Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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An Error Assessment of the Kriging Based Approximation Model Using a Mean Square Error

평균제곱오차를 이용한 크리깅 근사모델의 오차 평가

  • 주병현 (한국과학기술원 기계공학과) ;
  • 조태민 (한국과학기술원 기계공학과) ;
  • 정도현 (자동차부품연구원) ;
  • 이병채 (한국과학기술원 기계공학과)
  • Published : 2006.08.01
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Abstract

A Kriging model is a sort of approximation model and used as a deterministic model of a computationally expensive analysis or simulation. Although it has various advantages, it is difficult to assess the accuracy of the approximated model. It is generally known that a mean square error (MSE) obtained from the kriging model can't calculate statistically exact error bounds contrary to a response surface method, and a cross validation is mainly used. But the cross validation also has many uncertainties. Moreover, the cross validation can't be used when a maximum error is required in the given region. For solving this problem, we first proposed a modified mean square error which can consider relative errors. Using the modified mean square error, we developed the strategy of adding a new sample to the place that the MSE has the maximum when the MSE is used for the assessment of the kriging model. Finally, we offer guidelines for the use of the MSE which is obtained from the kriging model. Four test problems show that the proposed strategy is a proper method which can assess the accuracy of the kriging model. Based on the results of four test problems, a convergence coefficient of 0.01 is recommended for an exact function approximation.

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References

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