weld residual stress prediction using artificial neural network and...

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


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


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


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


357

Fig.7—Membership function for weld speed

Fig. 8—Membership function for arc voltage


358

Fig. 9—Membership function for weld current

Fig. 10—Membership function for 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.


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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