Rolling Bearing Fault Diagnosis based on DWT-BPNN
YANG PEIXI1, XIAOYANG ZHENG1, JIANGPING HE2
1School of Artificial Intelligence, Chongqing University of Technology, Chongqing 400054, CHINA
2School of Science, Chongqing University of Technology, Chongqing 400054, CHINA
Abstract: - For the fault diagnosis of rolling bearings, it is of great significance to improve the diagnostic
accuracy. Therefore, this paper presents a rolling bearing fault diagnosis method which combines Daubechies
wavelet (DW) with back propagation neural network (BPNN). Specifically, Daubechies wavelet transform is
utilized to decompose the vibration signal of the original data in to different frequency components, which can be
implemented to extract more prominent fault features. Then, the extracted features are input into BPNN
classification model for fault diagnosis by training and testing. Finally, various experiments are carried out on the
rolling bearing dataset of Western Reserve University to verify the effectiveness of this method. The results of
this study demonstrate that the proposed method is able to reliably identify different fault categories with higher
accuracy in comparison with the FT-BPNN methods based on Fourier transform under different loading
conditions, and provides a new and effective method for the fault diagnosis of rolling bearings.
Key-words: Rolling bearing; Fault diagnosis; BP neural network; Wavelet transform.
Received: June 17, 2022. Revised: February 14, 2023. Accepted: March 4, 2023. Published: March 15, 2023.
1 Introduction
Rolling bearing is one of the indispensable
components of mechanical equipment, and it is also
one of the most vulnerable components [1, 2].
According to data statistics, about 30% of the
malfunctions of rotating machines are caused by
rolling bearings [3]. Once the bearing fails, it may
affect the safe operation of the whole machinery and
equipment, which may cause economic losses or
endanger personal safety [4]. Therefore, the research
of reliable fault diagnosis methods and accurate
diagnosis of the health of rolling bearings can
effectively improve the safety and reliability of
equipment operation.
The traditional intelligent fault diagnosis
methods mainly based on machine learning and
statistical inference techniques, such as artificial
neural networks, random forest, K-nearest neighbor,
Naive Bayesian, support vector machines, fuzzy
inference and other developed methods, are almost all
need to extract the features of the raw data depended
on experience and lacking adaptability [2-7]. To solve
this issue, various signal processing methods such as
Fourier transform, variational mode decomposition,
wavelet decomposition and wavelet packet transform
are used to artificially select feature vector as the
input of the intelligent classifiers to realize the fault
recognition and classification.
This paper proposes a method combining
Daubechies wavelet transform and BPNN is proposed
for fault diagnosis of rolling bearings. It first utilizes
Daubechies wavelet transform (DWT) to decompose
the raw data into the low frequency and high
frequency components. The frequency signals at
different resolution levels can effectively represent
the discriminative fault characteristics of the rolling
bearing without redundant and leakage owing to its
orthogonality. The extracted features are introduced
into the BPNN model, and then the health status of
rolling bearings is classified by BPNN. The
experimental results demonstrate that the proposed
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method has great merits of high diagnosis accuracy
than the FT-BPNN method based on Fourier
transform.
The structure of this paper is organized as
follows: Section 2 introduces Daubechies wavelet
transform and back propagation neural network
structure. In Section 3, The method proposed in this
paper is introduced in detail. In Section 4, the
proposed method is applied to identify the different
fault categories of the rolling bearing, and the
diagnosis results are utilized to compare with the
FT-BPNN method. Finally, Section 5 gives some
conclusions of this research and prospects for the
future work.
2 Wavelet transform and BPNN
In this section, the concept and properties of
Daubechies wavelet basis is first introduced. In the
second step, the decomposition of DWT is
specifically described in this context. Finally, the
structure of BPNN is elaborately described.
2.1 Daubechies Wavelet Basis
Daubechies wavelet has been widely implemented to
diagnose faults in various fields as it can match the
transient components of the fault characteristics in
vibration signals. In this subsection, a family of
orthogonal Daubechies wavelets with compact
support is elaborately introduced, which has been
constructed by Daubechies [2-7].
For every even positive integer , each
Daubechies wavelet family is governed by the
two-scale relation
√2∑
ℎ
2
, （1）
where 0,1,⋯,1. Based on the scaling base
, the wavelet base function can be written
as
√2∑2
, （2）
where the
ℎ
and
are the low pass
and high pass filters, respectively, and
1
ℎ
. For example, Haar wavelet
1, 1/√2,1,1/
√2, and Daub 3 wavelet
1 √3, 3√3,3√3,1√3/4√2,
3, 2, 1, 0, respectively.
Furthermore, the corresponding wavelet base is
usually designed with vanishing moments that are
defined as follows.
0, for 01,（3）
which make it orthogonal to the low degree
polynomials, and so tend to compress non-oscillatory
functions. In addition, the scaling function has
support in 0, 1 ], while the corresponding
wavelet has support in the interval 1 /2, /2
and has/2vanishing wavelet moments.
2.2 Wavelet Transform
Wavelet transform can be considered as a
mathematical tool that converts a signal into a series
of scale and wavelet coefficients, respectively [6].
Sample onto the finest resolution level and apply the
filters , , then the low frequency components ,
and high frequency components , for resolution
levels can be calculated by
, ∑
ℎ
,, （4）
, ∑,. （5）
where , and , are the low frequency and high
frequency components at the resolution level , i.e.,
the approximation and detail coefficients, respectively.
Therefore, the signal is decomposed into a
hierarchical structure of detail and approximations at
the finest level as follows.
: ∑,
,
. （6）
The DWT is a advanced signal processing technique
which decomposes the extracted signal into a range of
varying frequencies and mother wavelets that helps in
defining the time-frequency multi-resolution analysis
(MRA).
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Fig. 1: Decomposition tree of wavelet transform.
The rolling bearing signal measured is
decomposed into approximate (s) and detailed (d)
coefficients representing the low-frequency and
high-frequency components respectively as shown in
Fig. 1. By invoking the norm function in MATLAB,
calculate d1, d2, d3, and s3 respectively to obtain
norm features. Then, these features are introduced
into the BPNN model.
2.3 A brief Introduction to BPNN
As one of the most important machine learning
structure models, the BPNN model has been widely
applied with great success to various fault recognition
fields. In this subsection, the structure of the BPNN
model is explained in details.
Fig. 2: Basic structure of BP network
The main structure of the BPNN model is a
multi-layer network, which consists of one input layer,
one or more hidden layers, and one output layer [7].
The input layer receives data, the output layer outputs
data, the neurons in the previous layer are connected
to the neurons in the next layer, and the information
transmitted by the neurons in the previous layer is
collected. The information is activated by the
activation function, and then the value is passed to the
next layer as elaborately depicted in Fig.2.
3 The proposed method
DWT is implemented to decompose the raw vibration
signal into different frequency components at
different resolution levels, which can improve the
diagnosis accuracy by the BPNN model.
Correspondingly, the flowchart is shown in Fig. 3 and
explained in detail.
3.1 Proposed Algorithm
In this subsection, the vibration signal of the dataset
provided of the Bearing Data Center of Case Western
Reserve University is first decomposed into 1
parts, which consist of one low frequency component
and high frequency components, respectively,
where denotes the resolution level. Finally, the
1 features are dimensionally reduced and then
input into the BPNN model for the fault condition
identification of the rolling bearing. For the situation
of the resolution level 3 ,the specific process of
the DWT-BPNN model is detailed demonstrated in
Fig. 3 as follows.
According to the flowchart demonstrated in Fig.
3, the general steps of the DWT-BPNN method are
described in detailed as follows.
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Fig. 3: Flowchart of the DWT-BPNN model for the
rolling bearing fault diagnosis
Step 1: The vibration signal of the rolling bearing
is collected under different loads for the fault
recognition using the DWT-BPNN method in this
work.
Step 2: The sample with 4096 points of the
vibration signal is decomposed into 4 frequency
components by DWT at resolution level 3 as shown in
Fig. 1. Then the norm function is invoked in
MATLAB to process d1, d2, d3, and s3 to obtain norm
features. And they are used as the input of the BPNN
model.
Step 3：The sample is randomly divided into 10
parts, 9 of which are used for training and 1 for testing.
The experiment was repeated ten times.
Step 4：Finally, the fault features are input into
the BPNN model to identify health conditions of the
rolling bearing.
4 Diagnosis Results and Analysis
For the situations of different loads, the high diagnosis
accuracy obtained by the proposed method is used to
compare with FT-BPNN method. The comparison
results show that the proposed method is more stable
and achieves the higher recognition accuracy. Finally,
two-dimensional visualizations of the different
classification features extracted by DWT-BPNN fault
diagnosis method is elaborately described by the
t-SNE method. In addition, all approaches described
above are implemented with Python and tested on a
computer with an AMD Ryzen 7 5800H CPU @ 3.20
GHz /4.40 GB RAM.
4.1 Description of Experiment Dataset
In this subsection, the vibration signal of the dataset
provided of the Bearing Data Center of Case Western
Reserve University is detailed described and the
corresponding ten fault categories are demonstrated in
Fig. 4. Then, how to adopt the configuration of
involved parameters and the training samples and the
testing samples of the fault identification using
vibration data of the rolling bearing are specifically
introduced, respectively.
Fig. 4: The raw vibration signal of 10 health
conditions of the bearing.
The components of the experimental apparatus
are mainly composed of a three-phase induction
motor, a torque transducer and a load motor. Each
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bearing data during testing are measured by
acceleration transducers on four different loads (0 hp,
1 hp, 2 hp and 3 hp) and the sampling rate is 12 kHz.
The rotating speed changes between 1730 and 1797
rpm based on the applied load. There are four bearing
health conditions: healthy condition (H), outer race
fault (OF), inner race fault (IF) and ball fault (BF).
The diameters of damage size are 0.007, 0.014, 0.021,
0.028 inches, respectively. Therefore, the dataset
includes 10 bearing health conditions under the 4
loads. Then, the detailed descriptions of motor
bearing are presented in Table 1. For the convenience
of analysis and classification, three faults (inner race,
outer race and ball) with 0.007 inches are simplified
as IR7, OR7 and B7, and abbreviation of other fault
types is similar to this, and the 10 health conditions
with different fault location and fault size are
artificially set as class label 1 to 10 in this paper,
respectively.
As shown in Fig. 4, the original data points under
10 health conditions were divided into 100 samples on
average, and each sample with 4096 data points is
obtained by a sliding window in a manner of partial
overlap. Then, 1000 samples can be obtained, each of
which is the vibration signal sequence of the bearing.
As illustrated in Fig. 4, the differences of a few
fault categories are obvious but the most of fault
patterns can not be easy to distinguish. Consequently,
it is very necessary to apply DWT-BPNN method to
effectively rectify different fault categories of the
rolling bearing.
4.2 DWT-BPNN
In this experiment, the raw rolling bearing signal is
mapped into high level representative fault
characteristics, i.e., the frequency components
obtained by DWT at resolution level 3 consist of one
low frequency component and three high frequency
components without any loss information. Then, 1000
frequency samples can be obtained by this process
and are implemented to verify the rolling bearing 10
fault categories by the BPNN model. For the purpose
of avoiding particularity and contingency, the
experiment is conducted by 10 trials. Finally, the
average testing accuracy is detailed listed in Table 2
for 10 trials.
In addition, the configuration parameters of the
BPNN model are elaborately illustrated in Table 3.
The learning rate is 0.005 and the iteration number is
1000. The optimizer uses Adam.
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Table 2. Average test accuracy of the two methods under various load
Table 3. The configuration parameters of the highest
average diagnosis accuracy.
In order to avoid contingency, ten trials are
carried out for diagnosing the same rolling bearing
dataset. Test results indicate that a better classification
performance can be obtained by using the proposed
fault diagnosis method in comparison with the
FT-BPNN method. Correspondingly, the
classification results of DWT-BPNN method for 10
trials are elaborately illustrated in Table 4.
4.3 Comparison with FT-BPNN
In this subsection, another one popular fault diagnosis
method the FT-BPNN method is implemented to
compare with DWT-BPNN method.
FT-BPNN method: First, the raw data is
transformed by Fourier transform. By invoking
function in , the artificially selected max、min、mean
and norm fault features are fed into BPNN for fault
diagnosis. The configuration parameters of the BPNN
model are elaborately illustrated in Table 3.
As shown in Fig. 5 and Table 5, The results of ten
experiments of DWT-BPNN method and FT-BPNN
method under four loads and the corresponding
histogram comparison are presented. Under each load,
the accuracy of the FT-BPNN method fluctuates
significantly. In addition, the DWT-BPNN method
performs better than the FT-BPNN method. This
indicates that the proposed method can efficiently
verify different fault categories of the rolling bearing
and has higher accuracy than the FT-BPNN method.
Fig. 5: Diagnosis accuracy of the above methods for 10 trials.
Table 4. Average test accuracy of the two methods under various loads.
Method 0hp 1hp 2hp 3hp
DWT-BPNN 0.9940±0.006633 0.9730±0.019519 1.0000±0.000000 1.0000±0.000000
FT-BPNN 0.9520±0.032496 0.9100±0.052536 0.9120±0.023152 0.9610±0.016401
Input layer Hidden
layer
Output
layer
Activation
function
4 128-24 10 Sigmoid
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(Note: the format of recognition result is average testing accuracy standard deviation)
Table 5. Diagnosis results of DWT-BPNN methods for each fault type.
Loads 1 2 3 4 5 6 7 8 9 10
0hp 1 1 0.99 0.99 0.99 0.99 0.98 1 1 1
1hp 0.97 0.99 1 0.97 0.98 0.95 0.93 0.97 0.98 0.99
2hp 1 1 1 1 1 1 1 1 1 1
3hp 1 1 1 1 1 1 1 1 1 1
Table 6. Diagnosis results of FT-BPNN methods for each fault type.
Loads 1 2 3 4 5 6 7 8 9 10
0hp 0.98 0.95 0.87 0.96 0.92 0.98 0.95 0.97 0.98 0.96
1hp 0.85 0.93 0.79 0.87 0.92 0.95 0.94 0.95 0.94 0.96
2hp 0.93 0.95 0.92 0.9 0.89 0.88 0.94 0.88 0.92 0.91
3hp 0.94 0.94 0.97 0.94 0.99 0.97 0.96 0.96 0.96 0.98
As illustrated in Fig. 6, the fault conditions can
be clearly distinguished at accuracy rate of 100% for
3hp load. This indicates that the proposed method can
efficiently recognize different fault categories of the
rolling bearing.
As shown in Fig.7, The T-SNE diagram of fault
diagnosis experiment using DWT-BPNN method
under 3hp load is shown. From the diagram, it can be
clearly seen that various fault characteristics are
effectively distinguished and has high diagnosis
accuracy as a whole.
Fig. 6: Multi-class confusion matrices of the
DWT-BPNN method for 3hp load.
Fig. 7: Features visualization based on t-SNE:
DWT-BPNN method for 3hp load.
5 Conclusions
This paper provides a method which can effectively
identify the fault of rolling bearing, and compared
with FT-BPNN method, it has higher accuracy. The
original rolling bearing fault data is processed by
wavelet transform, which makes its fault
characteristics more representative and has important
significance for improving the accuracy of fault
diagnosis.
Method 0hp 1hp 2hp 3hp
DWT-BPN
N
0.9940±0.006633 0.9730±0.019519 1.0000±0.000000 1.0000±0.000000
FT-BPNN 0.9520±0.032496 0.9100±0.052536 0.9120±0.023152 0.9610±0.016401
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Acknowledgements:
This work is funded by Fundamental and Advanced
Research Project of Chongqing CSTC of China, the
project No. are cstc2019jcyj-msxmX0386 and
cstc2020jcyj-msxmX0232.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
This work is funded by Fundamental and Advanced
Research Project of Chongqing CSTC of China, the
project No. are cstc2019jcyj-msxmX0386 and
cstc2020jcyj-msxmX0232.
