This thesis presents the development and implementation of a generalized optimization framework for use in sheet-stamping process simulation by finite element analysis. The generic framework consists of three main elements: a process simulation program, an optimization code, and a response filtering program. These elements can be filled by any combination of applicable software packages. Example sheet-stamping process simulations are presented to demonstrate the usage of the framework in various forming scenarios. Each of the example simulations is presented with a sensitivity analysis. These examples include analysis of a 2-dimensional single-stage forming, a 2-dimensional multi-stage forming, and two different 3-dimensional single-stage forming processes. A forming limit diagram is used to define failure in the 3-dimensional process simulations. Optimization results are presented using damage minimization, thinning minimization, and springback minimization with aluminum alloy 6061-T6 blanks.

[pt] O presente trabalho trata da aplicação da análise limite numérica (ALN) a problemas geotécnicos. Os meios (solo ou rocha) são considerados como contínuos convencionais e como contínuos de Cosserat. Da aplicação da formulação mista da análise limite e da discretização do meio por uma malha de elementos finitos é obtido um problema de programação matemática (PM). A aplicação desta metodologia nos contínuos de Cosserat (2D) fornece problemas de programação linear (PL) e nos contínuos convencionais (2D e 3D), problemas de programação não-linear (PNL). A solução do problema de PM foi através dos programas de otimização: LINDO (PL), LINGO (PNL), MINOS (PNL) e LANCELOT (PNL). Também foram implementados os algoritmos não lineares -Quase Newton com deflexão- e -Han-Powell-. A formulação é validada em problemas cuja solução analítica é conhecida ou em dados experimentais. Estes exemplos mostram a rapidez e a eficácia da ALN para a determinação da carga de colapso e do mecanismo de ruptura do problema. / [en] The present work treats of the application of the numerical limit analysis (NLA)to geomechanics problems. The soil or rock mass is considered as conventional continuous and Cosserat continuous. A mathematical programming (MP) problem is obtained through the application of the mixed formulation of limit analysis and the finite elements mesh. The application of this methodology in the Cosserat continuous (2D) supplies linear programming (LP) problems and in the conventional continuous (2D and 3D) nonlinear programming (NLP) problems. The solution of the problem of MP was through the LINDO (LP), LINGO (NLP), MINOS (NLP) and LANCELOT (NLP) programs. It was also implemented nonlinear algorithms -Quasi-Newton feasible point method- and -Han-Powell-.The formulation is validated in problems whose analytic solution is known or in experimental data. These examples show the speed and the effectiveness of NLA for the determination of the collapse load and of the mechanism of rupture of the problem. / [es] EL presente trabajo trata de la aplicación del análisis límite numérica (ALN) a problemas geotécnicos. Los medios (suelo o roca) son considerados como contínuos convencionales y como contínuos de Coserat. De la aplicación de la formulación mixta del análisis límite y de la discretización del medio por una malla de elementos finitos se obtiene un problema de programación matemática (PM). La aplicación de esta metodología en los contínuos de Coserat (2D) nos lleva a problemas de programación lineal (PL) y en los contínuos convencionales (2D y 3D), problemas de programación no lineal (PNL). La solución del problema de PM fue a través de los programas de optimización: LINDO (PL), LINGO (PNL), MINOS (PNL) y LANCELOT (PNL). También fueron implementados los algoritmos no lineares quase- Newton con deflexión y Han Powell . Se evalúa la formulación propuesta en problemas donde se conoce la solución analítica o en datos experimentales. Estos ejemplos muestran la rapidez y la eficacia de la ALN para la determinación de la carga de colapso y del mecanismo de ruptura del problema.

<p><br></p><p>How to set privacy parameters is a crucial problem for the consistent application of DP in practice. The current privacy parameters do not provide direct suggestions for this problem. On the other hand, different databases may have varying degrees of information leakage, allowing attackers to enhance their attacks with the available information. This dissertation provides an additional interpretation of the current DP notions by introducing a framework that directly considers the worst-case average failure probability of attackers under different levels of knowledge. </p><p><br></p><p>To achieve this, we introduce a novel measure of attacker knowledge and establish a dual relationship between (type I error, type II error) and (prior, average failure probability). By leveraging this framework, we propose an interpretable paradigm to consistently set privacy parameters on different databases with varying levels of leaked information. </p><p><br></p><p>Furthermore, we characterize the minimax limit of private parameter estimation, driven by $1/(n(1-2p))^2+1/n$, where $p$ represents the worst-case probability risk and $n$ is the number of data points. This characterization is more interpretable than the current lower bound $\min{1/(n\epsilon^2),1/(n\delta^2)}+1/n$ on $(\epsilon,\delta)$-DP. Additionally, we identify the phase transition of private parameter estimation based on this limit and provide suggestions for protocol designs to achieve optimal private estimations. </p><p><br></p><p>Last, we consider a federated learning setting where the data are stored in a distributed manner and privacy-preserving interactions are required. We extend the proposed interpretation to federated learning, considering two scenarios: protecting against privacy breaches against local nodes and protecting privacy breaches against the center. Specifically, we consider a non-convex sparse federated parameter estimation problem and apply it to the generalized linear models. We tackle two challenges in this setting. Firstly, we encounter the issue of initialization due to the privacy requirements that limit the number of queries to the database. Secondly, we overcome the heterogeneity in the distribution among local nodes to identify low-dimensional structures.</p>

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24386号 / 理博第4885号 / 新制||理||1699(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 平岡 裕章, 教授 COLLINS Benoit Vincent Pierre, 教授 坂上 貴之 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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The concentrations of heavy metals (Cd, Cu, Fe, Ni, Pb, Zn) were measured in water, and fish samples caught from the pond at Fishery Park in Unicoi County, TN. The water samples were collected once a week for 8 weeks. The amounts of metals in the muscle tissues, gill, and liver of the two fish species were measured. This was to determine if any correlation exists between the metal contents in water and those in the fish samples. The concentration ranges for the heavy metals found in the water samples are as follows: Zn 0.04-0.13; Cu, 0.00-0.00; Pb, 0.00-0.59; Cd, 0.0067-0.0071; Fe, 0.208-0.512; and Ni, 0.044-0.270 ppm. The concentration range for the heavy metals found in the fish tissues are as follows: Zn 0.0-0.48; Cu, 0.00-0.00; Pb, 0.00-0.43; Cd, 0.00-99.7; Fe, 25.7-1245.5; and Ni, 0.00-268.5 ppm. There was a strong correlation found between the water and fish tissue samples.

Let H be the Hawaiian Earring, and let H denote its fundamental group. Assume (Bi) is an inverse system of bouquets of circles whose inverse limit is H. We give an explicit bijection between finite normal covering spaces of H and finite normal covering spaces of Bi. This bijection induces a correspondence between a certain family of inverse sequences of these covering spaces. The correspondence preserves the inverse limit of these sequences, thus offering two methods of constructing the same limit. Finally, we characterize all spaces that can be obtained in this fashion as a particular type of fibrations of H.