發(fā)布時(shí)間：2018-12-08 20:45

【摘要】：試驗(yàn)設(shè)計(jì)是數(shù)理統(tǒng)計(jì)學(xué)中一個(gè)重要的分支,其應(yīng)用領(lǐng)域十分廣泛。隨著計(jì)算機(jī)技術(shù)的高速發(fā)展,許多試驗(yàn)都可以利用計(jì)算機(jī)進(jìn)行模擬,不僅可以節(jié)省時(shí)間和成本,還可以克服傳統(tǒng)實(shí)體試驗(yàn)在某些領(lǐng)域的局限性。計(jì)算機(jī)試驗(yàn)的研究主要分為建模預(yù)測(cè)和構(gòu)造設(shè)計(jì)兩個(gè)方向,其中,在建模預(yù)測(cè)方面,kriging模型成為一種影響深遠(yuǎn)的建模方法,研究人員以此為基礎(chǔ)對(duì)傳統(tǒng)的kriging模型進(jìn)行改進(jìn),從而得到了許多更精確的預(yù)測(cè)方法,使得構(gòu)建的模型能夠適應(yīng)更廣泛的響應(yīng)曲面。本文首先介紹了近些年來(lái)計(jì)算機(jī)試驗(yàn)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(shí)響應(yīng)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(lái)刻畫(huà)全局趨勢(shì),進(jìn)而由樣條基獨(dú)特的分段性,在每一段用具有不同方差的高斯過(guò)程來(lái)描述誤差部分,從而得到更加精確的預(yù)測(cè),使得它能更好地近似不同波動(dòng)變化的曲面。此外,對(duì)于已知的數(shù)據(jù),本文還給出并證明了真實(shí)響應(yīng)的最佳線性無(wú)偏估計(jì),討論了其相關(guān)的性質(zhì)以及模型未知參數(shù)的估計(jì)問(wèn)題。最后,通過(guò)三個(gè)例子說(shuō)明該模型相對(duì)于通常的kriging模型在預(yù)測(cè)上的優(yōu)勢(shì),以及在不同種類的設(shè)計(jì)下都能給出很好的預(yù)測(cè)。
[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(xué)位授予單位】：東北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：C815

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本文編號(hào)：2368972