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# PR_KR_SVR_RBF_ê·¼ì�¬ëª¨ë�¸ì´�&amp;i -...

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Practical Design Techniques (IV) Meta-model

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Copyright © FRAMAX Co., Ltd. All Rights Reserved. 2 & Gradient-Based Metamodeling      Function-Based Metamodeling  (Ü« ª * Metamodeling P9 + ª * Metamodeling  8
Copyright © FRAMAX Co., Ltd. All Rights Reserved. 3 Metamodeling Techniques Gradient-Based Approximations One-Point Approximations Two-Point Approximations Function-Based Approximations Regression Methods Interpolation Methods

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Copyright © FRAMAX Co., Ltd. All Rights Reserved. 4 Metamodeling Techniques Gradient-Based Approximations Gradient-Based Approximations
Copyright © FRAMAX Co., Ltd. All Rights Reserved. 5 One-Point Approximation : real function : approximate function ( 29 x g ( 29 x g ~ ( 29 1 x g ( 29 1 x x g Two-Point Approximation ( 29 x g ( 29 x g ~ ( 29 1 x g ( 29 1 x x g ( 29 2 x g ( 29 2 x x g : real function : approximate function Design Information ( 29 2 , 2 , 2 2 , 1 2 , , , n x x x x ( 29 ( 29 i x g g 2 2 , x x ( 29 1 , 1 , 2 1 , 1 1 , , , n x x x x ( 29 ( 29 i x g g 1 1 , x x Current Design Point Previous Design Point Concept of Gradient-Based Approximations Concept of Gradient-Based Approximations Gradient-Based Approximations

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Copyright © FRAMAX Co., Ltd. All Rights Reserved. 6 History of Gradient-Based Approximations Storaasli & Sobieszczanski Reciprocal Approximation Schmit & Farshi Linear Approximation Haftka & Shore Conservative Approximation Svanberg Method of Moving Asymptotes Fadel et al. TPEA Wang & Grandhi TANA1 & 2 Xu & Grandhi TANA3 One-Point Approximations Two-Point Approximations Wang & Grandhi TANA Kim et al. TDQA 1990 1994 1995 1998 2001 1974 1979 1987 Prasad Generalized Inverse-Power Approximation 1984 Xu & Grandhi TANA4 1999 TPEA : T wo- P oint E xponential A pproximation TANA: T wo-Point A daptive N onlinear A pproximation TDQA: T wo-Point D iagonal Q uadratic A pproximation ( 29 x x 1 i x g ( 29 x 1 g ( 29 x g ( 29 x g ( 29 x g ~ ( 29 x x 0 i x g ( 29 x x 1 i x g ( 29 x 0 g ( 29 x 1 g ( 29 x g ~ Gradient-Based Approximations
Copyright © FRAMAX Co., Ltd. All Rights Reserved. 7 ( 29 ( 29 ( 29 ( 29 = - + = n i i i i y y y g g g 1 0 0 0 ~ y y y y Basic Concept ( 29 x g ( 29 i i i x y y = Intervening variable ( 29 ( 29 ( 29 i i i i i x x y x g y g where = x y Taylor Series Expansion Linear Approximation i i x y = ( 29 ( 29 ( 29 ( 29 = - + = n i i i i L x x x g g g 1 0 0 0 ~ x x x x , Reciprocal Approximation i i x y 1 = ( 29 ( 29 ( 29 ( 29 = - + = n i i i i i i R x x x x x g g g 1 0 0 0 0 ~ x x x x , One-Point Approximations (1) One-Point Approximations (1) Gradient-Based Approximations One-Point Approximation

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Copyright © FRAMAX Co., Ltd. All Rights Reserved. 8 Conservative Approximation ( 29 = otherwise x x g x if x y i i i i i 1 0 ( 29 ( 29 ( 29 ( 29 = - + = n i i i i i x x x g C g g 1 0 0 0 ~ x x x x ( 29 = otherwise x x x g x if C where i i i i i 0 0 1 , MMA (Method of Moving Asymptotes) ( 29 - - = otherwise L x x g x if x U y i i i i i i i 1 0 1 ( 29 ( 29 ( 29 ( 29 = = - + - + - + -
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## This note was uploaded on 04/12/2010 for the course ME master taught by Professor Mon during the Spring '09 term at Hanyang University.

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PR_KR_SVR_RBF_ê·¼ì�¬ëª¨ë�¸ì´�&amp;i -...

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