Indian Journal of Engineering & Materials Sciences
Vol. 18, October 2011, pp. 351-360
Weld residual stress prediction using artificial neural network and
Fuzzy logic modeling
J Edwin Raja Dhasa*
& Somasundaram Kumanan
b
aDepartment of Automobile Engineering, Noorul Islam University, Nagercoil 629 180, India bDepartment of Production Engineering, National Institute of Technology, Tiruchirappalli 620 015, India
Received 26 February 2010; accepted 11 October 2011
Artificial intelligent tools such as expert systems, artificial neural network and fuzzy logic support decision-making are
being used in intelligent manufacturing systems. Success of intelligent manufacturing systems depends on effective and
efficient utilization of intelligent tools. Weld residual stress depends on different process parameters and its prediction and
control is a challenge to the researchers. In this paper, intelligent predictive techniques artificial neural network (ANN) and
fuzzy logic models are developed for weld residual stress prediction. The models are developed using Matlab toolbox
functions. Data set required to train the models are obtained through finite element simulation. Results from the fuzzy model
are compared with the developed artificial neural network model, and these models are also validated.
Keywords: Weld residual stress, Artificial neural network, Fuzzy logic, Finite element analysis
Weld residual stress is a major parameter in
evaluating the quality of weldments. Quality of weld
plays an important role in the performance of a
welded product as it improves fatigue strength,
corrosion resistance, creep life and reduces rework
and scrap. Due to intense concentration of heat in heat
source of welding, the regions near the weld line
undergo severe thermal cycles, thereby generating
inhomogeneous plastic deformation and residual
stresses in weldment. Welding-induced residual
stresses play an important role in the function of
welded structures. Different experimental methods
for directly measuring welding residual stresses are
available like X-ray diffraction1, Neutron diffraction,
Deep hole drilling2,3
holographic interferometry4.
All these methods require special equipments and are
expensive. These techniques are limited in obtaining
the entire picture of the residual stress distribution
in weldment. In 1971, Ueda5 applied finite element
method to analyse thermal elastic-plastics stress and
strain during welding and Nomoto6 pioneered finite
element method to analyze the thermal stress during
welding. Muhammad et al.7 investigated the finite
element simulation of laser beam welding induced
residual stresses and distortions in thin sheets. Andres
et al.8 applied finite element models to analyze
the thermal and mechanical phenomena observed in
welding processes. Although the finite element
method has emerged as one of the most attractive
approaches for computing residual stresses in welded
joints, its application to practical analysis and design
problems has been hampered by computational
difficulties and also this method of obtaining residual
stresses is not feasible for all welding parameters.
Lee et al.9
used multiple regression analysis for
prediction of process parameters for gas metal arc
welding and Yang et al.10
used linear regression
equations for modeling the submerged arc welds.
Due to the inadequacy and inefficiency of the mathematical models to explain the nonlinear properties existing between the input and output
parameters, intelligent systems such as ANN, fuzzy logic and expert system have emerged. ANN technique
11 is used to handle problems of
nonlinearity. Jeongick et al. 12
utilized ANN technique for back-bead prediction of gas metal arc welding process. Nagesh et al.
13 employed ANN
to predict weld bead geometry in shielded metal-arc welding process. Kim et al.
14 applied ANN to predict
bead height in robotic arc welding. Edwin et al.15
used ANN to predict weld bead width using artificial neural networks. Hakan Ates
16 applied ANN
technique for prediction of gas metal arc welding
parameters. ——————
*Corresponding author (E-mail: [email protected])
INDIAN J ENG. MATER. SCI., OCTOBER 2011
352
It is difficult to control process parameters
for welding process as the relationship between the
input and the output parameters are complex and
interrelated. Also, it is very difficult to control the
system in real time because the controlled system is
nonlinear, time-varying, uncertain and fast-response
controlled system. Fuzzy control17,18
systems are
effective to handle uncertain, nonlinear as well as
dynamic time-varying processes control systems.
Fuzzy logic model for predicting weld pool size in
gas metal arc welding processes was developed by
Boo et al.19
. Fuzzy logic is applied to control gap
parameters for electro discharge machining20
. Tarng
et al.21
used fuzzy logic in the Taguchi method for the
optimization of the submerged arc welding process.
Xue et al.22
used Fuzzy model to predict and control
the bead width in the robotic arc-welding process.
Neuro-fuzzy method is used to model hot extrusion
process23
. Xixia et al.24
used SVM-based fuzzy rules
acquisition system for pulsed GTAW process. This
paper addresses the development of ANN and fuzzy
logic models to predict the weld residual stress for
consistent weld quality. The validity of the developed
models is verified by confirmatory experiments.
Proposed Methodology Weld residual stress prediction (Fig. 1) undergoes
four stages of development: (i) data collection by
finite element simulation method, (ii) building ANN
and fuzzy logic models, (iii) training the developed
models and (iv) validation of the developed models.
The validated models are forwarded to predict the
residual stress of weld.
Data collection
In this work, prediction of residual stress of the butt
weld joint through simulated finite element models is
presented. The model is proposed, developed, tested
and validated for various weld conditions. Two mild
steel plates of dimensions 100 × 45 × 10 mm are
modeled to form a butt weld and simulated using
finite element analysis software. General purpose
finite element package ANSYS 5.4 version is used for
both thermal and stress analysis. The following
assumptions used during the analysis: (i) the welding
process is modeled as a single pass weld in this
analysis, (ii) the bottom surface of the weld area is
fixed to prevent body movement, (iii) no penetration
and overfill of the weldments are considered.
The material properties of the weld metal, bead
metal and heat affected zone are both temperature and
temperature-history dependent (Fig. 2). Finite element
analysis of welding is carried out in two stages as
thermal analysis and stress analysis. A non-linear
transient thermal analysis is conducted first to obtain
the global temperature history generated during the
welding process. Convention and radiation boundary
conditions are applied to the model. The heat flux
is applied over the weld bead as the load input to
the thermal analysis. Equation (1) gives the arc heat
input.
q = (ηa × V × I)/A … (1)
where q is the arc heat flux in w/m2, ηa is the arc
efficiency, V is the arc voltage in volts, I is the arc
current in amps and A is the weld bead area in m2.
Area of the weld bead is calculated by the
approximations from the empirical relations for the
corresponding welding current, arc voltage and
welding speed25,26
. Welding speed is incorporated in
the analysis using load step options. The governing
differential equation for two dimensional transient
heat transfer during welding is given by Eq. (2).
t
TpρcQ
y
yq
x
xq
∂
∂=+
∂
∂+
∂
∂
−
… (2)
where qx and qy are the components of heat flow rate
vector per unit area in the plate (x; y), Q the heat
Fig. 1—Developed scheme to predict weld residual stress
DHAS & KUMANAN: WELD RESIDUAL STRESS
353
generation, ρ the density, cp the specific heat and
(∂T/∂t) represents the temperature distribution with
respect to time which is expected as the output from
thermal analysis27
.
The model is meshed with thermal element
PLANE 55 for the weld bead region and PLANE
35 for the work piece. The quadrilateral shape of
PLANE 55 and the triangular shape element of
PLANE 35 make the developed finite element model
properly meshed with suitable thermal, structural and
material properties. The convection and radiation
surfaces are meshed with Link34 and Link31. The
real constant for the convection and radiation
elements are specified. For the structural analysis, the
thermal elements are converted to its corresponding
structural elements, i.e., Solid Quad 4 node 42 and
Triangle 6 node 2. These elements are capable
of exhibiting structural property without change in
mesh structure used for thermal analysis. Four
welding parameters are given as the input for this
analysis and they are arc efficiency, voltage, current
and welding speed. The working ranges of the
parameters were taken from the AWS handbook.
The amount of heat input to the model is found as
the product of arc efficiency, voltage and current.
A non-linear transient thermal analysis is conducted
first to obtain the global temperature history generated
during the welding process. Convention and radiation
boundary conditions are applied to the model.
In thermal analysis heat flux is given as the load
(arc heat) to the work-piece incorporating welding
speed in terms of load step time. At the end of
the heat load an extra load step with time equal to
the cooling time is added without any heat input.
In the solution phase, this part of the analysis gives
temperature distribution as the output and this result
is stored in a separate file. The temperature
distribution over time at a user-defined node is
obtained. The defined node is in the work-piece or
in weld bead.
A stress analysis is then carried out with the
temperatures obtained from the thermal analysis
as the loading to the stress model. The output
obtained out of this analysis is residual stress
Fig. 2—Material properties of mild steel
INDIAN J ENG. MATER. SCI., OCTOBER 2011
354
distribution over the work-piece after cooling.
Residual stress is obtained at the required nodes by
using the time history postprocessor.
Residual stresses are recorded in the weld bead
and in the work-piece/weld bead interface (Fig. 3).
The required results are tabulated for any node in the
work-piece or in weld bead using the time-history
postprocessor (Table 1).
Development of proposed ANN model
ANN model is proposed, developed and validated
to predict residual stress (Fig. 4). It is feed forward
back propagation network trained with Levenberg-
Marquardt back propagation algorithm. The data
required for training and testing the ANN model is
obtained from finite element analysis simulation
(Table 1). The learning function is gradient descent
algorithm with momentum weight and bias learning
function. The number of hidden layers and neurons
are determined through a trial and error method,
in order to accommodate the converged error. The
structure of the proposed neural network is 4-12-13-1
(4 neurons in the input layer, 12 neurons in 1st hidden
layer and 13 neurons in 2nd
hidden layer and 1 neuron
in the output layer). With a learning rate of 0.55 and
a momentum term of 0.9, the network is trained for
10000 iterations. The error between the desired and
the actual outputs is less than 0.001 at the end of the
training process and the command window shows
the input test data and output obtained from the
developed ANN model (Fig. 5).
Fig. 3—Stress distribution over butt-welded structure under study
Development of proposed fuzzy logic model
Fuzzy logic model for weld residual stress
prediction is developed in different stages (Fig. 6).
The first step in the development of fuzzy logic model
is to take the inputs and determine the degree to
which they belong to each of the appropriate fuzzy
sets via membership functions (Figs 7-11). In the
fuzzy logic system, the input is always a crisp
numerical value limited to the universe of discourse
of the input variable. The input crisp variables are
welding current, arc voltage, arc efficiency and
welding speed (Table 2). The output is a fuzzy degree
of membership in the qualifying linguistic set. The
fuzzy logic system is based on rules and each of the
rules depends on resolving the inputs into a number
of different fuzzy linguistic sets. Before the rules
are evaluated, the inputs are fuzzified according to
each of these linguistic sets. The inputs are fuzzified
and the degree to which each part of the antecedent
is accommodated for each rule. The input to the
fuzzy operator is two or more membership values
from fuzzified input variables. The output is a single
truth-value.
Every rule has a weight (a number between 0 and 1),
which is applied to the number given by the
antecedent. Once proper weighting has been assigned
to each rule, the implication method is implemented.
The result is a fuzzy set represented by a membership
function, which weights the linguistic characteristics
that are attributed to it. The decisions are based on
the testing of all the rules in fuzzy inference system.
The input of the aggregation process is the list of
truncated output functions returned by the implication
process for each rule. The input for the defuzzification
process is a fuzzy set and the output is a single
number. Fuzziness helps the rule evaluation during
the intermediate steps, the final desired output
for each variable is a single number. However, the
Fig. 4—Developed ANN architecture for residual stress prediction
DHAS & KUMANAN: WELD RESIDUAL STRESS
355
Table 1—Training data set obtained from finite element analysis
Residual stress Arc efficiency Welding
speed
Welding
voltage
Welding
current
Heat
input
Heat
flux Work piece/ Weld interface
% mm/s V A W W/m2 MN/m2
0.8 2 21 170 2856 14280000 67.90
0.8 2.5 21 170 2856 14280000 62.79
0.8 3.3 21 170 2856 14280000 74.50
0.8 4 21 170 2856 14280000 236.30
0.8 2 22 150 2640 13200000 63.00
0.8 2.5 22 150 2640 13200000 61.40
0.8 3.3 22 150 2640 13200000 115.00
0.8 4 22 150 2640 13200000 297.00
0.8 2 24 140 2688 13440000 64.44
0.8 2.5 24 140 2688 13440000 61.00
0.8 3.3 24 140 2688 13440000 108.50
0.8 4 24 140 2688 13440000 286.00
0.8 2 28 130 2912 14560000 69.00
0.8 2.5 28 130 2912 14560000 63.00
0.8 3.3 28 130 2912 14560000 73.60
0.8 4 28 130 2912 14560000 213.00
0.75 2 21 170 2677.5 13387500 60.90
0.75 2.5 21 170 2677.5 13387500 64.20
0.75 3.3 21 170 2677.5 13387500 110.00
0.75 4 21 170 2677.5 13387500 289.00
0.75 2 22 150 2475 12375000 60.04
0.75 2.5 22 150 2475 12375000 65.14
0.75 3.3 22 150 2475 12375000 178.00
0.75 4 22 150 2475 12375000 325.00
0.75 2 24 140 2520 12600000 60.70
0.75 2.5 24 140 2520 12600000 64.45
0.75 3.3 24 140 2520 12600000 143.20
0.75 4 24 140 2520 12600000 319.20
0.75 2 28 130 2730 13650000 65.30
0.75 2.5 28 130 2730 13650000 61.30
0.75 3.3 28 130 2730 13650000 100.10
0.75 4 28 130 2730 13650000 275.99
0.7 2 21 170 2499 12495000 60.36
0.7 2.5 21 170 2499 12495000 64.86
0.7 3.3 21 170 2499 12495000 162.80
0.7 4 21 170 2499 12495000 322.30
0.7 2 22 150 2310 11550000 58.93
0.7 2.5 22 150 2310 11550000 66.05
0.7 3.3 22 150 2310 11550000 254.00
0.7 4 22 150 2310 11550000 300.80
0.7 2 24 140 2352 11760000 58.90
0.7 2.5 24 140 2352 11760000 65.92
0.7 3.3 24 140 2352 11760000 238.70
INDIAN J ENG. MATER. SCI., OCTOBER 2011
356
Fig. 5—Command window showing the input test data and outputs obtained from the developed ANN model for weld residual stress
prediction
Fig. 6—Membership function for arc efficiency
DHAS & KUMANAN: WELD RESIDUAL STRESS
357
Fig.7—Membership function for weld speed
Fig. 8—Membership function for arc voltage
INDIAN J ENG. MATER. SCI., OCTOBER 2011
358
Fig. 9—Membership function for weld current
Fig. 10—Membership function for weld residual stress
DHAS & KUMANAN: WELD RESIDUAL STRESS
359
Fig. 11—An example from fuzzy logic modeling for prediction of weld residual stress
Table 2—Crisp input values used for fuzzy logic modeling
Input Crisp values
Welding current (A) 140 - 170
Arc voltage (V) 21 – 28
Arc Efficiency (%) 0.7 – 0.8
Welding speed (mm/s) 2.0 – 3.3
aggregate of a fuzzy set encompasses a range of
output values and so must be defuzzified in order
to resolve a single output value from the set.
Centroid method of defuzzification is used in
developing the model.
Results and Discussion After developing the fuzzy logic system
for the prediction of the weld bead width,
it is tested by giving various input values using
fuzzy rule viewer (Fig. 10). If the input
values are changed, the corresponding output is
automatically obtained from the developed fuzzy
system. The configurations of the computing
machine used are Intel Pentium IV 1.8 GHz
processor, 512 MB RAM and 80 GB Hard
Disk Drive. Confirmatory experiments are done
using X-ray diffraction method to validate the
developed fuzzy model. Residual stress after
cooling was determined by an advanced solid
state X-ray stress analyzer of type AST × 2001
which works on solid state X-ray camera’ principle.
The AST X2001 uses a modified ψ-inclination
technique28
to measure residual stresses. Stresses
were measured with Cr-Kct radiation yielding
Cr 21 l-reflection at an angle 2θ = 145° 8″. The
X-ray voltage is 30 kV and the X-ray current is
5.8 mA. The calibration distance D is 49.49 mm.
Experimentation was carried out at Welding Research
Institute, Tiruchirappalli, India. Percentage of error
is calculated by [(Actual value – Predicted value)/
Predicted value] × 100 (Table 3). The errors in
weld residual stress prediction by fuzzy model
very rarely exceed by 5% and fuzzy model was
able to predict with significant accuracy than ANN
model. Also the time elapsed by the developed
fuzzy logic model to predict the residual stress at
a particular node in the welded structure is 50% less
than finite element simulation of welding residual
stress and 30% less than that of ANN prediction
and it is extraordinarily less than the X-ray
diffraction method. The developed fuzzy logic
model is forwarded to predict weld residual stress
under different weld conditions.
INDIAN J ENG. MATER. SCI., OCTOBER 2011
360
Table 3—Percentage error from of the developed models with confirmatory experiment
Process parameters Residual stress, MN/m2 Percentage error, MN/m2
Welding
current, A
Arc voltage,
V
Arc
efficiency, %
Weld speed,
mm/s
Experiment
FEA
model
ANN
model
Fuzzy
model
FEA
model
ANN
model
Fuzzy
model
140 24 0.7 2 58 58.9 61.2 59.05 -1.52 -5.22 -1.77
170 21 0.8 3.3 79 74.5 73.2 74.5 6.04 7.92 6.04
140 24 0.75 2.5 63 64.45 60.11 61.30 2.32 4.8 2.77
Conclusions This paper has explored the application of
intelligent techniques for weld residual stress
prediction. Data for developing the ANN and fuzzy
model is obtained by finite element modeling of
the residual stress. Results from the fuzzy model
are compared with the results from the developed
ANN model. The fuzzy model predicts the weld
residual stress with good accuracy. Finally, the
models are validated.
Acknowledgements Authors express sincere thanks to the Ministry
of Human Resource Development, Government of
India for the sponsorship under the research and
development programme to undertake this research
work.
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