Metamodel Assisted Evolutionary Algorithm for Multi-objective Optimization of Non-steady Metal Forming Problems

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Submitted on 14 Aug 2013

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Metamodel Assisted Evolutionary Algorithm for

Multi-objective Optimization of Non-steady Metal

Forming Problems

Mohsen Ejday, Lionel Fourment

To cite this version:

Mohsen Ejday, Lionel Fourment. Metamodel Assisted Evolutionary Algorithm for Multi-objective Op-timization of Non-steady Metal Forming Problems. 13th ESAFORM Conference on Material Forming, Apr 2010, Brescia, Italy. pp.Pages 5-8, �10.1007/s12289-010-0689-0�. �hal-00851431�

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Table 1: $'9#"#'E."E*1(*)(7D !"#!()*'(,7E14(

'D56C82 %2 %_2 %&2 λ2 θ2 ψ942 ;&8'.992 /!!2 +!2 2 2 2 2 .I9BE7B2 /!!2 +!2 /"2 #2 2 %!2 2 CDF672/285782E27C25A62%!27(E274EFEC5A82. I9BE7B2C82A525A62E27252E@72CA52E5FA272965272 C9CC2 5A86ECA82 2F2 E852 52 ,CAB2 85FC5A82 E2 E672 5872525872DC4782262;&8'.9927C2++!!274EFEC5A88 (

! / * % + # " H $ /! !/ ! !* !% !+ !# !" !H !$ / 34 35 2

Figure 1: Comparison of the Pareto optimal front of C-Min-Ex obtained by M-Updated and NSGA-II

0+ 32938E57218(8)CE8

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7

7

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Figure 2: Comparison of the Pareto optimal fronts of KUR test problem obtained by M-Updated and NSGA-II

2

2

Figure 3: Pareto optimal solutions in the decision variable space for the test problem KUR

2

3

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2

Figure 4: Initial preform and forging dies.

.I9BE7B2

Table 3: /#.&".(*"E1#!(1(7D !"#!(1!(78

'D56C82 42 CA2φ2 '&2 /! /2 /!$$2 .I9BE7B2 /!/+2 /!H#2

2

Figure 5:2Isovalues of distance between the part and the

dies at the end of forging (blue/drak 1 proper filling).2

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752 5237C4782 E672 5A8CB767B2 CA2 72 ,557CAD2 7C672 B6E7CAD2 59CC5EC5A2 965272 08772 CDF672 "2 EAB2 7>FEC5A2 0/!112 72 F8FE2 CACC5EC5A2 5,2 72 E(CF2 B6E7CAD2,56722942EAB272788255A2CACC5EC5A2

5,2 72 E76CE2 BEED73942 7672 E672 752 B78CDA2

4E6CE2782 72 7A6EA72 BC72 87C.EAD72α 2 EAB2 72 EAB2 7AD2 C 208772CDF672"12

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/ CACC5722222  CACC5722222 2222222222222222222! / 94 94 ) 5C 3 ( ) 5C 2 6 5C α α α = 8 B =  B < <  8 0/!12 2

Figure 6:2Simulation of the wire drawing process.2

2

Figure 7:2Drawing die geometry and definition of the optimization parameters.

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5A,CCAD2 0212 72 <2 C82 772 6796787A7B2 7C2 ,772 EFEC5A82 012 CA2 E2 8CAD72 59CC5EC5A2 6FA2 72 <2 E5782 D7CAD2 E2 7CB72 6EAD72 5,2 59CE2 85FC5A82 72

F8FE62 8777B2 85FC5A2 5667895AB82 52 72 CACF2 ,567206CD27AB25,2CDF672H122F272<285782E2262 E79CAD2 E2 *K2 CA67E872 5,22_942 C2 C82 9588C272 52 D72 E2 %+K2B767E8725,272E76CE2BEED723942 " "% "# "H H H H% H# HH $ $ !!% !!%" !!+ !!+" !!# !!#" !!" !!"" !!H !!H" !!$ 6789 A 7 8 9 2

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E22E2D298

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A*B 2 76C2 '2 8C5C82 2 O5B7C62 2 P@2 D2 8CEAAE@5D5F2 7E5B7.E88C87B2 745FC5A2 86E7DC782 9A2 45A,2 5A2 9E6E72 965272 854CAD2 ,652AEF672&96CAD76276CA28E';Q2 !! 2 A%B 82 9ADE6E52 E2 :2 567A552 EAB2 2 CE6C2 9A76AE2

96788F672 EAB2 5FA76.9FA2 EC5A2 B78CDA2 CA2 Q. 8E97B2 F272 6B65,56CAD2 965788782 '2 FC. 5237C472 59CC8EC5A2 E9965E2 459F7682 EAB2 &6FF6782H"20 !!$12+$/#! 2

A+B M2D65@2'A2(7AB7B2'9965E2526656245A652CA2 (976C7AE2 EAB2 ;F76CE2 :EE2 &55CAD2 EAB2 4EFEC5A2 I8CAD2 72 787882 :2 78,6772 459FEC5AE27EAC82//20 !! 12$/*.$%+2 A#B 2C85@E2M2<6@C85272,CAC72BC,,767A7275B2E2

E62C6E662 C667DFE62 D6CB82 EAB2 C82 E99CEC5A2 CA2 E99C7B2 7EAC82 4592 N2 &6F2 //2 0/$H!12 H*. $+2

A"B 2 67C@59,2 ?2 ;E7F62 '2 EE88CA7F(2 2 RC5A2 54CAD2 7E82 8>FE6782 67895A872 8F6,E72 E9965(CEC5A2 56FEC5A2 EAB2 7E2 ,56CAD2 E99CEC5A824592N2&6F2H*20 !!+12/%//./% H2 AHB &2M2E782M2&C7A52:2&2EAD76256FEC5A25,2

72 'FB57.DEC82 IAC,562 ECA2 ?6976F272 B78CDA2 5,2 7(976C7A82 'B4EA782 CA2 ADCA776CAD2 &5,7E672 *%20 !!*12%$*.+!#2