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pplied Soft Computing Inaterials Design

ubhas Ganguly

epartment of MetallurgicalEngineering ,a ti on al In s t i tu t e of T e ch no l og y R ai p u r

, . -ai pu r C G

Lecture on

SOFT COMPUTING INDESIGN OF MATERIALS

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People in Soft Computing in MaterialsScience

Our CollaboratorsProf Krishna Rajan, Iowa State Univ, US

Prof Henrik Saxen, Abo Akademi, Finland

Prof N. Chakraborti, IIT, Kharagpur

Prof K. Deb, IIT, Kanpur

Prof Subhabrata Datta, BESU Shibpur

Prof Partha Chattopadhyay, BESU Shibpur

Dr. Arup Nandi, CMERI, Durgapur

Interests in MaterialsApplication

Advanced Steel Design: TRIP, HSLA, MPS

Aluminum alloys

Scintillater materials design

Oxide based piezoelectric

Process modeling & optimization: synthesis ofnanoporous silicon, HT of Steel .etc

Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

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Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

IntroductionArtificial Neural Network

Genetic AlgorithmFuzzy LogicRough SetConclusion

Plan of the talk

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H. K. D. H. Bhadeshia: Materials Sc & Tech,24 (2008) pp. 128-136.

MODELING

Data drivenPhysical

From impreciseknowledge

Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

Exp andTheory Computation

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Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

Acquisition fromexperimentation

Throughinferenceengine

Physicalconcepts of the

systemInformatics basedmaterials design

Data + Correlation + Theory = Knowledge-base

Soft computingcan playsome role

Materials Informatics and Roll of SoftComputing

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hat is softomputing ?

Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

Guiding principle of soft computing unlikehard computing,is to exploit the toleranceof

ImprecisionUncertainty

Partial truth

qPrincipal constituents of soft computing areFor prediction and classification models: artificial neural netw

fuzzy logic, rough set, support vector machines etc.

For design and optimization: genetic algorithm, geneticprogramming, simulated annealing, ant colony optimization,particle swarm optimization etc.

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ome members in softomputing ?

Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

Artificial Neural Network:Classification, prediction Modeling

Genetic Algorithm: Optimization

Fuzzy Logic: Imprecise knowledgebased modeling

Rough Set: addressing Uncertainty

....

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Soft computing approachin Materials Science and Engineering

qCommon phenomena in materials systems:Large number of variablescomplex and non-linear relationshipsimpreciseness and uncertainty

requirement of knowledge extraction fromdatabase generated from experiments.

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( )rtificial neural network ANNMimic functioning inside the human brainMost important functional unit in human brain a class of cellscalled NEURON

Dendrites

Cell Body

Axon

Synapse

=Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

http://heart.cbl.utoronto.ca/~berj/neuron.gif

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Different types of ANN

Multilayer Perceptrons

Radial Basis Function Networks

Probabilistic Neural Networks

Generalized Regression Neural Networks

SOFM / Kohonen Networks etc.

Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

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y = a + b (%C) +c (%Mn)

Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

Empirical Equations

y= a + b (%C) +c (%Mn)+ d(%C x %Mn)

y =sin (%C) + tanh (%Mn)

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y = a + b (%C) +c (%Mn)

Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

Empirical Equations

y= a + b (%C) +c (%Mn)+ d(%C x %Mn)

y =sin (%C) + tanh (%Mn)

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Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

Xi

WjiXiHj= f (WjiXi+j)

Y= WjHj+

Errorbackpropagation

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Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

Xi

WjiXi Hj= f (WjiXi+j)

Y= WjHj+

Errorbackpropagation

Transfer function

Illuminating the ANN BLACK BOX

+

+ bbxwW jiji

j

j tanh

1

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he strength ductilityissue

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trengthening Mechanisms insteel

Collective effect of all these

mechanisms determine theultimate properties

Grain Refinement

Solid solution hardening

Work hardening

Dispersion/precipitation hardening

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.ont

Strength

Ductility/Elongation

Superior steel { max , max }So it can be looked as an optimizationtask

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ExperimentalapproachExperimental search is quite slow and

exhaustive.

It is difficult to explore each and every

decision space.High possibility to rich local optima

instead of global optima.

Researcher may loose their motivation

towards the global optima.High cost involvement.

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odel based ptimization approachIdentifying the effective variables

influencing the system

Model for and

1. Complex relations2. Large no. of Variables

Need Multi-objective

Optimizationtool

Limited physical

models

Empirical routes are1. Regression2. ANN3. Fuzzy modeling or4. some coupling approach

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-trength ductility balancetudy in plain carbon steel

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bjective function development

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dentification of parameters

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-General multi objectiveproblemMin/MaxMin/Max ffmm(x) m=1,2,3..(x) m=1,2,3..

Subject toSubject to ggjj(x) 0 j = 1,2,...,J(x) 0 j = 1,2,...,J

hhkk(x)=0 k = 1,2,...,K(x)=0 k = 1,2,...,K

xxiiLL x xii x xiiUU i = 1,2,,ni = 1,2,,n

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:oal attainment A traditionalapproach

Need to selectweighing coefficientsand the design goal

prior to optimizationSingle iteration obtainone solution at a time

Weighted Goal attainment

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eneticalgorithmThe basic concept of GA is designed to simulate processesin natural system necessary for evolution, specificallythose that follow the principles first laid down by CharlesDarwin. As such they represent an intelligent exploitationof a random search within a defined search space to solvea problem. .

Algorithms that mimics naturalgenetics and natural selection i.e.the theory of Survival of the fittest

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.ont /*a pseudo code of simple genetic algorithm*/{

generate a random binary population;

repeat {

if (termination criterion) break

fitness evaluation;

selection;

crossover;mutation;} until (generation less than final);

binary to real mapping of solution;

}X-overpointO

P

ANN Modelto assessfitness

C

Mn Si

SRT

FRT

CR

Binary codedChromosome

Random Pop

Objective FunctionSelectionOperator

X-Over Operator

MutationOperator

Best Solution

New offspring

Matingpool

Simple GA

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Multi-objective GA and Pareto-optimalityapproach

F1

F2

Min--Max

F1

F2

Max--Min

F1

F2

Max--Max

F1

Min--MinF2

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arameters in GA search

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areto resultsGA based result

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tudy on Pareto solutions

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oncluding remarksThe multi-objective Genetic Algorithm can be used forcomplicated optimization ofstrength and ductility of lowcarbon steel using regression models.

The process is found to be superior particularly forgenerating the optimal front than the conventionaloptimization technique.

The GA based optimization has clearly indicated that

fine-grained pearlite-free microstructure is the bestsolution for a good strength-ductility balance in lowcarbon steel.

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system with further:omplexities HSLA steel

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SLA steels and designparametersDesign aspectsof HSLA Steel

lloyinglementsselection

election ofMAE

esign ofeformation schedule. .r trecrystallization

ther processingariables like, ,RT FRT CR etc

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ystem variables and modelingcomplexityLong list of parameters

Steel composition (Alloying + MAE), 8/9 nos.

SRTFRT

Cooling condition

Deformation at different temp. zone

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ttempt to optimize Regressionodel and GA

This formulation failedto obtain Pareto front in

GA run

Huge regression equation with16 system variables

??

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( )rtificial neural network ANNMimic functioning inside the human brainMost important functional unit in human brain a class of cells called NEURON

Dendrites

Cell Body

Axon

Synapse

=

http://heart.cbl.utoronto.ca/~berj/neuron.gif

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.ontThe ANNarchitecture

Xi

WjiXiHj= f (WjiXi+j)

Y= WjHj+

Errorbackpropagation

XCapturing experimental data

f(X)

Transfer function

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ttempt to model the Problemith ANN and GA

Pareto front usingANN basedformulation

ANN may be alternative tool

+

+ bbxwW jiji

j

j tanh

1

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oncluding remarks

The ANN found good tool for developing objectivefunction in formulation of multi-objective optimizationstudy of strength and ductility of HSLA steel using GA.

Fine grain structure with precipitates found to improvestrength-ductility balance.

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ome more studies on HSLAsteels

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re the chosen variablesignificant in the system?

new computational technique todentify the roll of variable in the:ystem by coupling ANN and GA NNPPGA

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raining the ANN Refers to calculation ofweights and biases for

.the various connections

-Methods include Back,Propagation Simulated

,Annealing Genetic.Algorithms etc

Reduce error by adjusting.weights

Problems include over,fitting speedyconvergence to local

.minima

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redator Prey Genetic Algorithm itness not byomination.heck opulationivided into/ .redators prey laced on ertices of a.rid redator kills.eak preys

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ormulation of NNPPGA

0

10

20

30

40

50

60

70

C Mn Si Al HD CD

ICTe

mp

ICTi

me

Btem

pBtim

e

No.ofconnections

WiXi

,Lower Layer FlexiblePredator Prey GA - ,Upper Layer Fixed Linear

Least Square Approach

(The weight connected toinput and hidden node isbeing mutated to using two

randomly picked nodes and a)mutation constant

Mutation Scheme

CrossoverScheme

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dentifying the factorshrough NNPPGA

0 1 0 2 0 3 0 4 0 5 0 6 0 7 00 .2

0 . 2 5

0 .3

0 . 3 5

0 .4

0 . 4 5

.

N um b e r o f co nn e ctio ns

0 20 40 60 80 100 120 10

0.2

0.4

0.6

0.8

0 20 40 60 80 100 120 10

0.2

0.4

0.6

0.8

1

Observation numbers

onga

on

Pareto front Predicted vs actual of a particular network

YS

All threeEL

UTS

Noof

conn

ectio

ns

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he Evolving Neural NetworkC content has major role in in combination with CR on thefinal properties through determining the phase fraction.

YS increases withCR and C content

as it promotes thelow temp. micro-constituent

In case of UTS :effect of CRis not so prominent after itreaches a certain rate. Itmeans that microstructurehas no major role indetermining UTS.

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oncluding remarksEvolved neural nets are able to mine knowledge fromthe database.

YS of HSLA steel mostly depends on solid solutionstrengthening.

UTS is strongly depended on precipitation hardening.

Both the factor has negative effect on ductility.

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tudy the work hardening ofSLA steel

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he formulation

The experimentaland ANN

predicted valuesof UTS and

%elongation inHSLA steel

+

+ bbxwW jiji

j

j tanh

1

Max strength

Max elongation

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Pareto optimal frontsin optimization of

UTS and %elongationfor HSLA steel

developed usingNSGA II

400

600

800

1000

1200

1 31 61 91 121 151 181

Preto solution n

15

20

25

30

35

40

%E

lo

ngation

UTS

Elongation

Region A

Strength ductility

analysis of Paretosolutions

ome and analysis of the results

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0.04

0.06

0.08

%C

1

1.5

2

%

Mn

0 20 40 60 80 100 120 140 160 180 2000.2

0.3

0.4

0.5

Pareto solution no.

%S

i

0.0

0.5

1.0

%C

r

0.92

0.97

1.02

%N

i

0.0

0.5

1.0

%M

o

0 20 40 60 80 100 120 140 160 180 2000.0

0.05

0.10

Pareto solution no.

%T

i

.ont

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10

20

30

40

D1(%)

20

25

30

D2(%)

0 20 40 60 80 100 120 140 160 180 2000

5

10

Pareto solution no.

D3(%)

850

860

870

880

FRT(deg.

C)

0

20

40

60

80

100

CR(deg.

C/s)

INDINGSq -est strength ductility combination ischieved through judicious combination of

( ),errite strengthening Cr finer(% )ecrystallize grain structure D2 and( , ).dequate austenite hardenability Ti Mnq t higher strength presence of secondhases dominate the work hardening.rocess

.ont

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oncluding remarksModerate strength with high ductility can be achievedby ferrite strengthening, fine recrystallized grainstructure and dislocation hardening.

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esign of TRIP aidedultiphase steel

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-hat are TRIP aided steels

Schematic of TRIP microstructure

Retained austenite in TRIP steel

Ar1

Ar3

Finish rolling temp. 8000C

Hot Rolling

OQ

Isothermal holdingICA

Typical heat treatmentPhase transformation

echanical behavior of TRIP

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ided steel

Superior TRIP steel { max , max }So it can be treated as a optimizationproblem

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5 20 25 30 35 40 4

% Elongation

UTS,MPa

TRIP

HSLA

Pareto optimal frontsin optimization of

UTS and %elongationfor the two steelsdeveloped using

NSGA II

40 0

60 0

80 0

1000

1 31 61 91 121 151 181

Pa reto solution

UTS,

MPa

15

20

25

30

35

Elongation

UTS

Elongatio

Region B Region C

ome results of similar study onRIP steel

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0.1

0.15

0.2

0.25

0.3

0.35

%C

0 20 40 60 80 100 120 140 160 180 2002.2

2.25

2.3

2.35

2.4

2.45

Pareto solution no

%M

n0

0.5

1

1.5

%S

i

0

0.5

1

%A

l

0 20 40 60 80 100 120 140 160 180 2000

0.5

1

1.5

Preto solution no.

%(

Si+Al)

q t high strength the TRIP phenomenon.ave taken the back seat Insteadtrong fine bainites has caused the.ajor strengthening

q t region C the steel has increasedhe carbon content further and.uctility has to be lowered

.ont

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dentifying the factors throughNNPPGA

0 1 0 2 0 3 0 4 0 5 0 6 0 7 00. 2

0 . 2 5

0. 3

0 . 3 5

0. 4

0 . 4 5

.

N um b e r o f co nne ct io ns

0 20 40 60 80 100 120 10

0.2

0.4

0.6

0.8

0 20 40 60 80 100 120 10

0.2

0.4

0.6

0.8

1

Observation numbers

onga

on

etail study on TRIP steeldesign

Development of models for optimization

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60

07/11/2011

Development of models for optimizationstudy

Physical modelAdditional fuzzylayer

ariables for optimization

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modelCMnSi

Amount of prior Cold workICA factor- Less significantICA time

IBT tempIBT time

07/11/2011

ContentsIntroduction

Artificial Neural Network

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As complexity rises, precise statements loose meaning andmeaningful statements loose precision

Fuzzy logic is both oldand new because,although the modern

and methodical scienceof fuzzy logic is stillyoung, the concepts offuzzy logic reach downto our bones.

UZZY

LOGIC

Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

Genetic AlgorithmFuzzy Logic

Rough SetConclusion

CRISP SETContents

IntroductionArtificial Neural Network

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CRISP SET

Conventional or crisp set are binary. Either anelement belongs to a set or does not.True False1 0

Generalization of crisp set. In fuzzy logic, the truth of any statement

becomes a matter of degree.

FUZZY SET

Shubhabrata Datta SOFT COMPUTING IN DESIGN OF MATERIALS

Genetic AlgorithmFuzzy Logic

Rough SetConclusion

Development of models for optimization

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64

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Development of models for optimizationstudy

Physical modelAdditional fuzzylayer

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esign through Pareto solutions

0.12 0.14 0.16 0.18 0.20

800

850

900

950

1000

1050

1100

UT

S(True),MPa

Unifrom true strain

TRIP 6

TRIP 5TRIP 4

TRIP 2TRIP 3

TRIP 1

TRIP 7

Concluding remarks

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chieving microstructure with highetained austenite may be more than thetrong bainite and good potential fortrain induced transformation may be aew area for superior TRIP aided steel.esign

Concluding remarks

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inal Summary

ooking some issues in steel design asptimization task could develop important.esign information nformatics through formulation of the

roblem in GA and in combination with thenown physical metallurgy of steel may.implify the complex processing route nalysis of the Pareto solution could helpo identify the scope for furtherxperimentation and improvement

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uture scope

Experimental studies on the Pareto solutions,particularly for TRIP-aided steel.

Applying the present concept in other steel

systems to design steel with complexmicrostructure having still higher strength andductility.

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ist of publications1.S. Ganguly, S. Datta and N. Chakraborti, Genetic Algorithms in optimization ofstrength and ductility of low carbon steels, Materials and Manufacturing

Processes, 22:5(2007), pp 650 658.

2.Shubhabrata Datta, Frank Pettersson, Subhas Ganguly, Henrik Saxn andNirupam Chakraborti, Designing high strength multi-phase steel for improvedstrength-ductility balance using Neural Networks and Multi-objective GeneticAlgorithm, ISIJ Int. vol 47 (2007) No 8, pp1193-2001.

3.Shubhabrata Datta, Frank Pettersson, Subhas Ganguly, Henrik Saxn andNirupam Chakraborti, Extraction of Factors Governing Mechanical Properties ofTRIP-Aided Steel by Genetic Algorithms and Neural Networks, Materials andManufacturing Processes, Vol. 23, 2008, 130137.

4.S. Ganguly, S. Datta, P.P. Chattopadhyay and N. Chakraborti: Designing themultiphase microstructure of steel for optimal TRIP Effect: a multi-objectivegenetic algorithm based approach, Materials and Manufacturing Processes, Vol24, ( 2009), pp 3137.

5.S. Ganguly, S. Datta and and N. Chakraborti, Genetic Algorithm Based Search onthe Role of Variables in the Work Hardening Process of Multiphase Steels,Computational Materials Science, Article in press.

6.S. Ganguly, S. Datta, P. P. Chattopadhyay, and N. Chakraborti, Modeling andoptimization of TRIP effect using fuzzy domain knowledge and milti-objectivegenetic algorithm, Computational Materials Science, Ready for Communication.

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Acknowledgement

ead of the Department ll other Faculty member ll the collaborators

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T h a n k y o uT h a n k y o u

Fuzzy Inference

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Basic steps in fuzzy inference design...

Input fuzzification

Rule evaluation

Output defuzzyfication

Fuzzy Inference

A typical rule may looks like.

If carbon contentis Low and Grain sizeis Small

THEN Strength of steel isMedium

Regression analysis

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Regression analysis

Strength of an alloy

Composition X1, X2, X3,

Deformation parameters Y1, Y2, Y3,

Heat treatment parameters Z1, Z2, Z3,

Regression Equations

y = a + b (X1) + c(X2) + + d (Y1) .... y = a + b (X1) + c(Y1) + + d (Y1 * Z1) .... y = a + sin (X1) + log (Y1) + + d (Z1)3 ....

HSLA steel data

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HSLA steel data

TRIP steel data

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TRIP steel data

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odel based optimization approachIdentifying the effective variablesinfluencing the system

Conventional Optimizationtoo difficult to handle the

Model for and

1. Complex relations2. Large no. of Variables

GA can worknicely

Multi-objectiveOptimization tool

No physical

model

Empirical routes are

popular1. Regression2. ANN3. Fuzzy modeling Or4. some coupling

approach