Analysis and optimization of stress wave propagation in two-dimensional granular crystals with defects

Granular crystals are compact periodic assemblies of elastic particles in Hertzian contact whose dynamic response can be tuned from strongly nonlinear to linear by the addition of a static precompression force. This unique feature allows for a wide range of studies that include the investigation of new fundamental nonlinear phenomena in discrete systems such as solitary waves, shock waves, discrete breathers and other defect modes. In the absence of precompression, a particularly interesting property of these systems is their ability to support the formation and propagation of spatially localized soliton-like waves with highly tunable properties. The wealth of parameters one can modify (particle size, geometry and material properties, periodicity of the crystal, presence of a static force, type of excitation, etc.) makes them ideal candidates for the design of new materials for practical applications. This thesis describes several ways to optimally control and tailor the propagation of stress waves in granular crystals through the use of heterogeneities (interstitial defect particles and material heterogeneities) in otherwise perfectly ordered systems. We focus on uncompressed two-dimensional granular crystals with interstitial spherical intruders and composite hexagonal packings and study their dynamic response using a combination of experimental, numerical and analytical techniques. We first investigate the interaction of defect particles with a solitary wave and utilize this fundamental knowledge in the optimal design of novel composite wave guides, shock or vibration absorbers obtained using gradient-based optimization methods.

Topology optimization of silicon anode structures for lithium-ion battery applications

This thesis presents a topology optimization methodology for the systematic design of optimal multifunctional silicon anode structures in lithium-ion batteries. In order to develop next generation high performance lithium-ion batteries, key design challenges relating to the silicon anode structure must be addressed, namely the lithiation-induced mechanical degradation and the low intrinsic electrical conductivity of silicon. As such, this work considers two design objectives of minimum compliance under design dependent volume expansion, and maximum electrical conduction through the structure, both of which are subject to a constraint on material volume. Density-based topology optimization methods are employed in conjunction with regularization techniques, a continuation scheme, and mathematical programming methods. The objectives are first considered individually, during which the iteration history, mesh independence, and influence of prescribed volume fraction and minimum length scale are investigated. The methodology is subsequently extended to a bi-objective formulation to simultaneously address both the compliance and conduction design criteria. A weighting method is used to derive the Pareto fronts, which demonstrate a clear trade-off between the competing design objectives. Furthermore, a systematic parameter study is undertaken to determine the influence of the prescribed volume fraction and minimum length scale on the optimal combined topologies. The developments presented in this work provide a foundation for the informed design and development of silicon anode structures for high performance lithium-ion batteries.

Optimization algorithms and ODE's in MDO

There is a need for a stronger theoretical understanding of Multidisciplinary Design Optimization (MDO) within the field. Having developed a differential geometry framework in response to this need, we consider how standard optimization algorithms can be modeled using systems of ordinary differential equations (ODEs) while also reviewing optimization algorithms which have been derived from ODE solution methods. We then use some of the framework's tools to show how our resultant systems of ODEs can be analyzed and their behaviour quantitatively evaluated. In doing so, we demonstrate the power and scope of our differential geometry framework, we provide new tools for analyzing MDO systems and their behaviour, and we suggest hitherto neglected optimization methods which may prove particularly useful within the MDO context. Copyright © 2013 by ASME.

The Application of Toolkit of Optimization in Designs of Accelerator Magnets

The traditional design of accelerator magnet usually involves many time consuming iterations of the manual analysis process. A software platform to do these iterations automatically is proposed in this paper. In this platform, we use DAKOTA (a open source software developed by Sandia National Laboratories) as the optimizing routine, which provides a variety of optimization methods and algorithms, and OPERA (software from Vector Fields) is selected as the electromagnetic simulating routine. In this paper, two examples of designs of accelerator magnets are used to illustrate how an optimization algorithm is chosen and the platform works.

Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping

Surrogate-based-optimization methods provide a means to achieve high-fidelity design optimization at reduced computational cost by using a high-fidelity model in combination with lower-fidelity models that are less expensive to evaluate. This paper presents a provably convergent trust-region model-management methodology for variableparameterization design models: that is, models for which the design parameters are defined over different spaces. Corrected space mapping is introduced as a method to map between the variable-parameterization design spaces. It is then used with a sequential-quadratic-programming-like trust-region method for two aerospace-related design optimization problems. Results for a wing design problem and a flapping-flight problem show that the method outperforms direct optimization in the high-fidelity space. On the wing design problem, the new method achieves 76% savings in high-fidelity function calls. On a bat-flight design problem, it achieves approximately 45% time savings, although it converges to a different local minimum than did the benchmark.

Two-stage RBF network construction based on particle swarm optimization

The conventional radial basis function (RBF) network optimization methods, such as orthogonal least squares or the two-stage selection, can produce a sparse network with satisfactory generalization capability. However, the RBF width, as a nonlinear parameter in the network, is not easy to determine. In the aforementioned methods, the width is always pre-determined, either by trial-and-error, or generated randomly. Furthermore, all hidden nodes share the same RBF width. This will inevitably reduce the network performance, and more RBF centres may then be needed to meet a desired modelling specification. In this paper we investigate a new two-stage construction algorithm for RBF networks. It utilizes the particle swarm optimization method to search for the optimal RBF centres and their associated widths. Although the new method needs more computation than conventional approaches, it can greatly reduce the model size and improve model generalization performance. The effectiveness of the proposed technique is confirmed by two numerical simulation examples.

Multiobjective design optimization of IGBT power modules considering power cycling and thermal cycling

Insulated-gate bipolar transistor (IGBT) power modules find widespread use in numerous power conversion applications where their reliability is of significant concern. Standard IGBT modules are fabricated for general-purpose applications while little has been designed for bespoke applications. However, conventional design of IGBTs can be improved by the multiobjective optimization technique. This paper proposes a novel design method to consider die-attachment solder failures induced by short power cycling and baseplate solder fatigue induced by the thermal cycling which are among major failure mechanisms of IGBTs. Thermal resistance is calculated analytically and the plastic work design is obtained with a high-fidelity finite-element model, which has been validated experimentally. The objective of minimizing the plastic work and constrain functions is formulated by the surrogate model. The nondominated sorting genetic algorithm-II is used to search for the Pareto-optimal solutions and the best design. The result of this combination generates an effective approach to optimize the physical structure of power electronic modules, taking account of historical environmental and operational conditions in the field.

Optimal Scheduling Methods to Integrate Plug-In Electric Vehicles with the Power System: A Review

The introduction of the Tesla in 2008 has demonstrated to the public of the potential of electric vehicles in terms of reducing fuel consumption and green-house gas from the transport sector. It has brought electric vehicles back into the spotlight worldwide at a moment when fossil fuel prices were reaching unexpected high due to increased demand and strong economic growth. The energy storage capabilities from of fleets of electric vehicles as well as the potentially random discharging and charging offers challenges to the grid in terms of operation and control. Optimal scheduling strategies are key to integrating large numbers of electric vehicles and the smart grid. In this paper, state-of-the-art optimization methods are reviewed on scheduling strategies for the grid integration with electric vehicles. The paper starts with a concise introduction to analytical charging strategies, followed by a review of a number of classical numerical optimization methods, including linear programming, non-linear programming, dynamic programming as well as some other means such as queuing theory. Meta-heuristic techniques are then discussed to deal with the complex, high-dimensional and multi-objective scheduling problem associated with stochastic charging and discharging of electric vehicles. Finally, future research directions are suggested.

Optimization techniques for power distribution planning with uncertainties: a comparative study

Important research effort has been devoted to the topic of optimal planning of distribution systems. The non linear nature of the system, the need to consider a large number of scenarios and the increasing necessity to deal with uncertainties make optimal planning in distribution systems a difficult task. Heuristic techniques approaches have been proposed to deal with these issues, overcoming some of the inherent difficulties of classic methodologies. This paper considers several methodologies used to address planning problems of electrical power distribution networks, namely mixedinteger linear programming (MILP), ant colony algorithms (AC), genetic algorithms (GA), tabu search (TS), branch exchange (BE), simulated annealing (SA) and the Bender´s decomposition deterministic non-linear optimization technique (BD). Adequacy of theses techniques to deal with uncertainties is discussed. The behaviour of each optimization technique is compared from the point of view of the obtained solution and of the methodology performance. The paper presents results of the application of these optimization techniques to a real case of a 10-kV electrical distribution system with 201 nodes that feeds an urban area.

Filters method in direct search optimization, new measures to admissibility

Constrained nonlinear optimization problems are usually solved using penalty or barrier methods combined with unconstrained optimization methods. Another alternative used to solve constrained nonlinear optimization problems is the lters method. Filters method, introduced by Fletcher and Ley er in 2002, have been widely used in several areas of constrained nonlinear optimization. These methods treat optimization problem as bi-objective attempts to minimize the objective function and a continuous function that aggregates the constraint violation functions. Audet and Dennis have presented the rst lters method for derivative-free nonlinear programming, based on pattern search methods. Motivated by this work we have de- veloped a new direct search method, based on simplex methods, for general constrained optimization, that combines the features of the simplex method and lters method. This work presents a new variant of these methods which combines the lters method with other direct search methods and are proposed some alternatives to aggregate the constraint violation functions.

Direct-search penalty/barrier methods

In Nonlinear Optimization Penalty and Barrier Methods are normally used to solve Constrained Problems. There are several Penalty/Barrier Methods and they are used in several areas from Engineering to Economy, through Biology, Chemistry, Physics among others. In these areas it often appears Optimization Problems in which the involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. In this work some Penalty/Barrier functions are tested and compared, using in the internal process, Derivative-free, namely Direct Search, methods. This work is a part of a bigger project involving the development of an Application Programming Interface, that implements several Optimization Methods, to be used in applications that need to solve constrained and/or unconstrained Nonlinear Optimization Problems. Besides the use of it in applied mathematics research it is also to be used in engineering software packages.

Staffing Optimization with Chance Constraints in Call Centers

Les centres d’appels sont des éléments clés de presque n’importe quelle grande organisation. Le problème de gestion du travail a reçu beaucoup d’attention dans la littérature. Une formulation typique se base sur des mesures de performance sur un horizon infini, et le problème d’affectation d’agents est habituellement résolu en combinant des méthodes d’optimisation et de simulation. Dans cette thèse, nous considérons un problème d’affection d’agents pour des centres d’appels soumis a des contraintes en probabilité. Nous introduisons une formulation qui exige que les contraintes de qualité de service (QoS) soient satisfaites avec une forte probabilité, et définissons une approximation de ce problème par moyenne échantillonnale dans un cadre de compétences multiples. Nous établissons la convergence de la solution du problème approximatif vers celle du problème initial quand la taille de l’échantillon croit. Pour le cas particulier où tous les agents ont toutes les compétences (un seul groupe d’agents), nous concevons trois méthodes d’optimisation basées sur la simulation pour le problème de moyenne échantillonnale. Étant donné un niveau initial de personnel, nous augmentons le nombre d’agents pour les périodes où les contraintes sont violées, et nous diminuons le nombre d’agents pour les périodes telles que les contraintes soient toujours satisfaites après cette réduction. Des expériences numériques sont menées sur plusieurs modèles de centre d’appels à faible occupation, au cours desquelles les algorithmes donnent de bonnes solutions, i.e. la plupart des contraintes en probabilité sont satisfaites, et nous ne pouvons pas réduire le personnel dans une période donnée sont introduire de violation de contraintes. Un avantage de ces algorithmes, par rapport à d’autres méthodes, est la facilité d’implémentation.

Hybrid optimization schemes for quantum control

Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a geometric phase gate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov’s method yields considerably better results than either one of the two methods alone.

Optimization of inverse reflector design

Aquesta tesi presenta un nou mètode pel disseny invers de reflectors. Ens hem centrat en tres temes principals: l’ús de fonts de llum reals i complexes, la definició d’un algoritme ràpid pel càlcul de la il•luminació del reflector, i la definició d’un algoritme d’optimització per trobar més eficientment el reflector desitjat. Les fonts de llum estan representades per models near-field, que es comprimeixen amb un error molt petit, fins i tot per fonts de llum amb milions de raigs i objectes a il•luminar molt propers. Llavors proposem un mètode ràpid per obtenir la distribució de la il•luminació d’un reflector i la seva comparació amb la il•luminació desitjada, i que treballa completament en la GPU. Finalment, proposem un nou mètode d’optimització global que permet trobar la solució en menys passos que molts altres mètodes d’optimització clàssics, i alhora evitant mínims locals.