Effective two-point function approximation for design optimization

Xu, Suqiang; Grandhi, Ramana V.

doi:10.2514/3.14115

Cited by 6 publications

(15 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently Xu and Grandhi (1998) developed TANA-3, which was the incomplete second order Taylor series expansion in terms of the intervening variables, in which Hessian matrix was diagonal and changeable. This approximation method used the intervening variables given in Eq.…”

Section: Review Of the Two-point Approximationsmentioning

confidence: 99%

“…(2) are negative or the denominator is close to 1. In the first case Xu and Grandhi (1998) where Pi and H are constants to be obtained in a closed form solution to match g(Xl)=g(Xl) and. V'g(Xl) =V'g(Xl).…”

Section: Review Of the Two-point Approximationsmentioning

confidence: 99%

“…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%

“…Based on these exponential intervening variables, Wang and Grandhi (1995) developed an improved two-point approximation using both function and gradient information of two data points, which were called TPEAchange, TANA, TANA-l and TANA-2. Recently, Xu and Grandhi (1998) developed TANA-3 having diagonal and changeable Hessian matrix in order to avoid the computational burden of solving n +I nonlinear equations for each function in TANA-2. Owing to its changeable quadratic terms, however, TANA-3 may make a point of inflection between two points used for approximation although the original function is convex between them.…”

Section: Introductionmentioning

confidence: 99%

“…This paper presents a new two-point approximation. Unlike other two-point approximations such as TPEA (Fadel et al, 1990), TANA, TANA-l, TANA-2 (Wang and Grandhi, 1995) and TANA-3 (Xu and Grandhi, 1998), 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.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Kim

Jeon

et al. 2001

KSME International Journal

View full text Add to dashboard Cite

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.

show abstract

Section: Review Of the Two-point Approximationsmentioning

confidence: 99%

Section: Review Of the Two-point Approximationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Kim

Jeon

et al. 2001

KSME International Journal

View full text Add to dashboard Cite

show abstract

Computational certification under limited experiments

Fish

Yuan

Kumar³

2018

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary A computational certification framework under limited experimental data is developed. By this approach, a high‐fidelity model (HFM) is first calibrated to limited experimental data. Subsequently, the HFM is employed to train a low‐fidelity model (LFM). Finally, the calibrated LFM is utilized for component analysis. The rational for utilizing HFM in the initial stage stems from the fact that constitutive laws of individual microphases in HFM are rather simple so that the number of material parameters that needs to be identified is less than in the LFM. The added complexity of material models in LFM is necessary to compensate for simplified kinematical assumptions made in LFM and for smearing discrete defect structure. The first‐order computational homogenization model, which resolves microstructural details including the structure of defects, is selected as the HFM, whereas the reduced‐order homogenization is selected as the LFM. Certification framework illustration, verification, and validation are conducted for ceramic matrix composite material system comprised of the 8‐harness weave architecture. Blind validation is performed against experimental data to validate the proposed computational certification framework.

show abstract

An adaptive quadratic approximation for structural and topology optimization

Khandelwal

2015

Computers & Structures

View full text Add to dashboard Cite

Effective two-point function approximation for design optimization

Cited by 6 publications

References 0 publications

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

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

Computational certification under limited experiments

An adaptive quadratic approximation for structural and topology optimization

Contact Info

Product

Resources

About