Efficiency of Neural Networks Study in the Design of Trusses

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1270
Efficiency of Neural Networks Study In the Design of Trusses
Shaikh Afran Akram1, Dr. R. J. Fernandes2, Basavaraj.G3
1Shaikh Afran Akram, P.G student, Dept. of Civil Engineering, SDMCET Dharwad, Karnataka, India
2Dr. R. J. Fernandes, Professor, SDMCET Dharwad, Karnataka, India
3Basavaraj.G, Assistant Professor, SDMCET Dharwad, Karnataka, India
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Abstract - Neural network are simply known as biological
nervous system. An Artificial Neural Network (ANN) is an
information processing system that is inspired by the way
biological nervous systems, such as the brain, process
information. This paper examines the efficiency of neural
network. Taking into consideration types of ANNs such as
Generalized Regression (GR) neural network, Radial Basis
Function (RBF) neural network, Linear Layer (LL) neural
network efficiency of ANNs is checked in the design of trusses.
The neural networking tool available in MATLAB(8.1) is used.
To train ANNs, various input and output data are provided
using an analysis and design package STAAD PRO. The ANNs
are trained with some values and are tested for both
interpolation and extrapolation. Then percentage error is
calculated in all three ANNs. Based on percentage error, the
efficiency of each ANN is compared in the design of trusses.
The study is made by increasing number of trainings, by
increasing number of input and output variables, by training
in the matrix form etc. From these results, suitability of each
ANN is studied and conclusions are drawn.
Key Words: Artificial Neural Networks, Generalized
Regression, Radial Basis Function, Linear Layer neural
networks.
1. INTRODUCTION
The progressive work of McCulloch and Pitts (1943)wasthe
establishment stone for the development of neural system
designs. In their paper, McCulloch and Pitts proposed the
unification of neuro – physiology with scientific rationale,
which gave significant results in neural network research.
Infact, the McCulloch – Pitts demonstrateevenimpactedVon
Neumann to attempt new outline innovation in the
development of EDVAC (Electronic Discrete Variable
Automatic Computer).ANN are great at solving algorithmic
and math problems, but often the world can't easily be
defined with a mathematical algorithm. Facial recognition
and language processing are examplesofproblemsthatcan't
easily be expressed into an algorithm, however these tasks
are of importance to humans. Neural networks are typically
arranged in layers. Layers are made up of a number of
interconnected 'nodes'. These interconnectednodescontain
an 'activation function'. Patterns are sent to the network
through the 'input layer', which communicates to one or
more 'hidden layers' where the actual processing is done
through a system of weighted 'connections'. The hidden
layers are then connected to an 'output layer' where the
answer is output. ANNs are used in optimization of
structures, in the field of concrete technology, character
recognition, image compression, etc.
1.1 Methodology
1 To develop ANN model for truss analysis, a neural
networking tool available in MATLAB is used.
2 The analysis is carried out by considering single, two
and three input parameters. To train ANN, various
input and output data are necessary.
3 The ANN has been analyzed by using the STAAD. Pro
2006 results. Once ANN is trained it is tested for
several values within trained range effectively and
calculating their percentage error by comparing with
STAAD. Pro 2006 results. After analyzing the neural
network performance one over the other and from
these results conclusions are drawn.
4 The network is then trained and used in solving
untrained instances of the problem in the design of
trusses.
2. TYPES OF ANNs USED FOR STUDY
Regularly neural systems are prepared and examined with
the goal that a specific input gives particular target output.
Such a condition is demonstrated as follows. There, the
system is balanced, in view of a correlation of theoutputand
the objective, until the point when the system output
coordinates the target. Regularly numerous such
input/target sets are utilized, in this directed learning, to
prepare a system.
Fig -1: Flow chart for training of neural network
In the present investigation, Generalized Regression (GR),
Radial-Basis- Function (RBF), Linear Layer (LL) neural
systems are utilized for approximating the yield of
examination of the trusses.

2.1 Radial Basis Neural Network (RBNN)
RBF’s are embedded in a two layer neural network, where
each hidden unit implements a radial activated function. The
output units implement a weighted sum of hidden unit
outputs. Theinput intoanRBF network is nonlinearwhilethe
output is linear. In order to use a Radial Basis Function
Network we need to specify the hidden unit activation
function, the number of processing units, a criterion for
modelinga giventask anda training algorithmforfindingthe
parameters of the network. Finding the RBF weights is called
network training. If we have at hand a set of input-output
pairs,called trainingset, weoptimizethenetworkparameters
in order to fit the network outputs to the given inputs. Radial
basis functions are embedded into a two-layer feed-forward
neural network. Such a network is characterized by a set of
inputs and a set of outputs. In between the inputs and
outputs there is a layer of processing units called hidden
units. Each of them implements a radial basis function.
Fig -2: Radial Basis Neural Network
2.2 Generalized Regression Neural Network
(GRNN)
The General Regression Neural Network (GRNN) is one of
the most popular neural networks. They have a parallel
structure where the learning is one fold that is input to
structure to output there is no iterative learning present
such as in the case of Multi Layer Perceptrons (MLP)making
them fast to some extents. GRNN are being used in medical
classification, predictive and diagnosticsproblemsbecause a
lot of noisy data is present is such cases.
The GRNN infrastructure consists of four layers input,
hidden, summation and output layer.
 The input layer merely transports the data
attributes to the next layer in a parallel archetype.
 The second layer consists of all the training
samples.
 In the summation layer the summation units or
neurons perform a dot product on the attributes of
the weight vector of the second layer.
 Then in the output layer the respective local
outputs are divided to get the predictions.
Fig -3: Generalized Regression Neural Network
2.3 Linear Layer (LL) Neural Network
Linear layer neural networks are the structures formed by
considering linear units,i.e., unitswithaninput/output(I/O)
mapping that is linear. These units are important for several
reasons:
1. They allow visualization of mappings.
2. They allow simplified analysis using techniques
from linear algebra and geometry.
3. They have a rich history.
4. They provide a starting place for consideration of
nonlinear units.
5. In themselves, they provide many useful mappings.
Each artificial neuron input has an associated weight
indicating the strength of its connection with either an
external input or another neuron output. w ij represents the
strength of the connection to neuron unit i from (either)
neuron unit j or input j.
Fig -4: Linear Layer Neural Network

3. MODEL VALIDATION
Fig -5: TRUSS 1
Truss 1 consists of vertically downward load of 10KN at the
top, young’s modulus is 200KN/mm2,cross-sectional area of
each leg is 2000mm2. Height is 5m.
Fig -6: TRUSS 2
Truss 2 consists of vertically downwardloadof150KN atthe
top, modulus of elasticity is 200GPA. Cross- sectional area of
diagonal legs is 2000 mm2 and bottom leg is 1500mm2,
height is 400mm and length is 800mm.
Fig -7: TRUSS 3
Truss 3 consists of vertical downward load of 150KN at the
top and horizontal load of 100KN, young’s modulus is
200GPA. Cross- sectional area of diagonal legs is 2000 mm2
and other legs with cross-sectional area of1000mm2,height
is 3000mm and length is 4000mm.
4. ANALYSIS OF TRUSSES
4.1. TRUSS 1 – Results Of Spread Constants on the
Performance of GR & RBF Neural Networks
ANNs are trained for various heights varying from 5m to
10m with values 5, 6, 7, 8, 9, 10m. These ANNs are
interpolated for heights varying from 5.25m to 9.75m with
several values such as 5.25, 5.75, 6.25, 6.75, 7.25, 7.75, 8.25,
8.75, 9.25, 9.75m. These ANNs are tested for spread
constants varrying from 0.7, 0.8, 0.9, 1.0, 2.0 & 3.0. The
percentage error is calculated for these spread constants in
case GR & RBF neural networks for interpolation.
0
1
2
3
4
5
S.C(0.7) S.C(0.8) S.C(0.9) S.C(1) S.C(2) S.C(3)
Chart -1: Percentage error for F1
0
1
2
3
4
5
S.C(0.7) S.C(0.8) S.C(0.9) S.C(1) S.C(2) S.C(3)
Chart -2: Percentage error for F2 & F3

0
1
2
3
4
5
S.C(0.7) S.C(0.8) S.C(0.9) S.C(1) S.C(2) S.C(3)
Chart -3: Percentage error for F1
0
1
2
3
4
5
S.C(0.7) S.C(0.8) S.C(0.9) S.C(1) S.C(2) S.C(3)
4.2. TRUSS 1 – Results Of Number Of Trainings On
The Performance Of ANNs
ANNs are trained and tested for heights varying from 5m to
10m with values 5, 6, 7, 8, 9, 10m. These ANNsaretested and
analyzed for both interpolation and extrapolation for set of
heights varying from 4m to 11m with values 4, 4.5, 5.25,
5.75, 6.25, 7.25, 7.75, 8.25, 8.75, 9.25, 9.75, 10.5, 11m. The
percentage error is calculated.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
F1 F2=F3 F1 F2=F3
G.R
R.B.F
L.L
Chart -5: Percentage error for F1, F2 & F3
4.3. TRUSS 1- Effect of Number of Output Variables
on the Performance of ANNs
The ANNs are built to find the force in each member of the
truss and the displacement in X, Y – direction. i.e., number of
output variables have been increased. ANNs are trained and
tested for heights varying from 5m to 10m with values 5, 6,
7, 8, 9, 10m and tested for the same set of heights. The
percentage error is calculated.
0
1
2
3
4
5
6
7
8
G.R
R.B.F
L.L
Chart -6: Percentage error for F1, F2, F3 & Displacement
in X & Y direction
4.4. TRUSS1 - Effect Of NumberOfTrainingsOnThe
Performance Of ANNs (When The Number Of
Output Variables Are Increased)
The ANNs are built to find the force in each member of the
truss and the displacement in X, Y – direction. i.e., number of
output variables have been increased. ANNs are trained and
tested for heights varying from 5m to 10m withvalues5,5.5,
6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10m and tested and analyzed for
the same set of heights. The percentage error is been found.
4.5. TRUSS 2- Effect Of NumberOfTrainingsOnThe
Performance Of ANNs
ANNs are trained for various heights varying from 0.4m to
1.0m with values 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0m. These ANNs
are tested for both interpolation and extrapolation for
heights ranging from 0.3m to 1.1mforvalues0.3,0.35,0.425,
0.475, 0.525, 0.575, 0.625, 0.675, 0.725, 0.775, 0.825, 0.875,
0.925, 0.975, 1.05 and 1.10m. The percentage error is
calculated.
Chart -4: Percentage error for F2 & F3

0
10
20
30
40
50
60
F1 F2=F3 F1 F2=F3
G.R
R.B.F
L.L
4.6. TRUSS 2- Effect Of Number Of Input Variables
On The Performance Of ANNs
ANNs are built to find the force in each member of the truss
and spans. i.e., number of input variables have been
increased. ANNs are trained and tested for heights varying
from 0.4m to 1.0m with values 0.4, 0.5, 0.6, 0.7,0.8,0.9,1.0m
and spans varying from 0.8m to 1.4mwiththevalues0.8, 0.9,
1.0, 1.1, 1.2, 1.3, 1.4 m. These ANNs is testedandanalyzedfor
the same set of heights as in tables 4.21 and spans varying
from 0.7m to 1.5m with values 0.7, 0.75, 0.825, 0.875, 0.925,
0.975, 1.025, 1.075, 1.125, 1.175, 1.225, 1.275, 1.325, 1.375,
1.45, 1.5 m. The percentage error is been found.
0
5
10
15
20
25
F1 F2=F3 F1 F2=F3
G.R
R.B.F
L.L
4.7. TRUSS 3 - Effect Of 2X2 Matrix Form Training
The ANNs are built up to find the force in each member of
the truss for various spans and heights. The ANNs are
trained and tested for spans ranging from 4m to 8m with
values 4m and 8m and heights ranging from 3m to 7m with
values 3m and 7m. These ANNs are tested only for
interpolation for a set of spans and heights.
0
5
10
15
20
25
30
35
F1 F2 F3 F4 F5 F6
G.R
R.B.F
L.L
Chart -9: Percentage error for F1, F2, F3, F4, F5, F6
ANNs are built up to find the force in each member of the
truss for various spans and heights. The ANNs are trained
and tested in 3 x 3 matrix form i.e ANNs is tested for spans
ranging from 4m to 8m with values 4m, 6m, 8m and heights
ranging from 3m to 7m with values 3m, 5m, 7m.TheseANNs
are tested only for interpolation for a set of spans and
heights.
ranging from 4m to 8m with values 4, 5.34, 6.68, 8m and
heights ranging from 3m to 7m with values 3, 4.34, 5.68, 7m.
These ANNs are tested only for interpolation for a set of
spans and heights.
ranging from 4m to 8m with values 4, 5, 6, 7, 8m and heights
ranging from 3m to 7m with values 3, 4, 5, 6, 7m. These
ANNs are tested only for interpolation for a set of spans and
heights.
4.11. TRUSS 3 – Effect Of Enlargement In The
Quantity Of InputVariablesOnTheResultsOfANNs
The ANNs are developed to find the force in each member of
the truss for the 6 input variables such as spans (L), heights
(H), and 4 groups of cross sectional area. i.e., A1, A2, A3 and
A4, where, A1 = cross- section area of top member, A2 =

cross sectional area bottom member,A3=cross-sectionarea
of vertical members & A4 = cross- section area diagonal
members. Now, the ANNs are trained and tested for the
spans 4m, 8m, heights 3m, 7m, cross-sectional area of top
member 600mm2, 850mm2, cross-sectional area of bottom
member 150mm2, 300mm2, cross-sectional area ofdiagonal
members 400mm2, 650mm2. i.e., the ANNs are trained in
the 2x2x2x2x2x2 matrix form.
5. CONCLUSIONS
As per the analysis on the results of GR, RBF and LL neural
networks the following conclusions are obtained.
 Extrapolation should not be taken into
consideration in GR, RBF, and LL neural networks.
 Taking in account interpolation, the results of GR,
RBF is reduced as the spread constant is
increased.
 In interpolation, the results of RBF is excellent as
compare to GR. GR shows excellent results for the
values away from trained end values. RBF and LL
shows good performance for all analyzed values.
 When ANNs are trained, analyzed and tested for
large number of values, there is little improvement
in the results of ANNs.
 ANNs remains constant even if output variables are
increased.
 If the output variables are increased there is very
much improvement in the result of ANNs.
 If the input variables are increased there is
reduction in results of ANNs.
 Taking into consideration matrix form training
results of RBF is better than GR and LL and GR
shows better results than LL or vice-versa. As
number of trainings are increased there is
improvement in the results of ANNs.
 RBF proves to be deprived for large number of
trainings and input variables.
 Results of GR and LL is reduced as there is increase
in number of input variables.
REFERENCES
[1] Adeli, H. and Park, H.S., “Counter propagation neural
networks in structural engineering”, ASCE Journal Of
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networks for the prediction of steel plate strengthened
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[4] Hadi, M.N.S., “Neural Networks applications in concrete
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[5] Yeh, I.C., “Modelling of strength of high-performance
concrete using artificial neural networks”, Journal of
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steel compression members in towers / trusses using
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