样条基下的分段Kriging模型
发布时间：2018-12-08 20:45
【摘要】：试验设计是数理统计学中一个重要的分支,其应用领域十分广泛。随着计算机技术的高速发展,许多试验都可以利用计算机进行模拟,不仅可以节省时间和成本,还可以克服传统实体试验在某些领域的局限性。计算机试验的研究主要分为建模预测和构造设计两个方向,其中,在建模预测方面,kriging模型成为一种影响深远的建模方法,研究人员以此为基础对传统的kriging模型进行改进,从而得到了许多更精确的预测方法,使得构建的模型能够适应更广泛的响应曲面。本文首先介绍了近些年来计算机试验建模方法的一些研究成果,然后基于用分段函数近似真实响应的思想,构建样条基下的分段kriging模型。该模型利用一组筛选后的样条基函数的线性组合来刻画全局趋势,进而由样条基独特的分段性,在每一段用具有不同方差的高斯过程来描述误差部分,从而得到更加精确的预测,使得它能更好地近似不同波动变化的曲面。此外,对于已知的数据,本文还给出并证明了真实响应的最佳线性无偏估计,讨论了其相关的性质以及模型未知参数的估计问题。最后,通过三个例子说明该模型相对于通常的kriging模型在预测上的优势,以及在不同种类的设计下都能给出很好的预测。
[Abstract]:Experimental design is an important branch of mathematical statistics. With the rapid development of computer technology, many experiments can be simulated by computer, which can not only save time and cost, but also overcome the limitations of traditional physical experiments in some fields. The research of computer experiment is mainly divided into two directions: modeling prediction and structural design. In modeling and prediction, kriging model has become a far-reaching modeling method, on which researchers have improved the traditional kriging model. Thus, many more accurate prediction methods are obtained, and the constructed model can adapt to a wider range of response surfaces. This paper first introduces some research achievements of computer experimental modeling methods in recent years, and then based on the idea of using piecewise functions to approximate real responses, a piecewise kriging model based on spline basis is constructed. The model uses a set of linear combinations of filtered spline basis functions to depict global trends, and then uses Gao Si processes with different variances to describe the error part in each segment by the unique piecewise character of the spline basis. Thus more accurate prediction can be obtained, which makes it better approximate to the surface with different fluctuations. In addition, for the known data, the optimal linear unbiased estimation of the real response is given and proved. The related properties and the estimation of the unknown parameters of the model are discussed. Finally, three examples are given to illustrate the advantages of this model over the conventional kriging model in prediction, and that the model can be well predicted under different designs.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C815
本文编号：2368972
[Abstract]:Experimental design is an important branch of mathematical statistics. With the rapid development of computer technology, many experiments can be simulated by computer, which can not only save time and cost, but also overcome the limitations of traditional physical experiments in some fields. The research of computer experiment is mainly divided into two directions: modeling prediction and structural design. In modeling and prediction, kriging model has become a far-reaching modeling method, on which researchers have improved the traditional kriging model. Thus, many more accurate prediction methods are obtained, and the constructed model can adapt to a wider range of response surfaces. This paper first introduces some research achievements of computer experimental modeling methods in recent years, and then based on the idea of using piecewise functions to approximate real responses, a piecewise kriging model based on spline basis is constructed. The model uses a set of linear combinations of filtered spline basis functions to depict global trends, and then uses Gao Si processes with different variances to describe the error part in each segment by the unique piecewise character of the spline basis. Thus more accurate prediction can be obtained, which makes it better approximate to the surface with different fluctuations. In addition, for the known data, the optimal linear unbiased estimation of the real response is given and proved. The related properties and the estimation of the unknown parameters of the model are discussed. Finally, three examples are given to illustrate the advantages of this model over the conventional kriging model in prediction, and that the model can be well predicted under different designs.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C815
【参考文献】
相关期刊论文 前1条
1 张润楚,王兆军;关于计算机试验的设计理论和数据分析[J];应用概率统计;1994年04期
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