be regarded as the
sum of two assumed mutually independent signal components,
namely the “background noise” n(t)and the “informative sig-
nal” x(t)which contains the diagnostic information. The model
can be written as follows:
y(t)=x(t)+n(t).(1)
The background noise intervenes in (1) is fair and widely
accepted to be modeled as stationary. In contrast, x(t)is well-
modeled by a series of damped impulse responses [7]. Such
transients, which have a localized signature both in time and in
frequency, are well-captured in a time-frequency decomposition,
whereas the stationary background noise n(t)is spread all over
the time-frequency plane.
Although several time-frequency decompositions are pos-
sible, the proposed approach only requires one with explicit
physics meaning and rich individual information. The STFT
meets these properties while being associated with efficient al-
gorithmic implementations. It truncates a segment of the Llong
signal y(t)with a positive and smooth Nw-long data-window
w[m], described as follows:
Y(i, fb)=Nw−1
m=0w[m]·y[iR +m]·e−j2πfb
iR+m
Fs(2)
where i(i=1,...,N, N =f loor[(L−Nw)/R +1]) de-
notes the time datum with window shift R(1<R<N
w)and
fb=b·Δfdenotes the frequency with frequency resolution
Δf=Fs/Nwand bin index b=1,...,N
w/2+1.
As shown in Fig. 2(a), STFT is regarded as the time-frequency
map of signal y(t). Although each transient resembles a damped
impulse response with specific frequency content, other details
of the STFT will make the deep learning more robust in the
masking of interfering signals. The logarithmic function is
proven to simply reduce relative amplitude of the impulse versus
other signal components, which has been successfully used in
envelope spectrum [31]. Inspired by such properties, this article
proposes a novel feature map by taking logarithmic of the STFT
as follows:
Ylog (i, fb)= log(Y(i, fb)) .(3)
Fig. 2. STFT (a) without and (b) with logarithmic function.
From inspection of Fig. 2(b), (3) is proven to magnify nu-
merous details of the STFT. As such, it significantly reduces the
gap between high energy and other details while retaining the
monotonicity of Y(i, fb).
III. LOG-STFT MODIFIED SELF-CALIBRATED RESIDUAL
NETWORK
This section introduces the proposed model, including the
theoretical basis of MSCResB, the proposed framework of
MSCResNet, as well as the flowchart of wheelset bearing fault
diagnosis.
A. Modified Self-Calibrated Residual Block
The traditional convolution may lead to less discriminative
feature maps as it can only learn similar patterns and cannot
obtain a large receptive field, which are not fully applicable to
the fault diagnosis. To alleviate the deficiency, self-calibrated
convolution (SCconv) was first proposed by Liu et al. [32] in
2020. It independently generates a weighted average coeffi-
cient matrix through down sampling and residual operations,
while weighting the features extracted by traditional convolu-
tion, thereby achieving self-calibration of the feature map. The
SCconv enables convolution layers to adaptively capture more
representative contextual information without introducing any
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7288 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 18, NO. 10, OCTOBER 2022
Fig. 3. Modified Self-calibration convolution, where rdenotes the average pooling rate and denotes element-wise multiplication.
additional parameter or adding to its complexity, or changing
the hyper-parameters.
However, its use in bearing fault classification is hindered by
the lack of interpretability as well as the high complexity with
redundant kernels. To overcome the shortcomings, the original
SCconv has been improved and a novel convolution option, i.e.,
modified SCconv (MSCconv) is proposed in Fig. 3. In particular,
the size of convolution kernel Kis [C, C, kh,k
w], where kh
and kware kernel size. The input Xis equally divided into
two portions {X1,X
2}, and different convolution operations are
performed, respectively. MSCconv has three convolution parts,
i.e., {K1,K
2,K
3}, where {K2,K
3}are utilized to calculate one
of the input portions as modified self-calibration. First, the input
X1is down sampled by an average pooling layer
T1=AvgP oolr(X1).(4)
After that, T1is convolved with the convolution kernel K2,
then a bilinear interpolation operator Up(·)is used to get the
initial self-calibrated reference of input X1
X
1=Up(T1∗K2).(5)
Next, the initial self-calibrated reference is executed by a
residual operation. To further characterize the feature map, a
more general activate function Activate(·)is proposed instead
of sigmoid, so as to transform the whole self-calibrated reference
into a weighted average index matrix ISC
ISC =Activate X1+X
1.(6)
With the information of original input X1and the initial self-
calibrated reference X
1, it is finally multiplied with features
extracted by a traditional convolution filter
Y1=ISC ·(X1∗K3).(7)
Since the extracted fruitful features by log-STFT have sig-
nificantly reduced the difficulty of fault classification for the
network, which is proven in Table VII, the network should be
simplified to improve its efficiency. In this article, the fourth con-
volution kernel K4of the original SCconvis found redundant and
TABLE I
SELF-CALIBRATED RESIDUAL NETWORK ARCHITECTURE
TABLE II
BEARING INFORMATION AND CLASS LABEL
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XIN et al.: FAULT DIAGNOSIS OF WHEELSET BEARINGS IN HSTS USING LOGARITHMIC STFT AND MSCRESNET 7289
TABLE III
WORKING CONDITION INFORMATION
TABLE IV
WORKING CONDITION INFORMATION
TABLE V
CLASSIFICATION ACCURACY,RUNNING TIME,AND MODEL SIZE OF
COMPARISON
therefore removed for the proposed network, its improvement
can be seen in Table V.
The convolution option for X2is a traditional convolution
filter K1and the output is marked as Y2. Both the intermediate
output portions {Y1,Y
2}are then concatenated as the output Y,
which has the same size as input X.
The main structure of an MSCResB is displayed in Fig. 4,
which includes the following four parts:
1) MSCconv layer, which has introduced in Section III-A.
2) Activation function.
TABLE VI
AVERAGE ACCURACY AND COST TIME OF SMALL NUMBER DATA
EXPERIMENT
TABLE VII
ACCURACY OF USING DIFFERENT FEATURE EXTRACTION METHODS
Fig. 4. Residual block architecture, where the weight layer denotes the
convolution layer, normalizing layer, or activation layer.
The rectified linear unit (ReLU) is used as activation function
in this article, since its biological rationality of unilateral inhi-
bition and wide excitation boundary will alleviate the vanishing
gradient problem. It can be written as follows:
f(x)=
xx>0
0x≤0.(8)
3) Batch normalization layer.
The input data of each batch will be transformed to a normal
distribution with 0 mean and 1 variance, thus solving the problem
of internal covariate shift [33].
4) Identity mapping.
The input is directly added to the output of the residual block,
so that the identity mapping can solve the degradation problem
in the network cost-effectively.
Note that if the input channel is not equal to the output
channel, there will be a down sampling layer to make them
identical.
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7290 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 18, NO. 10, OCTOBER 2022
Fig. 5. Log-STFT MSCResNet model for wheelset bearing fault diagnosis.
B. Modified Self-Calibrated Residual Neural Network
In this section, a novel CNN named MSCResNet is con-
structed to learn more discriminative feature maps. The details
of MSCResNet are shown in Table I.
Inspired by ResNet18 and ResNet50 [34], the time-frequency
map is first input into a traditional convolution layer with a set
of 7 ×7 convolution kernels. Then two MSCResBs are applied
to further extract detail information from the obtained shallow
feature map. The first residual block, which has the same spatial
size as input, contains two MSCconv layers. As the network
goes deeper, it is necessary to enlarge the channel dimension
to add more detailed features. Therefore, the second block with
an MSCconv layer and two 1 ×1 convolution layers is applied.
The 1 ×1 convolution layer after the MSCconv layer aims to
increase the channel number while using fewer parameters.
C. Proposed Log-STFT-MSCResNet Model
The problem of fault diagnosis under unknown working con-
ditions is defined as follows: given a multivariate time-series
segment ycollected under a condition that the model has never
seen before (e.g., different speed, vertical load, or lateral load),
the goal is to diagnose the bearing state (normal or certain fault
location and fault degree) lbelonging to y, where lis an element
in a predefined set of bearing state L.
The proposed log-STFT MSCResNet is designed for the prob-
lem earlier and the overall fault diagnosis process is presented
in Fig. 5. First, the raw vibration signals are transformed into
time-frequency maps by STFT with logarithmic, thus the fault
patterns of each category are enhanced before the network input,
which helps to reduce the classification difficulties of the net-
work. Then, the MSCResNet is trained to extract discriminative
representations layer by layer.
IV. EXPERIMENTAL VALIDATION
The effectiveness and robustness of the proposed model will
be validated in this section.
Fig. 6. Industrial railway axle bearing test rig.
A. Description of Dataset and Data Preparing
The vibration data of wheelset bearings used for analyzing the
performance of the proposed method have been acquired from
an industrial railway axle bearing test rig, which is specially
designed for locomotive running gear axle bearing signal anal-
ysis. As shown in Fig. 6, the test rig is set up, which is mainly
composed of a transmission, two wheelset bearings which are
assembled to the ends of an axle, two load sets for lateral and
vertical, respectively, and, to simulate the effect of natural wind,
two fan motors for each bearing are added.
One normal bearing and eight fault bearings with different
locations and degrees are used to design nine data collection
experiments, all of which are collected from the running gear
of the real train. There are totally nine types of bearings, with
different damage degree and location in each, and more details
can be found in Table II. In particular, some typical faults are dis-
played in Fig. 7. The accelerometers are mounted on 12 o’clock
(directly in the vertical load zone) of the bearing to acquire
the single-channel vibration data. To approach the real train
operating environment, 24 conditions –i.e., 3 speeds, 4 vertical
loads, and 2 lateral loads – are designed and implemented as
shown in Table III. For each working condition, vibration signal
is sampled for 90 s at a frequency of 16 384 Hz.
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XIN et al.: FAULT DIAGNOSIS OF WHEELSET BEARINGS IN HSTS USING LOGARITHMIC STFT AND MSCRESNET 7291
Fig. 7. Photos of different fault. (a) IR1 and IR2. (b) ORB. (c) B1 (left),
B2 (right). (d) C.
To compare the performance between different methods, a
standard dataset is constructed. After comparing the perfor-
mance of the proposed model with different sample lengths,
the measured signal is divided by every 0.5 s to guarantee its
robustness and efficiency. In particular, each sample consists of
8192 sampling points; each working condition consists of 180
samples; each class consists of 24 working conditions and there
are 9 classes in total.
B. Performance of All-Conditions Bearing Fault
Diagnosis
1) Model Initialization: Aiming to simulate an unknown
working condition, 24 working conditions are randomly divided
into 18, 3, and 3 which are regarded as training, validation,
and testing dataset, respectively. The details of the datasets are
displayed in Table IV.
The value of Nwdirectly controls the frequency resolution,
which is required to cover at least the duration of a transient.
As for the window shift R, it should be taken sufficiently small
to keep enough diagnostic information while not increasing too
much the computational cost and the dependence on adjacent
segments; a typical choice is within 50% and 75% overlap with
a Hanning window.
According to principle earlier, the Nwis set to 64 and the
Hanning window is chosen with the window shift Rset at 48,
i.e., 75% of Nw. The feature maps under different working
conditions of IR1, B1, and B3 are presented in Fig. 8 as some
examples. It can be seen from the diagrams that the similarity
among different conditions in the same class is very high while
it is relatively small among different classes. For instance, from
Fig. 8(a), figures under all conditions have the common features
at 2 KHz, which is quite different from other classes. Addition-
ally, there are some similar local features at 6 K–8 KHz under
both Condition 2-1-1 and 2-3-3. Along these lines, the MSCconv
simultaneously encodes such common and local features into
individual feature maps, so as to expand the learned knowledge
to unknown areas (i.e., variable working conditions).
Mini-batch gradient descent is utilized to optimize the net-
work parameter by minimizing the cross-entropy loss error
between the output and the true label [22]. By comparing various
combinations of learning rate and batch size in the experiment,
the learning rate is set to 0.003 and the batch size is 512 so that
the model reaches the best performance with shortest cost time.
Tanh is chosen to be the activation function used for MSCconv
as it will avoid the zigzag path that the original one may occur
during training. The entire program was written with python
3.7. The computer used for testing had an Intel Xeon Silver
4210 CPU, 64.00 GB memory, and a GPU of NVIDIA GeForce
GTX 2080 Titan with 11.00-GB GPU memory.
2) Robustness Validation: To avoid contingency caused by
a random split, the proposed model was tested for 20 times. The
results obtained are shown in Fig. 9. It shows that our model has
an accuracy rate of over 99% in 18 out of 20 trials, with only
once down to 98.99% in trail 15 and once down to 98.70% in
trail 20. In a word, the mean accuracy of 20 trails is of 99.76%.
This indicates the effectiveness and stability of the MSCResNet
proposed in this article under different working conditions. To
further illustrate how a given log-STFT input is transformed
by MSCResB, the output of the first block in the network is
visualized as Fig. 10. It is shown that the model could extract
rich individual information from different positions of log-STFT
such as high energy, edge, and global, which undoubtedly im-
proves the performance of detection.
In order to investigate the performance of the proposed
method, the confusion matrix of trail 1 is drawn in the upper left
of Fig. 11. It is observed that almost all samples can be correctly
classified. Especially, the false alarm rate is 0%, showing the
excellent outlier detection ability of the model. The main clas-
sification failure showed in confusion matrix is among C and N.
It is further verified that there are some similarities between the
cage fault signal and the normal signal under certain working
conditions, which results in a common and undistinguishable
signature. Furthermore, t-SNE is applied to visualize the clas-
sification result. It maps the multidimensional data to a lower
dimensional space and attempts to find patterns in the data by
identifying observed clusters based on similarity of data points
with multiple features. The t-SNE of trail 1 is displayed in the
bottom left of Fig. 11. It can be seen that 9 classes can be divided
clearly. From inspection of the t-SNE, some of classes are split
into a few pieces, which shows its potential for more difficult
fault diagnosis task.
3) Comparison of Different Methods: To objectively verify
the superiority of the proposed method, some other methods
proven to be very robust and accurate in fault diagnosis or picture
recognition fields were also used. These methods contain state-
of-art networks such as LSTM [18] selu-LeNet5 [21], 3-layer
CNN (3L-CNN), multilayer perceptron (MLP), and ResNet18
[34]. To further investigate its performance, a comparison be-
tween the original SCconv (SCResNet) and MSCconv under
the same network structure is made and discussed. To make
networks fit the abovementioned problem, some parameters of
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7292 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 18, NO. 10, OCTOBER 2022
Fig. 8. Logarithm of STFT under different classes and conditions. (a) IR1. (b) B1. (c) B3. It can be seen that all conditions of IR1 have higher
energy both at 2 KHz and 4 K–8 KHz at the pulse, whereas B1 has a relatively lower energy at 4 K–8 KHz. When facing the small damage degree
like B3, the energy caused by the impulse is not obvious, the logarithmic function enlarges almost all detail so it is much different from the others.
Overall, the log-STFT could expand the discrimination between different classes while maintaining the similarity of the characteristics of different
working conditions for each class.
Fig. 9. Test accuracy of 20 trails. The mean accuracy is of 99.76%.
several models are revised. All the methods are trained under
the same strategy.
Table V shows the comparison result of accuracy, time con-
sumption, and model size. Benefiting from log-STFT and suffi-
cient training data, almost all the models would have a relatively
high accuracy except LSTM. Due to the large receptive field and
great generalization ability, the proposed MSCResNet achieves
the highest classification accuracy, relatively short training time,
and small model size. Additionally, comparing with SCconv,
the MSCconv reduces the parameters of model and shorten
the training cost while ensuring the accuracy. From the above-
mentioned test phenomena, a conclusion can be drawn that our
method is superior to the others in comprehensive performance.
For real-time diagnostics, the proposed model has a shorter
deployment time and can be implemented on hardware like
FPGA card. Moreover, confusion matrix and t-SNE of ResNet18
and 3L-CNN are, respectively, shown in the middle and right
side of Fig. 11. Compared with MSCResNet on the left, errors
in ResNet18 and 3L-CNN are more scattered and numerous.
C. Fault Diagnosis Under Small Dataset and New
Conditions
For deep learning, it is difficult to achieve a huge number of
fault training data in the real environment of HST. Meanwhile,
there are various unknown speeds and loads that might never
exist in training set but possibly exist in reality. Thus, it is
necessary to investigate the robustness of different models under
small number of training data with unknown working conditions.
As a result, 2 working conditions from the rotating speed of
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XIN et al.: FAULT DIAGNOSIS OF WHEELSET BEARINGS IN HSTS USING LOGARITHMIC STFT AND MSCRESNET 7293
Fig. 10. One of the samples in IR2 (left) and some of its typical feature maps (middle and right) after first MSCResB. It is observed that the
proposed model could extract fruitful individual information from (a) high energy, (b) global, (c) edge, and (d) other details of log-STFT, so that all
details would be used to improve the classification performance for different fault types.
Fig. 11. Confusion matrix and t-SNE of top 3 methods: MSCResNet, ResNet18, and 3L-CNN.
589 rpm and 786 rpm, respectively, are randomly selected as
training set; 2 working conditions from that of 983 rpm are
selected as test set. This would allow the network to encounter
speeds that have never existed in the training set, which is a
severe task for networks. The proposed model is still compared
with those ones mentioned in IV-B-3), which use the same
strategy to train.
To avoid the random influence of incomplete selection, it is
tested for 20 times for each model whose results are displayed
in Fig. 12. In addition, the average accuracy and average cost
time are shown in Table VI. The superiority of performance
further proves the versatility and generalization ability of the
proposed method, the confusion matrix and t-SNE of which in
trail 1 is displayed in Fig. 13. Nevertheless, under such harsh
working conditions, it still unavoidably loses some accuracy in
a reasonable range.
Moreover, in the case of using the same MSCResNet, the
advantages of different feature extraction methods are tested, in-
cluding log-STFT, STFT, cyclic modulation coherence (CMC),
and continuous wavelet transform (CWT), and results are shown
in Table VII. It is proven that the details magnified by log-STFT
enable the network to learn much more knowledge about the
fault information, thus leading to a significant improvement in
terms of diagnosis accuracy.
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7294 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 18, NO. 10, OCTOBER 2022
Fig. 12. Test accuracy of each model for 20 trails under small number
data.
Fig. 13. MSCResNet confusion matrix and t-SNE of small number
data experiment trail 1.
V. C ONCLUSION
This article proposed a novel framework, i.e., log-STFT
MSCResNet, to address the issue of wheelset bearing fault
diagnosis under unknown working conditions. In order to re-
tain explicit physical meaning of fault signature as well as the
fruitful individual information, the STFT was first utilized to
decompose the measured signal into time-frequency domain.
Then, the logarithmic function was further used to enlarge the
details of STFT, which was proven to help reduce the difficulty
of classification for network. After that, with great interpretable
structure, generalization ability, and large receptive field, the
MSCResNet was proposed to diagnose the fault type from
unknown working condition data. Experimental results have
shown that the effectiveness and robustness of the proposed
method were superior to those of the other state-of-art methods.
It also has well-performance in model size and cost time, which
indicated its great potential in industrial applications.
The future work includes improving the generalization abil-
ity of the network to deal with the case of few-shot data in
real HST-bearing fault diagnosis scenario. In addition, a more
efficient network structure will be explored to further reduce the
computation cost.
REFERENCES
[1] L. Su, L. Ma, N. Qin, D. Huang, and A. H. Kemp, “Fault diagnosis of high-
speed train bogie by residual-squeeze net,” IEEE Trans. Ind. Informat.,
vol. 15, no. 7, pp. 3856–3863, Jul. 2019.
[2] G. Xu, D. Hou, H. Qi, and L. Bo, “High-speed train wheel set bearing
fault diagnosis and prognostics: A new prognostic model based on ex-
tendable useful life,” Mech. Syst. Signal Process., vol. 146, Jan. 2021,
Art. no. 107050.
[3] Y. Lei, Y. Bin, X. Jiang, F. Jia, N. Li, and A. Nandi, “Applications of
machine learning to machine fault diagnosis: A review and roadmap,”
Mech. Syst. Signal Process., vol. 138, Jan. 2020, Art. no. 106587.
[4] G. Manhertz and A. Bereczky, “STFT spectrogram based hybrid evalua-
tion method for rotating machine transient vibration analysis,” Mech. Syst.
Signal Process., vol. 154, Jun. 2021, Art. no. 107583.
[5] J. Antoni, G. Xin, and N. Hamzaoui, “Fast computation of the spectral
correlation,” Mech.Syst. Signal Process., vol. 92, pp. 248–277, Aug. 2017.
[6] J. Antoni, “Fast computation of the kurtogram for the detection of transient
faults,” Mech. Syst. Signal Process., vol. 21, no. 1, pp. 108–124, Jan. 2007.
[7] G. Xin, N. Hamzaoui, and J. Antoni, “Semi-automated diagnosis of
bearing faults based on a hidden Markov model of the vibration signals,”
Measurement, vol. 127, pp. 141–166, Oct. 2018.
[8] Z. Liu, X. Tang, X. Wang, J. E. Mugica, and L. Zhang, “Wind turbine blade
bearing fault diagnosis under fluctuating speed operations via Bayesian
augmented Lagrangian analysis,” IEEE Trans. Ind. Informat., vol. 17,
no. 7, pp. 4613–4623, Jul. 2021.
[9] G. Xin, N. Hamzaoui, and J. Antoni, “Extraction of second-order cy-
clostationary sources by matching instantaneous power spectrum with
stochastic model – Application to wind turbine gearbox,” Renewable
Energy, vol. 147, no. 1, pp. 1739–1758, Mar. 2020.
[10] H. Pan, Y. Yu, J. Zheng, X. Li, and J. Cheng, “Symplectic geometry mode
decomposition and its application to rotating machinery compound fault
diagnosis,” Mech. Syst. Signal Process., vol. 114, pp. 189–211, Jan. 2019.
[11] Z. Zheng and G. Xin, “Fault feature extraction of hydraulic pumps based
on symplectic geometry mode decomposition and power spectral entropy,”
Entropy, vol. 21, May 2019, Art. no. 476.
[12] G. Xin, Y. Qin, L. Jia, S. Zhang, and J. Antoni, “Low-rank and sparse
model: A new perspective for rolling element bearing diagnosis,” in Proc.
Int. Conf. Intell. Rail Transp., 2018, pp. 1–5.
[13] B. Yang, R. Liu, and X. Chen, “Fault diagnosis for a wind turbine generator
bearing via sparse representation and shift-invariant K-SVD,” IEEE Trans.
Ind. Informat., vol. 13, no. 3, pp. 1321–1331, Jun. 2017.
[14] L. Wan, K. Gong, G. Zhang, X. Yuan, C. Li, and X. Deng, “An ef-
ficient rolling bearing fault diagnosis method based on spark and im-
proved random forest algorithm,” IEEE Access, vol. 9, pp. 37866–37882,
2021.
[15] F. Ben Abid, S. Zgarni, and A. Braham, “Distinct bearing faults detection
in induction motor by a hybrid optimized SWPT and aiNet-DAG SVM,”
IEEE Trans. Energy Convers., vol. 33, no. 4, pp. 1692–1699, Dec. 2018.
[16] D. H. Pandya, S. H. Upadhyay, and S. P. Harsha, “Fault diagnosis of
rolling element bearing with intrinsic mode function of acoustic emission
data using APF-KNN,” Expert Syst. Appl., vol. 40, no. 10, pp. 4137–4145,
Aug. 2013.
[17] Z. Yang, X. Wang, and P. K. Wong, “Single and simultaneous fault diagno-
sis with application to a multistage gearbox: A versatile dual-ELM network
approach,” IEEE Trans. Ind. Informat., vol. 14, no. 12, pp. 5245–5255,
Dec. 2018.
[18] J. Lei, C. Liu, and D. Jiang, “Fault diagnosis of wind turbine based on long
short-term memory networks,” Renewable Energy, vol. 133, pp. 422–432,
Apr. 2019.
Authorized licensed use limited to: Beijing Jiaotong University. Downloaded on May 08,2023 at 05:57:37 UTC from IEEE Xplore. Restrictions apply.

XIN et al.: FAULT DIAGNOSIS OF WHEELSET BEARINGS IN HSTS USING LOGARITHMIC STFT AND MSCRESNET 7295
[19] X. Zheng, J. Wu, and Z. Ye, “An end-to-end CNN-BiLSTM attention
model for gearbox fault diagnosis,” in Proc. IEEE Int. Conf. Prog. Infor-
mat. Comput., 2020, pp. 386–390.
[20] Y.Li, B. Qiu, M. Wei, W.Sun, and X. Liu, “Deep learning based end-to-end
rolling bearing fault diagnosis,” in Proc. Prognostics Syst. Health Manage.
Conf., 2019, pp. 1–6.
[21] Y. Zhang, K. Xing, R. Bai, D. Sun, and Z. Meng, “An enhanced convolu-
tional neural network for bearing fault diagnosis based on time–frequency
image,” Measurement, vol. 157, no. 99, Jun. 2020, Art. no. 107667.
[22] Z. Chen, A. Mauricio, W. Li, and K. Gryllias, “A deep learning method for
bearing fault diagnosis based on cyclic spectral coherence and convolu-
tional neural networks,” Mech. Syst. Signal Process., vol. 140, Jun. 2020,
Art. no. 106683.
[23] J. Li, X. Yao, X. Wang, Q. Yu, and Y. Zhang, “Multiscale local features
learning based on BP neural network for rolling bearing intelligent fault
diagnosis,” Measurement, vol. 153, no. 12, Mar. 2019, Art. no. 107419.
[24] T. Li et al., “WaveletKernelNet: An interpretable deep neural network for
industrial intelligent diagnosis,” IEEE Trans. Syst., Man, Cybern.: Syst.,
to be published, doi: 10.1109/TSMC.2020.3048950.
[25] W. Mao, W. Feng, Y. Liu, D. Zhang, and X. Liang, “A new deep auto-
encoder method with fusing discriminant information for bearing fault di-
agnosis,”Mech. Syst. Signal Process., vol. 150, Mar.2021, Art. no. 107233.
[26] H. Shao, H. Jiang, H. Zhang, W. Duan, T. Liang, and S. Wu, “Rolling
bearing fault feature learning using improved convolutional deep belief
network with compressed sensing,” Mech. Syst. Signal Process., vol. 100,
pp. 743–765, Feb. 2018.
[27] H. Hu, B. Tang, X. Gong, W. Wei, and H. Wang, “Intelligent fault diagnosis
of the high-speed train with big data based on deep neural networks,” IEEE
Trans. Ind. Informat., vol. 13, no. 4, pp. 2106–2116, Aug. 2017.
[28] D. Peng, H. Wang, Z. Liu, W. Zhang, M. J. Zuo, and J. Chen, “Multibranch
and multiscale CNN for fault diagnosis of wheelset bearings under strong
noise and variable load condition,” IEEE Trans. Ind. Informat., vol. 16,
no. 7, pp. 4949–4960, Jul. 2020.
[29] H. Wang, Z. Liu, D. Peng, and Y. Qin, “Understanding and learning
discriminant features based on multiattention 1DCNN for wheelset bearing
fault diagnosis,”IEEE Trans. Ind. Informat., vol. 16, no. 9, pp. 5735–5745,
Sep. 2020.
[30] G. Xu, D. Hou, H. Qi, and L. Bo, “High-speed train wheel set bearing
fault diagnosis and prognostics: A new prognostic model based on ex-
tendable useful life,” Mech. Syst. Signal Process., vol. 146, Jan. 2021,
Art. no. 107050.
[31] P. Borghesani and M. R. Shahriar, “Cyclostationary analysis with loga-
rithmic variance stabilisation,” Mech. Syst. Signal Process., vol. 70-71,
pp. 51–72, Mar. 2021.
[32] J. Liu, Q. Hou, M. Cheng, C. Wang, and J. Feng, “Improving convolutional
networks with self-calibrated convolutions,” in Proc. IEEE/CVF Conf.
Comput. Vis. Pattern Recognit., 2000, pp. 10093–10102.
[33] S. Ioffeand C. Szegedy, “Batch normalization: Accelerating deep network
training by reducing internal covariate shift,” in Proc. 32nd Int. Conf.
Mach. Learn., 2015, pp. 448–456.
[34] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image
recognition,” in Proc. IEEE/CVF Conf. Comput. Vis. Pattern Recognit.,
2016, pp. 770–778.
Ge Xin received the B.Eng. and M.Eng. de-
grees from Northwestern Polytechnical Univer-
sity, Xi’an, China, in 2010 and 2013, respec-
tively, and the Ph.D. degree from the University
of Lyon, Lyon, France, in 2017.
He is currently an Associate Professor with
Beijing Jiaotong University, Beijing, China. His
research interests include signal processing,
machine learning, and inverse problems in ap-
plication to rail traffic scenarios.
Dr. Xin served as one of the Editorial Board
Members for the Applied and Computational Mathematics and an Edito-
rial Assistant for the Smart and Resilient Transportation journals.
Zhe Li received the B.Eng. degree in 2016
from Beijing Jiaotong University, Beijing, China,
where he is currently working toward the M.Eng.
degree in control science and engineering.
His research interests include rotating ma-
chinery fault diagnosis, health state estimation,
and RUL prediction of high-speed trains.
Limin Jia received the Ph.D. degree from the
China Academy of Railway Sciences, Beijing,
China, in 1991.
He is currently a Professor with the State Key
Laboratory of Rail Traffic Control and Safety,
Beijing Jiaotong University, Beijing. His current
research interests include safety science and
engineering, control science and engineering,
transportation engineering, safety technology
and engineering, and system science.
Qitian Zhong received the B.Eng. degree in
2020 from the Beijing Jiaotong University, Bei-
jing, China, where he is currently working to-
ward the M.Eng. degree in transportation plan-
ning and management.
His research interests include rail vehicle fault
diagnosis, health state estimation, and predic-
tion of RUL.
Honghui Dong (Member, IEEE) received the
Ph.D. degree from the Institute of Automation,
Chinese Academy of Sciences, Beijing, China,
in 2007.
He is currently a Professor with Beijing Jiao-
tong University, Beijing. His current research
interests include pattern recognition and intelli-
gent systems, as well as transportation science
and engineering.
Nacer Hamzaoui is currently a Full Professor
with the University of Lyon, Lyon, France. He
is the Director of the Department of Mechanical
Engineering Design (GMC), University of Lyon.
His research interests include machinery condi-
tion monitoring, vibroacoustic analysis, sound,
and vibratory perception.
Jerome Antoni received the M.S. degree in
mechanical engineering from the University of
Technology of Compiegne, Compiegne, France,
in 1995, and the Ph.D. degree in signal process-
ing from the Grenoble Institute of Technology,
Grenoble, France, in 2000.
He is currently a Full Professor with the Uni-
versity of Lyon, Lyon, France. His current re-
search interests include development of signal
processing methods in mechanical applications,
including vibration-based condition monitoring
and the resolution of inverse problems in acoustics and vibration.
Dr. Antoni served as a Handling Editor for the International Journal of
Condition Monitoring,theInternational Journal of Rotating Machinery,
and the Diagnostika, an Associate Editor for the Mechanical Systems
and Signal Processing and Applied Sciences. He is currently the Direc-
tor of the Laboratoire Vibrations Acoustique (LVA), University of Lyon.
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