IMMURO-20

Modelling of MR Damper with Adaptive Neural Network and Particle

Swarm Optimisation Technique

GIGIH PRIYANDOKOA, MOHD SYAKIRIN RAMLI

B

AFaculty of Mechanical Engineering BFaculty of Electrical Engineering

Universiti Malaysia Pahang

26600 Pekan, Pahang Darul Makmur

MALAYSIA

[email protected], [email protected]

MUSA MAILAH

Department of Applied Mechanics & Design

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia (UTM)

81310 Skudai, Johor Darul Takzim

MALAYSIA

[email protected]

Abstract: - This paper presents a novel method for the non-parametric modelling of a magneto-rheological

(MR) damper using adaptive neural network (NN) that incorporates a particle swarm optimization (PSO)

method. In this approach, the adaptive NN method using adaptive back-propagation (BP) learning algorithm is

used to update the weights in real-time. Initial values of the weights and biases are optimized using PSO in an

off-line manner. The experimental data were presented in time histories of the displacement, velocity and force

parameters measured both for constant and variable current settings and at selected frequency applied to the

damper. The model parameters are determined using a set of experimental measurements corresponding to

different current constant values. It has been shown that the MR damper model response via the proposed NN

approach is in good agreement with the MR damper test rig counterpart.

Key-Words: - Magneto-rheological damper, Adaptive neural network, Particle swarm optimization, Non-

parametric modelling

1 Introduction Magneto-rheological (MR) fluid can be categorised

as a type of smart material that has the unique

ability to change its properties when a magnetic

field is applied. The MR fluid dampers are semi-

active control devices that have received

considerable interest due to their mechanical

simplicity, high dynamic range, low power

requirements, large force capacity and robustness

[1]. Various applications of MR dampers have been

considered, such as in civil structures [2] and semi-

active automotive suspensions [3]. MR fluid

dampers possess inherent nonlinear behaviours and

it is difficult to predict the relationship between

these inputs and outputs.

Identification techniques can be classified into

two categories, namely, the parametric and non-

parametric techniques. The former is based on the

mechanical idealization involving representation by

an arrangement of springs and viscous dashpots.

The most used parametric model for the

identification of an MR damper is the Bouc–Wen

model [4]. This is a semi-empirical relationship in

which 14 parameters are determined for a given

damper through curve fitting of experimental

results. The parametric models are useful for direct

dynamic modelling of the MR dampers, i.e., the

prediction of the damper force for given inputs.

Non-parametric models do not make any

assumptions on the underlying input/output

relationship of the system being modelled.

Consequently, an elevated amount of input/output

data has to be used to identify the system, enabling

the subsequent reliable prediction of the system’s

response to arbitrary inputs within the range of the

training data. The advantage of the non-parametric

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models over the parametric models is that the

former are identified only on the basis of plant

operational data without requiring a detailed

physical understanding of the process or the

knowledge of the material properties, geometry and

other characteristics of the plant [5]. The non-

parametric identification techniques proposed for

MR dampers are finite element formulation [6],

neural network (NN) [7] and neuro-fuzzy modelling

[8]. A NN controller has been trained to model in

some way the dynamics of the plant. In the

aforementioned references grouping can be carried

out: (a) a direct learning architecture [9] in which a

neural network directly copies the plant dynamics

using input-output data taken from the plant, or a

model of it; (b) an indirect learning architecture, in

which a NN mimics the dynamics of the plant only

as a result of being used to control it [10, 11]. Direct

learning schemes are usually implemented off-line,

while indirect learning is carried out on-line with the

plant under the control of a trainee NN.

The NNs have been used to emulate the dynamic

behaviours of an MR damper. However, the

selection of network structures and training of

samples are often complicated tasks but are essential

for setting up an accurate NN model. Moreover, the

training speed is normally long due to slow

convergence [12]. A main limitation of NN is that

the results they deliver are at times difficult to

interpret physically. Billings et al. [13]

demonstrated that NN could be used successfully

for the identification and control of non-linear

dynamical systems. The learning algorithm that is

used most frequently is the back-propagation (BP)

method. Although the BP training has proved to be

efficient in many applications, its convergence tends

to be slow and yields to suboptimal solutions. To

counter this problem, a particle swarm optimization

(PSO) technique is proposed and incorporated into

the NN system. Generally, the PSO is characterized

as a simple heuristic of a well balanced mechanism

with flexibility to enhance and adapt to both global

and local exploration abilities. It is a stochastic

search technique with reduced memory requirement,

computationally effective and easier to implement

[14-15].

The paper is organized as follows: Section 2

describes the MR damper dynamic characteristics

while Section 3 presents the experimental

conditions. Section 4 highlights the application of

the NN model. The PSO model is presented in

Section 5 and the PSO optimised adaptive NN is

introduced in Section 6. The results of the

simulation study are subsequently discussed and

analysed in Section 7. Finally, the paper is

concluded in Section 8.

2 MR Damper Dynamic

Characteristics The development of MR damper model is based on

the original equipment (OE) shock absorber used in

the passenger vehicle. In this study, an original

shock absorber from Proton Waja model has been

chosen as the benchmark in developing the MR

damper model in terms of geometrical design and

performance. Table 1 shows the parameters of the

original damper that were considered in this model.

Fig. 1 depicts a photo of the original Proton Waja’s

damper.

Table 1. Proton Waja’s original damper measurement

Particulars Measurement

Stroke

Piston rod length

Stroke of stopper (from end valve)

Inner tube thickness

Inner tube diameter

Inner tube height

Gap between inner tube and outer tube

150 mm (± 75 mm)

350 mm

65 mm

2 mm

35 mm

302 mm

5 mm

Fig. 1. Proton Waja’s original damper

An MR damper typically consists of a piston rod,

electromagnet, accumulator, bearing, seal, and

damper cylinder filled with MR fluid. The magnetic

field generated by the electromagnet changes the

characteristics of the MR fluid, which consists of

small magnetic particles in non-conducting a fluid

base. The development and modelling of MR

damper was performed by considering the geometric

and magnetic circuit design. In order to assist the

development of the MR damper, an Excel

spreadsheet shown in Fig. 2 was used [16].


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Fig. 2. MR damper parameter design spreadsheet

3 Experimental Conditions The selected experimental conditions applied to the

MR damper test rig as shown in Fig. 3 are as

follows: frequency = 0.15 Hz, amplitude = 2 cm and

given current according to the following increments:

0.0, 0.5, 1.0, 1.5, 2.0 A. Figs. 4-8 show the various

responses of the MR damper under the following

conditions: frequency is 0.15 Hz, with amplitude 2

cm and current 0.0 A. Fig. 4 shows the displacement

response depicting almost a true sinusoidal

characteristic for the given conditions. Fig. 5 shows

the velocity response in which the trend is opposite

to the displacement response with peak velocities of

±0.15 m/s within the same period. Fig. 6 shows the

force response. Again, it can be seen that the trend

follows that of the velocity curve with peak forces at

±140 N. For all the current input, the response

related to the displacement vs force and velocity vs

force characteristics are illustrated in Figs. 7 and 8,

respectively. All the fundamental response curves in

Figs. 4-8 shall serve as the basis for the

implementation and verification of the non-

parametric modelling process of the experimental

MR damper system via the proposed intelligent

approach.

. Fig. 3. A MR damper test rig

0 0.2 0.4 0.6 0.8 1-0.03

-0.02

-0.01

0

0.01

0.02

0.03

time (s)

displacement (m)

Fig. 4. Displacement response of the MR damper

0 0.2 0.4 0.6 0.8 1-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

time (s)

velocity (m/s)

Fig. 5. Velocity response of the MR damper

0 0.2 0.4 0.6 0.8 1-150

-100

-50

0

50

100

150

time (s)

force (N)

Fig. 6. Force response of the MR damper

-0.03 -0.02 -0.01 0 0.01 0.02 0.03-150

-100

-50

0

50

100

150

dispacement (m)

force (N)

Fig. 7. Displacement-force curve of the MR damper

-0.2 -0.1 0 0.1 0.2-150

-100

-50

0

50

100

150

velocity (m/s)

force (N)

Fig. 8. Velocity-force curve of the MR damper.

A major drawback of the MR damper is its

nonlinear force-displacement and hysteretic force-

velocity response. The test displacement of MR

damper, a sinusoidal wave at 0.15 Hz and 2 cm

magnitude is shown in Fig. 4, the velocity response

is depicted in Fig. 5, and the force produced by MR

damper as presented in Fig. 6 is applied in this

experiment, the force –displacement curve as

resultant damper force at a magnetization current of

0.0 A is shown in Fig. 7, that the non-linearity

between displacement and force is evident. Fig. 8


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depicts the hysteresis relating the damper force

versus velocity. As can be seen from the figures, the

damper hysteresis curves exhibit plump loops, the

damping is strong, the instability of MR fluid makes

less smooth curve, so the performance of liquid on

the stability of the entire damper is also very

important. From the force-velocity diagram it can be

seen that the damper biggest damping force

increases with the increasing speed. The MR

damper exhibits an almost viscous property when

zero control current is applied (passive property), as

evident from the near-elliptical force–displacement

curve and near-linear force–velocity curve with

relatively small hysteresis as shown in Figs. 7 and 8.

The force-velocity characteristics of the MR

dampers can be represented as the symmetric bi-

nonlinear curves with hysteresis at lower velocities,

followed by linearly increasing force at higher

velocities. A force-limiting behaviour is also evident

during transition between low and high velocity

responses. The damping force can therefore be

expressed as a function of the piston velocity and

control current, with appropriate consideration of

the force-limiting behaviour.

4. Neural Network A neural network (NN) is basically a model

structure and contains an algorithm for fitting the

model to some given data. The NN is placed in

parallel with the plant and the error between the

output of the system and the network output, is used

as the real time training signal. NN have a potential

for intelligent control systems because they can

learn and adapt, approximate nonlinear functions,

suited for parallel and distributed processing, and

they naturally model multivariable systems. The

structure of the multilayer NN used in the study

consists of the input, output and hidden layers. Fig.

11 shows a typical multilayer architecture of the NN

model. The learning algorithm is an optimization

method capable of finding the weight coefficients

and learning rate for a given NN and a training set.

This algorithm is based on minimizing the error of

the NN output compared to the required output. The

required function is specified by the training set.

The error of network (e) relative to the training set is

defined as the sum of the partial errors of network ek

relative to the individual training patterns and

depends on network configuration w [17]:

( )∑ ∑= =

−==p

k

p

k

kkk dOee

1 1

2

2

1 (1)

where p is number of available patterns, ek is

partial network error, Ok is output of neural

networks, dk is teach data or desired output.

Updating real time the weights of each layer using a

typical BP method for time t > 0 is calculated in

order to minimize error as follows [17]:

( ))2()1()1(

)1(

)1()1()(

−−−+∂−∂

=−∆

−∆+−=

ttte

t

ttt

jkjk

jk

jk

jkjkjk

ωωβω

αω

ωωω (2)

where 0 < α < 1 is the learning rate, β is the

momentum. The speed of training is dependent on

the set constant α. If a low value is chosen, the

network weights react very slowly. On the contrary,

a high value may cause the algorithm fail to

converge. Therefore, it is usual that the parameter α

is set experimentally via a trial-and-error technique

within the bounded range.

Fig. 11. An architecture of the NN

5. Particle Swarm Optimization The particle swarm optimization (PSO) idea was

originally introduced by Kennedy and Eberhart [14]

in 1995 as a technique through individual

improvement plus population cooperation and

competition, which is based on the simulation of

simplified social model, such as bird flocking, fish

schooling and the swarm theory. Its mechanism

enhances and adapts to the global and local

exploration. Some of the key advantages are that

this method does not need the calculation of

derivatives, that the knowledge of good solutions is

retained by all particles and these particles in the

swarm share information between them. PSO is less

sensitive to the nature of the objective function, can

be used for stochastic objective functions and can

easily escape from local minima. The basic PSO

algorithm consists of three steps, namely, (a)

generating particles’ positions and velocities, (b)

velocity update and (c) position update. Here, a

particle refers to a point in the design space that


ISBN: 978-1-61804-173-9 127

changes its position from one move (iteration) to

another based on velocity updates. First, the

positions, ikx , and velocities, i

kv , of the initial

swarm of particles are randomly generated using

upper and lower bounds on the design variables

values, minx and maxx , as expressed in (3) and (4).

The positions and velocities are given in a vector

format with the superscript and subscript denoting

the ith particle at time k. In (3) and (4), rand is a

uniformly distributed random variable that can take

any value between 0 and 1.

)( minmaxmin0 xxrandxx i −+= (3)

t

xxrandxv i

∆

−+==

)(

time

position minmaxmin0 (4)

The second step is to update the velocities of all

particles at time k+1 using the particles objective or

fitness values which are functions of the particles

current positions in the design space at time k. The

fitness function value of a particle determines which

particle has the best global value in the current

swarm, gkp , and also determines the best position

pbest of each particle over time, i.e. in current and

all previous group moves gbest. The velocity update

formula uses these two pieces of information for

each particle in the swarm along with the effect of

current motion, ikv , to provide a search direction,

ikv 1+ , for the next iteration. The velocity update

formula includes some random parameters

represented by the uniformly distributed variables,

rand() to ensure good coverage of the design space

and avoid entrapment in local minima. The three

values that effect the new search direction, namely,

current motion, particle own memory, and swarm

influence are incorporated via a summation

approach with three weight factors, i.e., the inertia

factor, w, self confidence factor, c1 and swarm

confidence factor, c2. This can be expressed as:

( ) ( )t

xprandc

t

xprandcwvv

ik

gk

ik

iik

ik ∆

−+

∆

−+=+ 211 (5)

The position of each particle is updated using its

velocity vector given by:

tvxx ik

ik

ik ∆+= ++ 11 (6)

Clerc and Kennedy [15] proposed a constriction

factor in order to prevent explosion, to ensure

convergence and to eliminate the parameter that

restricts the velocities of the particles. The velocities

of particles are updated, now, using the following

equation:

( ) ( )

∆

−+

∆

−+=+

t

xprandc

t

xprandcvv

ik

gk

ik

iik

ik 211 χ

(7)

where

4,

42

221

2

>+=−−−

= ccc

ccc

χ

(8)

6. PSO Optimised Adaptive Neural

Network Adaptive NN approaches to the modelling of

processes and systems share with the pure NN

approach the distinct advantage of performing the

model-building and parameter-tuning phases

automatically on the basis of the incoming data,

without any mathematical description of the process

or system to be modelled. The training algorithm for

the proposed NN in this paper is BP with PSO. It is

usual that the NN parameters related to the weights,

biases and learning rates (thresholds) of the BP

algorithm are randomly initialized. Moreover, the

parameters of the NN were determined by using

PSO method in an off-line manner after a number of

trial runs. The pseudo code of the training procedure

is as follows:

Begin PSO

For each particle

Initialize particle (v0 and p0)

End

Do For each particle

Calculate fitness value

If fitness better than pbest update pbest

End

Determine gbest from all particles

For each particle

Update velocity to formula (16)

Update position to formula (15)

End

While maximum iterations or minimum error

criteria is not attained

Begin Neural Network

Initialize weights (wi) and learning rateθ

Do

Input xi(t) with desired output d(t)

Calculate error to formula (1)

Adapt weights to formula (2)

While not done


ISBN: 978-1-61804-173-9 128

7. Results and Discussion This section presents the application of evolving

adaptive NN to emulate the MR damper. The

development of the evolving adaptive NN for

modelling an MR damper is outlined as follows: (a)

collect sample high-quality training and testing data

as produced by the given MR damper model and (b)

validate the new model through comparison of its

output to the output of the given MR damper model.

The results based on the experimental test data and

that of the NN approach for the conditions of MR

damper at frequency 0.15 Hz, amplitude is 2 cm and

current is 0.0 A are shown in Figs. 12-13 while the

overall results are depicted in Figs. 14-15. As can be

seen from Figs. 12-13, the dynamic curves of the

MR damper derived from NN model are very close

to the experimental results, thereby verifies the

effectiveness of the proposed NN method. It is

obvious that the BP network model can accurately

capture or describe the dynamic characteristics of

the MR damper.

0 0.2 0.4 0.6 0.8 1-0.03

-0.02

-0.01

0

0.01

0.02

0.03

time (s)

displacement (m)

NN

test data

Fig. 12. The MR damper displacement curves of the NN

model output and test data

0 0.2 0.4 0.6 0.8 1-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

time (s)

velocity (m/s)

NN

test data

Fig. 13. The MR damper velocity curves of the NN

model output and test data

-0.03 -0.02 -0.01 0 0.01 0.02 0.03-1500

-1000

-500

0

500

1000

1500

displacement (m)

force (N)

2 A

1.5 A

1 A

0.5 A

0 A

Fig. 14. The MR damper force-displacement curves of

the NN model output (red dotted line) and test results

(solid line) for five constant current levels

-0.2 -0.1 0 0.1 0.2-1500

-1000

-500

0

500

1000

1500

velocity (m/s)

force (N)

0.5 A

0 A

1 A

1.5 A

2 V

Fig. 15. The MR damper force-velocity curves of the NN

model output (red dotted line) and test results (solid line)

for five constant current levels

8 Conclusion An alternative approach to modelling a MR damper

using NN with PSO and BP training methods have

been presented and successfully applied. By using

the experimental MR damper test rig data, the

nonlinear characteristics of the damper can be

captured without having to resort to its dynamic

model (equations of motion). The NN model

responses and the actual test rig outputs are almost

identical which implies that the NN model has

captured the real MR damper characteristics.

Further rigorous investigation should be carried out

to evaluate the proposed model performance

compared with other methods.

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