An effective two-point function approximation for design optimization

Xu, Suqiang; Grandhi, Ramana V.

doi:10.2514/6.1998-1968

Cited by 12 publications

(14 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A number of classical reliability analysis methods are discussed in [38], including Mean-Value First-Order Second-Moment (MVFOSM), First-Order Reliability Method (FORM), and Second-Order Reliability Method (SORM). More recent methods which seek to improve the efficiency of FORM analysis through limit state approximations include the use of local and multipoint approximations in Advanced Mean Value methods (AMV/AMV+ [72]) and Two-point Adaptive Nonlinearity Approximation-based methods (TANA [66,75]), respectively. Each of the FORM-based methods can be employed for "forward" or "inverse" reliability analysis through the reliability index approach (RIA) or performance measure approach (PMA), respectively, as described in [64].…”

Section: Reliability Analysismentioning

confidence: 99%

Solution-verified reliability analysis and design of bistable MEMS using error estimation and adaptivity.

Eldred¹,

Subia²,

Neckels³

et al. 2006

View full text Add to dashboard Cite

This report documents the results for an FY06 ASC Algorithms Level 2 milestone combining error estimation and adaptivity, uncertainty quantification, and probabilistic design capabilities applied to the analysis and design of bistable MEMS. Through the use of error estimation and adaptive mesh refinement, solution verification can be performed in an automated and parameter-adaptive manner. The resulting uncertainty analysis and probabilistic design studies are shown to be

show abstract

Section: Reliability Analysismentioning

confidence: 99%

Solution-verified reliability analysis and design of bistable MEMS using error estimation and adaptivity.

Eldred¹,

Subia²,

Neckels³

et al. 2006

View full text Add to dashboard Cite

show abstract

“…TANA-3: This multipoint approximation uses a two-point exponential approximation [109,38] built with response value and gradient information from the current and previous iterates.…”

Section: Surrogate Modelsmentioning

confidence: 99%

“…current and previous expansion points. Based on the two-point exponential approximation concept (TPEA, [38]), the two-point adaptive nonlinearity approximation (TANA-3, [109]) approximates the limit state as:…”

Section: Chapter 6 Uncertainty Quantification Capabilitiesmentioning

confidence: 99%

DAKOTA, a multilevel parellel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis:version 4.0 uers's manual.

Griffin

Eldred²,

Martinez-Canales

et al. 2006

View full text Add to dashboard Cite

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradientbased methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the DAKOTA software and provides capability overviews and procedures for software execution, as well as a variety of example studies. 4 The DAKOTA leadership team consists of Mike Eldred (principal investigator), Tony Giunta (product manager), Shane Brown (support manager), and Scott Mitchell (department manager). DAKOTA development team members include

show abstract

“…Many local approximations are available, such as the "rst-order direct, reciprocal and conservative approximations. For this multipoint approximation (MPA), the two-point approximation (TANA-3) [4] is used as a local approximation.…”

Section: Multipoint Approximation Based On Local Approximationsmentioning

confidence: 99%

“…Di!erent two-point approximation formulations have been proposed. These approaches include the two-point exponential approximation proposed by Fadel et al [1] and the two-point adaptive nonlinear approximation series TANA [2], TANA1 [3], TANA2 [3] and TANA3 [4] by Wang, Grandhi and Xu. There was even an extension to a three-point approximation presented by Salajegheh [5].…”

Section: Introductionmentioning

confidence: 99%

Multipoint approximation development: thermal structural optimization case study

Grandhi

2000

Int. J. Numer. Meth. Engng.

Self Cite

View full text Add to dashboard Cite

SUMMARYFunction approximation is one of the most important "elds of research in design optimization. Accurate function approximation reduces the repetitive cost of "nite element analysis. Many local approximations, such as one-and two-point local approximations, are already available. These are, however, only valid in a small domain and require stringent move-limits on design variables. The objective of this research is to achieve an e$cient and accurate multipoint approximation to constraints by integrating the most accurate segment of all local approximations previously constructed. The proposed multipoint approximation is constructed by combining weighting functions with local function approximations. With function and gradient information at a series of points, local approximations are established at those points. Once established, all local approximations are blended into a multipoint approximation by use of a weighting function. Function and gradient values of this multipoint approximation correspond directly with exact counterparts at the points where the local approximations were generated. Finally, the multipoint approximation is applied to a plate and wing box thermal-structural optimization. Published in

show abstract

An effective two-point function approximation for design optimization

Cited by 12 publications

References 6 publications

Solution-verified reliability analysis and design of bistable MEMS using error estimation and adaptivity.

Solution-verified reliability analysis and design of bistable MEMS using error estimation and adaptivity.

DAKOTA, a multilevel parellel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis:version 4.0 uers's manual.

Multipoint approximation development: thermal structural optimization case study

Contact Info

Product

Resources

About