对称化偏差及其改进

发布时间：2018-06-01 02:59

本文选题：试验设计 + 均匀设计　；参考：《华中师范大学》2017年硕士论文

【摘要】：均匀设计是一种稳健设计,是最常用的空间填充设计之一.在没有充分的先验信息时,试验区域中的每一个试验点被认为同等重要,因此均匀设计主张将试验点均匀地分布在目标区域中.为了度量设计点在试验区域分布的均匀性,许多偏差被定义和发展.在文献中,最常用的偏差有:星偏差、中心化偏差(CD)、可卷偏差(WD)、对称化偏差(SD)和混合偏差(MD)等.为了比较不同的偏差,最近覆盖率的定义被提出,本文根据覆盖率的定义和再生核希尔伯特空间中核函数的定义,推导出各种偏差的覆盖率公式,并针对公式研究了现有的各种不同偏差在覆盖率意义下的优良性,发现对称化偏差具有常值覆盖率,具有突出的优良性.利用对称化偏差这样的优良性,我们借鉴了混合偏差的思想构造了新的混合偏差.最后,我们从不同的角度研究了对称化偏差,及新的混合偏差,如:覆盖率、GMA准则等.
[Abstract]:Uniform design is a robust design. It is one of the most commonly used space filling designs. In the absence of sufficient prior information, each test point in the test area is considered equally important, so the uniform design advocates that the test points are evenly distributed in the target area. In order to measure the uniformity of the distribution of the design points in the test area, many of the design points are distributed. Deviation is defined and developed. In the literature, the most commonly used deviations are: Star deviation, centralization deviation (CD), coiling deviation (WD), symmetric deviation (SD) and mixed deviation (MD). In order to compare different deviations, the definition of the recent coverage rate is proposed. In this paper, the definition of the coverage rate and the definition of the kernel function in the regenerated kernel Hilbert space are derived. The formula of the coverage rate of various deviations is given, and the excellent properties of the existing different deviations in the sense of coverage are studied. It is found that the symmetry deviation has the constant coverage rate and has the outstanding quality. By using the good of symmetry deviation, we use the idea of mixing deviation to construct a new mixing deviation. Finally, We have studied the symmetry deviation and new mixing bias from different angles, such as coverage, GMA criterion and so on.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.6

【参考文献】