Comparison of Response Surface Construction Methods for Derivative Estimation Using Moving Least Squares, Kriging and Radial Basis Functions

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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Response Surface Method Based on Radial Basis Functions for Modeling Large-Scale Structures in Model Updating

Computer-Aided Civil and Infrastructure Engineering ◽

10.1111/j.1467-8667.2012.00803.x ◽

2012 ◽

Vol 28 (3) ◽

pp. 210-226 ◽

Cited By ~ 68

Author(s):

LinRen Zhou ◽

GuiRong Yan ◽

JinPing Ou

Keyword(s):

Response Surface ◽

Radial Basis Functions ◽

Response Surface Method ◽

Large Scale ◽

Model Updating ◽

Basis Functions ◽

Large Scale Structures ◽

Surface Method ◽

Radial Basis ◽

Scale Structures

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Response Surface Based Cost Model for Onshore Wind Farms Using Extended Radial Basis Functions

Volume 1: 36th Design Automation Conference, Parts A and B ◽

10.1115/detc2010-29121 ◽

2010 ◽

Cited By ~ 10

Author(s):

Jie Zhang ◽

Souma Chowdhury ◽

Achille Messac ◽

Luciano Castillo ◽

Jose Lebron

Keyword(s):

Response Surface ◽

Radial Basis Functions ◽

Wind Farm ◽

Cost Model ◽

Wind Farms ◽

Labor Cost ◽

Basis Functions ◽

Onshore Wind ◽

Radial Basis ◽

The Cost

This paper develops a cost model for onshore wind farms in the U.S.. This model is then used to analyze the influence of different designs and economic parameters on the cost of a wind farm. A response surface based cost model is developed using Extended Radial Basis Functions (E-RBF). The E-RBF approach, a combination of radial and non-radial basis functions, can provide the designer with significant flexibility and freedom in the metamodeling process. The E-RBF based cost model is composed of three parts that can estimate (i) the installation cost, (ii) the annual Operation and Maintenance (O&M) cost, and (iii) the total annual cost of a wind farm. The input parameters for the E-RBF based cost model include the rotor diameter of a wind turbine, the number of wind turbines in a wind farm, the construction labor cost, the management labor cost and the technician labor cost. The accuracy of the model is favorably explored through comparison with pertinent real world data. It is found that the cost of a wind farm is appreciably sensitive to the rotor diameter and the number of wind turbines for a given desirable total power output.

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