Vibration signals of gearbox are sensitive to the existence of the fault. Based on vibration signals, this paper presents an implementation of deep learning algorithm convolutional neural network (CNN) used for fault identification and classification in gearboxes. Different combinations of condition patterns based on some basic fault conditions are considered. 20 test cases with different combinations of condition patterns are used, where each test case includes 12 combinations of different basic condition patterns. Vibration signals are preprocessed using statistical measures from the time domain signal such as standard deviation, skewness, and kurtosis. In the frequency domain, the spectrum obtained with FFT is divided into multiple bands, and the root mean square (RMS) value is calculated for each one so the energy maintains its shape at the spectrum peaks. The achieved accuracy indicates that the proposed approach is highly reliable and applicable in fault diagnosis of industrial reciprocating machinery. Comparing with peer algorithms, the present method exhibits the best performance in the gearbox fault diagnosis.
Gearboxes play crucial roles in the mechanical transmission systems, are used to transmit power between shafts, and are expected to work 24 hours a day in the production system. Any failures with the gearboxes may introduce unwanted downtime, expensive repair, and even human casualties. Therefore it is essential to detect and diagnose faults in the initial stage [
Machine fault identification can be done with different methodologies such as vibration signature analysis, lubricant signature analysis, noise signature analysis, and temperature monitoring. The gearbox conditions can be reflected by such measurements as vibratory, acoustic, thermal, electrical, and oilbased signals [
Various studies exist, of algorithms for detection and diagnostics of faults in gearboxes; among these are support vector machines and artificial neural network. A support vector machines based envelope spectrum was proposed by Guo et al. [
Recently, deep learning received great success in the classification field. The deep learning gained better classification performance owing to its “deeper” representations for the faulty features. Up to now, different deep learning networks such as deep belief network [
This paper presents a study for the application of the convolutional neural network in the identification and classification of the gearboxes fault. Convolutional neural network (CNN) is a type of feedforward artificial neural network. Its individual neurons are tiled in such a way that they respond to overlapping regions in the visual field [
The most successful methods of vibrationbased fault diagnoses are composed of two main steps: extracting the sensitive features and classifying the condition patterns. In the vibrationbased fault diagnosis, the most commonly used features have been generated from the temporal [
The rest of this paper is structured as follows. The CNN model and method of extracting statistical features are introduced in Section
In this section, we first present the representations of the convolutional neural network. And then the approach of extracting the sensitive features is introduced, where some classical statistical parameters are calculated from the time and the frequency.
Convolutional neural network was inspired by the visual system’s structure [
A typical convolutional neural network [
At each location of each layer, there are a number of different neurons. Each has its set of input weights that is associated with neurons in a rectangular patch in the previous layer. The same set of weights, but a different input rectangular patch, is associated with neurons at different locations.
Figure
Architecture of convolutional neural networks.
Convolutional layers move forward with deriving the back propagation updates in a network, which compose feature maps by convolving kernels over feature maps in layers below them. At a convolution layer, the previous layer’s feature maps are convolved with learnable kernels and put through the activation function to form the output feature map. Each output map may combine convolutions with multiple input maps. In general, it is calculated as follows [
A subsampling layer produces downsampled versions of the input maps. If there are
To discriminate between
The gearbox condition can be reflected by the information included in different features in frequency and time domain. From the set of signals obtained from the measurements of the vibrations at different speeds and loads, the features in frequency and time domain are obtained. From the group of graphs the values that can be used as input parameters for the CNN are selected. Sixty percent of the samples set are used for the training of the CNN, and forty percent are used for testing.
Usually, statistical parameters are good indices for extracting the condition information. In this research, statistical measurements such as standard deviation, skewness, and kurtosis for each node are used. Standard deviation, skewness, and kurtosis are computed from the acquired time domain data; the formulas used for this are shown in Table
Formula for the evaluation of statistical values.
Feature  Definition 

Mean 



Standard deviation 



Skewness 



Kurtosis 

Figure
Frequency spectrum in function of the speed, under the following condition patterns: 375 W load,
Frequency spectrum under five combinations of different condition patterns.
With the objective of reducing the amount of input data to the CNN the spectrum was split in multiple bands, because with this number of bands the root mean square (RMS) values keep track of the energy in the spectrum peaks [
Vectors of the features of the preprocessed signal are formed as input parameters for the CNN as follows:
To validate the effectiveness of the proposed method, we carried out the experiments on a gearbox fault experimental platform. Figure
Gear
Gear
Bear
Bear
Gears
Test’s conditions.
Characteristic ( 
Value 

Sample frequency  44100 [Hz] (16 bits) 
Sampled time  10 [s] 
Power  1000 [W] 
Minimum speed  700 [RPM] 
Maximum speed  1600 [RPM] 
Minimum load  250 [W] 
Maximum load  750 [W] 
Speeds  1760, 2120, 2480, 2840, 3200 [mm/s] 
Loads  375, 500, 625, 750 [W] 
Number of loads per test  10 
Type of accelerometer  Uniaxial 
Trademark  ACS 
Model  ACS 3411LN 
Sensibility  330 [mV/g] 
Nomenclature of gears fault.
Designator  Description 

1  Normal 
2  Gear with face wear 0.4 [mm] 
3  Gear with face wear 0.5 [mm] 
4  Gear with chafing on tooth 50% 
5  Gear with chafing on tooth 100% 
6  Gear with pitting on tooth depth 0.05 [mm], width 0.5 [mm], and large 0.05 [mm] 
7  Gear with pitting on teeth 
8  Gear with incipient fissure on 4 mm teeth to 25% of profundity and angle of 45° 
9  Gear teeth breakage 20% 
10  Gear teeth breakage 50% 
11  Gear teeth breakage 100% 
Nomenclature of bears fault.
Designator  Description 

1  Normal 
2  Bearing with 2 pits on outer ring 
3  Bearing with 4 pits on outer ring 
4  Bearing with 2 pits on inner ring 
5  Bearing with 4 pits on inner ring 
6  Bearing with race on inner ring 
7  Bearing with 2 pits on ball 
8  Bearing with 2 pits on ball 
Condition patterns of the experiment.
Number of patterns  Basic faults  

Gear faults  Bear faults  







 
A  7  3  1  1  1  2  3  1 
B  7  3  6  8  1  1  1  1 
C  5  5  1  1  6  7  2  1 
D  7  1  1  1  6  7  2  1 
E  1  2  1  1  1  6  3  1 
F  1  3  1  1  1  5  3  1 
G  2  9  1  1  6  7  3  1 
H  5  5  1  1  6  3  2  4 
I  2  6  1  1  6  5  2  1 
J  1  11  1  1  1  3  4  1 
K  1  1  1  1  1  6  3  1 
L  1  1  1  1  1  1  3  1 
(a) The internal configuration of the gearbox; (b) positions for accelerometers.
To evaluate the performance of the proposed method for gearbox fault diagnosis, first, we constructed 12 condition patterns as listed in Table
In this section, the implementation of classifier based on CNN will be introduced. Figure
The size of input feature map,
The number of alternating convolution and subsampling layers that decides the architecture of CNN is as follows. Two schemes are investigated: one is two convolutional layers and two subsampling layers; another is one convolutional layer and one subsampling layer.
The number of output feature maps of convolution layer,
The scale of subsampling layer,
For each input map convolve with corresponding kernel and add to output map; the convolutional kernel is usually a matrix of
Training and testing process block diagram.
To confirm the optimal architecture of CNNbased classifier for gearbox fault diagnosis, some parameter tunings are performed. Table
Parameters tuning of the architecture of CNN.
Number  Architecture of CNN  Classification rate  Time (s/epoch)  






 
#1 

6  2  12  2  5  86.73%  11.6 s 
#2 

8  2  8  2  5  88.48%  12.8 s 
#3 

12  2  12  2  5  92.50%  21.7 s 
#4 

8  4  —  —  5  86.71%  8.00 s 
#5 

6  2  12  2  5  90.23%  3.90 s 
#6 

8  2  8  2  5  89.50%  3.80 s 
#7 

6  2  6  1  5  95.71%  2.40 s 
#8 

6  1  6  1  5  98.77%  4.50 s 
#9 








#10 








#11 








Implementation of classifier based on CNN and statistical features.
The training is done in first instance with the 12 patterns indicated in Table
Parameters tuning of CNN.

Epochs  

300  250  200  150  100  50  
12  97.98%  98.0% 

96.71%  95.35%  89.46% 
8  97.92%  98.19% 

97.98%  96.31%  91.19% 
6  97.98%  97.27% 

96.71%  96.25%  93.1% 
Confusion matrix is an effective tool and is a visualization tool of the performance of a classification algorithm. Each column of the confusion matrix represents the instances in a predicted class (output class), while each row represents the instances in an actual class (target class). Figure
Confusion matrix using CNN.
To further validate the robustness of the present CNN model, a fault condition pattern library was constructed, which has 58 kinds of combinations based on the basis patterns described in Tables
Comparisons of classification rate with SVM using 20 test cases.
Number  1  2  3  4  5  6  7  8  9  10 

CNN 










SVM  73.8%  77.4%  65.9%  67.5%  65.5%  79.2%  69.1%  81.5%  66.8%  72.0% 


Number  11  12  13  14  15  16  17  18  19  20 


CNN 










SVM  72.3%  66.4%  55.9%  64.7%  63.5%  67.0%  62.1%  61.3%  64.0%  60.9% 


Mean  Std.  Least  Most  Median  


CNN 






SVM  67.8%  6.49%  55.9%  81.5%  66.8% 
In addition, the CNN method was compared with “shallow” learning algorithms SVM. As for the SVM, one of the most important representatives in the “shallow” learning community, good classification results can be found for the gearbox fault diagnosis, which is similar with some existing researches (e.g., [
Confusion matrix using SVM.
In this paper, a deep learning technique based CNN for the vibration measurements has been proposed to diagnose the fault patterns of the gearbox. The present CNN method identifies and classifies faults in gearbox by using the vibration signals measured with an accelerometer. Feature representations are selected as the input parameters of the CNN with a vector formed by RMS values, standard deviation, skewness, kurtosis, rotation frequency, and applied load. For evaluating the proposed CNN method, the gearbox fault diagnosis experiments were carried out using different techniques. The results show that the present method has the outstanding performance of the gearbox fault diagnosis, comparing with peer methods. This type of classifiers could make a contribution to maintenance routines for industrial systems, towards lowering costs and guarantying a continuous production system, and, with the appropriate equipment, online diagnostics could be performed.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by Natural Science Foundation Project of CQ CSTC (nos. cstc2012jjA40041 and cstc2012jjA40059), Science Research Fund of Chongqing Technology and Business University (no. 20115605), the National Natural Science Foundation of China (51375517), and the Project of Chongqing Innovation Team in University (KJTD201313).