Structural topology optimization has been extensively studied in aeronautical, civil, and mechanical engineering applications in order to improve performance of systems. This thesis focuses on an optimal design of damping treatment using topology optimization, and the reduction of computational expense of the topology optimization procedure. This thesis presents mainly two works on topology optimization. In the first work, topology optimization is implemented to optimally design damping treatments in unconstrained-layer damping material. Since the damping effect relies on the placement of damping treatment, and the weight of damping material may be an important factor, the placement of damping material is optimally determined using topology optimization with an allowable maximum. Unconstrained-layer plate and shell structures are modeled. The damping layer on the unconstrained-layer structures is considered as the design domain. Using topology optimization, the damping layer is designed numerically, and then experimentally validated by comparing the damping effects. In the numerical example, the topological damping treatment usually provides much higher damping effects compared to other approaches such as strain energy distribution (SED) and an evolutionary structural optimization (ESO). In the second work, a numerical algorithm, named as reducible design variable method (RDVM) topology optimization, is proposed in order to efficiently reduce the computational expense. Since it usually requires thousands to millions of design variables and up to hundreds of iterations in topology optimization, the major difficulty is its computational expense. The RDVM topology optimization is implemented into static (minimization of compliance) and dynamic (maximization of the fundamental resonance frequency) problems. The RDVM significantly reduces computing time, as confirmed by numerical examples. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2011-07-08 10:10:20.606

<p> This thesis addresses recent trends and developments of the adjoint-variable method (AVM) for microwave structures with the time-domain transmission-line modeling (TD-TLM) method. </p> <p> Design sensitivity analysis of high-frequency (HF) structures is concerned with estimating the sensitivity of the response with respect to the design parameters. This information is essential at different stages of the design cycle such as the optimization, tolerance analysis, and yield analysis. </p> <p> Traditional approaches of sensitivity calculations involve estimating the sensitivities thought fmite-difference approximations. They suffer from formidable simulation time, as the full-wave analysis of practical HF structure requires extensive computational time. For a structure with N design parameters, at least N+l system analyses are required to extract the design response and its sensitivities. The adjoint variable method, on the other hand, supplies the sensitivity information in a very efficient way. Using at most two system analysis, the algorithm provides the design responses and its sensitivities, regardless of the number of the design parameters. </p> <p> In this thesis two contributions have been achieved which aims at enhancing the efficiency of the TLM-A VM framework. The first contribution is a reformulation of the AVM. This reformulation results in casting both the original and the adjoint systems in mathematically identical forms. It is shown that both systems can thus be modeled using a single TLM simulator with the only difference in the excitation. The second contribution focuses on generalizing the A VM algorithm by employing it for more advanced TLM nodes. The compatibility of the symmetrical condensed node (SCN) with the AVM algorithm has been verified in previous work for a general 3-D problem. Here, this is extended to include the hybrid symmetrical condensed node (HSCN), which is more efficient in terms of memory saving and simulation time. The new approaches are all illustrated through sensitivity estimation of different waveguide structures. </p> / Thesis / Master of Applied Science (MASc)

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This thesis covers recent advances in the adjoint variable method for the sensitivity estimations through time-domain electromagnetic simulations. It considers both frequency-independent and frequency-dependent response functions, and at the same time, provides a novel adjoint treatment for addressing dispersive sensitivity parameters in the material constitutive relation. With this proposed adjoint technique, response sensitivities with respect to all N sensitivity parameters can be computed through at most one extra simulations regardless of the value of N. This thesis also extends the existing adjoint technique to estimate all N^2 second-order sensitivity entries in the response Hessian matrix through N additional simulations. All adjoint sensitivity techniques presented in this thesis are numerically validated through various practical examples. Comparison shows that our produced adjoint results agree with those produced through central finite-difference approximations or through exact analytical approaches. / Dissertation / Doctor of Engineering (DEng)

We propose an efficient wideband theory for adjoint variable sensitivity analysis of problems with general anisotropic materials. The method is formulated based on the transmission line numerical modeling technique. The anisotropic material properties of potential interest are the full tensors of permittivity, permeability, electrical conductivity, magnetic resistivity, magnetoelectric coupling, and electromagnetic coupling. The tensors may contain non-diagonal elements. Our method estimates the gradients of the desired response with respect to all designable parameters using at most one extra simulation, regardless of their number. In contrast, in the conventional sensitivity analysis method using central finite differences, the number of the required simulations scales linearly with the number of designable parameters. The theory has been implemented for sensitivity analysis of the two and three-dimensional structures. The available adjoint variable method (AVM) sensitivities enable the optimization-based design of anisotropic and dispersive anisotropic structures. We apply our AVM technique to optimization-based wideband invisibility cloak design of arbitrary-shape objects. Our method optimizes the voxel-by-voxel constitutive parameters of an anisotropic cloak. This results in a large number of optimizable parameters. The associated sensitivities of a wideband cloaking objective function are efficiently estimated using our anisotropic adjoint variable method technique. A gradient-based optimization algorithm utilizes the available sensitivity information to iteratively minimize the visibility objective function and to determine the constitutive parameters of the optimal cloak. / Thesis / Doctor of Philosophy (PhD)

High-accuracy electromagnetic design and analysis of electric machines is enhanced by the use of various numerical methods. These methods solve Maxwell’s equations to determine the distribution of the electric and magnetic fields throughout the considered machine structure. Due to the complicated architectures of the machines and the nonlinearity of the utilized magnetic materials, it is a very challenging task to obtain an analytical solution and, in most cases, only a numerical solution is possible. The finite element method (FEM) is one of the standard numerical methods for electromagnetic field analysis. The considered machine domain is divided into finite elements to which the field equations are applied. FEM solvers are utilized to develop optimization procedures to assist in achieving a design that meets the required specifications without violating the design constraints. The design process of electric machines involves adjusting the machine parameters. This is usually done through experience, intuition, and heuristic approaches using FEM software which gives results for various parameter changes. There is no guarantee that the achieved design is the optimal one. An alternative approach to the design of electric machines exploits robust gradient-based optimization algorithms that are guaranteed to converge to a locally-optimal model. The gradient-based approaches utilize the sensitivities of the performance characteristics with respect to the design parameters. These sensitivities are classically calculated using finite difference approximations which require repeated simulations with perturbed parameter values. The cost of evaluating these sensitivities can be significant for a slow finite element simulation or when the number of parameters is large. The adjoint variable method (AVM) offers an alternative approach for efficiently estimating response sensitivities. Using at most one extra not-iterative simulation, the sensitivities of the response to all parameters are estimated. Here, a MATLAB tool has been developed to automate the design process of switched reluctance motors (SRMs). The tool extracts the mesh data of an initial motor model from a commercial FEM software, JMAG. It then solves for magnetic vector potential throughout the considered SRM domain using FEM taking into consideration the nonlinearity of the magnetic material and the motor dynamic performance. The tool calculates various electromagnetic quantities such as electromagnetic torque, torque ripple, phase flux linkage, x and y components of flux density, air-region stored magnetic energy, phase voltage, and phase dynamic currents. The tool uses a structural mapping technique to parametrize various design parameters of SRMs. These parameters are back iron thickness, teeth height, pole arc angle, and pole taper angle of both stator and rotor. Moreover, it calculates the sensitivities of various electromagnetic quantities with respect to all these geometric design parameters in addition to the number of turn per phase using the AVM method. The tool applies interior point optimization algorithm to simultaneously optimize the motor geometry, number of turns per phase, and the drive-circuit control parameters (reference current, and turn-on and turn-off angles) to increase the motor average dynamic torque. It also applies the ON/OFF topology optimization algorithm to optimize the geometries of the stator teeth for proper distribution of the magnetic material to reduce the RMS torque ripple. A 6/14 SRM has been automatically designed using the developed MATLAB tool to achieve the same performance specifications as 6110E Evergreen surface-mounted PM brushless DC motor which is commercially available for an HVAC system. / Thesis / Doctor of Philosophy (PhD)

This dissertation is intended to provide a statistical foundation for the IV models and shed lights on a number of issues related to the IV method. The first chapter shows that the theoretical Instrumental Variable model can be derived by reparameterization of a well-specified statistical model defined on the joint distribution of the involved random variables as the actual (local) data generation process. This reveals the covariance structure of the error terms of the usual theory-driven instrumental variable model. The revealed covariance structure of the IV model have important implications, particularly, for designing simulation studies. Monte Carlo simulations are used to reexamine the Nelson and Startz (1990a) findings regarding the performance of IV estimators when the instruments are weak. The results from the simulation exercises indicate that the sampling distribution of ^Î _IV is concentrated around ^Î _OLS. The second chapter considers the underlying joint distribution function of the instrumental variable (IV) model and presents an alternative definition for the exogenous and relevant instruments. The paper extracts a system of independent and orthogonal equations that covers up a non-orthogonal structural model and argues that the estimated IV regression is well-specified if the underlying system of equations is well-specified. It proposes a new instrument relevancy measure that does not suffer from the first-stage <i>R²</i> deficiencies. Third chapter argues the application of the IV method in estimation of models with omitted variable. The paper considers the implicit parametrization of statistical models and presents five conditions for an appropriate instruments. Two of them are empirically measurable and can be tested. This improves the literature by adding one more objective criterion for the selection of instruments. This chapter applies the IV method to estimate the rate of return to education in Iran. It argues that the education of two cohorts of Iranians was delayed or cut short by the Cultural Revolution. Therefore, the Cultural Revolution, as an exogenous shock to the supply of education, establishes the year of birth as the exogenous and relevant instrument for education. Using the standard Mincerian earnings function with control for experience, ethnicity, location of residence and sector of employment, the instrumental variable estimate of the return to schooling is equal to 5.6&#37;. The estimation results indicate that the Iranian labor market values degrees more than years of schooling. / Ph. D.

Thesis (MEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: There are two methods generally used for heliostat field layout optimization: the field growth method and the pattern method. A third, less commonly used method also exists: the free variable method. Each of these three methods offers its own set of advantages and disadvantages. The purpose of this study is to explore the subject of heliostat field layout optimization and to examine the free variable method. In order to achieve this objective, optimization was conducted using the free variable method. To perform optimization, a technical model of the heliostat field was constructed using approximating functions from literature and geometric analysis. Results of this study indicated that the free variable method is possible using a gradient-based optimization algorithm. The free variable method was applied to redesign the field of a commercial plant, PS10, located in Spain. The original plant was improved by 1.2% in annual intercepted energy. The study has demonstrated some of the characteristics, advantages and pitfalls of the free variable method and has proved useful in contributing to the understanding of heliostat field layout optimization. The free variable method requires more research and development before it may be used commercially. / AFRIKAANSE OPSOMMING: Daar word oor die algemeen twee metodes gebruik om 'n heliostaatveld se uitleg te optimeer: die terreinvermeerderingsmetode (field growth) en die patroonmetode (pattern). 'n Derde, minder algemeen gebruikte metode bestaan ook: die vrye veranderlike metode (free variable). Elkeen van hierdie drie metodes bied sy eie voordele en nadele. Die doel van hierdie studie is om die onderwerp van heliostaat veld uitleg optimalisering te verken en die vrye veranderlike metode te ondersoek. Ten einde te hierdie oogmerk te bereik, is die optimalisering uitgevoer met gebruik van die vrye veranderlike metode. Om optimalisering uit te voer, is 'n tegniese model van die heliostaat veld gebou met behulp van benader funksies van letterkunde en geometriese analise. Resultate van hierdie studie het aangedui dat die vrye veranderlike metode moontlik is deur gebruik te maak van 'n gradientbebaseerde optimeeringslagoritme. Die vrye veranderlike metode is ook aangewend om die terrien van 'n kommersiele aanleg, PS10 in Spanje, te herontwerp. Die oorspronklike aanleg is in jaarlikse onderskep energie verbeter met 1.2%. Die studie het sommige van die eienskappe, voordele en slaggate van die vrye veranderlike metode getoon en het nuttige bewys om by te dra tot die begrip van heliostaat veld uitleg optimalisering. Die vrye veranderlike metode vereis meer navorsing en ontwikkeling voordat dit kommersieel gebruik kan word.