高斯过程响应面法研究

A new response surface method baesd on gaussian process

新型的高斯过程响应面法具有灵活性好、精度高和能量化不确定性等优点,但某些关键技术细节还存在争议。本文简要介绍了高斯过程响应面法的基本理论,结合算例详细讨论了关键技术细节的处理方法;提出了先验期望函数选用低阶多项式、相关函数选用高斯形式、粗糙度参数用边缘后验众数法固定、模型有效性必须经过验算点检验等应用建议。

Compared to the traditional response surface method (RSM), Gaussian process RSM has some remarkable advantages such as more flexibility, higher precision and quantifiable uncertainty. However, how to deal with some important technical details has been puzzling users. In this paper, the basic theory of the new method is introduced, and these technical details are discussed thoroughly and illustrated with an artificial example. Then, some suggestions such as selecting a low order polynomial as the prior expectation function, employing the Gaussian covariance function, fixing the roughness parameters at their marginal posterior mode values, and assessing the model validity using validation data, are given for engineering applications.