Non-planar lifting surfaces offer potentially significant gains in aerodynamic efficiency by lowering induced drag. Non-aerodynamic considerations, such as structures can impact the overall efficiency. Here, a panel method and equivalent beam finite element model are used to explore non-planar configurations taking into account the coupling between aerodynamics and structures. A single discipline aerodynamic optimization and a multidisciplinary aerostructural optimization are investigated. Due to the complexity of the design space and the presence of multiple local minima, an augmented Lagrangian particle swarm optimizer is used. The aerodynamic optimum solution found for rectangular lifting surfaces is a box wing, while allowing for sweep and taper yields a joined wing. Adding parasitic drag in the aerodynamic model reduces the size of the non--planar elements. The aerostructural optimal solution found is a winglet configuration when the span is constrained and a wing rake when there is no such constraint.

The design of optimal strictly positive real (SPR) compensators using numerical optimization is considered. The plants to be controlled are linear and nonlinear flexible manipulators. For the design of SISO and MIMO linear SPR controllers, the optimization objective function is defined by reformulating the H2-optimal control problem subject to the constraint that the controllers must be SPR. Various controller parameterizations using transfer functions/matrices and state-space equations are considered. Depending on the controller form, constraints are enforced (i) using simple inequalities guaranteeing SPRness, (ii) in the frequency domain, or (iii) by implementing the Kalman-Yakubovich- Popov lemma. The design of a gain-scheduled SPR controller using numerical optimization is also considered. Using a family of linear SPR controllers, the time dependent scheduling signals are parameterized, and the objective function of the optimizer seeks to find the form of the scheduling signals which minimizes the manipulator tip tracking error while minimizing the control effort.

Non-planar lifting surfaces offer potentially significant gains in aerodynamic efficiency by lowering induced drag. Non-aerodynamic considerations, such as structures can impact the overall efficiency. Here, a panel method and equivalent beam finite element model are used to explore non-planar configurations taking into account the coupling between aerodynamics and structures. A single discipline aerodynamic optimization and a multidisciplinary aerostructural optimization are investigated. Due to the complexity of the design space and the presence of multiple local minima, an augmented Lagrangian particle swarm optimizer is used. The aerodynamic optimum solution found for rectangular lifting surfaces is a box wing, while allowing for sweep and taper yields a joined wing. Adding parasitic drag in the aerodynamic model reduces the size of the non--planar elements. The aerostructural optimal solution found is a winglet configuration when the span is constrained and a wing rake when there is no such constraint.

This thesis is a study of the geometric design of solar concentrating collectors. In this work, a numerical optimization methodology was developed and applied to various problems in linear solar concentrator design, in order to examine overall optimization success as well as the effect of various strategies for improving computational efficiency. Optimization is performed with the goal of identifying the concentrator geometry that results in the greatest fraction of incoming solar radiation absorbed at the receiver surface, for a given collector configuration. Surfaces are parametrically represented in two-dimensions, and objective function evaluations are performed using various Monte Carlo ray-tracing techniques. Design optimization is performed using a gradient-based search scheme, with the gradient approximated through finite-difference estimation and updates based on the direction of steepest-descent. The developed geometric optimization methodology was found to perform with mixed success for the given test problems. In general, in every case a significant improvement in performance was achieved over that of the initial design guess, however, in certain cases, the quality of the identified optimal geometry depended on the quality of the initial guess. It was found that, through the use of randomized quasi-Monte Carlo, instead of traditional Monte Carlo, overall computational time to converge is reduced significantly, with times typically reduced by a factor of four to six for problems assuming perfect optics, and by a factor of about 2.5 for problems assuming realistic optical properties. It was concluded that the application of numerical optimization to the design of solar concentrating collectors merits additional research, especially given the improvements possible through quasi-Monte Carlo techniques.

This thesis is a study of the geometric design of solar concentrating collectors. In this work, a numerical optimization methodology was developed and applied to various problems in linear solar concentrator design, in order to examine overall optimization success as well as the effect of various strategies for improving computational efficiency. Optimization is performed with the goal of identifying the concentrator geometry that results in the greatest fraction of incoming solar radiation absorbed at the receiver surface, for a given collector configuration. Surfaces are parametrically represented in two-dimensions, and objective function evaluations are performed using various Monte Carlo ray-tracing techniques. Design optimization is performed using a gradient-based search scheme, with the gradient approximated through finite-difference estimation and updates based on the direction of steepest-descent. The developed geometric optimization methodology was found to perform with mixed success for the given test problems. In general, in every case a significant improvement in performance was achieved over that of the initial design guess, however, in certain cases, the quality of the identified optimal geometry depended on the quality of the initial guess. It was found that, through the use of randomized quasi-Monte Carlo, instead of traditional Monte Carlo, overall computational time to converge is reduced significantly, with times typically reduced by a factor of four to six for problems assuming perfect optics, and by a factor of about 2.5 for problems assuming realistic optical properties. It was concluded that the application of numerical optimization to the design of solar concentrating collectors merits additional research, especially given the improvements possible through quasi-Monte Carlo techniques.

The release of flammable and toxic chemicals in petrochemical facilities is a major concern when designing modern process safety systems. While the proper selection of the necessary types of gas detectors needed is important, appropriate placement of these detectors is required in order to have a well-functioning gas detection system. However, the uncertainty in leak locations, gas composition, process and weather conditions, and process geometries must all be considered when attempting to determine the appropriate number and placement of the gas detectors. Because traditional approaches are typically based on heuristics, there exists the need to develop more rigorous optimization based approaches to handling this problem. This work presents several mixed-integer programming formulations to address this need. First, a general mixed-integer linear programming problem is presented. This formulation takes advantage of precomputed computational fluid dynamics (CFD) simulations to determine a gas detector placement that minimizes the expected detection time across all scenarios. An extension to this formulation is added that considers the overall coverage in a facility in order to improve the detector placement when enough scenarios may not be available. Additionally, a formulation considering the Conditional-Value-at-Risk is also presented. This formulation provides some control over the shape of the tail of the distribution, not only minimizing the expected detection time across all scenarios, but also improving the tail behavior. In addition to improved formulations, procedures are introduced to determine confidence in the placement generated and to determine if enough scenarios have been used in determining the gas detector placement. First, a procedure is introduced to analyze the performance of the proposed gas detector placement in the face of “unforeseen” scenarios, or scenarios that were not necessarily included in the original formulation. Additionally, a procedure for determine the confidence interval on the optimality gap between a placement generated with a sample of scenarios and its estimated performance on the entire uncertainty space. Finally, a method for determining if enough scenarios have been used and how much additional benefit is expected by adding more scenarios to the optimization is proposed. Results are presented for each of the formulations and methods presented using three data sets from an actual process facility. The use of an off-the-shelf toolkit for the placement of detectors in municipal water networks from the EPA, known as TEVA-SPOT, is explored. Because this toolkit was not designed for placing gas detectors, some adaptation of the files is necessary, and the procedure for doing so is presented.

Semidefinite programming is a powerful modeling tool for a wide range of optimization and feasibility problems. Its prevalent use in practice relies on the fact that a (nearly) optimal solution of a semidefinite program can be obtained efficiently in both theory and practice, provided that the semidefinite program and its dual satisfy the Slater condition. This thesis focuses on the situation where the Slater condition (i.e., the existence of positive definite feasible solutions) does not hold for a given semidefinite program; the failure of the Slater condition often occurs in structured semidefinite programs derived from various applications. In this thesis, we study the use of the facial reduction technique, originally proposed as a theoretical procedure by Borwein and Wolkowicz, as a preprocessing technique for semidefinite programs. Facial reduction can be used either in an algorithmic or a theoretical sense, depending on whether the structure of the semidefinite program is known a priori. The main contribution of this thesis is threefold. First, we study the numerical issues in the implementation of the facial reduction as an algorithm on semidefinite programs, and argue that each step of the facial reduction algorithm is backward stable. Second, we illustrate the theoretical importance of the facial reduction procedure in the topic of sensitivity analysis for semidefinite programs. Finally, we illustrate the use of facial reduction technique on several classes of structured semidefinite programs, in particular the side chain positioning problem in protein folding.

The current paradigm in the lens distortion characterization industry is to use simple radial distortion models with only one or two radial terms. Tangential terms and the optimal distortion centre are also seldom determined. Inherent in the models currently used is the assumption that lens distortion is radially symmetrical. The reason for the use of these models is partly due to the perceived instability of more complex lens distortion models. This dissertation shows, in the first of its three hypotheses, that higher order models are indeed beneficial, when their parameters are determined using modern numerical optimization techniques. They are both stable and provide superior characterization. Although it is true that the first two radial terms dominate the distortion characterization, this work proves superior characterization is possible for those applications that may require it. The third hypothesis challenges the assumption of the radial symmetry of lens distortion. Building on the foundation provided by the first hypothesis, a sample of lens distortion models of similar and greater complexity to those found in literature are modified to have a radial gain, allowing the distortion corrections to vary both with polar angle and distance from the distortion centre. Four angular gains are evaluated, and two provide better characterization. The elliptical gain was the only method to both consistently improve the characterization and not ‘skew’ the corrected images. This gain was shown to improve characterization by as much as 50% for simple (single radial term) models and by 7% for even the most complex models. To create an undistorted image from a distorted image captured through a lens which has had its distortion characterized, one needs to find the corresponding distorted pixel for each undistorted pixel in the corrected image. This is either done iteratively or using a simplified model typically based on the Taylor expansion of a simple (one or two radial coefficients) distortion model. The first method is accurate yet slow and the second, the opposite. The second hypothesis of this research successfully combines the advantages of both methods without any of their disadvantages. It was shown that, using the superior characterization of high order radial models (when fitted with modern numerical optimization methods) together with the ‘side-effect’ undistorted image points created in the lens distortion characterization, it is possible to fit a ‘reverse’ model from the undistorted to distorted domains. This reverse characterization is of similar complexity to the simplified models yet provides characterization equivalent to the iterative techniques. Compared to using simplified models the reverse mapping yields an improvement of more than tenfold - from the many tenths of pixels to a few hundredths. / Dissertation (MEng)--University of Pretoria, 2009. / Electrical, Electronic and Computer Engineering / unrestricted

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第22861号 / 情博第740号 / 新制||情||127(附属図書館) / 京都大学大学院情報学研究科先端数理科学専攻 / (主査)教授 青柳 富誌生, 教授 磯 祐介, 教授 田口 智清 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第18613号 / 情博第537号 / 新制||情||95(附属図書館) / 31513 / 京都大学大学院情報学研究科知能情報学専攻 / (主査)教授 山本 章博, 教授 黒橋 禎夫, 教授 阿久津 達也 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM