IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 69, NO. 10, OCTOBER 2020
7319
An Improved Quantum-Inspired Differential
Evolution Algorithm for Deep Belief Network
Wu Deng , Member, IEEE, Hailong Liu , Member, IEEE, Junjie Xu , Member, IEEE,
Huimin Zhao , Member, IEEE, and Yingjie Song , Member, IEEE
Abstract— Deep belief network (DBN) is one of the most
representative deep learning models. However, it has a disadvantage that the network structure and parameters are basically
determined by experiences. In this article, an improved quantuminspired differential evolution (MSIQDE), namely MSIQDE algorithm based on making use of the merits of the Mexh wavelet
function, standard normal distribution, adaptive quantum state
update, and quantum nongate mutation, is proposed to avoid
premature convergence and improve the global search ability.
Then, the MSIQDE with global optimization ability is used to
optimize the parameters of the DBN to construct an optimal
DBN model, which is further applied to propose a new fault
classification, namely MSIQDE-DBN method. Finally, the vibration data of rolling bearings from the Case Western Reserve
University and a real-world engineering application are carried
out to verify the performance of the MSIQDE-DBN method.
The experimental results show that the MSIQDE takes on
better optimization performance, and the MSIQDE-DBN can
obtain higher classification accuracy than the other comparison
methods.
Index Terms— Deep belief network (DBN), fault classification,
multistrategies, parameter optimization, quantum-inspired differential evolution (QDE).
Manuscript received October 21, 2019; revised January 26, 2020; accepted
March 13, 2020. Date of publication March 25, 2020; date of current version
September 15, 2020. This work was supported in part by the National
Natural Science Foundation of China under Grant 61771087, Grant 51605068,
Grant 51475065, and Grant 51879027, in part by the Open Project Program of
the Traction Power State Key Laboratory of Southwest Jiaotong University
under Grant TPL2002, in part by the State Key Laboratory of Mechanical
Transmissions of Chongqing University under Grant SKLMT-KFKT-201803,
and in part by the Key Laboratory of Air Traffic Control Operation Planning
and Safety Technology of CAUC under Grant 600001010932. The Associate
Editor coordinating the review process was John Sheppard. (Corresponding
author: Huimin Zhao.)
Wu Deng is with the College of Electronic Information and Automation,
Civil Aviation University of China, Tianjin 300300, China, and also with
the Traction Power State Key Laboratory, Southwest Jiaotong University,
Chengdu 610031, China (e-mail: dw7689@163.com).
Hailong Liu is with the School of Electronics and Information
Engineering, Dalian Jiaotong University, Dalian 116028, China (e-mail:
18340807855@163.com).
Junjie Xu is with the College of Electronic Information and Automation,
Civil Aviation University of China, Tianjin 300300, China (e-mail:
connyadmin@163.com).
Huimin Zhao is with the College of Electronic Information and Automation,
Civil Aviation University of China, Tianjin 300300, China, and also with the
State Key Laboratory of Mechanical Transmissions, Chongqing University,
Chongqing 400044, China (e-mail: hm_zhao1977@126.com).
Yingjie Song is with the Co-innovation Center of Shandong Colleges
and Universities: Future Intelligent Computing, Shandong Technology and
Business University, Yantai 264005, China (e-mail: songyj@sdtbu.edu.cn).
Color versions of one or more of the figures in this article are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIM.2020.2983233
I. I NTRODUCTION
N THE research of fault diagnosis, the time-domain or
frequency-domain analysis methods are usually used to
diagnose faults by the vibration monitoring data [1]–[3]
because the time-domain signal can directly be used to extract
fault features, which are beneficial to keep the basic characteristics of the signal. In time-domain analysis, the dimensionless indexes of pulse, kurtosis, peak, and waveform are
widely used, but these indexes are only sensitive to some
fault types, and may be poorer for other fault types [4]–7].
Therefore, the traditional dimensionless indexes are combined
and optimized to construct new dimensionless indexes for fault
classification. However, it is difficult to obtain a dimensionless
index with better classification ability for the sample data with
a large aliasing.
As a typical representative of deep learning, deep belief
network (DBN) forms a more abstract high-level representation by combining low-level features to discover distributed
feature representation [8]. It can directly obtain high-level
features from low-level signals layer by layer using greedy
learning. The DBN can avoid the brought complexity and
uncertainty of traditional feature extraction, and enhance
recognition intelligence. Therefore, the DBN is widely applied
in fault classification [9]–[14]. Tran et al. [15] presented a new
diagnosis method using Teager–Kaiser energy operator and
DBN. Chen and Li [16] presented an approach using sparse
autoencoder and DBN for multisensor feature fusion. Shao et
al. [17] presented an electric locomotive bearing fault diagnosis method using DBN. Zhao et al. [18] presented a fault diagnosis method using principal component analysis (PCA) and a
broad learning system. Qin et al. [19] presented an optimized
DBN with logistic sigmoid units. However, the structure and
parameters of DBN are basically determined by experiences.
This could not only bring man-made influence diagnosis error,
but is also not conducive to optimize the network structure,
which results in higher calculation cost and slow speed, and
cannot meet the actual needs of the fault classification.
Differential evolution (DE) algorithm is a heuristic
optimization algorithm, which uses the difference guiding
algorithm between individuals to search in the solution
space [20]. Quantum computing is a new computing technique
for solving various problems [21]. Quantum-inspired
DE (QDE) makes full use of the fast performance of quantum
computing and the optimization ability of the DE [22]. It can
prevent premature convergence, promote fast convergence,
I
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 69, NO. 10, OCTOBER 2020
and ensure the diversity of population. In recent years,
the researchers have studied QDE for solving complex
problems. Draa et al. [23] presented a QDE for the N-queens
problem. Su and Yang [24] presented a QDE to learn the
Takagi–Sugeno fuzzy. Xu et al. [25] presented a multiobjective
evolutionary algorithm to optimize the design of the hydraulic
excavator shovel attachment. The other optimization methods
are presented in [26]–[31]. In general, the QDE can effectively
prevent premature convergence, promote fast convergence,
and ensure the diversity of population. However, it has low
global search ability and difficultly in determining parameters.
To solve the experience selection of the DBN parameters,
the QDE with better optimization performance is used to select
the parameter of the DBN; an improved QDE algorithm based
on multistrategies, namely MSIQDE, is proposed to optimize
the parameters of the DBN to obtain a fault classification
(MSIQDE-DBN) method which is used to deal with the fault
classification problem. The MSIQDE-DBN method can eliminate the interference of human factors and adaptively select the
optimal parameters of the DBN, so as to effectively improve
the classification accuracy and meet the actual requirements.
The rest of this article is organized as follows. Section II
introduces the QDE. Section III describes an improved QDE
with multistrategies. Section IV describes an optimized DBN
model. A fault classification is discussed in Section V.
Section VI discusses and compares the outcomes by experiment and analysis. Section VII includes the conclusion and
future works.
II. QDE
In the QDE, a quantum chromosome is randomly selected
from the quantum population. The Q-bit is used as the base
vector, and the Q-bit of the other two quantum chromosomes
is used as the difference vector. The generation method is
described as
t
t
t
(5)
+ F0 · rand · θr2
− θr3
θit = θr1
where F0 is mutation coefficient, t is the number of iterations. r1 , r2 , and r3 are randomly generated exclusive integers
in [1, NP].
The mutated quantum chromosomes are screened. If the
chromosome values exceed range [−π, π], the quantum chromosome values are generated randomly. The screening method
is described as
θi,t j new =
(1)
where α and β represent the probabilistic amplitudes of
the corresponding states. The normalized condition must be
satisfied with |α|2 + |β|2 = 1.
A quantum chromosome with length m can be expressed as
α1 α2 . . . αm
|
.
(2)
q=
β1 β2 . . . βm
(3)
because the sum of probabilistic amplitudes of two states of
each single Q-bit is 1, i.e., α 2 +β 2 = 1. Therefore, α and β can
correspond to cosθ and sinθ one by one, respectively, so Q-bit
can also be expressed as (cosθ, sinθ )T . In the QDE, there are
NP individuals in population, and each individual is composed
of D Q-bits. Then, the i th individual x i can be expressed as
x i = x i,1 x i,2 |∧ x i,m cos(θi,1 ) cos(θi,2 ) ∧ cos(θi,m ) = sin(θi,1 ) sin(θi,2 ) ∧ sin(θi,m ) (4)
θi, j = π · rand
θi,t j ,
ifθi,t j > −π and θi,t j < π
π · rand, else.
(6)
C. Quantum Crossover Operation
To ensure the diversity of quantum population and enhance
the global search ability, quantum mutation individuals and
predetermined parent individuals are mixed to generate new
individuals. The crossover operation is described as
t
In QDE, the Q-bit is used to represent chromosomes. A pair
of complex numbers (α, β) are used to define a Q-bit, which is
represented as the vector [α, β]T . So a Q-bit can be expressed
as
A 3 Q-bits chromosome can be expressed as
√ √ √ 1/√2 1/ √2 1/
√ 2
q=
1/ 2 −1/ 2 3/2
B. Quantum Mutation Operation
θ i, j =
A. Chromosome Coding With Real Number
|ϕr = α| 0r + β|1r
where rand is a random number in [0, 1], i ∈ (1, 2, . . . , N P),
and NP is the number of individuals in the population.
if rand < CR or j = rand
θi,t j ,
θi,t j new , else
(7)
where CR is the quantum crossover coefficient.
D. Quantum Selection Operation
In the QDE, the greedy strategy is used to evaluate the
objective function values of the test vectors to select individuals with better fitness values for the next generation. The
selection process is described as
t
θit ,
if f x it < f x i
u ki =
(8)
t
θ i, j , else
where x ik is the chromosome without quantum mutation and
quantum crossover of the kth iteration.
III. I MPROVED QDE W ITH M ULTISTRATEGIES
For the low global search ability and difficultly in determining parameters of QDE, the multistrategies of standard normal
distribution, Mexh wavelet function, adaptive quantum state
update, and quantum nongate mutation are used to propose
an improved QDE (MSIQDE) in this article. In the MSIQDE,
the Mexh wavelet function is used to improve the mutation
coefficient from falling into the local optimum and to ensure
the diversity of population. The standard normal distribution
is used to improve the crossover coefficient by increasing the
value diversity of parameters and to improve the global search
performance. The adaptive quantum state update is used to
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DENG et al.: IMPROVED QDE ALGORITHM FOR DBN
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dynamically adjust the position of the quantum chromosome
at each iteration to speed up the convergence. The quantum
nongate mutation is used to mutate the quantum chromosome
to keep the optimal position of the memory. So the MSIQDE
with different strategies can effectively improve the global
search ability and population diversity, avoid premature convergence, accelerate the convergence, and prevent falling into
local optimum.
A. Mutation Coefficient Using Mexh Wavelet
In the QDE, the mutation coefficient F0 is the most
important factor. To keep the diversity of the population
and to improve the convergence speed, the Mexh wavelet
function is used to improve the mutation coefficient. Mexican
Hat is the second derivative of the Gauss function. It has
better localization characteristics in both time and frequency
domains, and R (t)dt = 0. Therefore, it is used to improve
the mutation coefficient, whose value is randomly selected
between (0, 1). The mutation coefficient based on the Mexh
wavelet is described as
1
x2
2
(9)
F0 = √ · π − 4 · 1 − x 2 · e− 2 .
3
B. Crossover Coefficient Using Standard Normal
Distribution
In quantum crossover operation, the crossover coefficient
CR represents the crossover probability to reflect the probability of inheriting information from the parent population.
The larger CR value makes the new population to depend
more on the mutation process and inherits less information
from the parent population, so as to achieve a larger range of
global search and reduce the possibility of falling into the local
optimum. On the contrary, the smaller CR encourages local
search around the parent population, which can accelerate the
convergence and improve the solution accuracy. In this article,
the standard normal distribution is used to improve the CR.
The expression is described as
CR = N (0, 1) .
(10)
C. Adaptive Quantum State Update Strategy
Based on the traditional quantum mutation, the crossover,
selection, and quantum gate mutation, the adaptive state update
of the quantum rotation angle is used to adjust the position of
the quantum chromosome for each iteration. The adaptive state
update strategy of the quantum rotation angle is described as
θit = θmin + fit ∗ (θmax −θ min ) ∗ rand ∗ exp(G/Gm) (11)
(12)
fit = (fit Best − fit i )/fitBest
where θmin is the lower limit of the angle which is set to
0.001π. θmax is the upper limit of angle which is set to 0.05π.
fit Best is the global optimal value, and fit i is the fitness value
of the current individual. rand is the random number in [0, 1],
G and Gm are the current number and maximum number of
iterations, respectively.
D. Quantum Nongate Mutation Strategy
In quantum computation, a series of transformations of
Q-bits are used to realize the logical transformation function.
A quantum device that realizes logical transformation within
a certain time interval is called a quantum gate. In this article,
quantum nongate is used to mutate the quantum chromosome,
and the mutation probability Pm is set. If Pm > rand, then
some quantum bits in the quantum chromosome are randomly
selected to mutate. The optimum position of the memory is
kept. The quantum nongate mutation strategy is described as
cos(θi,1 ) cos(θi,2 ) ∧ cos(θi,m ) u ki = sin(θ ) sin(θ ) ∧ sin(θ ) i,1
i,2
i,m
⎞
⎛
π
−
θ
cos
i, j
01
cos θi, j
2
⎠
=⎝
π
10
sin(θ i, j )
− θi, j
sin
2
⎧
⎨ π − θ k , if Pm > rand
2
v i,k j =
i, j
⎩ θk ,
else.
(13)
(14)
(15)
i, j
IV. O PTIMIZE THE PARAMETERS OF DBN
A. DBN
The DBN is one of the neural networks which is stacked by
multiple restricted Boltzmann machine (RBM) networks and
a supervised back propagation (BP) network [12]. Each RBM
consists of a visible layer and a hidden layer.
Let v i and h j denote the first i th neuron in the visible layer
and the j th neuron in the hidden layer, respectively. For a
group of (v, h), the energy function of RBM is defined as
E (v, h|θ ) = −
I
i=1
ai v i −
J
j =1
bjh j −
J
I v i ωi j h j
(16)
i=1 j =1
where θ = (ωi j , ai , b j ) is the parameters of RBM, ωi j is the
weight between the node v i in the visible layer and the node h j
in the hidden layer, ai and b j are the bias values of v i and h j ,
respectively.
According to the energy function, the joint probability
distribution of (v, h) can be obtained
(17)
p(v, h|θ ) = e−E(v,h|θ ) / [Z (θ )]
−E(v,h|θ )
is the normalization factor.
where Z (θ ) = v h e
Because there is no connection between the layers in the
RBM when the state of the nodes in the visible layer is
determined, the activation states of the nodes in the hidden
layer are independent of each other. Therefore, the activation
probability of the node in the j th hidden layer is described as
I
vi ω j i
(18)
p h j = 1|v, θ = σ b j +
i=1
where σ (x) = 1/(1 + e−x ) is the sigmoid function.
At the same time, the activation probability of the node in
the i th visible layer can be obtained
⎛
⎞
J
hi ω j i ⎠ .
p(v i = 1|h, θ ) = σ ⎝ai +
(19)
j =1
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RBM is a random neural network with activation function of
the sigmoid. The parameter θ = (ωi j , ai , b j ) is obtained by
continuous iterations, and θ = (ωi j , ai , b j ) is fitted with the
given training data. The parameter θ ∗ can be obtained by the
maximum logarithmic likelihood function on the training set
θ ∗ = argθ maxL (θ ) = argθ max
T
ln p(v (t) |θ ).
(20)
t=1
The logarithmic likelihood divergence of RBM is calculated by
the contrast divergence algorithm and the random gradient rise
method is used to solve the maximum logarithmic likelihood
function. The updated formulas of the parameters are described
as
ωi j = ε(v i h j data − v i h j recon )
ai = ε(v i data − v i recon )
b j = ε h j data − h j recon
(21)
(22)
(23)
where ε is the learning rate of pretraining, ·data is the
mathematical expectation of training data, and ·recon is the
mathematical expectation of the reconstructed model.
For the output layer, if the output of the i th node is oi , the
expectation is di , the sensitivity is δi , then the δi is described
as
δi = oi (1 − oi ) (di − oi ) .
(24)
The expression of sensitivity in the lth hidden layer is
described as
l l+1
δil = yil 1 − yil
ωi j δ j .
(25)
j
The updating formulas of the weights and biases of each
layer in the DBN under the learning rate ε are described as
ωil j = ωil j + ε ∗ yil δl+1
j
a lj
blj
=
=
a lj
blj
+ε∗
+ε∗
δl+1
j
δl+1
j .
(26)
(27)
(28)
B. Optimized Parameters of DBN Using MSIQDE
The DBN model has strong approximation ability to the
nonlinear function; it is widely applied in the fields of
online prediction, classification, and fault diagnosis. In the
application, the connection weights and biases of DBN are
initialized randomly, which in turn leads to the insufficient
global optimization ability and eventually falls into the local
optimum. Therefore, the connection weights and biases of
DBN seriously affect the classification accuracy. The MSIQDE
algorithm takes on the global search ability, diversity of
population, and fast convergence. Therefore, the MSIQDE
with global optimization ability is introduced into the DBN
to optimize the connection weights of each node. A parameter
optimization method for DBN based on MSIQDE is proposed
to obtain an optimized DBN (MSIQDE-DBN) model in order
to avoid the blindness of parameter selection, reduce the
impact on modeling accuracy, and enhance the classification
and forecasting ability.
Fig. 1.
Flow of the MSIQDE-DBN.
C. Model of the MSIQDE-DBN
The flow of the MSIQDE-DBN is shown in Fig. 1.
V. FAULT C LASSIFICATION BASED ON MSIQDE-DBN
A. New Fault Classification Method
Fault diagnosis is used to select the appropriate method,
to determine the fault type, location, severity, and so on. In past
years, different fault diagnosis methods are proposed to realize
fault classification and to obtain better classification results.
But some of these methods could not effectively recognize
the early faults and fault classification with large-scale data.
The DBN is one of the neural networks; it is a probability generating model. Compared to the traditional discriminant neural
network, the generating model establishes a joint distribution
between observation data and labels. Therefore, the MSIQDEDBN is applied in fault classification in order to propose a new
fault classification method for realizing fault classification with
higher accuracy for rotating machinery.
B. Detailed Steps of Fault Classification Method
Step 1: The data are normalized and divided into training
set (TrainData) and test set (TestData).
Step 2: Initialize the parameters of the MSIQDE-DBN,
which include population number (NP), quantum chromosome
length (N), the maximum number of iterations (Gm), mutation
probability (Pm), crossover probability (Pc), the number of
hidden layers, the number of connecting nodes in each layer,
learning rate, initial momentum factor, unsupervised training
times, supervised iteration times, and so on.
Step 3: The quantum chromosome length is determined
according to the number of layers of RBMs. The quantum
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DENG et al.: IMPROVED QDE ALGORITHM FOR DBN
population is initialized and the quantum chromosome is
encoded.
Step 4: According the objective of classification, the fitness
function is constructed.
Step 5: The quantum population is evaluated, and the initial
fitness value of each individual in the population is calculated.
Step 6: The quantum mutation operation and quantum
crossover operation are carried out, and the population is
normalized to the feasible solution space.
Step 7: Implement the quantum mutation operation and the
quantum crossover operation.
Step 8: The parameters of the DBN and the fitness value of
new population are obtained and compared with the original
population in order to carry out the greedy selection operation.
Step 9: The updated quantum population is obtained by the
adaptive quantum state update and quantum nongate mutation.
Step 10: The parameters of the updated DBN and the
fitness value of the quantum population are obtained by the
individuals of the updated population, and the optimal values
are saved.
Step 11: Compare calculation results. If the end conditions
are met, the results are output and the optimal MSIQDE-DBN
is obtained. Otherwise, return to Step 5.
Step 12: The training set is used to train MSIQDE-DBN to
obtain an optimal MSIQDE-DBN classification method.
Step 13: The test set is keyed in and the MSIQDE-DBN to
obtain fault classification results.
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Fig. 2.
Fitness value of individual for time-domain data.
TABLE I
C LASSIFICATION A CCURACY OF T IME -D OMAIN S IGNALS
VI. E XPERIMENT AND A NALYSIS
In this section, the experiments on two data sets,
i.e., the data of rolling bearings from the Case Western
Reserve University (CWRU) and a real-world application
engineering are used to evaluate the performance of the
MSIQDE-DBN by comparison with the DBN, DE-DBN,
QDE-DBN, quantum-behaved genetic algorithm (QGA)-DBN,
and quantum-behaved particle swarm optimization (QPSO)DBN in terms of classification accuracy and running time
for time-domain data and frequency-domain data, respectively.
The parameters are set as follows. The DBN is set as five
layers of neurons and four RBMs. The population number
is 50, the length of the chromosome is 3-D, the number of
iterations are 200 and 20 for time-domain data and frequencydomain data, respectively. The upper and lower limits of nodes
are 16 and 1500, respectively. The training times of RBM are
20, the number of unsupervised training of RBM is 80, and
the fine-tuning times of BP are set as 100 and 200 for the
time-domain data, the fine-tuning times of BP are set as 10
and 20 for the frequency-domain data. The learning rate of the
first three layers of RBM is 0.012, and that of the last layer
of linear RBM is 0.001. The penalty coefficient of weight is
0.0002, and the initial momentum is 0.5.
All experiments are carried out on Intel (R) core (TM)
i5-7400 CPU 3 GHz, 8G RAM, Win 10, and MATLAB
R2018a.
A. Experiments on the CWRU Data Set
1) Experimental Data: In this article, the experiments are
carried out on the CWRU data set that is 12K drive end rolling
bearing data from the CWRU [32]. The sampling frequency
is 12 kHz, and the data are divided into no-load (HP0),
1 HP (HP1), 2 HP (HP2), and 3 HP (HP3). Under each load,
the faults include inner ring fault, outer ring fault, and rolling
element fault. For each type of fault, there are three kinds of
damages –0.1778, 0.3556, and 0.5334 mm, respectively. The
data are intercepted by 1024 lengths and there are ten kinds
of classifications.
2) Experiment Results and Analysis for Time-Domain Data:
In the experiment, the training data are 500 × 1024 and the
test data are 300 × 1024. The fitness value of the individual
for bearing time-domain data (error rate of fault diagnosis) is
shown in Fig. 2.
The fault classification accuracies of the time-domain data
with different number of hidden layer nodes are shown
in Table I. The comparison results of error rate changes are
shown in Fig. 3.
As can be seen from Table I and Fig. 3, the optimal classification accuracies are 47.62%, 55.92%, 59.38%, 59.38%,
58.85%, and 64.62% using the DBN, DE-DBN, QDE-DBN,
QGA-DBN, QPSO-DBN, and MSIQDE-DBN, respectively.
The proposed MSIQDE-DBN can improve the classification
accuracy by about 15% than the DBN. With the increase in the
fine-tuning value, the classification accuracies and the running
time are also gradually increased. Therefore, the experiment
results show that the MSIQDE can effectively and feasibly
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Fig. 3.
Comparison results of error rate.
Fig. 4.
Fitness value of individual for frequency-domain data.
TABLE II
C LASSIFICATION A CCURACY OF F REQUENCY-D OMAIN S IGNALS
Fig. 5.
Comparison results of error rate.
Fig. 6.
Fitness value of individual for time-domain data.
When the frequency spectrum of bearing vibration signal is
input, the number of different nodes has a greater impact
on the classification results. If the parameters of DBN are
unreasonable, the classification accuracy will be unsatisfactory.
The MSIQDE algorithm is used to select reasonable
connection weights of each node to obtain optimized DBN
model, which can effectively improve classification accuracy.
Therefore, the experiment results show that the MSIQDE
algorithm can effectively optimize the parameters of the DBN
model and the MSIQDE-DBN can obtain high classification
accuracy. The running time of the frequency-domain data is
much less than that of the time-domain data.
B. Experiments on the Actual Engineering Data Set
optimize the parameters of DBN, and the MSIQDE-DBN can
obtain better classification accuracy than other models.
3) Experiment Results and Analysis for Frequency-Domain
Data: The 12K driver data are transformed by the frequency
spectrum data using fast Fourier transform (FFT). The training
data are 300 × 513 and the test data are 1300 × 513. The
fitness value of the individual for bearing frequency-domain
data (error rate of fault classification) is shown in Fig. 4.
The classification accuracies of the frequency-domain data
with different number of hidden layer nodes are shown
in Table II. The comparison results of error rate changes are
shown in Fig. 5.
As can be seen from Table II and Fig. 5, the optimal classification accuracies are 98.84%, 99.23%, 99.38%, 99.15%,
99.15%, and 99.7% using the DBN, DE-DBN, QDE-DBN,
QGA-DBN, QPSO-DBN, and MSIQDE-DBN, respectively.
1) Experimental Data: In this article, the experiments are
carried out on the actual engineering data set, i.e., the vibration
signals of the QPZZ-II rotary machinery under 1500 r/min.
The sampling frequency is 12 kHz and the sampling time
is 100 s. Nine kinds of fault vibration signals and one normal
vibration signal are collected under no-load. The intercept
length of vibration signal is 1024 and there are ten kinds of
classifications.
2) Experiment Results and Analysis for Time-Domain Data:
The training data are 500 × 1024 and the test data are
300 × 1024. The fitness value of the individual for bearing
time-domain data (error rate of fault diagnosis) is shown
in Fig. 6.
The classification accuracies of the time-domain signals
with different number of hidden layer nodes are shown
in Table III. The comparison results of error rate are shown
in Fig. 7.
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DENG et al.: IMPROVED QDE ALGORITHM FOR DBN
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TABLE III
C LASSIFICATION A CCURACY OF T IME -D OMAIN S IGNALS
Fig. 8.
Fitness value of individual for frequency-domain data.
TABLE IV
C LASSIFICATION A CCURACY OF F REQUENCY-D OMAIN S IGNALS
Fig. 7.
Comparison results of error rate.
As can be seen from Table III and Fig. 7, the optimal
classification accuracies are 50.31%, 59%, 61.31%, 60.69%,
61.38%, and 66.23% using the DBN, DE-DBN, QDE-DBN,
QGA-DBN, QPSO-DBN, and MSIQDE-DBN, respectively.
The MSIQDE-DBN can improve the classification accuracy
by about 16% than the DBN. With the increase in the finetuning value, the classification accuracies and the running time
are also gradually increased. Therefore, the experiment results
show that the MSIQDE can effectively and feasibly optimize
the parameters of DBN, which can obtain better classification
accuracy than other models.
3) Experiment Results and Analysis for Frequency-Domain
Data: The collected data are transformed by the frequency
spectrum data using FFT. The training data are 300 × 513 and
the test data are 1300 × 513. The fitness value of the individual
for bearing time-domain data (error rate of fault classification)
is shown in Fig. 8.
The classification accuracies of the frequency-domain data
with different number of hidden layer nodes is shown
in Table IV. The comparison results of error rate changes are
shown in Fig. 9.
As can be seen from Table III and Fig. 9 for the frequencydomain data of actual engineering, the optimal classification
accuracies are 95.23%, 96.46%, 96.38%, 96%, 96.23%, and
96.92%, and the running times are 5.85, 13.96, 11.76, 31.95,
9.16, and 25.02 s using the DBN, DE-DBN, QDE-DBN, QGADBN, QPSO-DBN, and MSIQDE-DBN, respectively. The
running time of DBN is 5.85 s, which is the least running time.
Fig. 9.
Comparison results of error rate.
The optimal classification accuracy of the MSIQDE-DBN is
96.92%, which is highest classification accuracy. Therefore,
the experiment results show that the MSIQDE can better
optimize the parameters of DBN and the MSIQDE-DBN can
effectively classify the faults of rolling bearings in actual
engineering application. It is an effective classification method
for rotating machinery in industrial application.
From the experiment results of time- and frequency-domain
data of CWRU and actual engineering, we can see that the
DBN model cannot deal better with time-domain data.
However, it can deal better with frequency-domain data.
The running times of the DBN model for frequency-domain
data are much lesser than those for time-domain data.
The optimal classification accuracies of the MSIQDE-DBN
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 69, NO. 10, OCTOBER 2020
can reach 99.7% and 96.92% for frequency-domain data
of CWRU and actual engineering, respectively. However,
the running time of the MSIQDE-DBN is a little more.
In general, the MSIQDE-DBN has better generalization
ability and robustness in fault classification.
VII. C ONCLUSION AND F UTURE W ORK
In this article, an improved QDE (MSIQDE) algorithm with
multistrategies of the Mexh wavelet function, standard normal
distribution, adaptive quantum state update, and quantum
nongate mutation is presented to optimize the connection
weights of DBN to obtain an optimal DBN, which is applied
in fault classification to propose a new fault classification
method, called MSIQDE-DBN. The data of CWRU and actual
engineering application are used to assess the effectiveness
of the MSIQDE-DBN method. The MSIQDE-DBN algorithm
is compared with four state-of-the-art algorithms of DBN,
DE-DBN, QGA-DBN, and QPSO-DBN. The optimal
classification accuracies of the MSIQDE-DBN can reach
99.7% and 96.92% for frequency-domain data of CWRU and
actual engineering application, respectively. Therefore, the
experiment results demonstrate that the MSIQDE algorithm
is significantly better than the rest of the compared methods.
The MSIQDE-DBN method can obtain better classification
accuracy, and takes on better generalization ability and
robustness in fault classification.
In the upcoming research, the structure optimization of
DBN can be performed on each layer, respectively, to further
improve the DBN. At the same time, the complexity of the
MSIQDE-DBN needs to be further reduced substantially in
future works.
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DENG et al.: IMPROVED QDE ALGORITHM FOR DBN
Wu Deng (Member, IEEE) received the Ph.D.
degree in computer application technology from
Dalian Maritime University, Dalian, China, in 2012.
Since 2019, he was a Professor with the College of Electronic Information and Automation,
Civil Aviation University of China, Tianjin, China.
His research interest includes artificial intelligence,
optimization method, and fault diagnosis.
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Huimin Zhao (Fellow, IEEE) received the Ph.D.
degree in mechanical engineering from Dalian Maritime University, Dalian, China, in 2013.
Since 2019, she has been a Professor with the
College of Electronic Information and Automation,
Civil Aviation University of China, Tianjin, China.
Her research interest includes artificial intelligence,
signal processing, and fault diagnosis.
Hailong Liu (Member, IEEE) received the B.S.
degree in optoelectronic engineering from Shandong
Normal University, Jinan, China, in 2017. He is
currently pursuing the Ph. D. degree with Dalian
Jiaotong University, Dalian, China.
His research interest includes deep learning and
fault classification.
Junjie Xu (Fellow, IEEE) received the Ph.D. degree
in computer application technology from Dalian
Maritime University, Dalian, China, in 2016.
Since 2016, she has been a Lecturer with the
College of Computer Science and Technology, Civil
Aviation University of China, Tianjin, China. Her
research interest includes artificial intelligence and
information safety.
Yingjie Song (Fellow, IEEE) received the Ph.D.
degree in computer application technology from
Dalian Maritime University, Dalian, China, in 2013.
Since 2013, she has been an Associate Professor
with the College of Computer Science and Technology, Shandong Institute of Business and Technology,
Yantai, China. Her research interest includes artificial intelligence and signal processing.
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