计算机实验的最优线性无偏预测和正交设计

发布时间：2018-07-03 01:33

本文选题：计算机实验 + 高斯函数　；参考：《北京建筑大学》2017年硕士论文

【摘要】：随着计算机实验在科学实验和工业设计等诸多领域的广泛应用,需要解决的统计问题也越来越多。在实际应用中,我们常常会遇到来自于不同精度的计算机实验,精度高的计算机实验计算速度慢,而计算速度快的计算机实验计算精度低。面对这种情况,通常采用的方法是将各个精度计算机实验分开研究,这无疑是一种浪费。另外,随着精度的提高,计算速度减慢,鉴于成本与时间的花费,我们可得到的设计集数减少,基于较少的设计集对试验点进行预测往往不太理想,所以我们提出在便宜的低精度实验中加入少量昂贵的高精度实验,就可以将不同精度的数据联系起来,在此基础上对任意点的计算机输出进行预测,就有可能兼顾高低精度计算机实验的优点,从而提高整体的预测精度。鉴于此,本文将文献中已有的单精度计算机实验的最优线性无偏预测分别推广到两精度、多精度、连续精度计算机实验,具体工作如下:1.研究了两精度计算机实验任意处计算机输出的最优线性无偏预测。本文在已有文献低精度模型和高精度模型的基础之上,利用拉格朗日乘数法求出任意点处高精度计算机输出的最优线性无偏预测,当模型中的参数未知时,提出用分层最大似然估计给出经验最优线性无偏预测,并通过数值模拟和实例验证方法的可行性。结果显示,此方法有利于提高两精度计算机实验预测准确性与计算高效性。2.研究了多精度计算机实验任意处计算机输出的最优线性无偏预测。本文给出了s个精度的计算机实验,随着t的增大(其中t(?){1,2,…,s}),计算机实验的精度增加,速度减慢,利用拉格朗日乘数法求出第s精度任意点处计算机输出的最优线性无偏预测,当模型中的参数未知时,通过分层最大似然估计给出经验最优线性无偏预测,最后通过数值模拟验证方法的可行性,结果显示,此方法对于提高多精度计算机实验模型的预测准确性与计算高效性有显著作用。3.研究了连续精度计算机实验任意处真实值的最优线性无偏预测。本文在第五章引入调节参数t＞0,它决定着数值计算的精度以及计算时间,随着t的减小,计算精度提高,计算速度减慢,t越趋近于0,计算机输出越趋近于真实值,利用拉格朗日乘数法求出任意点处真实值的最优线性无偏预测,最后通过数值模拟和实例验证方法的可行性,结果显示,此方法对于连续精度计算机实验的预测有着良好的表现。计算机实验的另一重要部分为试验设计,本文探讨了一类不限定在拉丁超立方设计中的正交空间填充设计,并提出用分组坐标下降算法来构造这类设计,数值模拟表明此算法能够有效找到具有很好的空间填充性质的正交设计。另外,正交的最大最小距离设计在计算机实验预测方面的表现与常用设计是可以相比的。
[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.
【学位授予单位】：北京建筑大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212

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