Multivariate Hermite Approximation for Design Optimization

Wang, L.; Grandhi, Ramana V.; Canfield, Robert A.

doi:10.1002/(sici)1097-0207(19960315)39:5<787::aid-nme881>3.0.co;2-5

Cited by 24 publications

(13 citation statements)

References 11 publications

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“…Dyn et al [45] use radial basis functions to build global approximation surfaces to interpolate smooth data. Wang et al [46] present multivariate Hermite approximations for multidisciplinary design optimization which uses data generated during the course of iterative optimization; it is compared against linear, reciprocal and other standard approximations, but shows inefficiencies because it requires more data points. Wavelet modeling uses a special form of a basis function which is especially effective in modeling sharp jumps in a response surface [47].…”

Section: Additional Metamodeling Approachesmentioning

confidence: 99%

Metamodels for Computer-based Engineering Design: Survey and recommendations

Simpson

Poplinski

Koch³

et al. 2001

EWC

1,609

919

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Section: Additional Metamodeling Approachesmentioning

confidence: 99%

Metamodels for Computer-based Engineering Design: Survey and recommendations

Simpson

Poplinski

Koch³

et al. 2001

EWC

1,609

919

View full text Add to dashboard Cite

“…Wang and Grandhi [7] proposed an approximation approach based on the multiple function and gradient information by using Hermite interpolation concepts. This approximation possesses the property of reproducing the function and gradient information of known data points.…”

Section: Multi-point Approximation Approachmentioning

confidence: 99%

“…The three-bar truss example shown in Figure 4 is taken from Reference [7]. This example has also been used by Wang and Grandhi (1996) to illustrate the e ectiveness of the multi-point Hermite interpolation approach. The truss is designed for crosssectional areas A A ; A B and A C (= A A ) under stress and displacement constraints.…”

Section: Application To Structural Optimizationmentioning

confidence: 99%

A new three-point approximation approach for design optimization problems

Guo

Yamazaki

Cheng

2001

Int. J. Numer. Meth. Engng.

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In this paper, a newly developed three‐point approximation scheme is proposed. The expression of this scheme consists of a linear combination of the direct and reciprocal linear Taylor expansions as well as of the lumped diagonal terms of the second‐order direct and inverse terms. The unknown parameters of the expression are computed on the basis of the function and gradient values at three points in the design space. Based on this approach, the accuracy of the existing constraint approximation methods can be improved. The effectiveness of the proposed approach is demonstrated on a number of numerical examples. The numerical results are also compared with those of the previously published work. Copyright © 2001 John Wiley & Sons, Ltd.

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“…In the 1990's, in order to make full use of the known information to construct approximate functions, many multi-point approximations have been developed (Wang and Grahdhi, 1995, 1996a, 1996bFadel et al, 1990;Xu and Grandhi, 1998). Among them, two-point approximation methods, first introduced by Fadel et, al, (1990), are widely used for their simplicity.…”

Section: Introductionmentioning

confidence: 99%

Efficient mechanical system optimization using two-point diagonal quadratic approximation in the nonlinear intervening variable space

Kim

Jeon

et al. 2001

KSME International Journal

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For efficient mechanical system optimization, a new two-point approximation method is presented. Unlike the conventional two-point approximation methods such as TPEA, T ANA, TANA-l, TANA-2 and TANA-3, this introduces the shifting level into each exponential intervening variable to avoid the lack of definition of the conventional exponential intervening variables due to zero-or negative-valued design variables. Then a new quadratic approximation whose Hessian matrix has only diagonal elements of different values is proposed in terms of these shifted exponential intervening variables. These diagonal elements are determined in a closed form that corrects the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second -order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the previous point. Finally, in order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

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Multivariate Hermite Approximation for Design Optimization

Cited by 24 publications

References 11 publications

Metamodels for Computer-based Engineering Design: Survey and recommendations

Metamodels for Computer-based Engineering Design: Survey and recommendations

A new three-point approximation approach for design optimization problems

Efficient mechanical system optimization using two-point diagonal quadratic approximation in the nonlinear intervening variable space

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