本文關(guān)鍵詞：三水平triple設(shè)計(jì)的構(gòu)造與應(yīng)用　出處：《吉首大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 試驗(yàn)設(shè)計(jì) double設(shè)計(jì) triple設(shè)計(jì) 示性函數(shù) 水平置換 分辨度 最小低階混雜 均勻設(shè)計(jì) 可卷L_2-偏差

【摘要】：試驗(yàn)設(shè)計(jì)是數(shù)理統(tǒng)計(jì)學(xué)中最重要的分支之一,它使研究人員能夠找到好的試驗(yàn)有效地進(jìn)行數(shù)據(jù)分析.隨著科學(xué)技術(shù)的發(fā)展,試驗(yàn)涉及的因素個(gè)數(shù)眾多,且每個(gè)因素的水平也較多,此時(shí)完全因子設(shè)計(jì)要求的試驗(yàn)次數(shù)大大超過了人們的承受程度.從經(jīng)濟(jì)的角度出發(fā),通常采用部分因子設(shè)計(jì),它是完全因子設(shè)計(jì)的一個(gè)子集或部分,在實(shí)際生活中應(yīng)用最廣泛的是兩水平和三水平的部分因子設(shè)計(jì).而試驗(yàn)設(shè)計(jì)的一個(gè)重要任務(wù)是如何從眾多部分因子設(shè)計(jì)中找到“好”的設(shè)計(jì),即用最少的試驗(yàn)次數(shù)獲得最多的有用信息.對(duì)于什么樣的設(shè)計(jì)是“好”的設(shè)計(jì),人們基于不同的角度給出了許多設(shè)計(jì)篩選準(zhǔn)則,其中最常見的是分辨度準(zhǔn)則和最小廣義低階混雜準(zhǔn)則.在構(gòu)建兩水平部分因子設(shè)計(jì)時(shí)一種被稱為doubling的方法經(jīng)常被使用,尤其在構(gòu)造大型設(shè)計(jì)時(shí),利用doubling來構(gòu)造設(shè)計(jì)既簡(jiǎn)單又有用,在構(gòu)造分辨度為ⅣV的設(shè)計(jì)時(shí),doubling也十分有用,最近已有許多文獻(xiàn)討論了double設(shè)計(jì)的一些性質(zhì)和應(yīng)用.但是,目前的double設(shè)計(jì)僅限于兩水平,于是本文考慮能否把兩水平的double設(shè)計(jì)進(jìn)行推廣,使得構(gòu)造三水平或者更高水平的大型設(shè)計(jì)也變得簡(jiǎn)單有效?同時(shí)可以看到兩水平double設(shè)計(jì)的原理一一折疊反轉(zhuǎn)其實(shí)是一種非常特殊的水平置換,并且水平置換在設(shè)計(jì)構(gòu)造上也有眾多應(yīng)用,因此從水平置換的角度來推廣double設(shè)計(jì)的概念就會(huì)有更多選擇.但是經(jīng)過嘗試性的探索,可以發(fā)現(xiàn)如果行只翻2倍,無論怎么從5種水平置換方式里挑選方案都存在原來的列和新構(gòu)造的列不會(huì)正交,這就意味著所構(gòu)造的設(shè)計(jì)性質(zhì)非常差.但是深入分析,可以發(fā)現(xiàn)如果行翻了3倍就會(huì)避免這一缺點(diǎn).因此,本文基于水平置換推廣了double設(shè)計(jì)的概念：提出三水平triple設(shè)計(jì)的概念.均勻設(shè)計(jì)及均勻性理論是由我國(guó)學(xué)者率先提出的一種全新的部分因子設(shè)計(jì)理論和方法,被廣泛用于“計(jì)算機(jī)仿真試驗(yàn)”和國(guó)防、農(nóng)業(yè)、工業(yè)、醫(yī)藥和高新技術(shù)創(chuàng)新等領(lǐng)域,已取得了顯著的經(jīng)濟(jì)效益和社會(huì)效益.偏差則是衡量均勻設(shè)計(jì)的測(cè)度,常用的偏差有中心化L2-偏差(CD),可卷L2-偏差(W D)，，離散偏差(DD),Lee偏差(LD)等等.基于以上考慮,本論文主要進(jìn)行了以下3個(gè)方面的工作：(1)探索三水平triple設(shè)計(jì)的形式和結(jié)構(gòu),基于水平置換構(gòu)造了三水平的triple設(shè)計(jì)T(A),并且以示性函數(shù)為工具,討論了T(A)的幾個(gè)優(yōu)良性質(zhì).(2)討論了T(A)在可卷L2-偏差下的均勻性：將T(A)的可卷L2-偏差與A的混雜建立了一個(gè)等量關(guān)系,并且利用泰勒公式給出了T(A)在可卷L2-偏差下緊的下界.(3)討論了T(A)及其投影設(shè)計(jì)在構(gòu)造最小低階混雜設(shè)計(jì)上的幾個(gè)應(yīng)用.下面簡(jiǎn)要介紹一下各章的內(nèi)容.第一章概述了試驗(yàn)設(shè)計(jì)的相關(guān)背景及論文的創(chuàng)新點(diǎn)和結(jié)構(gòu).第二章簡(jiǎn)要介紹了基本概念、符號(hào),并給出后面章節(jié)要用到的相關(guān)結(jié)論.第三章討論了基于水平置換構(gòu)造了三水平的triple設(shè)計(jì)T(A),并以示性函數(shù)為工具初步分析了triple設(shè)計(jì)的幾個(gè)優(yōu)良性質(zhì).如果A的分辨度為Ⅲ,T(A)的分辨度也是Ⅲ.并且進(jìn)一步地到了T(A)的三類投影設(shè)計(jì)：如果A的分辨度為Ⅲ或者Ⅳ,那么T(A)的投影設(shè)計(jì)的分辨度也是Ⅲ或者Ⅳ.第四章深入討論了T(A)在可卷L2-偏差下均勻性和混雜情況.將T(A)的可卷L2-偏差與A混雜建立了一個(gè)等量關(guān)系,發(fā)現(xiàn)若A有較小的低階混雜,T(A)會(huì)具有較小的可卷L2-偏差和低階混雜.同時(shí),本章節(jié)給出了T(A)在可卷L2-偏差下緊的下界,便于計(jì)算機(jī)搜索triple設(shè)計(jì)的均勻設(shè)計(jì).第五章討論了T(A)及其投影設(shè)計(jì)的幾個(gè)應(yīng)用.本章節(jié)選取了幾個(gè)初始設(shè)計(jì)A,得到的T(A)及其投影設(shè)計(jì)在可卷L2-偏差下的均勻性都比較好,有的甚至比UD主頁(yè)中對(duì)應(yīng)的均勻設(shè)計(jì)還要好,并且他們均具有最小的低階混雜.第六章對(duì)全文工作進(jìn)行總結(jié)和對(duì)未來的工作進(jìn)行了展望.
[Abstract]:The experimental design is one of the most important branches in mathematical statistics, it allows researchers to find a good test effectively for data analysis. With the development of science and technology, a large number of test factors involved, and each factor level is more, the number of test requirements set complete factor greatly exceeds the tolerance level of people. From an economic point of view, usually by fractional factorial design, it is a subset of the full factorial design or part of application in real life is the most widely used part of two level and three level factorial design. An important task of experimental design is how to find a "good" design from many parts factor design, to obtain the most useful information by using the minimal number of tests. For the design of what is "good" design, people from different angles are given based on many design. Standards, is one of the most common resolution criterion and the minimum generalized aberration. In the construction of two level fractional factorial design method called doubling is often used, especially in the construction of large-scale design, using doubling structure design is simple and useful, in the construction of the resolution for the design of IV V when the doubling is also very useful, recently many literatures discussed some properties and applications of double design. However, the current design of the double is limited to the two level, so this paper consider whether to design double two level promotion, the large design structure of the three level or higher level becomes simple and effective? See the principle of two level double design one fold reversal is actually a very special level of replacement, and the level of replacement in the design also has many applications, from the level of replacement The angle to promote the concept of double design will have more choices. But after a tentative exploration, can be found only if the row over 2 times, no matter how columns are not orthogonal from the 5 level replacement selection schemes all have the original columns and new structures, which means that the structure design is made very nature poor. But the in-depth analysis, we can find that if the line over 3 times will avoid the shortcomings. Therefore, this paper generalizes the concept of horizontal displacement based on double design: put forward the concept of three level triple design. Uniform design and uniform theory is proposed by our Ancient Chinese Literature Search took the lead in a new design theory and some factors method, is widely used in "computer simulation" and national defense, industry, agriculture, medicine and other fields of high-tech innovation, has achieved remarkable economic and social benefits. The deviation is a measure of the uniform design 鐨勬祴搴

本文編號(hào)：1371092