本文選題：因析設(shè)計(jì) + 混合水平��； 參考：《東南大學(xué)》2015年博士論文

【摘要】：本文主要研究了因析設(shè)計(jì)中的幾類典型問題,包括利用矩陣象理論研究了非正規(guī)因析設(shè)計(jì)的混雜度量及其在全局敏感性分析中的應(yīng)用、利用矩陣象工具建立了廣義分辨度指標(biāo)、建立了廣義可變分辨度設(shè)計(jì)的一般理論及相應(yīng)設(shè)計(jì)的構(gòu)造方法、完整討論了4類部分純凈主效應(yīng)設(shè)計(jì)的存在性和構(gòu)造、給出了通過區(qū)組因子達(dá)到正交的主效應(yīng)設(shè)計(jì)的若干構(gòu)造方法、及其在均勻性準(zhǔn)則下的最優(yōu)設(shè)計(jì).主要內(nèi)容如下：第一章著重介紹試驗(yàn)設(shè)計(jì)的基本概念以及重要理論,介紹了因析設(shè)計(jì)、因子分組設(shè)計(jì)的研究進(jìn)展.第一章的結(jié)尾處,大致陳述了本文的主要工作,并闡釋了創(chuàng)新點(diǎn).第二章我們通過運(yùn)用矩陣象的相關(guān)性質(zhì),提出了一種區(qū)分帶有復(fù)雜混雜結(jié)構(gòu)的非正規(guī)設(shè)計(jì)的混雜度量工具,其可以適用于正規(guī)設(shè)計(jì),也可以適用于非正規(guī)設(shè)計(jì),實(shí)例分析表明該準(zhǔn)則相比于幾種經(jīng)典方法有更強(qiáng)的區(qū)分能力.另一方面,本章還考慮了當(dāng)所采用正交表強(qiáng)度小于所需強(qiáng)度時(shí),對(duì)全局敏感性分析的影響.基于矩陣象理論,我們首先推廣了方差分析高維模型下的別名矩陣,然后通過依次最小化平方混雜度,給出了一種敏感性指標(biāo)的估計(jì)方法.討論了用二水平16次設(shè)計(jì)和四水平64次設(shè)計(jì)來估計(jì)低階顯著性敏感性指標(biāo)和高階敏感性指標(biāo)的例子.所有例子表明當(dāng)設(shè)計(jì)的平方混雜度越小時(shí),其全局敏感性指標(biāo)的估計(jì)具有更小的偏差和方差.第三章討論當(dāng)組內(nèi)因子間存在不可忽略交互效應(yīng)時(shí)的廣義可變分辨度設(shè)計(jì)D(n, (m1, m2),(τ1,τ2)τ3,τ).我們討論了廣義可變分辨度設(shè)計(jì)的存在性條件,并給出了與折衷設(shè)計(jì)、純凈折衷設(shè)計(jì)、帶有部分純凈二因子交互作用設(shè)計(jì)之間的關(guān)系.最后我們給出了廣義可變分辨度設(shè)計(jì)的構(gòu)造方法.第四章論證了廣義可變分辨度設(shè)計(jì)在方差分析高維模型下估計(jì)參數(shù)時(shí)具有A最優(yōu)性.模型分別考慮了不含交互作用和含有交互作用兩種情形.最后也通過模擬進(jìn)行了驗(yàn)證比較.第五章研究了部分純凈主效應(yīng)設(shè)計(jì).純凈效應(yīng)準(zhǔn)則是選擇最優(yōu)設(shè)計(jì)的一個(gè)重要原則.在一個(gè)分辨度為V的設(shè)計(jì)中,所有主效應(yīng)是純凈的.但如果還有信息表明部分二階交互效應(yīng)是不存在的,則可以得到一類新的設(shè)計(jì),其所含有的主效應(yīng)與可能存在的二階交互效應(yīng)均正交.且這類設(shè)計(jì)的列數(shù)可以大于分辨度V的設(shè)計(jì)列數(shù).我們稱其為部分純凈主效應(yīng)設(shè)計(jì).本章完整的討論了所有可能的部分純凈主效應(yīng)設(shè)計(jì).并對(duì)這4類設(shè)計(jì)的存在性進(jìn)行了研究,最后發(fā)現(xiàn)其中3類是不存在的.對(duì)可能存在的第4類設(shè)計(jì)給出了相應(yīng)的構(gòu)造方法.第六章研究了通過區(qū)組因子達(dá)到正交的主效應(yīng)設(shè)計(jì)(POTB)的若干構(gòu)造方法.這類設(shè)計(jì)的處理因子能夠通過區(qū)組因子達(dá)到兩兩正交.然而,文獻(xiàn)中的構(gòu)造方法較少.本章我們提出若干構(gòu)造試驗(yàn)次數(shù)較小,多水平的,飽和POTB設(shè)計(jì)的方法,且這些設(shè)計(jì)均是可連接的和方差平衡的.第七章討論了上述設(shè)計(jì)(通過區(qū)組設(shè)計(jì)得到正交的主效應(yīng)設(shè)計(jì))中的正交性可以在水平置換下保持不變.然而,水平置換可以改變?cè)O(shè)計(jì)的幾何結(jié)構(gòu)和統(tǒng)計(jì)性質(zhì).于是本章進(jìn)一步采用均勻性來區(qū)分同一參數(shù)下的POTB設(shè)計(jì).通過本章提出的最優(yōu)化算法可以得到很多最優(yōu)的或者近似最優(yōu)的均勻POTB設(shè)計(jì).
[Abstract]:This paper mainly studies several typical problems in the factorial design, including the use of matrix image theory to study the hybrid measurement of the irregular factorial design and its application in the global sensitivity analysis. The generalized resolution index is established by the matrix image tool, and the general theory of the generalized variable discrimination design and the corresponding design are established. In this method, the existence and construction of the 4 kinds of pure main effect design are discussed, and some construction methods of the main effect design through the region group factor are given and the optimal design under the uniformity criterion are given. The main contents are as follows: the first chapter introduces the basic concepts and important theories of the experimental design, and introduces the basic concepts. In the end of the first chapter, the main work of this paper is roughly stated and the innovation point is explained. In the second chapter, by using the related properties of matrix images, we propose a hybrid metric tool for irregular design with complex hybrid structures, which can be applied to regular design, It can be applied to irregular design. Example analysis shows that the criterion has a better distinction than several classical methods. On the other hand, this chapter also considers the influence on the global sensitivity analysis when the strength of the orthogonal table is less than the required strength. Based on the matrix image theory, we first generalize the high dimensional model of variance analysis. The alias matrix, and then an estimation method of sensitivity index is given by minimizing the square miscellaneous degree in turn. An example of estimating low order saliency sensitivity index and high order sensitivity index with two level 16 times design and four level 64 times design is discussed. All examples show that the overall sensitivity of the design is the hourly mixed degree of design. The estimation of the perceptual index has smaller deviations and variance. In the third chapter, we discuss the generalized variable resolution design D (n, (M1, M2), (tau, tau 2) tau 3, tau (tau) when there is no neglecting the interaction effect among the factors in the group. We discuss the existence condition of the generalized variable resolution design, and give the tradeoff design, the pure compromise design, with some part. The relationship between the interaction design of the pure two factor interaction. Finally, we give the construction method of the generalized variable resolution design. The fourth chapter demonstrates that the generalized variable resolution design has the A optimality in the estimation of the parameters under the high dimensional model of variance analysis. The model considers two cases without interaction and interaction, respectively. In the fifth chapter, the fifth chapter studies the design of the partial pure main effect. The pure effect criterion is an important principle for the selection of optimal design. In a design with a resolution of V, all the main effects are pure. But if there is any information that the part of the two order interaction effect does not exist, we can get a new kind of new type. The main effect contained in the design is orthogonal to the possible two order interaction effects. And the number of columns in this type of design can be larger than the number of design columns of the resolution V. We call it a part of the pure main effect design. This chapter completely discusses all possible parts of the pure main effect design. And the existence of these 4 kinds of design is studied. Finally, we find that the 3 types are nonexistent. The corresponding construction methods are given for the possible fourth types of design. The sixth chapter studies several construction methods of the main effect design (POTB) through the region group factor. The processing factor of this kind of design can reach 22 orthogonal by the region group factor. However, the construction method in the literature is more than that in the literature. In this chapter, we propose a number of smaller, multi horizontal, saturated POTB design methods, and these designs are both connectable and variance balanced. The seventh chapter discusses that the above design (through the design of the orthogonal main effect design by the area group design) can remain unchanged under the horizontal displacement. However, the horizontal displacement can be maintained. In order to change the geometric structure and statistical properties of the design, this chapter further uses uniformity to distinguish the POTB design under the same parameter. The optimization algorithm proposed in this chapter can obtain many optimal or approximately optimal uniform POTB designs.
【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：TB47

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本文編號(hào)：2090710