Structural parameters optimization of permanent magnet spherical motor based on BP neural network model Lufeng Ju1,2,d ,Guang Ma1,eand Xuejing Cao1,f
Fangfang Zhou1,a,Guoli Li 1, 2,b, Rui Zhou 1, 3,c
3. Engineering Research Center of Power Quality,
1.School of Electrical Engineering and Automation,
Ministry of Education, Anhui University, Hefei, 230601,
Anhui University, Hefei, 230601, Anhui, China
Anhui, China
2.National Engineering Laboratory of Energy-Saving Motor & Control Technology, Anhui University, Hefei,
c.
[email protected] d.
[email protected] 230601, Anhui, China
e.
[email protected] f.
[email protected] a.
[email protected] b.
[email protected] Abstract—In order to obtain a larger torque for a
permanent magnet spherical motor may become a hot
permanent magnet spherical motor, the method of
research topic in the future and has broad application
optimizing the structural parameters of the permanent
prospects in [2].
magnet spherical motor is studied. Based on the premise of volume minimization, this paper proposes a set of nonlinear data fitting by BP neural network, using genetic algorithm and particle swarm algorithm to calculate the maximum torque and the corresponding structural parameters. According to the sample data of the structural parameters of spherical motor and torque, BP neural
The structural parameters of spherical motors such as magnetic field and torque characteristics have a direct impact on the performance, therefore the spherical motor structural parameters optimization is an important topic in the research of spherical motors. In the permanent magnet spherical motor, the magnetic force is analyzed
network is trained to fit the sample space, and then
by the Lorenz force method, and then the torque of the
parameters of the optimal algorithm are found in
motor is obtained. This needs to integrate the current
combination with the BP neural network. Due to its
density and the magnetic flux density in the whole stator
accuracy and feasibility, the finite element analysis is used
winding,
to verify the optimization results. Finally the particle
complicated.
swarm
permanent magnet spherical motor is a nonlinear
algorithm
determines
structure
parameters
optimization for permanent magnet spherical motor. Keywords—permanent magnet spherical motor; BP neural network; genetic algorithm; particle swarm optimization
and
the The
calculation structure
process
optimization
is of
more the
problem with many variables and the strict constraint conditions where the structure size is one of the main constraints. Optimizing the magnetic field of the permanent magnet motor can effectively improve the efficiency of the motor, the power density, and reduce
I. INTRODUCTION There has been large- scale applications of multidegree-of-freedom industrial equipment, such as robot, mechanical joints and positioning device. Traditionally, motor control systems consist of two or more than two single degree of freedom, their mechanical structure is complex, the rigidity is low, and the reaction is slow due to the increase in size, which affect the stability of the systems in [1]. Due to its high mechanical integration,
the volume and quality of the motor. The structural parameters of the spherical motor directly affect the output characteristics of the motor and the research on the optimization of the structural parameters is an important part of the research of the spherical motor. In this paper, the optimization algorithm is proposed to optimize the parameters of the trained BP neural network, and the accuracy of this method is verified by the finite element analysis.
fast response and high positioning accuracy, the
c 978-1-5090-6161-7/17/$31.00 2017 IEEE
1831
The sample data of the structural parameters for the
then the electromagnetic torque is calculated by using
spherical motor torque are used to fit into the sample
the Maxwell's tensor method. In [5], the torque model of
space trained by BP neural network. The optimization
the whole motor can be formed by the superposition of a
algorithm is applied to optimize the parameters of BP
pair of stator and rotor pole interaction models. Figure 2
network and get the best parameters.
is the torque characteristic curve of stator and rotor poles obtained by calculation.
II. BASIC STRUCTURE AND FINITE ELEMENT ANALYSIS Before establishing the BP neural network model of the permanent magnet spherical motor, the training set is set
Figure 3 is the torque characteristics curves corresponding to the coil diameter ' HP , rotor magnetic pole high
up, which is the sample space . In this paper, the prototype of the permanent magnet spherical motor is shown in Figure 1. The motor rotor adopts a spherical structure. 4 layer cylindrical magnetic pole is averagely distributed on the rotor ball surface. 24 individual stator
K SP
, coil aperture G , and coil ampere
turns 1, . Figure 4 the torque characteristics curves corresponding to the air gap J , the length of the stator coil KHP and the radius of the rotor pole U SP .
coils with equal latitude interval are distributed on both sides of the equatorial plane. The output shaft of the rotor is longitudinal vertical to the spherical surface, which is used to output the torque in [3].
Fig. 2 The torque characteristic curve of stator and rotor poles
Fig. 1 The prototype of the permanent magnet spherical motor
Due to the different structure between the permanent magnet spherical motor and the traditional motor, the structure of the spherical motor is complex. The structure design and production of the motor are difficult, so the ball type motor is still in the research and exploration stage. Using Ansoft analysis software to establish the
Fig. 3 The torque characteristics curves corresponding to the coil
simulation model of the permanent magnet spherical motor, the simulation results provide the model support for the optimization of the parameters of the spherical motor in [4].
diameter
' HP , rotor pole high K SP , coil aperture G 1,
At present, the main method is to use the integral equation to analyze the motor air gap magnetic field, and
1832
2017 12th IEEE Conference on Industrial Electronics and Applications (ICIEA)
, and coil ampere
TABLE 1 SAMPLE SPATIAL DATA DISTRIBUTION Feature Attributes
1, KHP G J
Level 1 1000 9
Level 2 1500 10
Level 3 3000 11
Level 4 3500 12
Level 5 4000 13
1 1 7
2 1.5 8
3 2 9
4 2.5 10
5 3 11
rpm
III. NONPARAMETRIC MODELING OF BP NEURAL NETWORK BP neural network is a multilayer feed forward neural network, which belongs to the gradient descent Fig. 4 The torque characteristics curves corresponding to the air gap J , the length of the stator coil KHP and the radius of the rotor pole U SP
algorithm, which is mainly characterized by the forward transmission of signals and the back propagation of error and is a supervised learning algorithm. The BP model established in this paper is to convert the input and output of a set of samples into a nonlinear
In the research of permanent magnet spherical motor, there are many parameters affecting the performance of the spherical motor. The main parameters are as follows: coil ampere turns 1, , air gap J , stator and rotor angle θ , rotor magnetic pole height K SP , rotor magnetic pole
USP , stator coil length KHP , coil outer diameter ' HP , coil aperture G and so on. It can be seen from
radius
Figure 2, the torque on the offset angle has a nonlinear change and the torque takes the maximum at a fixed offset angle θ = D .can be seen from Figure 3 and Figure 4, The coil outer diameter K SP presents a very small range of variation, taking into account the constraints ' HP of the structure of the volume under the conditions of a relatively large torque. The impact of
optimization problem.
In the
permanent
magnet
spherical motor, the structure parameters and torque output are highly nonlinear system and there is no explicit state equation to describe them, so it is difficult to accurately model. In this case, the relationship between the structure parameters and the torque output can be established on BP neural network. The method considers the unknown system as a black box. In the sample space of above 576 sets of data, 500 sets are randomly selected to train the BP neural network, enable the network to express the unknown function. Then we can use the trained BP neural network to predict the torque output of the 76 sets of structure parameter data in [7] and verify the feasibility of BP neural network.
these two factors on the torque relative to other parameters can be ignored. In the following calculation, take K SP = PP and ' HP = PP . The sample space is established by using the coil ampere turns 1, , the air gap J , the rotor pole radius
U SP , the stator coil length KHP and the coil aperture G as the characteristic attributes. From the data in Table 1, we can see that there are
group data. According to
orthogonal test method, among 576 group data, 500 of them are training set and 76 are test set in[6].
A nonlinear model is established in MATLAB. According to the Kolmogrov theorem, the network structure is set to 5—11—1, the output layer uses the logsig-type activation function. For the spherical motor sample space, there is a big difference between the ampere turn factor and other factors. So in the process of establishing BP neural network model of spherical motor, there is a need for data normalization to solve the data index comparability. BP neural network is set up and the data normalization processing can be carried out after the network training[8], that is after training convergence of prediction samples to torque prediction. The predicted results are shown in Figure 5 and the error results are shown in Figure 6.
2017 12th IEEE Conference on Industrial Electronics and Applications (ICIEA)
1833
a generational evolutionary relationship to conduct the global search, which has strong robustness and stability [9]. The fitness function directly affects the convergence speed of genetic algorithm and this is the key to finding the optimal solution. This paper is to find the maximum value of the function, the value of the function as an individual of the size of the fitness value. The greater the value of the individual degree of adaptation value, the greater the individual in [10]. Structural parameters optimization of the permanent magnet spherical motor uses genetic algorithm combined with BP neural network to solve the unknown nonlinear function, that is, the torque and the corresponding Fig. 5 torque output results
structural parameters. The flow chart of the optimization algorithm is shown in Figure 7.
Fig. 6 error results of torque prediction
Compared with the traditional electric motor, the magnetic field model and torque model of spherical motor are three-dimensional, which is much more complex compared to the two-dimensional model. Therefore, we can't use the method of magnetic circuit for the traditional motor in calculation. Because the need for large-scale iterative calculation in the process of optimization, finite element method calculation time is too long, so it is difficult to achieve optimal goal. From the BP neural network prediction results and the prediction error, it can be seen that BP neural network
Fig. 7 Flow chart of genetic algorithm optimization
error range was less than 1%, so the BP neural network can accurately predict the output torque and predict the
Trained BP neural network is applied to find the
approximate actual output torque as output torque.
maximum value of the nonlinear function by genetic
Compared with the finite element analysis, the BP neural
algorithm.
network has the advantage suitable for broader
generation, population size is 20, crossover rate is 0.4,
applications.
and mutation probability is 0.2. The floating point code
Iterative
genetic
algorithm
has
300
used with individual length is 5. IV. PARAMETER OPTIMIZATION OF SPHERICAL MOTOR
In the process of optimizing the parameters of
A. Parameter optimization of genetic algorithm
spherical motor, the results show great difference after
The genetic algorithm was proposed as an optimization algorithm based on the natural selection of the biological world and the genetic mechanism. It uses
the repeated execution of the genetic algorithm
1834
optimization program.
In the 10 times optimization
process, the variation curve of the optimal individual
2017 12th IEEE Conference on Industrial Electronics and Applications (ICIEA)
fitness value is shown in Figure 8. The maximum torque
values to the initial particle position and the particle
is 0.68, and the structural parameters are:
velocity. The BP neural network is used to calculate the
1, = , G = , J = , KHP = , USP = .
particle degree of adaptation to determine the structural parameters and torque values. PSO based on the function of the optimization algorithm flow chart is shown in Figure 9.
Fig. 8 Fitness curve
The degree of adaptation of the fitness curve reflects the trend of torque variation in the evolution process. The degree of adaptation is increased slowly before the 250 generation, after which it is stable at 0.68. In the process of genetic algorithm optimization, degree of adaptation in the whole evolutionary algorithm is more and more tend to high ratio, which indicates that the population is towards good direction of development. B. Particle swarm optimization algorithm
Fig.9 Flow chart for particle swarm optimization algorithm
Particle swarm optimization (PSO) algorithm is a swarm intelligence optimization algorithm in addition to
The particle swarm algorithm is used in BP neural
fish swarm algorithm and ant colony algorithm which is
network training after finding the maximum value of the
an intelligent optimization algorithm for simulating the
nonlinear function and the permanent magnet spherical
foraging behavior of birds.
motor structure parameter optimization. The fitness
PSO algorithm initializes a group of random particles
function is nonlinear function fitting into the BP neural
in the solution space; each particle follows the current
network training. The population particle number is 20,
optimal particle solution space to find the optimal
the dimension of each particle is 5, the number of
solution through the iteration. In the iteration, the
iterations of the algorithm is 300, and the learning factor is:F = , F = .
particle updates its position and velocity by the
In the optimization process with repeated execution of
following:
particle swarm optimization process, the result is a gap,
9 LGN + = 9LGN + FU 3LGN − ; LGN + F U 3JGN − ; JGN ;
but the gap is not large. In the repeated execution of particle swarm optimization program, the results are
; LGN + = ; LGN + 9 LGN + , where F and F are non-negative learning factors, U and U are evenly distributed random numbers between 0
similar. In the 10 times optimization process, the changing curve of the optimal individual fitness value is shown in Figure 10. The maximum torque is 0.734, and
and 1. Particle and velocity initialization give random
2017 12th IEEE Conference on Industrial Electronics and Applications (ICIEA)
1835
the structural parameters are: 1, = ˈ G = ˈ
J = ˈ KHP = ˈand USP = .
Results of finite element analysis and genetic algorithm and particle swarm optimization algorithm for the torque show that the errors are very small. The error of the genetic algorithm is below 5%; the errors of particle
swarm
algorithm
are
below
1%.
The
optimization results of the particle swarm algorithm are far better than those of the genetic algorithm. Therefore, it is better to use the particle swarm optimization algorithm to optimize the structural parameters of the corresponding torque to meet the expected requirements. Fig.10 Fitness curve
V. SUMMARY
The fitness curve reflects the changing trend of the
In this paper, the BP neural network is feasible in
torque in the process of evolution. Before the 150
modeling the torque of the permanent magnet spherical
generation the value of the size of the gap is very large;
motor through the data sample space. The genetic
after the 150 generation the value tends to be fixed.
algorithm and particle swarm optimization are used to
Compared with the genetic algorithm, the convergence
treat nonlinear model of BP neural network to search for
speed in PSO is increased a lot.
the optimal. Through the verification with Ansoft finite
C. Verification
of
Results
of
Two
Optimization
element analysis, it is found that the particle swarm optimization algorithm can find the optimal solution of
Algorithms
the most appropriate, the numerical error of torque is The structural parameters and the torque size obtained from the two optimization algorithms are difference. To verify the accuracy of the results obtained
small, and the optimization results are stable. Therefore the parameters in the spherical motor using particle swarm optimization algorithm is more suitable.
by the algorithms, take three group structural parameters ACKNOWLEDGMENT
obtained to conduct finite element analysis. The verification results are shown in table 2. (Torque
This work is supported by
representation of the torque obtained by optimization
Research Key Program of Anhui Provincial Education
algorithm; T-Torque representation of the torque
Department (KJ2016A021) .
the National Science
obtained by finite element analysis). REFERENCES [1]
TABLE. 2 RESULTS OF STRUCTURAL PARAMETER ANALYSIS DOJ RUL WKP
*$
362
1836
J K HP
USP
7RUTXH
7 7RUTXH
HUURU
1,
G
[2]
[3]
[4]
[5]
Qunjing Wang, Zheng Li, Kun Xia, Weidong Jiang, and Tao Zhao, A novel permanent magnet spherical stepper motor structure parameters and torque characteristics of the calculation and analysis of, Chinese of the CSEE, 2006,10:158-165. Li Zheng, Wang Yongtao, Ge 421, Zhao Guanghui. Research on multi DOF permanent magnet spherical motor advances in [J]. micro motor, 2011,09:66-70. Song Peng, Li Hongfeng, Xia long, to history. The calculation and analysis of numerical [J]. Journal of Tianjin University of permanent magnetic spherical motor torque characteristics, 2009,07:608-613. Li Zheng, Lun Qing Qing, Wang Qunjing, Zhang Lu. Modeling and structure analysis of three degree of freedom motor with permanent magnet rotor [J]. Journal of Harbin Institute of Technology, 2016,03:33-38. R. A. Sosseh and Kok-Meng Lee, "Finite element torque modeling for the design of a spherical motor," Control,
2017 12th IEEE Conference on Industrial Electronics and Applications (ICIEA)
Automation, Robotics and Vision, 2002. ICARCV 2002. 7th International Conference on, 2002, pp. 390-395 vol.1. [6] Liu Ruijiang, Zhang Yewang, Wen Jian, Tang Jian. Study on the design and analysis of orthogonal experiment [J]. experimental technology and management, 2010,09:52-55. [7] Qin Changwei, Wang Qunjing, Chen Quan, Hu Cungang. Application of BP neural network in three level inverter harmonic elimination [J]. power electronics technology, 2015,04:7-9+14. [8] Fan Zhenyu. BP neural network model and learning algorithm of [J]. software development, 2011,07:66-68. [9] Ma Yongjie, Wen Xia. Study on Genetic Algorithm in cloud [J]. Application Research of computers, 2012,04:1201-1206+1210. [10] Kalyanmoy Deb,Nikhil Padhye. Enhancing performance of particle swarm optimization through an algorithmic link with genetic algorithms[J]. Computational Optimization and Applications,2014,573:.
2017 12th IEEE Conference on Industrial Electronics and Applications (ICIEA)
1837
