An end-to-end fault diagnostics method based on convolutional neural network for rotating machinery with multiple case studies

Abstract

The fault diagnostics of rotating components are crucial for most mechanical systems since the rotating components faults are the main form of failures of many mechanical systems. In traditional diagnostics approaches, extracting features from raw input is an important prerequisite and normally requires manual extraction based on signal processing techniques. This suffers of some drawbacks such as the strong dependence on domain expertise, the high sensitivity to different mechanical systems, the poor flexibility and generalization ability, and the limitations of mining new features, etc. In this paper, we proposed an end-to-end fault diagnostics model based on a convolutional neural network for rotating machinery using vibration signals. The model learns features directly from the one-dimensional raw vibration signals without any manual feature extraction. To fully validate its effectiveness and robustness, the proposed model is tested on four datasets, including two public ones and two datasets of our own, covering the applications of ball screw, bearing and gearbox. The method of manual, signal processing based feature extraction combined with a classifier is also explored for comparison. The results show that the manually extracted features are sensitive to the various applications, thus needing fine-tuning, while the proposed framework has a good robustness for rotating machinery fault diagnostics with high accuracies for all the four applications, without any application-specific manual fine-tuning.

Full text

Journal of Intelligent Manufacturing
https://doi.org/10.1007/s10845-020-01671-1
An end-to-end fault diagnostics method based on convolutional
neural network for rotating machinery with multiple case studies
Yiwei Wang1·Jian Zhou1·Lianyu Zheng1·Christian Gogu2
Received: 29 November 2019 / Accepted: 15 September 2020
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
The fault diagnostics of rotating components are crucial for most mechanical systems since the rotating components faults
are the main form of failures of many mechanical systems. In traditional diagnostics approaches, extracting features from raw
input is an important prerequisite and normally requires manual extraction based on signal processing techniques. This suffers
of some drawbacks such as the strong dependence on domain expertise, the high sensitivity to different mechanical systems,
the poor flexibility and generalization ability, and the limitations of mining new features, etc. In this paper, we proposed an
end-to-end fault diagnostics model based on a convolutional neural network for rotating machinery using vibration signals.
The model learns features directly from the one-dimensional raw vibration signals without any manual feature extraction.
To fully validate its effectiveness and robustness, the proposed model is tested on four datasets, including two public ones
and two datasets of our own, covering the applications of ball screw, bearing and gearbox. The method of manual, signal
processing based feature extraction combined with a classifier is also explored for comparison. The results show that the
manually extracted features are sensitive to the various applications, thus needing fine-tuning, while the proposed framework
has a good robustness for rotating machinery fault diagnostics with high accuracies for all the four applications, without any
application-specific manual fine-tuning.
Keywords Fault diagnostics ·Rotating machinery ·Vibration signals ·Convolutional neural network
Introduction
Rotating machinery is the essential equipment playing a
crucial character in the modern industry. As indispensable
key transmission devices of rotating machinery, the typi-
cal rotating components such as ball screws, bearings, and
gears, are the leading cause of failure in essential industrial
equipment such as induction motors, wheelset of high-speed
railway bogie, aero-engines, wind-turbine, etc. According to
statistics, 30–51% of rotating machinery failure are caused
by these key components (Islam and Kim 2019a; Zhao
et al. 2020). Failure of the rotating components results
in machine performance degradation, unwanted downtime,
BLianyu Zheng
lyzheng@buaa.edu.cn
1School of Mechanical Engineering and Automation, Beihang
University, Beijing 100191, China
2Institut Clément Ader (UMR CNRS 5312)
INSA/UPS/ISAE/Mines Albi, Université de Toulouse,
31400 Toulouse, France
economic losses and even human casualties. Normally, the
rotating components are installed deep inside the machine
and undergo a long degradation process from healthy to
failure. It is not practical to frequently shut down and disas-
semble the machines to examine their health state. If damaged
rotating components are left unattended, it may cause sec-
ondary damage for the machines. On the other hand, due to
different working conditions and other uncertainties, even
the same type of rotating components may exhibit their own
degradation process individually, making it difficult to accu-
rately estimate the health states based on statistics of large
samples. Therefore, online monitoring and real-time fault
diagnostics of individual rotating components based on man-
ufacturing big data is an urgent demand.
Smart manufacturing, which is characterized by the inte-
gration of Artificial Intelligence (AI) with recent emerging
technologies (Lee et al. 2018), enables online monitoring and
massive manufacturing data acquisition from sensors and ter-
minals installed in equipment. However, the data must be
converted into useful information before it can be of value
to the industry. Prognostics and health management (PHM)
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Journal of Intelligent Manufacturing
Fault classification
SVM
Signal processing based
feature extraction
Raw vibration
data
Data
segmentation
Time domain features
Frequency features
Time-frequency
features
FNN
Deep learning flow
LSTM
Results
Raw vibration
data
Data
segmentation Results
(a)
(b)
Fig. 1 Diagnostics methods: traditional versus deep learning based
is such a bridge converting manufacturing big data to use-
ful information. As an emerging discipline receiving great
attention from both academia and various industries, PHM
has been listed as a part of the “standard architecture of smart
manufacturing” proposed by China. PHM deeply fuses AI
into manufacturing industries through a complete architec-
ture containing functions such as intelligent fault diagnostics,
prognostics, predictive maintenance, etc. (Vogl et al. 2019;
Xia and Xi 2019). This fusion enables timely online fault
diagnostics of devices as well as their future state predic-
tion, and consequently, results in the improvement of the
maintainability, supportability, reliability and safety of essen-
tial industrial equipment. As an important part consisting of
PHM, intelligent fault diagnostics provide solutions for real-
time fault diagnostics of individual rotating components.
For rotating machinery, the vibration signal is widely
used for fault diagnostics due to various advantages, such
as continuous monitoring without stopping the machines,
ease of use, sensitivity towarding faults etc. Traditional intel-
ligent fault diagnostics normally contains two sequential
steps of manually extracting features from raw vibration
signals followed by establishing the mapping between the
extracted features and the corresponding states based on
classification techniques such as support vector machine
(SVM) (Goyal et al. 2019) or feedforward neural network
(FNN), as shown in Fig. 1a. Whether a fault sensitive feature
can be extracted affects the performance of the diagnos-
tics model significantly, and hence lots of effort are devoted
to extracting suitable features before a classification algo-
rithm can be employed. The features are normally extracted
from time domain (Park et al. 2018), frequency domain,
or time-frequency domain using various signal processing
techniques such as fast Fourier transform, Hilbert-Huang
transform (Feng and Pan 2012), empirical mode decompo-
sition (Liu et al. 2018), variation mode decomposition (Yan
and Jia 2018), wavelet transform (Dhamande and Chaudhari
2018 ; Wang et al. 2018a), intrinsic time scale decompo-
sition (Feng et al. 2016), local mean decomposition (Wang
et al. 2018b), etc. Manually extracting features, while having
led to satisfying results in the past, also exhibits some draw-
backs. The complex signal processing techniques required by
feature extraction highly depend on the expertise and prior
knowledge, and also require lots of human labour. In addition,
manually extracted features are normally empirical and thus
sensitive to changes. These empirical features reduce the flex-
ibility and the generalization ability of the diagnostics model,
i.e., the model performs highly accurately for one particu-
lar diagnostics task while much less accurately for another
task. Therefore, significant human labour and expertise are
required for exploring and designing suitable features for dif-
ferent diagnostics tasks (Jing et al. 2017). These difficulties
in feature extraction seriously hinder fault diagnostics evolv-
ing into a mature technology that can be widely deployed in
industry.
The strong feature-learning ability of deep learning such
as auto encoder and convolutional neural network (CNN)
provides a potential solution to the aforementioned draw-
backs (Hamadache et al. 2019; Zhao et al. 2019;Lietal.
2019a; Jia et al. 2018). The hierarchical structures of multiple
neural layers enable deep learning networks to directly mine
information from raw data layer by layer (Fig. 1b). Compared
with other deep learning methods, CNN significantly reduces
the number of parameters to be optimized by the strategies of
weight sharing and sub-sampling. CNN also has strong anti-
noise ability because of its insensitivity to the local change
due to the convolution process. Inspired by the successful
employment of CNN in image classification area, it is easy
to think of converting waveform signal into images and then
using CNN for fault diagnostics. Hoang and Kang (2019)
converted vibration signal into grayscale images through a
simple method proposed by Nguyen et al. (2013), and then
fed the images into CNN for bearing diagnostics. Chen et al.
(2019) proposed a scheme combining discrete wavelet trans-
formation (DWT) with CNN for planetary gearboxes fault
diagnostics. A series of sets of wavelet coefficients of DWT
were used as the input of CNN. Wang et al. (2019) proposed
a conversion method converting vibration signals from mul-
tiple sensors to images. A bottleneck layer optimized CNN
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Journal of Intelligent Manufacturing
was used for rotating machinery diagnostics. Islam and Kim
(2019b) used 2D representation of acoustic emission sig-
nal processed by wavelet packet transform as the input of
an adaptive deep CNN for bearing fault diagnostics. Wang
et al. (2017) converted time sequences signal of gear box
into time-frequency images using continuous wavelet anal-
ysis and then fed the images into a deep CNN. Zhu et al.
(2019a) transformed multiple vibration signals of a rotor
into symmetrized dot pattern (SDP) images before classified
by CNN. Zhu et al. (2019b) employed short-time Fourier
transform to convert one-dimensional signals of bearing into
a time-frequency graph and then a novel capsule network
was proposed for diagnosing. Liang et al. (2020) employed
wavelet transform to extract time-frequency image features
from raw signals. Generative Adversarial Networks (GANs)
were used to generate additional fake training images for data
augmentation purposes. A CNN model was built for fault
modes classification. The proposed method was validated on
a gearbox application. Chen et al. (2020) used cyclic spec-
tral analysis to obtain the two-dimensional Cyclic Spectral
Coherence maps of vibration signals and a CNN model was
constructed to learn high-level feature representations and
conduct fault classification. The method was validated on a
public dataset of bearing faults published by the Case Western
Reserve University (CWRU). Zhang et al. (2020) processed
the raw vibration signals to gray-scale images without any
predetermined parameters and then fed into a CNN with two
dropout layers and two fully-connected layers for fault clas-
sification. CWRU bearing dataset were used for validation.
It can be seen that most studies require one additional
step that converts 1D vibration signal into 2D represen-
tations before using the CNN model, which circumvent
some drawbacks of manually feature extraction but still need
application-specific adaptation. Recently, directly extracting
features from one-dimensional raw vibrational data without
any signal processing techniques has begun to be proposed
by researchers. This provides an end-to-end solution for fault
diagnostics, which reduces the dependencies on expertise and
prior knowledge, and hence facilitates the use and deploy-
ment of diagnostics model. Wu et al. (2019) optimized the 2D
CNN to be a one-dimensional CNN that is suitable for pro-
cessing vibration signals, and validated the proposed model
on gearbox application. Li et al. (2018a) proposed a 1D CNN
model with the residual learning algorithm for bearing fault
diagnostics, and the raw data without any pre-processing
were fed into the built model. Li et al. (2020) developed an
adaptive 1D separable convolution with residual connection
network for diagnosing gear pitting. Peng et al. (2019)pro-
posed a deeper 1D CNN based on a 1D residual block for the
fault diagnostics of wheelset bearings in high-speed trains.
Wide convolution kernel and dropout technology were used
in the CNN to enhance the network’s generalization perfor-
mance. The traditional fault diagnostics, 1D CNN and 2D
CNN methods employed in the literature reviewed above are
summarized in Table 1.
The above studies focus only on one specific application.
Specifically, bearings and gearboxes are more extensively
studied than ball screws, whose fault diagnostics studies are
very limited due to lack of public dataset. The generaliz-
ability of CNN to fault diagnostics of rotating components
is necessary to be fully investigated. In this paper, we pro-
pose an end-to-end fault diagnostics method based on CNN
using raw vibration signal. A CNN model consisting of three
stacks of convolutional and pooling layer, dropout layer and
fully connected layer is proposed. The alternating convo-
lution and pooling layers of the CNN model automatically
extract feature maps from raw data layer by layer. The soft-
max function is used as the activation function of the last
fully connected layer for dealing with multi-class classifica-
tion problems. No manually extracted feature is necessary. To
fully validate the effectiveness and the generalizability of the
proposed model for fault diagnostics of rotating components,
we tested on four datasets, including two public ones and two
of our own, covering the applications of ball screw, bear-
ing and gearbox. These three types of rotating components
are the typical ones that are widely used as the key compo-
nents in essential industrial equipment such as machine tools,
high-speed trains, aero-engines, wind-turbine, gas-turbine,
etc. To our best knowledge, our work firstly validates the
CNN model for fault diagnostics in such wide applications.
Moreover, the signal processing based feature extraction
combined with long short-term memory (LSTM) network
(the combination method is referred to as traditional method
here) is also explored and compared with the proposed CNN
model. Specifically, three typical engineered features, i.e.,
(a) wavelet packet energy (WPE) based on wavelet packet
decomposition, (b) instantaneous frequency (IF), and (c)
instantaneous spectral entropy (ISE) based on power spec-
trogram, are constructed from the raw vibration data and then
used as the input of an LSTM network. The proposed CNN
model is compared with the traditional method in terms of
accuracy and robustness in various applications
The remainder of the paper is organized as follows. “The
CNN-based diagnostics framework for rotating machin-
ery” section details the structure and the feature learning
mechanism of the proposed model. In “Case studies and dis-
cussions” section, the generalization of the proposed model
is verified by four case studies covering the commonly used
rotating components of ball screw, bearing and gear. The
generalizability and robustness of the proposed model is fur-
ther discussed by the comparison with traditional methods.
Finally, conclusions and perspectives are given in “Conclu-
sions and future work” section.
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Journal of Intelligent Manufacturing
Table 1 Summary of different categories of fault diagnostics
Category Method Advantage/disadvantage References
Traditional fault diagnostics First manually extract features
based on signal processing
techniques such as Fourier
transform, Hilbert-Huang
transform, empirical mode
decomposition, wavelet
transform, etc.
Then feed the features to classifier
such as support vector machine,
shallow neural networks, etc.
Signal processing techniques
highly depends on expertise and
prior knowledge
Manually extracted features are
application-specific and quite
sensitive to environment or
working conditions.
Require lots of skilled labour to
explore and design suitable
features for new diagnostics
task.
Goyal et al. (2019), Feng and Pan
(2012), Liu et al. (2018), Yan
and Jia (2018), Dhamande and
Chaudhari (2018), Wang et al.
(2018a,b), Feng et al. (2016),
andJingetal.(2017)
2D convolutional neural network First convert raw vibration signal
to 2D representations such as
grayscale images,
time-frequency images,
symmetrized dot pattern
images, cyclic spectral
coherence maps, etc.
Then feed the 2D representations
to 2D convolutional neural
network for classification.
Circumvent some drawbacks of
manually feature extraction but
still need application-specific
adaptation.
Hoang and Kang (2019), Nguyen
et al. (2013), Wang et al.
(2017,2019), Islam and Kim
(2019b), Zhu et al. (2019a,b);
Chen et al. (2020), Zhu et al.
(2019), Chen et al. (2019),
Liang et al. (2020)andZhang
et al. 2020
1D convolutional neural network Use 1D convolutional neural
network to accomplish direct
feature extraction from raw
vibration signal and
classification.
Provide end-to-end solutions for
fault diagnostics
Reduce the dependencies on
expertise and prior knowledge
Reduce the sensitivities to
environment or working
conditions
Facilitate the use and deployment
of diagnostics models.
Wu et al. (2019), Li et al.
(2018b,2020) and Peng et al.
(2019)
Fig. 2 A typical architecture of CNN (Jing et al. 2017)
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Journal of Intelligent Manufacturing
The CNN-based diagnostics framework
for rotating machinery
Convolutional neural networks (CNNs), first proposed by
LeCun for image processing, has two characteristics, i.e.,
spatially shared weights and spatial pooling (Goodfellow
et al. 2019). The architecture of a typical CNN is illus-
trated in Fig. 2, which is structured by series of stages (Jing
et al. 2017). The convolutional layer convolves multiple fil-
ters with raw input data and generate feature maps. Pooling
layer often follows the convolutional layer to reduce the size
of feature map and extract the most significant local features
(Li et al. 2019b). The last stage of the architecture consists
of a fully-connected layer, which is normally a multi-class
classification model.
The schematic diagram of the proposed framework is illus-
trated in Fig. 3. The sliding window method was used to
segment the raw time sequence vibration data of each health
state and then reshape to a matrix before feeding into the
neural network. The one-hot encoding method is used to
manually create the labels of samples, which serve as the
output of the network. For example, if there are three classes
of data, the first class is encoded as (1, 0, 0), the second (0,
1, 0), and the third (0, 0, 1). The self feature learning abil-
ity is realized by the hidden layers, which is comprised of
stacks of alternated convolutional layers and pooling layers.
One-dimensional convolution kernels and pooling kernels
are used in the network since the input is a one-dimensional
time series signal. The structure of the CNN model and the
feature learning process are detailed below.
Structure of the proposed CNN model
The structure of the proposed model is illustrated in Fig. 4,
including three stacks of convolution-pooling layers and a
fully connected layer. In the convolutional layer, multiple
filters are convolved with raw input data and generate trans-
lation invariant features. In the subsequent pooling layer, the
feature is compressed by sliding a fixed-length window fol-
lowing several rules such as average, max and so on. In the
first two stacks maxpooling layer is used while in the last
stack the average pooling layer is used. The data flow from
the input of the network to the final output in Fig. 4is detailed
by explaining the entities (denoted by the Greek letters) and
the actions (denoted by arrows).
1αis the input matrix of the network, which has the shape
(m1,n1). Note that we use the form (m,n) to represent a
m-by-nmatrix. The subscript of mand nas well as fand
sthat will be introduced later represents the index of the
layer.
2βiis a filter with shape (h,n), in which, i 1,2,…,f1.f1
is the number of filters in the 1st layer. h is the kernel size
of the convolution.
3γis the output matrix of the 1st convolution layer, having
the shape (m1,f1).
4Fromαto γ, the convolution operation is carried out,
which is detailed as follows. The dot product between
filter βiand a concatenation vector αk:k+h−1defines the
convolution operation.
cjϕ(βi·αk:k+h−1+b)(1)
in which, ·represents the dot product, bthe bias term
and ϕthe non-linear activation function. αk:k+h−1is a
h-length window starting from the k-th row to the (k +
h-1)-th row, which is defined as:
αk:k+h−1=αk⊕αk+1 ⊕···⊕αk+h−1(2)
where ⊕is the concatenation operation of two vectors.
As defined in Eq. 1, the output scalar cjcan be regarded
as the activation of the filter βion the corresponding
concatenation vector αk:k+h−1. By sliding the filter βi
through αand applying zero padding technique, m1out-
put scalar cjcan be obtained, forming a column vector ci,
also known as a feature map:
ci[c1,c2, ..., cj, ..., cm1](3)
One filter corresponds to one column vector. Since there
are f1filters in the first layer, the output matrix γis thus
(m1,f1) matrix. From the above operation it can be seen
that one filter performs multiple convolution operations,
during which the weights of the filter are shared. The
feature map ci, obtained by convolving one filter βiover
the input data, represents the feature of the input data
extracted from a certain level. By convolving the input
data with multiple filters, a high-dimensional feature map
containing multiple column vectors that reflect the input
data from different perspectives are extracted.
5. μis the output matrix of the 2nd layer, having the
shape (m2/s2,n2), where s2is the pooling length of
the 2nd layer. Note that m2and n2denote input size
of the 2nd layer. Since the output of the current layer
is the input of the next layer, m2m1and n2
f1.
6Fromγto μ, max pooling operation is carried out, which
is detailed as follows. The max operation is taken over
the s2consecutive values in ci. Then the compressed
column vector his obtained as:
hi[h1,h2, ..., hl, ..., hm/s](4)
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Journal of Intelligent Manufacturing
Fig. 3 Framework of proposed diagnostics model
1
st
layer: 1D convoluon 3
rd
layer: 1D convoluon2
nd
layer: Max Pooling 5
th
layer: 1D convoluon4
th
layer: Max Pooling 6
th
layer:
GlobalAveragePoolin g Fully connected layer
1
In
out
i
β
11
:( , )mnα
i
c
11
:( , )mfγ
4
2
6
5
222
:( , )msnμ
22
:( , )mnγ
3
i
h
l
h
Stack 1 Stack 2 Stack 3
Take average value
Take max value
(m
3
, f
3
)
(m
3
, n
3
)(m
4
, n
4
)
(m
5
, f
5
)
(m
5
, n
5
)(m
6
, n
6
)
(m
4
/s
4
, n
4
)(m
6
/s
6
, n
6
)
j
c
p
1
p
2
p
k
Max(p1,p2, ,p
k
,)
Fig. 4 Structure of proposed CNN network
where hl=max[c(l−1)s+1,c(l−1)s+2,···,cls]
From above we see that when a matrix goes through one
convolution layer, its number of rows keep unchanged
and the number of column equals to the number of
filters. In the case of pooling layer, the number of
columns keeps unchanged while the number of rows is
compressed depending on the pooling length.
7. In the 2nd and 3rd stacks, the convolution and pooling
propagate. The only difference is that the number of
filters and the pooling length varies.
8 The output of the 7th layer is flattened and connected
with a fully connected layer, which is similar to a tra-
ditional multilayer neural network and can be applied
through different classification. The dropout technique
is employed to prevent overfitting. The softmax func-
tion (Behley et al. 2013) is used as the last layer, which
gives the probability of being each label. Specifically,
assuming a K-label classification task, the output of the
softmax function can be calculated as Eq. 5, in which
Wkand bkare the weight matrix and bias, P(yk|x;
Wk,bk) is the probability of being the k-th label (denoted
as pkin Fig. 4) given the input xand the correspond-
ing weight and bias. Here xis the vector after drop
out in the fully connected layer. The final output of the
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Journal of Intelligent Manufacturing
network is the health sate label with the highest proba-
bility.
⎡
⎢
⎢
⎣
P(y1|x;W1,b1)
...
P(yk|x;Wk,bk)
P(yK|x;WK,bK)
⎤
⎥
⎥
⎦
=1
K
k1exp(Wkx+bk)
⎡
⎢
⎢
⎣
exp(W1x+b1)
...
exp(Wkx+bk)
exp(WKx+bK)
⎤
⎥
⎥
⎦
(5)
Hyperparameters
The activation function of all the convolutional layers is the
Relu function due to its ability to avoid gradient vanishing
and to its fast convergence. The loss function of the CNN
model is cross-entropy and the precision function is categor-
ical accuracy. L2 regularization term is set for the first and
third convolution layers to reduce overfitting. The parameter
of L2 term is a trade-off between the effectiveness of training
and overfitting, i.e., a too-large value will lead to inadequate
training and a too-small value is not enough to reduce the
risk of overfitting. We set this value to 0.001 based on the
prior study (Ng 2004). Dropout is set for the fully connected
layer to reduce overfitting by directly setting the neurons of
the network to zero in a given proportion. We referred to
the study of the founder of the dropout technique (Srivastava
et al. 2014) and set this proportion to 0.5, which is a typical
value in deep learning.
The initial weight of the network is set by the glorot
uniform function, and the bias are set to 0. The weight is opti-
mized by the adaptive moment estimation (ADAM) solver
with initial learning rate 0.001 and exponentially decayed
rate 0.1. Adam solver is a combination of the Momentum
and RMSProp optimization algorithms. It designs an inde-
pendent adaptive learning rate for different parameters by
calculating the first-order moment estimation and second-
order moment estimation of the gradient, which typically
gives better optimization performance than the alternative
stochastic gradient descent with momentum (SGDM) solver
(Kingma and Ba 2015). Adam algorithm is currently the most
widely used optimization algorithm embedded in the field of
machine learning and deep learning.
The mini batch training strategy is adopted here. Specif-
ically, the training examples are divided into small batches.
The model parameters will be updated after each batch pass-
ing through the network. The passing through of one batch
is called one iteration. When the entire training example is
passed through the network once and each example has the
opportunity to update the model parameters, it is one epoch.
The execution environment is an Intel e5-2620v4 CPU and
a GeForce RTX2080Ti GPU. The above network setting and
the execution environment will be used in all the following
cases.
Case studies and discussions
Case 1: Ball screw lubrication states diagnostics
Experiment and data preparation
In this case study, the proposed model is validated for diag-
nosing the lubrication states of the ball screw. Ball screws
are crucial mechanical components being intensively used in
many engineering systems that requires precise positioning
such as the feed system in machine tool, and in high precision
leveling systems for aircrafts and missiles (Li et al. 2018a).
The growing demand for high speed and large lead for ball
screws makes it increasingly important to keep good lubrica-
tion in order to reduce the friction. Indeed, correct lubrication
is vital to ball screws since the lubrication affects signifi-
cantly its performance. Poor lubrication may increase the
friction and impairs the positioning accuracy of ball screws.
In addition, abnormal vibration caused by poor lubrication
accelerates the damage of the machine tool and affects the
quality of machining. Therefore, monitoring and online diag-
nosing of the lubrication state of the ball screw is important
for improving position accuracy and lifetime of ball screws.
Very few reports are available regarding ball screw lubri-
cation state diagnostics. Motivated by this, we design an
experiment that simulates the different lubrication states of
ball screws. The experiment is carried out in the test bench
which was originally designed for measuring the friction
torque of a ball screw, as shown in Fig. 5. The drive sys-
tem drives the nut moving along the screw back and forth.
Three states labeled as “Grease”, “Oil”, and “Absent” are
simulated by (1) lubricating the ball screw using grease, (2)
lubricating using oil and (3) removing the original lubricant,
respectively. These three health states simulate the typical
lubrication states that ball screws may encounter in real work-
ing environment. The vibration signals corresponding to the
three states are acquired at a sampling rate 5 kHz with the
data acquisition system Prosig P8020, as shown in Fig. 6.
128-s data are acquired for each lubrication states.
The raw time domain signals of one round trip (forward
and reverse motion) of the nut under “Absent” lubrication is
shown in Fig. 7. Two parts can be clearly seen, which cor-
respond to the signals of forward and reverse motions of the
nut, respectively. The abrupt “peaks” are due to the sharp
slowdown and stop of the nut near the end of the motions.
The data near the beginning and end of the motions are dis-
carded. Only the “steady state” data in the middle stage of
the motions are retained. For conciseness, the full raw sig-
nals under “Oil” and “Grease” lubrications are not presented.
Instead, the retained segment of the forward motion of the
three lubrication conditions are given in Fig. 8a. It can be seen
that the differences among the three states are quite small,
thus we further transform the signal into frequency domain
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Journal of Intelligent Manufacturing
Fig. 5 Ball screw test bench
Fig. 6 Data acquisition set-up
Forwar d motion Rever se motion
Retained data Retained data
Peak due to sharp
slowd own
Absent
Fig. 7 Raw signal under “Absent” lubrication
using FFT, as shown in Fig. 8b. The differences among the
three cases are not obvious and it is hard to see appropriate
patterns, making it more challenging to correctly distinguish
different lubrication conditions.
The raw vibration signal is divided into segments to form
the input samples of the network. For each state, there are
128 ×5000 6.4 ×105data point. 6400 samples are selected
as one segment and is further reshaped to a (64, 100) matrix. It
is worth pointing out that the sample length should be traded
off between the number of samples and the feature infor-
mation that one sample contains. A too-short length of time
window may carry incomplete feature information, leading
to the difficulty of diagnostics, while a long length of time
window will result in insufficient training data. Based on the
sampling rate of data used in this paper as well as other related
research works, we take 6400 data points as one sample. 80%
data (80 samples) are reserved for training and the rest 20%
(20 samples) for testing. Finally, the training/testing samples
taken from each lubrication state form the overall training
sets (80 ×3240 samples) and the testing sets (20 ×3
60 samples). The input/output shape, the kernel size, stride
and number of filters of each layer during the training process
are reported in Table 2. Note that the above hyperparameters
(the kernel size, stride and number of filters of each layer)
remain unchanged in all the following case studies.
Results and discussions
The diagnostics accuracy on the test set is 100% and all
the three states are correctly classified (thus the confusion
matrix is not given). In order to better illustrate the fea-
ture learning process of the CNN model, the t-distributed
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Journal of Intelligent Manufacturing
(a) (b)
Fig. 8 Retained segment of the forward motion of the three lubrication conditions: (a) in the time domain, (b) in the frequency domain
Table 2 Parameters of the
proposed model No. of
layer
Layer Input shape Kernel size/stride/number of filters Output shape
1 Convolution (240, 64, 100) (3, 100)/1/64 (240, 64, 64)
2 Maxpooling (240, 64, 64) 3/3 (240, 21, 64)
3 Convolution (240, 21, 64) 3 ×64/1/128 (240, 21, 128)
4 Maxpooling (240, 21, 128) 3/3 (240, 7, 128)
5 Convolution (240, 7, 128) 3 ×128/1/128 (240, 7, 128)
6 Average pooling (240, 7, 128) / (240, 128)
7 Dropout (240, 128) / (240, 64)
8 Fully connected (240, 64) / (240, 3)
stochastic neighbour embedding (t-SNE) technique (Maaten
and Hinton 2008) is used to illustrate the output of each layer.
t-SNE is a machine learning algorithm for high dimensional
data visualization using nonlinear dimensionality reduction
technique. For the current case study, the feature outputted
by each layer is high-dimensional, whose shape is given in
Table 2(e.g., after dropout layer, the feature that is fed into the
fully connected layer for classification is a 1-by-64 vector).
We use the t-SNE technique to reduce the feature after each
layer to two-dimensional space in order to show how the data
“flow” from input to output, and thus to see how the features
belonging to the same state aggregate. Figure 9shows this
process during testing, in which the distance between points
represents the similarity of different samples. The symbols
“1” (red), “2” (blue) and “3” (green) in the figures represents
the “Absent”, “Oil”, and “Grease” lubrication states, respec-
tively. We see that the in the input layer, the dots of the three
states are completely mixed and no pattern can be observed
to distinguish different fault modes. With the convolutional
and pooling operations implemented, the mixed dots gradu-
ally separated, and in the output layer, dots belonging to the
same state are clustered and dots belongs to different state
are completely separated. In the output layer of Fig. 9,it
can be seen that all the features belonging to the same state
are clustered and the features belonging to different state are
completely separated. There is no confusion, corresponding
to 100% accuracy.
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Journal of Intelligent Manufacturing
Fig. 9 Model testing process
visualization by t-SNE, case
study 1
Input l ayer 1st layer 2nd layer
3rd layer 4th layer 5th layer
6th layer Output layer
Two well-known and widely used machine learning meth-
ods, i.e., feedforward backpropagation (BP) network and
support vector machine (SVM) are used here as comparison
methods. The sample length remains the same as that used
by the CNN model, and accordingly, the number of train-
ing samples and testing samples are unchanged. Since these
two methods normally accept low-dimensional or moderate-
dimensional data as input, each raw sample is pre-processed
by wavelet packet decomposition (WPD) to extract a feature
vector. Specifically, based on our prior knowledge on the
study of fault diagnostics using the vibration signal, a five-
level WPD is applied on each raw sample and accordingly
2532 frequency sub-bands of the raw sample are obtained.
The energy of each sub-band is calculated and concatenated
to form a 1-by-32 feature vector, which is the input of the BP
neural network and SVM.
A typical three-layer BP neural network is used. The num-
ber of neurons in the input layer and output layer are 32 and
3, which equals to the length of the feature vector and to the
three lubrication states, respectively. A hidden layer contain-
ing 10 neurons is adopted. Note that the number of neurons
in the hidden layer is typically an empirical value. Too many
or too few neurons may reduce the classification accuracy
of the network. We gradually increased the number of neu-
rons from 5 to 20, and finally set this value to 10, where the
network achieved its highest accuracy.
The basic SVM for binary classification is employed and
is turned into multi-classes classifiers by the strategy of “one-
vs-all”. The strategy involves training a single SVM classifier
for each class, with the samples of that class as positive
samples and all other samples as negatives. Specifically, for
the current case study of ball screw, we trained three basic
SVM classifiers that are able to diagnose “Absent”, “Oil”, and
“Grease”, respectively. The Radial Basis Function (RBF) is
used as the kernel function.
The diagnostics accuracies of BP neural network and
SVM are 95%, and 90%. The corresponding confusion matri-
ces are given in Fig. 10a, b, respectively. The last column in
the matrix shows the percentages of examples predicted to
belong to each label that are correctly classified (also called
precision, or positive predictive value). For example, in the
1st row of Fig. 10a, 19 samples are classified by the proposed
model as lubrication state “Absent”, while 18 out of these 19
are correctly classified. One sample that should belong to
label “Oil” are incorrectly classified as “Absent”. The pre-
cision for label “Absent” hence equals to 18/19 94.7%.
The row at the bottom of the matrix shows the percentages
of all the samples belonging to each class that are correctly
classified (also called sensitivity or true positive rate, recall,
probability of detection, etc.). For example, in the 1st col-
umn of Fig. 10a there are 20 samples of “Absent”. 18 out
of 20 are correctly classified and one sample is incorrectly
identified. The sensitivity for label “Absent” is thus 18/20
90%. The value in the bottom right corner is the overall
classification accuracy of the network, which equals to the
number of correctly classified samples divided by the total
number of testing samples, in this case, 95%.
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Journal of Intelligent Manufacturing
Fig. 10 Confusion matrices of
case study 1, given by aBP
neural network and bSVM
18
30.0 %
4
2.0%
0
0.0%
2
3.33%
16
26.7 %
0
0.0%
0
0%
0
6.2%
20
33.3 %
100%
0.0%
80.0 %
20.0 %
100%
0.0%
90.0 %
10.0 %
81.8 %
18.2 %
88.9 %
11.1 %
100%
0.0%
90.0 %
10.0 %
18
30.0 %
1
1.6%
0
0.0%
2
3.3%
19
31.7 %
0
0.0%
0
0.0%
0
0.0%
20
33.3 %
100%
0.0%
95.0 %
5.0%
100%
0.0%
90.0 %
10%
94.7 %
5.3%
90.5 %
9.5%
100%
0.0%
95.0 %
5.0%
Absent Oil GreaseAbsent Oil Grease
TargetTarget
Output of network
Output of netw ork
(a) (b)
Compared with the proposed CNN model, the overall
accuracies of the BP neural network and SVM are lower. Fig-
ure 10 indicates that confusions occur between the lubrication
states of “Absent” and “Oil”. Objectively, in real working
environment, the differences between “Absent” and “Oil”
are indeed small. This is also reflected in Fig. 8that the time-
domain and frequency-domain signals of these two states are
very similar and hard to be visually distinguished. In contrast
to the BP neural network and SVM, the CNN can well clas-
sify these two states.
Case study 2: Bearing fault diagnostics using CWRU
dataset
Data description and preparation
The public bearing fault dataset from Case Western Reserve
University (CWRU) (Case Western Reserve University
Bearing Data Center Website, https://csegroups.case.edu/
bearingdatacenter/home) is used to validate the proposed
model in this section. A benchmark study of CWRU dataset
was studied by (Smith and Randall 2015). As shown in
Fig. 11, the test bench consists of a 2 hp motor (1 hp 
735 W), a torque transducer/encoder, a dynamometer, and
control electronics. SKF-6202 deep groove ball bearings are
used as the test bearings and support the motor shaft. The
experiments were performed under four working conditions,
as reported in Table 3. Four fault modes: “Outer race fault”,
“Inner race fault”, “Ball fault” and “Normal” are introduced.
For each fault mode, a single fault point with three severi-
ties levels, i.e., fault diameters of 0.007 mil, 0.014 mil, and
0.021 mil were seeded, which is regarded as a different fault
mode. Therefore, there are 10 fault modes. Vibration data of
each fault type under each working condition were collected
using accelerometers, which were attached to the housing
with magnetic bases. The sampling rate was 48 kHz.
Fig. 11 Test bench of case study 2 [Case Western Reserve Uni-
versity Bearing Data Center Website, https://csegroups.case.edu/
bearingdatacenter/home]
Table 3 Description of working conditions
Working condition Motor load (hp) Motor speed (rpm)
1 0 1797
2 1 1772
3 2 1750
4 3 1730
The number of data acquired of each fault type under each
working condition are reported in Table 4. The amount of
data provided is different for each working condition. To
adapt this variation, the data preparation is adjusted. The
training/testing ratio is set to be 4:1. For conditions 2–4, the
number of data for each label is truncated to 4.8 ×105.6.4×
103data points are segmented and further reshaped to (64,
100) matrix as one sample. Thus 4.8 ×105/6.4 ×10375
samples for each fault mode are obtained. For condition 1,
the mode of the inner race damage with 0.014 mil is left out
due to insufficient data. Indeed, we are aware of some data
augmentation techniques such as adding noise or Genera-
tive Adversarial Network that may mitigate the problem of
123

Journal of Intelligent Manufacturing
Table 4 Description of CWRU bearing fault data
Fault mode Fault label Number of data points available in each working condition
Condition 1 Condition 2 Condition 3 Condition 4
Normal 1 243,938 483,903 483,903 485,643
Inner race fault with fault diameter 0.007 mil 2 243,938 486,224 485,643 485,643
Inner race fault with fault diameter 0.014 mil 3 63,788 489,125 487,964 485,063
Inner race fault with fault diameter 0.021 mil 4 244,339 485,063 491,446 491,446
Outer race fault with fault diameter 0.007 mil 5 243,538 486,804 486,804 487,964
Outer race fault with fault diameter 0.014 mil 6 245,140 484,483 486,804 488,545
Outer race fault with fault diameter 0.021 mil 7 246,342 489,125 487,964 489,125
Ball fault with fault diameter 0.007 mil 8 243,938 487,384 486,804 488,545
Ball fault with fault diameter 0.014 mil 9 249,146 486,224 487,384 486,804
Ball fault with fault diameter 0.021 mil 10 243,938 486,804 487,384 486,804
Fig. 12 Model testing process
visualization under condition 2,
case study 2
Input layer 1
st
layer 2
nd
layer
3
rd
layer 4
th
layer 5
th
layer
6
th
layer Output layer
1 - red
2 - yellow
3 - blue
4 - green
5 - verdigris
6 - magenta
7 - gray
8 - pink
9 - meadow
10 - purple
1
3
2
4
5
96
7
8
10
insufficient data, but such an investigation will be left for our
coming work. The data of other modes is truncated to 2.4 ×
105.2.4×103data points are segmented and further reshaped
to (24, 100) as one sample. 100 samples are obtained for each
fault label, and there are hence 80 ×9720 samples for
training and 20 ×9180 samples for testing.
Results and discussions
For each condition the diagnostics accuracy on the test set is
100%. Due to the space limitation, only the feature learning
process during testing of condition 2 are visualized by t-SNE,
asshowninFig.12. The 10 symbols in different colours
represents the 10 fault labels of condition 2. It can be seen
that from the 5th layer, features of same fault mode have
already been well aggregated and the features belonging to
different modes have been well separated.
Case study 3: Bearing fault diagnostics with private
dataset
Experiment and data preparation
In this case study, we validate the proposed model with the
bearing fault dataset acquired from our own test bench, as
shown in Fig. 13. Seven health states are considered, includ-
123

Journal of Intelligent Manufacturing
Bearing
Accelerometer
Laser sensor
Speed
controller
Motor
Fig. 13 Private test bench for bearing fault
ing the normal state, four types of single-point faults (i.e.,
inner race, outer race and ball), and three types of compound
faults (i.e., inner race and ball, inner race and outer race, outer
race and ball). Based on the literature and based on our obser-
vations and experiences, these faults are the most frequently
occurs. The vibration data are collected from an NSK-6308
deep groove ball bearing in the experiment performed under
three motor speeds 1500 rpm, 2000 rpm and 2500 rpm at
the sampling rate 20 kHz. For each health state under each
motor speed, the data acquisition lasts for 256 seconds, thus
5.12 ×106data points are acquired. 6.4 ×103data points
are segmented and further reshaped to (64, 100) matrix as
one sample. Thus 800 samples are obtained for each health
state. The train/test ratio is set to 4:1. Figure 14 illustrates the
vibration signal recorded in one second corresponding to the
eight health states. For confidentiality reasons, the raw data
is normalized to (−1, 1).
Results and discussions
The diagnostics confusion matrices obtained on the test set
for all three motor speeds are shown in Fig. 15, where the
accuracies are nearly 100%. Labels 0–6 representes the fol-
lowing fault modes, i.e., 0-ball, 1-inner race, 2-outer race,
3-compound fault of inner race and ball, 4-compound fault
of outer race and ball, 5-compound fault of outer race and
inner race, 6-normal.
Due to the space limitation, only the feature learning
process during testing under the motor speed 1500 rpm is
visualized by t-SNE, as shown in Fig. 16. It can be seen that
in the output layer the features of same fault mode have been
well aggregated and the features belonging to different modes
have been well separated. Note that in the output layer, the
samples belonging to “6” are totally aggregate. Very few con-
fusions occur between “3” and “4”, and between “4” and “5”,
which is consistent with the confusion matrix of Fig. 15a.
Case study 4: PHM 2009 spur gearbox challenge data
Data description and preparation
The 2009 PHM data challenge of gearbox fault data is used
in this case study. Readers are referred to “PHM data chal-
lenge 2009,https://www.phmsociety.org/competition/PHM/
09” for more information about the experiment setting. The
overview of the apparatus is shown in Fig. 17a, including
the drive system, a tachometer for providing zero-crossing
information, the testing gearbox, and two accelerometers for
collecting data. Two sets of gears, i.e., spur gears and helical
gears were tested. We used the data of the spur gear since it
contains more fault modes than that of the helical gears. The
spur gearbox is a generic industrial one containing 3 shafts,
4 gears and 6 bearing, as shown in Fig. 17b. The teeth of the
input gear, 1st idler gear, 2nd idler gear and the output gear
are 32, 96, 48, and 80, respectively. Therefore, from input
to output the gear reduction ratio is (16/48) ×(24/40), or 5
to 1 reduction. For the gearbox, instead of single-point fault,
eight types of compound faults caused by gear chipped, gear
eccentric, bearing ball fault, shaft imbalance, shaft keyway
fault, etc. are considered. The detail descriptions of the eight
fault types are reported in Table 5. The faults were seeded in
the experiments. These faults covered the common failures
of gearboxes in real cases.
The experiments were carried out under 10 working condi-
tions, i.e., 1800, 2100, 2400, 2700, 3000 rpm (revolutions per
minute) shaft speed under high and low loading, respectively.
For each fault type under each working condition, vibration
signals were sampled synchronously from accelerometers
mounted on both the input and output shaft retaining plates,
as shown in Fig. 18. Data were acquired with a sampling
rate 66.67 kHz and sampling time 4 s, and thus 266,655 data
points are obtained and further truncated to 2.56 ×105for
each fault type. Additionally, for each working condition,
the experiment was repeated twice.
For data preparation, 6.4 ×103data points are segmented
and reshaped to (64, 100) as one sample. Therefore, 80 sam-
ples are obtained for each label. We randomly draw 80%
data (64 samples) for training and the 20% data (16 samples)
for testing. Finally, the training/testing data taken from each
label form the training sets (512 samples) and the testing sets
(128 samples).
Results and discussions
For all the 10 working conditions, the testing accuracy of
the eight types of faults are 100%. Due to space limitation,
we only show the feature learning process during testing at
working condition 2700 rpm under low loading as an exam-
ple, as given in Fig. 19. The labels 1–8 represent the fault
label as listed in Table 6.
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Journal of Intelligent Manufacturing
Fig. 14 Visualization of the raw vibration data of the eight heath states
The fivefold cross validation is used to evaluate the model.
All samples and corresponding labels are randomly divided
into five groups (the total number of samples in each group
is the same). Each round four out of the five groups are used
for training the model and the remaining is used for testing.
By cross validation, the model has been tested five times
and all the samples have the chance of being training/testing
data. Since the samples are totally divided randomly, in each
group the number of samples belonging to each label may
imbalanced. For all the ten working conditions, the testing
accuracies are 100%. We take working condition 2700 rpm
shaft speed and low loading as an example and show the
confusion matrices of the five testing results in Fig. 20.
Comparison with traditional diagnostics methods
The method of signal processing based feature extraction
combined with a long short-term memory (LSTM) network
123

Journal of Intelligent Manufacturing
159
14.2%
0
0.0%
0
0.0%
2
0.2%
152
13.6%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
163
14.5%
163
14.5%
163
14.5%
27
33.3%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
1
1.2%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
2
0.2%
1
0.1%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
167
14.9%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
27
33.3%
98.8%
1.2%
100.0%
0.0%
100.0%
0.0%
98.8%
1.2%
99.4%
0.6%
100.0%
0.0%
148
13.2%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
100.0%
0.0%
100.0%
0.0%
98.0%
2.0%
100.0%
0.0%
98.7%
1.3%
100.0%
0.0%
100.0%
0.0%
100.0%
0.0%
99.6%
0.4%
02134
56
(c)
motor speed 2500 rpm
161
14.4%
0
0.0%
0
0.0%
0
0.2%
152
13.6%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
163
14.6%
163
14.6%
164
14.6%
27
33.3%
0
0.0%
0
0.0%
0
0.0%
1
0.3%
1
1.2%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
1
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.3%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
167
14.9%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
27
33.3%
100.0%
0.0%
100.0%
0.0%
100.0%
0.0%
98.8%
1.2%
100.0%
0.0%
100.0%
0.0%
148
13.2%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
100.0%
0.0%
100.0%
0.0%
99.3%
0.7%
100.0%
0.0%
100.0%
1.3%
100.0%
0.0%
100.0%
0.0%
99.4%
0.6%
99.8%
0.2%
02134
56
100.0%
0.0%
100.0%
0.0%
100.0%
0.0%
100.0%
0.0%
100.0%
0.0%
98.2%
1.8%
98.2%
1.8%
99.5%
0.5%
(b)
motor speed 2000 rpm
Output health st ate label of network
161
14.4%
0
0.0%
0
0.0%
0
0.2%
152
13.6%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
163
14.6%
162
14.5%
164
14.6%
27
33.3%
0
0.0%
0
0.0%
0
0.0%
3
0.3%
1
1.2%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
3
0.3%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
164
14.6%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
27
33.3%
100.0%
0.0%
100.0%
0.0%
100.0%
0.0%
98.2%
1.8%
100.0%
0.0%
98.2%
1.8%
148
13.2%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
100.0%
00.0%
02134
56
(a)
motor speed 1500 rpm
Actual health state lab e Actual health state labe Actual health state lab e
Fig. 15 Confusion matrix of case study 3 under three motor speed, given by proposed CNN model
Fig. 16 Model testing process
visualization under motor speed
1500 rpm, case study 3
Input layer 1
st
layer 2
nd
layer
3
rd
layer 4
th
layer 5
th
layer
6
th
layer Output layer
2
0
4
3
5
6
1
0 - red
1 - yellow
2 - blue
3 - green
4 - verdigris
5 - magenta
6 - gray
as a classifier (which is referred to as traditional method from
now on) is utilized to compare with the proposed.
CNN model in the above four case studies. The flowchart
of the traditional method is shown in Fig. 21. The time
domain signal of different health states is firstly divided
into data segments. Then three manually extracted features,
i.e., wavelet packet energy (WPE) based on wavelet packet
decomposition (Zhang et al. 2013), instantaneous frequency
(IF) (Boashash 1992a,1992b) and instantaneous spectral
entropy (ISE) (Pan et al. 2008) based on power spectrogram,
123

Journal of Intelligent Manufacturing
Fig. 17 Gearbox used in 2009
PHM data challenge [PHM data
challenge 2009,https://www.
phmsociety.org/competition/
PHM/09]
Tested gearbox
Drive system
Tachometer
Accelerometer
Table 5 Fault modes description of 2009 PHM spur gears
Fault label Fault description
Gear Bearing Shaft
32T 96T 48T 80T IS:IS ID:IS OS:IS IS:OS ID:OS OS:OS Input Output
1 Good Good Good Good Good Good Good Good Good Good Good Good
2 Chipped Good Eccentric Good Good Good Good Good Good Good Good Good
3 Good Good Eccentric Good Good Good Good Good Good Good Good Good
4 Good Good Eccentric Broken Ball Good Good Good Good Good Good Good
5 Chipped Good Eccentric Broken Inner Ball Outer Good Good Good Good Good
6 Good Good Good Broken Inner Ball Outer Good Good Good Imbalance Good
7 Good Good Good Good Inner Good Good Good Good Good Good Keyway
Sheared
8 Good Good Good Good Good Ball Outer Good Good Good Imbalance Good
Tteeth of the gear, IS input shaft, ID idler shaft, OS output side, OS output side, IS input side
Fig. 18 The location of input
and output shaft accelerometers
[PHM data challenge 2009,
https://www.phmsociety.org/
competition/PHM/09]
Locati on of input
shaft accelerom eter
Location of outpu t
shaft accelerometer
are constructed from each data segment. The LSTM serves
as the classifier. Therefore, three traditional methods, i.e.,
WPD-LSTM, IF-LSTM, ISE-LSTM are compared.
The architecture of the LSTM is composed of a sequence
input, one LSTM layer, a fully connected layer and a soft-
max layer. The fully connected layer multiplies the input
by the weight matrix and adds a bias vector. The output
is finally calculated by a softmax transfer function. For the
hyperparameters of LSTM, through initial trials we found
that the number of LSTM units and batch size are two obvi-
ous parameters that affect the accuracy, given an appropriate
learning rate. Specifically, we changed the number of LSTM
units consecutively from 22to 29for the four case studies
and found that a large amount of LSTM units are normally
required when the number of training samples is large, and
verse vice. For instance, in case study 1, where 240 training
samples are available, a LSTM network with 128 units (or
even fewer) performs better than that with 256 units, while
in case study 2 in which 720 training samples are available, a
LSTM network with 256 units are better than that with fewer
units. In terms of batch size, we find that a smaller batch size
tends to result in a higher accuracy but the training oscilla-
tion increases accordingly. In addition, too small batch sizes
suffer the risk of non-convergence.
123

Journal of Intelligent Manufacturing
Fig. 19 Model testing process
visualization under 2700 rpm
and low loading, case study 4
Input layer 1
st
layer 2
nd
layer
3
rd
layer 4
th
layer 5
th
layer
6
th
layer Output layer
Specifically, the accuracies with all three features of WPE,
IF and ISE in case study 3 are high. Figure 22 illustrates
the confusion matrices in case study 3 under motor speed
1500 rpm as an example. The accuracies of IF-LSTM and
ISE-LSTM are acceptable in the application of gearbox under
the low loading condition, but dramatically decrease under
the high loading as well as in the case of ball screw. WPE,
which performs the best among the three manually extracted
features in many cases but suffers the risk of non-convergence
in some working conditions of gearbox application. The con-
fusion matrices given by the traditional methods for gearbox
application under speed 2700 rpm and low loading are shown
in Fig. 23 as an example. The accuracy given by WPE-LSTM
is very low due to non-convergence. In contrast, the proposed
CNN model can well identify the eight health states under
this working condition, which can be clearly visualized in
Fig. 19.
Through the comparison among the proposed CNN model
and the traditional methods in various applications under
various working conditions, it can be seen that the pro-
posed CNN model exhibits much more robustness, giving
consistently high accuracies in all four case studies. More-
over, the end-to-end structure of the CNN model requires
less reliance on empirical expertise and advanced signal pro-
cessing techniques, which enables the proposed model to be
easily adapted to different diagnostics tasks.
Conclusions and future work
Manual feature extraction based on signal processing tech-
niques is normally required in traditional diagnostics for
rotating machinery, which has the drawbacks such as strong
dependencies on the expertise and prior knowledge, the
requirement for lots of skilled human labour, the sensitiv-
ity to changes, etc., and thus requires extensive fine-tuning.
Some recent works based on deep learning convert the vibra-
tion signal to images based on some time-frequency methods,
which can circumvent some of the previous drawbacks but
still need application-specific adaptation. In this paper, we
proposed an end-to-end health state diagnostics model based
on convolutional neural network (CNN), which can directly
learn feature representation from the raw vibration signal
and no manually extracted feature is required. In addition,
to fully validate the effectiveness and the generalizability of
the proposed model for fault diagnostics of the rotating com-
ponent, we carried out tests on four datasets, including two
public ones and two datasets of our own, covering the appli-
cations of ball screw, bearing and gearbox. The results show
high diagnostics accuracies for all the four tasks. To our best
knowledge, our work firstly validates the CNN model in such
wide applications.
Moreover, the signal processing based feature extraction
combined with long short-term memory (LSTM) network
123

Journal of Intelligent Manufacturing
14
10.9%
0
0.0%
0
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12
9.4%
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20
15.6%
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9.4%
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17.2%
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33.3%
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4.7%
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33.3%
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14.1%
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24
18.8%
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0
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True Label
Predicted label
22
17.2%
0
0.0%
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0
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16
12.5%
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22
17.2%
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12
9.4%
27
33.3%
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1.2%
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27
33.3%
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100.0%
0.0%
100.0%
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100.0%
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16
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0
0.0%
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0
0.0%
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00.0%
100.0%
0.0%
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0.0%
100.0%
0.0%
100.0%
0.0%
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0.0%
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0.0%
100.0%
0.0%
164
14.6%
0
0.0%
0
0.0%
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0.0%
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0.0%
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00.0%
164
14.6%
0
0.0%
0
0.0%
0
0.0%
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0.0%
0
0.0%
0
0.0%
0
0.0%
100.0%
0.0%
8
6.3%
0
0.0%
0
0.0%
True Label
Predicted label
14
10.9%
0
0.0%
0
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0
0.0%
16
12.5%
0
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0
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0
0.0%
0
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0
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0
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14
10.9%
20
15.6%
12
9.4%
27
33.3%
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20
15.6%
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0
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27
33.3%
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14
10.9%
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164
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164
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0
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100.0%
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18
14.1%
0
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True Label
Predicted label
16
12.5%
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0
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18
14.1%
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20
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22
17.2%
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0.0%
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18
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0.0%
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0.0%
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164
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164
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0
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0.0%
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0.0%
100.0%
0.0%
8
6.3%
0
0.0%
0
0.0%
True Label
Predicted label
14
10.9%
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0.0%
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0.0%
0
0.0%
18
14.1%
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0.0%
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0.0%
0
0.0%
0
0.0%
0
0.0%
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10
7.8%
18
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14
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27
33.3%
0
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0.0%
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18
14.1%
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0.0%
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27
33.3%
100.0%
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14
10.9%
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0.0%
100.0%
00.0%
100.0%
0.0%
100.0%
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100.0%
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100.0%
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164
14.6%
0
0.0%
0
0.0%
0
0.0%
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0
0.0%
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100.0%
00.0%
164
14.6%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
0.0%
0
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0
0.0%
100.0%
0.0%
22
17.2%
0
0.0%
0
0.0%
True Label
Predicted label
Fig. 20 Testing accuracies of fivefold cross validation under the working condition 2700 rpm shaft speed and low loading
(here is referred to as traditional method) is also explored and
compared with the proposed CNN model. Specifically, three
typical engineered features, i.e., (a) wavelet packet energy
(WPE) based on wavelet packet decomposition, (b) instanta-
123

Journal of Intelligent Manufacturing
Fig. 21 Flowchart of the
implementation of the
traditional methods
Dat a seg me ntati onDat a seg me ntati onDat a seg me ntati on
Wavelet packet decompos ition, Power spectr ogram
Build LSTM network
Train network
Input test set
Diagnostics result
wavelet packet energy (WPE), Instantaneous frequency(IF), Instantaneous
spectral entropy (ISE)
. . . . . . . . .
Extracted features of training sets
Trained model
Extracted features of testing sets
Testing set Training set
Health state 1 Health state 2 Health state n
. . .
Actual health state lab el
0213456
(a)
WPE-LS TM
(b)
IF-LSTM
(c)
ISE-LS TM
0213456 0213456
Actual health state lab el Actual health state lab el
Fig. 22 Confusion matrix of case study 3 under motor speed 1500, given by the traditional method
123

Journal of Intelligent Manufacturing
Output health state label of network
1324567
(a) WPE-LS TM (b) IF-LSTM (c) ISE-LSTM
Actual health state label
813245678 13245678
Actual health state label Actual health state label
Fig. 23 Confusion matrix of case study 4 under speed 2700 rpm and low loading, given by the traditional method
Table 6 Accuracies of proposed CNN and traditional methods in all case studies
Case study Working
conditions
Number of labels Proposed CNN model (%) WPE-LSTM (%) IF-LSTM (%) ISE-LSTM (%)
1 500 rpm, 0 load 3 100 97.3 ±3.2 86.8 ±4.3 69.6 ±5.6
2 1797 rpm, 0 load 9 100 79.4 ±5.0 89.2 ±2.5 90.3 ±3.5
1772 rpm, 1hp load 10 100 92.7 ±5.2 86.4 ±6.0 82.2 ±4.5
1750 rpm, 2hp load 10 100 82.2 ±7.4 86.8 ±1.8 88.7 ±3.6
1730 rpm, 3hp load 10 100 92.4 ±7.0 86.8 ±3.6 79.4 ±4.6
3 1500 rpm, 0 load 7 99.5 ±0.5 96.3 ±2.1 97.5 ±2.4 92.2 ±2.5
2000 rpm, 0 load 7 99.8 ±0.5 95.4±5.9 99.1 ±2.3 92.3 ±2.1
2500 rpm, 0 load 7 99.5 ±0.5 98.5±3.4 94.6 ±2.4 99.4 ±2.1
4 1800 rpm, low load 8 100 93.4 ±3.6 90.1 ±2.3 81.9 ±4.1
1800 rpm, high load 8 100 91.0 ±1.7 82.1 ±7.3 84.5 ±2.3
2100 rpm, low load 8 100 99.5 ±0.5 88.0 ±8.4 89.4 ±5.4
2100 rpm, high load 8 100 – 83.5 ±3.4 84.0 ±2.1
2400 rpm, low load 8 100 98.6 ±1.7 89.9 ±2.5 90.7 ±1.8
2400 rpm, high load 8 100 86.8 ±2.4 82.2 ±2.9 81.1 ±2.7
2700 rpm, low load 8 100 – 97.1 ±1.9 89.7 ±2.4
2700 rpm, high load 8 100 92.2 ±4.6 84.0 ±1.6 76.9 ±2.7
3000 rpm, low load 8 100 95.2 ±5.9 90.9 ±4.0 91.0 ±1.7
3000 rpm, high load 8 100 96.1 ±2.7 82.2 ±1.6 76.8 ±2.1
“–” represents non-convergence
neous frequency (IF), and (c) instantaneous spectral entropy
(ISE) based on power spectrogram, are constructed from the
raw vibration data and then used as the input of a clas-
sifier (LSTM network). The results indicate that manually
extracted features based on signal processing techniques are
indeed sensitive to diagnostics tasks. One feature performs
well in one task but may fail to give satisfactory accuracy
or lead to non-convergence in another task. The comparison
shows that the proposed CNN based model has indeed good
robustness and ability of generalization that is easy to adapt
to different diagnostics task without any manual tuning.
The limits of the current work, and the corresponding
future work are summarized as follows. The current work
used the data acquired from the test benches of the laboratory.
Next, we will investigate the performance of the proposed
model in real industry environment. In the current work, the
high diagnostics accuracy of each application is based on the
assumptions that sufficient labeled data are available, and that
the training and testing data are from the same distribution,
which may be a limiting factor in industrial applications.
To release these assumptions, our future work will focus
on transfer learning methods, which are able to transfer
123

Journal of Intelligent Manufacturing
vibration-based diagnostics capabilities to new working con-
ditions, experimental protocols and instrumented devices
while avoiding the requirement for new labeled fault data.
By this way, the diagnostics models trained with laboratory
data have the potential of being used in the real industry envi-
ronment. In the current work, the fault data of each label are
balanced. In our future work, we will focus on building the
diagnostics model when the fault data are unbalanced, i.e.,
only small fault data or even no fault data are available for
some specific fault labels, since in practice, faults of high-
stakes industrial devices are rare. In addition to the single
fault type considered in the current work, we will study the
fault diagnostics of compound faults. The issue of low signal
to noise ratio in the acquired vibration signal caused by the
strong coupling of different components is also our interests
for future work.
Acknowledgements The present work was funded by the National Nat-
ural Science Foundation of China (No.51805262) and the Graduate
Student Innovation Fund of Beihang University (YCSJ-03-2019-06).
The authors gratefully acknowledge the Key Laboratory of Performance
Test for CNC Machine Tool Components affiliated of Ministry of Indus-
try and Information Technology of China for providing the ball screw
test bench and experiment materials.
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