基于支持向量机的小样本响应曲面法研究

A Study on the Small Sample Response Surface Methodology Based on SVM

当影响因素和响应输出的关系较为复杂时,应用传统响应曲面法(RSM)、非参数响应曲面法(NPRSM)和人工神经网络(ANN)难以拟合真实的响应曲面,不仅需要大的样本量,而且泛化风险大,不易达到全局最优。将RSM归结为可有限制地主动获取样本的小样本机器学习问题,提出了一种基于支持向量机(SVM)的RSM。以大间隔网格取样,利用SVM拟合过程,对拟合方程寻优确定极值大致区域,再逐步缩小间隔求精。算例研究表明,该方法的拟合与泛化性能优于NPRSM和基于ANN的RSM,能在小样本条件下建立全局性数值模型,寻优可以得到多个极值。

When the relationship between influential input variables and out response is very complex, it＇s hard to find the real response surface by using traditional response surface methodology（RSM） or nonparametric RSM （NPRSM） or artificial neural networks （ANN）. Although large sample size is required, these methods bring high generalization risk and can hardly reach the global optimum. To improve this, RSM is recognized as a small sample size machine learning issue of getting samples under constraint conditions. And a new RSM based on support vector machine （SVM） is developed. At first, the data are sampled with wide interval grid and the process is fitted by using SVM. Then the approximate areas including the extremisms are determined by optimizing the regression model. Finally, the exact results could be obtained step by step by shortening the intervals. The simulation research shows that the fitting and generalization performance of the proposed method is superior to that of NRSM or ANN based on RSM. Under the circumstance of small sample, the method can yield a comprehensive numerical model and obtain several process extremisms in optimizing.