本文選題：計算機實驗 + 高斯函數(shù)　； 參考：《北京建筑大學》2017年碩士論文

【摘要】：隨著計算機實驗在科學實驗和工業(yè)設(shè)計等諸多領(lǐng)域的廣泛應用,需要解決的統(tǒng)計問題也越來越多。在實際應用中,我們常常會遇到來自于不同精度的計算機實驗,精度高的計算機實驗計算速度慢,而計算速度快的計算機實驗計算精度低。面對這種情況,通常采用的方法是將各個精度計算機實驗分開研究,這無疑是一種浪費。另外,隨著精度的提高,計算速度減慢,鑒于成本與時間的花費,我們可得到的設(shè)計集數(shù)減少,基于較少的設(shè)計集對試驗點進行預測往往不太理想,所以我們提出在便宜的低精度實驗中加入少量昂貴的高精度實驗,就可以將不同精度的數(shù)據(jù)聯(lián)系起來,在此基礎(chǔ)上對任意點的計算機輸出進行預測,就有可能兼顧高低精度計算機實驗的優(yōu)點,從而提高整體的預測精度。鑒于此,本文將文獻中已有的單精度計算機實驗的最優(yōu)線性無偏預測分別推廣到兩精度、多精度、連續(xù)精度計算機實驗,具體工作如下:1.研究了兩精度計算機實驗任意處計算機輸出的最優(yōu)線性無偏預測。本文在已有文獻低精度模型和高精度模型的基礎(chǔ)之上,利用拉格朗日乘數(shù)法求出任意點處高精度計算機輸出的最優(yōu)線性無偏預測,當模型中的參數(shù)未知時,提出用分層最大似然估計給出經(jīng)驗最優(yōu)線性無偏預測,并通過數(shù)值模擬和實例驗證方法的可行性。結(jié)果顯示,此方法有利于提高兩精度計算機實驗預測準確性與計算高效性。2.研究了多精度計算機實驗任意處計算機輸出的最優(yōu)線性無偏預測。本文給出了s個精度的計算機實驗,隨著t的增大(其中t(?){1,2,…,s}),計算機實驗的精度增加,速度減慢,利用拉格朗日乘數(shù)法求出第s精度任意點處計算機輸出的最優(yōu)線性無偏預測,當模型中的參數(shù)未知時,通過分層最大似然估計給出經(jīng)驗最優(yōu)線性無偏預測,最后通過數(shù)值模擬驗證方法的可行性,結(jié)果顯示,此方法對于提高多精度計算機實驗模型的預測準確性與計算高效性有顯著作用。3.研究了連續(xù)精度計算機實驗任意處真實值的最優(yōu)線性無偏預測。本文在第五章引入調(diào)節(jié)參數(shù)t＞0,它決定著數(shù)值計算的精度以及計算時間,隨著t的減小,計算精度提高,計算速度減慢,t越趨近于0,計算機輸出越趨近于真實值,利用拉格朗日乘數(shù)法求出任意點處真實值的最優(yōu)線性無偏預測,最后通過數(shù)值模擬和實例驗證方法的可行性,結(jié)果顯示,此方法對于連續(xù)精度計算機實驗的預測有著良好的表現(xiàn)。計算機實驗的另一重要部分為試驗設(shè)計,本文探討了一類不限定在拉丁超立方設(shè)計中的正交空間填充設(shè)計,并提出用分組坐標下降算法來構(gòu)造這類設(shè)計,數(shù)值模擬表明此算法能夠有效找到具有很好的空間填充性質(zhì)的正交設(shè)計。另外,正交的最大最小距離設(shè)計在計算機實驗預測方面的表現(xiàn)與常用設(shè)計是可以相比的。
[Abstract]:With the extensive application of computer experiments in many fields, such as scientific experiment and industrial design, more and more statistical problems are needed to be solved. In practical applications, we often encounter computer experiments from different precision. High precision computer experiments are slow, and the computational accuracy of computer experiments with fast calculation speed is low. In the face of this, the usual method is to separate the precision computer experiments, which is no doubt a waste. In addition, with the improvement of the precision, the speed of calculation is slow. In view of the cost and time, the number of design sets can be reduced and the prediction based on less design sets is often less ideal. By adding a small amount of expensive and high precision experiments to the cheap and low precision experiments, we can connect the data of different precision. On this basis, we can predict the output of the computer at any point. It is possible to give consideration to the advantages of the high and low precision computer experiment so as to improve the accuracy of the whole prediction. The optimal linear unbiased prediction of single precision computer experiments has been extended to two precision, multi precision and continuous precision computer experiments. The specific work is as follows: 1. the optimal linear unbiased prediction of computer output at any place of two precision computer experiments is studied. This paper is based on the basis of the low precision model and the high precision model in the literature. On the basis of the Lagrange multiplier method, the optimal linear unbiased prediction of high precision computer output at any point is obtained. When the parameters in the model are unknown, the empirical optimal linear unbiased prediction is given by the hierarchical maximum likelihood estimation, and the feasibility of the method is verified by numerical simulation and example. The results show that this method is beneficial to improve the method. Two precision computer experiment prediction accuracy and high efficiency.2. study the optimal linear unbiased prediction of computer output at any place in a multi precision computer experiment. This paper gives a computer experiment with s precision, with the increase of T (of which t (?) {1,2,... S}), the accuracy of the computer experiment is increased and the speed is slowed down. The optimal linear unbiased prediction of the output of the computer is obtained by the Lagrange multiplier method. When the parameters in the model are unknown, the empirical optimal linear unbiased pretest is given by the hierarchical maximum likelihood estimation. Finally, the feasibility of the method is verified by numerical simulation. The results show that this method plays a significant role in improving the accuracy and efficiency of the multi precision computer experimental model..3. studies the optimal linear unbiased prediction of the real value at any place in the continuous precision computer experiment. In the fifth chapter, the adjustment parameter t > 0 is introduced, which determines the accuracy and time of the numerical calculation, with the T The calculation precision is improved and the calculation speed is slowed down. The more the t becomes close to 0, the more the computer output is close to the real value. The Lagrange multiplier method is used to find the optimal linear unbiased prediction of the real value at any point. Finally, the feasibility of the method is verified by numerical simulation and example. The result shows that this method is used for the continuous precision computer experiment. The prediction has good performance. Another important part of the computer experiment is the experimental design. In this paper, a class of non limited space filling designs in the Latin hypercube design is discussed, and the group coordinate descent algorithm is proposed to construct this kind of design. The numerical simulation shows that this method can effectively find a good space filling property. Qualitative orthogonal design. In addition, the performance of the orthogonal maximum and minimum distance design in computer experiment prediction is comparable with the commonly used design.
【學位授予單位】：北京建筑大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212

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