optimization of welding process parameter

8/2/2019 Optimization of Welding Process Parameter

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CHAPTER 1

INTRODUCTION


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INTRODUCTION

Joints of dissimilar metal combinations are employed in different

applications requiring certain special combination of properties as well as to

save cost incurred towards costly and scarce materials. Conventional fusion

welding of many such dissimilar metal combinations is not feasible owing to

the formation of brittle and low melting intermetallics due to metallurgical

incompatibility, wide difference in melting point, thermal mismatch, etc.

Solid-state welding processes that limit extent of intermixing are generally

employed in such situations. Friction welding is one such solid-state welding

process widely employed in such situations. The joining of materials by

conventional welding techniques becomes difficult if the physical properties

such as melting temperature and thermal expansion coefficient of the two

materials differ a lot, as it is necessary to have controlled melting on both

sides of weld joints simultaneously. Even if this criterion is met, it may notbe possible to have an appropriate joint when the two materials are

metallurgically incompatible. At the same time, the welding process,

generally involves many input and output parameters. To produce the joints

with highest quality, the proper process parameters have to be selected. The

suitable process parameters, to obtain the required output, need many

experiments and thus make the process to consume more time and money.

Here the interest is to screen the experiments using the computational

methods to analyze and optimize friction welding and other welding process

parameters respectively.


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1.1.

FRICTION WELDING PROCESS

Friction welding is a class of solid-state welding processes that generates heat

through mechanical friction between a moving work piece and a stationary

component, with the addition of a lateral force called "upset" to plastically

displace and fuse the materials. Technically, because no melt occurs, friction

welding is not actually a welding process in the traditional sense, but a

forging technique. However, due to the similarities between these techniques

and traditional welding, the term has become common. Friction welding is

used with metals and thermoplastic in a wide variety of aviation and

automotive applications.

1.1.1 PROCESS MECHANISM

The mechanism of friction welding is schematically illustrated in

Fig. 1.2 for better understanding of the process. As the pieces are initially

contacted, micro asperities come into contact area.

i. One component is rotated while the other is advanced into pressurecontact with it.

ii. Heat is produced at the faying surfaces. Overheating of metals cannotoccur as the weld zone temperature is always stabilized below melting

point.

iii.Softened material begins to extrude in response to the applied pressure,creating an annular upset.

iv.Heat is conducted away from the interfacial area for forging to takeplace.


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v. Rotation is stopped and a forge force is applied to complete the weld.vi.The joint undergoes hot working to form a homogenous, full surface,full diameter, high-integrityweld.

Fig 1.1. Process mechanism of the friction welding process.

1.2. INTRODUCTION TO OPTIMIZATION:

Optimization is getting the best under the given circumstances.

Optimization is the process of getting the maximum or minimum value of thefunction. (S.S. Roa, 2009). Best in the sense may be maximum or minimum

under the given circumstances. One may need the maximum salary or the

minimum expense. Optimizationcan be defined as the process of finding the

conditions that give the maximum or minimum value of a function.


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1.2.1.STATEMENT OF AN OPTIMIZATION PROBLEM:

Optimization problem may be stated as follows (S.S.Roa, 2009):Find

X={ x1, x2, x3, x4 xn } which minimize or maximize the

function f (X) ,

Subjected to constraints,

gi(X) 0, i= 1, 2, 3, 4, n

li (X) = 0, j = 1, 2, 3,4., n

Where,

X is an ndimensional design vector,

f (X) is the objective function,

gi (X) is the inequality constraints

lj (X) is the equality constraints

The above is said to be unconstraint optimization problem.

The constrained optimization technique is stated as follows:

Find

X={ x1, x2, x3, x4 xn } which minimize or maximize the function

f(X)

1.2.2.TYPES OF OPTIMIZATION PROBLEM:

The various methods of optimization are defined as the

follows:

i. Calculus methodsii. Calculus of variations

iii. Nonlinear programmingiv. Geometric programming


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v. Quadratic programmingvi. Linear programming

vii.

Dynamic programmingviii. Integer programming

ix. Stochastic programmingx. Separable programming

xi. Multi objective programmingThe above is said to be traditional optimization technique.

Following are some of the modern optimization techniques:

i. Genetic algorithmsii. Simulated annealing

iii. Ant colony optimizationiv. Particle swarm optimizationv. Neural networks

vi. Fuzzy optimization.

1.2.3.APPLICATION OF OPTIMIZATION TECHNIQUE:

Optimization techniques are used in the application such as

design of aircraft and aerospace structures for minimum weight design of

civil engineering structures such as frames, foundations, bridges, towers,

chimneys, and dams for minimum cost, optimum design of linkages, cams,

gears, machine tools, and other mechanical components, Selection of

machining conditions in metal-cutting processes for minimum production

cost, design of material handling equipment, such as conveyors, trucks,


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and cranes, for minimum cost, design of pumps, turbines, and heat transfer

equipment for maximum efficiency, shortest route taken by a salesperson

visiting various cities during one tour, optimal production planning,controlling, and scheduling, analysis of statistical data and building

empirical models from experimental results to obtain the most accurate,

optimum design of control systems.(S.S. Roa, 2009).


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CHAPTER 2

GENETIC ALGORITHM


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GENETIC ALGORITHM

An algorithm is a series of steps for solving a problem. A genetic

algorithm is a problem solving method that uses genetics as its model of

problem solving. Its a search technique to find approximate solutions to

optimization and search problems. Basically, an optimization problem looks

really simple. One knows the form of all possible solutions corresponding to a

specific question. The set of all the solutions that meet this form constitute the

search space. The problem consists in finding out the solution that fits the

best, i.e. the one with the most payoffs, from all the possible solutions. Each

solution is represented through a chromosome, which is just an abstract

representation. Coding all the possible solutions into a chromosome is the

first part, but certainly not the most straightforward one of a Genetic

Algorithm. A set of reproduction operators has to be determined, too.

Reproduction operators are applied directly on the chromosomes, and are

used to perform mutations and recombination over solutions of the problem.

Appropriate representation and reproduction operators are really something

determinant, as the behavior of the GA is extremely dependant on it.

Frequently, it can be extremely difficult to find a representation, which

respects the structure of the search space and reproduction operators, which

are coherent and relevant according to the properties of the problems.

Selection is supposed to be able to compare each individual in the

population. Selection is done by using a fitness function. Each chromosome

has an associated value corresponding to the fitness of the solution it

represents. The fitness should correspond to an evaluation of how good the

candidate solution is. The optimal solution is the one, which maximizes the


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fitness function. Genetic Algorithms deal with the problems that maximize

the fitness function. But, if the problem consists in minimizing a cost

function, the adaptation is quite easy. Either the cost function can betransformed into a fitness function, for example by inverting it; or the

selection can be adapted in such way that they consider individuals with low

evaluation functions as better. Once the reproduction and the fitness function

have been properly defined, a Genetic Algorithm is evolved according to the

same basic structure. It starts by generating an initial population of

chromosomes. This first population must offer a wide diversity of genetic

materials. The gene pool should be as large as possible so that any solution of

the search space can be engendered. Generally, the initial population is

generated randomly. Then, the genetic algorithm loops over an iteration

process to make the population evolve. Each iteration consists of the

following steps:

i. SELECTION: The first step consists in selecting individuals forreproduction. This selection is done randomly with a probability

depending on the relative fitness of the individuals so that best ones are

often chosen for reproduction than poor ones.

ii. REPRODUCTION: In the second step, offspring are bred by theselected individuals. For generating new chromosomes, the algorithm

can use both recombination and mutation.

iii. EVALUATION: Then the fitness of the new chromosomes isevaluated.


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iv. REPLACEMENT: During the last step, individuals from the oldpopulation are killed and replaced by the new ones.

The general optimization procedure using a genetic algorithm is

Step 1: Choose a coding to represent problem parameters, a selectionoperator, a crossover operator and a mutation operator. Choose

population size n, crossover probability pc, and mutation probability

pm. Initialize a random population of strings of size.. Choose a

maximum allowable generationnumber tmax. Set t=0.

Step 2: Evaluate each string in the population.

Step 3: If t > tmax or other termination criteria is satisfied, terminate.

Step 4: Perform reproductions on the population.

Step 5: Perform crossovers on pair of strings with probabilitypc.

Step 6: Perform mutations on strings with probabilitypm.

Step 7: Evaluate strings in the new population. Set t = t+ 1 and go toStep 3.


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The flowchart showing the process of GA is as shown in Fig. 2.1

YES

NO

FIG 2.1. FLOW CHART FOR GENETIC ALGORITHM

START

CREATE INITIAL RANDOM

POPULATION

EVALUATE FITNESS FOR

EACH

POPULATION

STORE BEST INDIVIDUAL

CREATING MATING POOL

CREATE NEXT GENERATIONBY APPLYING

CROSSOVER

OPTIMALOR GOOD

SOLUTION

REPRODUCE AND IGNORE

FEW

POPULATIONS

PERFORM MUTATION

STOP


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In short, the basic four steps used in simple Genetic Algorithm to solve a

problem are,

The representation of the problem

The fitness calculation Various variables and parameters involved in controlling the algorithm The representation of result and the way of terminating the algorithm

2.1. COMPARISON OF GENETIC ALGORITHM WITH OTHER

OPTIMIZATION TECHNIQUES:

The principle of GAs is simple: imitate genetics and natural selection

by a computer program: The parameters of the problem are coded most

naturally as a DNA-like linear data structure, a vector or a string. Sometimes,

when the problem is naturally two or three-dimensional also corresponding

array structures are used. A set, called population, of these problem dependent

parameter value vectors is processed by GA. To start there is usually a totally

random population, the values of different parameters generated by a random

number generator. Typical population size is from few dozens to thousands.

To do optimization we need a cost function or fitness function as it is usually

called when genetic algorithms are used. By a fitness function we can select

the best solution candidates from the population and delete the not so good

specimens. The nice thing when comparing GAs to other optimization

methods is that the fitness function can be nearly anything that can be

evaluated by a computer or even something that cannot! In the latter case it

might be a human judgment that cannot be stated as a crisp program, like in

the case of eyewitness, where a human being selects among the alternatives

generated by GA. So, there are not any definite mathematical restrictions on

the properties of the fitness function. It may be discrete, multimodal etc. The


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main criteria used to classify optimization algorithms are as follows:

continuous / discrete, constrained / unconstrained and sequential / parallel.

There is a clear difference between discrete and continuous problems.Therefore it is instructive to notice that continuous methods are sometimes

used to solve inherently discrete problems and vice versa. Parallel algorithms

are usually used to speed up processing. There are, however, some cases in

which it is more efficient to run several processors in parallel rather than

sequentially. These cases include among others such, in which there is high

probability of each individual search run to get stuck into a local extreme.

Irrespective of the above classification, optimization methods can be further

classified into deterministic and non-deterministic methods. In addition

optimization algorithms can be classified as local or global. In terms of

energy and entropy local search corresponds to entropy while global

optimization depends essentially on the fitness i.e. energy landscape.

Genetic algorithm differs from conventional optimization techniques in

following ways:

i. GAs operate with coded versions of the problem parameters rather thanparameters themselves i.e., GA works with the coding of solution set

and not with the solution itself.

ii. Almost all conventional optimization techniques search from a singlepoint but GAs always operate on a whole population of points(strings)

i.e., GA uses population of solutions rather than a single solution from

searching. This plays a major role to the robustness of genetic

algorithms. It improves the chance of reaching the global optimum and

also helps in avoiding local stationary point.


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iii. GA uses fitness function for evaluation rather than derivatives. As aresult, they can be applied to any kind of continuous or discrete

optimization problem. The key point to be performed here is to identifyand specify a meaningful decoding function.

iv. GAs use probabilistic transition operates while conventional methodsfor continuous optimization apply deterministic transition operates i.e.,

GAs does not use deterministic rules.

2.2. ADVANTAGES OF GENETIC ALGORITHM

The advantages of genetic algorithm includes,

Parallelism Liability Solution space is wider The fitness landscape is complex Easy to discover global optimum The problem has multi objective function Only uses function evaluations. Easily modified for different problems. Handles noisy functions well. Handles large, poorly understood search spaces easily Good for multi-modal problems Returns a suite of solutions. Very robust to difficulties in the evaluation of the objective function. They require no knowledge or gradient information about the response

surface


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Discontinuities present on the response surface have little effect onoverall optimization performance

They are resistant to becoming trapped in local optima.

They perform very well for large-scale optimization problems Can be employed for a wide variety of optimization problems

2.3. LIMITATION OF GENETIC ALGORITHM

The limitation of genetic algorithm includes,

The problem of identifying fitness function Definition of representation for the problem Premature convergence occurs The problem of choosing the various parameters like the size of the

population,

mutation rate, cross over rate, the selection method and its strength. Cannot use gradients. Cannot easily incorporate problem specific information Not good at identifying local optima No effective terminator. Not effective for smooth unimodel functions Needs to be coupled with a local search technique. Have trouble finding the exact global optimum Require large number of response (fitness) function evaluations Configuration is not straightforward


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2.4. APPLICATIONS OF GENETIC ALGORITHM

Genetic algorithms have been used for difficult problems (such as NP-hardproblems), for machine learning and also for evolving simple programs. They

have been also used for some art, for evolving pictures and music. A few

applications of GA are as follows:

Nonlinear dynamical systemspredicting, data analysis Robot trajectory planning Evolving LISP programs (genetic programming) Strategy planning Finding shape of protein molecules TSP and sequence scheduling Functions for creating images Controlgas pipeline, pole balancing, missile evasion, pursuit Designsemiconductor layout, aircraft design, keyboard configuration,

communication networks

Schedulingmanufacturing, facility scheduling, resource allocation Machine LearningDesigning neural networks, both architecture and

weights, improving classification algorithms, classifier systems

Signal Processingfilter design Combinatorial Optimizationset covering, traveling salesman (TSP),

Sequence scheduling, routing, bin packing, graph coloring and

partitioning.

2.5. TERMINOLOGIES AND OPERATORS OF GA

Genetic Algorithm uses a metaphor where an optimization problem

takes the place of an environment and feasible solutions are considered as


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individuals living in that environment. In genetic algorithms, individuals are

binary digits or of some other set of symbols drawn from a finite set. As

computer memory is made up of array of bits, anything can be stored in acomputer and can also be encoded by a bit string of sufficient length. Each of

the encoded individual in the population can be viewed as a representation,

according to an appropriate encoding of a particular solution to the problem.

For Genetic Algorithms to find a best optimum solution, it is necessary to

perform certain operations over these individuals. This part of the chapter

discusses the basic terminologies and operators used in Genetic Algorithms to

achieve a good enough solution for possible terminating conditions.

2.6. INDIVIDUALS

An individual is a single solution. Individual groups together two forms of

solutionsas given below:

1. The chromosome, which is the raw genetic information (genotype)that the GAdeals.

2. The phenotype, which is the expressive of the chromosome in the termsof themodel.

A chromosome is subdivided into genes. A gene is the GAs

representation of a single factor for a control factor. Each factor in the

solution set corresponds to gene in the chromosome\

2.7. GENES

Genes are the basic instructions forbuilding a Generic Algorithms. A

chromosomeis a sequence of genes. Genes may describe a possible solution

to a problem, without actually being the solution. A gene is a bit string of

arbitrary lengths. The bit string is a binary representation of number of


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intervals from a lower bound. Agene is the GAs representation of a single

factor value for a control factor, where control factor must have an upper

bound and lower bound.

2.8. FITNESS

The fitness of an individual in a genetic algorithm is the value of an

objective function for its phenotype. For calculating fitness, the chromosome

has to be first decoded and the objective function has to be evaluated. The

fitness not only indicates how good the solution is, but also corresponds to

how close the chromosome is to the optimal one.

2.9. POPULATIONS

A population is a collection of individuals. A population consists of a

number of individuals being tested, the phenotype parameters defining the

individuals and some information about search space.

2.10. DATA STRUCTURES

The main data structures in GA are chromosomes, phenotypes,

objective function values and fitness values. This is particularly easy

implemented when using MATLAB package as a numerical tool. An entire

chromosome population can be stored in a single array given the number of

individuals and the length of their genotype representation. Similarly, the

design variables, or phenotypes that are obtained by applying some mapping

from the chromosome representation into the design space can be stored in a

single array. The actual mapping depends upon the decoding scheme used.


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The objective function values can be scalar or vectorial and are necessarily

the same as the fitness values. Fitness values are derived from the object

function using scaling or ranking function and can be stored as vectors.

2.11. SEARCH STRATEGIES

The search process consists of initializing the population and then

breeding new individuals until the termination condition is met. There can be

several goals for the search process, one of which is to find the global optima.

This can never be assured with the types of models that GAs work with.

There is always a possibility that the next iteration in the search would

produce a better solution. In some cases, the search process could run for

years and does not produce any better solution than it did in the first little

iteration. Another goal is faster convergence. When the objective function is

expensive to run, faster convergence is desirable, however, the chance of

converging on local, and possibly quite substandard optima is increased.

Apart from these, yet another goal is to produce a range of diverse, but still

good solutions. When the solution space contains several distinct optima,

which are similar in fitness, it is useful to be able to select between them,

since some combinations of factor values in the model may be more feasible

than others. Also, some solutions may be more robust than others.

2.12. ENCODING

Encoding is a process of representing individual genes. The process can

be performed using bits, numbers, trees, arrays, lists or any other objects. The

encoding depends mainly on solving the problem. For example, one can

encode directly real or integer numbers


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2.12.1. BINARY ENCODING

Each chromosome encodes a binary (bit) string. Each bit in the stringcan represent some characteristics of the solution. Every bit string therefore is

a solution but not necessarily the best solution. Another possibility is that the

whole string can represent a number. The way bit strings can code differs

from problem to problem Binary encoding gives many possible chromosomes

with a smaller number of alleles. On the other hand this encoding is not

natural for many problems and sometimes corrections must be made after

genetic operation is completed. Binary coded strings with 1s and 0s are

mostly used. The length of the string depends on the accuracy.

In this,

Integers are represented exactly Finite number of real numbers can be represented Number of real numbers represented increases with string length

The other encoding methods are

i. Octal Encodingii. Hexadecimal Encoding

iii. Permutation Encodingiv. Value Encodingv. Tree Encoding

2.13. BREEDING

The breeding process is the heart of the genetic algorithm. It is in this

process, the search process creates new and hopefully fitter individuals. The

breeding cycle consists of three steps:


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a. Selecting parents.b. Crossing the parents to create new individuals (offspring or children).c.

Replacing old individuals in the population with the new ones.

2.13.1. SELECTION

Selection is the process of choosing two parents from the population

for crossing.After deciding on an encoding, the next step is to decide how to

perform selection i.e., how to choose individuals in the population that will

create offspring for the next generation and how many offspring each will

create. The purpose of selection is to emphasize fitter individuals in the

population in hopes that their off springs havehigher fitness. Chromosomes

are selected from the initial population to be parents for reproduction. The

problem is how to select these chromosomes.

Selection is a method that randomly picks chromosomes out of the

population according to their evaluation function. The higher the fitness

function, the more chance an individual has to be selected. The selection

pressure is defined as the degree to which the better individuals are favored.

The higher the selection pressured, the more the better individuals are

favored. This selection pressure drives the GA to improve the population

fitness over the successive generations. Selection has to be balanced with

variation form crossover and mutation. Too strong selection means sub

optimal highly fit individuals will take over the population, reducing the

diversity needed for change and progress; too weak selection will result in too

slow evolution. The various selection methods are discussed as follows:


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ROULETTE WHEEL SELECTION

Roulette selection is one of the traditional GA selection techniques.The commonlyused reproduction operator is the proportionate reproductive

operator where a string is selected from the mating pool with a probability

proportional to the fitness. Theprinciple of roulette selection is a linear search

through a roulette wheel with theslots in the wheel weighted in proportion to

the individuals fitness values. A target value is set, which is a random

proportion of the sum of the fit nesses in the population.The population is

stepped through until the target value is reached. This is onlya moderately

strong selection technique, since fit individuals are not guaranteed to be

selected for, but somewhat have a greater chance. A fit individual will

contribute more to the target value, but if it does not exceed it, the next

chromosome in linehas a chance, and it may be weak. It is essential that the

population not be sorted by fitness, since this would dramatically bias the

selection. The above described Roulette process can also be explained as

follows: The expected value of an individual is that fitness divided by the

actual fitness of the population. Each individual is assigned a slice of the

roulette wheel, the size of the slicebeing proportional to the individuals

fitness. The wheel is spun N times, where N is the number of individuals in

the population. On each spin, the individual under the wheels marker is

selected to be in the pool of parents for the next generation Roulette wheel

selection is easier to implement but is noisy. The rate of evolutiondepends on

the variance of fitnesss in the population.

Roulette wheel selection is easier to implement but is noisy. The rate of

evolution depends on the variance of fitnesss in the population.


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RANDOM SELECTION

This technique randomly selects a parent from the population. In terms

of disruptionof genetic codes, random selection is a little more disruptive, onaverage, thanroulette wheel selection.

RANK SELECTION

The Roulette wheel will have a problem when the fitness values differ

very much. If the best chromosome fitness is 90%, its circumference occupies

90% of Roulette wheel, and then other chromosomes have too few chances to

be selected. Rank Selection ranks the population and every chromosome

receives fitness from the ranking. The worst has fitness 1 and the best has

fitness N. It results in slow convergence but prevents too quick convergence.

It also keeps up selection pressure when the fitness variance is low. It

preserves diversity and hence leads to a successful search. In effect, potential

parents are selected and a tournament is held to decide which of the

individuals will be the parent. There are many ways this can be achieved and

two suggestions are,

1. Select a pair of individuals at random. Generate a random number, R,between 0 and 1. IfR < r use the first individual as a parent. If the

R>=r then use the second individual as the parent. This is repeated to

select the second parent. The value ofris a parameter to this method.

2. Select two individuals at random. The individual with the highestevaluation becomes the parent. Repeat to find a second parent.

the other selection method are:


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Tournament Selection Boltzmann Selection

Stochastic Universal Sampling

2.14. CROSSOVER (RECOMBINATION)

Crossover is the process of taking two parent solutions and producing

from them a child. After the selection (reproduction) process, the population

is enriched with better individuals. Reproduction makes clones of good

strings but does not create new ones. Crossover operator is applied to the

mating pool with the hope that it creates a better offspring.

1. Crossover is a recombination operator that proceeds in three steps:2. The reproduction operator selects at random a pair of two individual

strings for the mating.

3. A cross site is selected at random along the string length.Finally, the position values are swapped between the two strings following

the cross site. That is, the simplest way how to do that is to choose randomly

some crossover point and copy everything before this point from the first

parent and then copy everything after the crossover point from the other

parent. The various crossover techniques are discussed as follows:

2.14.1. SINGLE POINT CROSSOVER

The traditional genetic algorithm uses single point crossover, where the

two mating chromosomes are cut once at corresponding points and the

sections after the cuts exchanged. Here, a cross-site or crossover point is

selected randomly along the lengthof the mated strings and bits next to the


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cross-sites are exchanged. If appropriate siteis chosen, better children can be

obtained by combining good parents else it severelyhampers string quality.\

2.14.2. TWO POINT CROSSOVER

Apart from single point crossover, many different crossover algorithms

have been devised, often involving more than one cut point. It should be

noted that adding furthercrossover points reduces the performance of the GA.

The problem with addingadditional crossover points is that building blocks

are more likely to be disrupted. However, an advantage of having more

crossover points is that the problem spacemay be searched more thoroughly.

2.14.3. MULTI-POINT CROSSOVER

There are two ways in this crossover. One is even number of cross-sites

and the otherodd number of cross-sites. In the case of even number of cross-

sites, cross-sites are selected randomly around a circle and information is

exchanged. In the case ofodd number of cross-sites, a different cross-point is

always assumed at the stringbeginning.

2.14.4. UNIFORM CROSSOVER

Uniform crossover is quite different from the N-point crossover. Each

gene in the offspring is created by copying the corresponding gene from one

or the other parent chosen according to a random generated binary crossover

mask of the same length as the chromosomes. Where there is a 1 in the

crossover mask, the gene is copied from the first parent, and where there is a

0 in the mask the gene is copied from the second parent. A new crossover


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mask is randomly generated for each pair of parents. Offspring, therefore

contain a mixture of genes from each parent. The number of effective

crossing point is not fixed, but will average L/2 (where L is the chromosomelength). The other type of cross over are:

Three Parent Crossover Crossover with Reduced Surrogate Shuffle Crossover Precedence Preservative Crossover Ordered Crossover Partially Matched Crossover

2.14.5. CROSSOVER PROBABILITY

The basic parameter in crossover technique is the crossover probability

(Pc). Crossover probability is a parameter to describe how often crossover

will be performed. If there is no crossover, offspring are exact copies of

parents. If there is crossover, offspring are made from parts of both parents

chromosome. If crossover probability is 100%, then all offspring are made by

crossover. If it is 0%, whole new generation is made from exact copies of

chromosomes from old population (but this does not mean that the new

generation is the same!). Crossover is made in hope that new chromosomes

will contain good parts of old chromosomes and therefore the new

chromosomes will be better. However, it is good to leave some part of old

population survive to next generation.


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2.15. MUTATION

After crossover, the strings are subjected to mutation. Mutationprevents the algorithmto be trapped in a local minimum. Mutation plays the

role of recovering thelost genetic materials as well as for randomly disturbing

genetic information. It is an insurance policy against the irreversible loss of

genetic material. Mutation has traditionally considered as a simple search

operator. If crossover is supposed toexploit the current solution to find better

ones, mutation is supposed to help for the exploration of the whole search

space. Mutation is viewed as a background operator to maintain genetic

diversity in the population. It introduces new genetic structures in the

population by randomly modifying some of its building blocks. Mutation

helps escape from local minimas trap and maintains diversity in the

population. It also keeps the gene pool well stocked, and thus ensuring

periodicity. A search space is said to be ergodic if there is a non-zero

probability of generating any solution from any population state. There are

many different forms of mutation for the different kinds of representation. For

binary representation, a simple mutation can consist in inverting the value of

each gene with a small probability. The probability is usually taken about 1/L,

where L is the length of the chromosome. It is also possible to implement

kind of hill-climbing mutation operators that do mutation only if it improves

the quality of the solution. Such an operator can accelerate the search. But

care should be taken, because it might also reduce the diversity in the

population and makes the algorithm converge toward some local optima.

Mutation of a bit involves flipping a bit, changing 0 to 1 and vice-versa.


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2.15.1. FLIPPING

Flipping of a bit involves changing 0 to 1 and 1 to 0 based on amutation chromosome generated

2.15.2. INTERCHANGING

Two random positions of the string are chosen and the bits

corresponding to those positions are interchanged.

2.15.3. REVERSING

A random position is chosen and the bits next to that position are

reversed and child chromosome is produced.

2.15.4. MUTATION PROBABILITY

The important parameter in the mutation technique is the mutation

probability (Pm). The mutation probability decides how often parts of

chromosome will be mutated.If there is no mutation, offspring are generated

immediately after crossover (or directly copied) without any change. If

mutation is performed, one or more parts ofa chromosome are changed. If

mutation probability is 100%, whole chromosome is changed, if it is 0%,

nothing is changed. Mutation generally prevents the GA from falling into

local extremes. Mutation should not occur very often, because then GAwill

in fact change to random search.


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2.16. REPLACEMENT

Replacement is the last stage of any breeding cycle. Two parents aredrawn froma fixed size population, they breed two children, but not all four

can return to the population, so two must be replaced i.e., once off springs are

produced, a method must determine which of the current members of the

population, if any, should be replaced by the new solutions. The technique

used to decide which individual stayin a population and which are replaced in

on a par with the selection in influencing convergence. Basically, there are

two kinds of methods for maintaining the population; generational updates

and steady state updates.

2.16.1. RANDOM REPLACEMENT

The children replace two randomly chosen individuals in the

population. The parentsare also candidates for selection. This can be useful

for continuing the searchin small populations, since weak individuals can be

introduced into the population.

2.16.2. WEAK PARENT REPLACEMENT

In weak parent replacement, a weaker parent is replaced by a strong

child. With thefour individuals only the fittest two, parent or child, return to

population. This processimproves the overall fitness of the population when

paired with a selection technique that selects both fit and weak parents for

crossing, but if weak individuals and discriminated against in selection the

opportunity will never raise to replace them.


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2.16.3. BOTH PARENTS

Both parents replacement is simple. The child replaces the parent. Inthis case, eachindividual only gets to breed once. As a result, the population

and genetic material moves around but leads to a problem when combined

with a selection technique that strongly favors fit parents: the fit breed and

then are disposed of.

2.17. SEARCH TERMINATION (CONVERGENCE CRITERIA)

In short, the various stopping condition are listed as follows:

Maximum generationsThe genetic algorithm stops when thespecified numbers of generations have evolved.

Elapsed timeThe genetic process will end when a specified time haselapsed. Note: If the maximum number of generation has been reached

before the specified time has elapsed, the process will end.

No change in fitnessThe genetic process will end if there is nochange to the populations best fitness for a specified number of

generations. Note: If the maximum number of generation has been

reached before the specified number of generation with no changes has

been reached, the process will end.

Stall generationsThe algorithm stops if there is no improvement inthe objective function for a sequence of consecutive generations of

length Stall generations.


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Stall time limitThe algorithm stops if there is no improvement in theobjective function during an interval of time in seconds equal to Stall

time limit. The termination or convergence criterion finally brings the

search to a halt. The following are the few methods of termination

techniques

2.17.1. BEST INDIVIDUAL

A best individual convergence criterion stops the search once the

minimum fitnessin the population drops below the convergence value. This

brings the search to a faster conclusion guaranteeing at least one good

solution.

2.17.2. WORST INDIVIDUAL

Worst individual terminates the search when the least fit individuals in

the population have fitness less than the convergence criteria. This guarantees

the entire population to be of minimum standard, although the best individual

may not be significantly better than the worst. In this case, a stringent

convergence value may never be met, in which case the search will terminate

after the maximum has been exceeded.

2.17.3. SUM OF FITNESS

In this termination scheme, the search is considered to have satisfaction

converged when the sum of the fitness in the entire population is less than or


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equal to the convergence value in the population record. This guarantees that

virtually all individuals in the population will be within a particular fitness

range, although it is better to pair this convergence criteria with weakest genereplacement, otherwise a few unfit individuals in the population will blow out

the fitness sum. The population size has to be considered while setting the

convergence value.

2.17.4. MEDIAN FITNESS

Here at least half of the individuals will be better than or equal to the

convergence value, which should give a good range of solutions to choose

from.


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CHAPTER 3

LITERATURE REVIEW


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LITERATURE REVIEW

Sathiya.A et.,al., (2008) applied successfully to process similarjoints of stainless steel (AISI 304).The friction processed joints exhibited

comparable strength with the base material and joint strength decreased with

an increase in the friction time. The material shear flow and dimples at the

fractured surface confirms the ductile mode of failure of joints during tensile

testing. Hardness at the joint zone increases with the increase in friction time.

The increase in hardness at the joint zone is due to the thermal history of the

joining process. Friction welding method can be applied successfully to

process similar joints of stainless steel (AISI 430).The processed joints

exhibited better mechanical and metallurgical characteristics, than the fusion

joints. Because of the solid state bonding technique, the problems associated

with fusion joining are minimized in the case of friction welding. The joints

exhibited 95.52% of parent materials tensile strength. The tensile specimen

failures were associated primarily with the weld interface region. The fracture

is predominantly associated with material (shear like) flow. The toughness of

the friction welded ferritic stainless steel is comparatively higher than fusion

processed joints due to the refinement of grain size at the weld zone.

The ultimate capacity of the arc spot welding was modeled based

on the experimental data using Artificial neural network in the literature(Abdulkadir Cevik et,al., 2008). The main objective in the study is to obtain

the explicit formulation of nominal shear stress as a function of the geometric,

and the mechanical properties of the spot welding. The proposed model is

obtained using the Neural network (NN) tool box of MATLAB. The

statistical analysis of the proposed model and the experimental is being

carried out for the train sets and test sets for which the correlation coefficient

is found as 0.984 and 0.969 respectively. The parametric study is made to


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investigate the effect of changing geometric parameters and the yield strength

on the nominal shear strength of arc spot welds.

An intelligent system was being developed by I.S. Kim

et.al(2005).,using MATLAB/SIMULINK software. The mathematical model

incorporating the different welding parameters and complex geometrical

features is developed based on the regression and the neural networks. In the

method of modeling using the multiple regression models, the Analysis Of

Variance technique (ANOVA) is performed on the factorial design to

quantify the effect of welding parameters. Then the multiple correlation

coefficients and the Fratio were to measure the goodness of fit. In the

method of modeling using the ANN method, Back-Propagation (BP) method

is being used and at the same time the generalized delta rule is used as the

learning algorithm. With the learning rate of 0.6 and the momentum term of

0.9, the network is trained for 2,00,000 iteration. The error between the

desired and the actual output is less than 0.001 at the end of the trainingprocess. By comparing the above two methods, the neural network model is

found to be comparatively best, which is capable of making the prediction of

the experimental result with the reasonable accuracy.

According to Cemal Meran, ( 2006) welding was the major joining

process in the industry. Three main parameters such as welding current,

welding velocity, and arc length have a big influence on the quality welding.

The work by Cemal Meran(2006), deal with the use of stochastic search

process, which is the basis for the genetic algorithms in developing estimation

of the welding parameters for the joined brass plates. The obtained result is

being compared with the experimental value for the verification, ehich

showed a good agreement.


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In order to evaluate the effect of process parameters, such as tool

rotational speed, transverse speed and axial force, on the tensile strength of

friction welded RDE-40 aluminium alloy, the Taguchis parametric designand optimization approach was used( A. K. Lakshminarayanan., et.al., 2008).

Through the Taguchis parametric design approach, the optimum level of the

process parameter was determined. The optimal value is found to be 303MPa.

Rather than the wellknown effect of the process parameter on the

quality of the welding, the study made by Serder et.al.,(2008) focuses on the

sensitivity analysis of the process parameters and fine tuning requirements of

the parameters for optimum weld bead geometry. Changeable process

parameters such as welding current, welding voltage and welding speed are

used as design variables. Experimental work is based on the three level

factorial design and the mathematical modeling is based on the multiple

curvilinear regression analysis. Effect of all the three design parameters on

the bead width and bead height show that small changes in theses parametershave very important role in the quality of welding operation.

Conventional regression analysis were carried out by Parikshit

Dutta et.al.,(2007), on some of the experimental data of a tungsten inert gas

(TIG) welding process parameters to find its effect. At the same time,

Artificial Neural Network (ANN) concept is used to find the effect of various

process parameters, in which thousand training data were employed. Back

Prorogation Neural Network (BPNN) and genetic neural system (GA-NN) are

the type of ANN which is used for the modeling purpose. The performance of

all those techniques were being compared and it is concluded that Neural

Network (NN) based approaches were seen to be more adoptive, which may

be due to the reasons that it is based on the principle of steepest descent

method.


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An empirical model was developed by G. Padmanaban et.al., to

predict the maximum tensile strength of AZ31B magnesium alloy. The

process parameter includes laser power, welding speed and focal position.The response surface methodology is used as an optimization tool to predict

the maximum tensile strength. The experiments were conducted based on a

three factor, three level, central composite face centered matrix with full

replication technique. A maximum tensile strength of 212MPa is obtained

under the welding conditions in which the laser power is 2.5Kw, welding

speed of 5.0m/min, and focal position of -1.5mm. Comparatively welding

speed is the most factor which has the greater influence compared to others.

The mathematical model was developed for the analysis and

simulation of the correlation between the friction stir welding of aluminium

plates and mechanical properties using Artificial Neural Network (ANN). The

model can be used to calculate mechanical properties of welded Al plates as

the function of weld speed and tool rotation speed. The combined effect ofweld speed and tool rotation speed on the mechanical properties of welded Al

plates was simulated and then the comparison between the measured and

calculated data. The calculated results were in good agreement with the

measured value.

The works carried out by G. Mahendran et al..,(2008) developed

diffusion bonding windows for joining AZ3113 Magnesium and AA 2024

Aluminium alloys. By the experimental work, the optimal process parameters

were found. The constructed bonding windows may act as the reference map

for selecting appropriate process parameters to obtain high strength bonds. It

is concluded by the author that the highest shear strength is obtained at the

bonding temperature of 4250C, the bonding pressure of 20MPa, and the

holding time of 45min due to the formation of optimum thick diffusion layer

at the interface of MgAl alloys.


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Further experimental studies were carried out by G.Mahendran et

al., (2010) on Magnesium and Copper using diffusion bonding methods.

Three factor five-level, central composite rotatable design matrix method isused for the purpose of designing the experiments. Empirical relationship

were developed in order to predict the diffusion layer thickness, hardness and

strength of the joint. The response surface methodology is used for

optimization and which is found as follows: joints fabricated at the bonding

pressure of 12MPa, the bonding time of 30mins, the bonding temperature of

4500C , which yields a maximum shear strength and bond strength of 66 and

81MPa respectively.

The diffusion bonding process studied in Nickel alloy, Su236, by

Ravishankar B et.al.,(2009) under the temperature ranges from 1123-1323k

and the compressive strength of 90% of yield strength, determined the

importance of the process parameters, the mechanism responsible for bonding

and the joint characteristic. The experimental results were compared with themodel developed by John Pilling. The mechanism of bonding was evaluated

by grain growth equation. The quality of bond was assessed using optical

metallographic and lap shear testing. The bonding mechanism and

composition of the interface were determined using quantified EPMA line

analysis.

The non conventional technique is being used by S. Suresh Kumar

at.al.,(2009). The ultrasonic A-scan method is used to evaluate the quality of

the welded joints and to study the interface properties of the joint of diffusion

bonded of Ti-6Al-4V, in that work the experiment is carried out for the given

material for the pressure ranges from 1.6 4MPa, and the bonding time of

4hours. The shear strength of the bond is to be correlated with the fractional

area bonded which is measured ng metallographic techniques and ultrasonic

technique, which is the non-destructive method.


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The optimal setting of the welding process parameters was

identified by Sathiya. P., et.al.,(2009) using non conventional technique such

as Genitic Algorithm, Simulated Annealing, Particle Swarm Optimization.Thje mathematical model relating the process parameters is developed using

Artificial Neural Network (ANN). The welding is carried out in Stainless

Steel (AISI 304). The optimized value obtained through genetic algorithm

closely resembles the experimental value.

TABLE 3.1. OPTIMIZED PROCESS PARAMETRE AND

EXPERIMENTAL VALUE (Sathiya. P., et.al., 2009)

Process parameter Optimized value Experimental value

Upsetting Pressure(UP) 17.7028 bar 17bar

Upsetting Time (UT) 4.2663 sec 4sec

Heating Time (HT) 35.1078 bar 35 bar

Upsetting Time 4.025 sec 4 sec


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CHAPTER 4

OPTIMIZING THE

PROCESS PARAMETERS

OF FRICTION WELDING

PROCESS


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OPTIMIZING THE PROCESS PARAMETERS OF FRICTION

WELDING PROCESS

4.1. PROCEDURE FOR OPTIMIZING THE PROCESS

PARAMETERS

The optimumprocess parameter of the friction welding process, is to be

found for maximizing the tensile strength of the Al/SS joint

(Purushothaman.L et.al, 2009). From the quoted literature, the experimentaldatas were taken since those work concentrate only on developing the

experimental matrix for the various process parameters and the tensile

strength of the Al/SS joint. From the experimental data the following work

are being carried out using MATLAB.

4.2. DEVELOPING THE MODEL BASED ON THE MULTIPLE

LINEAR REGRESSION METHOD:

4.2.1. FEASIBLE LIMITS AND THE EXPERIMENTAL DESIGN

MATRIX:

The feasible working limits of friction welding process parameters

from the literature is identified and presented in Tables 4.1. The experimental

design matrix is presented in table 4.


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Table 4.1. Working Limits of friction welding

# Parameter Notation Unit

Levels

(-2) (-1) 0 (+1) (+2)

1

Friction

Pressure Frp Ton 1 1.25 1.5 1.75 2

2Friction

Time Frt sec 3 3.75 4.5 5.25 6

3

Forging

Pressure Fop Ton 1 1.25 1.5 1.75 2

4

Forging

Time Fot sec 3 3.75 4.5 5.25 6

Due to wide range of factors, it was decided to use four factors, five

levels, central composite face centered design matrix to optimise the

experimental conditions, which fits the second order response surfaces very

accurately. Central composite rotational design matrix with the star points are

at the center of each face of factorial space was used, so = 2. This variety

requires 5 levels of each factor. The upper limit and lower limit of a factor

were coded as +2 and2 respectively


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Table 4.2. Experimental Design Matrix

Expt.

Coded values Original values

Tensile

strength(MPa)

A B C D TS

1 1 1 1 1 1.75 5.25 1.75 5.25 139

2 0 2 0 0 1.5 6 1.5 4.5 108

3 1 1 1 -1 1.75 5.25 1.75 3.75 106

4 -1 1 1 -1 1.25 5.25 1.5 3.75 88

5 0 0 0 2 1.5 4.5 1.5 6 143

6 1 -1 1 1 1.75 3.75 1.75 5.25 114

7 1 1 -1 -1 1.75 5.25 1.25 3.75 728 -1 1 -1 1 1.25 5.25 1.25 5.25 104

9 0 0 -2 0 1.5 4.5 1 4.5 64

10 0 0 0 0 1.5 4.5 1.5 4.5 186

11 0 0 0 0 1.5 4.5 1.5 4.5 190

12 0 0 2 0 1.5 4.5 2 4.5 112

13 -1 -1 -1 -1 1.25 3.75 1.25 3.75 36

14 -2 0 0 0 1 4.5 1.5 4.5 67

15 0 -2 0 0 1.5 3 1.5 4.5 68

16 -1 -1 1 -1 1.25 3.75 1.75 3.75 67

17 0 0 0 0 1.5 4.5 1.5 4.5 184

18 2 0 0 0 2 4.5 1.5 4.5 104

19 -1 1 1 1 1.25 5.25 1.75 5.25 123

20 1 1 -1 1 1.75 5.25 1.25 5.25 123

21 -1 -1 -1 1 1.25 3.75 1.25 5.25 84

22 0 0 0 0 1.5 4.5 1.5 4.5 185

23 -1 1 -1 -1 1.25 5.25 1.25 3.75 51

24 1 -1 1 -1 1.75 3.75 1.5 3.75 8625 1 -1 -1 -1 1.75 3.75 1.25 3.75 58

26 0 0 0 -2 1.5 4.5 1.5 3 62

27 1 -1 -1 1 1.75 3.75 1.25 1.75 102

28 0 0 0 0 1.5 4.5 1.5 4.5 184

29 -1 -1 1 1 1.25 3.75 1.75 5.25 98

30 0 0 0 0 1.5 4.5 1.5 4.5 180


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4.2.2. DEVELOPING RESPONSE SURFACE MODELS:

Response Surface Models are multivariate polynomial models. They

typically arise in the design of experiments where they are used to determine a set

of design variables that optimize a response.. Squared terms produce the simplest

models in which the response surface has a maximum or minimum, and so an

optimal response. Response surface models are multivariate polynomial models.

They typically arise in the design of, where they are used to determine a set of

design variables that optimize a response. The second order polynomial

(regression) equation used to represent the response surface Y is given by

Y = b0 + bi xi + bii xi2

+ bij xi xj +er

In order to estimate the regression coefficients, a number of experimental

design techniques are available.All the coefficients were obtained applying central

composite rotatable centered design using the MATLAB software package.

Tensile Strength = 184.83+9.29 * X1 + 10.04 * X2 + 11.96 * X3 + 20.21 *X4-

0.062 * X1 * X2 -0.69 * X1 * X3 - 0.69 * X1 * X4 + 1.31 * X2 * X3 + 1.31 * X2 *

X4- 4.31 * X3 * X4 -24.89 * X12- 24.26 * X2

2- 24.26 * X3

2- 20.64 * X4

2

4.2.3. OPTIMIZATION USING GENETIC ALGORITHM:

Genetic algorithms are computerized search and optimization algorithms

based on the mechanics of natural genetics and natural selection. GA is very


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different from traditional search and optimization methods used in engineering

problems. Because of its simplicity, ease of operation, minimum requirements and

global perspective, GA has been successfully used in a wide variety of problems.

GENETIC ALGORITHM TOOLBOX IN MATLAB

In order to estimate the maximum tensile strength, the following steps are to

be followed:

i. Firstly the model which is developed using response surface method whichrelates the tensile stength and the process parameter is typed in editor

window.

ii. Then the editor window is saved using any name.iii. After opening the optimization toolbox, the fitness function is entered with

the filename saved.

iv. Then the number of the variables is entered and the lower and the upperbound is entered.

v. If needed the parameters of the GA toolbox is changed, otherwise it is set asdefault and optimization is started to run

vi. After executing the problem, the results will be displayed.

GENETIC ALGORITHM PARAMETERS

i. The parameters used for GA is given below.ii. Population size = 100


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iii. Length of chromosome = 40iv. Selection operator: Roulette methodv.

Crossover operator : Single point operator

vi. Crossover probability = 0.9vii. Mutation probability = 0.01

viii. Fitness parameter : Tensile strength .

Fig 4.1. Editor window of the MATLAB


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Fig 4.2. GA TOOLBOX IN MATLAB


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4.3. OPTIMIZED PROCESS PARAMETERS OF FRICTION WELDING:

The optimized result and the maximized tensile strength of the

friction welding process parameters and the experimental results are shown as

follows:

Table 4.3. Optimized Process Parameters of Friction Welding

S.N

O

Process

paramete

r

Values of process parameter Tensile strength (MPa)

Predicted Experimental Predicted Experimental

1 Friction

pressure(ton)

1.525 1.5

192.674 1902 Friction

time (sec)

4.65 4.5

3 Forging

pressure

(ton)

1.55 1.5

4 Forging

time (sec)

4.8 4.5


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CHAPTER 5

OPTIMIZING THE

PROCESS PARAMETERS

OF OTHER WELDING

PROCESS


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OPTIMIZING THE PROCESS PARAMETERS OF OTHER

WELDING PROCESS

The optimization process is being carried out in some of the

welding process such as diffusion bonding and laser welding process. The

empirical model relating the output variable and the input process parameter

are taken from the available standard literature already published.

5.1. OPTIMIZING THE LASER WELDING PROCESS PARAMETERS

An empirical model was developed by G. Padmanaban et.al, to

predict the maximum tensile strength of laser welded AZ31B magnesium

alloy. The response surface methodology is used as an optimization tool to

predict the maximum tensile strength. The experiments were conducted based

on a three factor, three level, central composite face centered matrix with full

replication technique.The process parameter includes, laser power, welding

speed, focal position

The empirical model developed by the authors relating the tensile

strength and the process parameter that includes laser power, welding speed

and focal position is shown as below. The process parameters and their

working limits is shown in Table 5.1

Tensile Strength = 206.39-3.60 * X1 + 5.40 * X2 -0.80 * X3 +0.63 * X1 *

X2+0.88 * X1 * X3-2.37 * X2 * X3 +0.77 * X122.23 * X2

2-19.38 * X3

2.(

G. Padmanaban et.al.,)


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Table 5.1. Process Parameters and their Working Limits of Laser Welding

Process

S.No Parameter UnitLevels

(-1) 0 (+1)

1

Laser

power Watts 2500 3000 3500

2

Welding

Speed m/min 4.5 5 5.5

3

Focal

position Mm 0 -1.5 -3

5.1.1. OPTIMIZATION USING GA TOOLBOX IN MATLAB

Genetic algorithms are computerized search and optimization algorithms

based on the mechanics of natural genetics and natural selection. GA is very

different from traditional search and optimization methods used in

engineering problems. Because of its simplicity, ease of operation, minimum

requirements and global perspective, GA has been successfully used in a wide

variety of problems.In order to estimate the maximum tensile strength, the

following steps are to be followed:

i. Firstly the model which is developed using response surface methodwhich relates the tensile stength and the process parameter is typed in

editor window.

ii. Then the editor window is saved using any name.iii. After opening the optimization toolbox, the fitness function is entered

with the filename saved.

iv. Then the number of the variables is entered and the lower and the upperbound is entered.


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v. If needed the parameters of the GA toolbox is changed, otherwise it isset as default and optimization is started to run. After executing the

problem, the results will be displayed.


The parameters used for GA is given below.

Population size = 100 Length of chromosome = 40 Selection operator: Roulette method Crossover operator : Single point operator Crossover probability = 0.9 Mutation probability = 0.01 Fitness parameter: Tensile strength.

5.1.2. OPTIMIZED PROCESS PARAMETERS OF LASER WELDING:

The optimized result and the maximized tensile strength of the laser

welding process parameters and the experimental results are shown as

follows:


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Table 5.2. Optimized Process Parameters of Laser Welding

S.NO Process

parameter

Values of process parameter Tensile strength (MPa)

Predicted

(RSM)

Predicted

(GA)

Experimental Predicted

(RSM)

Predicted

(GA)

Experimental

1 Laserpower

(Watts)

2520 2500 2500

212.25 213.712 212

2 WeldingSpeed

(m/min)

5.24 5 5

3 Focal

position

(mm)

-1.19 -1.65 -1.5

5.2. OPTIMIZING THE DIFFUSION BONDING PROCESS

PARAMETERS

Experimental studies were carried out by G.Mahendran et al.,

(2010) on Magnesium and Copper using diffusion bonding methods. Three

factor five-level, central composite rotatable design matrix method is used for

the purpose of designing the experiments. Empirical relationship was

developed in order to predict the diffusion layer thickness, hardness and

strength of the joint using the response surface methodology.

In this part of the work, the shear strength and the bond strength of

the diffusion bonded Magnesium and Copper is to be maximized for the

optimum process parameters.


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The mathematical model relating the shear strength, tensile

strength and the process parameters is shown as below:

Shear Strength = 58.97-4.33 * X1 -3.26 * X2 -3.35 * X3 +1.59 * X12

1.59 * X22+3.42 * X3

2

Bond Strength = 74.46-4.58 * X1 -3.38 * X2 -3.48 * X3 -1.12 * X1 * X2 -

1.69 * X12+1.87 * X2

2-1.51* X3

2

The process parameter and their working limits are shown in table

5.3.

Table 5.3. Process Parameters and their Working Limits of Diffusion Bonding

5.2.1. OPTIMIZATION USING GA TOOLBOX IN MATLAB

In this problem the objective functions are Shear Strength and

Bond Strength of the Diffusion Bonded Magnesium and Copper joints. So the

problem falls under the multhiobjective optimization problem.

S.No Parameter Unit

Levels

-

1.682-1 0 1 1.682

1 BondingTemperature

0C 425 450 475 500 525

2Bonding

PressureMPa 4 8 12 16 20

3Holding

TimeMin 10 20 30 40 50


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The parameters used for GA is given below.

GA Solver : GAMULTIOBJ (Multi objective Optimization using GA)

Population size = 60 Population type : double vector Length of chromosome = 40 Selection operator: Tournament Crossover operator : Single point operator Crossover probability = 0.8 Mutation probability = 0.01 Mutation function : Adaptive Feasible Fitness parameter : Shear strength and Bond Strength .

5.2.2. OPTIMIZED PROCESS PARAMETERS OF LASER WELDING:

The optimized result and the maximized tensile strength of the laserwelding process parameters and the experimental results are shown as

follows:

Table 5.4. Optimized Process Parameters of Friction Welding

S.NOProcess

parameter /

Unit

Values of process

parameterShear strength (MPa) Bond strength (MPa)

Predicted

(GA) Experimental

Predicted

(GA) Experimental

Predicted

(GA) Experimental

1

Bonding

Temperature

/0C

449.37 450

69.742 66 80.083 812

Bonding

Pressure /

Mpa

10.62 8

3Holding

Time / min

19.77 20


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CHAPTER 6

CONCLUSION


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CONCLUSION

The following important conclusions are made from the above investigation:

i. From the literature survey friction welding process, the research worksof the welding are studied well. The possibilities of the research in

welding process especially in the friction welding and the diffusion

bonding process were identified.ii. Modeling techniques for the solid state welding processes were

surveyed. Most of the studies showed that the conventional regression

method is used for modeling solid state welding process. Very few

literatures were published on the modeling of the welding process

parameters using Artificial Neural Network (ANN). Finite element

method is also used to model the mechanism of these welding

processes and to simulate it.

iii. Conventional optimization techniques such as Design OfExperiments(DOE), response surface methodology, statistical methods

such as Analysis of variance (ANOVA), correlation analysis were used

as the optimization tool in many literatures, whereas very few

literatures were interested to investigate on the non-traditional

optimization techniques such as Genetic Algorithm, particle swarm

optimization, simulated annealing, etc.,

iv. The optimization of friction welding, laser welding and diffusionbonding process parameters were carried for the specific objective

functions. As a special case the multi objective optimization of

diffusion bonding process parameters in order to maximize the shear

strength and the bond strength of the welded joints.


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v. The optimized results of the process parameters and the objectivefunction of the friction welding, laser welding and diffusion bonding

process are being compared with the experimental results and in some

case it is being compared with the other Conventional optimization

technique results which are all in good agreement.


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REFERENCES


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REFERENCES

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processing technology. J. Vol 202, pp 137144.

2. Cemal Meran, ( 2006) Prediction of the optimized welding parametersfor the joined brass plates using genetic algorithm, Materials and

design. J.vol 27, pp 3563633. Hasan Okuyucu, Adem Kurt, Erol Arcaklioglu (2007)., Artificial

neural network application to the friction stir welding of aluminum

plates. Materials and design. J. Vol 28, pp 78-84.

4. Kim. I.S, Son.J.S, Park.C.E, Kim.I.J, Kim.H.H(2005), Aninvestigation into an intelligent system for predicting bead geometry in

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