Moving least squares response surface approximation: Formulation and metal forming applications

This paper presents a new method to construct response surface function and a new hybrid optimization method. For the response surface function, the radial basis function is used for a zeroth-order approximation, while new bases is proposed for the moving least squares method for a first-order approximation. For the new hybrid optimization method, the gradient-based algorithm and pattern search algorithm are integrated for robust and efficient optimization process. These methods are based on: (1) multi-point approximations of the objective and constraint functions; (2) a multi-quadric radial basis function for the zeroth-order function representation or radial basis function plus polynomial based moving least squares approximation for the first-order function approximation; and (3) a pattern search algorithm to impose a descent condition. Several numerical examples are presented to illustrate the accuracy and computational efficiency of the proposed method for both function approximation and design optimization. The examples for function approximation indicate that the multi-quadric radial basis function and the proposed radial basis function plus polynomial based moving least squares method can yield accurate estimates of arbitrary multivariate functions. Results also show that the hybrid method developed provides efficient and convergent solutions to both mathematical and structural optimization problems.

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Homogenized limit analysis of masonry structures with random input properties: polynomial Response Surface approximation and Monte Carlo simulations

STRUCTURAL ENGINEERING AND MECHANICS ◽

10.12989/sem.2010.34.4.417 ◽

2010 ◽

Vol 34 (4) ◽

pp. 417-447 ◽

Cited By ~ 22

Author(s):

G. Milani ◽

D. Benasciutti

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Response Surface ◽

Limit Analysis ◽

Masonry Structures ◽

Random Input ◽

Response Surface Approximation ◽

Surface Approximation ◽

Polynomial Response Surface

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RESPONSE SURFACE MODEL USING MOVING LEAST SQUARES METHOD

The Proceedings of OPTIS ◽

10.1299/jsmeoptis.2000.4.181 ◽

2000 ◽

Vol 2000.4 (0) ◽

pp. 181-186

Author(s):

Akihiro KAMINAGA ◽

Katsuyuki SUZUKI ◽

Daiji FUJII ◽

Hideomi OHTSUBO

Keyword(s):

Least Squares ◽

Response Surface ◽

Least Squares Method ◽

Response Surface Model ◽

Moving Least Squares ◽

Surface Model ◽

Moving Least Squares Method

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Practical Implementation of Robust Design Assisted by Response Surface Approximation and Visual Data-Mining

Journal of Mechanical Design ◽

10.1115/1.3125207 ◽

2009 ◽

Vol 131 (6) ◽

Cited By ~ 17

Author(s):

Koji Shimoyama ◽

Jin Ne Lim ◽

Shinkyu Jeong ◽

Shigeru Obayashi ◽

Masataka Koishi

Keyword(s):

Data Mining ◽

Response Surface ◽

Robust Design ◽

Robust Design Optimization ◽

Computational Time ◽

Practical Implementation ◽

Visual Data ◽

Visual Data Mining ◽

Response Surface Approximation ◽

Surface Approximation

A new approach for multi-objective robust design optimization was proposed and applied to a practical design problem with a large number of objective functions. The present approach is assisted by response surface approximation and visual data-mining, and resulted in two major gains regarding computational time and data interpretation. The Kriging model for response surface approximation can markedly reduce the computational time for predictions of robustness. In addition, the use of self-organizing maps as a data-mining technique allows visualization of complicated design information between optimality and robustness in a comprehensible two-dimensional form. Therefore, the extraction and interpretation of trade-off relationships between optimality and robustness of design, and also the location of sweet spots in the design space, can be performed in a comprehensive manner.

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