Hydraulic pump is regarded as the heart of hydraulic system. Achieving the real-time fault diagnosis of hydraulic pump is of great importance for the maintenance of the entire system. An accurate fault clustering solution with self-adaptive signal processing is needed for extracting performance degradation information hidden in the nonlinear and non-stationary signals of hydraulic pumps. Therefore, a fault diagnosis approach based on ensemble empirical mode decomposition (EEMD), kernel principal component analysis (KPCA), and learning vector quantization (LVQ) network is proposed in this study. First, EEMD is employed to acquire more significant intrinsic mode functions (IMFs), thus overcoming the drawback of empirical mode decomposition, and further extracting the energy values of each IMF to form the feature vector. Second, KPCA, a nonlinear dimension reduction method, is used to remove redundancies of the extracted feature vector for high accuracy of fault diagnosis. Finally, LVQ is employed to classify faults based on the reduced feature vector. The efficiency and accuracy of the proposed method is validated by a case study based on the vibration dataset of a plunger pump

Chao Wang

Hang Yuan

Jian Ma

Zili Wang

English

Vibroengineering PROCEDIA

 188 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
Fault diagnosis for hydraulic pump based on EEMD-
KPCA and LVQ 
Chao Wang1, Zili Wang2, Jian Ma3, Hang Yuan4 
Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100191, China 
School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China 
3Corresponding author 
E-mail: 1frost1061@126.com, 2wzl@buaa.edu.cn, 3majian3128@126.com, 4buaayuanhang@163.com 
(Accepted 12 September 2014) 
Abstract. Hydraulic pump is regarded as the heart of hydraulic system. Achieving the real-time 
fault diagnosis of hydraulic pump is of great importance for the maintenance of the entire system. 
An accurate fault clustering solution with self-adaptive signal processing is needed for extracting 
performance degradation information hidden in the nonlinear and non-stationary signals of 
hydraulic pumps. Therefore, a fault diagnosis approach based on ensemble empirical mode 
decomposition (EEMD), kernel principal component analysis (KPCA), and learning vector 
quantization (LVQ) network is proposed in this study. First, EEMD is employed to acquire more 
significant intrinsic mode functions (IMFs), thus overcoming the drawback of empirical mode 
decomposition, and further extracting the energy values of each IMF to form the feature vector. 
Second, KPCA, a nonlinear dimension reduction method, is used to remove redundancies of the 
extracted feature vector for high accuracy of fault diagnosis. Finally, LVQ is employed to classify 
faults based on the reduced feature vector. The efficiency and accuracy of the proposed method is 
validated by a case study based on the vibration dataset of a plunger pump. 
Keywords: hydraulic pump, fault diagnosis, ensemble empirical mode decomposition, kernel 
principal component analysis, learning vector quantization. 
1. Introduction 
Hydraulic system has been widely used in the areas of aeronautics, astronautics, metallurgy, 
etc. As the power source of a hydraulic system, hydraulic pump is often regarded as the heart of 
the system. Operating condition of hydraulic pump has a direct impact on the performance of the 
hydraulic system and even on the entire system [1]. Therefore, it would be particularly important 
to realize real-time fault diagnosis of hydraulic pump [2]. 
As a rotating machinery, vibration characteristics of hydraulic pump will changes with its 
performance. Therefore, reliable feature representative of the pump condition can be extracted by 
the processing and analysis of the vibration signal measuring on the pump [3]. However, due to 
the complexity of the hydraulic pump failure mechanism and operating environment, vibration 
signals of abnormal hydraulic pump are nonlinear and non-stationary, and normally buried in the 
noise signals. It is difficult to extract effective fault characteristics by using common signal 
processing methods. Wavelet-based method has been widely used as an effective way to process 
nonlinear and non-stationary signal. But it has some inevitable deficiencies such as interference 
terms, border distortion and energy leakage [4]. Empirical mode decomposition (EMD), proposed 
by Huang et al., was then demonstrated to be superior to wavelet analysis in many applications 
[5]. Based on local properties of the signal, EMD can decompose any complicated data set in to a 
finite number of intrinsic mode functions (IMF), which represents a simple oscillatory mode. But 
one of the major drawbacks of EMD is the problem of mode mixing, which will debase the 
physical meaning of IMF. To solve this problem, EEMD was proposed for substantial 
improvement over the original EMD by using noise assisted data analysis [6]. 
Neural network is broadly used as an intelligent classifier to recognize fault patterns. 
Back-propagation (BP) network is one of the most widely used neural network in many areas. But 
it has some shortage in convergence rate and training time [7]. Learning Vector Quantization was 
introduced by Teuvo Kohonen as a supervised counterpart of vector quantization systems, which 
FAULT DIAGNOSIS FOR HYDRAULIC PUMP BASED ON EEMD-KPCA AND LVQ.  
CHAO WANG, ZILI WANG, JIAN MA, HANG YUAN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 189 
applies a winner-take-all Hebbian learning-based approach [8]. LVQ network has a fast 
convergence rate, short training time, and a simple but accurate output, which is good for real-time 
fault diagnosis [7]. 
Training a neural network with high-dimensional data is a time-consuming process. To 
improve the real-time performance and accuracy of fault diagnosis, dimension reduction methods 
are usually applied for feature reduction. Principal Component Analysis (PCA) and Fisher 
Discriminant Analysis (FDA) are both commonly used dimension reduction method. However, 
linear correlation among the variables is assumed in these methods, which degrades their 
performance in nonlinear systems. Kernel Principal Component Analysis (KPCA) was proposed 
by Schölkopf et al. as a nonlinear form of Principal Component Analysis [9]. By computing 
principal components in high dimensional feature spaces which is related to input space by some 
nonlinear map, KPCA has a better performance in nonlinear systems, for example, hydraulic 
system. 
Aiming at processing the nonlinear and non-stationary vibration signals and acquiring accurate 
fault diagnosis, an approach based on EEMD, KPCA, and LVQ is proposed in this study. 
2. Methodology 
2.1. Procedure of the proposed method 
The fault diagnosis method proposed in this paper can be summarized as three parts (Fig. 1): 
a) Feature Extraction: EEMD is employed to decompose the original signal into finite IMFs. 
Energy values of the IMFs are extracted to form the feature vector. 
b) Feature Reduction: KPCA is employed to reduce the dimension of the feature vector. Only 
the principal components which contain most of the information are selected for further analysis. 
c) Fault Diagnosis: the reduced feature vectors are sent to the LVQ network for training. With 
the trained LVQ network, fault mode of the current sample can be judged.  
Raw signal
Feature 
extraction
Feature 
reduction
Fault
diagnosis
IMFs
Energy feature 
vectors
Reduced feature 
vectors
Diagnosis 
results
EEMD
Energy 
extraction
KPCA
LVQ 
network
Training
Classification
 
Fig. 1. Procedure of the proposed approach 
 
Fig. 2. Test plunger pump rig 
2.2. Signal processing by ensemble empirical mode decomposition 
EMD has been widely used in fault diagnosis as an effective self-adaptive analysis tool for 
non-stationary and nonlinear signals [5]. Based on local properties of the signal, EMD can 
decompose any complicated data set in to a finite number of IMFs which represents a simple 
oscillatory mode. But one of the major drawbacks of EMD is the problem of mode mixing, which 
FAULT DIAGNOSIS FOR HYDRAULIC PUMP BASED ON EEMD-KPCA AND LVQ.  
CHAO WANG, ZILI WANG, JIAN MA, HANG YUAN 
190 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
will debase the physical meaning of IMF. To solve this problem, EEMD was proposed for 
substantial improvement over the original EMD by using noise assisted data analysis [6]. 
The principle of the EEMD can be described as follows. First, by adding Gaussian random 
white noise sequence, which is uniformly distributed and its standard deviation of amplitude is 
constant, the original signal generate enough extreme point to avoid mode mixing. Second, apply 
EMD decomposition to the signal with Gaussian white noise to acquire their corresponding IMFs. 
Since the statistical mean of uncorrelated random sequence is zero, calculate the ensemble average 
of the corresponding IMFs to eliminate the effect of Gaussian white noise on the true IMFs. At 
last, the ensemble mean is treated as the true IMF. As is described above, it is not hard to find that 
EEMD decomposition does avoid mode mixing while eliminate the effect of adding Gaussian 
white noise. 
The EEMD algorithm is detailed as follows: 
1) Add a white noise signal ௝݊(ݐ) to the targeted signal ݔ(ݐ): 
ݔ௝(ݐ) = ݔ(ݐ) + ௝݊(ݐ), (1)
where ݔ௝(ݐ)  represents the noise-added signal of the ݆ th trial, ݆ =1, 2, 3,..., ܯ  and ܯ  is the 
initialized number of the trial. 
2) Decompose the noise-added signal ݔ௝(ݐ) into a finite number of IMFs ܿ௜௝ and the residue ݎ௝ 
using EMD method: 
ݔ௝(ݐ) = ෍ ܿ௜௝
ே
௜ୀଵ
+ ݎ௝, (2)
where ܰ is the number of IMFs, and ݅ =1, 2, 3,..., ܰ. 
3) Proceed step (1) and (2) for ܯ times, and each time add a different random white noise signal. 
4) Calculate the ensemble means ܿ௜ of each corresponding IMF for the ܯ trials: 
ܿ௜ =
൫∑ ܿ௜௝ெ௝ୀଵ ൯
ܯ ,   ݆ = 1, 2, 3, . . . , ܯ, ݅ = 1, 2, 3, . . . , ܰ.
(3)
5) Report ܿ௜ (݅ =1, 2, 3,..., ܰ) as the final IMFs. 
2.3. Feature extraction by energy extraction 
When different faults appear in hydraulic pump, the corresponding resonance frequency 
components appear in the vibration signals, and the energy of fault vibration signal in each IMF 
changes with the frequency distribution. In this paper, energy of each IMF is extracted as the fault 
feature. (Assuming that the energy of residual energy can be ignored.) Each IMF ܿ௜(ݐ)  is 
processed with: 
ܧ௜ = න |ܿ௜(ݐ)|ଶ݀ݐ
ାஶ
଴
, (4)
where ܧ௜ is the energy of each IMF, normalized as below: 
௜ܶ
ᇱᇱ = ቌܧଵ ൭෍ ܧ௜
ே
௜ୀଵ
൱
ିଵ
, ܧଶ ൭෍ ܧ௜
ே
௜ୀଵ
൱
ିଵ
, … , ܧே ൭෍ ܧ௜
ே
௜ୀଵ
൱
ିଵ
ቍ, (5)
FAULT DIAGNOSIS FOR HYDRAULIC PUMP BASED ON EEMD-KPCA AND LVQ.  
CHAO WANG, ZILI WANG, JIAN MA, HANG YUAN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 191 
where ௜ܶᇱᇱ is the normalized feature vector, which carries the information of signal. 
2.4. Dimension reduction of feature vector by kernel principal component analysis 
KPCA was firstly proposed by Schölkopf et al as a nonlinear form of Principal Component 
Analysis [9]. The main idea of KPCA is to compute principal components in high dimensional 
feature spaces, which is related to input space by some nonlinear map, by using integral operator 
kernel functions. Its algorithm can be briefly described as follows. 
Assuming that the training data for KPCA is ܠ௞ ∈ ܴ௠ (݇ =1, 2, 3,..., ݊). Φ(⋅) is a nonlinear 
function that maps the input vectors ܠ௞ ∈ ܴ௠  to the feature space ܨ.  Assuming that  
∑ Φ(ܠ௞)௡௞ୀଵ = 0. So the covariance matrix of Φ(ܠ௞) in the feature space ܨ can be given as: 
۱ = 1݊ ෍ Φ(ܠ௞)Φ(ܠ௞)
்
௡
௞ୀଵ
. (6) 
The nonzero eigenvalues of the covariance matrix ۱ is ߣ, and the eigenvector is ܞ. ߣܞ = ۱ܞ, 
and ܞ can be expanded by Φ(ܠ௞) as: 
ܞ = ෍ ߙ௞Φ(ܠ௞)
௡
௞ୀଵ
. (7) 
Define a size ݊ × ݊ kernel matrix ۹ = (݇௜௝)ଵஸ௜ஸ௡,ଵஸ௝ஸ௡  in which the coefficients ߙ௞  can be 
obtained. ݇௜௝ = 〈Φ(ܠ௜), Φ(ܠ௝)〉, where 〈⋅,⋅〉  represents the dot product operator. The principal 
components ݐ can be extract by calculate the projection of a vector Φ(ܠ) onto eigenvector ܞ௞ in 
feature space ܨ: 
ݐ௞ = 〈ݒ௞, Φ(ܠ)〉 = ෍ ߙ௜௞
௡
௜ୀଵ
〈Φ(ܠ௜), Φ(ܠ)〉. (8) 
2.5. Fault diagnosis based on learning vector quantization network 
LVQ, proposed by Teuvo Kohonen, is regarded as a special artificial neural network, which 
serves as a supervised counterpart of vector quantization systems and applies a winner-take-all 
Hebbian learning algorithm [8]. An LVQ network consists of three layers: the input layer that 
includes one neuron for each parameter; the competitive layer of the hidden layer in which 
learning and classification operates; and the output layer comprises only one neuron for each class. 
A weight matrix is designed between the input layer and the hidden layer, which includes the 
classification information. 
3. Experimental verification 
3.1. Experiment setup 
In this study, several groups of data generated from a test plunger pump fig were employed to 
verify the effectiveness and practicality of the proposed method (Fig. 2). Two commonly 
occurring faults, slipper loose and valve plate wear, were injected into the test plunger pump fig. 
The vibration signals were acquired by an acceleration transducer from the end face of the plunger 
pump. In the experiment, the motor speed was 528 r/min, and the sampling rate was 1000 Hz. 
FAULT DIAGNOSIS FOR HYDRAULIC PUMP BASED ON EEMD-KPCA AND LVQ.  
CHAO WANG, ZILI WANG, JIAN MA, HANG YUAN 
192 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
3.2. Feature extraction 
In the analysis, 300 groups of data are selected to be trained from three different conditions 
(normal, slipper loose, and valve plate wear), together with another 30 groups of data selected 
from similar conditions as the testing groups. 
Each raw data is decomposed into 8 IMFs by EEMD (Fig. 3). Then, energy value of each IMF 
is extracted to form the initial feature vector. 
 
Fig. 3. A sample of decomposition results with EEMD 
3.3. Feature reduction 
The characteristic matrix, composed of 300 groups of eigenvector, is processed with KPCA to 
obtain the principal components as well as their contributions (Fig. 4(a)). As is shown in the figure, 
the contribution of first two principal components has reached 0.91 while the first three reached 
0.98. In order to increase efficiency, only the first three principal components which contribute 
98 % of the information are used as eigenvector. The distribution of feature points are directly 
shown in Fig. 4(b). 
 
a) 
 
b) 
Fig. 4. a) Contributions of principal components, b) distribution of feature points 
3.4. Fault diagnosis 
The reduced 300×3 characteristic matrix is sent to LVQ network for training. The learning 
function of the network is LVQ2. Normal condition is targeted as (1, 0, 0), while swash plate wear 
as (0, 1, 0) and rotor wear as (0, 0, 1). 
0 50 100 150 200 250 300 350 400 450 500-0.01
00.01
raw
 si
gn
al
0 50 100 150 200 250 300 350 400 450 500-2
02
x 10-3
IM
F1
0 50 100 150 200 250 300 350 400 450 500-5
05
x 10-3
IM
F2
0 50 100 150 200 250 300 350 400 450 500-2
02
x 10-3
IM
F3
0 50 100 150 200 250 300 350 400 450 500-1
01
x 10-3
IM
F4
0 50 100 150 200 250 300 350 400 450 500-2
02
x 10-3
IM
F5
0 50 100 150 200 250 300 350 400 450 500-5
05
x 10-4
IM
F6
0 50 100 150 200 250 300 350 400 450 500-5
05
x 10-4
IM
F7
0 50 100 150 200 250 300 350 400 450 500-5
05
x 10-5
IM
F8
0 50 100 150 200 250 300 350 400 450 5000
12
x 10-3
RE
S
sample
1 2 3 4 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
principal components
co
ntr
ibu
tio
ns
FAULT DIAGNOSIS FOR HYDRAULIC PUMP BASED ON EEMD-KPCA AND LVQ.  
CHAO WANG, ZILI WANG, JIAN MA, HANG YUAN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 193 
The 30 groups of testing data are also processed by EEMD and KPCA with the same principle 
as training data. The 30 feature vectors extracted from testing data are sent to the trained LVQ 
network. The diagnosis results can be judged from the outputs of the LVQ network (partly 
described in Table 1). 
In the results, all 30 outputs are correctly corresponding to the real fault modes, which means 
the accuracy rate of diagnosis is 100 %. The diagnosis result reveals the effectiveness and accuracy 
of the proposed approach. 
Table 1. Diagnosis results 
No. 1 2 … 15 16 … 29 30 
Fault modes Normal Normal … Swash plate wear 
Swash 
plate wear … 
Rotor 
wear 
Rotor 
wear 
Feature 
vectors 
(–0.1541, 
–0.0691, 
0.1273) 
(–0.2145, 
–0.0120, 
–0.0662) 
… 
(–0.0111, 
–0.1853, 
–0.0283) 
(0.0279, 
–0.2138, 
–0.0239) 
… 
(0.2080, 
–0.0416, 
–0.0089) 
(0.1807, 
0.03340, 
–0.0248) 
LVQ 
outputs (1,0,0) (1,0,0) … (0,1,0) (0,1,0) … (0,0,1) (0,0,1) 
4. Conclusions 
To address the problem existing in fault diagnosis for the nonlinear and non-stationary 
vibration signal of a hydraulic pump, an approach combining EEMD-KPCA with LVQ is 
proposed in this study. EEMD was applied to decompose the original signals into a finite number 
of IMFs with certain physical significance. Energy values of the IMFs were extracted as feature 
vector, which was further reduced by using KPCA. The reduced feature vector was then input to 
the trained LVQ network. Two commonly occurring hydraulic pump faults were used to validate 
the effectiveness of the proposed approach.  
Acknowledgements 
This research was supported by the National Natural Science Foundation of China (Grant 
No. 61074083, 50705005, and 51105019), and by the Technology Foundation Program of 
National Defense (Grant No. Z132013B002). 
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Fault diagnosis for hydraulic pump based on EEMD-KPCA and LVQ

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Fault diagnosis for hydraulic pump based on EEMD-KPCA and LVQ

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