This work considers the application of a µ-model approach on the cell means to a special yet important class of experimental designs. These include full factorial, completely nested, and mixed models with one or more observations per cell. By limiting attention to full models, an approach to the general data situation is developed which is both conceptually simple and computationally advantageous. Conceptually, the method is simple because the design related effects are defined as if the cell means are single observations. This leads to a rather simple algorithm for generating main effect contrasts, from which associated interaction contrasts can also be formed. While the sums of squares found from these contrasts are not additive with non-orthogonal data, they do lead to the class of design related hypotheses with the clearest interpretation in terms of the cells. The computational method is advantageous because the sum of squares for each source of variation is evaluated separately. This avoids the storage and inversion of a potentially large matrix associated with alternative methods, and allows the user to evaluate only those sources of interest. The methodology outlined in this work is programmed into a user-easy, interactive terminal version for the analysis of these n-factor design models.

The main objective of this research is to develop an innovative multi-fidelity multi-disciplinary design, analysis and optimization suite that integrates certain solution generation codes and newly developed innovative tools to improve the overall optimization process. The research performed herein is divided into two parts: (1) the development of an MDAO framework by integration of variable fidelity physics-based computational codes, and (2) enhancements to such a framework by incorporating innovative features extending its robustness. The first part of this dissertation describes the development of a conceptual Multi-Fidelity Multi-Strategy and Multi-Disciplinary Design Optimization Environment (M3 DOE), in context of aircraft wing optimization. M3 DOE provides the user a capability to optimize configurations with a choice of (i) the level of fidelity desired, (ii) the use of a single-step or multi-step optimization strategy, and (iii) combination of a series of structural and aerodynamic analyses. The modularity of M3 DOE allows it to be a part of other inclusive optimization frameworks. The M3 DOE is demonstrated within the context of shape and sizing optimization of the wing of a Generic Business Jet aircraft. Two different optimization objectives, viz. dry weight minimization, and cruise range maximization are studied by conducting one low-fidelity and two high-fidelity optimization runs to demonstrate the application scope of M3 DOE. The second part of this dissertation describes the development of an innovative hybrid optimization framework that extends the robustness of M3 DOE by employing a proper orthogonal decomposition-based design-space order reduction scheme combined with the evolutionary algorithm technique. The POD method of extracting dominant modes from an ensemble of candidate configurations is used for the design-space order reduction. The snapshot of candidate population is updated iteratively using evolutionary algorithm technique of fitness-driven retention. This strategy capitalizes on the advantages of evolutionary algorithm as well as POD-based reduced order modeling, while overcoming the shortcomings inherent with these techniques. When linked with M3 DOE, this strategy offers a computationally efficient methodology for problems with high level of complexity and a challenging design-space. This newly developed framework is demonstrated for its robustness on a non-conventional supersonic tailless air vehicle wing shape optimization problem. / Ph. D.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20152号 / 理博第4237号 / 新制||理||1609(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 堤 誉志雄, 教授 上田 哲生, 教授 國府 寛司 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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We consider Yang-Baxter relations with orthogonal or symplectic symmetry, in particular L matrices defining the related Yangian algebra. We study the conditions resulting from the truncation of the expansion of L(u).

The Hellmann-Feynman theorem is presented together with certain allied theorems. The origin of the Hellmann-Feynman theorem in quantum physical chemistry is described. The theorem is stated with proof and with discussion of applicability and reliability. Some adaptations of the theorem to the study of the variation of zeros of special functions and orthogonal polynomials are surveyed. Possible extensions are discussed.

This thesis is an extension of the development of orthogonal statistics which can be used to investigate sampling properties of moment estimators. This work is particularized for estimators of parameters of the negative binomial distribution. / Master of Science

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