L'imagerie quantitative des propriétés physiques du sous-sol est fondamentale pour de nombreuses applications impliquant des échelles d'exploration très variées: géotechnique pour l'imagerie de la proche surface, exploration à l'echelle crustale, reconstruction lithosphérique et imagerie globale pour la compréhension fondamentale des processus géodynamiques, mais aussi pour l'exploitation optimale des ressources du sous-sol.Parmi les méthode géophysiques, les méthodes sismiques ont le pouvoir de résolution le plus élevé. La densification des dispositifs d'acquisition, la mise au point de sources et de capteurs large bande et l'augmentation de la puissance de calcul ouvrent de nouvelles perspectives pour le développement et l'application de méthodes non conventionnelles d'imagerie sismique pour une extraction plus complète de l'information contenue dans les données sismiques. Parmi ces méthodes d'imagerie non conventionnelles, les méthodes d'inversion du champ d'onde complet, fondées sur la résolution complète de l'équation d'onde pour le problème direct (modélisation sismique) et la résolution d'un processus d'optimisation pour le problème inverse, font actuellement l'objet de nombreux développements méthodologiques, tant au sein des communautés industrielles qu'académiques.Le challenge numérique est la résolution du problème direct en trois dimensions pour un grand nombre de sources sismiques caractéristique des acquisitions pétrolières massives, et le challenge méthodologique est la gestion de la non-linéarité du problème inverse résultant de l'éclairage incomplet du sous-sol depuis la surface par des sources de bande-passante limitée. L'apport attendu de ces méthodes est la résolution de l'imagerie sismique de l'ordre de la demi-longueur d'onde propagée, sa capacité à imager des cibles complexes d'un point de vue structural notamment sous des écrans salifères ou basaltiques et la quantification des paramètres physiques caractérisant le sous-sol tels que la vitesse de propagation des ondes de compression à laquelle peuvent s'ajouter la densité, l'atténuation, la vitesse de propagation des ondes de cisaillement et des paramètres caractérisant l'anisotropie du milieu.L'objectif de cette thèse est de poursuivre le développement d'une méthode d'imagerie sismique acoustique 3D par l'inversion du champ d'onde complet et de l'appliquer à des données réelles pétrolières 3D de fond de mer enregistrées sur le champ pétrolier de Valhall en Mer du Nord et de fournir une des premières évaluations du potentiel des méthodes d'inversion des formes d'onde pour l'imagerie de milieux géologiques 3D L'inversion est effectuée en domaine fréquentiel où un nombre limité de fréquences est inversé suivant un protocole hiérarchique maintenant bien éprouvé procédant des basses fréquences vers les hautes fréquence: cette approche multi-échelle favorise la prise en compte de la non-linéarité du problème inverse.L'approche de modélisation en domaine temporel avec extraction du champ monochromatique par une transformée de Fourier discrète est effectuée pour calculer les champs d'onde monochromatique nécessaires à la résolution du problème inverse. L'algorithme d'optimisation du problème inverse est fondé sur une méthode de gradients conjugués préconditionés ou sur une méthode quasi-Newton. Les méthodes sont appliquées dans le cadre de l'approximation visco-acoustique isotrope où le milieu est paramétré par la vitesse de propagation des ondes de compression, l'atténuation et la densité. Seule, la composante hydrophone acquise en fond de mer est inversée. L'enjeu méthodologique de cette thèse est de fournir un modèle tri-dimensionelle du champ pétrolier de Valhall dans un cube de dimensions approximatives 18 km x 12 km x 5 km en poussant l'inversion à la fréquence la plus élevée possible. / Quantitative imaging of the subsurface physical properties is fundamental to many applications involving very various explorations, such as geotechnical imaging of the near surface, petroleum exploration, crustal lithospheric exploration. This helps us to understand the fundamental of geodynamic processes and also to exploit the resources of subsurface. Among the geophysical methods, seismic methods can give a higher resolution. The improvements of the acquisition in size and density, the multifold/multicomponent wide-aperture and wide-azimuth acquisitions, and the increased high-performance computing power open new perspectives to develop and apply non-conventional seismic imaging methods for extraction more complete and continuous information in the seismic data. Among these non-conventional methods, the full waveform inversion method based on the complete resolution of the wave equation for the direct problem (seismic modeling) and the resolution of optimization process for the inverse problem, are currently the subject of many methodological developments, in both industrial and academic communities. The numerical challenge is the resolution of the three-dimensional direct problem for a large number of seismic sources, typically few to tens of thousands in petroleum industry acquisition. The methodological challenge is the management of the non-linearity of the inverse problem resulting from the incomplete illumination of subsurface from the surface survey with a limited bandwidth source. The expected contribution of these methods is to reach a spatial resolution of half-a-wavelength. It has the ability to image complex structure targets such as saline or salt-bearing basaltic and to quantify the subsurface physical parameters such as velocity, density, attenuation, anisotropic parameters and so on. The objective of this thesis is to develop a method of three-dimensional seismic imaging by full waveform inversion and apply it to real ocean-bottom data set recorded in the Valhall oil field (in the North Sea) and to provide an early evaluation of the potentialities of full waveform inversion for imaging three-dimensional geological environments . The inversion is performed in frequency domain. A limited number of frequencies is inverted following a hierarchical protocol from low to high frequencies. This multi-scale approach helps to reduce the non-linearity of the inverse problem. The modeling approaches is performed in time domain and monochromatic wavefields are extracted by discrete Fourier transform to solve the inverse problem in frequency domain. The optimization algorithm of the inverse problem is based on conjugate gradients method or quasi-Newton method. The method is applied in the framework of the visco-acoustic isotropic approximation, where the medium is parameterized by the velocity of compressional wave propagation, attenuation, and density. The hydrophone data component located at the seabed is inverted. The methodological issue of this thesis is to develop by full waveform inversion a three-dimensional high-resolution velocity model of the Valhall oil field in a cube with a size of 18 km $\times$ 12 km $\times$ 5 km, and to push the inversion towards frequencies as high as possible.

Um desafio constante no projeto aerodinâmico de uma superfície é obter a forma geométrica que permite, baseado em uma determinada medida de mérito, o melhor desempenho possível. No contexto de projeto de aeronaves de transporte, o desempenho ótimo em cruzeiro é a principal meta do projetista. Nesse cenário, o uso da Dinâmica do Fluidos Computacional como não só uma ferramenta de análise mas também de síntese torna-se uma forma atrativa para melhorar o projeto de aeronaves que é uma atividade dispendiosa em termos de tempo e recursos financeiros. O método adotado para projeto aerodinâmico é baseado na teoria de controle ótimo. Essa abordagem para o problema de otimização aerodinâmica foi inicialmente proposta por Jameson (1997) e é chamada de método adjunto. Esse método apresenta uma grande diminuição de custo computacional se comparado com a abordagem de diferenças finitas para a otimização baseada em gradiente. Essa dissertação apresenta o método adjunto contínuo aplicado às equações de Euler. Tal método está inserido no contexto de um ciclo de projeto inverso aerodinâmico. Nesse ciclo, tanto o código computacional de solução das equações do escoamento quanto o código de solução das equações adjuntas foram desenvolvidos ao longo desse trabalho. Além disso, foi adotada uma metodologia de redução do gradiente da função de mérito em relação às variáveis de projeto. O algorítmo utilizado para a busca do mínimo da função de mérito é o steepest descent. Os binômios de Bernstein foram escolhidos para representar a geometria do aerofólio de acordo com a parametrização proposta por Kulfan e Bussoletti (2006). Apresenta-se um estudo dessa parametrização mostrando suas características relevantes para a otimização aerodinâmica. Os resultados apresentados estão divididos em dois grupos: validação do ciclo de projeto inverso e aplicações práticas. O primeiro grupo consiste em exercícios de projeto inverso nos quais são estabelecidas distribuições de pressão desejadas obtidas a partir de geometrias conhecidas, desta forma garante-se que tais distribuições são realizáveis. No segundo grupo, porém, as distribuições desejadas são propostas pelo projetista baseado em sua experiência e, portanto, não sendo garantida a realizabilidade dessas distribuições. Em ambos os grupos, incluem-se resultados nos regimes de escoamento transônico e subsônico incompressível. / A constant endeavor in aerodynamic design is to find the shape that yields optimum performance, according to some context-dependent measure of merit. In particular for transport aircrafts, an optimum cruise performance is usually the designers main goal. In this scenario the use of the Computational Fluid Dynamics (CFD) technique as not only an analysis tool but as a design tool becomes an attractive aid to the time and financial resource consuming activity that is aircraft design. The method adopted for aerodynamic design is based on optimal control theory. This approach to the design problem was first proposed by Jameson (1997) and it is called adjoint method. It shows a great computational cost advantage over the finite difference approach to gradient-based optimization. This dissertation presents an Euler adjoint method implemented in context of an inverse aerodynamic design loop. In this loop both the flow solver and the adjoint solver were developed during the course of this work and their formulation are presented. Further on, a gradient reduction methodology is used to obtain the gradient of the cost function with respect to the design variables. The method chosen to drive the cost function to its minimum is the steepest descent. Bernstein binomials were chosen to represent the airfoil geometry as proposed by Kulfan and Bussoletti (2006). A study of such geometric representation method is carried on showing its relevant properties for aerodynamic optimization. Results are presented in two groups: inverse design loop validation and practical application. The first group consists of inverse design exercises in which the target pressure distribution is from a known geometry, this way such distribution is guaranteed to be realizable. On the second group however, the target distribution is proposed based on the designers knowledge and its not necessarily realizable. In both groups the results include transonic and subsonic incompressible conditions.

Orientador: Patricio Anibal Letelier Sotomayor / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T20:03:53Z (GMT). No. of bitstreams: 1 Manoel_JoaoPauloPitelli_D.pdf: 2670867 bytes, checksum: 990119329fe5abbf22d8a42384ff3e72 (MD5) Previous issue date: 2011 / Resumo: Espaços-tempo classicamente singulares serão estudados de um ponto de vista quântico. A utilização da mecânica quântica será feita de duas maneiras. A primeira consiste em encontrar a função de onda do Universo, resolvendo a equação de Wheeler-DeWitt para as variáveis canônicas do espaço-tempo. A segunda consiste em acoplar conformemente campos escalares e spinoriais ao campo gravitacional, estudando o comportamento de pacotes de ondas neste espaço-tempo curvo / Abstract: Classically singular spacetimes will be studied from a quantum mechanical point of view. The use of quantum mechanics will be handled in two different ways. The first consists in finding the wave function of the universe by solving the Wheeler-DeWitt equation for the canonical variables of spacetime. The second is through the conformal coupling of scalar and spinorial fields with the gravitational field, where we will study the behavior of wave packets in this curved spacetime / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Un modèle de surface continentale (LSM en anglais) est un modèle numérique décrivant les échanges d'eau et d'énergie entre la surface terrestre et l'atmosphère. La physique de la surface de la terre comprend une vaste collection de processus complexes. L'équilibre entre la complexité du modèle et sa résolution, confronté à des limitations de calcul, représente une question fondamentale dans le développement d'un LSM. Les observations des phénomènes étudiés sont nécessaires afin d’adapter la valeur des paramètres du modèle à des variables reproduisant le monde réel. Le processus d'étalonnage consiste en une recherche des paramètres du modèle qui minimisent l’écart entre les résultats du modèle et un ensemble d'observations. Dans ce travail, nous montrons comment l'assimilation variationnelle de données est appliquée aux bilans d'énergie et d'eau du modèle de surface continentale ORCHIDEE afin d’étalonner les paramètres internes du modèle. Cette partie du modèle est appelé SECHIBA. Le logiciel YAO est utilisé pour faciliter la mise en œuvre de l'assimilation variationnelle 4DVAR. Une analyse de sensibilité a été réalisée afin d'identifier les paramètres les plus influents sur la température. Avec la hiérarchie des paramètres obtenue, des expériences jumelles à partir d'observations synthétiques ont été mises en œuvre. Les résultats obtenus suggèrent que l'assimilation de la température de surface a le potentiel d'améliorer les estimations de variables, en ajustant correctement les paramètres de contrôle. Enfin, plusieurs assimilations ont été faites en utilisant des observations de données réelles du site SMOSREX à Toulouse, France. Les expériences faites en utilisant différentes valeurs initiales pour les paramètres, montrent les limites de l'assimilation de la température pour contraindre les paramètres de contrôle. Même si l'estimation des variables est améliorée, ceci est dû à des valeurs finales des paramètres aux limites des intervalles prescrit de la fonction de coût. Afin de parvenir à un minimum, il faudrait permettre aux paramètres de visiter des valeurs irréalistes. Les résultats montrent que SECHIBA ne simule pas correctement simultanément la température et les flux et la relation entre les deux n’est pas toujours cohérente selon le régime (ou les valeurs des paramètres que l’on utilise). Il faut donc travailler sur la physique pour mieux simuler la température. En outre, la sensibilité des paramètres à la température n’est pas toujours suffisante, donnant une fonction de coût plate dans l’espace des paramètres prescrit. Nos résultats montrent que le système d'assimilation mis en place est robuste, puisque les résultats des expériences jumelles sont satisfaisants. Le couplage entre l'hydrologie et la thermodynamique dans SECHIBA doit donc être revu afin d'améliorer l'estimation des variables. Une étude exhaustive de l'erreur des mesures doit être menée afin de récupérer des termes de pondération dans la fonction de coût. Enfin, l'assimilation d'autres variables telles que l'humidité du sol peut maintenant être réalisée afin d'évaluer l'impact sur les performances de l’assimilation. / A land surface model (LSM) is a numerical model describing the exchange of water and energy between the land surface and the atmosphere. Land surface physics includes an extensive collection of complex processes. The balance between model complexity and resolution, subject to computational limitations, represents a fundamental query in the development of a LSM. With the purpose of adapting the value of the model parameters to values that reproduces results in the real world, measurements are necessary in order to compare to our estimations to the real world. The calibration process consists in an optimization of model parameters for a better agreement between model results and a set of observations, reducing the gap between the model and the available measurements. Here we show how variational data assimilation is applied to the energy and water budgets modules of the ORCHIDEE land surface model in order to constrain the model internal parameters. This part of the model is denoted SECHIBA. The adjoint semi-generator software denoted YAO is used as a framework to implement the 4DVAR assimilation. A sensitivity analysis was performed in order to identify the most influent parameters to temperature. With the parameter hierarchy resolved, twin experiments using synthetic observations were implemented for controlling the most sensitive parameters. Results obtained suggest that land surface temperature assimilation has the potential of improving the output estimations by adjusting properly the control parameters. Finally, several assimilations were made using observational meteorology dataset from the SMOSREX site in Toulouse, France. The experiments implemented, using different prior values for the parameters, show the limits of the temperature assimilation to constrain control parameters. Even though variable estimation is slightly improved, this is due to final parameter values are at the edge of a variation interval in the cost function. Effectively reaching a minimum would require allowing the parameters to visit unrealistic values. SECHIBA does not correctly simulates simultaneously temperature and fluxes and the relationship between the two is not always consistent according to the regime (or parameter values that are used). We must therefore work on the physical aspects to better simulate the temperature. Likewise, the parameter sensitivity to temperature is not always sufficient, giving as a result a flat cost function. Our results show that the assimilation system implemented is robust, since performances results in twin experiments are satisfactory. The coupling between the hydrology and the thermodynamics in SECHIBA must be reviewed in order to improve variable estimation. An exhaustive study of the prior errors in the measurements must be conducted in order to retrieve more adapted weighing terms in the cost function. Finally, the assimilation of other variables such as soil moisture should be performed to evaluate the impacts in constraining control parameters

We have performed 3D ambient noise tomography of the Bohemian Massif. We invert adopted inter-station dispersion curves of both Love and Rayleigh waves in periods 4-20 s, which were extracted from ambient noise cross-correlations, using a two-step approach. In the first step, the inter-station dispersion curves are localized for each period into the so-called dispersion maps. To account for finite-frequency effects, gradient method employing Fréchet kernels is used. Assuming membrane wave approximation of the surface wave propagation at each period, the kernels were calculated using the adjoint method. To reduce the effect of data noise, the kernels were regularized by Gaussian smoothing. The proper level of regularization is assessed on synthetic tests. In the second step, the phase-velocity dispersion maps are inverted into a 3D S-wave velocity model using the Bayesian approach. The posterior probability density function describing the solution is sampled by more than one million models obtained by Monte-Carlo approach (parallel tempering). The calculated variance of the model shows that the well resolved part corresponds to the upper crust (i.e., upper 20 km). The mean velocity model contains mainly large scale structures that show good correlation with the main geologic domains of the Bohemian...

The thesis addresses time-domain inverse electromagneticscattering for determining unknown characteristics of an objectfrom observations of the scattered .eld. Applications includenon-destructive characterization of media and optimization ofmaterial properties, for example the design of radar absorbingmaterials.A nother interesting application is the parameteroptimization of subcell models to avoid detailed modeling ofcomplex geometries. The inverse problem is formulated as an optimal controlproblem where the cost function to be minimized is thedi.erence between the estimated and observed .elds, and thecontrol parameters are the unknown object characteristics. Theproblem is solved in a deterministic gradient-basedoptimization algorithm using a parallel 2D FDTD scheme for thedirect problem.This approach is computationally intensive sincethe direct problem needs to be solved in every optimizationiteration in order to compute an estimated .eld.H ighlyaccurate analytical gradients are computed from the adjointformulation.In addition to giving better accuracy than .nitedi.erences, the analytical gradients also have the advantage ofonly requiring one direct and one adjoint problem to be solvedregardless of the number of parameters. When absorbing boundary conditions are used to truncate thecomputational domain, the equations are non-reversible and theentire time-history of the direct solution needs to be storedfor the gradient computation.Ho wever, using an additionaldirect simulation and a restart procedure it is possible tokeep the storage at an acceptable level. The inverse method has been successfully applied to a widerange of industrial problems within the European project,IMPACT (Inverse Methods for Wave Propagation Applications inTime-Domain).T he results presented here includecharacterization of layered dispersive media, determination ofparameters in subcell models for thin sheets and narrow slotsand optimization problems where the observed .eld is given bydesign objectives.

The stability and the receptivity of three-dimensional flat plate boundary layers is studied employing parabolised stability equations. These allow for computationally efficient parametric studies. Two different sets of equations are used. The stability of modal disturbances in the form of crossflow vortices is studied by means of the well-known classical parabolised stability equations (PSE). A new method is developed which is applicable to more general vortical-type disturbances. It is based on a modified version of the classical PSE and describes both modal and non-modal growth in three-dimensional boundary layers. This modified PSE approach is used in conjunction with a Lagrange multiplier technique to compute spatial optimal disturbances in three-dimensional boundary layers. These take the form of streamwise oriented tilted vortices initially and develop into streaks further downstream. When entering the domain where modal disturbances become unstable optimal disturbances smoothly evolve into crossflow modes. It is found that non-modal growth is of significant magnitude in three-dimensional boundary layers. Both the lift-up and the Orr mechanism are identified as the physical mechanisms behind non-modal growth. Furthermore, the modified PSE are used to determine the response of three-dimensional boundary layers to vortical free-stream disturbances. By comparing to results from direct numerical simulations it is shown that the response, including initial transient behaviour, is described very accurately. Extensive parametric studies are performed where effects of free-stream turbulence are modelled by filtering with an energy spectrum characteristic for homogeneous isotropic turbulence. It is found that a quantitative prediction of the boundary layer response to free-stream turbulence requires detailed information about the incoming turbulent flow field. Finally, the adjoint of the classical PSE is used to determine the receptivity of modal disturbances with respect to localised surface roughness. It is shown that the adjoint approach yields perfect agreement with results from Finite-Reynold-Number Theory (FRNT) if the boundary layer is assumed to be locally parallel.  Receptivity is attenuated if nonlocal and non-parallel effects are accounted for. Comparisons to direct numerical simulations and extended parametric studies are presented.

Au cours des processus de conception,l’optimisation de formes apporte aux industriels dessolutions pour l’amélioration des performances desproduits. En particulier, les structures minces quiconstituent environ 70% d’un véhicule, sont une préoccupationdans l’industrie automobile. La plupartdes méthodes d’optimisation pour ces structures surfaciquesprésentent certaines limites et nécessitent desexpertises à chaque niveau de la procédure d’optimisation.L’objectif de cette thèse est de proposer une nouvellestratégie d’optimisation de formes pour les coquesminces. L’approche présentée consiste à exploiter leséquations de coques du modèle de Koiter en se basantsur une analyse isogéométrique. Cette méthode permetde réaliser des simulations sur la géométrie exacteen définissant la forme à l’aide de patchs CAO. Lesvariables d’optimisation choisies sont alors les pointsde contrôle permettant de piloter leur forme. La définitiondes patchs permet également de dégager ungradient de forme pour l’optimisation à l’aide d’uneméthode adjointe.Cette méthode a été appliquée pour des critères mécaniquesissus des bureaux d’études Renault. Des résultatsd’optimisation pour un critère de compliance sontprésentés. La définition et l’implémentation de critèresvibro-acoustiques sont discutés à la fin de cette thèse.Les résultats obtenus témoignent de l’intérêt de la méthode.Toutefois, de nombreux développements serontnécessaires avant d’être en mesure de l’appliquer dansl’industrie. / During the design process, optimizationof shapes offers manufacturers solutions for improvingproducts performances. In particular, thin shellstructures that represent about 70 % of a vehicle, area concern in the automotive industry. Most optimizationmethods for surface structures have limitationsand require expertise at every level of the optimizationprocedure.The aim of this thesis is to propose a new strategyfor the shape optimization of thin shell structures.The approach presented rely on using the Koiter’sshell model based on an isogeometric analysis. Thismethod allows for simulations on the exact geometryby defining the shape using CAD patches. Selectedoptimization variables are the control points used tocontrol the shape of the CAD patches. Variations ofthese points allows to scan a wide design space withfew parameters. The definition of patchs also enablesto find a gradient with respect to the shape for theoptimization by using the adjoint state method.This method was applied to mechanical criteria fromthe Renault design offices. Optimization results for acompliance criterion are presented. The definition andimplementation of vibro-acoustic criteria are discussedat the end of this thesis. The results demonstratethe interest of the method. However, many developmentswill be needed before being able to apply it inthe industry.

Optical fibers play a vital role in modern telecommunication systems and networks. An optical fiber link imposes some linear and nonlinear distortions on the propagating light-wave signal due to the inherent dispersive nature and nonlinear behavior of the fiber. These distortions impede the increasing demand for higher data rate transmission over longer distances. Developing efficient and computationally non-expensive digital signal processing (DSP) techniques to effectively compensate for the fiber impairments is therefore essential and of preeminent importance. This thesis proposes two DSP-based approaches for mitigating the induced distortions in short-reach and long-haul fiber-optic communication systems. The first approach introduces a powerful digital nonlinear feed-forward equalizer (NFFE), exploiting multilayer artificial neural network (ANN). The proposed ANN-NFFE mitigates nonlinear impairments of short-haul optical fiber communication systems, arising due to the nonlinearity introduced by direct photo-detection. In a direct detection system, the detection process is nonlinear due to the fact that the photo-current is proportional to the absolute square of the electric field intensity. The proposed equalizer provides the most efficient computational cost with high equalization performance. Its performance is comparable to the benchmark compensation performance achieved by maximum-likelihood sequence estimator. The equalizer trains an ANN to act as a nonlinear filter whose impulse response removes the intersymbol interference (ISI) distortions of the optical channel. Owing to the proposed extensive training of the equalizer, it achieves the ultimate performance limit of any feed-forward equalizer. The performance and efficiency of the equalizer are investigated by applying it to various practical short-reach fiber-optic transmission system scenarios. These scenarios are extracted from practical metro/media access networks and data center applications. The obtained results show that the ANN-NFFE compensates for the received BER degradation and significantly increases the tolerance to the chromatic dispersion distortion. The second approach is devoted for blindly combating impairments of long-haul fiber-optic systems and networks. A novel adjoint sensitivity analysis (ASA) approach for the nonlinear Schrödinger equation (NLSE) is proposed. The NLSE describes the light-wave propagation in optical fiber communication systems. The proposed ASA approach significantly accelerates the sensitivity calculations in any fiber-optic design problem. Using only one extra adjoint system simulation, all the sensitivities of a general objective function with respect to all fiber design parameters are estimated. We provide a full description of the solution to the derived adjoint problem. The accuracy and efficiency of our proposed algorithm are investigated through a comparison with the accurate but computationally expensive central finite-differences (CFD) approach. Numerical simulation results show that the proposed ASA algorithm has the same accuracy as the CFD approach but with a much lower computational cost. Moreover, we propose an efficient, robust, and accelerated adaptive digital back propagation (A-DBP) method based on adjoint optimization technique. Provided that the total transmission distance is known, the proposed A-DBP algorithm blindly compensates for the linear and nonlinear distortions of point-to-point long-reach optical fiber transmission systems or multi-point optical fiber transmission networks, without knowing the launch power and channel parameters. The NLSE-based ASA approach is extended for the sensitivity analysis of general multi-span DBP model. A modified split-step Fourier scheme method is introduced to solve the adjoint problem, and a complete analysis of its computational complexity is studied. An adjoint-based optimization (ABO) technique is introduced to significantly accelerate the parameters extraction of the A-DBP. The ABO algorithm utilizes a sequential quadratic programming (SQP) technique coupled with the extended ASA algorithm to rapidly solve the A-DBP training problem and optimize the design parameters using minimum overhead of extra system simulations. Regardless of the number of A-DBP design parameters, the derivatives of the training objective function with respect to all parameters are estimated using only one extra adjoint system simulation per optimization iterate. This is contrasted with the traditional finite-difference (FD)-based optimization methods whose sensitivity analysis calculations cost per iterate scales linearly with the number of parameters. The robustness, performance, and efficiency of the proposed A-DBP algorithm are demonstrated through applying it to mitigate the distortions of a 4-span optical fiber communication system scenario. Our results show that the proposed A-DBP achieves the optimal compensation performance obtained using an ideal fine-mesh DBP scheme utilizing the correct channel parameters. Compared to A-DBPs trained using SQP algorithms based on forward, backward, and central FD approaches, the proposed ABO algorithm trains the A-DBP with 2.02 times faster than the backward/forward FD-based optimizers, and with 3.63 times faster than the more accurate CFD-based optimizer. The achieved gain further increases as the number of design parameters increases. A coarse-mesh A-DBP with less number of spans is also adopted to significantly reduce the computational complexity, achieving compensation performance higher than that obtained using the coarse-mesh DBP with full number of spans. / Thesis / Doctor of Philosophy (PhD) / This thesis proposes two powerful and computationally efficient digital signal processing (DSP)-based techniques, namely, artificial neural network nonlinear feed forward equalizer (ANN-NFFE) and adaptive digital back propagation (A-DBP) equalizer, for mitigating the induced distortions in short-reach and long-haul fiber-optic communication systems, respectively. The ANN-NFFE combats nonlinear impairments of direct-detected short-haul optical fiber communication systems, achieving compensation performance comparable to the benchmark performance obtained using maximum-likelihood sequence estimator with much lower computational cost. A novel adjoint sensitivity analysis (ASA) approach is proposed to significantly accelerate sensitivity analyses of fiber-optic design problems. The A-DBP exploits a gradient-based optimization method coupled with the ASA algorithm to blindly compensate for the distortions of coherent-detected fiber-optic communication systems and networks, utilizing the minimum possible overhead of performed system simulations. The robustness and efficiency of the proposed equalizers are demonstrated using numerical simulations of varied examples extracted from practical optical fiber communication systems scenarios.

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