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你可能喜欢Services on DemandArticleIndicatorsCited by SciELO Related linksSharePrint version ISSN J. Braz. Soc. Mech. Sci. & Eng. vol.26 no.1 Rio de Janeiro Jan./Mar. 2004 http://dx.doi.org/10.-00005
TECHNICAL PAPERS
GMAW welding optimization using genetic algorithms
D. S. C C. V. Gon& Sebasti&o
S. C. J V. A. Ferraresi
Federal University of Uberl&ndia, Faculty
of Mechanical Engineering, Av. Jo&o Naves de &Avila, 2.121,
Uberl&ndia, MG. Brazil, ,
This article explores the possibility of using
Genetic Algorithms (GAs) as a method to decide near-optimal settings of a GMAW
welding process. The problem was to choose the near-best values of three control
variables (welding voltage, wire feed rate and welding speed) based on four
quality responses (deposition efficiency, bead width, depth of penetration and
reinforcement), inside a previous delimited experimental region. The search
for the near-optimal was carried out step by step, with the GA predicting the
next experiment based on the previous, and without the knowledge of the modeling
equations between the inputs and outputs of the GMAW process. The GAs were able
to locate near-optimum conditions, with a relatively small number of experiments.
However, the optimization by GA technique requires a good setting of its own
parameters, such as population size, number of generations, etc. Otherwise,
there is a risk of an insufficient sweeping of the search space.
Keywords: Optimization,GMAW, genetic algorithm,
Introduction
The GMAW welding process is easily found in any
industry whose products requires metal joining in a large scale. It establishes
an electric arc between a continuous filler metal electrode and the weld pool,
with shielding from an externally supplied gas, which may be an inert gas, an
active gas or a mixture. The heat of the arc melts the surface of the base metal
and the end of the electrode. The electrode molten metal is transferred through
the arc to the work where it becomes the deposited weld metal (weld bead).
The quality of the welded material can be evaluated
by many characteristics, such as bead geometric parameters (penetration, width
and height) and deposition efficiency (ratio of weight of metal deposited to
the weight of electrode consumed). These characteristics are controlled by a
number of welding parameters, and, therefore, to attain good quality, is important
to set up the proper welding process parameters. But the underlying mechanism
connecting then (welding parameters and quality characteristics) is usually
not known.
The experimental optimization of any welding process
is often a very costly and time consuming task, due to many kinds of non-linear
events involved. One of the most widely used methods to solve this problem is
the Response Surface Methodology (RSM), in which the experimenter tries to approximate
the unknown mechanism with an appropriate empirical model, being the function
that represents it called a response surface model. Identifying and fitting
from experimental data a good response surface model requires some knowledge
of statistical experimental design fundamentals, regression modeling techniques
and elementary optimization methods (Myers and Montgomery, 1995). This and other
techniques (such as Taguchi) provide good results over regular experimental
regions, i.e., with no irregular points. However, it is often very difficult
to establish an arc, and melt-through may occur under certain experimental points
needed to satisfy the specific experimental design. The data obtained may be
impossible to analyze or provide poor results, what often forces the experimenter
to modify the design space (Kim and Rhee, 2001).
Therefore, it is important to move the experimental
region closer to the region of interest, which show relatively good weld quality.
This process is particularly of interest when experimentation begins far from
the region of optimal conditions. The full factorial design can result in optimal
settings of the welding process parameters without deriving a model for the
welding process. But as the number of the input parameters increases, the number
of experiments exponentially increases and the full factorial method for the
problem becomes unrealistic (Kim and Rhee, 2001).
Recently, some articles have tried to overcome
these problems with a new approach for experimental optimization. They suggest
using Genetic Algorithms (GAs) to sweep a region of interest and select the
optimal (or near optimal) settings to a process. The GA is a global optimization
algorithm, and the objective function does not need to be differentiable. This
allows the algorithm to be used in solving difficult problems, such as multimodal,
discontinuous or noisy systems. After the GAs have found a regular region, further
experimental optimization can be performed with conventional techniques, such
as response surface methodology. Some examples of this kind of work are Sette
et al (1996), Busacca et al (2001) and Kim and Rhee (2001).
The goal of this article is to explore the GAs
technique in the determination of the near-optimal GMAW process parameters,
welding voltage (T), wire feed speed (F) and welding speed (S). The search for
the optimum was based on the minimization of an objective function, which takes
into account the economic aspects (deposition efficiency, dexp) and
the geometric characteristics (penetration, pexp, width, wexp,
and reinforcement, rexp) of the bead.
Nomenclature
b = number of bits
d = deposition efficiency, %
f = fitness
F = wire feed speed, m/min
GA = genetic algorithms
GMAW = gas metal arc welding
i = relative to a specific run (or
experiment)
Of = objective function
N = population size
p = depth of penetration, mm
pr = probability
r = bead reinforcement, mm
RSM = response surface methodology
S = welding speed, cm/min
T = welding voltage, V
V = variable
w = bead width, mm
Superscripts
max = relative to maximum values
min = relative to maximum values
o = relative to initial population
Subscripts
exp = relative to experimental value
t = relative to target
Genetic Algorithms
Genetic algorithms are a set of computer procedures
of search and optimization based on the concept of the mechanics of natural
selection and genetics. Holland (1975) made the first presentation of the GA
techniques in the beginning of the 60's and further development can be credited
to Goldberg (1989).
The GAs operate over a set of individuals, usually
represented by a binary string comprised between 0 and 1. This binary codification
is randomly generated over the search space, where each individual represents
a possible problem solution. When determining the solution within the search
range, the genetic algorithm simultaneously considers a set of possible solutions.
This parallel processing of the algorithm may prevent the convergence of one
particular local extreme point. Another characteristic of these algorithms is
as the GAs only use the fitness
the fitness function does
not need to be continuous or differentiable.
The GMAW welding optimization procedure using genetic
algorithm is shown in . In this figure, initial
population means the possible solutions of the optimization problem, and
each possible solution is called an individual. In this work, a possible solution
is formed by values of the welding voltage, To; the wire feed speed,
Fo and the welding speed, So, which are shown as a binary
string. However, they need to be changed into real numbers when being applied
to the optimization problem, since the experimenter sets the welding equipment
with real values, instead of binary codes.
Decoding is the process of changing the
input variables that are coded as a binary string into a real number. The binary
codification is used to represent each variable Vi as a b-bit
binary number, which approximates 2b discrete numbers in the
range of the variables, according to:
are the lower and upper bounds of the i-th continuous variable and bin
is an integer number between zero and 2b-1. Each individual,
represented by the binary string, is transformed into a real number by Equation
(1) and applied to the optimization problem.
After decoding, the values of each individual obtained
(T, F and S), are used to set up the welding experiment. While the experiment
is being conducted, the algorithm stands by until the weld bead is completed
and the desired responses (pexp, dexp, wexp
and rexp) are measured. According to the results of the welding experiments,
the fitness value of the previous welding condition is calculated.
The fitness evaluation is a necessary procedure
to decide the survival of each individual. Individuals with large fitness values
are what the user wants to maximize. Considering the minimization of an objective
function, during the evaluation operation, a proper fitness index is assigned
to each candidate set in such a way that the lower the value of the objective
function associated to an individual candidate, the higher the fitness index
given to it. The responses used in this study were used to make the fitness
function, Equation (2), as shown below:
Of(i) - Value of the objective function at the
pt - Target (desirable) value
pexp(i) - Experimental value for
the depth of penetration at the "i"
dt - Target value for the depo
dexp(i) - Experimental value for
the deposition efficiency at the "i"
wt - Target value f
wexp(i) - Experimental value for
the bead width at the "i"
rt - Target value for the b
rexp(i) - Experimental value for
the bead reinforcement at the "i"
cp,cd,cw and cr -Weights that give different
status (importance) to each response.
The responses evaluated in this work do not have
equal importance. The most important response is the depth of penetration, followed
by the deposition efficiency, bead width and reinforcement. In order to transpose
these statuses to the objective function, weights were included. These weights
are the values put in front of each response term (0.5, 0.3, 0.1 and 0.1) respectively.
The next step is to use each individual fitness
and the genetic operator (reproduction, crossover and mutation) to produce the
next generation of the new population (T, F and S). The individual
evolution (that is, the problem solution) is done by three operators (Goldberg,1989):
Selection – 
this process is responsible for the choice of which individual, and how many
copies of it, will be passed to the next generations. An individual is selected
if it has a high fitness value, and the choice is biased towards the fittest
members. This study used the biased roulette wheel selection to imitate Darwin's
survival of the fittest theory (Goldberg, 1989). This selection approach is
based on the concept of selection probability for each individual proportional
to the fitness value. For individual k with fitness fk,
its selection probability, pk, is calculated as follows:
where n is population size. Then a biased roulette
wheel is made according to these probabilities. The selection process is based
on spinning the roulette wheel n times. The individuals selected from the selecting
process are then stored in a mating pool.
Crossover - this step takes two
strings (parents) from the mating pool and performs a randomly exchange in some
portions between them to form a new string (children). After selection, crossover
proceeds in three steps. First, two strings (referred to as parents) are selected
randomly from the mating pool. Second, an arbitrary location (called the crossover
site) in both strings is selected randomly. Third, the portions of the strings
following the crossover site are exchanged between two parent strings to form
two offspring strings. This crossover does not occur with all strings, but is
limited by the crossover rate.
Mutation - in a binary coding scheme,
it involves switching individual bits along the string, changing a zero to one
or vice-versa. This operator keeps the diversity of the population and reduces
the possibility that the GAs find a local minimum or maximum instead of the
global optimal solution, although this is not ever guaranteed. The mutation
rate is usually set at a low value to avoid losing good strings. It also provides
information that did not exist in the initial stage.
The main characteristic of the GAs is that they
operate simultaneously with a huge set of search space points, instead of a
single point (as the conventional optimization techniques). Besides, the applicability
of the GAs is not limited by the need of computing gradients and by the existence
of discontinuities in the objective function (performance indexes). This is
so because the GAs work only with function values, evaluated for each population
individual. The major drawback in the GAs is the large use of computational
effort when compared with the traditional optimization methods.
Experimental Procedure
The aim of this article is to find the optimum
adjusts for the welding voltage, wire feed speed and welding speed in a GMA
welding process. The optimum adjusts are the ones that deliver the pre-selected
values of four responses: deposition efficiency (100%), bead width (8.5 mm),
depth of penetration (5.3 mm) and reinforcement (1.5 mm). These values were
developed in Correia & Ferraresi (2001). In other words, the optimum parameters
are those who deliver responses the closest possible of the cited values. And
it is assumed that the near optimum point is within the following experimental
region, defined by the GA search ranges for T, V and S (see in the ).
The application involved in this work is the welding
of 9.5 mm thick mild steel with a square-groove butt joint (1.2 mm root opening).
A single pass welding process was used. The filler metal was an AWS classification
ER 70S-6 with a 1.2 mm diameter electrode. The shielding gas used was 100% CO2
with a 13 l/min flow rate.
Inside the experimental space, the GAs chose, randomly,
the initial welding setup, i.e., the parameters values of the first experiment.
After it (the first exp.) was done, its response characteristics were measured
and fed into the GAs. Then, based in the previous information, the algorithm
chose another setup, which was done and its data again fed into the algorithm.
The process continued until the optimum was found, i.e., until the objective
function (Eq. 2) reached its minimum. The parameters of GA computations are
shown on .
In the GA, the population size, crossover rate
and mutation rate are important factors in the performance of the algorithm.
A large population size or a higher crossover rate allows exploration of the
solution space and reduces the chances of settling for poor solution. However,
if they are too large or high, it results in wasted computation time exploring
unpromising regions of the solution space. In this work, the population size
and number of generation are small in order to maintain the total number of
experiments in an acceptable level.
About the mutation rate, if it is too low, many
binary bits that may be useful are never tried. However, if it's too high, there
will be much random perturbation, and the offspring will loose the good information
of the parents. The 1% value is within the typical range for the mutation rate.
The crossover rate is 90 %, i.e., 90% of the pairs are crossed, whereas the
remaining 10% are added to the next generation without crossover. The chosen
type of crossover was single, which means that a new individual is formed when
the parent genes are swapped over at some random single point along their chromosome.
Accuracy is the bit quantity for each variable.
Results and Discussion
presents the settings
and the resultant values of the evaluated responses for all the experiments
performed, as well as the values of the correspondent objective function.
All the experiments performed according to the
genetic algorithm had a relatively good quality (in the sense of lack of bead
defects) with no problems of melt-through, porosity or cracks. Considering quality
as closeness to defined targets, the genetic algorithm did not manage to achieve
all the established targets. The final value of the objective function was 0.11,
which is a relatively low value (compared to its initial value) and can be considered
satisfactory weld quality, according to Kim and Rhee (2001). And this final
value for the objective function repeats itself in the last four experiments
with the same settings, suggesting that
this is not some random error (this stabilization can be better seen in the
shows that
the discrepancy between targets and obtained values was quite big for some responses,
mainly the bead width and the bead reinforcement.
The discrepancy between target and final values
can not be credited to insufficient generations, since the
shows a good pattern of stabilization for the objective function. In addition,
show that the stabilization also exists when considering the individual values
of the setting parameters. The welding voltage had a minor variation in its
last values, but nothing significant in terms of practical purposes. The wire
feed speed and the welding speed presented good stabilization in their final
values. It should be said that maybe a higher population size would allow a
better sweeping of the search space. An evaluation on the influence of new values
for the GA parameters (other than presented in )
should be considered in future works.
The explanation for the GA inability in accomplishing
all targets can be credited to the weights used in the objective function (Equation
2). As seen, the most important responses are the depth of penetration (0.5
weight) and the deposition efficiency (0.3 weight) and the minimization process
was led by these ones. But a look in
reveals that
there are other compromises available, such as experiment 2, where lower deposition
efficiency gives room to better adjusted bead width and bead reinforcement.
A final note on the GA optimization is about its
inner mechanism of random search.
shows the experimental
region that should be investigated and the points suggested by the GA. These
points are not equally distributed in the search space, as in a conventional
statistical project would be. And many of the points are coincident, which reduces
even more the swept region. So, there is a chance of existing non-tested points
with even a better compromise between the responses.
Conclusion
The possibility of a GMAW welding optimization
procedure using genetic algorithm is inves more specifically,
the determination of the near-optimal GMAW process parameters, welding voltage
(T), wire feed speed (F) and welding speed (S). The search for the optimum was
based on the minimization of an objective function, which takes into account
the economic aspects (deposition efficiency) and the geometric characteristics
(penetration, width and reinforcement) of the bead.
It was found that the GA can be a powerful tool
in experimental welding optimization, even when the experimenter does not have
a model for the process. The most important response (depth of penetration)
had a difference from its target lower than 4%.
However, the optimization by GA technique requires
a good setting of its own parameters, such as population size, number of generations,
etc. Otherwise, there is a risk of an insufficient sweeping of the search space.
In addition, it is suggested the use of conventional statistical projects to
investigate the space around the conditions found by the GA, in order to obtain
models and/or perform a fine-tuning of the optimal parameters.
References
Busacca, P. G., Marseguerra, M. And Zio, E., 2001,
"Multiobjective Optimization by Genetic Algorithms: Application to Safety
Systems", Reliability Engineering and System Safety, No. 72, pp. 59-74.
&&&&&&&&[  ]Correia, D. S. & Ferraresi, V. A., 2001, "Metodologia
de Custo da N&o Qualidade Aplicada na Soldagem", Anais do XVI Congressso
Brasileiro de Engenharia Mec&nica, Uberl&ndia, Brazil.&&&&&&&&[  ]Goldberg, D. E., 1989, "Genetic Algorithms
in Search, Optimization and Machine Learning", Addison-Wesley, 435p.&&&&&&&&[  ]Holland, J. H., 1975, "Adaptation in Natural
and Artificial System", Ann Arbor, MI: University of Michigan Press, 406p.&&&&&&&&[  ]Kim, D. and Rhee, S., 2001, "Optimization
of Arc Welding Process Parameters using a Genetic Algorithm", Welding Journal,
July, pp. 184-189.&&&&&&&&[  ]Myers, R. H. and Montgomery, D. H., 1995, "Response
Surface Methodology", John Wiley & Sons, USA, 705p.&&&&&&&&[  ]Sette, S., Boullart, L. and Langenhove, L., 1996,
"Optimising a Production Process by a Neural Network/Genetic Algorithm Approach",
Engng. Applic. Artif. Intell., Vol. 9, No. 6, pp. 681-689.&&&&&&&&[  ]&
Presented at COBEF 2003 – II Brazilian
Manufacturing Congress, 18-21 May 2003, Uberl&ndia, MG. Brazil. Paper
accepted October, 2003. Technical Editor: Alisson Rocha Machado.}