1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 5, Issue 2, February (2014), pp. 08-16
© IAEME: www.iaeme.com/ijmet.asp
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IJMET
©IAEME
EXTRACTION OF NUMERICAL MODEL THROUGH OPTIMIZATION OF
ANN MODEL FOR MANUALLY DRIVEN BRICK MAKING MACHINE
Mr. P. A. Chandak1,
1
Mr. J. P. Modak2
Asst. Professor, Mechanical Engineering, DMIETR, Wardha, India
Emeritus Professor, Mechanical Engineering, PCE, Nagpur, India
2
ABSTRACT
Considerable research work is carried in development of process units energized by Human
Powered Flywheel Motor (HPFM). The process units tried so far are mostly rural based [12] such as
wood turning, wood strip cutting, electricity generation, low head water lifting, etc. The HPFM
comprises of three subsystems namely (i) HPFM, (ii) Torsionally flexible clutch and (iii) A Process
Unit.
Brick making is one of the processes and experiments were conducted to model the system in
order to enhance its productivity. The experimental data based mathematical model was also
formulated for the system, but the model could not predict the experimental findings accurately and
precisely.
The present research work utilizes artificial neural network (ANN) technique for modelling
of brick making process. The author applies an exhaustive optimization technique which could be
used for almost all applications under ANN modelling and emerges with unmatched result.
The document extracts the mathematical model through optimized ANN model for the
projected process of manufacturing of bricks and compares prediction through it. This technique of
development of mathematical model could be engaged in future for production of controllers based
on linear electronic circuit, microprocessor, etc.
The article compares the predictions of experimental findings through previous empirical and
ANN based mathematical model as well, enlightening the strength of ANN Modelling.
Key Words: MATLAB, ANN Modelling, Mathematical Modelling, ANN parameters, etc.
8

2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 2, February (2014), pp. 086359(Online),
-16, © IAEME
1. INTRODUCTION TO MANUALLY DRIVEN BRICK MAKING MACHINE
riven
1.1. Working of Manually Driven Brick Making Machine
A manually driven Auger-type brick making [1] [2] [9] [10] machine developed by Dr. J. P.
type
[
Modak is as shown in figure. The operator drives the flywheel (17) though chain (25) and a pair of
gears (19, 20). The chain drive is utilized for first stage transmission because the drive is required to
be irreversible. This is achieved with the conventional bicycle drive with a free wheel (21). When the
ieved
flywheel attains sufficient speed, the single jaw clutch (13, 15) is engaged. The clutch drives the
auger screw through a pair of gears (9, 10). The mix fed through hopper (3). A cone (2) connects the
cone
drum (30) to the die (1). The cone eliminates the rotary motion of the mix before it enters the die.
The extracted column is collected in a detachable mould (4). It is lined on the inside by Perspex to
provide least resistance to motion of the column. The column is subsequently demoulded by placing
it upside down on the platform. The mould is moved horizontally, leaving the column on the
platform. About one or two hours after the column is laid on the platform, it becomes stiff enough to
be cut by a cutter to form bricks of standard size.
1. DIE, 2. CONE, 3. HOPPER, 4. AL MOULD, 5. MOULDING STAND, 6. CONVEYOR SCREW,
7. CONVEYER SHAFT, 8. HOPPER, 9. GEAR, 10. PINION, 11. PINION SHAFT, 12. BEARING,
MOVABLE HALF CLUTCH, 14.CLUTCH LEVER, 15.FIXED HALF CLUTCH, 16.FLYWHEEL
SHAFT, 17.FLYWHEEL, 18, BEARING FOR FLYWHEEL, 19. PINION II, 20. GEAR II,
21. FREWHELL, 22. INTERMEDIATE SHAFT, 23. BEARING FOR INTERMEDIATE SHAFT,
24. CRANK GEAR, 25. PINION FOLLOWER CHAIN, 26. DRIVER SEAT, 27. HANDLE,
28. BRACKET, 29. FRAME, 30. CONVEYOR DRUM.
Fig. 1. Manually Driven Brick Making Machine [1]
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3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME
Following process variables were involved in experimentation.
variables is tabulated in Table I.
TABLE I.
Sr
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Symbols and type of
PROCESS VARIABLES WITH THEIR SYMBOLS [1]
Description of variables
Type of variable
Symbol
Dimension
Weight of lime
Weight of sand
Weight of flyash
Weight of water
Outside diameter of screw
Inside diameter of screw
Pitch of Screw
Larger Diameter of Cone
Smaller Diameter of Cone
Length of cone
Length of die
Moment of Inertia of flywheel
Angular velocity of flywheel
Acceleration of due to gravity
Gear ratio
Length of square side of die
Strength of brick
Length of Extruded Brick Column
Time of Extrusion
Maximum length of Extruded Brick
Column Pressure of Extrusion
Critical
Instantaneous Torque on the angular
shaft
Independent
Independent
Independent
Independent
Independent
Independent
Independent
Independent
Independent
Independent
Independent
Independent
Independent
Independent
Independent
Independent
Dependent
Dependent
Dependent
Dependent
Dependent
WL
Ws
Wf
Ww
D1
D2
P
D1
D3
LC
LD
I
W
G
G
S
Sb
Lb
Te
Lbm
Pc
ML-1T-2
ML-1T-2
ML-1T-2
ML-1T-2
L
L
L
L
L
L
L
ML2
T-1
LT-2
L
ML-1T-2
L
T
L
ML-1T-2
Dependent
T
ML-1T-2
1.2. Experimental observations and Empirical Model
The experimental observations [1] were recorded in tabulated form. As the variables involved
were high in number dimensionless pi terms were evaluated. And an empirical model was generated
to predict the experimental findings. The model was as follows [1].
‫ 1ܦ / ܾܮ‬ൌ 0.0043 ሺ‫1ܦ/ܦܮ‬ሻ െ 1.8091 ‫ כ‬ሺ‫݂ܹ݃ܫ/21ܦ‬ሻ 0.139 ‫ כ‬ሺ‫ܩ‬ሻ 0.2766 ‫ כ‬ሺ√ ‫ܹ .݃/1ܦ‬ሻ 1.27
‫ כ‬ሺ‫1ܦ/ܿܮ‬ሻ െ 1.977 ‫ כ‬ሺܲ/ ‫1ܦ‬ሻ1.3075 ‫ כ‬ሺ‫1ܦ / 2ܦ‬ሻ0.8313
……… (1) [2]
The above equation (1) was derived through traditional methods of modelling and found
unsatisfactory in prediction of experimental findings. This limits its further application in
development of controller for the machine system.
Hence it is required to adapt new modelling technique which could give better and
satisfactory results in prediction of experimental and unseen data. The paper utilizes ANN modelling
technique for modelling of machine system and emerges with inimitable solution to above defined
problem.
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4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME
2. MODIFICATIONS IN THE DATABASE
The experimental evidences developed during experimentation were very little in number. As
a result experimental database was found to be insufficient for training and validation of the model
generated though ANN simulation.
In order to develop ANN model, the existing database was modified and improved in
magnitude by maneuvering plots on the basis of present experimental evidences. The intermediate
positions in the plot are positioned and noted [6]. This database generated is as follows.
TABLE II.
Sr.
No.
1
↓
240
↓
550
↓
710
↓
912
↓
1555
MODIFIED DATA [11] [3]
Independent Variables
LD/D1
0.2
↓
0.5
↓
0.5
↓
0.5
↓
0.5
↓
0.5
D12/Ig.Wf
3.7
↓
2.10
↓
3.7
↓
3.7
↓
3.7
↓
3.7
G
4.5
↓
4.5
↓
2.8
↓
4.5
↓
4.5
↓
4.5
√(D1/g).W
9.19
↓
9.19
↓
9.19
↓
2.84
↓
9.19
↓
9.19
Lc/ D1
0.5
↓
0.5
↓
0.5
↓
0.5
↓
0.43
↓
0.5
P/ D1
0.24
↓
0.24
↓
0.24
↓
0.24
↓
0.24
↓
0.24
D2 / D1
0.4
↓
0.4
↓
0.4
↓
0.4
↓
0.4
↓
0.39
Dependent
Variables
Lb / D1
1.174
↓
0.854
↓
1.455
↓
0.203
↓
0.995
↓
1.157
3. ARTIFICIAL NEURAL NEWORK (ANN) PARAMERS INVOLVED IN MODELLING
Important ANN Parameters [4] [5] [6] involved in modeling through artificial neural network
are as follows
•
•
•
•
•
•
•
•
Network Topology
Number of Layers in the network
Number of Neurons
Learning Algorithm
Training Methods
Activation functions/ Transfer Functions used
Type of Networks
Performance function
4. OPTIMIZATION THROUGH DISCIPLINED MODIFICATION OF ANN PARAMETERS
The ANN parameters are sequentially modified as shown in table III and prediction through
each model is examined through their plots.
Every parameter posses its diversified standard values out of which some are chosen and their
effects are observed after and during training. The table III shows the program number and respected
value of each parameter. For each case of a program one parameter is varied and other parameters
were allocated some constant standard value.
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5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME
Program
Number
P1
P2
P3
P4
P5
P6
P8
P9
P10
P11
P12
P13
P14
P15
P16
P17
P18
P19
P20
P21
TABLE III. SEQUENTIAL MODELLING EVALUATION [4]
Types of transfer
Type of
function
Hidden
Training
Performance
layer Size
20
100
200
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
Function
trainlm
trainlm
trainlm
trainb
trainbfg
trainbr
trainlm
trainlm
trainlm
trainlm
trainlm
trainlm
trainlm
trainlm
trainlm
trainlm
trainlm
trainlm
trainlm
trainlm
Function
mse
mse
mse
mse
mse
mse
mae
sse
sse
sse
sse
sse
sse
sse
sse
sse
sse
sse
sse
sse
Layer1
logsig
logsig
logsig
logsig
logsig
logsig
logsig
logsig
tansig
logsig
logsig
logsig
tansig
tansig
logsig
logsig
logsig
logsig
logsig
logsig
Layer2
purelin
purelin
purelin
purelin
purelin
purelin
purelin
purelin
purelin
purelin
hardlim
tansig
logsig
satlin
satlin
poslin
tansig
tansig
tansig
tansig
Type of
Learning
Algorithm
learngd
learngd
learngd
learngd
learngd
learngd
learngd
learngd
learngd
learngd
learngd
learngd
learngd
learngd
learngd
learngd
learncon
learngd
learnh
learnk
It is not possible to include all the graphs generated for each program because of limitations
of the paper. Hence some of them are shown to understand the methodology of optimization.
Fig. 2. Percentage error with 100 Neurons [4]
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6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME
Fig. 3. Percentage error with training Function “trainlm” [4]
Fig. 4. Percentage error with performance Function “sse” [4]
Fig. 5. Percentage error with layer transfer Function “logsig, tansig” [4]
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7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME
Fig. 6. Percentage error with Learn Function “learncon” [4]
5. EXTRACTION OF NUMERICAL MODEL
The optimized network has specific values of ANN parameters assigned to it. The network
architecture [7] (fig7) shows the mathematics involved [5].
Fig. 7. Architecture of Artificial Neural Network for the optimized network.
The numerical model extracted through optimized ANN model is as follows.
ܱ‫ ݐݑ݌ݐݑ‬ൌ ‫݈݊݅݁ݎݑ݌‬ሺ‫ כ ܹܮ‬ሺ‫݃݅ݏ݊ܽݐ‬ሺ‫ ܾ כ ܹܫ‬൅ ‫ܾܫ‬ሻሻ ൅ ܱܾሻ
Where,
LW = Weight Matrix of Output layer of AN
IW = Weight Matrix of Input layer of ANN
Purelin = Function of Output layer of ANN
……….(2)
Ob = Bias Matrix of Output Layer of ANN
Ib = Bias Matrix of Input Layer of ANN
Tansig = Function of input layer of ANN
The above equation (2) [8] gives numerical statement for optimized ANN model for which
the transfer functions are ‘tansig’ and ‘purelin’ assigned to input and output layer respectively. IW
and LW are weight matrices multiplied respectively to input vectors of input layer and output layer.
Transferring the above product matrix through transfer function gives output of each layer. The
output of input layer becomes input for output layer.
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8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME
Fig. 8. Prediction of experimental findings with optimized ANN model
The comparative analysis (fig 7) shows the close curves among the experimental findings and
its predication though the numerical model.
Fig. 9. Percentage error in prediction through optimized ANN model
6. CONVERSATION ON RESULTS
•
•
•
•
•
As the neuron size is amplified, error in prediction of experimental results decreases while
higher neuron size leads to higher training time.
Training styles have great influence on performance of the network. Hence it is to be picked
appropriately.
Performance function has little effect on prediction but wants to observe.
Transfer functions plays key role in output of ANN model. Each layer has to assign a transfer
function independently and their combination results to overall outcome.
The numerical model developed gives very good results in prediction of experimental data.
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9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME
7. CONCLUSION
The paper is illustrating methodology of optimization of ANN model and developing a
numerical model through ANN modelling. This model has great affinity towards development of
controller based on numerical model. Hence this method may be used in many of the application
where researchers are striving to atomize any of the process fully or partially.
8. REFERENCES
JOURNAL PAPERS:
[1]
[2]
[3]
[4]
Modak J P and Askhedkar R D “Hypothesis for the extrusion of lime flash sand brick using a
manually driven Brick making machine”, Bulding Research and Information U.K., V22, N1,
Pp 47-54, 1994
Modak J P and Bapat A R “Manually driven flywheel motor operates wood turning
machine”, Contempory Ergonomics, Proc. Ergonomics Society annual convension
13-16 April, Edinburg, Scotland, Pp 352-357, 1993.
Chandak P A, Modak J P, “Optimization of artificial neural network model for improvement
of artificial intelligence of manually driven brick making machine powered by HPFM”,
International Journal of Chaos, Control Modelling and Simulation, Vol 2, No 3, Sep 2013.
Chandak P A, Lende A R, Modak J P, “A literature review on Methodology & Fundamental
of Development of mathematical model through Simulation of artificial neural network”,
International journal of computer application, Vol 4, issue 1, to be published, 2014.
BOOKS:
[5]
[6]
[7]
[8]
S. N. Shvanandam, “Introduction to Neural Network using Matlab 6.0”, McGraw Hill
publisher.
Stamtios V. Kartaplopoulos , Understanding Neural Networks and Fuzzy Logics, IEEE Pres.
Neural Network Toolbox TM 7 User’s Guide R2010a, Mathworks.com
Rudra Pratap, “Getting Started with Matlab7,” Oxford, First Indian Edition 2006.
THESIS:
[9]
A. R. Bapat, “Experimental Optimization of a manually driven flywheel motor”, M.E. Thesis,
VNIT, Nagpur.
[10] A. R. Bapat, “Experimentation of Generalized experimental model for a manually driven
flywheel motor”, PhD Thesis, VNIT, Nagpur.
[11] P. A. Chandak.”Modelling of Manually driven brick making machine through Artificial
Neural Network”, M. Tech. Thesis, PCE, Nagpur, 2007.
PROCEEDINGS:
[12] Modak J P, “Human powered flywheel motor, Concept, Design, Dynamics and
Applications”, International Federation for the promotion of Mechanism and Machine
Science, IFToMM, Proceedings of World Congress, 1987.
16