The research conducted in this dissertation is divided into two main parts. The first part provides further improvements in power system state estimation and the second part implements Contingency Constrained Optimal Power Flow (CCOPF) in a stochastic multiple contingency framework. As a real-time application in modern power systems, the existing Newton-QR state estimation algorithms are too slow and too fragile numerically. This dissertation presents a new and more robust method that is based on trust region techniques. A faster method was found among the class of Krylov subspace iterative methods, a robust implementation of the conjugate gradient method, called the LSQR method. Both algorithms have been tested against the widely used Newton-QR state estimator on the standard IEEE test networks. The trust region method-based state estimator was found to be very reliable under severe conditions (bad data, topological and parameter errors). This enhanced reliability justifies the additional time and computational effort required for its execution. The numerical simulations indicate that the iterative Newton-LSQR method is competitive in robustness with classical direct Newton-QR. The gain in computational efficiency has not come at the cost of solution reliability. The second part of the dissertation combines Sequential Quadratic Programming (SQP)-based CCOPF with Monte Carlo importance sampling to estimate the operating cost of multiple contingencies. We also developed an LP-based formulation for the CCOPF that can efficiently calculate Locational Marginal Prices (LMPs) under multiple contingencies. Based on Monte Carlo importance sampling idea, the proposed algorithm can stochastically assess the impact of multiple contingencies on LMP-congestion prices.

In this study, the method of deciding the water level of the initial tsunami is proposed by using spatial-temporal focusing (Coalescence) theory and waveform inversion reciprocal with Green function. Tsunami and earthquake are so closely bonded that the current tsunami numerical model is dependent on the parameters of the fault and the initial tsunami water level by calculating the theory of half flexibility. But in fact, it is not easy to have the parameters of seabed fault so that the initial tsunami water level is very hard to get a accurate value. On the other hand, although the parameters of fault can be speculated by seismic waves, because ground is uneven medium, therefore, it is still a lot of improvement to get the parameters of fault by using seismic waves. For the tsunami simulation, if you have the value of the initial tsunami water level, the fault parameters can be estimated.Since the propagation of tsunami in the ocean is a linear behavior, the propagating process is affected by the topography of the ocean and the nonlinear effect so minimal that it is to satisfy the linear shallow water equations and the requirement of reversibility;However, in fact, the values of the water level measured by the tide stations on the coast are influenced by the shoaling effect so that the reversibility of linear system can not be directly applied to Coastal areas.Therefore, the overall Inversion procedure on this study consists of two parts; the first one is that the usage of variable coefficient Korteweg-de Vries (vKdV) equation and the Coalescence theory inverses the data gathered by the Coastal tide stations to the water level data where the depth is more than 50m on the linear region, and compares the above results with the stimulation and confirms the accuracy of the inversed waveform;The second one is that according to the reversibility of the linear system the use of least squares and least squares QR- decomposition (LSQR) method reproduce the initial tsunami wave source that compares with the initial tsunami wave source by stimulating and has a very good conformity. The seismic parameters can be easily decided by the above results.

Conditioning geologic models to production data and assessment of uncertainty is generally done in a Bayesian framework. The current Bayesian approach suffers from three major limitations that make it impractical for field-scale applications. These are: first, the CPU time scaling behavior of the Bayesian inverse problem using the modified Gauss-Newton algorithm with full covariance as regularization behaves quadratically with increasing model size; second, the sensitivity calculation using finite difference as the forward model depends upon the number of model parameters or the number of data points; and third, the high CPU time and memory required for covariance matrix calculation. Different attempts were used to alleviate the third limitation by using analytically-derived stencil, but these are limited to the exponential models only. We propose a fast and robust adaptation of the Bayesian formulation for inverse modeling that overcomes many of the current limitations. First, we use a commercial finite difference simulator, ECLIPSE, as a forward model, which is general and can account for complex physical behavior that dominates most field applications. Second, the production data misfit is represented by a single generalized travel time misfit per well, thus effectively reducing the number of data points into one per well and ensuring the matching of the entire production history. Third, we use both the adjoint method and streamline-based sensitivity method for sensitivity calculations. The adjoint method depends on the number of wells integrated, and generally is of an order of magnitude less than the number of data points or the model parameters. The streamline method is more efficient and faster as it requires only one simulation run per iteration regardless of the number of model parameters or the data points. Fourth, for solving the inverse problem, we utilize an iterative sparse matrix solver, LSQR, along with an approximation of the square root of the inverse of the covariance calculated using a numerically-derived stencil, which is broadly applicable to a wide class of covariance models. Our proposed approach is computationally efficient and, more importantly, the CPU time scales linearly with respect to model size. This makes automatic history matching and uncertainty assessment using a Bayesian framework more feasible for large-scale applications. We demonstrate the power and utility of our approach using synthetic cases and a field example. The field example is from Goldsmith San Andres Unit in West Texas, where we matched 20 years of production history and generated multiple realizations using the Randomized Maximum Likelihood method for uncertainty assessment. Both the adjoint method and the streamline-based sensitivity method are used to illustrate the broad applicability of our approach.

Diffuse optical tomography is a promising imaging modality that provides functional information of the soft biological tissues, with prime imaging applications including breast and brain tissue in-vivo. This modality uses near infrared light( 600nm-900nm) as the probing media, giving an advantage of being non-ionizing imaging modality. The image reconstruction problem in diffuse optical tomography is typically posed as a least-squares problem that minimizes the difference between experimental and modeled data with respect to optical properties. This problem is non-linear and ill-posed, due to multiple scattering of the near infrared light in the biological tissues, leading to infinitely many possible solutions. The traditional methods employ a regularization term to constrain the solution space as well as stabilize the solution, with Tikhonov type regularization being the most popular one. The choice of this regularization parameter, also known as hyper parameter, dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience. In this thesis, a simple back projection type image reconstruction algorithm is taken up, as they are known to provide computationally efficient solution compared to regularized solutions. In these algorithms, the hyper parameter becomes equivalent to filter factor and choice of which is typically dependent on the sampling interval used for acquiring data in each projection and the angle of projection. Determining these parameters for diffuse optical tomography is not so straightforward and requires usage of advanced computational models. In this thesis, a computationally efficient simplex Method based optimization scheme for automatically finding this filter factor is proposed and its performances is evaluated through numerical and experimental phantom data. As back projection type algorithms are approximations to traditional methods, the absolute quantitative accuracy of the reconstructed optical properties is poor .In scenarios, like dynamic imaging, where the emphasis is on recovering relative difference in the optical properties, these algorithms are effective in comparison to traditional methods, with an added advantage being highly computationally efficient. In the second part of this thesis, this hyper parameter choice for traditional Tikhonov type regularization is attempted with the help of Least-Squares QR-decompisition (LSQR) method. The established techniques that enable the automated choice of hyper parameters include Generalized Cross-Validation(GCV) and regularized Minimal Residual Method(MRM), where both of them come with higher over head of computation time, making it prohibitive to be used in the real-time. The proposed LSQR algorithm uses bidiagonalization of the system matrix to result in less computational cost. The proposed LSQR-based algorithm for automated choice of hyper parameter is compared with MRM methods and is proven to be computationally optimal technique through numerical and experimental phantom cases.

Tesis por compendio / [ES] La prueba médica de Tomografía Computarizada (TC) es esencial actualmente en la práctica clínica para el diagnóstico y seguimiento de múltiples enfermedades y lesiones, siendo una de las pruebas de imagen médica más importante por la gran cantidad de información que es capaz de aportar. Sin embargo, a diferencia de otros métodos de diagnóstico por imagen que son inocuos, la prueba de TC utiliza rayos X, que son ionizantes, por lo que suponen un riesgo para los pacientes. Es por ello que es necesario desarrollar métodos que permitan reducir la dosis de radiación a la que se expone a los pacientes que se realizan un estudio, sin comprometer la calidad de imagen puesto que sino se estaría sometiendo a un riesgo a estas personas sin que un diagnóstico de calidad esté garantizado. Durante el desarrollo de esta tesis se han investigado métodos de reconstrucción de imagen TC que se basan en reducir el número de proyecciones usadas, con el objetivo de reducir el tiempo de exposición a los rayos X. Esta estrategia de reducción de dosis está en fase de investigación, a diferencia de otras que están implantadas en la práctica clínica y ya han sido desarrolladas por los propios fabricantes de los escáneres. Por tanto, nos hemos centrado en los llamados métodos algebraicos de reconstrucción, que son los más apropiados para este tipo de adquisición de proyecciones puesto que son capaces de trabajar con menos información que los métodos clásicos conservando una buena calidad de imagen. En concreto, se ha estudiado a fondo el comportamiento del método LSQR para la resolución de este problema, combinado con una técnica de filtrado llamada Soft Thresholding Filter y una técnica de aceleración llamada FISTA. Además, se ha introducido el filtro de imagen Bilateral que es capaz de mejorar la calidad de las imágenes cuando se combina con los métodos anteriores. El estudio multiparamétrico realizado se ha llevado a cabo en un entorno de computación distribuida Grid, para analizar cómo los distintos parámetros que intervienen en el proceso de reconstrucción pueden influir sobre la imagen resultado. Dicho estudio se ha diseñado para hacer uso de la potencia de cómputo de la plataforma distribuida aunque el software que se necesita no esté disponible. La instalación de dicho software se puede realizar en el tiempo de ejecución de los trabajos, o en se puede empaquetar en una imagen que estará instalada en un contenedor Docker, lo que es una opción muy interesante para sistemas donde no tengamos privilegios. El esquema seguido para la creación y lanzamiento de los trabajos es fácilmente reproducible. Por otra parte, se han planteado dos métodos algebraicos directos para la reconstrucción de TC basados en la factorización de la matriz que modela el sistema. El primero es el método SVD, que se ha probado mediante la librería SLEPc, obteniendo mayores tasas de uso de memoria principal, por lo que ha sido descartado en favor del método QR. La primera aproximación a la resolución se ha hecho mediante la librería SuiteSparseQR, desarrollando después un método propio siguiendo la técnica Out-Of-Core que permite almacenar las matrices en el propio disco duro en lugar de cargarlas en memoria, por lo que el tamaño del problema puede aumentar sin que el coste del hardware sea muy alto. Dicho método obtiene reconstrucciones de alta calidad cuando el rango de la matriz factorizada es completo. En los resultados se muestra como para una resolución alta, garantizar el rango completo todavía supone una reducción del número de proyecciones con respecto a métodos tradicionales. Por tanto, en esta tesis se ha llevado a cabo la investigación y el posterior desarrollo mediante librerías y técnicas de computación de Altas Prestaciones de varios métodos algebraicos de reconstrucción de TC basados en la reducción de proyecciones que permiten mantener una buena calidad de imagen. Dichos métodos han sido optimizados para lograr los menores tiempos de reconstrucción posibles, con el fin de hacerlos competitivos y que algún día puedan ser instaurados en la práctica clínica. / [CA] Actualment, la prova mèdica de tomografia computeritzada (TC) és essencial en la pràctica clínica per al diagnòstic i el seguiment de múltiples malalties i lesions, sent una de les proves d'imatge mèdica més importants a causa de la gran quantitat d'informació que és capaç d'oferir. Tanmateix, a diferència d'altres mètodes d'imatge médica, la prova CT utilitza raigs X, que són ionitzants i suposen un risc per als pacients. Per això, és necessari desenvolupar mètodes que permetin reduir la dosi de radiació a la qual estan exposats els pacients sotmesos a un estudi, sense comprometre la qualitat de la imatge, ja que en cas contrari estarien sotmetent a aquestes persones a un risc sense que es garantís l'avantatge d'un diagnòstic d'alta qualitat. Durant el desenvolupament d'aquesta tesi, s'han investigat diversos mètodes de reconstrucció d'imatges CT basats en la reducció del nombre de projeccions utilitzades, amb l'objectiu de reduir el temps d'exposició als raigs X. Aquesta estratègia de reducció de dosis es troba en fase investigació, a diferència d'altres que s'implementen a la pràctica clínica i que ja han estat desenvolupades pels propis fabricants d'escàners. Per tant, ens hem centrat en els anomenats mètodes de reconstrucció algebraica, que són els més adequats per a aquest tipus d'adquisició de projecció, ja que són capaços de treballar amb menys informació que els mètodes clàssics mantenint una bona qualitat d'imatge. Concretament, s'ha estudiat a fons el comportament del mètode LSQR per resoldre aquest problema, combinat amb una tècnica de filtratge anomenada Soft Thresholding Filter i una tècnica d'acceleració anomenada FISTA. A més, s'ha introduït un filtre d'imatges anomenat filtre bilateral, que és capaç de millorar la qualitat de les imatges quan es combina amb els mètodes anteriors. L'estudi multiparamètric de LSQR es va dur a terme en un entorn informàtic distribuït Grid, per analitzar com els diferents paràmetres implicats en el procés de reconstrucció poden influir en la imatge resultant. Aquest estudi ha estat dissenyat per fer ús de la potència de càlcul de la plataforma distribuïda encara que el programari requerit no estigui disponible. La instal·lació d'aquest programari es pot fer en el moment d'executar els treballs o es pot empaquetar en una imatge que s'instal·larà en un contenidor Docker, que és una opció molt interessant per a sistemes on no tenim privilegis. L'esquema seguit per a la creació i el llançament dels treballs es pot reproduir fàcilment per a estudis multiparamètrics d'aquest tipus. D'altra banda, s'han proposat dos mètodes algebraics directes per a la reconstrucció CT basats en la factorització de la matriu que modela el sistema. El primer és el mètode SVD, que s'ha provat mitjançant la biblioteca SLEPc, obtenint taxes d'ús més alt de memòria principal, motiu pel qual s'ha descartat a favor del mètode QR. La primera aproximació a la resolució s'ha fet a través de la biblioteca SuiteSparseQR, desenvolupant posteriorment la nostra pròpia implementació mitjançant la tècnica Out-Of-Core que permet emmagatzemar les matrius al disc dur en lloc de carregar-les a la memòria, de manera que la mida de el problema pot augmentar sense que el cost del maquinari sigui molt alt. Aquest mètode obté reconstruccions d'alta qualitat quan el rang de la matriu factoritzada és complet. En els resultats es demostra que per a una alta resolució, garantir el rang complet encara significa una reducció del nombre de projeccions en comparació amb els mètodes tradicionals. Per tant, en aquesta tesi s'ha dut a terme la investigació i el desenvolupament posterior de diversos mètodes de reconstrucció algebraica de CT mitjançant biblioteques i tècniques de computació d'altes prestacions. Aquests mètodes basats en la reducció de projeccions, que permeten mantenir una bona qualitat d’imatge, s’han optimitzat per aconseguir els temps de reconstrucció més breus possibles, per tal de fer-los competitius perquè algun dia puguin implementarse a la pràctica clínica. / [EN] The Computerized Tomography (CT) medical test is currently essential in clinical practice for the diagnosis and monitoring of multiple diseases and injuries, being one of the most important medical imaging tests due to the large amount of information it is capable of providing. However, unlike other safe imaging methods, the CT test uses X-rays, which are ionizing, posing a risk to patients. That is why it is necessary to develop methods that allow reducing the radiation dose to which patients undergoing a study are exposed, without compromising image quality since otherwise they would be subjecting these people to a risk without the benefit of a high-quality diagnosis being guaranteed. During the development of this thesis, several CT image reconstruction methods that are based on reducing the number of projections used have been investigated, with the aim of reducing the time of exposure to X-rays. This dose reduction strategy is in research phase, unlike others that are implemented in clinical practice and have already been developed by the scanner manufacturers themselves. Therefore, we have focused on the algebraic reconstruction methods, which are the most appropriate for this type of projection acquisition since they are capable of working with less information than the classical methods while maintaining good image quality. Specifically, the behavior of the LSQR method to solve this problem has been thoroughly studied, combined with a filtering technique called Soft Thresholding Filter and an acceleration technique called FISTA. In addition, the so-called Bilateral filter has been introduced, which is capable of improving the quality of images when combined with the above methods. The multiparametric LSQR study was carried out in a Grid distributed computing environment, to analyze how the different parameters involved in the reconstruction process can influence the resulting image. This study has been designed to make use of the computing power of the distributed platform even if the software required is not available. The installation of said software can be done at the time of execution of the jobs, or it can be packaged in an image that will be installed in a Docker container, which is a very interesting option for systems where we do not have privileges. The scheme followed for the creation and launch of the jobs is easily reproducible for multiparametric studies of this type. On the other hand, two direct algebraic methods have been proposed for CT reconstruction based on the factorization of the matrix that models the system. The first is the SVD method, which has been tested using the SLEPc library, obtaining higher rates of main memory usage, which is why it has been discarded in favor of the QR method. The first approximation to the resolution has been made through the SuiteSparseQR library, later developing our own implementation using the Out-Of-Core technique that allows the matrices to be stored on the hard drive itself instead of loading them in memory, so the size of the problem can increase without the cost of the hardware being very high. This method obtains high-quality reconstructions when the rank of the factored matrix is complete. In the results it is shown that for a high resolution, guaranteeing the full rank still means a reduction in the number of projections compared to traditional methods. Therefore, in this thesis, research and subsequent development of several algebraic CT reconstruction methods has been carried out using libraries and High Performance Computing techniques. These methods based on the reduction of projections, which allows maintaining good image quality, and have been optimized to achieve the shortest possible reconstruction times, in order to make them competitive so that one day they can be implemented in clinical practice. / This research has been supported by Universitat Politècnica de València and partially funded by TIN2015-66972-C5-4-R, ENE2014-59442-P-AR and TIN2013-44390-R projects of the "Ministerio de Economía y Competitividad" of Spain, as well as the Spanish ”Generalitat Valenciana” PROMETEOII/2014/008, PROMETEO/2018/035 projects and ACIF/2017/075 predoctoral grant. This work has also been co-financed by FEDER and FSE funds, and the “Spanish Ministry of Science, Innovation and Universities” under Grant RTI2018-098156-B-C54 / Chillarón Pérez, M. (2021). Análisis y desarrollo de algoritmos de altas prestaciones para reconstrucción de imagen médica TAC 3D basados en la reducción de dosis [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/180116 / TESIS / Compendio