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Noise Eliminated Ensemble Empirical Mode Decomposition Scalogram Analysis for Rotating Machinery Fault Diagnosis

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Rotating machinery is one of the major components of industries that suffer from various faults due to the constant workload. Therefore, a fast and reliable fault diagnosis method is essential for machine condition monitoring. In this study, noise eliminated ensemble empirical mode decomposition (NEEEMD) was used for fault feature extraction. A convolution neural network (CNN) classifier was applied for classification because of its feature learning ability. A generalized CNN architecture was proposed to reduce the model training time. A sample size of 64×64×3 pixels RGB scalograms are used as the classifier input. However, CNN requires a large number of training data to achieve high accuracy and robustness. Deep convolution generative adversarial network (DCGAN) was applied for data augmentation during the training phase. To evaluate the effectiveness of the proposed feature extraction method, scalograms from related feature extraction methods such as ensemble empirical mode decomposition (EEMD), complementary EEMD (CEEMD), and continuous wavelet transform (CWT) are classified. The effectiveness of scalograms is also validated by comparing the classifier performance using grayscale samples from the raw vibration signals. All the outputs from bearing and blade fault classifiers showed that scalogram samples from the proposed NEEEMD method obtained the highest accuracy, sensitivity, and robustness using CNN. DCGAN was applied with the proposed NEEEMD scalograms to further increase the CNN classifier’s performance and identify the optimal number of training data. After training the classifier using augmented samples, the results showed that the classifier obtained even higher validation and test accuracy with greater robustness. The proposed method can be used as a more generalized and robust method for rotating machinery fault diagnosis.
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sensors
Article
Noise Eliminated Ensemble Empirical Mode Decomposition
Scalogram Analysis for Rotating Machinery Fault Diagnosis
Atik Faysal 1, Wai Keng Ngui 1,* , Meng Hee Lim 2and Mohd Salman Leong 2


Citation: Faysal, A.; Ngui, W.K.; Lim,
M.H.; Leong, M.S. Noise Eliminated
Ensemble Empirical Mode
Decomposition Scalogram Analysis
for Rotating Machinery Fault
Diagnosis. Sensors 2021,21, 8114.
https://doi.org/10.3390/s21238114
Academic Editors: Mohammad
N. Noori, Marco Domaneschi and
Naiwei Lu
Received: 14 October 2021
Accepted: 24 November 2021
Published: 4 December 2021
Publisher’s Note: MDPI stays neutral
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Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1College of Engineering, Universiti Malaysia Pahang, Pekan Pahang 26600, Malaysia; faisal.atik@gmail.com
2Institute of Noise and Vibration, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia;
limmenghee@gmail.com (M.H.L.); salman.leong@gmail.com (M.S.L.)
*Correspondence: wkngui@ump.edu.my
Abstract: Rotating machinery is one of the major components of industries that suffer from various
faults due to the constant workload. Therefore, a fast and reliable fault diagnosis method is essential
for machine condition monitoring. In this study, noise eliminated ensemble empirical mode decom-
position (NEEEMD) was used for fault feature extraction. A convolution neural network (CNN)
classifier was applied for classification because of its feature learning ability. A generalized CNN
architecture was proposed to reduce the model training time. A sample size of 64
×
64
×
3 pixels RGB
scalograms are used as the classifier input. However, CNN requires a large number of training data to
achieve high accuracy and robustness. Deep convolution generative adversarial network (DCGAN)
was applied for data augmentation during the training phase. To evaluate the effectiveness of the
proposed feature extraction method, scalograms from related feature extraction methods such as
ensemble empirical mode decomposition (EEMD), complementary EEMD (CEEMD), and continuous
wavelet transform (CWT) are classified. The effectiveness of scalograms is also validated by compar-
ing the classifier performance using grayscale samples from the raw vibration signals. All the outputs
from bearing and blade fault classifiers showed that scalogram samples from the proposed NEEEMD
method obtained the highest accuracy, sensitivity, and robustness using CNN. DCGAN was applied
with the proposed NEEEMD scalograms to further increase the CNN classifier’s performance and
identify the optimal number of training data. After training the classifier using augmented samples,
the results showed that the classifier obtained even higher validation and test accuracy with greater
robustness. The proposed method can be used as a more generalized and robust method for rotating
machinery fault diagnosis.
Keywords:
convolution neural network; empirical mode decomposition; deep convolution genera-
tive adversarial network; continuous wavelet transform
1. Introduction
When any fault occurs in a rotating machinery part, the vibration data carry the
fault information in a series of periodic impulses. Due to the presence of various signals
and noise in the environment, the fault information in raw vibration data may be easily
submerged in the noise. Thus, the separation of faulty information might get complicated.
Generally, signal-processing methods are applied to extract the tiniest information possible.
Typically, the baseline condition has smaller impulses, and fault conditions have relatively
higher impulses, making them easier to differentiate. However, in the practical field, the
search for the fault occurrence in the whole signal is unfeasible by human convention.
Thus, the use of artificial intelligence for finding the fault pattern in the signal is a popular
method [
1
]. Artificial intelligence or machine learning methods offer automated fault
diagnosis by learning from the fault features from the previous data.
Typically, signal processing requires skilled human interaction to select tunable pa-
rameters during preprocessing. The time-frequency adaptive decomposition methods
Sensors 2021,21, 8114. https://doi.org/10.3390/s21238114 https://www.mdpi.com/journal/sensors
Sensors 2021,21, 8114 2 of 29
can automatically decompose a signal without skilled human intervention. A robust
time-frequency analysis, empirical mode decomposition (EMD), was first presented in
1998. Since its arrival, EMD has been applied to stationery and non-stationary signals
in numerous fault diagnosis research [
2
,
3
]. In EMD, the time scale is divided into a set
of orthogonal components known as intrinsic mode function (IMF). In papers [
4
,
5
], the
authors used EMD and EEMD for bearings and gears fault diagnosis. Nguyen et al. [
6
]
proposed a novel fault diagnosis technique for rolling bearing. A combination of EMD, NB
classifier, and noise components threshold was suggested for their approach. However, the
major drawback is the mode mixing of the IMFs.
To solve the mode-mixing problem, Huang and Wu [
7
] proposed the EEMD, which
can overcome the limitations of EMD. Wu et al. [
8
] added an autoregressive model with
EEMD to detect looseness faults of rotor systems. EEMD-based methods were proposed by
Lei et al. [
9
] to identify initial rub-impact faults of rotors and compared EEMD with EMD
to show superiority. Nonetheless, white noise can still be highly present in the IMFs of
EEMD after even performing a bunch of ensembles. To significantly decrease the white
noise, many ensembles are required that enhance the computational cost. Yeh et al. [
10
]
proposed CEEMD to reduce the limitations of EEMD. CEEMD adds white noise in positive
and negative pairs that can reduce the residual noise in the reconstructed signal with fewer
ensembles. Yang [
11
] combined CEEMD and wavelet threshold for noise reduction of
rolling bearing vibration signals. IMFs were obtained using CEEMD and selected based
on kurtosis index and correlation coefficients. The fault impulses were obtained using
the envelope spectrum. CEEMD can significantly decrease white noise, but it does not
eliminate the limitations and needs further attention. To address this problem, Faysal
et al. [
12
] proposed noise eliminated EEMD, which reduces the white noise in the IMFs
while maintaining the same number of ensembles. In this method, the ensemble white
noise is also decomposed and subtracted from the original ensemble IMFs. Therefore, more
white noise can be eliminated from the resulting IMFs.
Lately, deep learning has become the most attractive research trend in the area of AI.
With the ability to learn features from raw data by deep architectures with many layers of
non-linear data processing units, the deep neural network (DNN) model is a promising
tool for intelligent fault diagnosis. In supervised learning algorithms, the convolution layer
model is the most influential architecture for computer vision and pattern recognition [
13
].
Generally, the CNN architecture is a handy tool for image processing and learning features
from the input images. The wavelet representation of images can be an ideal input because
it can extract the most information from 1D time-domain signals and represent them with
both time and frequency information. The wavelet images can be presented as spectrogram
or scalogram plots [
14
]. Kumar et al. applied grayscale spectrogram images from analytical
WT as the input of CNN for centrifugal pump defects identification [
15
]. Analysis showed
that the proposed improved CNN significantly improved identification accuracy by about
3.2% over traditional CNN. Nevertheless, compared to the spectrogram representations,
which produce a constant resolution, a scalogram approach is more suitable for the chore
of fault classification due to its detailed depiction of the signal. Wavelet scalogram rep-
resentations have been proven effective and gaining more popularity over spectrogram
representation [
16
]. Scalogram is defined as the time-frequency representation that depicts
the obtained energy density using CWT [
17
]. Verstraete et al. applied CNN on two public
bearing datasets for fault diagnosis [
18
]. Three different types of input images were pro-
duced, namely, STFT spectrogram, wavelet scalogram, and HHT image. Comparing the
output accuracy from all the image types, the wavelet scalogram appeared to be the best fit.
The previous research shows that the wavelet scalograms have a much higher advantage
than the other image representations.
As the years went by, the CNN architecture has also increased in its size and layers to
obtain better performance [
19
21
]. Although these models perform with good accuracy,
their training time is very high, which is a high price for a small improvement. Moreover,
CNN can be computationally cumbersome and not all the processing units can afford that.
Sensors 2021,21, 8114 3 of 29
The embedded system can only process up to a certain limit; on the other hand, a quick
processing system is anticipated in the practical fields. For this reason, researchers have
been more focused on a lightweight CNN model without much compromise of accuracy.
A lightweight CNN consists of only a few convolution layers and fully connected layers.
Therefore, it uses less random-access memory and processing units. Fang et al. used two
CNN models, where the first one was a 1D CNN to extract the multichannel features
from the original signal [
22
]. Later, a lightweight CNN was applied where the weights
were adjusted via a spatial attention mechanism to classify the features. The experimental
results demonstrate that the proposed method has excellent anti-noise ability and domain
adaptability. Thus, it is a widespread practice in fault diagnosis research to choose a
lightweight CNN model over a very deep CNN for faster model training.
Although CNN is very handy in image processing, a downside is that this classifier
requires massive training data to generalize well. Several data augmentation techniques
are available to introduce more data during the training phase. The most common ones
are (1) geometrical transformation and (2) the addition of white noise. In geometrical
transformation, the image is rotated, flipped, adjusted brightness, transitioned, and cropped
to augment new samples [
23
]. However, this approach would not work well with the
wavelet scalograms because scalograms are a graphical representation, unlike images of
objects. A transformed representation of a graph would have a new meaning and may
result in reduced accuracy. In the second approach of white noise addition, some degree of
noise is added with the original signal to introduce some abnormality in the training data.
This technique works well because the test data might be noisy in the practical field and
differ considerably from the training data. However, white noise addition is not the best
approach for the ensemble algorithms, such as EEMD, CEEMD, and NEEEMD, because
these algorithms already use ensemble noise to reduce the white noise.
One of the most impressive and arising techniques in deep learning, generative
adversarial networks (GANs), has been getting much attention ever since its arrival [
24
].
GANs is an unsupervised learning algorithm used for image generation where it takes some
real images and produces similar outputs from complete white noise. Thus, GANs can be
used for data augmentation, where the augmented data never existed before, and it saves
the classifier from repeated training samples. Arjovsky proposed Wasserstein GAN, which
is a big step towards the improvement of GANs to produce realistic images [
25
]. However,
WGAN works best for medical images, and the performance of images generated from
signals is unknown. Wang proposed a fault diagnosis method for planetary gearbox by
combining GANs and autoencoder [
26
]. However, as it uses the vanilla GANs, the output
is comparatively noisy, and the use of autoencoders can lose necessary data, which needs
additional research. Radford proposed DCGAN, which uses convolution instead of dense
layers and produces high-resolution hyper-realistic images [
27
]. Since its arrival, DCGAN
has been a popular tool for data augmentation in medical imaging and fault diagnosis
fields. A method called FaultFace was proposed for ball-bearing joint failure detection,
which uses a 2D representation of time-frequency signals from an unbalanced dataset [
28
].
DCGAN was applied to generate more 2D samples for employing a balanced dataset.
The obtained output proves that the FaultFace strategy can achieve good performance
for an unbalanced dataset. Liang used wavelet image samples of different bearing and
gearbox load conditions as the input of CNN classifier [
29
]. After using the augmented
image samples from DCGAN, the classifier performed more accurately for various load
conditions and obtained higher robustness. Therefore, DCGAN appears to be an ideal fit
for GAN-based data augmentation using vibration signals.
2. Proposed Method
The proposed fault diagnosis method consists primarily of feature extraction, clas-
sification, and data augmentation for optimum training samples selection. The feature
extraction process includes input generation from grayscale images and scalogram images.
The grayscale samples are generated from the raw signal. The scalogram samples are
Sensors 2021,21, 8114 4 of 29
generated from EEMD, CEEMD, and NEEEMD. Since those image samples are wavelet
scalograms, CWT scalograms are also considered for performance comparison. The image
samples are classified using CNN. The best-performing model is selected from here based
on accuracy and precision. Moreover, the model’s robustness for noisy test samples is
also considered to validate the best model selection. Then, DCGAN is applied to produce
augmented samples within a range for the best-performing model. The optimum training
samples are identified via this process. The model trained on optimum training samples is
compared with the previous one to compare the performance improvement. The flowchart
of the proposed method is illustrated in Figure 1.
Figure 1. The complete research flow chart.
The key contributions of this study are:
1.
This work utilizes an improved algorithm named NEEEMD to incorporate NEEEMD
features with supervised classification for automated fault diagnosis. This study
proves the effectiveness of NEEEMD as a feature extraction algorithm.
2.
The IMFs were concatenated to generate a single scalogram image containing all the
features from all the IMFs. Therefore, the need for multiple input channels in a CNN
classifier was avoided, reducing significant computational complexity.
3.
A generalized CNN model that contains four convolution layers was proposed for
all the bearing and blade classification models. The proposed classifier contains con-
siderably fewer parameters than many state-of-the-art deep neural network models.
However, it can still obtain very impressive accuracy for both bearing and blade
datasets.
4.
The power of DCGAN was utilized to generate augmented samples in order to supply
more training data. DCGAN helped to generate augmented samples on demand and
assisted in finding the optimum training samples.
3. Data Collection
Two different datasets were used in this study to validate the proposed method. The
first dataset is from the Case Western Reserve University bearing dataset [
30
]. The sec-
ond dataset is turbine blade data from Universiti Teknology Malaysia [
31
]. They are
described chronologically in the following sub-sections. All the programming mate-
rials applied to analyze the datasets of this study are open for public usage (refer to
Supplementary Materials).
3.1. Bearing Dataset
In the bearing dataset, the acceleration data was measured from a 2-hp reliance electric
motor bearings placed at the 12 o’clock position. Drive end data were taken from bearing
model SKF 6205-2RS JEM. The sampling frequency was 12 kHz. The rotor shaft’s rotating
speed was considered 1797 rpm, and the motor load was 0 hp. The setup of the test rig is
shown in Figure 2. The bearing dataset mainly has three different fault types at various
severity. These faults are inner race fault, outer race fault, and ball fault. Another fault-free
Sensors 2021,21, 8114 5 of 29
condition is the normal condition. A visual representation for these four conditions is
presented in Figure 3.
Figure 2. Experimental setup for the bearing data collection.
Figure 3. Four bearing conditions (a) normal condition, (b) inner race fault, (c) outer race fault, (d) ball fault.
3.2. Blade Dataset
The dataset contains vibration signals obtained from the rotor blades operating under
constant rotational speed conditions. All blade fault conditions were measured with the
sampling rate was 5 kHz for all states, and the rotating speed was set to 1200 rpm (20 Hz).
The blade fault simulated in a test rig to collect vibration signals is shown in Figure 4. A
three-phase synchronous motor was used in the test rig to control the rotational speed
during the experiment.
Sensors 2021,21, 8114 6 of 29
Figure 4. Test rig to simulate blade fault.
Blade rubbing (BR) fault was artificially added in the test rig by adding a metal sheet
to a regular blade and thus increasing its length. A 1 mm thick metal sheet was used
as the rubbing medium. Because of its hardy characteristics, it prevents wearing out of
the rotor casing. The blade rubbing condition was introduced such that the blade edge
slightly touched the rotor casing’s inner surface. The blade loss (BL) fault was included
by replacing a normal blade with a blade of partial loss. For this experiment, a blade with
one-fourth loss was used as a rotor blade in the first, second, and third rows. A normal
blade was replaced with another tightened blade in the opposite direction set into the rotor
disk to introduce the blade twist (BT) fault. For this work, an artificially induced single
twisted blade fault condition was added to the different rows of the rotor blade in the test
rig. All the blade fault conditions are presented in Figure 5.
Figure 5. Different blade fault conditions.
Sensors 2021,21, 8114 7 of 29
4. Classification Models
In this study, mainly two different classification models are developed using bearing
and the blade dataset. The bearing dataset has only one classification model, and the blade
dataset contains three classification models. A detailed description of those models is
provided in the following subsection.
4.1. Bearing Fault Classification
Collected vibration signals include the following operating conditions: (1) normal
condition, (2) inner race fault, (3) ball fault, and (4) outer race fault. Each fault condition
includes three different fault sizes, 0.007, 0.014, and 0.021 inches in diameter. In total,
10 different conditions (1 normal, 9 fault conditions) were considered for the fault diagnosis,
and the fault categories are presented in Table 1.
Table 1. Different bearing fault conditions considered in this study.
Fault Normal Inner Race Outer Race Ball
Class 0 1 2 3 4 5 6 7 8 9
Severity N/A 0.00700 0.01400 0.02100 0.00700 0.01400 0.02100 0.00700 0.01400 0.02100
In this work, 600 data points are taken in each bearing sample. The bearing dataset has
10 different classes and 200 samples in each class. For each class, the data are partitioned
into train, validation and test set in such a way that the train, validation and test set have
50%, 25%, 25% data, respectively. The training set has 100 samples to train the classifier
model, and the validation set has 50 samples to observe and maintain the performance
of the training set. Later, 50 testing samples are used to measure the performance of the
classifier. For 10 classes in total, the classifier consists of 2000 samples, where 1000, 500,
and 500 are for train, validation, and test, respectively.
4.2. Blade Fault Classification
In the blade fault test rig, three different blade faults were induced in different rotor
rows. A total of 21 different blade fault conditions based on the fault type and rotor
location were examined in this study. The blade data are divided into two different
categories for classification: (1) Fault diagnosis: 3-class classification, (2) fault localization:
7-class classification. A detailed description of each category is provided in Tables 2and 3.
Here, R(number) represents the row location of fault occurrence for the particular dataset.
Table 2. Datasets for the blade fault diagnosis classifier.
Type Rub Loss Twist
Class 0 1 2
Data
BR-R1 BL-R1 BT-R1
BR-R2 BL-R2 BT-R2
BR-R3 BL-R3 BT-R3
BR-R12 BL-R12 BT-R12
BR-R13 BL-R13 BT-R13
BR-R23 BL-R23 BT-R23
BR-R123 BL-R123 BT-R123
The 3-class fault diagnosis classification has 7 sets of fault data in each class and
21 total sets of data for the whole classifier. The total train, validation, and test data for this
model are 5250, 1575, and 1575. Each class contains 1750, 525, and 525 train, validation and
test samples.
The 7-class fault localize classification has 3 sets of fault data in each class and 21 total
datasets for the whole classifier. The total train, validation, and test data for this model are
Sensors 2021,21, 8114 8 of 29
5250, 1575, and 1575. Therefore, each class contains 750, 225, and 225 train, validation, and
test samples.
Table 3. Datasets for the blade fault localization classifier.
Type Row 1 Row 2 Row 3 Row 1,2 Row 1,3 Row 2,3 Row 1,2,3
Class 0 1 2 3 4 5 6
Data
BR-R1 BR-R2 BR-R3 BR-R12 BR-R13 BR-R23 BR-R123
BL-R1 BL-R2 BL-R3 BL-R12 BL-R13 BL-R23 BL-R123
BT-R1 BT-R2 BT-R3 BT-R12 BT-R13 BT-R23 BT-R123
5. NEEEMD
The NEEMD takes a different approach than CEEMD to eliminate the white noise in
the final stage. Instead of adding a negative white noise at the primary stage, it subtracts
the IMFs of the same white noise from the final IMFs. The steps of NEEEMD are followings:
1.
Add ensemble white noise
wi(t)
(whose length is the same as the original signal with
a mean of 0 and the standard deviation of 1 to the original signal
X(t)
and obtain
Xi(t).
2.
Decompose
Xi(t)
using EMD (see Appendix A) [
32
] and obtain the ensemble means
of the IMFs, cj(t).
cj(t)=1
M
M
i=1
cij (t)(1)
3. Take the input ensemble white noise wi(t)and apply EMD on each one of it.
Wi=
N
j=1
wcij(t)+wri(t)(2)
where
j=
1, 2,
. . .
,
N
, N is the number of IMFs and
wcij(t)
is the IMFs of noise
(ci1,ci2, . . . , ciN). wri(t)denotes the residue of the ith trail.
4. Compute the ensemble means of the IMFs for the noise.
wcj(t)=1
M
M
i=1
wcij(t)(3)
Subtract the IMFs of noise from the IMFs obtained from EEMD for the reduction of
white noise.
IMFj=cj(t)wcj(t)(4)
5. The original signal can be obtained such that,
X(t)=
M
i=1
IMFij(t)+rM j (t)wrMj (t)(5)
where wrM(t)is the residue of the white noise.
Decomposing the signal provides several IMFs and a residual signal, which is a
monotonous signal. For visualization, one random sample from the bearing and blade
signal is decomposed using NEEEMD. Figure 6represents the outputs of NEEEMD for both
bearing and blade samples. Here, no mode mixing phenomena were observed in the IMFs.
Moreover, the residuals were monotonous, containing virtually no necessary information.
Sensors 2021,21, 8114 9 of 29
Figure 6. Decomposition results from NEEEMD.
It is necessary to prove the superiority of NEEEMD over EEMD and CEEMD statis-
tically. All the statistical analyses of the bearing and blade datasets show a similar trend
for EEMD, CEEMD, and NEEEMD. However, only one random sample from the bearing
and blade datasets is presented in this study due to space constraints. The final IMFs of
NEEEMD are supposed to have less white noise presence than EEMD and CEEMD. To
illustrate the effect of reduced white noise, signal-to-noise ratio (SNR) is considered. SNR
is computed using the original and reconstructed signals, where the reconstructed signal is
the sum of the resulting IMFs. The formula for computing SNR is provided in Equation (6).
It is the ratio of the power of the original signal to the power of the reconstructed signal.
The SNR of NEEEMD from one random bearing and blade fault sample is compared with
EEMD and CEEMD. The outputs are presented in Figure 7. It is seen that in both bearing
and blade samples, EEMD obtained the lowest SNR value. CEEMD obtained higher SNR
than EEMD, whereas NEEEMD obtained the highest SNR. Therefore, the reconstructed
signal from NEEEMD has less noise in it than EEMD and CEEMD.
SN RdB =10log10 Poriginal sign al
Preconstructed signal !=10log10 P(X(t))
PM
i=1IMFij (t)+rM j(t)wrM j(t)!(6)
A frequently used statistical evaluation parameter, RRMSE, is implemented to cal-
culate the restoration error to further emphasize the proposed method’s effect. The ratio
between the root-mean-square of the original and reference signal to the root-mean-square
of the reference signal is defined as RRMSE [
33
]. The equation for RRMSE is presented
as follows:
RRMSE =||ab||
b(7)
Here, ais the original signal, and bis the reconstructed signal.
Sensors 2021,21, 8114 10 of 29
Figure 7. SNR values for reconstructed signals of bearing and blade samples.
Figure 8represents the RRMSE values from a random bearing and sample. EEMD
obtained higher RRMSE values, 0.0705 for bearing, and 0.0361 for blade sample. CEEMD
had a lower reconstructed error than EEMD, 0.0695 and 0.0339 for bearing and blade,
respectively. NEEEMD achieved the lowest RRMSE, which are 0.0629 and 0.0304 for
bearing and blade. Therefore, NEEEMD has a much lower reconstruction error than EEMD
and CEEMD, and proves to be more effective than those previous two improvements.
Figure 8. RRMSE values of the bearing and blade samples.
Next, the signal strength is considered to evaluate the degree of information the
reconstructed signal carries. The kurtosis value is an excellent parameter for measuring the
signal strength. Wang et al. [
34
] used the multiplication of the kurtosis in the time and the
envelope spectrum domain, which can be applied to determine the strength of the signal.
The method is called TESK and is defined as:
tk =kc.kes (8)
Sensors 2021,21, 8114 11 of 29
where,
kc=E(X(t)µc)4
σ4
c
(9)
kes =E(es(f)µes)4
σ4
es
(10)
where,
X(t)
as the IMF to be analyzed,
σc
as the standard deviation of
X(t)
,
µc
as the mean
of
X(t)
,
es(f)
as the envelope power spectrum of
X(t)
,
µes
as the mean of
es(f)
,
µes
as the
standard deviation of es(f)and E(.)as the expectation operator.
The higher the
tk
value, the more information the signal contains. Thus, the total
value of
tk
from different signals can be compared to determine the performance of the
algorithms. Figure 9shows the
tk
values from both bearing and blade samples. For the
bearing sample, EEMD has the lowest signal strength, as the
tk
value is 32.64. The second
highest is CEEMD with
tk
value of 33.97. NEEEMD has the highest signal strength as it
obtained the highest
tk
value, 35.71. The
tk
values of the blade sample were relatively
closer since the sample length is smaller than the bearing sample. Nevertheless, NEEEMD
obtained the highest
tk
value as well. The
tk
values are 26.08, 26.38, and 27.14 for EEMD,
CEEMD, and NEEEMD, respectively. Therefore, in both bearing and blade samples, the
NEEEMD signal contains the highest signal strength.
Figure 9. tk values from the bearing and blade samples.
6. Features for Deep Learning
The deep learning classifiers in this study work with two types of input samples,
namely, grayscale images and scalogram images. The 2D grayscale vibration images
are produced from the 1D raw vibration data [
35
]. The produced image dimension is
64 ×64 pixels.
However, each bearing data sample has 600 data points. Therefore, the
samples are converted from a 1
×
600 vector to a 20
×
30 matrix and produced the 2D
grayscale images. Still, the generated images have a size of 20
×
30 pixels, so the images are
upsampled to produce images of size 64
×
64. The blade sample length is 500. Therefore,
images are upsampled from a 20
×
25 matrix in this case. Since the images are 2D grayscale,
the number of the input channel for CNN, in this case, is 1.
Scalograms are one type of time-frequency representation that uses CWT analysis to
obtain the energy density of the signal. A sliding window is used in wavelet representation,
which has different resolutions in different regions. CWT decomposes the raw signal into
a time scale, which is represented by scaling and translating operations. Morlet wavelet
Sensors 2021,21, 8114 12 of 29
is applied with the time-bandwidth product and symmetry parameter set to 60 and 3,
respectively. According to the range of energy of the wavelet in frequency and time,
the minimum and maximum scales are automatically determined using 10 voices per
octave [
36
]. Points out of the cone of influence have been handled by the approximation
used in MathWorks MATLAB [37].
Typically, when a signal is decomposed using the adaptive methods, it produces
several IMFs. In the previous studies, the authors considered all the individual IMFs as in-
dividual samples and applied multichannel CNN for classification [
38
40
]. However, that
approach requires n-channel CNN for n-IMFs, enhancing the preprocessing and classifica-
tion duration ntimes. For practical application, it is burdensome to do all the computation
for the desired outcome. Thus, in this study, all the IMFs have been concatenated and
flattened into a single signal. From the single signal, one scalogram image is produced.
Thus, the computation time for nIMFs was reduced to 1/ntimes. Figure 10 represents
the proposed approach for scalogram images input into the classifier model. Here, five
IMFs were generated using all the decomposition methods of this study. Concatenating
these five IMFs produces a single sample with a length of five times the original sample.
Thus, the length of the bearing sample would be 3000, and the blade sample would be 2500.
Next, one single scalogram is generated from that sample.
Figure 10. The process of scalogram generation.
The colors in the scalogram plot show the relative values of the CWT coefficients.
The light areas mean higher values of the CWT coefficients, and therefore, the signal is
Sensors 2021,21, 8114 13 of 29
very similar to the wavelet. On the other hand, dark area means lower values of the CWT
coefficients, and it shows that the corresponding time and scale versions of the wavelet
are dissimilar to the signal. An RGB (three channels) representation of the time-frequency
image is better than a grayscale (one channel) image because more channels contain
higher information. Therefore, only RGB scalograms of 64
×
64 pixels are produced in this
study. The scalograms are generated from EEMD, CEEMD, and NEEEMD. Moreover, the
scalograms are also obtained from the vibration signals, which are purely CWT scalograms.
Figure 11 represents one random sample from each different image type for the bearing
and blade dataset. Here, the grayscale samples contain no color values as it has only black
and white pixels. Scalograms from the decomposition have five concatenated IMFs, which
are clearly visible in their scalogram images. Finally, the CWT scalograms are the pure
scalogram samples that are generated from the original sample.
Figure 11. Input samples for deep learning using (a) bearing, (b) blade dataset.
7. Deep Learning Classifier
The proposed classifier architecture (Figure 12) consists of only four convolution
layers and two dense layers. The input layer of the CNN model consists of three channels
that take 64
×
64 size RGB images. The first convolution layer has 64 output filters with
a kernel size of 5
×
5. The first convolution layer is followed by three other convolution
layers where the output filter size is 32, 64, and 96, respectively, and a 3
×
3 kernel is used
in all of them. ‘Same’ padding is used in all these convolution layers. A max-pooling
layer of 2
×
2 pixels is applied after every convolution layer. The output from these three
convolution layers is flattened and connected to two dense layers and their respective
dropout layers. The first dense layer has 512 neurons with a dropout factor of 0.4 and
the second one has 256 neurons with a dropout value of 0.2. ReLU activation function
is applied in all of the layers. A softmax activation function is used in the output layer
where the layer size is the same as the number of data classes. In the case of binary class, a
sigmoid activation function is applied as per convention with only one hidden unit [
41
].
The bearing model architecture with the number of parameters is presented in Table 4. All
models were generated in Python using the Keras library. The total number of parameters
and total trainable parameters for this model is 1,006,410.
Sensors 2021,21, 8114 14 of 29
Figure 12. The proposed CNN architecture.
Table 4. Parameters of the proposed CNN model.
Model: “Sequential”
Layer (type) Output Shape Parameter #
conv2d (Conv2D) (None, 64, 64, 32) 2432
max_pooling2d (MaxPooling2D) (None, 32, 32, 32) 0
conv2d_1 (Conv2D) (None, 32, 32, 32) 9248
max_pooling2d_1 (MaxPooling2D) (None, 16, 16, 32) 0
Sensors 2021,21, 8114 15 of 29
Table 4. Cont.
Model: “Sequential”
conv2d_2 (Conv2D) (None, 16, 16, 64) 18,496
max_pooling2d_3 (MaxPooling2D) (None, 8, 8, 64) 0
conv2d_3 (Conv2D) (None, 8, 8, 96) 55,392
max_pooling2d_3 (MaxPooling2D) (None, 4, 4, 96) 0
flatten (Flatten) (None, 1536) 0
dense (Dense) (None, 512) 786,944
dropout (Dropout) (None, 512) 0
dense_1 (Dense) (None, 256) 131,328
dropout_1 (Dropout) (None, 256) 0
dense_2 (Dense) (None, 10) 2570
Total parameters: 1,006,410
Trainable parameters: 1,006,410
Non-trainable parameters: 0
Hyperparameters Tuning
Training the CNN model corresponds to a bunch of optimizable parameters. Among
the tunable parameters, the most prominent are learning rate, optimizer, loss function, and
batch size. An ideal set of these parameter selections for an individual architecture leads to
better classification performance. The grid search method was applied in hyperparameter
tuning, and the optimum parameters were selected [42].
The deep neural network algorithms use stochastic gradient descent to minimize the
error. The learning rate indicates how the model estimates the error each time the weights
are updated. Choosing the learning rate is important because a slow learning rate may
take a long time to converge, whereas a high learning rate may miss convergence at all.
On the other hand, the loss function is used to differentiate the performance of the model
between the prediction score and the ground truth. Among many types of loss functions,
the cross-entropy loss function is used extraneously and employed in this study.
It is crucial to obtain a low loss using the loss function. To minimize the loss function,
implementing an appropriate optimizer is important. An appropriate optimizer sets a
bridge between the learning rate and loss function during the gradient descent. The Adam
optimizer is an adaptive learning rate optimization algorithm designed especially for DNN.
Adam uses momentum in order to accelerate the learning rate when the learning rate
becomes slow after a few iterations. The use of Adam can help to prevent being stuck in
the local minima of the loss. Adam optimizer is applied to optimize the loss function where
the learning rate is set at 0.0001.
The other few important factors of hyperparameters are epoch, early stopping. Epoch
refers to how many iterations of forward and backward propagation are conducted before
the algorithm is stopped. Another handy trick while training the algorithm is that it is
divided into mini-batches instead of taking all the input train samples. This strategy
requires less memory usage and trains faster. The early stopping method observes the
validation loss or accuracy to monitor if the model is being overfitted. When the model
starts to get overfit, the training process is terminated even before the highest number of
epochs is reached. In this study, the training data are divided into batches of 16, and the
epoch is set at 100. The early stopping criterion is utilized to avoid overfitting the model.
As a result, the increase of validation loss is observed for 15 instances, and the best model
is saved based on the lowest validation loss. Thus, the overfitting problem is avoided, and
the model converges to the minimum loss at an epoch lower than 100 in most cases.
8. Data Augmentation Using DCGAN
In this study, DCGAN was utilized because of its ability to use convolution and
deconvolution layers in the discriminator and generator to produce high-quality image
outputs. The model architecture and the hyperparameters are primarily adopted from
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the original DCGAN paper [
27
]. The paper proposed a 64
×
64
×
3 RGB image as the
input. The DCGAN model has a few deviations from the original GAN. The pooling
layers are replaced with convolution layers. Batch normalization is used in the generator
and discriminator. LeakyReLu activation function is used in all the layers except for
the generator output layer, which is ‘tanh’. The generator model has a 100-dimensional
uniform distribution noise vector, Zis given as input.
Some of the hyperparameters are adjusted according to the need for the dataset.
All weights were initialized from a zero-cantered normal distribution with a standard
deviation of 0.02. In the LeakyReLU, the slope of the leak was set to 0.2 in all models. The
Adam optimizer was used with a learning rate of 0.0002 and momentum of 0.5. Binary
cross-entropy was used as the loss function. The training samples from each fault type are
given into the DCGAN model for the generator to imitate. Since few training samples were
available, the batch size while training DCGAN was only 32. It is challenging to generate
fake samples using only a few training data. Thus, 10,000 epochs were used to train the
model, and the desired number of fake samples were generated once the highest number
of epochs was reached.
9. Outputs from the Classifiers
This section compares outputs from NEEEMD scalograms classification using CNN
with related scalograms and grayscale images. The train, validation, and test accuracies
are obtained for comparison. Moreover, the individual class performance from the test
results is used to obtain the sensitivity values for comparison. The sensitivity values are
considered because this study emphasizes mainly the correct identification of fault types.
Table 5represents the output accuracy from the bearing fault classifiers, and
Table 6
represents its class sensitivity. The order of validation and test accuracies for the CNN
classifiers are grayscale, CWT, EEMD, CEEMD, and NEEEMD scalograms. Here, the lowest
validation and test accuracies are 95.60% and 94.40%, obtained by the grayscale images.
The highest validation and test accuracy obtained by NEEEMD scalograms are 98.20%
and 98%. The sensitivity values show that NEEEMD scalograms obtained the highest
sensitivity for each individual class. In other methods, some classes obtained the highest
sensitivity but not for all classes. Therefore, all the classes had the most correctly identified
fault occurrence using the NEEEMD scalogram samples for the bearing classifier.
Table 5. All undertaken classifiers’ accuracy for bearing fault classification.
Method Accuracy
Train (%) Validation (%) Test (%)
Grayscale image + CNN 99.10 95.60 94.40
CWT scalogram + CNN 98.20 97.60 97
EEMD scalogram + CNN 98.60 97.60 97.20
CEEMD scalogram + CNN 98.40 98 97.60
NEEEMD scalogram + CNN 98.40 98.20 98
Table 6. All undertaken classifiers’ sensitivity values for bearing fault classification.
Method Sensitivity
Class 0 1 2 3 4 5 6 7 8 9
Grayscale image + CNN 1 0.84 0.88 0.9 1 0.86 1 1 0.96 1
CWT scalogram + CNN 1 0.9 0.9 0.9 1 1 1 1 1 1
EEMD scalogram + CNN 1 0.92 0.9 0.9 1 1 1 1 1 1
CEEMD scalogram + CNN 1 0.92 0.92 0.9 1 1 1 1 1 1
NEEEMD scalogram + CNN 1 0.96 0.94 0.9 1 1 1 1 1 1
The output accuracy and sensitivity for the blade fault diagnosis classifier are pre-
sented in Tables 7and 8. The order of the validation and test accuracy is similar to the
Sensors 2021,21, 8114 17 of 29
order of bearing fault classifier output. All the output accuracies of the scalograms had
small differences among train, validation, and test accuracy, indicating a well-trained clas-
sifier. However, the validation and test accuracies had comparatively lower accuracy than
the training accuracy in grayscale samples. Therefore, the classifier trained on grayscale
samples was more overfit than the others. EEMD obtained slightly higher accuracy than
CWT scalograms, and the same goes for CEEMD when compared with EEMD. NEEEMD
scalograms obtained the highest validation and test accuracies, which were 97.84% and
96.31%. All the output accuracies are reflected in the sensitivity of classes. In grayscale
samples, a large proportion of class 0 was misclassified. On the other hand, the NEEEMD
scalogram classifier had the highest individual class sensitivity.
Table 7. All undertaken classifiers’ accuracy for blade fault diagnosis classification.
Method Accuracy
Train (%) Validation (%) Test (%)
Grayscale image + CNN 96.32 88.63 83.49
CWT scalogram + CNN 99.30 96.83 94.35
EEMD scalogram + CNN 99.64 97.33 94.66
CEEMD scalogram + CNN 99.67 97.59 95.37
NEEEMD scalogram + CNN 99.42 97.84 96.31
Table 8. All undertaken classifiers’ sensitivity values for fault diagnosis classification.
Method Sensitivity
Class 0 1 2
Grayscale image + CNN 0.739 0.922 0.844
CWT scalogram + CNN 0.95 0.933 0.947
EEMD scalogram + CNN 0.952 0.933 0.954
CEEMD scalogram + CNN 0.968 0.939 0.954
NEEEMD scalogram + CNN 0.983 0.95 0.956
Tables 9and 10 list the output accuracy and sensitivity from blade fault localize
classifiers. The NEEEMD scalograms obtained the highest validation and test accuracy for
CNN as well. However, the grayscale and CWT samples obtained a highly overfit model.
The validation and test accuracies deviate much from the training accuracy. The grayscale
samples had a train, validation, and test accuracy of 98.38%, 71.75%, and 59.81%. For the
CWT scalograms, the train, validation, and test accuracies are 95.98%, 75.17%, and 68.44%.
These outputs indicate the poor performance of grayscale and CWT scalograms for a
higher-class classification. On the other hand, the scalogram samples from EEMD, CEEMD,
and NEEEMD obtained much less overfit classifier as the validation and test accuracies
were very close to the training accuracy. NEEEMD obtained the highest validation and
test accuracies, 93.27%, and 92.25%, respectively. In terms of sensitivity, a few classes from
grayscale and CWT samples are below 0.50, meaning more samples were misclassified
and correctly classified. On the other hand, NEEEMD had the highest sensitivity for all
individual classes. Therefore, the NEEEMD scalogram can still obtain very high accuracy
and sensitivity for a higher-class classification.
This section shows that the combination of NEEEMD scalograms and the CNN model
performed the best. The grayscale samples and CNN. In most of the scalograms and CNN
models, the output performance was very close to each other. Thus, more analysis is
needed for additional justification of the best model for different situations. Therefore,
all of the scalogram classification models will be undertaken for further evaluation using
model robustness for noisy test samples.
Sensors 2021,21, 8114 18 of 29
Table 9. All undertaken classifiers’ accuracy for blade fault localization classification.
Method Accuracy
Train (%) Validation (%) Test (%)
Grayscale image + CNN 98.38 71.75 59.81
CWT scalogram + CNN 95.98 75.17 68.44
EEMD scalogram + CNN 98.15 91.87 91.05
CEEMD scalogram + CNN 98.35 92.13 91.68
NEEEMD scalogram + CNN 97.59 93.27 92.25
Table 10. All undertaken classifiers’ sensitivity values for blade fault localization classification.
Method Sensitivity
Class 0 1 2 3 4 5 6
Grayscale image + CNN 0.858 0.422 0.871 0.827 0.524 0.347 0.338
CWT scalogram + CNN 0.693 0.56 0.56 0.729 0.827 0.613 0.809
EEMD scalogram + CNN 0.924 0.907 0.96 0.827 0.929 0.849 0.933
CEEMD scalogram + CNN 0.924 0.911 0.991 0.836 0.964 0.853 0.938
NEEEMD scalogram + CNN 0.933 0.916 0.991 0.844 0.973 0.853 0.947
9.1. Robustness Evaluation
When predicting new data, the data can be quite deviated from the original signal, or
they may contain high noise in the real application. Therefore, it is essential to ensure that
the model can still hold good robustness when classifying new data. Gaussian white noise
is added with the test samples and it is predicted using the trained model to verify the
robustness of all the models. The white noise is added directly to the scalogram images (as
salt-pepper noise) and incremented at a step of 0.05 standard deviation (SD). The outputs
from the scalogram samples of NEEEMD, CEEMD, EEMD, and CWT are compared. The
grayscale vibration image classification using CNN and the machine learning classifiers
are not considered as they already performed with considerably low accuracy in the earlier
stage. The outputs from all the datasets and classifiers are obtained in the following figures.
In Figure 13, the bearing test dataset with different noise levels shows accuracies in
the descending order of NEEEMD, CEEMD, EEMD, and CWT. The CWT samples model’s
robustness keeps falling most for a higher order of noise. The NEEEMD, CEEMD, and
EEMD models’ robustness are close, but the NEEEMD model could maintain the highest
robustness all the way. In Figure 14, the models’ robustness for the fault diagnosis classifier
is obtained. The robustness of CWT was the lowest for all the SD, followed by EEMD.
The robustness of NEEEMD and CEEMD are very close. The robustness of NEEEMD is
higher than CEEMD for all the SDs except for only 0.35 SD, where it lags by a tiny portion.
Apart from that, the NEEEMD samples for the fault diagnosis model performed with
the highest robustness. In Figure 15, the differences in robustness for the fault localize
classifiers were much higher in the earlier stages of noise SDs. The robustness of NEEEMD
is much higher than all the other comparable methods. However, at the highest level of
noise SD, these performance differences shrink. Nevertheless, for different noise SD levels,
the accuracy curve of CEEMD, EEMD, CWT overlap at some point. Meaning, these three
models’ order of robustness varies at different noise SDs. On the other hand, the accuracies
of the NEEEMD model are comparatively higher than the other scalogram samples. These
outputs indicate that the proposed NEEEMD scalograms with CNN classifier can provide
the highest robustness than the other methods considered in this study.
Sensors 2021,21, 8114 19 of 29
Figure 13. Performance of bearing fault classifier on noisy data.
Figure 14. Performance of blade fault diagnosis classifier on noisy data.
9.2. Performance with Augmented Samples
Now that it is established that the proposed NEEEMD scalograms + CNN models
performed better than all the other methods, additional improvement in performance is
conducted. The goal is to increase the number of training samples with the augmented data
to investigate how the classifier performance changes. The fake samples from DCGAN
output show that the fake samples could significantly mimic the original samples of
the respective classes. However, DCGAN takes in a complete white noise to perform
augmentation, and the presence of some noise can still be seen in the output samples.
How to further improve this output and reduce noise is another research problem. For the
classifier models, it can be predicted that adding the augmented samples in proportion
with the original training samples should somewhat improve the accuracy. Nevertheless,
populating the classifier with too many fake samples might have a reverse effect because
the classifier would learn most from the fake data. DCGAN is applied to the samples
from every single class of bearing and blade data. The desired amount of augmented
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samples are generated during the process. One random output of bearing and blade data
using DCGAN are presented in Figure 16 for visualization. The augmented samples have
some degree of white noise presented in them as it is completely generated from random
white noise. However, the augmented scalograms still successfully very much mimic the
real scalograms.
Figure 15. Performance of blade fault localization classifier on noisy data.
Figure 16. Augmented image samples from DCGAN.
Sensors 2021,21, 8114 21 of 29
In [
43
], the authors attempted to find the relation between classifier accuracy and the
train size. They considered three different CNN classifier models from different literature
and gradually increased the training accuracy. It is observed that as the training size is
increased, the accuracy also improves. However, after a turning point, the accuracy and
model robustness are decreased. Moreover, it is established that for DNN, there is no
definite right number of samples as the right number depends on the types of data and
model architecture. It shows how the accuracy is the highest at the turning point, and the
number of samples is the right number of samples for the model.
The bearing dataset has only 100 training samples. To observe how the model reacts to
the increased training samples, the augmented samples are increased at a step of 50 for each
class. Thus, for each increment, 500 new fake samples are added. The accuracy obtained
using fake samples from DCGAN is listed in Table 11. As the number of training samples
is increased, the validation and test accuracy also increase. The highest validation and
test accuracy are obtained at fake samples of 150 per class, i.e., a total of 2500 training
samples. This is the turning point of our classifier model for the increased samples, and
beyond this point, the accuracy keeps falling gradually. Therefore, the validation and test
accuracy are enhanced from 98.2% to 99.6% and 98% to 99.6%, respectively, whereas it
falls to 97.4% and 97.2%, respectively. Figure 17 shows the performance improvement of
NEEEMD + DCGAN
from NEEEMD only. In only NEEEMD scalograms output, all the
inner race fault classes had several misclassified samples. On the other hand, in NEEEMD
+ DCGAN output, only class 1 and class 2 contain misclassified samples. The higher fault
severity of inner race, i.e., class 2 and class 3 had all correctly classified samples. Therefore,
apart from class 1, all the other classes of NEEEMD + DCGAN were correctly classified.
Thus, it can be concluded that, DCGAN improved the classifier robustness and produced
more correctly classified samples.
Table 11.
Performance of bearing fault classifier for different numbers of augmented training samples
(optimal number highlighted in bold).
Fake Data/Class Accuracy
Train (%) Validation (%) Test (%)
No fake 98.40 98.20 98
50 99.0 98.6 98.2
100 99.6 98.8 98.8
150 99.69 99.60 99.60
200 98.33 98.2 98
250 98.93 98 98
300 98.65 97.8 97.8
350 99.24 97.8 97.6
400 99.62 97.8 97.4
450 98.62 97.4 97.4
500 99.71 97.4 97.2
The fault diagnosis model has 3 fault classes, each containing 1750 samples. The fake
samples are added in a batch of 100 for each class. It means that for 3 classes, 300 samples
are added with the training data in each step. At around 300 fake samples for each
class, i.e., 900 more added samples and 5250 original samples (6150 total samples), the
classifier reaches its turning point and achieves the highest accuracy, as shown in
Table 12.
The validation and test accuracy rose to 98.60% and 98.29% from 97.84% and 96.31%,
respectively, and again fell to 96.76% and 95.24%. The confusion matrix for the 3-class
classifier is shown in Figure 18. Here, all the classes had more correctly classified samples
than the previous model with no augmentation. Class 0, 1, and 2 had 2, 20, and 9 more
correctly classified samples, respectively, than the previous best model. As a result, the
sensitivity for each class of the NEEEMD + DCGAN improved.
Sensors 2021,21, 8114 22 of 29
Figure 17. Confusion matrix of NEEEMD and NEEEMD + DCGAN at the turning point for bearing fault classification.
Table 12.
Performance of blade fault diagnosis classifier for different numbers of augmented training
samples (optimal number highlighted in bold).
Fake Data/Class Accuracy
Train (%) Validation (%) Test (%)
No fake 99.42 97.84 96.31
100 99.33 98.03 96.76
200 99.63 98.03 97.21
300 99.63 98.60 98.29
400 99.96 98.16 98.03
500 99.66 97.90 96.89
600 99.46 97.59 96.70
700 99.91 97.46 96.19
800 99.23 97.08 96.00
900 99.69 96.83 95.24
1000 99.04 96.76 95.24
Figure 18. Confusion matrix of NEEEMD and NEEEMD + DCGAN at the turning point for blade fault diagnosis.
The fault localize model has 7 fault classes, each containing 750 samples. The fake
samples are added in a batch of 100 for each class. This means that for 7 classes, 700 samples
are added with the training data in each step. From Table 13, around 400 fake samples for
each class, i.e., 2800 more added samples and 5250 original samples (total 8050 training
samples), the classifier reaches its turning point and achieves the highest accuracy. The
validation and test accuracy raise to highest 94.67% and 93.59% from 93.27% and 92.25%,
respectively, and again falls to 91.68% and 89.84%. The confusion matrix is shown in
Figure 19.
Here, only class 6 had the same number of correctly classified samples in both
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cases. All the other classes in NEEEMD + DCGAN contain higher classified samples than
NEEEMD only. The number of increased correctly classified samples are 3, 7, 1, 6, 1, and 3,
in the order of the classes, respectively.
Table 13.
Performance of blade fault localization classifier for different numbers of augmented
training samples (optimal number highlighted in bold).
Fake Data/Class Accuracy
Train (%) Validation (%) Test (%)
No fake 97.59 93.27 92.25
100 96.62 93.46 92.57
200 97.85 93.78 93.21
300 98.61 93.97 93.27
400 98.06 94.67 93.59
500 98.05 93.40 92.19
600 97.85 93.33 91.68
700 98.35 92.95 91.68
800 96.88 92.95 90.79
900 97.13 92.32 90.48
1000 98.56 91.68 89.84
Figure 19. Confusion matrix of NEEEMD and NEEEMD + DCGAN at the turning point for blade fault localization.
The improved performance using NEEEMD and DCGAN samples at the turning
point is compared with the NEEEMD scalograms + CNN output and presented in
Table 14.
The train, validation, test accuracies, and sensitivity values are considered to compare
the bearing fault classification and three blade fault classifications. All four models show
impressive improvements in validation and test accuracies. The sensitivity values for
the classes are also obtained. All of the classes from NEEEMD + DCGAN show higher
sensitivity values than the NEEEMD samples. Therefore, the fake samples generated from
the DCGAN help to increase the CNN performance.
9.3. Improvement in Robustness
For all cases, the model accuracy increases up to a point with the increment of train-
ing samples. It can be concluded that the right amount of training samples will make
the classifier more accurate. However, in order to develop a more robust model, some
researchers tried to add some degree of white noise to the training data during the training
phase. This technique also helps to reduce the overfitting problem. It first showed the
effect of added white noise during backpropagation for a more generalized model [44]. It
is found that the input noise is effective for a more generalized classification and regression
model. Kosko et al. showed that noise could generalize the classifier as well as speed up
Sensors 2021,21, 8114 24 of 29
backpropagation learning [
45
]. The augmented samples using DCGAN has some presence
of noise in all of them. Since these noisy augmented samples are incorporated with the
other training samples, a more robust classifier is expected. Gaussian white noise is added
with the test samples and predicted using the trained model to verify our hypothesis. The
outputs from the scalogram samples of NEEEMD + DCGAN are compared with NEEEMD
to observe the performance improvement. The outputs from all the datasets and classifiers
are obtained in the following figures.
Table 14. Improvement in classifiers’ performance using the augmented training samples from DCGAN.
Model CNN Input
Bearing fault
NEEEMD
(Samples: 1000)
Accuracy Train: 98.40%, validation: 98.20%, test: 98%
Class 0 1 2 3 4 5 6 7 8 9
Sensitivity 1 0.96 0.94 0.9 1 1 1 1 1 1
NEEEMD + DCGAN
(Samples: 2500)
Accuracy Train: 99.69%, validation: 99.6%, test: 99.6%
Sensitivity 0 1 2 3 4 5 6 7 8 9
Class 1 0.96 1 1 1 1 1 1 1 1
Blade fault
diagnosis
NEEEMD (Samples:
5250)
Accuracy Train: 99.42%, Val: 97.84%, Test: 96.31%
Class 0 1 2
Sensitivity 0.983 0.95 0.956
NEEEMD + DCGAN
(Samples: 6150)
Accuracy Train: 99.63%, Val: 98.60%, Test: 98.29%
Class 0 1 2
Sensitivity 0.987 0.989 0.973
Blade fault
localization
NEEEMD (Samples:
5250)
Accuracy Train: 97.59%, Val: 93.27%, Test: 92.25%
Class 0 1 2 3 4 5 6
Sensitivity 0.933 0.916 0.991 0.844 0.973 0.853 0.947
NEEEMD + DCGAN
(Samples: 8050)
Accuracy Train: 98.06%, validation: 94.67%, test: 93.59%
Class 0 1 2 3 4 5 6
Sensitivity 0.947 0.947 0.996 0.895 0.978 0.867 0.947
In Figure 20, for the bearing fault classifier, as the noise SD levels rise, the NEEEMD
+ DCGAN model performed with significantly higher robustness than the NEEEMD
scalograms model. In Figure 21, for the blade fault diagnosis model, the NEEEMD +
DCGAN model maintains relatively constant higher robustness than the NEEEMD model.
In Figure 22, the fault localization model for NEEEMD + DCGAN has higher robustness at
all the noise SDs except 0.35 SD. At 0.35 SD, the robustness is the same for both NEEEMD
+ DCGAN and NEEEMD samples only. Apart from this only exception, the NEEEMD +
DCGAN model performed with considerably higher robustness in all the classifier models.
This proves that the augmented samples from DCGAN not only improved our classification
accuracy, but also enhanced the models’ robustness.
Figure 20. Performance of bearing fault classifier on noisy data.
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Figure 21. Performance of blade fault diagnosis classifier on noisy data.
Figure 22. Performance of blade fault localization classifier on noisy data.
10. Conclusions
In this work, the effectiveness of NEEEMD scalograms is verified by classifying using
CNN and compared with scalograms from CWT, EEMD, CEEMD, and grayscale images.
The scalogram samples obtained much higher accuracy than grayscale image samples.
The NEEEMD scalograms obtained the highest accuracy in all the classifier models. On
the other hand, the grayscale images and CWT scalograms obtained an overfit model for
a higher-class classification. Nevertheless, the outputs of the scalograms samples had a
small difference in terms of accuracy. Therefore, additional validation is conducted by
considering model robustness for noisy test samples. The NEEEMD scalograms and CNN
model obtained the highest robustness in all the methods. Next, augmented samples
from DCGAN are used with the original samples to train the NEEEMD scalograms and
CNN classifier again. The number of augmented samples is increased within a range
to observe how the classifier performance varies. Thus, the optimal number of training
samples is obtained where the classifier obtained improved validation and accuracy. The
model robustness at this point is compared with the previous robustness from NEEEMD
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scalograms and CNN. It is found that the augmented samples from DCGAN improve
classifier accuracy and increase model robustness.
Supplementary Materials:
All of the coding files used to obtain the results of this study can be found
at https://github.com/atik666/Data-Final.
Author Contributions:
Conceptualization, A.F. and W.K.N.; methodology, A.F. and W.K.N.; software,
A.F.; validation, W.K.N., M.H.L. and M.S.L.; formal analysis, W.K.N., M.H.L. and M.S.L.; investigation,
A.F.; resources, W.K.N.; data curation, A.F. and W.K.N.; writing—original draft preparation, A.F.;
writing—review and editing, W.K.N., M.H.L. and M.S.L.; visualization, A.F.; supervision, W.K.N.;
project administration, W.K.N., M.H.L. and M.S.L.; funding acquisition, W.K.N., M.H.L. and M.S.L.
All authors have read and agreed to the published version of the manuscript.
Funding:
This work was supported in part by the Institute of Noise and Vibration UTM through the
Higher Institution Centre of Excellence (HICoE) under grant R.K130000.7809.4J226, grant
R.K130000.7809.4J227, and grant R.K130000.7809.4J228. Additional funding for this research also
came from the Ministry of Higher Education Malaysia for the financial support provided under the
Fundamental Research Grant Scheme (FGRS) no. FRGS/1/2018/TK03/UMP/02/24 grant (Univer-
sity reference RDU190157).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Appendix A.1. EMD
The time-frequency domain analysis EMD simply decomposes a vibration signal into
several IMFs. The IMF function needs to fulfill two criteria:
1.
The number of extrema and zero crossings in the whole vibration series must be the
same or differ at most by one.
2. The mean of upper and lower envelopes must be zero at any given point.
When the above two criteria are satisfied, an IMF is reported by c
1
. The first residue
r1
is obtained from the difference between the signal and the first IMF and is used to
decompose the next IMF. The decomposition process has to be repeated to find the
n
th
IMF until a monotonic residue is reported. The method of decomposition is repeated
n
times until the residue becomes monotonic to obtain the
nth
IMF. The original signal can
be reassembled by summing the nIMFs and the nth residue presented as follows:
X(t)=
n
i=1
ci+rn
where X(t)is the original signal, ciis the ith IMF, and rnis the nth residue.
Appendix A.2. EEMD
EEMD is an improvement of EMD, which was suggested to solve the mode-fusing
problem of EMD. The white noise of a finite amplitude is added with the ensembles of
EMD to generate the IMFs. The added noise dissolves in the whole time-frequency plane
uniformly, thus solving the mode-mixing problem. For an original signal,
X(t)
, the EEMD
algorithm follows the following steps:
1.
Add a bunch of white noise to the original signal with a mean of 0 and the standard
deviation of 1 to obtain a series of ensembles.
Xi(t)=X(t)+wi(t)
Sensors 2021,21, 8114 27 of 29
where
wi(t)
is the white noise signal of the same length as
x(t)
and
i=
1, 2,
. . .
,
M
,
M is the number of ensembles.
2. Decompose the ensembles using EMD to obtain the IMFs.
Xi(t)=
N
j=1
cij (t)+ri(t)
where
j=
1, 2,
. . .
,
N
, N is the number of IMFs and
cij (t)
is the IMFs (
ci1
,
ci2
,
. . .
,
ciN
).
ri(t)denotes the residue of the ith trail.
3. In the end, determine the ensemble means of the consequent IMFs.
cj(t)=1
M
M
i=1
cij (t)
Appendix A.3. CEEMD
CEEMD was proposed to overcome the drawbacks and increase the performance of
EEMD. In CEEMD, white noise is added in pairs (both positive and negative) to reduce the
presence of noise. The paired white noises can decrease the white noise in the final residue
successfully. The CEEMD algorithm for a signal X(t)has the following steps:
1. Add a pair of white noise to x(t)the same way as EEMD.
X1(t)=X(t)+wi(t)X2(t)=X(t)wi(t)
2. Decompose X1(t)and X2(t)using EMD to obtain the IMFs.
3. Obtain two ensemble IMFs sets by repeating the steps M times.
IMF1=1
M
M
i=1
IMF1iI MF2=1
M
M
i=1
IMF2i
4. The final IMFs are obtained from the mean of positive and negative ensembles.
IMF =(IMF1+IMF2)/2
5. The final result is obtained as,
X(t)=
M
i=1
IMFi(t)+rM(t)
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Failure detection is employed in the industry to improve system performance and reduce costs due to unexpected malfunction events. So, a good dataset of the system is desirable for designing an automated failure detection system. However, industrial process datasets are unbalanced and contain little information about failure behavior due to the uniqueness of these events and the high cost for running the system just to get information about the undesired behaviors. For this reason, performing correct training and validation of automated failure detection methods is challenging. This paper proposes a methodology called FaultFace for failure detection on Ball-Bearing joints for rotational shafts using deep learning techniques to create balanced datasets. The FaultFace methodology uses 2D representations of vibration signals denominated faceportraits obtained by time-frequency transformation techniques. From the obtained faceportraits, a Deep Convolutional Generative Adversarial Network is employed to produce new faceportraits of the nominal and failure behaviors to get a balanced dataset. A Convolutional Neural Network is trained for fault detection employing the balanced dataset. The FaultFace methodology is compared with other deep learning techniques to evaluate its performance in for fault detection with unbalanced datasets. Obtained results show that FaultFace methodology has a good performance for failure detection for unbalanced datasets.
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An improved CNN is proposed for the diagnosis of defects in components of a centrifugal pump. The improvement is attained by modifying the cost function of CNN. For defect identification, first, grey scale acoustic images are obtained by processing acoustic signals using analytical wavelet transform (AWT). Second, a new entropy based divergence function, a type of regularization function is introduced in the cost function of CNN which avoids redundant activation of hidden layer in CNN, thus ensuring sparsity by reducing number of training parameters and avoid over-fitting problem in CNN. Third, modeling of improved CNN is done using grey scale acoustic images. After, training, finally test data is applied to improved CNN for the identification of defects. Experimental results achieved while diagnosis defects of centrifugal pump show that the proposed improved CNN has a significant improvement of identification accuracy of about 3.2% over traditional CNN.
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We show that the backpropagation algorithm is a special case of the generalized Expectation-Maximization (EM) algorithm for iterative maximum likelihood estimation. We then apply the recent result that carefully chosen noise can speed the average convergence of the EM algorithm as it climbs a hill of probability. Then injecting such noise can speed the average convergence of the backpropagation algorithm for both the training and pretraining of multilayer neural networks. The beneficial noise adds to the hidden and visible neurons and related parameters. The noise also applies to regularized regression networks. This beneficial noise is precisely the noise that makes the current signal more probable. We show that such noise also tends to improve classification accuracy. The geometry of the noise-benefit region depends on the probability structure of the neurons in a given layer. The noise-benefit region in noise space lies above the noisy-EM (NEM) hyperplane for classification and involves a hypersphere for regression. Simulations demonstrate these noise benefits using MNIST digit classification. The NEM noise benefits substantially exceed those of simply adding blind noise to the neural network. We further prove that the noise speed-up applies to the deep bidirectional pretraining of neural-network bidirectional associative memories (BAMs) or their functionally equivalent restricted Boltzmann machines. We then show that learning with basic contrastive divergence also reduces to generalized EM for an energy-based network probability. The optimal noise adds to the input visible neurons of a BAM in stacked layers of trained BAMs. Global stability of generalized BAMs guarantees rapid convergence in pretraining where neural signals feed back between contiguous layers. Bipolar coding of inputs further improves pretraining performance.
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The fault detection of rotating machinery systems especially its typical components such as bearings and gears is of special importance for maintaining machine systems working normally and safely. However, due to the change of working conditions, the disturbance of environment noise, the weakness of early features and various unseen compound failure modes, it is quite hard to achieve high-accuracy intelligent failure monitoring task of rotating machinery using existing intelligent fault diagnosis approaches in real industrial applications. In the paper, a novel and high-accuracy fault detection approach named WT-GAN-CNN for rotating machinery is presented based on Wavelet Transform (WT), Generative Adversarial Nets (GANs) and convolutional neural network (CNN). The proposed WT-GAN-CNN approach includes three parts. To begin with, WT is employed for extracting time-frequency image features from one-dimension raw time domain signals. Secondly, GANs are used to generate more training image samples. Finally, the built CNN model is used to accomplish the fault detection of rotating machinery by the original training time-frequency images and the generated fake training time-frequency images. Two experiment studies are implemented to assess the effectiveness of our proposed approach and the results demonstrate it is higher in testing accuracy than other intelligent failure detection approaches in the literatures even in the interference of strong environment noise or when working conditions are changed. Furthermore, its result in the stability of testing accuracy is also quite excellent.