In actual intelligent fault diagnosis of mechanical equipment, the sample data that can be measured is very limited. How to identify the type of fault relies on as little as possible of the sample and as low as possible of the low-dimensional feature vector uniquely require research in actual mechanical machinery and equipment intelligent fault diagnosis. By using the threshold noise reduction, improving the cubic spine interpolation, signal SVM extending and so on to improve EEMD method; researched the cross-validation model grid optimization SVM parameters, obtained the optimal parameters of SVM by using Sigmoid kernel function; applied optimal excellent SVM parameters, SVM by using Sigmoid kernel function in the ultra-low-dimensional ultra-small-sample four categories intelligent fault diagnosis classification accuracy rate reached 100 %, SVM parameter optimization can enhance the method combined the improved EEMD with SVM in ultra-low-dimensional ultra-small-sample four categories fault diagnosis accuracy

Baiyong Zhang

Jiong Sun

Kai Chai

Kai Liu

English

Vibroengineering PROCEDIA

  © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533 241 
Combined improved EEMD with SVM in 
ultra-low-dimensional ultra-small-sample application of 
multi-classification intelligent fault diagnosis 
Baiyong Zhang1, Kai Liu2, Jiong Sun3, Kai Chai4 
1Department of Weapon Engineering, Naval University of Engineering, Wuhan, China 
2, 3Office of Research and Development, Naval University of Engineering, Wuhan, China 
4College of Power Engineering, Naval University of Engineering, Wuhan, China 
1Corresponding author 
E-mail: 1346624729@qq.com, 2186830330@qq.com, 31050034843@qq.com, 4chaikai0805@163.com 
(Received 11 November 2016; accepted 17 November 2016) 
Abstract. In actual intelligent fault diagnosis of mechanical equipment, the sample data that can 
be measured is very limited. How to identify the type of fault relies on as little as possible of the 
sample and as low as possible of the low-dimensional feature vector uniquely require research in 
actual mechanical machinery and equipment intelligent fault diagnosis. By using the threshold 
noise reduction, improving the cubic spine interpolation, signal SVM extending and so on to 
improve EEMD method; researched the cross-validation model grid optimization SVM 
parameters, obtained the optimal parameters of SVM by using Sigmoid kernel function; applied 
optimal excellent SVM parameters, SVM by using Sigmoid kernel function in the 
ultra-low-dimensional ultra-small-sample four categories intelligent fault diagnosis classification 
accuracy rate reached 100 %, SVM parameter optimization can enhance the method combined the 
improved EEMD with SVM in ultra-low-dimensional ultra-small-sample four categories fault 
diagnosis accuracy. 
Keywords: EEMD, SVM, ultra-low-dimensional ultra-small-sample, multi-classification, 
intelligent diagnosis. 
1. Introduction 
Intelligent diagnosis is the development direction of mechanical condition monitoring and 
fault diagnosis. Typical feature extraction of the fault and choose appropriate machine learning 
method is two key factors of intelligent diagnosis [1]. 
Empirical Mode Decomposition (EMD) [2] method as a new signal analysis theory, is suitable 
for extracting the actual nonlinear the nonstationary signal. But it has serious endpoint effect and 
modal aliasing phenomenon, and has a bad effect on the accuracy of the analysis results. Thus, 
the solution to end effect and modal aliasing phenomenon has become the key to successful 
application EMD machinery fault diagnosis. Numerous scholars are focusing on the research of 
end effect and Ensemble Empirical Mode Decomposition (EEMD) [3] can effectively resolve 
modal aliasing phenomenon in EMD. 
For mechanical intelligent diagnosis, currently that the most used methods are neural networks 
and support vector machine (SVM) [4]. As the training samples of neural network are particularly 
large; there are some difficulties in actual use. SVM does not pursue the number of samples tends 
to infinity when the optimal solution, and the pursuit of finite sample optimal solution, has had a 
large number of applications in the current intelligent classification.  
This paper proposed an improved EEMD based on the EEMD method, and successfully 
applied the method combined the method combined the improved EEMD with SVM [5], and 
boosted SVM classification accuracy by optimizing the parameters to study the  
ultra-low-dimensional ultra-small-sample intelligent classification of mechanical fault diagnosis 
of the condition. 
COMBINED IMPROVED EEMD WITH SVM IN ULTRA-LOW-DIMENSIONAL ULTRA-SMALL-SAMPLE APPLICATION OF MULTI-CLASSIFICATION 
INTELLIGENT FAULT DIAGNOSIS. BAIYONG ZHANG, KAI LIU, JIONG SUN, KAI CHAI 
242 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533  
2. Fault diagnosis steps of combination improved EEMD with SVM 
Fault diagnosis steps of combination Improved EEMD with SVM is as follows [6]:  
(1) Train sample by improved EEMD decomposition. Improved EEMD decomposition get ܯ 
groups ܰ order IMF component ܥଵ, ܥଶ,…, ܥே and surplus ܴ. Mainly including the following: 
a) Threshold noise by improved EEMD; 
b) On the threshold of the signal x(t) after noise reduction SVM extension [7]; 
c) In continuation of the signal by adding a set of zero mean and variance equal to the random 
white noise sequence [8]; 
d) Extension of SVM and processing noise composite signal ݔଵ(ݐ) obtained after the treatment 
with EMD group IMF component {[ܿଵଵ, ܿଵଶ, … , ܿଵ௡], [ܿଶଵ, ܿଶଶ, … , ܿଶ௡], … , [ܿ௠ଵ, ܿ௠ଶ, … , ܿ௠௡]} and 
group m headroom [ܿ௥ଵ, ܿ௥ଶ, … , ܿ௥௡]. 
IMF component obtained m corresponding group mean {ܥଵ, ܥଶ, … , ܥ௡} and ݉ mean surplus ܴ, 
then: 
ݔ଴(ݐ) = ܴ + ෍ ܥ௜
௡
௜ୀଵ
. (1)
Among: 
ܥଵ =
1
݉ ෍ ܿ௜ଵ
௠
௜ୀଵ
,    ܴ = 1݉ ෍ ݎ௜௡
௠
௜ୀଵ
, ܥଶ =
1
݉ ෍ ܿ௜ଶ
௠
௜ୀଵ
,  ܥଷ = 1݉ ෍ ܿ௜ଷ
௠
௜ୀଵ
. (2)
e) Truncation SVM extension part as the original signal final decomposition results [9]. 
The improved EEMD method proposed in this paper made the following main improvements: 
1) The threshold noise suppression pulse interference and noise pollution, so that the signal 
before the EEMD decomposition of the signal itself and contains only zero mean and variance 
equal to the random white noise sequence [12]. 
2) Improved the cubic spine interpolation method suppresses “overshoot” and “undershoot” 
phenomenon. Extreme points of all of the signal is formed by a straight line segment connecting 
the upper and lower envelope line; strike the upper and lower envelope envelopes of line; 
inflection point of the flat line a cubic smoothing spine connected to form the mean of the signal 
envelope. 
3) Extension of SVM signals suppression end effect. Before joining the white noise signal 
SVM extension, increasing the length of the signal sequence of data to improve the accuracy of 
the results decomposition, inhibit the end effect. 
3. The method combined the improved EE-MD with SVM in ultra-low-dimensional 
ultra-small-sample intelligent diagnosis case analysis 
Examples used the bearing signal that easily measured to multi-classification intelligent 
diagnosis. In order to prevent too little samples are not persuasive in the study and have some 
effect on improvements intelligent classification and recognition results by the method combined 
improved EEMD with SVM in ultra-low-dimensional ultra-small-sample application. Measured 
respectively collected bearing in normal state, ball fault and inner ring and outer ring fault 
vibration signal of the four kinds of typical conditions 50 group a total of 200 sample data, and 
then to a random sample from the required training and testing of small samples for research. 
The experiment measured by using photoelectric counting rotor speed, collected bearing 
vertical level and axial vibration signal by 4 channel sensors. Sampling frequency is set to 10 kHz, 
and analyzing frequency is 2 kHz. 
COMBINED IMPROVED EEMD WITH SVM IN ULTRA-LOW-DIMENSIONAL ULTRA-SMALL-SAMPLE APPLICATION OF MULTI-CLASSIFICATION 
INTELLIGENT FAULT DIAGNOSIS. BAIYONG ZHANG, KAI LIU, JIONG SUN, KAI CHAI 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533 243 
3.1. Improved feature extraction EEMD 
Process all 200 samples of bearing vibration signal sample data by improved EEMD method 
to threshold noise reduction, then let the sample data signal after noise cancellation decomposes 
by improved EEMD method. To get the bearing state of four different 200 groups of the IMF and 
the surplus ܴ, seek the energy of each group of IMF and the surplus ܴ, to obtain a total of 200 
group 9 dimension (dimension 8 IMF component C1-C8 and 1 order surplus ܴ) normalized 
eigenvector energy as a sample preparation, Fig. 1 is 200 groups 9D energy statistics distribution. 
 
Fig. 1. 200 groups 9D energy statistics distribution 
3.2. The method combined the improved EEMD with SVM in ultra-low-dimensional ultra-
small-sample intelligent diagnosis 
Bearing four types of 20 groups of two-dimensional feature vector data will serve as input to 
the SVM training sample set in the classification training, establish ultra-low-dimensional 
ultra-small-sample classification model for classification test, observe the method combined the 
improved EEMD with SVM in ultra-low-dimensional ultra-small-sample case four classification 
results. Fig. 2 is a group of two randomly selected 20-dimensional feature vector class labels and 
distributions. 
 
Fig. 2. Ultra-low-dimensional ultra-small-sample test set category labels  
and 20 groups of two-dimensional feature vector 
SVM using Sigmoid kernel function, set penalty parameter ܿ = 1, kernel function gamma 
function parameter ݃ = 1. The training set input to the SVM for training, establish classification 
model. 
The test sample set input to the established model of SVM classifier to classify and then obtain 
the prediction labels of the test sample (Fig. 3(a)). 
COMBINED IMPROVED EEMD WITH SVM IN ULTRA-LOW-DIMENSIONAL ULTRA-SMALL-SAMPLE APPLICATION OF MULTI-CLASSIFICATION 
INTELLIGENT FAULT DIAGNOSIS. BAIYONG ZHANG, KAI LIU, JIONG SUN, KAI CHAI 
244 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533  
 
a) Ultra-low-dimensional ultra-small-sample  
multiple classification 
 
b) Large sample of two  
high-dimensional classification 
Fig. 3. Large sample of ultra-low-dimensional ultra-small-sample sample label SVM prediction 
SVM use Sigmoid kernel function to create classifier which let 10 groups of normal state all 
the data among the test sample miscalculate into race fault. Ball bearing failure, the failure of inner 
ring and outer ring altogether 30 sets of data in total mistaken for normal state, correct rate of four 
classifications is 0. 
Whether the method combined the improved EEMD with SVM when uses Sigmoid kernel 
function to create a classifier can have the correct classification functions? For simplicity, this 
paper conducted normal and ball bearings, inner ring and outer ring three kinds of fault state of 
binary classification recognition under the condition of high dimension large sample (Fig. 3(b)), 
the binary classification accuracy rate of normal and ball bearings, inner ring and outer ring three 
kinds of fault state recognition under the condition of high dimension large sample is 92.5 %, 
Fig. 3 is a high-dimensional large sample and low-dimensional small sample classification 
accuracy comparison. 
4. The method combined the improved EE- MD with SVM ultra-low-dimensional ultra-
small-sample SVM parameter optimization and diagnostics 
In order to improve the ultra-low-dimensional ultra-small-sample four classifications  
accuracy, to further enhance the classification accuracy, this paper interactive test mode through 
the grid optimization method to find the best adapted kernel function parameters ܿ and ݃. 
4.1. SVM parameter optimization 
The SVM applied to the bearing of the ultra-low-dimensional ultra-small-sample classification 
test, just set the parameters ܿ  and ݃, determined by using the grid optimization, observe and 
compare the classification accuracy rate changes. 
Training samples after parameter optimization are still using ultra-low-dimensional 
ultra-small-sample four classified training samples and Sigmoid kernel function, and used the grid 
optimization method to determine the parameters ܿ and ݃: 
1) Parameter ܿ, ݃ values in a wide range, can set ܿ ∈ [2-30 230], ݃ ∈ [2-5 220], in log2ܿ as 
the ܺ -axis, log2݃  as the ܻ -axis, then the point ( log2ܿ , log2݃ ) constitute the grid plane  
log2ܿ − log2݃; Set classification accuracy (%) as the ܼ-axis, the combination constitutes a SVM 
classification accuracy 3D space grid. 
2) Training samples and the corresponding labels are divided into six subsets, apply the 
interactive test mode, part of a randomly selected subset of the subset as training samples and test 
samples subset, through all points (log2ܿ , log2݃) in the log2ܿ − log2݃  grid plane for SVM 
training, create a series of classifiers, calculate multiple classification accuracy and then obtain 
3D spatial distribution of SVM classification accuracy (Fig. 4). 
3) The 3D spatial distribution of the SVM classification accuracy projected into the grid plane 
log2ܿ − log2݃. Connect all the same classification accuracy rate corresponding points, and then 
obtain classification accuracy contour (Fig. 5)  
In Fig. 5, find the curve of the highest classification accuracy; all points on the curve (log2ܿ, 
COMBINED IMPROVED EEMD WITH SVM IN ULTRA-LOW-DIMENSIONAL ULTRA-SMALL-SAMPLE APPLICATION OF MULTI-CLASSIFICATION 
INTELLIGENT FAULT DIAGNOSIS. BAIYONG ZHANG, KAI LIU, JIONG SUN, KAI CHAI 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533 245 
log2݃ ) can make SVM classification model create the highest classification accuracy; 
Corresponding values of ܿ  and ݃  can be as the best parameter ܿ  and ݃ . Choose one set of 
parameters ܿ = 0.00093132, ݃ = 0.03125 as the best SVM parameters. 
 
Fig. 4. The 3D spatial distribution of SVM 
classification accuracy 
 
Fig. 5. SVM classification accuracy contour 
 
4.2. Ultra-low-dimensional ultra-small-sample four classifications fault identification after 
optimization 
By Sigmoid kernel function and the optimal parameters ܿ, ݃, let the above training sample set 
make SVM training again to establish the classification model. 
The ultra-low-dimensional ultra-small-sample test sample set input to the already established 
model of SVM classifier to classify to obtain the predicted label of the test sample set (Fig. 6). 
 
Fig. 6. Ultra-low-dimensional ultra-small-sample test set prediction labels 
Classification results showed that: when the parameter ܿ , ݃ through the grid optimization 
method, SVM that used Sigmoid kernel function classification accuracy rate reached 100 %, under 
the conditions of ultra-low-dimensional ultra-small-sample multi-classification bearing four states 
entirely correctly distinguish. SVM classification results will be different in the same kernel 
function under different parameter settings. Interactively test mode and grid optimization method 
can find the optimal SVM parameters to help achieve the desired learning outcomes and 
generalization performance, thereby enhancing the method combined the improved EEMD with 
SVM in ultra-low-dimensional ultra-small-sample fault intelligent diagnostic accuracy. 
5. Conclusions 
This paper successfully applied the method combined the improved EEMD with SVM to the 
ultra-low-dimensional ultra-small-sample four categories intelligent fault diagnosis. 
1) Proposed by using the threshold noise reduction, improved cubic spine interpolation, signal 
SVM extension and other measures to improve EEMD approach. 
2) Researched the cross-validation model grid optimization SVM parameters, obtained 
optimal parameters of the SVM by using Sigmoid kernel function. 
70 70 7074.5 74.5 74.5
74.5 74.5
74.5 74.5
74.5 74.5 74.5
74.574.5
74.5 74.5
79 7979
79 79
7979
79 79
79 79
83.5 83.5 83.5
83.583.5
83.5 83.5
83.5
88 88 88
88
92.5 92.5
92.5
97 97 97 97
log2c
log
2g
-30 -20 -10 0 10 20 30
-5
0
5
10
15
20
COMBINED IMPROVED EEMD WITH SVM IN ULTRA-LOW-DIMENSIONAL ULTRA-SMALL-SAMPLE APPLICATION OF MULTI-CLASSIFICATION 
INTELLIGENT FAULT DIAGNOSIS. BAIYONG ZHANG, KAI LIU, JIONG SUN, KAI CHAI 
246 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. DEC 2016, VOL. 10. ISSN 2345-0533  
3) Applied the cross-validation model grid optimization SVM optimal parameters, SVM by 
using Sigmoid kernel function to the ultra-low-dimensional ultra-small-sample four categories 
intelligent fault diagnosis classification accuracy rate reached 100 %, SVM parameter 
optimization can improve the method combined the improved EEMD with SVM in 
ultra-low-dimensional ultra-small-sample four categories fault diagnosis accuracy. 
Acknowledgement 
This project was financially supported by Natural Science Foundation of China (51175511). 
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Combined improved EEMD with SVM in ultra-low-dimensional ultra-small-sample application of multi-classification intelligent fault diagnosis

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Combined improved EEMD with SVM in ultra-low-dimensional ultra-small-sample application of multi-classification intelligent fault diagnosis

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