局部均值分解 Local Mean Decomposition
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2009 International Conference on Measuring Technology and Mechatronics Automation
Mechanical Fault Diagnosis Based on Local Mean Decomposition Method
Baojia Chen
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710049, China e-mail: chenxf@mail.xjtu.edu.cn, hzj@mail.xjtu.edu.cn, jiyongtan@stu.xjtu.edu.cn
(iv). Subtract m11(t) from the original signal.
h11(t) x(t) m11(t)
(3)
Divide h11(t) by a11(t) to get frequency modulation
signal s11(t) .
s11(t) h11(t) / a11(t)
and Nuttall theorem [7]. Therefore it avoids negative frequency. Another advantage is that LMD integrates two signal processing procedures: decomposition and demodulation. In this paper, the LMD method has been applied in the analysis of the machinery fault signals and extracted the fault feature efficiently.
local extremaBiblioteka Baidu(n1, n2,ni ,) .
(ii). Calculate the local mean mi (t) and the local envelop
ai (t) of each two successive extrema by
mi (ni ni1) / 2
(1)
Abstract—With the effect of periodical impulses, most machinery fault vibration signals are muticomponent modulation signals. The effective decomposition approach is the key to demodulate signals and extract fault characteristics. Local mean decomposition (LMD) is a new kind of timefrequency analysis approach, which can decompose the signals adaptively into a set of product function (PF) components. The envelope of PF is the instantaneous amplitude and instantaneous frequency can be calculated by the derivative of the unwrapped phase of modulation signal with uniform amplitude. The method bypasses the Hilbert transform totally. Therefore, it involves no question about negative frequency of no physical meaning. Through the successful mechanical fault diagnosis examples, it shows that LMD has high theoretical value and engineering practicability.
II. LMD THEORY
A. LMD method
The basic idea of LMD is similar to EMD. The purposes are all to decompose the complex multicomponent modulation signals into a linear combination of a set of mono-component signals. The iterative decomposing result of LMD is a set of PFs and the local mean of signal is obtained by moving averaging. The detailed LMD method is implemented by iterating through the following loop. (i). Suppose x(t) is a discrete time series. Find all the
College of Mechanical and Material Engineering China Three Gorges University Yichang, 443002, China e-mail: cbjia@163.com
Xuefeng Chen, Zhengjia He, Jiyong Tan
(vi). Subtract PF1 from the original signal resulting in a
new signal u1(t) . Take u1(t) as the new signal and
repeat above all procedure k times until uk is a
Local mean decomposition (LMD) is a new kind of adaptive time-frequency analysis method proposed by Jonathan S. Smith [6] in 2005. LMD can decompose the complex multicomponent modulation signals into a linear combination of a finite set of mono-component named as product function (PF). A PF is the product of an envelope signal and a frequency demodulation signal with uniform amplitude. The envelope is the instantaneous amplitude of PF and contains amplitude modulation information. The derivation of the unwrapped phase of frequency modulation signal with uniform frequency is the IF of PF and contains frequency modulation information. Without using HT, the LMD method bypasses the limitations of Bedrosian theorem
where
a1(t) a11(t)a12 (t)a1n (t) q indicates the number
n
q1
a1q
(t
)
(5)
of iterations,
q 1,2,, n . Then the PF1 will be obtained by
PF1(t) a1(t)s1n (t)
(6)
(i)~(iv). If satisfies condition, multiply all the smoothed
local envelopes during iteration to get the envelope
signal a1(t) of first PF PF1,
978-0-7695-3583-8/09 $25.00 © 2009 IEEE
Keywords-Modulation signal; local mean decomposition; Fault diagnosis
I. INTRODUCTION
When the faults exist in the mechanical systems, with the effect of periodical impulses, the machinery vibration signals usually present the feature of modulation. The amplitude envelope, phase and instantaneous frequency (IF) from modulated signals contain rich fault information. Since that, demodulation is the premise to extract fault feature, diagnose fault type and decide the fault position accurately [1-2]. Currently, the commonly used demodulation methods include Hilbert transform (HT) demodulation, energy operator demodulation, generalized detection-filtering demodulation and so on [3-5]. But such methods are only applicable to the mono-component modulated signals. In fact, most machinery fault vibration signals are multicomponent modulated signals.
(4)
(v). Check whether s11(t) is a uniform amplitude
frequency modulation signal, viz. its
envelope a12 ( t ) 1 . If not satisfies condition, take
s11(t) as a new signal and repeat above procedures
ai ni ni1 / 2
(2)
(iii). Smooth The local mean and the local envelop using
moving averaging to form smoothed local mean
m11(t) and smoothed local envelope a11(t) .
681
DOI 10.1109/ICMTMA.2009.373
Authorized licensed use limited to: BEIHANG UNIVERSITY. Downloaded on November 26, 2009 at 07:04 from IEEE Xplore. Restrictions apply.
Mechanical Fault Diagnosis Based on Local Mean Decomposition Method
Baojia Chen
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710049, China e-mail: chenxf@mail.xjtu.edu.cn, hzj@mail.xjtu.edu.cn, jiyongtan@stu.xjtu.edu.cn
(iv). Subtract m11(t) from the original signal.
h11(t) x(t) m11(t)
(3)
Divide h11(t) by a11(t) to get frequency modulation
signal s11(t) .
s11(t) h11(t) / a11(t)
and Nuttall theorem [7]. Therefore it avoids negative frequency. Another advantage is that LMD integrates two signal processing procedures: decomposition and demodulation. In this paper, the LMD method has been applied in the analysis of the machinery fault signals and extracted the fault feature efficiently.
local extremaBiblioteka Baidu(n1, n2,ni ,) .
(ii). Calculate the local mean mi (t) and the local envelop
ai (t) of each two successive extrema by
mi (ni ni1) / 2
(1)
Abstract—With the effect of periodical impulses, most machinery fault vibration signals are muticomponent modulation signals. The effective decomposition approach is the key to demodulate signals and extract fault characteristics. Local mean decomposition (LMD) is a new kind of timefrequency analysis approach, which can decompose the signals adaptively into a set of product function (PF) components. The envelope of PF is the instantaneous amplitude and instantaneous frequency can be calculated by the derivative of the unwrapped phase of modulation signal with uniform amplitude. The method bypasses the Hilbert transform totally. Therefore, it involves no question about negative frequency of no physical meaning. Through the successful mechanical fault diagnosis examples, it shows that LMD has high theoretical value and engineering practicability.
II. LMD THEORY
A. LMD method
The basic idea of LMD is similar to EMD. The purposes are all to decompose the complex multicomponent modulation signals into a linear combination of a set of mono-component signals. The iterative decomposing result of LMD is a set of PFs and the local mean of signal is obtained by moving averaging. The detailed LMD method is implemented by iterating through the following loop. (i). Suppose x(t) is a discrete time series. Find all the
College of Mechanical and Material Engineering China Three Gorges University Yichang, 443002, China e-mail: cbjia@163.com
Xuefeng Chen, Zhengjia He, Jiyong Tan
(vi). Subtract PF1 from the original signal resulting in a
new signal u1(t) . Take u1(t) as the new signal and
repeat above all procedure k times until uk is a
Local mean decomposition (LMD) is a new kind of adaptive time-frequency analysis method proposed by Jonathan S. Smith [6] in 2005. LMD can decompose the complex multicomponent modulation signals into a linear combination of a finite set of mono-component named as product function (PF). A PF is the product of an envelope signal and a frequency demodulation signal with uniform amplitude. The envelope is the instantaneous amplitude of PF and contains amplitude modulation information. The derivation of the unwrapped phase of frequency modulation signal with uniform frequency is the IF of PF and contains frequency modulation information. Without using HT, the LMD method bypasses the limitations of Bedrosian theorem
where
a1(t) a11(t)a12 (t)a1n (t) q indicates the number
n
q1
a1q
(t
)
(5)
of iterations,
q 1,2,, n . Then the PF1 will be obtained by
PF1(t) a1(t)s1n (t)
(6)
(i)~(iv). If satisfies condition, multiply all the smoothed
local envelopes during iteration to get the envelope
signal a1(t) of first PF PF1,
978-0-7695-3583-8/09 $25.00 © 2009 IEEE
Keywords-Modulation signal; local mean decomposition; Fault diagnosis
I. INTRODUCTION
When the faults exist in the mechanical systems, with the effect of periodical impulses, the machinery vibration signals usually present the feature of modulation. The amplitude envelope, phase and instantaneous frequency (IF) from modulated signals contain rich fault information. Since that, demodulation is the premise to extract fault feature, diagnose fault type and decide the fault position accurately [1-2]. Currently, the commonly used demodulation methods include Hilbert transform (HT) demodulation, energy operator demodulation, generalized detection-filtering demodulation and so on [3-5]. But such methods are only applicable to the mono-component modulated signals. In fact, most machinery fault vibration signals are multicomponent modulated signals.
(4)
(v). Check whether s11(t) is a uniform amplitude
frequency modulation signal, viz. its
envelope a12 ( t ) 1 . If not satisfies condition, take
s11(t) as a new signal and repeat above procedures
ai ni ni1 / 2
(2)
(iii). Smooth The local mean and the local envelop using
moving averaging to form smoothed local mean
m11(t) and smoothed local envelope a11(t) .
681
DOI 10.1109/ICMTMA.2009.373
Authorized licensed use limited to: BEIHANG UNIVERSITY. Downloaded on November 26, 2009 at 07:04 from IEEE Xplore. Restrictions apply.