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Min-Max Distance Response Surface and Kreisselmerier-Steinhauser Function |
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Abstract: The current Response Surface Methodology(RSM) is based on the least squares method. This paper proposes a new response surface fitting method, which let the maximum distance among the response hypersurface function and sample values be minimized. In this method, a mathematical model is built based on the characteristics of Kreisselmerier-Steinhauser function. The coefficients of the response hyper-surface function can be determined by taking derivatives, carrying out Taylor expansions and numerical iterations. The result of the least squares method is used as the initial value in the process of numerical iteration. According to a series of calculated cases, three conclusions are reached. First, the response hyper-surface function obtained from the Kreisselmerier-Steinhauser function method satisfies the condition of minimizing the maximum distance. Second, compared with the counterpart obtained from the least squares method, the response hyper-surface function obtained from this method could noticeably reduce the maximum distance in case that the RMS of sample values increases in a small scale. Third, the adoption of a method of changing stretching factor could lead to a better solution. The method proposed in this paper not only provides a response surface method but also can ensure the maximum distance among the response hyper-surface function and sample values minimized in practical engineering problems.
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Received: 15 September 2009
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Corresponding Authors:
yu hui ping
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