【摘要】：試驗設計是數(shù)理統(tǒng)計學中一個重要的分支,其應用領域十分廣泛。隨著計算機技術(shù)的高速發(fā)展,許多試驗都可以利用計算機進行模擬,不僅可以節(jié)省時間和成本,還可以克服傳統(tǒng)實體試驗在某些領域的局限性。計算機試驗的研究主要分為建模預測和構(gòu)造設計兩個方向,其中,在建模預測方面,kriging模型成為一種影響深遠的建模方法,研究人員以此為基礎對傳統(tǒng)的kriging模型進行改進,從而得到了許多更精確的預測方法,使得構(gòu)建的模型能夠適應更廣泛的響應曲面。本文首先介紹了近些年來計算機試驗建模方法的一些研究成果,然后基于用分段函數(shù)近似真實響應的思想,構(gòu)建樣條基下的分段kriging模型。該模型利用一組篩選后的樣條基函數(shù)的線性組合來刻畫全局趨勢,進而由樣條基獨特的分段性,在每一段用具有不同方差的高斯過程來描述誤差部分,從而得到更加精確的預測,使得它能更好地近似不同波動變化的曲面。此外,對于已知的數(shù)據(jù),本文還給出并證明了真實響應的最佳線性無偏估計,討論了其相關(guān)的性質(zhì)以及模型未知參數(shù)的估計問題。最后,通過三個例子說明該模型相對于通常的kriging模型在預測上的優(yōu)勢,以及在不同種類的設計下都能給出很好的預測。
[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.
【學位授予單位】：東北師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：C815

【參考文獻】

相關(guān)期刊論文 前1條

1 張潤楚,王兆軍;關(guān)于計算機試驗的設計理論和數(shù)據(jù)分析[J];應用概率統(tǒng)計;1994年04期

，

本文編號：2368972