最大差值极小化的响应面函数拟合方法

The Fitting of Response Surface Function with Maximum Difference Minimization Method

为了满足实际工程问题中响应函数与样本值最大距离极小化的需求,本文提出一种新的响应面函数的拟合方法。该方法将样本点的响应面函数拟合问题转换为求解一类线性规划问题。建立数学模型,采用数值方法拟合出一次和二次响应面函数的表达式。通过多个数值算例,与K-S函数法实现最大差值极小化拟合的响应面函数结果以及最小二乘法拟合响应面结果进行比较,本文方法均得到较小的最大离差值,结果表明该方法的可行性和有效性,丰富了响应面的构造方法。

In order to meet the requirements of minimizing the maximum distance between the response function and the sample values in practical engineering problems,a new method of fitting the response surface function is proposed in this paper.The problem of fitting the response surface function with sample points is transformed into one of solving a linear programming problem in this method.A mathematical model about sample points is established.Linear and quadratic response surface function expressions are fitted by numerical methods.Comparing the fitted results of minimizing the maximum difference by the Kreisselmerier-Steinhauser（K-S） function method and those by the least squares method,the method used in this paper give results better agreed with those of the K-S function method,with the maximum differences smaller than that of the least squares method.Four numerical examples show that this method is reasonable and effective.In addition,this method provides a new constructing method for the response surface function.