Journal of Engineering Science and Technology Review 6 (2) (2013) 24-28
Research Article
Harmonic Wavelet Envelope Method Applied in Railway Bearing Fault Diagnosis
Dechen Yao
1*
, Limin Jia
1
, Min Li
1
, Yong Qin
1
, Wei Peng
2
, Guangwu Liu
3
and Shaohuang Pang
3
1
State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University Beijing, China
2
Beijing Materials handling research institute, Beijing, 100007, China
2
Guangzhou Metro.Guangzhou, 510030, China
Received 25 June 2012; Accepted 15 January 2013
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Abstract
The working state of rolling bearing has an important influence on the operation of trains, directly related to the safety of
train passengers. Therefore, it has great significance to conduct train bearing fault diagnosis. In this paper, based on
harmonic wavelet envelope, a method for the fault diagnosis of railway bearings is proposed. First of all, the harmonic
wavelet packet was used to translate vibration signal into time-scale representation. Then the decomposed signal was
demodulated. Finally, through the analysis of the envelope spectrum, the bearing fault feature frequency was extracted. In
order to verify the validity of diagnosis method, outer race fault bearing and ball fault bearing were tested. The test
results show that the diagnosis method is effective and practical.
Keywords: Harmonic Wavelet, Envelope, Fault Diagnosis, Rolling Bearing
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1. Introduction
The railway bearing vibration signals usually undergo a
complex pathway before being collected by sensors.
Because of the strong interference of outside, the required
failure information is often submerged by the background
noise, which is not conducive to signal feature extraction of
the fault signal. Especially some early failure of the bearing,
whose signal energy is small and the signal-to-noise ratio is
low, making the signal processing and fault identification
more difficult.
The vibration signal of the fault bearing is a non-stationary
signal. Traditional spectrum analysis method can’t
effectively deal with non-stationary signals, For example,
the FFT is used to analyze and observe the signal amplitude
difference in frequency domain for damage diagnosis, and it
is applicable to stationary signal feature extraction. Most
practical dyadic wavelet is constructed by multi-resolution
analysis of the two-scale equation, which usually hasn’t
clear mathematical expressions. Moreover, when the number
of wavelet coefficients is small, the shape of the wavelet is
irregular. In this paper, Harmonic wavelet envelope method
is proposed to conduct bearing fault diagnosis, and the study
is supported by rolling bearing test, which has achieved
satisfying results.
2. Harmonic wavelet
The harmonic wavelet, constructed by Cambridge University
in 1993, is a complex wavelet with clear expression that has
strict box-shaped spectrum and good filtering properties [1].
Frequency function
( ) ω
e
Ψ
and
() ω
o
Ψ
are given as:
= Ψ
0
4 / 1
) (
π
ω
ε
()
< ≤ −
− < ≤ −
= Ψ
0
4 2 4 /
2 4 4 /
π ω π π
π ω π π
ω
ο
i
i
And
( ) ω
e
Ψ
and
() ω
o
Ψ
make up a complex function:
( ) ( ) ( )
e o
i ω ω ω Ψ = Ψ + Ψ (3)
Then, the time-domain expression of the harmonic
wavelet is obtained as:
() (sin 4 sin 2 )/2
e
t t t t ψ π π π = −
() (cos 4 cos 2 )/2
o
t t t t ψ π π π = − −
Thus, the time-domain expression of the complex
function:
4 2
() () () ( )/ 2
i t i t
e o
t t i t e e i t
π π
ψ ψ ψ π = + = −
The real part and imaginary part are shown in Fig. 1
and Fig. 2:
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* E-mail address: shmily137@sina.com
ISSN: 1791-2377 © 2013 Kavala Institute of Technology. All rights reserved.
(1)
(2)
(6)
(5)
(4)
π ω π π ω π 4 2 2 4 < ≤ − < ≤ −
Other
Other