Instrumentation & Measurement Magazine 26-2 - 43

i.e., the convolution layer coming-first takes the RGB image
X as its input. It contains 64 convolution kernels with a size of
7×7 and a step size of 2, which are determined by the size of
the RGB image.
For the two ResNet blocks in every ResNet layer, the first
down-sample residual block (DRB-n) is used to pass the shallow
features forward with a shortcut connection. It gives an
output feature map as:
G ResNet G

10
ii
()
(6)
for i =1, 2, 3, 4. The following identity residual block (IRB-n) is
used for the dimension reduction through a down-sampling
operation and outputs a feature map as:
GG ResNet( )
ii
21
(7)
for i =1, 2, 3, 4 where an additional convolutional layer and a
BN block are introduced into the shortcut connection for the
dimensional agreement transformation. Then, the output feature
map of the ResNet layer i is generated by splicing original
input feature and deep features, i.e.,
Y  Trans( ) G 2
i iiX 
It is exactly the input of the following ResNet layer, i.e.:
ii 1
XY

(8)
y
The distribution probability of labeled fault type is described
by:

y Py i x
()i
   N
( |)
exp( [ ])
j0
exp(input i[ ])
input i
(10)
where input[i] is the vector output of the fully-connected layer,
and N is the number of the labels. ( |)Py i x
is defined as the
probability of the sample x predicted by the model as the label
i. Equation (10) maps the outputs of multiple neurons into the
range of (0,1) with their summation to 1 [6]. Assuming that the
ith output node is the output node of the correct category,
y
its probability to the category.
The cross-entropy loss is calculated by:
n
H p q
( , )   ( ) log( ) ()i

yi y
i1
where p is the probability distribution predicted by the model,
q is the true probability distribution, y(i)
bution, and ()i
is the predicted probability distribution. The
smaller the value of cross-entropy is, the closer their probability
distributions are. The parameters in the model are trained
by minimizing the loss function through optimization algorithms
such as the stochastic gradient descent (SGD), root
mean square prop (RMSprop), and adaptive momentum estimation
(Adam).
(9)
where the symbol '' means the splicing operation of two
vectors to generate an expanded vector. Trans(.) means the
transformation of the previous output feature map Xi-1
the dimension agreement with G2i. Trans(.) represents the
to meet
transformation on the feature map realized by the transition
layer. For the ResNet layer 2, layer 3 and layer 4, it consists of
a BN layer, an ReLU activation function, a convolutional layer
with m convolution kernels and an average pooling layer. m
are selected as 128, 256 and 512, respectively. Specifically for
the layer 1, it has X1
= G01
.
Finally, the obtained feature map of the RGB input image is
propagated to a down-sampling layer by the average pooling
and a fully-connected block to generate the prediction results
of the machinery fault diagnosis.
Dense ResNet Fault Diagnosis Model
The adaptation to working conditions and environmental
noises is realized by two steps. In the first step, RGBDResNet
is pre-trained by the source domain samples to
obtain the characteristics of the source domain distribution.
In the second step, for adaption to the target domain distribution,
the RGB-DResNet model is retrained through a
transfer learning adjustment by a small amount of target domain
data. Thus, a RGB-TDResNet model is finally derived
which makes full use of the samples in the source domain
and is endowed with the diagnosis adaption to the target
domain.
April 2023
Experimental Validation Results
The proposed RGB-TDResNet model was verified on the dataset
from Case Western Reserve University (CWRU) [9]. The
vibration signals at the drive end 6205-2RS JEM SKF bearing
under the loads of 0 HP, 1 HP, 2 HP and 3 HP were selected
for the experimental validation. Every working condition
contains five types of fault data collected at the sampling frequency
of 12 kHz, i.e., the ball damage at 0.007 inches with the
label of 1 (B007), the ball damage at 0.014 inches with the label
of 2 (B014), the inner race damage at 0.007 inches with the label
of 3 (IR007), the inner race damage at 0.014 inches with the
label of 4 (IR014) and the normal bearing with the label of 5
(Normal). The setting of the label depends on the type of fault
and the severity of the fault, regardless of the speed of the motor
and the location of the vibration sensor.
The Pearson product-moment correlation coefficient
(PPMCC) was used to quantify the difference between the
source and target domains. The PPMCC is defined as:
n
ρ( ,)X Y 
cov( , )

X Y

XY
1
 X X Y Y)
i 1
( 
ii
)(
(12)
nn
 X X YY)ii
22
(

) (
ii1
It gives the correlation coefficients of 0.0051, 0.0190, 0.0081 for
0 HP with regard to 1 HP, 2 HP and 3 HP, respectively. Considering
that the smaller PPMCC means a greater difference
between two variables, it can be thought that there is a big gap
between the signal of 0 HP and the signals of 1 HP, 2 HP and 3
HP. During the experiments, after the model training upon the
IEEE Instrumentation & Measurement Magazine
43
(11)
is the target distri()i
is
Instrumentation & Measurement Magazine 26-2

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