DETECTION OF MECANICAL DEFECTS BY NEURAL NETWORKS
“Experimental Analysis”
Bouzouane Bélaid1 and Hamzaoui Nacer2
1
Laboratoire de Mécanique Avancée (LMA), Université des Sciences et de la Technologie
Houari Boumédiène, BP 32, El Alia, 16111 Bab Ezzouar, Alger Algérie.
2
Laboratoire de Vibrations Acoustique (LVA), INSA de Lyon, Bât. Antoine de Saint
Exupéry, 25 bis, Avenue Jean Capelle, 69621 Villeurbanne Cedex, France.
Abstract :
Various methods are implemented to identify the nature of a defect on a rotating machine, by using
vibratory measures; they differ in their precision, simplicity of implementation and their sensitivity to errors
measurement. The identification of several defects combination is still difficult to implement by conventional
signal processing, as the vibration signal that emerges is disturbed, thus making any identification so hard.
In this study, we proposed a method based on the neural networks to identify one defect or several
combinations of mechanical defects. Thus we propose the neuronal method: the Radial Basis Function (RBF).
We highlight their capacity to detect the defect and their sensibility with regard to a signal noise characterizing
the other independent sources to the defects. This evaluation will be done with measurement will be carried out
on a housing bearing and test bench made up of a toothed gearing on two floors, and without lubrication. Some
provoked defects will be analyzed in this study.
Keywords:
Neural Network, Radial Basis Function, Back Propagation, Diagnosis Bearings defaults, Diagnosis gears
defaults, Signal processing.
I. INTRODUCTION
Awareness in industry of the importance of conditional maintenance dawned early, and
account was taken of the significant role played by vibration when diagnosing defects in
rotating machines. Indeed, changes in the vibratory signature of rotating machines are often
the first physical manifestation of an anomaly, potential causes of damage and or faults.
Moreover, the global parameters resulting from this signature are good indicators for
monitoring the condition of rotating machine and mention can be made of a global vibratory
velocities ranging from 10 to 1000 Hz, the crest factor and kurtosis.
However, diagnoses also call on other investigation techniques, such as spectral analysis
[1], though this is often insufficient in particular when the signal results from a defect
generated by defective bearings and gears. Cepstral analysis, Envelope analysis, Short-Time
Fourier Transform [2] and wavelet transforms [3] can be used to solve such problems.
Nevertheless, few systems make use of these techniques and monitoring remains the
responsibility of a specialist. Furthermore, detecting defects is more painstaking as a signal
generated by a bearing may be masked by noise or other defects.
The more complex mechanical systems and rotating machines, in particular become, the
more difficult it is to maintain them. Also, as machines are becoming increasingly automated,
a new type of maintenance is being implemented, based on condition monitoring maintenance
using neural networks. Mention can be made of the Wenlung Li’s [4] experimental study of
an expert system that uses a neural network based on acoustical signals to diagnose unbalance
on a rotating machine. It relies on a Back propagation Neural network (BPN) with one hidden
layer.
The article by Lay Wuxing [5] is interesting when approaching this type of problem.
Indeed, each tooth in a gear is engaged in alternation thus the load conditions are also
alternated. Moreover, Gaussian type noise is generated leading to measurements that make
detecting gear defects very difficult.
This paper proposes an approach for classifying gear defects in order to achieve good
identification, by using two step-treatments: the “cumulative” method and “Radial Basis
Networks”. The first is used to minimize Gaussian noise and the second is a network that allows
rapid convergence of the network. The Radial Basis Network is then used as a classifier for the
different states of the gearing cycle, i.e. different normal or defective conditions. The results
showed that this method of classification based on the combination of “cumulative” and
Radial Basis Networks is very promising and provides better precision.
Here, we use Radial Basis Networks in order to identify gear and bearing defects
simultaneously. The purpose of this work is to provide additional analysis for defect
identification by using the neuronal approach. A demonstration is presented of the capacity of
this technique to identify the defect to be diagnosed.
II. THEORICAL STUDY
1.
Neural networks
An elementary neuron is a programmable controller composed of several inputs Xi, one output
(see Fig. 1), and a transfer function between the neuron’s inputs and its output.
f is the activation function, the parameters wi and b are respectively the weight and the bias that are
the unknowns of the problem, allowing the network to adapt to the desired output.
x1
1 Output
w1
N inputs

xN
wN
f()
a
b
Figure 1. Formal neuron.
Output a is given by the expression:
N
a  f   a i  b 
1

(1)
The generalization of the neuron to a larger system in order to solve more complex
problems leads to forming neural networks. This requires the introduction of multiple outputs
and at least one intermediate layer called hidden layer with several neurons (see Fig. 2).
Each neuron is adjustable, by changing the weights wi and bias bi to adapt the network
from the input vector X to the output vector A.
X = (x1, ……, xN) and A = (a1, ……, a m).
To achieve this, we use a learning base containing a set of vectors Xj and Ann, nn
being the number of training sets. For each set the training consists in evaluating parameters
wi and bi in order to minimize the total error between the desired output and the output
calculated by the network.
The final stage of the network is its application. The network is presented with a non
trained set X and by interpolation: if X resembles Xj, it will have the label Aj.
Input layer
x1
w21
w 11
, 1
Output layer
Hidden layer
, 1

f1
2
a 11 w1 , 1

f2
F
b 12
ig
b
1
w 11
u
, N
fr1

f2
1

2
a
w
e
1
2
xN
m , 2
w
1
2, N
2
1.
b2
bm
N
e
Figure
u 2. Neural networks.
r
Outputs ai are given by :
o
a m  f 2 (a 11 w n2m ,1  a 12 w 2m , 2  b 2m )
e
f
where :
o
a 12  f1 ( x 1 w 12 ,1 r ......  x N w 22 , N  b12 )
m
el
a 11  f1 ( x 1 w 11,1  ......  x N w 12, N  b11 )
a1
1
a2
(2)
2. Radial Basis Network
This network is a network with error back-propagation whose hidden layer activation
function is a Gaussian function (see Fig. 3)
 (x  c j ) T (x  c j ) 
f1 ( x )  exp 
,
2  j2


Nc is the number of neurons on the hidden layer.
2  j : Characterizes the Gaussian flatness
2
j  1, ......., N c
(3)
cj designates the center of the activation function of the radial neuron, usually taken as equal to wi .
thus we obtain :
 xi  wi j
f1 ( x )  exp 
2  j2


,

j  1, ......., N c et i  1,......, N
(4)
frames the Euclidian norm and N represents the number of neurons in the input layer.
Contrary to the sigmoid neurons, the radial neurons work locally, thereby considerably reducing the
size of the calculations and thus treating the problem with one input of the network containing several
neurons.
Figure3. Activation function of the hidden layer
III. Experimental Analysis
1. Description of the test bench and experimental protocol
The test bench consists of a two stage toothed gear and a bearing housing (see Fig. 4)
both hooded by a structure made of steel plate, of which the lid and one side were made of
Plexiglas to allow vibrometer measurements.
The four pinions had straight teeth with a modulus of 2mm. The number of teeth were
Z1 = 45, Z2 = 65, Z3 = 50 and Z4 = 42 respectively. Bearings with one line of balls (SKF
6002 type) were assembled on the six housings.
In order to generate the different series of training sets and the sets to test the network,
we simulated tooth defects in the form of scratch on one tooth on pinions 1 and 3. Three types
of degradation were imposed on wheel 1: moderate, accentuated and very accentuated. Two
types of degradation were imposed on pinion 3: moderate and accentuated. Similarly, on the
bearing of housing P2 defects were simulated on the inner ring and the outer ring in the form
of scratches. Two types of degradation were employed for each ring: moderate and
accentuated.
When running the motor at N = 1800 rpm, the combination of these various defects
enabled us to generate 60 different series (including the signal generated by the machine in its
new state) in the form of signals collected at a sampling rate of 48000 Hz with an acquisition
time of 10s. Fifty series were chosen for the training and ten were chosen to test the network.
The accelerometer allowing acquisition was placed on bearing housing P2. The signals and
the series used to test the network were taken between the higher and lower limits of the
series chosen for training the interpolation network. Measurements were performed in the
lubricated case.
P1
1
3
2
P2
4
Figure 4. Test bench (two stage speed reduction gear ).
A Radial Basis Function network was used as a very high sampling rate was applied for
the signals used for the training, Fe = 48 000 Hz during acquisition time T = 10s (see Fig.5).
Moreover, this type of network is better adapted to the signals in the presence of a strong
noise, which is the case in reality, as shown previously.
1
x 10
4
Ampltude (mg)
0.5
0
-0.5
-1
-1.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time (s)
Figure 5. Signal of gear defect on wheel 3 and on the external ring of the bearing.
During training, we presented the amplitudes of the sampled signal to the network. The
output is binary: 1 if there is defect and 0 otherwise. The position of the activated neuron
depends on the type of defect (see Table 2).
Simulated Defects
Gear 1 : 03 degradations (moderate, accentuated, aggravated)
Gear 3 : 02 degradations (moderate, accentuated)
Bearing : housing P2
Defect on external ring : 02 degradations (moderate, accentuated)
Table1. Simulated defects.
Normal (without defects)
Gear defect 1
Gear defect 3
External ring bearing defect
Gear defect 1 and external ring bearing defect
(
(
(
(
(
Neurons of the output layer
1 ; 0 ; 0 ; 0 ; 0 )
0 ; 1 ; 0 ; 0 ; 0 )
0 ; 0 ; 1 ; 0 ; 0 )
0 ; 0 ; 0 ; 1 ; 0 )
0 ; 0 ; 0 ; 0 ; 1)
Table2. Training series and their corresponding outputs.
2. Determination of the natural frequencies of the structure
Fig. 6 shows the spectrum of the gear defect on pinion 1. We noted spectral emergences
around 750 Hz and 3000 Hz. Measurements were taken on the housing P2 (see Fig. 4).
1500
Amplitude (mg)
without defect
with accentuated defect
with moderate defect
1000
500
0
0
1000
2000 3000 4000
Frequency (Hz)
5000
6000
Figure 6. Spectrum of defects on the wheel N°1 at N = 1800 rpm.
This spectrum shows the full difficulty of diagnosis in the presence of frequencies of
higher amplitude related to the vibratory response of the main structure. The amplitudes of
these frequencies increase with the aggravation of the defect that acts like a loading force. We
carried out an experimental modal analysis to identify the frequencies and natural modes of
the structure encasing the speed reduction gear. These frequencies correspond to the natural
frequencies of this structure. Fig. 7, shows the four natural modes placed under stress during
our vibratory measurements. These modes were obtained by experimental modal analysis
(vibratory measurements at several points of the envelope of the speed reduction gear), the
excitation point is a pulse on the steel plate close to the bearing housing P2.
(a) 752 Hz
(b) 3000 Hz
Figure7. Vibration modes of the structure encasing the speed reduction gear.
The advantage of the neuronal approach is that during training it integrates these
different types of information related to the proper frequencies of the structure or to a specific
background noise, so as to take into account new events such as the emergence or aggravation
of a mechanical defect in the detection.
3. Results :
Table 3 shows the results obtained by transmitting signals of non learned defects to the
network. Neuron1, which corresponds to the normal case (without defect), is activated
whereas the others are not, thereby demonstrating efficient identification. The results
presented in this paper concern the lubricated case.
We obtained the same results for the other types of defects: gear1, gear 3 and bearing.
The neuron matching the defect was activated each time. However, when introducing a
moderate bearing defect alone or combined with a gear defect (gear 1 in this case), the
network tented to detect no defect for the first case and a gear defect for the second case.
Generalization
Neuron 1
Normal
Gear 1
Gear 3
Gear 3
Bearing BE moderate
R Bearing BE
Bearing BE
Gear 1+ Bearing BE
Gear 1+ Bearing BE
Gear 1+ Bearing BE moderate
0.9194
0.1223
0.1198
-0.0101
0.6627
0.1188
0.1077
-0.0912
0.1702
-0.0208
Neuron 2Ne
Neuron
Neuron 3 4
-0.1054
0.1052 0.1151
- 0.1117 0.1239
0.9017
-0.1235
0.9526 0.1287
0.0238
0.9367 0.0601
0.0277
- 0.0063 0.3016
0.2275
- 0.1191 0.8871
-0.2254
- 0.0081 0.8702
-0.3912
- 0.1046 0.0991
0.4702
0.1113 0.1209
- 0.0106 0.0219
0.7811
Neuron
5
0.1109
0.1109
0.1184
0.0001
0.0150
0.1024
-0.1877
0.6106
0.5642
0.2030
Table 3. The example tested and their corresponding output neurons.
Fig. 8, shows the rate of detection for each case treated. It clearly shows the capacity of
the network to identify the defect. However, the results are less good in the case of combined
defects.
Figure 8. Detection rate of simulated defects.
Conclusion
The study enabled us to show that the Radial Basis Function network adapted for
detecting and identifying defects, with regard to background noise signal sampling. The
implementation of this network enabled us to systematically identify the type of defect.
However, identification is more difficult in the case of combined bearing and gear defects
than a gear defect alone.
The results showed that identification becomes tedious and erroneous in the presence of
noise, corresponding to a non lubricated case in a real situation. It is therefore necessary to
process the signals measured.
Taking this work further, it would be interesting to consider the neuronal method in
combination with the wavelet method and filtring in a non lubricated case.
Bibliography
[1] M. SID AHMED. Traitement du signal pour détecter de manière précoce les défaillances
des machines. Forum FIST 91, Orléans 1991.
[2] RANDALL, R.B. Developments in Digital Analysis Techniques for Diagnostics of
Bearings and Gears. Fifth International Congress on Sound and Vibration, December 15-18,
(1997),pages 300- 309 Adelaide, South Australia.
[3] V. PURUSHOTHAM, S. NARAYANAN and SURYANARAYANA A.N. PRASOD.
Multi-faults diagnosis of rolling bearing element using wavelet analysis and hidden Markov
model based fault recognition. NDT&E International, Volume 38, Issue 8, December 2005,
Pages 654-664.
[4] WENLUNG Li, Y.P. TSAI and C.L. CHIU. The experimental study of the expert system for
diagnosing unbalances by ANN and acoustic signals. Journal of Sound and Vibration, Volume
272, Issue 1+2, April 2004, Pages 69-83.
[5] Lai WUXING, Peter W. TSE, Zhang GUICAI and Shi TIELIN. Classification of gear fault
using cumulants and the radial basis function network. Mechanical Systems and Signal
Processing Volume18, Issue 2, Mars 2004, Pages 381–389