International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 12, December 2013
ISSN 2319 - 4847
Comparative Analysis amongst Prediction of
Field Findings through Empirical Model and
Optimized Neural Network Mathematical
Model for Human Powered Flywheel Motor
Arati R. Lende1 and J. P. Modak2
1
Ex Assistant. Professor, DMIETR, Sawnagi (M), Wardha, MH, India
2
Emeritus Professor and Dean (R&D), PCE, Nagpur, MH, India
Abstract
Neural Network is one of the most emerging tools in fitting function, future forecasting, pattern recognition, etc. This article
signifies the effective methodology of Neural Network modeling for prediction of field findings.
J. P. Modak and their associates had already carried out lots of investigations over development of applications utilizing Human
Powered Flywheel Motor as an energy source. The applications tried so far are mostly rural based such as brick making, low head
water lifting, wood turning, wood strip cutting, electricity generation, etc. The productivity of the above mentioned applications
had great affection towards rider thereby affecting quality and quality of production.
The paper evaluates optimum artificial neural network (ANN) parameters for prediction of experimental findings accurately
through sequential variation of each ANN parameter. The most favorable values of each parameter are selected and a
mathematical model is extracted in the course of it.
This document also compares the prediction amongst ANN based mathematical model and traditionally generated empirical
model.
Keywords: Artificial Neural Network (ANN), mathematical model, empirical model.
1. INTRODUCTION TO HUMAN POWERED FLYWHEEL MOTOR (HPFM)
1.1 Working of Human Powered Flywheel Motor Energized Process Unit
This machine system comprises three sub systems namely (i) HPFM [11] (ii) Torsionally Flexible Clutch (TFC) (iii) A
Process Unit. The process units tried so far are mostly rural based such as brick making machine [1] [3](both rectangular
and keyed cross sectioned), Low head water lifting, Wood turning, Wood strips cutting, electricity generation etc.
The Figure 1 shows the schematic arrangement of pedal operated flywheel motor which comprises of following elements
Figure 1 Schematics of Human Powered Flywheel Motor
R= Rider
M = mechanism (01-OA-B-02-01)
BSC = Big Sprocket Chain Drive
SSC = Small Sprocket Chain Drive
GSR = Gear of Speed Rise
PSR = Pinion of Speed Rise
FW= Flywheel
CH = Chain
CS = Counter Shaft
FS = Flywheel Shaft
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Volume 2, Issue 12, December 2013
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1.2 Study of already available experimental data
The various parameters involved [11] in the experimentation are
Table 1: Independent Variables and their symbols
Mechanical Efficiency
Symbol
I
R
T
ME
5
Gear Ratio
G
6
Angular Velocity of Flywheel
ω
Sr. No.
1
2
3
Independent Variable
Moment of Inertia of Flywheel
Input by the Rider
Time
4
Table 2: Range of Variation of Independent parameter i.e. Rider(R)
Range of age
20-25Years
Height
Weight
Blood Pressure
155-170cm
40-55
140-70
Pulse rate
68-80/min.
The observations recorded during the experimentation are as below
Table 3: Experimental observations
Independent Variables
1
Dependent variable
Log (I/RT2)
Log (ME)
Log (G)
Log (ω T)
-7.4270
0.00
0.3010
3.6305
↓
↓
↓
↓
↓
23
-7.1792
0.0662
0.0010
3.5570
↓
↓
↓
↓
↓
50
-7.2694
0.0600
0.0010
3.5004
↓
↓
↓
↓
↓
82
-6.1549
0
0.301
3.0767
↓
↓
↓
↓
↓
141
-5.9717
0
0.301
2.8587
↓
↓
↓
↓
↓
200
-7.2694
0
0.0569
3.4107
1.3 Empirical Model
The experimental Independent variables were reduced by evaluating dimensionless pi terms by Buckingham pi theorem
and a mathematical equation was generated by traditional method to predict the experimental findings. The equation [12]
is as shown.
ω T = 1.288 ( I/RT2)-0.46 (ME)-0.87 (G)0.40
2. EXECUTION OF ARTIFICIAL NEURAL NETWORK MODELING AND ITS OPTIMIZATION
Modeling a system through ANN simulation [9] involves use of ANN parameters appropriately. A topology is nothing but
the complete architecture of network formed through the use of ANN parameters. The ANN parameters should be varied
systematically in an attempt to identify best topology for a specified problem. The number of layers was restricted to two
as the variables involved were high in number. A table for evaluation of modeling technique is formed [5] as below. The
shaded column indicates the variation of that particular parameter and shaded row shows the slandered value of that
parameter.
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Table 4: Sequence of variation of ANN Parameters
Training
Number
Hidden
layer Size
Type of
Training
Function
Performance
Function
Layer1
Layer2
Type of
Learning
Algorithm
T1
20
trainlm
mse
tansig
purelin
learngd
T2
50
trainlm
mse
tansig
purelin
learngd
T3
100
trainlm
mse
tansig
purelin
learngd
T4
150
trainlm
mse
tansig
purelin
learngd
T5
250
trainlm
mse
tansig
purelin
learngd
T6
300
trainlm
mse
tansig
purelin
learngd
T7
500
trainlm
mse
tansig
purelin
learngd
T8
600
trainlm
mse
tansig
purelin
learngd
T9
700
trainlm
mse
tansig
purelin
learngd
T10
500
trainb
mse
tansig
purelin
learngd
T11
500
trainbfg
mse
tansig
purelin
learngd
T12
500
trainlm
mse
tansig
purelin
learngd
T13
500
trainbr
mse
tansig
purelin
learngd
T14
500
traingdm
mse
tansig
purelin
learngd
T15
500
traingb
mse
tansig
purelin
learngd
T16
500
traincgf
mse
tansig
purelin
learngd
T17
500
traincgp
mse
tansig
purelin
learngd
T18
500
trainlm
mse
tansig
purelin
learngd
T19
500
trainlm
mae
tansig
purelin
learngd
T20
500
trainlm
sse
tansig
purelin
learngd
T21
500
trainlm
mae
tansig
purelin
learngd
T22
500
trainlm
mae
logsig
purelin
learngd
T23
500
trainlm
mae
tansig
logsig
learngd
T24
500
trainlm
mae
tansig
Purelin
Learncon
T25
500
trainlm
mae
tansig
Purelin
Learngd
T26
500
trainlm
mae
tansig
Purelin
Learnh
T27
500
trainlm
mae
tansig
Purelin
Learnk
Types of transfer function
3. VARIATION IN PREDICTION OF ANN MODEL WITH VARIATION OF ANN PARAMETERS
The graphs for each program are generated which illustrate the effect of each variation on prediction of model. Skipping
few of the bad predictions all other graphs are shown as below The percentage error in prediction is also plotted to
compare and select the best of the topology amongst these topologies.
Figure 2 Predictions with 20 Neurons
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Figure 3 Percentage errors in predication with 20 Neurons
Figure 4 Predictions with 50 Neurons
Figure 5 Percentage errors in predication with 50 Neurons
Figure 6 Predictions with 20 Neurons
Figure 7 Percentage errors in predication with 150 Neurons
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Figure 8 Predictions with 300 Neurons
Figure 9 Percentage errors in predication with 300 Neurons
Figure 9 Predictions with 500 Neurons
Figure 10 Percentage errors in predication with 500 Neurons
Figure 18 Predictions with 600 Neurons
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Figure 11 Percentage errors in predication with 600 Neurons
Figure 12 Predictions with 700 Neurons
Figure 13 Percentage errors in predication with 700 Neurons
Figure 14 Predictions with training Function “trainlm”
Figure 15 Percentage errors in predication with training Function “trainlm”
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Figure 16 Predictions with training Function “trainbr”
Figure 17 Percentage errors in predication with training Function “trainbr”
Figure 18 Predictions with training Function “traincgb”
Figure 19 Percentage errors in predication with training Function “traincgb”
Figure 20 Predictions with training Function “traincgp”
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Figure 21 Percentage errors in predication with training Function “traincgp”
Figure 22 Predictions with performance Function “mse”
Figure 23 Percentage errors in predication with performance Function “mse”
Figure 24 Predictions with performance Function “mae”
Figure 25 Percentage errors in predication with performance Function “mae”
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Figure 26 Predictions with performance Function “sse”
Figure 27 Percentage errors in predication with performance Function “sse”
Figure 28 Predictions with transfer Function “tansig, purelin”
Figure 29 Percentage errors in predication with transfer Function “tansig, purelin”
Figure 30 Predictions with transfer Function “logsig, purelin”
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Figure 31 Percentage errors in predication with transfer Function “logsig, purelin”
Figure 32 Predictions with learning Function “learncon”
Figure 33 Percentage errors in predication with learning Function “learncon”
Figure 34 Predictions with learning Function “learngd”
Figure 35 Percentage errors in predication with learning Function “learngd”
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Figure 36 Predictions with learning Function “learnh”
Figure 37 Percentage errors in predication with learning Function “learnh”
The training program T28 was selected on the basis of minimum percentage error occurred in prediction of evidences.
4. DEDUCTION OF MATHEMATICAL MODEL THROUGH ANN MODEL
Once a model is trained the values of weights and biases along with the function of the input layer and hidden layer
defines the prediction of a model. The mathematical model generated from the algorithm T28 is as follows
Output = 1* (LW * (2/(1 + exp(-2 * (IW * b + Ib))) - 1) + Ob) ………… Mathematical model
Where,
LW = Weight Matrix of Output layer of ANN
Ob = Bias Matrix of Output Layer of ANN
IW = Weight Matrix of Input layer of ANN
Ib = Bias Matrix of Input Layer of ANN
b = input matrix
Purelin = Function of Output layer of ANN
Tansig = Function of input layer of ANN
The matrix dimensions of variables above variables are too large to show in this paper.
5. COMPARING PREDICTION OF EVIDENCES WITH ANN MATHEMATICAL MODEL AND
EMPIRICAL MODEL
The figures shown below give comparative analysis amongst prediction of evidences with ANN mathematical model and
previously drawn empirical model.
Figure 38 Comparison between experimental evidences (red) and prediction through empirical model (blue)
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Figure 39 Comparison between experimental evidences (red) and prediction through ANN mathematical model (blue)
Figure 40 Percentage error in prediction through ANN mathematical model (red) and Empirical equation (blue)
The figure 38 shows the prediction of experimental evidences (red) with previously drawn empirical model (blue) which
is much deflected compared to the experimental findings. On the contrary artificial neural network based mathematical
model show much better results as in figure 39. The figure 40 compares percentage error in prediction at every stage of
the experimentation which also implies that neural prediction (red) is much better than the empirical model (blue).
6. CONCLUSION
The paper carries a systematic method of optimization of artificial neural network model and comes out with a audacious
solution for prediction of experimental findings. The plots carried for each variation of ANN parameter clearly signifies
its effect on prediction of the model. The mathematical model deduced may be utilized for future research in development
of a controller for Human Powered Flywheel Motor.
References
[1] Modak J. P. and Askhedkar R. D. “Hypothesis for the extrusion of lime flash sand brick using a manually driven
Brick making machine”, Building Research and Information U.K., V22,NI, Pp 47-54, 1994
[2] Modak J. P. and Bapat A. R. “Manually driven flywheel motor operates wood turning machine”, Contempory
Ergonomics, Proc. Ergonomics Society annual convension13-16April, Edinburg, Scotland, Pp 352-357, 1993.
[3] Sohoni V. V., Aware H. V. and Modak J. P. “Manual Manufacture of Keyed Bricks”, Building Research and
Information UK, Vol 25, N6, 1997, 354-364.
[4] Modak J. P.”Design and Development of Manually Energized Process Machines having Relevance to
Village/Agriculture and other productive operations, Application of manually energized flywheel motor for cutting of
wood strip”, Human Power, send for Publications.
[5] H. Schenck Junior “Theory of Engineering Experimentation”, MC Graw Hill, New York.
[6] A. R. Lende, “Modelling of pedal driven flywheel motor by use of ANN”, M. Tech. Thesis, PCE, Nagpur
[7] S. N. Shvanandam, “Introduction to Neural Network using Matlab 6.0”, McGraw Hill publisher.
[8] Stamtios V. Kartaplopoulos , Understanding Neural Networks and Fuzzy Logics, IEEE Press
[9] Neural Network Toolbox TM 7 User’s Guide R2010a, Mathworks.com
[10] Rudra Pratap, “Getting Started with Matlab7,” Oxford, First Indian Edition 2006.
[11] A. R. Bapat, “Experimental Optimization of a manually driven flywheel motor”, M.E. Thesis, VNIT, Nagpur.
[12] A. R. Bapat, “Experimentation of Generalized experimental model for a manually driven flywheel motor”, PhD
Thesis, VNIT, Nagpur.
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
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[13] A. R. Lende, J. P. Modak “Modellling and Simulation of Human Powered Flywheel Motor for field data in the course
of artificial neural network- a step forward in the development of artificial intelligence
AUTHOR
Prof. (Ms) A. R. Lende received her Bachelor degree in Mechanical Engineering from BDCOE, Sewagram in
2004 and Master degree in Mechanical Engineering Design from PCE, Nagpur in 2007. She had registered
her Ph.D. in 2009. She had given her teaching services to MIT, Kothrud, Pune and DMIETR, Wardha for
three and two years respectively. The author also has an industrial experience of one year in the field of design
and implementations. She also had worked in many mechanical engineering design projects and published papers in that
region.
Dr. J. P. Modak is an Emeritus Professor and Dean (R&D) PCE, Nagpur. He has guided number of Ph.D. and
PG Projects in the field of Design engineering, mathematical modeling, Artificial Intelligence, Vibration, etc.
He is also consultant for many industries. He have delivered number of key not lectures, expert lectures at
various conferences and workshops. He became a guiding light for researchers for driving research in
systematic manner.
The author had contributed through large number of papers in reputed international Journals & Conferences for
developing research and path of research.
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