Pseudo-fault signal assisted empirical mode decomposition (PFS-EMD) is put forward for fault detection and isolation, which is built upon EMD, envelope analysis and pseudo-fault signal. And this method has been proved that it is usable in fault diagnosis of simple gear pair. However, this method is still need further study that whether it can be used for fault diagnosis of complex gearbox. Moreover, planetary gearbox fault diagnosis is much more complicated than fixed-axis gearbox. This paper makes a further study of PFS-EMD and focuses on its application. Combining with the seeded failure experimental data of planetary gearbox, this paper show that PFS-EMD can enhance fault information and weaken other useless information in complex gearbox fault diagnosis

Jianmin Zhao

Xianglong Ni

Xin Zhang

Zhendong Du

English

Vibroengineering PROCEDIA

 138 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533  
Planetary gearbox fault diagnosis based on pseudo-fault 
signal assisted EMD 
Xianglong Ni1, Jianmin Zhao2, Zhendong Du3, Xin Zhang4 
Mechanical Engineering College, Shijiazhuang, China 
1Corresponding author 
E-mail: 1ni_phm@163.com, 2jm_zhao@hotmail.com, 3du_phm@163.com, 4zxyx361@163.com 
(Received 28 October 2016; accepted 30 October 2016) 
Abstract. Pseudo-fault signal assisted empirical mode decomposition (PFS-EMD) is put forward 
for fault detection and isolation, which is built upon EMD, envelope analysis and pseudo-fault 
signal. And this method has been proved that it is usable in fault diagnosis of simple gear pair. 
However, this method is still need further study that whether it can be used for fault diagnosis of 
complex gearbox. Moreover, planetary gearbox fault diagnosis is much more complicated than 
fixed-axis gearbox. This paper makes a further study of PFS-EMD and focuses on its application. 
Combining with the seeded failure experimental data of planetary gearbox, this paper show that 
PFS-EMD can enhance fault information and weaken other useless information in complex 
gearbox fault diagnosis. 
Keywords: planetary gearbox, fault diagnosis, pseudo-fault signal, EMD. 
1. Introduction 
Vibration is an important monitoring method of rotating machinery, and it is great significance 
to accurately extract the fault information from vibration signals [1]. Signal processing methods 
are usually used to analyze and extract the fault characteristic frequency, and they are becoming 
a common technology in rotating machinery condition monitoring process. Wavelet transform 
(WT) [2] and empirical mode decomposition (EMD) [3] are two widely used methods of signal 
processing. WT method needs to choose different wavelet basis functions to determine the wavelet 
coefficients in order to reconstruct the signal [2]. Compared with WT, the EMD method does not 
need basis function in the process of characteristic frequency extraction from vibration signal, 
which is a kind of adaptive nonlinear and non-stationary data analysis method [4]. The EMD 
method decomposes nonlinear and non-stationary signal into a series of intrinsic mode function 
(IMF). And the IMF is a kind of basically orthogonal, adaptive and complete expression, which 
is confirmed by original signal rather than preset basic functions [5]. EMD is widely used in 
processing non-linear and non-stationary signal [6].  
Dheeraj proposed a idea of injecting pseudo-fault signal to the signal envelope in fault 
detection and isolation of rotating machinery [7]. The method is built upon EMD, envelope 
analysis and pseudo-fault signal. He proved this method is usable in fault diagnosis of simple gear 
pair. However, it is still need further study that whether this method can be used for fault diagnosis 
of complex gearbox. 
As the advantages of strong load-bearing capacity, large transmission ratio, etc., planetary 
gearboxes are widely used in modern industry. Planetary gearboxes significantly differ from 
fixed-axis gearboxes because of their unique structure [8]. As a result, planetary gearbox fault 
diagnosis are much more complicated than fixed-axis gearbox. 
This paper makes a further study of PFS-EMD and focuses on its application. Combining with 
the seeded failure experimental data of planetary gearbox, this paper verifies the effectiveness of 
PFS-EMD in complex gearbox fault diagnosis. 
2. Pseudo-fault signal theory 
In PFS-EMD method, the frequency of masking signal is predetermined by the known system 
fault frequency, thus it is considered as pseudo-fault signal. In order to clearly describe the concept 
PLANETARY GEARBOX FAULT DIAGNOSIS BASED ON PSEUDO-FAULT SIGNAL ASSISTED EMD.  
XIANGLONG NI, JIANMIN ZHAO, ZHENDONG DU, XIN ZHANG 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533 139 
of pattern recognition, the fault signal is assumed as two closer frequency band signal components. 
In this article, two signal components are expressed by the sine function: 
ܻሺݐሻ = ௛ܻሺݐሻ + ௟ܻሺݐሻ = ܣ௛sinሺ2ߨ ௛݂ݐሻ + ܣ௟sinሺ2ߨ ௟݂ݐሻ, (1)
where ℎ  represents the higher frequency components, ݈  on behalf of the low frequency 
components. 
When performing EMD (The procedure for performing the EMD method is shown in Fig. 1), 
the first step in the sifting process is to find the extreme value point of signal and create upper and 
lower envelope. Moreover, the extreme value distribution depends on the signal component. 
Pseudo-fault signal is used to change the distribution of extreme value. As a result, the average 
envelope got by EMD should contain only low frequency components: 
ܻሺݐሻ ≈ ௟ܻሺݐሻ. (2)
 
Fig. 1. Procedure for performing the EMD 
2.1. The positive fault IMF 
The positive synthesized signal ܻାሺݐሻ is obtained from envelope signal ௘ܻ௢௣ሺݐሻ (containing 
fault information) and pseudo-fault signal ௉ܻிௌሺݐሻ. EMD Processing ܻାሺݐሻ and achieving the 
positive IMF ܺାሺݐሻ: 
ܻାሺݐሻ = ௛ܻሺݐሻ + ௟ܻሺݐሻ + ௉ܻிௌሺݐሻ, (3)
௉ܻிௌሺݐሻ = ܤ௉sin൫2ߨ ௣݂ݐ൯. (4)
In pseudo-fault signal ௉ܻிௌሺݐሻ, in order to make the mean extrema rate of ܻାሺݐሻ is equal to 
௉ܻிௌሺݐሻ (namely ௘݂௫ = ௣݂), ܤ௉ should be big enough. Let ሼݐ௜௨, ܻାሺݐ௜௨ሻሽ as the set of local maxima 
of ܻାሺݐሻ, and ܻାሺݐ௜௨ሻ can be written as: 
ܻାሺݐ௜௨ሻ = ௛ܻሺݐ௜௨ሻ + ௟ܻሺݐ௜௨ሻ + ௉ܻிௌሺݐ௜௨ሻ. (5)
The ideal curve, which connect all of maxima value (namely upper envelope), can be expressed 
as: 
ܻ௨ሺݐሻ = ෍ሾ ௛ܻሺݐ௜௨ሻ + ௟ܻሺݐ௜௨ሻ + ௉ܻிௌሺݐ௜௨ሻሿsinc ቆ
ݐ − ݐ௜௨
௘ܶ௫
ቇ
௜
, (6)
where ௘ܶ௫ is the sampling interval of extrema. 
PLANETARY GEARBOX FAULT DIAGNOSIS BASED ON PSEUDO-FAULT SIGNAL ASSISTED EMD.  
XIANGLONG NI, JIANMIN ZHAO, ZHENDONG DU, XIN ZHANG 
140 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533  
Because of sampling for the extreme value, the higher frequency components of signals will 
loss information as aliasing, the lower frequency components will be reconstructed by the means 
of minimum information loss. As the assumption ௘݂௫ = ௣݂, the pseudo-fault signal will produce a 
constant DC term. Therefore, the upper envelope can be expressed as: 
ܻ௨ሺݐሻ = ௟ܻሺݐሻ + ௛ܻ௨ሺݐሻ + ܤ௉௨, (7)
where ܤ௉௨  is a constant, ௛ܻ௨ሺݐሻ  is the edition of higher frequency components after aliasing. 
Similarly, the lower envelope can be written as: 
ܻ௕ሺݐሻ = ௟ܻሺݐሻ + ௛ܻ௕ሺݐሻ + ܤ௉௕. (8)
The average envelope can be obtained as: 
ܻାሺݐሻ = ܻ
௨ሺݐሻ + ܻ௕ሺݐሻ
2 = ௟ܻሺݐሻ +
௛ܻ௨ሺݐሻ + ௛ܻ௕ሺݐሻ
2 +
ܤ௉௨ + ܤ௉௕
2 . (9)
In the Eq. (9), it is the lower frequency component in the first term of right hand expression, 
and it is average envelope for the higher frequency components after aliasing. Averaging operation 
further weaken the influence of higher frequency components by aliasing envelope [9]. As a result, 
the positive IMF ܺାሺݐሻ can be calculated as: 
ܺାሺݐሻ = ௛ܻሺݐሻ + ௉ܻிௌሺݐሻ + ߞଵሺݐሻ, (10)
where ߞଵሺݐሻ is the error signal. 
2.2. The negative fault IMF 
The negative fault IMF ܺିሺݐሻ is extracted through the similar series of operation on negative 
synthesized signal ܻିሺݐሻ: 
ܺିሺݐሻ = ௛ܻሺݐሻ − ௉ܻிௌሺݐሻ + ߞଶሺݐሻ. (11)
Ignoring the error terms in Eqs. (10) and (11), the output signal after PFS-EMD operation can 
be achieved as: 
ܺሺݐሻ = ܺ
ାሺݐሻ + ܺିሺݐሻ
2 ≈ ௛ܻሺݐሻ. (12)
FFT
Fault frequency
Fj
Masking PFS


EMD
sifting
EMD
sifting
Mean filter PFSY t
 eopY t
 eopY F
 Y t
 Y t
 X t
 X t
 X t
Envelope 
extraction
EMD sifting
 Y t
 IMFY t
 
Fig. 2. Procedure for performing the PFS-EMD 
It can be found from Eq. (12) that the pseudo-fault signal can help in separating signals of 
closer frequency bands, which is out of reach for standard EMD method. The signal dealing 
PLANETARY GEARBOX FAULT DIAGNOSIS BASED ON PSEUDO-FAULT SIGNAL ASSISTED EMD.  
XIANGLONG NI, JIANMIN ZHAO, ZHENDONG DU, XIN ZHANG 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533 141 
process of PFS-EMD method are shown in Fig. 2. 
3. PFS-EMD method 
The proposed PFS-EMD method is used to extract the fault characteristics of rotating 
machinery, the specific steps are as follows: 
(a) Calculating the failure frequency ܨ௝  (݆ =  1, 2,..., ݉ ) corresponding to various failure  
modes. 
(b) Identifying the ݅th IMF that there is a peak close to ܨ௝ in frequency spectrum: 
ቚargmaxி ܥ௜ሺܨሻ − ܨ௝ቚ
ܨ௝ ≤ ߝ,
where ܥ௜ሺܨሻ is Fourier transform of the ݅th IMF ܥ௜ሺݐሻ, ߝ is a very small value and it is taken as 
0.05 in this paper. 
(c) Structuring a pseudo-fault signal, which with constant amplitude and constant frequency: 
௉ܻிௌሺݐሻ = ܤ௉sin൫2ߨߙிܨ௝ݐ൯, (13)
ܤ௉ = ߙ஻maxሺ|ܥ௜ሺܨሻ|ሻ. (14)
On the advice of previous research [7], this paper let ߙி = 1.1 and ߙ஺ = 1.6. 
(d) Performing standard EMD to get the first IMF ܺାሺݐሻ from ܥ௜
ାሺݐሻ = ܥ௜ሺݐሻ + ௉ܻிௌሺݐሻ and 
get the second IMF ܺିሺݐሻ from ܥ௜ି ሺݐሻ = ܥ௜ሺݐሻ − ௉ܻிௌሺݐሻ.  (e) Obtaining fault indicator signal: 
ܺሺݐሻ = ܺ
ାሺݐሻ + ܺିሺݐሻ
2 . (15)
(f) Extracting fault information from fault indicator signal ܺሺݐሻ. 
4. Planetary gearbox fault diagnosis 
A case study is carried out for planetary gearbox fault diagnosis based on PFS-EMD. In order 
to validate the effectiveness of the proposed method, a seeded failure experiment of planetary 
gearbox to obtain failure data. The experiment rig consists of a test planetary gearbox, a drive 
motor, a speed and torque sensor, and a magnetic powder brake, as shown in Fig. 3. There are four 
accelerometers fitted onto the casing of gearbox to record vibration data, as shown in Fig. 4. 
Schematic map of planetary gearbox structure and related configuration parameters are shown in 
Fig. 5. The failure is seeded on sun gear, planet gear and ring gear, respectively, as shown in Fig. 6. 
Fault characteristic frequencies of every gear is shown in Table 1. 
 
Fig. 3. Planetary gearbox experiment rig 
PLANETARY GEARBOX FAULT DIAGNOSIS BASED ON PSEUDO-FAULT SIGNAL ASSISTED EMD.  
XIANGLONG NI, JIANMIN ZHAO, ZHENDONG DU, XIN ZHANG 
142 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533  
Frequency spectrum of sun gear fault is shown as Fig. 7, blue frequency spectrum is 
decomposed by standard EMD without pseudo-fault signal, red frequency spectrum is 
decomposed by PFS-EMD. It can be found that the amplitude of red frequency spectrum is lower 
than blue frequency spectrum in whole frequency bands. But in fault frequency of sun gear  
( ௌ݂ = 56.97), the amplitude of red signal is significantly higher than blue signal. This phenomenon 
shows that fault information has been enhanced, while other useless information has been 
weakened. 
Table 1. Fault characteristic frequencies of every gear (Hz) 
Fault frequency of sun gear ௌ݂ Fault frequency of planet gear ௉݂ Fault frequency of ring gear ோ݂ 
55.093 3.730 4.906 
 
Fig. 4. Mounted location of accelerometers 
 
Fig. 5. Schematic map of planetary gearbox structure 
 
Fig. 6. Implanted wear fault: a) sun gear, b) planet gear, and c) ring gear 
56 97Sf .
 
Fig. 7. Frequency spectrum of sun gear fault 
Frequency spectrums of planet gear fault and ring gear fault are shown as Fig. 8. It cannot 
found the fault characteristic frequency information in the frequency spectrums, which are 
decomposed by standard EMD without pseudo-fault signal. While in the frequency spectrums 
which are decomposed by PFS-EMD, there are two significant peaks in fault characteristic 
frequencies of planet gear fault and ring gear fault, the fault features are obvious. 
In order to further verify the effect of the proposed method, signal to noise ratios (SNR) are 
analyzed. The SNR can be caudated as follow: 
PLANETARY GEARBOX FAULT DIAGNOSIS BASED ON PSEUDO-FAULT SIGNAL ASSISTED EMD.  
XIANGLONG NI, JIANMIN ZHAO, ZHENDONG DU, XIN ZHANG 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533 143 
ܴܵܰ = 10 ⋅ lg ܵሺ ଴݂ሻܰሺ ଴݂ሻ, (16)
ܵሺ ଴݂ሻ stand for spectrum amplitude of frequency ଴݂, ܰሺ ଴݂ሻ is average spectrum amplitude. All 
SNR of every gear fault is shown in Table 2. It can be found that the SNR of PFS-EMD is much 
greater than EMD without PFS. It shows that PFS-EMD can enhance useful information in fault 
diagnosis. 
3 798Pf .
a) 
4 83Rf .
 
b) 
Fig. 8. Frequency spectrum: a) planet gear fault, b) ring gear fault 
Table 2. SNR of every gear fault 
 SNR of sun gear fault SNR of planet gear fault SNR of ring gear fault 
EMD without PFS 10.2976 3.4278 2.3679 
EMD with PFS 15.5547 8.4135 8.0443 
5. Conclusions 
This paper is meant to further investigate the theory and application in complex gearbox of 
PFS-EMD. Pseudo-fault signal theory is future studied and the specific steps of PFS-EMD are 
given. A case study of planetary gearbox fault diagnosis based on PFS-EMD is analysis, which 
include sun gear fault, planet gear fault and ring gear fault. The frequency spectrum and SNR 
show that PFS-EMD can enhance fault information and weaken other useless information in 
complex gearbox fault diagnosis. 
References 
[1] Li M., Xu J., Yang J., Yang D. Multiple manifolds analysis and its application to fault diagnosis. 
Mechanical Systems and Signal Processing, Vol. 23, 2009, p. 2500-2509. 
[2] Gilles J. Empirical wavelet transform. IEEE Transactions on Signal Processing, Vol. 61, 2013, 
p. 3999-4010. 
[3] Lei Y. G., Lin J., He Z. J., Zuo M. J. A review on empirical mode decomposition in fault diagnosis 
of rotating machinery. Mechanical Systems and Signal Processing, Vol. 35, 2013, p. 108-126. 
[4] Bi N., Sun Q. Y., Huang D. R., Yang Z. H., Huang J. W. Robust image watermarking based on 
multiband wavelets and empirical mode decomposition. IEEE Transactions on Image Processing, 
Vol. 16, 2007, p. 1956-1966. 
[5] Lv Y., Yuan R., Song G. B. Multivariate empirical mode decomposition and its application to fault 
diagnosis of rolling bearing. Mechanical Systems and Signal Processing, Vol. 81, 2016, p. 219-234. 
[6] Klionski D. M., Oreshko N. I., Geppener V. V. Applications of empirical mode decomposition for 
processing nonstationary signal. Pattern Recognition and Image Analysis, Vol. 18, 2008, p. 390-399. 
[7] Singh D. S., Zhao Q. Pseudo-fault signal assisted EMD for fault detection and isolation in rotating 
machines. Mechanical Systems and Signal Processing, Vol. 81, 2016, p. 202-218. 
[8] Lei Y. G., Han D., Lin J., et al. Planetary gearbox fault diagnosis using an adaptive stochastic 
resonance method. Mechanical Systems and Signal Processing, Vol. 38, 2013, p. 113-124. 
[9] Yang Y., Miao C., Deng J. Research on the mechanism of masking signals technique to improve 
empirical mode decomposition. Journal of Information and Computational Science, Vol. 9, 2012, 
p. 3509-3516. 


Planetary gearbox fault diagnosis based on pseudo-fault signal assisted EMD

https://www.jvejournals.com/article/17903/pdf

Planetary gearbox fault diagnosis based on pseudo-fault signal assisted EMD

Abstract

Similar works

Full text

Available Versions

Vibroengineering PROCEDIA