A sequential optimization sampling method for metamodels with radial basis functions.

Guang Pan,Zhidong Yang,Pengcheng Ye,Peng Wang

doi:10.1155/2014/192862

Guang Pan, Zhidong Yang + Show 2 more

Open Access

https://doi.org/10.1155/2014/192862

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Abstract

Metamodels have been widely used in engineering design to facilitate analysis and optimization of complex systems that involve computationally expensive simulation programs. The accuracy of metamodels is strongly affected by the sampling methods. In this paper, a new sequential optimization sampling method is proposed. Based on the new sampling method, metamodels can be constructed repeatedly through the addition of sampling points, namely, extrema points of metamodels and minimum points of density function. Afterwards, the more accurate metamodels would be constructed by the procedure above. The validity and effectiveness of proposed sampling method are examined by studying typical numerical examples.

Highlights

In engineering, manufacturing companies strive to produce better and cheaper products more quickly
In engineering design we are faced with different problems, but we try to do with a surrogate model essentially what we do every day in our mind: make useful predictions based on limited information and assumptions
The last section is the closure of the paper where we summarize the important observations made from our study

Summary

Introduction

In engineering, manufacturing companies strive to produce better and cheaper products more quickly. In our mind we are constructing metamodels using the direction of the road, its derivatives with respect to distance along the road, and local elevation information This information is coupled with assumptions based on our experience of going round many bends in the past. Deng et al [26] proposed a sequential sampling design method based on Kriging. Wei et al [27] proposed a sequential sampling method adopting a criterion to determine the optimal sampling points, which maximized the value of the product of curvature and square of minimum distance to other design sites. A new sequential optimization sampling method with extended radial basis functions is proposed. A new metamodeling algorithm integrating a sequential optimization sampling method is presented. The last section is the closure of the paper where we summarize the important observations made from our study

Radial Basis Functions

The Sequential Optimization Sampling Method

Numerical Examples

Sampling methods

Conclusions

70 Function 1 Function 2 Function 3 60