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Parameter Optimization Design Model of Permanent Magnet
Retarder Based on Artificial Neural Network Algorithm

Fengyan Yi*a, Ren Heb, Zhenjun Luoc, d
a Shandong Jiaotong University, Jinan, 250023, China,
b Jiangsu University, Zhenjiang, 212013, China,
c Wuhan University of Technology, Wuhan, 430067, China,
d Hubei Institute for Food and Drug Control, Wuhan, Hubei, 430064, China.
yi_fengyan@163.com

Permanent magnet retarder wins high favor of large cars with easy installation, low power consumption and
small size. But this retarder is easily affected by outside conditions or road conditions, so that the temperature
field, the magnetic field, the relationship between design parameters will be changed, and the brake torque will
further be affected. Through research we found that the parameter design of permanent magnet retarder is the
most important point. An optimized parameter enables the brake torque to come into full play and to adjust its
external environment. The paper presents the parameter optimization design model of permanent magnet
type retarder based on neural network algorithm. In the model, the design parameters of permanent magnet
retarder is taken as input values, all influencing factors as the hidden layer of neural network, and the weight
coefficient and threshold values of various scene parameters are constantly adjusted to conform to meet
practical needs. In addition, according to the results of the output layer, the values of the design parameters
are constantly adjusted to reach the ultimate goal of optimizing the design parameters. The comparison of
experimental analysis shows that with practicability and reliability, the model can provide a more intelligent,
simpler method for the design of permanent magnet retarder.

1. Research background

The large automobile of brake apparatus is an important guarantee for safe driving. In the case of constant
speed downhill or high speed slow braking, the large automobile needs to keep the speed below 30 km/h. In
general, the automobile needs to use the brake system to slow down the speed. There is a marked defect in
the brake: frequent or prolonged use of easy to cause brake drum and friction plate heat, leading to a sharp
drop in brake torque, brake failure, thus causing traffic accidents. This phenomenon is more prominent in the
long running on the slope of the large motor vehicles in the road. If we want to fundamentally solve these
problems, the economic practical approach is to install auxiliary brake device for reducing the speed of the
vehicle, so that it can reach the standard of safe driving.
Generally speaking, the design parameters of permanent magnet retarder are empirical method, trial method,
and physical structure analysis method. Although the optimized design parameters can be found when under
certain conditions, but it takes a long time or the efficiency is slow . And if the condition changes, there is a
process of re searching for the optimization parameters. Therefore, a lot of studies tend to establish the model
for the design of structure parameters of permanent magnet retarder. These models can be more
comprehensive, more specific and more optimized. For example: three dimensional model of brake torque, the
temperature field of the motor brush and so on. This article is the use of artificia l intelligence algorithm in the
neural network, combined with the permanent magnet retarder of various factors, and then put forward the
parameter optimization design model. The feature of the model is that it has the function of intelligent analysis,
and it can have a feedback mechanism. Through the mechanism to adjust the design parameters in order to
achieve the purpose of fast find the optimization value.

CHEMICAL ENGINEERING TRANSACTIONS

VOL. 46, 2015

A publication of

The Italian Association
of Chemical Engineering
Online at www.aidic.it/cet

Guest Editors: Peiyu Ren, Yancang Li, Huiping Song
Copyright © 2015, AIDIC Servizi S.r.l.,

ISBN 978-88-95608-37-2; ISSN 2283-9216

DOI: 10.3303/CET1546039

Please cite this article as: Yi F.Y., He R., Luo Z.J., 2015, Parameter optimization design model of permanent magnet retarder based on
artificial neural network algorithm, Chemical Engineering Transactions, 46, 229-234 DOI:10.3303/CET1546039

229

2. Structure influence factor analysis and parameter

2.1 The principle of application and the structure for permanent magnet retarder
Permanent magnet retarder has the advantages of small volume, low energy consumption, convenient
installation, so that the structure is different from other kinds of retarder. It mainly consists of three parts: the
mechanical device, the control device and the auxiliary device. They are the basic parts: rotor drum, stator,
permanent magnet, magnet, magnetic holder, movable iron bracket and so on. As actual picture shown in
Figure 1 below:

Figure 1: The permanent magnet retarder

Figure 2: Structure diagram of permanent magnet retarder

The application principle of permanent magnet retarder is to enter the working state through a braking device.
After entering the state, the two column poles are alternating with each other, and the magnetic force of the
permanent magnet is generated by the reverse. After the magnetic pole piece of the stator in the rotor drum to
form a loop, the rotor drums cutting lines to form a vortex. The kinetic energy of the car is converted into eddy
current loss, which is dissipated by heat. And thus it generates the brake or slow speed on the drive shaft. The
whole process is the converting kinetic energy into heat energy. The concrete structure is shown in Figure 2.

2.2 The parameters and influence factors of the brake torque
The key design of permanent magnet retarder is the selection of the parameters. The traditional design idea is
to set up the objective function or model, and study the relationship between the design parameters and the
objective function or model. In actually, permanent magnet retarder under the influence of many factors,
objective function or model generally do not have self-learning or modulate the function that the design
parameters can only meet the needs of a situation, but for a condition may is not suitable. In other words,
there is no effect on the actual operating conditions. This section is analysis of permanent magnet retarder
with the various influencing factors, in order to get the relationship between influence factors and parameters.
Brake torque is an important index to measure the parameters of the design parameters. All parameters are
designed with the aim of maximizing brake torque. Permanent magnet retarder can optimize the design
parameters mainly have the following several kinds: the radius rotor r , circumference width w , the air gap
 , axial length L , permanent magnet height pmh and so on. The effects of these parameters on the brake

torque are both positive and negative, some of the impact of large, and some of the impact of small. So it is
necessary to analyze these factors separately.
1) The relationship of electromagnetic field and structural parameters
The expression of the brake torque is derived by the equivalent magnetic circuit method, as shown in the
formula (1), W representation method as formula (2):

230

20
3

)
3

2
(

2 hwrK

hHhwLr
T

pmc









(1)

60/2 nw  (2)

innin
xy   (3)

The influence of the design parameters of the rotor drum radius, circumference width, the air gap, axial length
and permanent magnet height on the brake torque is derived by the above formula. According to many
experiments and analysis, the relationship between these parameters and brake torque is approximately
linear. Thus, the formula (3) can be used to express the relationship between them.
So that r , w ,  , L , pmh can be set to a set of input values ),,,,( 54321 xxxxx , i is the corresponding

weight adjustment factor. The formula of the five input array are related to the weight coefficient, can be
expressed as ),,,,(

54321
 . The weight value coefficient of the radius rotor is positive. The weight value

coefficient of circumference width is negative. The weight value coefficient of air gap width is negative. The
weight value coefficient of axial length is positive. The weight value coefficient of the permanent magnet height
is positive. Through the learning process of neural network is to adjust

i
 and value

i
 . So these two values

can be infinitely similar to the practical application.
2) The relationship of temperature field and structural parameters
Permanent magnet retarder with the increase of temperature, its performance tends to decline. When the
kinetic energy of the retarder is converted to heat dissipating. If retarder temperature rising, brake torque
decreased. Therefore, the rotor temperature influence on the performance of permanent magnet retarder
greatly. Through the research and the experiment, we find that the heat dissipation structure of the rotor can
effectively improve the heat flux of the rotor; reduction of rotor temperature rise and temperature rise rate;
reduce the temperature effect on the permanent magnet demagnetization; to improve the permanent magnet
retarder braking stability and service life influence. The heat capacity expression of the rotor is shown in the
formula (4):

 rLhcmCQ 2 (4)

g
B

Z
R

AA
B

)421)((1





(5)

From the formula, the main parameters influenced by the temperature of the permanent magnet retarder are:
the radius rotor r, the air gap  , axial length L. The relationship of the parameters can be represented by the
formula (3). The array of hidden layers is ),,,(

876
 , According to the formula (4) and the effect of brake

torque to derive corresponding weights and threshold.
3) The relationship of magnetic flux leakage and structural parameters
When the permanent magnet retarder work, it produced the magnetic lines of force that can not be completely
closed the magnet holding frame, there are still a small amount of magnetic flux through the rotor drum,
caused by brake can not be completely removed, thereby affecting the brake torque and braking effect. The
magnetic flux leakage effect is mainly related to the magnetic induction intensity of the air gap. A formula (5) is
the magnetic induction intensity of air gap. It can be known that the magnetic leakage phenomenon is mainly
related to the rotor and air gap. Hidden layer array is ),(

109
 . Similarly, according to the formula (5) derived

weights and threshold.
4) Other factors
Other factors influencing the performance of permanent magnet retarder are analysis of coupling effect of
multi physical field, control mode, reasonable distribution of joint brake torque and so on. All of them have a
certain effect on the design of structure parameters. They can be represented by a hidden array of neurons.

3. Parameters optimization model and establishment process

3.1 Artificial neural network algorithm
Artificial neural network is a kind of intelligent arithmetic model which imitates the brain neurons of animals. It
has self - learning, self - training, fuzzy processing, can consider many factors and conditions. The neural
network, which is formed by the hierarchical form, is divided into at least three layers, which are input layer,

231

hidden layer and output layer. BP neural network and RBF neural network are typical application. BP artificial
neural network is selected in this paper.

3.2 Design principle based on neural network algorithm
According the section 2.1 and 2.2, we can get the brake torque of permanent magnet retarder is affected by
many factors. These factors also affect each other. Therefore, the permanent magnet retarder design is a
multi-parameter optimization design process. The ultimate goal is to improve the overall performance of
permanent magnet retarder, which is to find the global optimal solution. The figure as shown below:

Figure 3: Permanent magnet retarder optimization design process

The model is divided into four parts. Its specific process as following:
(1) The first part is the design of the input layer. In this paper, we design five parameters, and give the range
of the selected parameters. The requirement of this part is that the number of neurons in the input layer is
consistent with the number of the designed parameters.
(2) The second part is the design of the hidden layer. W e select a single hidden layer. The hidden layer of this
part is designed that relationship between specific parameters and weights. The relationship between the
weight and the corresponding threshold continuously adjusted to the height of linear fitting, according the
section 2.2. And left some place for expansion, so as to avoid other of the factors not considered.
(3) The third part is the design of the output layer. The parameters of each input layer correspond to the result
of an output layer, the output layer is in the range of [-1, 1]. The value of the output layer is close to 0, proving
that the design value is in accordance with the requirements. If the value of the output layer is [ -1, 0], proving
that the design value is too small, vice versa.
(4) The fourth part is the learning process of neural network, continuing to build a new array of input layers to
repeatedly test. A set of parameters, which is calculated as a set of 0 parameters, is used as the optimal value
for the input layer. This can be determined by the optimization results of the model.

4. Experiment and simulation

The experiment of this paper is to verify the effect of the model, which is used to explain the practicability of
the algorithm. Through the actual test value and the simulation of ANSYS software, it is proved that the design
of the model is feasible. We use formula calculation to determine the hidden layer neuron's threshold and
weights, and then define the input layer of five design parameters range. The range as follow: Radius rotor
(170-240 mm), Circumference with (40-60 mm), Air gap (0.5-2.0 mm), Axial length (60-100 mm), Permanent
magnet height (5-20 mm).
In the first experiment, the minimum value of each parameter is selected, and the next experiment, they
results are fed back to the input layer, to determine whether the input val ue should be increased or reduced.
After the weight and range adjustment or selection, then the neural network model is calculated, so that the
optimal value has been obtained. In this paper, the experimental iteration numbers are about 90, and the
experimental evaluation performance index is the maximum brake torque. In addition, we choose the optimal
design method based on genetic algorithm (the algorithm is also to maximize the retarder braking torque as
the goal). Comparison of the two algorithms can highlight the superiority. The experimental graph obtained by
the simulation software is shown in Figure 4:

232

Figure 4: Permanent magnet retader parameter optimization experiment

In this diagram, we can see artificial neural network algorithm at about 70 times to reach the maximum, we get
the maximum brake torque, genetic algorithm at about 90 times to reach the maximum. In this place, the
design parameters of permanent magnet retarder are the best optimal value. The optimal design parameters
from two algorithms are compared with the expected values of the physics experiment as shown in Table 1:

Table 1: Optimized results and comparison

Content 1x mm 2x mm 3
x

mm 4
x mm 5

x
mm Brake torque (N•m)

Expected value 206 44 0.9 91 18 689
Optimized value-1 (blue) 204 45 0.8 86 17 672
Optimized value-2 (red) 205 45 0.8 87 18 674

The results in Table 1, we conclusion that artificial neural network algorithm retarder optimization model can
quickly find and expected value approximation to a set of design parameters. Their brake torque is almost
similar. This shows that the model is more practical and the structural parameters are optimized. Further to
verify the scientific nature of the model, the influence of various permanent magnet retarder design factors can
provide a reliable fuzzy algorithm model.

5. Conclusions and prospect

In this paper, analysis of the structural principle of permanent magnet type of retarder, Artificial neural network
algorithm is selected, all effects of permanent magnet retarder factors as hidden layer regulating function,
practical formulas for the ultimate goal constructed based on artificial neural network algorithm of pe rmanent
magnet type of retarder structural parameters optimization design model. In this model, the experimental
results are obtained by using the simulation software and the actual physical calculation formula. The end of
the experiment shows that the value of the simulation experiment is similar to the expected value, and the
brake torque is small, which proves that the model is practical, scientific and reliable.
There is still a gap between the optimal value and the expected value of the actual calculat ion. This shows
that the design parameters of permanent magnet retarder are also affected by other factors. Therefore, in the
next step of research experiments and need to more carefully and accurately research and analysis of
permanent magnet type of retarder design factors. When we find these factors and give the corresponding
weights and thresholds, it makes the design factors to consider more comprehensive, more expectations.

233

Acknowledgements

This work is supported by the Key Project of Shandong Provincial Natural Science Foundation, China (NO:
ZR2013EEM012), Hubei Provincial Nature Foundation, China (NO: 2014CFC1021).

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