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For many questions of complex analysis of several variables classical potential theory does not provide suitable tools and is replaced by pluripotential theory. The latter got many important applications within complex analysis and related fields. Pluripolar sets play a special role in pluripotential theory. These are the exceptional sets this theory. Complete pluripolar sets are especially important. In the thesis we study complete pluripolar sets and pluripolar hulls. We show that in some sense there are many complete pluripolar sets. We show that on each closed subset of the complex plane there is continuous function whose graph is complete pluripolar. On the other hand we study the propagation of pluripolar sets, equivalently we study pluripolar hulls. We relate the pluripolar hull of a graph to fine analytic continuation of the function. Fine analytic continuation of an analytic function over the unit disk is related to the fine topology introduced by Cartan and to the previously known notion of finely analytic functions. We show that fine analytic continuation implies non-triviality of the pluripolar hull. Concerning the inverse direction, we show that the projection of the pluripolar hull is finely open. The difficulty to judge from non-triviality of the pluripolar hull about fine analytic continuation lies in possible multi-sheetedness. If however the pluripolar hull contains the graph of a smooth extension of the function over a fine neighborhood of a boundary point we indeed obtain fine analytic continuation.

QC 20100601

A power system with multiple interconnected areas needs to be operated coordinately for the purposes of the system reliability and economic operation, although each area has its own ISO under the market environment. In consolidation of different areas under a common grid coordinator, analysis of a power system becomes more computationally demanding. Furthermore, the analysis becomes more challenging because each area cannot obtain the network operating or economic data of other areas. This dissertation investigates decomposition algorithms for multi-area power system transfer capability analysis and economic dispatch analysis. All of the proposed algorithms assume that areas do not share their network operating and economic information among themselves, while they are willing to cooperate via a central coordinator for system wide analyses. The first proposed algorithm is based on power transfer distribution factors (PTDFs). A quadratic approximation, developed for the nonlinear PTDFs, is used to update tie-line power flows calculated by Repeated Power Flow (RPF). These tie-line power flows are then treated as injections in the TTC calculation of each area, as the central entity coordinates these results to determine the final system-wide TTC value. The second proposed algorithm is based on REI-type network equivalents. It uses the Continuation Power Flow (CPF) as the computational tool and, thus, the problem of voltage stability is considered in TTC studies. Each area uses REI equivalents of external areas to compute its TTC via the CPF. The choice and updating procedure for the continuation parameter employed by the CPF is implemented in a distributed but coordinated manner. The third proposed algorithm is based on inexact penalty functions. The traditional OPF is treated as the optimization problems with global variables. Quadratic penalty functions are used to relax the compatible constraints between the global variables and the local variables. The solution is proposed to be implemented by using a two-level computational architecture. All of the proposed algorithms are verified by numerical comparisons between the integrated and proposed decomposition algorithms. The proposed algorithms lead to potential gains in the computational efficiency with limited data exchanges among areas.

Traditionally, the design of complex aerospace systems requires iteration among segregated disciplines such as aerodynamic modeling and trajectory optimization. Multidisciplinary design optimization algorithms have been developed to efficiently orchestrate the interaction among these disciplines during the design process. For example, vehicle capability is generally obtained through sequential iteration among vehicle shape, aerodynamic performance, and trajectory optimization routines in which aerodynamic performance is obtained from large pre-computed tables that are a function of angle of attack, sideslip, and flight conditions. This numerical approach segregates advancements in vehicle shape design from advancements in trajectory optimization. This investigation advances the state-of-the-art in conceptual hypersonic aerodynamic analysis and trajectory optimization by removing the source of iteration between aerodynamic and trajectory analyses and capitalizing on fundamental linkages across hypersonic solutions. Analytic aerodynamic relations, like those derived in this investigation, are possible in any flow regime in which the flowfield can be accurately described analytically. These relations eliminate the large aerodynamic tables that contribute to the segregation of disciplinary advancements. Within the limits of Newtonian flow theory, many of the analytic expressions derived in this investigation provide exact solutions that eliminate the computational error of approximate methods widely used today while simultaneously improving computational performance. To address the mathematical limit of analytic solutions, additional relations are developed that fundamentally alter the manner in which Newtonian aerodynamics are calculated. The resulting aerodynamic expressions provide an analytic mapping of vehicle shape to trajectory performance. This analytic mapping collapses the traditional, segregated design environment into a single, unified, mathematical framework which enables fast, specialized trajectory optimization methods to be extended to also include vehicle shape. A rapid trajectory optimization methodology suitable for this new, mathematically integrated design environment is also developed by relying on the continuation of solutions found via indirect methods. Examples demonstrate that families of optimal hypersonic trajectories can be quickly constructed for varying trajectory parameters, vehicle shapes, atmospheric properties, and gravity models to support design space exploration, trade studies, and vehicle requirements definition. These results validate the hypothesis that many hypersonic trajectory solutions are connected through fast indirect optimization methods. The extension of this trajectory optimization methodology to include vehicle shape through the development of analytic hypersonic aerodynamic relations enables the construction of a unified mathematical framework to perform rapid, simultaneous hypersonic aerodynamic and trajectory optimization. Performance comparisons relative to state-of-the-art methodologies illustrate the computational advantages of this new, unified design environment.

No description available.

No description available.

The dynamics around managing urban infrastructure are changing dramatically. Today???s infrastructure management challenges ??? in the wake of shrinking coffers and stricter stakeholders??? requirements ??? include finding better condition assessment tools and prediction models, and effective and intelligent use of hard-earn data to ensure the sustainability of urban infrastructure systems. Wastewater collection networks ??? an important and critical component of urban infrastructure ??? have been neglected, and as a result, municipalities in North America and other parts of the world have accrued significant liabilities and infrastructure deficits. To reduce cost of ownership, to cope with heighten accountability, and to provide reliable and sustainable service, these systems need to be managed in an effective and intelligent manner. The overall objective of this research is to present a new strategic management framework and related tools to support multi-perspective maintenance, rehabilitation and replacement (M, R&R) planning for wastewater collection networks. The principal objectives of this research include: (1) Developing a comprehensive wastewater collection network asset database consisting of high quality condition assessment data to support the work presented in this thesis, as well as, the future research in this area. (2) Proposing a framework and related system to aggregate heterogeneous data from municipal wastewater collection networks to develop better understanding of their historical and future performance. (3) Developing statistical models to understand the deterioration of wastewater pipelines. (4) To investigate how strategic management principles and theories can be applied to effectively manage wastewater collection networks, and propose a new management framework and related system. (5) Demonstrating the application of strategic management framework and economic principles along with the proposed deterioration model to develop long-term financial sustainability plans for wastewater collection networks. A relational database application, WatBAMS (Waterloo Buried Asset Management System), consisting of high quality data from the City of Niagara Falls wastewater collection system is developed. The wastewater pipelines??? inspections were completed using a relatively new Side Scanner and Evaluation Technology camera that has advantages over the traditional Closed Circuit Television cameras. Appropriate quality assurance and quality control procedures were developed and adopted to capture, store and analyze the condition assessment data. To aggregate heterogeneous data from municipal wastewater collection systems, a data integration framework based on data warehousing approach is proposed. A prototype application, BAMS (Buried Asset Management System), based on XML technologies and specifications shows implementation of the proposed framework. Using wastewater pipelines condition assessment data from the City of Niagara Falls wastewater collection network, the limitations of ordinary and binary logistic regression methodologies for deterioration modeling of wastewater pipelines are demonstrated. Two new empirical models based on ordinal regression modeling technique are proposed. A new multi-perspective ??? that is, operational/technical, social/political, regulatory, and finance ??? strategic management framework based on modified balanced-scorecard model is developed. The proposed framework is based on the findings of the first Canadian National Asset Management workshop held in Hamilton, Ontario in 2007. The application of balanced-scorecard model along with additional management tools, such as strategy maps, dashboard reports and business intelligence applications, is presented using data from the City of Niagara Falls. Using economic principles and example management scenarios, application of Monte Carlo simulation technique along with the proposed deterioration model is presented to forecast financial requirements for long-term M, R&R plans for wastewater collection networks. A myriad of asset management systems and frameworks were found for transportation infrastructure. However, to date few efforts have been concentrated on understanding the performance behaviour of wastewater collection systems, and developing effective and intelligent M, R&R strategies. Incomplete inventories, and scarcity and poor quality of existing datasets on wastewater collection systems were found to be critical and limiting issues in conducting research in this field. It was found that the existing deterioration models either violated model assumptions or assumptions could not be verified due to limited and questionable quality data. The degradation of Reinforced Concrete pipes was found to be affected by age, whereas, for Vitrified Clay pipes, the degradation was not age dependent. The results of financial simulation model show that the City of Niagara Falls can save millions of dollars, in the long-term, by following a pro-active M, R&R strategy. The work presented in this thesis provides an insight into how an effective and intelligent management system can be developed for wastewater collection networks. The proposed framework and related system will lead to the sustainability of wastewater collection networks and assist municipal public works departments to proactively manage their wastewater collection networks.

Made available in DSpace on 2014-06-11T19:30:50Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-02-18Bitstream added on 2014-06-13T20:07:53Z : No. of bitstreams: 1 matarucco_rr_dr_ilha.pdf: 2669428 bytes, checksum: c42a359efd2169b25baa0b6c3a967339 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho apresenta dois métodos para a análise estática de contingências em Sistemas Elétricos de Potência utilizando o Método da Continuação. No primeiro método a margem de carregamento pós-contingência é obtida a partir do ponto de máximo carregamento do caso base. A magnitude de tensão de uma barra qualquer é usada como parâmetro na etapa de parametrização do fluxo de carga continuado. O ramo selecionado para avaliação da contingência é parametrizado por um fator de escalonamento que possibilita a remoção gradual do ramo e assegura a convergência nos casos em que o método diverge para a retirada total da linha de transmissão. Em geral, para a maioria das contingências analisadas são necessárias poucas iterações para a determinação do ponto de máximo carregamento pós-contingência. Mostra-se que o método pode ser usado como uma técnica alternativa para a averiguação e até mesmo para a obtenção da lista de contingências críticas fornecida pela função de análise de segurança de sistemas elétricos. No outro método, o qual obtém o ponto de máximo carregamento de pós-contingência a partir do caso base, as variáveis ângulo de fase e magnitude de tensão de uma barra k qualquer, e a perda total de potência ativa, são propostas como parâmetros para a etapa de parametrização do fluxo de carga continuado utilizado na averiguação da lista de contingências críticas fornecida pela função de análise de segurança de sistemas elétricos. Nos casos em que há divergência do fluxo de carga, o método proposto possibilita confirmar se esta ocorre devido à deficiência numérica do método em si ou a inexistência de um ponto de operação factível de pós-contingência. O uso da perda total de potência ativa como parâmetro traz como vantagem a possibilidade da determinação de pontos além do ponto de singularidade sem a necessidade... / This work presents two methods for static contingency analysis of electric power systems by using Continuation Methods. In the first the post-contingency loading margin is obtained from the base case maximum loading point. The voltage magnitude of any bus can be used as a parameter in the parameterization step of the proposed continuation power flow. The branch selected for contingency evaluation is parameterized by a scaling factor which allows its the gradual removal and assures the continuation power flow convergence for the cases where the method would diverge for the complete transmission line removal. In general, for most of the analyzed contingencies little iterations are necessary for the determination of the post-contingency maximum loading point. It is shown that the method can be used as an alternative technique to verify and even to obtain the list of critical contingencies supplied by the electric power systems security analysis function. In the other method, which obtains the maximum loading point from the base case, new parameters, namely the voltage magnitudes, phase angles and the total power losses, for evaluating the effects of branch outages. The approach can be used as a verification tool after a list of critical contingencies had been ranked according to their severities by the contingency selection functions. It is then possible to find whether the non-convergence of a power flow is due to a numerical problem or to an infeasible operating situation. The mains advantage of using the total real power losses as a parameter is that it is not necessary to change parameters during the solutions tracing until beyond the simple limit point, where the original Jacobian is singular. The proposed methods facilitate the development and the implementation of continuation methods for contingencies analysis

Objectifs de la thèse : l’analyse à rupture de structure de type solides et membranes et la modélisation de la rupture quasi-fragile par la méthode des éléments finis à forte discontinuité en cas de solide 2D. Dans ce travail, la méthode de continuation avec une équation de contrainte quadratique est présentée sous sa forme linéarisée. En présence de ruptures locales, la méthode de continuation standard peut échouer. Afin d’améliorer la performance de cette méthode, nous proposons de nouvelles versions plus sophistiquées qui prennent en compte les ruptures locales des matériaux. D’une part, une version est basée sur une équation supplémentaire adaptative imposant une limitation. Cette version est considérée relativement satisfaisante pour les matériaux adoucissants. D’autres versions sont basées sur le contrôle de la dissipation incrémentale pour les matériaux inélastiques. Plusieurs formulations d’éléments finis à forte discontinuité sont présentées en détails pour l’analyse de rupture quasi-fragile. Les approximations discrètes du champ de déplacement sont basées sur des éléments quadrilatéraux isoparamétriques ou des éléments quadrilatéraux enrichis par la méthode des modes incompatibles. Afin de décrire la formation d’une fissure ainsi que son ouverture, la cinématique de l’élément est enrichie par quatre modes de séparation et des paramètres cinématiques. On a également proposé un nouvel algorithme de repérage de fissure pour l’évaluation de la propagation de la fissure à travers le maillage. Plusieurs exemples numériques sont réalisés afin de montrer la performance de l’élément quadrilatéral à forte discontinuité ainsi que l’algorithme de repérage de fissure proposé. / The thesis studies: the methods for failure analysis of solids and structures, and the embedded strong discontinuity finite elements for modelling material failures in quasi brittle 2d solids. As for the failure analysis, the consistently linearized path-following method with quadratic constraint equation is first presented and studied in detail. The derived path-following method can be applied in the nonlinear finite element analysis of solids and structures in order to compute a highly nonlinear solution path. However, when analysing the nonlinear problems with the localized material failures (i.e. materialsoftening), standard path-following methods can fail. For this reason we derived new versions of the pathfollowing method, with other constraint functions, more suited for problems that take into account localized material failures. One version is based on adaptive one-degree-of-freedom constraint equation, which proved to be relatively successful in analysing problems with the material softening that are modelled by the embedded-discontinuity finite elements. The other versions are based on controlling incremental plastic dissipation or plastic work in an inelastic structure. The dissipation due to crack opening and propagation, computed by e.g. embedded discontinuity finite elements, is taken into account. The advantages and disadvantages of the presented path-following methods with different constraint equations are discussed and illustrated on a set of numerical examples. As for the modelling material failures in quasi brittle 2d solids (e.g. concrete), several embedded strong discontinuity finite element formulations are derived and studied. The considered formulations are based either on: (a) classical displacement-based isoparametric quadrilateral finite element or (b) on quadrilateral finite element enhanced with incompatible displacements. In order to describe a crack formation and opening, the element kinematics is enhanced by four basic separation modes and related kinematic parameters. The interpolation functions that describe enhanced kinematics have a jump in displacements along the crack. Two possibilities were studied for deriving the operators in the local equilibrium equations that are responsible for relating the bulk stresses with the tractions in the crack. For the crack embedment, the major-principle-stress criterion was used, which is suitable for the quasi brittle materials. The normal and tangential cohesion tractions in the crack are described by two uncoupled, nonassociative damage-softening constitutive relations. A new crack tracing algorithm is proposed for computation of crack propagation through the mesh. It allows for crack formation in several elements in a single solution increment. Results of a set of numerical examples are provided in order to assess the performance of derived embedded strong discontinuity quadrilateral finite element formulations, the crack tracing algorithm, and the solution methods. / Doktorska disertacija obravnava: (i) metode za porušno analizo trdnih teles in konstrukcij, ter (ii) končne elemente z vgrajeno močno nezveznostjo za modeliranje materialne porušitve v kvazi krhkih 2d trdnih telesih. Za porušno analizo smo najprej preučili konsistentno linearizirano metodo sledenja ravnotežne poti skvadratno vezno enačbo (metoda krožnega loka). Metoda omogoča izračun analize nelinearnih modelov, ki imajo izrazito nelinearno ravnotežno pot. Kljub temu standardne metode sledenja poti lahko odpovedo,kadar analiziramo nelinearne probleme z lokalizirano materialno porušitvijo (mehčanje materiala). Zatosmo izpeljali nove različice metode sledenja poti z drugimi veznimi enačbami, ki so bolj primerne zaprobleme z lokalizirano porušitvijo materiala. Ena različica temelji na adaptivni vezni enačbi, pri katerivodimo izbrano prostostno stopnjo. Izkazalo se je, da je metoda relativno uspešna pri analizi problemov zmaterialnim mehčanjem, ki so modelirani s končnimi elementi z vgrajeno nezveznostjo. Druge različicetemeljijo na kontroli plastične disipacije ali plastičnega dela v neelastičnem trdnem telesu ali konstrukciji.Upoštevana je tudi disipacija zaradi širjenja razpok v elementih z vgrajeno nezveznostjo. Prednosti inslabosti predstavljenih metod sledenja ravnotežnih poti z različnimi veznimi enačbami so predstavljeni naštevilnih numeričnih primerih. Za modeliranje porušitve materiala v kvazi krhkih 2d trdnih telesih (npr. betonskih) smo izpeljali različne formulacije končnih elementov z vgrajeno močno nezveznostjo v pomikih. Obravnavane formulacije temeljijo bodisi (a) na klasičnem izoparametričnem štirikotnem končnem elementu bodisi (b) na štirikotnem končnem elementu, ki je izboljšan z nekompatibilnimi oblikami za pomike. Nastanek in širjenje razpoke opišemo tako, da kinematiko v elementu dopolnimo s štirimi osnovnimi oblikami širjenja razpoke in pripadajočimi kinematičnimi parametri. Interpolacijske funkcije, ki opisujejo izboljšano kinematiko, zajemajo skoke v pomikih vzdolž razpoke. Obravnavali smo dva načina izpeljave operatorjev, ki nastopajo v lokalni ravnotežni enačbi in povezujejo napetosti v končnem elementu z napetostmi na vgrajeni nezveznosti. Kriterij za vstavitev nezveznosti (razpoke) temelji na kriteriju največje glavne napetosti in je primeren za krhke materiale. Normalne in tangentne kohezijske napetosti v razpoki opišemo z dvema nepovezanima, poškodbenima konstitutivnima zakonoma za mehčanje. Predlagamo novi algoritem za sledenje razpoki za izračun širjenja razpoke v mreži končnih elementov. Algoritem omogoča formacijo razpok v več končnih elementih v enem obtežnem koraku. Izračunali smo številne numerične primere, da bi ocenili delovanje izpeljanih formulacij štirikotnih končnih elementov z vgrajeno nezveznostjo in algoritma za sledenje razpoki kot tudi delovanje metod sledenja ravnotežnih poti.