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Convergence of a Numerical Method for Reconstructing Faults from Boundary MeasurementsJiang, Yulong 17 May 2020 (has links)
In this thesis we derive the convergence order of a regularized error functional for reconstructing faults from boundary measurements of displacement fields. The convergence was proved to occur as the regularization parameter converges to zero but the convergence order was unknown. This functional is used to solve an inverse problem related to a half-space linear elasticity model. We first discuss this related model and review some basic properties of this functional and then we derive the convergence order for small regularization parameters. This study is a first, but essential, step toward analyzing the convergence order of related numerical methods. The reconstruction method of faults studied in this thesis was built from a model for real-world faults between tectonic plates that occur in nature. This model was first proposed by geophysicists and was later analyzed by mathematicians who were interested in building efficient numerical methods with proof of convergence.
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Filtering and reconstruction in image processingKnutsson, Hans January 1982 (has links)
Image processing is a broad field posing a wide range of problems. The Work presented in this dissertation is mainly concerned with filter design subjectto different criteria and constraints. The first part describes the development of a new radiographic reconstruction method designated Ectomography. The method is novel in that it allows reconstruction of an arbitrarily thick layer of an object using limited viewing angle. The subject of the second partis estimation and filtering of local image information. Quadrature filters are designed enabling accurate orientation and frequency estimates. The extracted information is shown to provide a good basis fo r efficient image enhancement and coding procedures.
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Microstructure et macro-comportement acoustique : approche par reconstruction d'une cellule élémentaire représentativePerrot, Camille January 2006 (has links)
The fundamental issue of determining acoustic properties of porous media from their local geometry is examined in this PhD dissertation thesis, thanks to a sample of open-cell aluminum foam analyzed by axial computed microtomography. Various geometric properties are measured to characterize the experimental sample at the cell size level. This is done in order to reconstruct a porous medium by means of idealized three- and two- dimensional unit-cells.The frequency dependant thermal and velocity fields governing the propagation and dissipation of acoustic waves through rigid porous media are computed by Brownian motion simulation and the finite element method, respectively. Macroscopic behavior is derived by spatial averaging of the local fields. Our results are compared to experimental data obtained from impedance tube measurements. Firstly, this approach leads to the identification of the macroscopic parameters involved in Pride and Lafarge semiphenomenological models. Secondly, it yields a direct access to thermal and viscous dynamic permeabilities. However, the bi-dimensional model underestimates the static viscous permeability as well as the viscous characteristic length; what thus require a three-dimensional implementation.
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Exploring everyday functioning in older adults with chronic pain : new insights with new technologyWilson, Gemma January 2014 (has links)
Chronic pain is a widespread problem, especially in the older population, and can affect various aspects of daily living. At a time when it has been acknowledged that the population is increasingly ageing, research regarding the effects of chronic pain on the daily living of older adults is essential. Furthermore, the development of innovative technology is changing the way that much research is being conducted, and can lead to the retrieval of novel information, using a fresh approach. The adoption of this technology in the field of chronic pain research has the potential to examine various aspects of the daily living of older adults living with chronic pain using a different approach to previous research. This study is underpinned by a Critical Realist ontology and Hermeneutic epistemology and follows a Generic Qualitative Research methodology (Caelli, et al., 2003). The aim of the study was not to generalise the findings but to gather a deep theoretical description of the outcomes and offer an explanation of these findings based on an analysis of the multiple research methods used within the study. This study had two main aims and was split into two sections according to the aims. Firstly, Part A of this study aimed to explore a range of day-to-day patterns and experiences of functioning in older adults suffering from chronic pain. Part B aimed to explore the usability, acceptance and experience of the technology used to measure functioning as part of the first aim of this study. Part B also aimed to look at the practicalities the participants were faced with when using the technology. A mixed methods design was used for Part A in which 15 older adults (65+) living with chronic pain (pain >3 months) took part in an in-depth study lasting seven days. As well as the 15 core participants that took part in the study, two older adults (65+) without chronic pain and two younger adults (<65) with chronic pain took part in the study in order to provide some insight into the effects of either pain, or age, on functioning. Part A used four data collection techniques to gather data upon the daily functioning of older adults with chronic pain; the Daily Reconstruction Method diary (Kahneman, Krueger, Schkade, Schwarz, Stone, 2004), the Sensecam (also known as the Vicon Revue, Vicon©), the LifeShirt (Vivometrics Inc) and a semi-structured interview. However, although the LifeShirt was validated, as part of this PhD, and used throughout the study, the gathered data was not analysed due to multiple problems with the data. The Daily Reconstruction Method, Sensecam and the semi-structured interview were each analysed separately before the results of the Daily Reconstruction Method and Sensecam were integrated into the themes derived from the semi-structured interviews. The integrated results led to the development of two themes, each with sub-themes; ‘effect on daily living’ and ‘managing pain and functioning’. The themes from Part A highlighted the way in which pain affected functioning and the modifications to daily functioning as a result of chronic pain. The way in which individuals perceived the management of their own pain and functioning, as well as strategies and assistive devices to manage pain and functioning were also discussed. This study has furthered current knowledge due to the idiographic nature of the study, as well as multiple, novel, data collection tools used, adding additional details to how tasks have been modified, reduced, or terminated. Part B of this study used the Unified Theory of Acceptance and Use of Technology (UTAUT, Venkatesh, et al., 2003), the Flow-State Scale (Jackson & Marsh, 1996) and semi-structured interviews to explore participants’ use of both the Sensecam and LifeShirt. The questionnaires and interviews were carried out with all of the individuals that carried out Part A of this research. From the semi-structured interviews two main themes were reported, each with sub-themes; ‘expectations and experiences’ and ‘awareness of equipment’. Two concepts developed from the themes within Part B that were specific to the participants’ experiences of wearing wearable technology in this study, as opposed to ‘typical’ non-wearable technology; specifically, the importance of design and the importance of others. Both of these overarching concepts affected the expectations of the technology, the experiences of using the technology, as well as the awareness of the technology during use. Furthermore, both concepts will remain and are long-lasting, despite the development of the technology in this field, but there are specific details that are contemporary and are specific to either the Sensecam or the LifeShirt as used in this study.
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The use of the source reconstruction method for antenna characterizationNarendra, Chaitanya 14 April 2016 (has links)
This thesis studies the use of the Source Reconstruction Method (SRM) to characterize antennas. The SRM calculates equivalent sources/currents on an arbitrarily shaped reconstruction surface to represent the original antenna. This is done by enforcing that the original antenna and equivalent currents radiate the same field at user selected measurement locations. These equivalent currents spatially characterize the original antenna because they can be used in direct radiation problems to obtain field estimates anywhere outside the reconstruction surface, including the far-field.
First a spherical SRM algorithm is implemented and the diagnostic capabilities of the SRM are also synthetically shown through an example with an array of elementary dipoles. It is then shown that the SRM compares well to pre-existing commercial antenna software over different frequencies and can also be used successfully with a partial dataset. It is demonstrated that the equivalent currents can also provide meaningful information with experimental data.
Next the hierarchical matrix framework is studied in conjunction with the SRM to decrease the algorithm's memory requirement and increase the speed of execution. It is shown that it is beneficial to use the hierarchical matrix framework with the SRM when using Love's condition or with measured data on a surface very close to the reconstruction surface.
The SRM is then used to obtain incident field estimates in microwave imaging systems. Using a 2D transverse magnetic framework, we show that even with the limited data available in typical microwave tomography setups the SRM can produce incident field estimates in the imaging domain. These estimates are then used along with an MR-GNI algorithm to image synthetic and experimental objects with uncalibrated measured data. / October 2016
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Contribuição ao desenvolvimento de técnicas de visualização térmica para monitoração de processos envolvendo fluidos multifásicos / Contribution to the development of techniques of thermal visualization for monitoring of processes involving fluid multiphasesCampos, Gisleine Pereira de 22 October 2004 (has links)
Técnicas de reconstrução térmica inversa são muito usadas em diferentes aplicações tais como a determinação de propriedades térmicas de novos materiais, controle da produção de calor, temperatura em processos de manufatura, etc. Apesar da ampla aplicabilidade, o problema inverso é intrinsecamente mal condicionado e tem sido tema de trabalhos de vários pesquisadores. A solução de um problema térmico inverso tridimensional é significantemente complexa, e, assim requer uma formulação que não contenha condições experimentais não realistas tais como confinamento bidimensional e estabilidade do campo térmico com relação a mudanças em parâmetros internos. Uma das abordagens adotada é baseada na formulação variacional sobre a forma do erro quadrático para reconstrução da distribuição de condução de calor interna e coeficiente de condução de calor parietal para um problema tridimensional. Dentro desta estrutura, a natureza mal condicionada do problema se manifesta na superfície de otimização por produzir topologias problemáticas tais como, vários mínimos locais, pontos de sela, vales e platôs ao redor da solução etc. Para viabilizar a abordagem escolhida, um modelo numérico foi escrito baseado na discretização por diferenças finitas da equação diferencial governante e condições de contorno. O erro funcional foi definido pela comparação entre medidas experimentais e numéricas de temperatura. O objetivo foi realizar simulações numéricas a fim de mapear a superfície de otimização correspondente e identificar a estrutura problemática associada ou patologia, chegando assim à reconstrução do coeficiente de convecção h. / Inverse thermal reconstruction techniques are widely used in different applications such as the determination of thermal properties of new materials, control of heat generation, temperature in manufacturing processes, etc. Despite the broad range of applicability, an inverse problem is intrinsically ill conditioned and has been the subject of the work of several researchers. The solution of an inverse 3-dimesional thermal problem is significantly complex, and, thus, requires a formulation that do not contain unrealistic experimental conditions such as 2-dimensional confinement and steadiness of the thermal field with respect to changes in internal parameters. One of the most adopted is the variational formulation based on quadratic error forms for the reconstruction of the internal heat conduction distribution and convection coefficient for a 3-dimensional problem. Within this framework, the ill conditioned nature of the problem manifests itself on the optimization surface by producing problematic topologies such as contour and multiple local minima, saddle points, plateaux around the solution pit and so on. To be able to apply th method a numerical model was written based on a finite difference discretization of the governing differential equation and boundary conditions. An error functional was defined by comparing experimental and numerical measurement temperatures. Numerical simulations aiming at mapping the corresponding optimization surfaces andatidentifing the associated problematic structures or pathologies, resulting in the reconstruction of convection coefficient.
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Development of a GPS Occultation Retrieval Method for Characterizing the Marine Boundary Layer in the Presence of Super-RefractionXie, Feiqin January 2006 (has links)
The marine boundary layer (MBL) is the region where energy, momentum and masses are exchanged between the ocean surface and the free troposphere. The lack of observations with high vertical resolution over the ocean significantly restricts the understanding of the complex physical processes that occur inside the MBL. The relatively short vertical extent of the MBL (average about 1~2 km) and the frequent cloudiness at its top make probing the MBL extremely difficult from the space. Several features of the Global Positioning System (GPS) radio occultation (RO) technique suggest that it has a great potential for sensing the MBL. These features include global coverage, high vertical resolution, and the ability of GPS signals to penetrate clouds.Over moist marine areas, a large negative moisture gradient often exists across the thermal inversion capping the MBL, which can cause super-refraction (SR) or ducting. A large number of high-resolution soundings have shown that SR occurs about 90% of the time in a year over the subtropical and tropical oceans and even 50% at high-latitudes during the summer. In the presence of SR, the reconstruction of refractivity from RO data becomes an ill-posed inverse problem, i.e., a given RO bending angle profile is consistent with a continuum (an infinite number) of refractivity profiles. The standard Abel retrieval gives the minimum refractivity solution of the continuum and thus produces the largest negative bias, consistent with a negative bias that is often present in the retrieved refractivity profiles in the moist lower troposphere. Simulation studies indicate a large variation of the negative refractivity biases (could be over -15%). The impact of diffraction effects and the open-loop receiver tracking on the bending angle and refractivity retrievals are assessed. A novel approach is developed and tested to reconstruct the vertical refractivity structure within and below the SR layer, which yields a much-improved retrieval, especially below the SR layer (less than 0.5% error). Such a reconstruction method should greatly enhance our ability to measure the MBL globally using the GPS RO technique as well as to improve the MBL parameterizations used in weather and climate models.
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Contribuição ao desenvolvimento de técnicas de visualização térmica para monitoração de processos envolvendo fluidos multifásicos / Contribution to the development of techniques of thermal visualization for monitoring of processes involving fluid multiphasesGisleine Pereira de Campos 22 October 2004 (has links)
Técnicas de reconstrução térmica inversa são muito usadas em diferentes aplicações tais como a determinação de propriedades térmicas de novos materiais, controle da produção de calor, temperatura em processos de manufatura, etc. Apesar da ampla aplicabilidade, o problema inverso é intrinsecamente mal condicionado e tem sido tema de trabalhos de vários pesquisadores. A solução de um problema térmico inverso tridimensional é significantemente complexa, e, assim requer uma formulação que não contenha condições experimentais não realistas tais como confinamento bidimensional e estabilidade do campo térmico com relação a mudanças em parâmetros internos. Uma das abordagens adotada é baseada na formulação variacional sobre a forma do erro quadrático para reconstrução da distribuição de condução de calor interna e coeficiente de condução de calor parietal para um problema tridimensional. Dentro desta estrutura, a natureza mal condicionada do problema se manifesta na superfície de otimização por produzir topologias problemáticas tais como, vários mínimos locais, pontos de sela, vales e platôs ao redor da solução etc. Para viabilizar a abordagem escolhida, um modelo numérico foi escrito baseado na discretização por diferenças finitas da equação diferencial governante e condições de contorno. O erro funcional foi definido pela comparação entre medidas experimentais e numéricas de temperatura. O objetivo foi realizar simulações numéricas a fim de mapear a superfície de otimização correspondente e identificar a estrutura problemática associada ou patologia, chegando assim à reconstrução do coeficiente de convecção h. / Inverse thermal reconstruction techniques are widely used in different applications such as the determination of thermal properties of new materials, control of heat generation, temperature in manufacturing processes, etc. Despite the broad range of applicability, an inverse problem is intrinsically ill conditioned and has been the subject of the work of several researchers. The solution of an inverse 3-dimesional thermal problem is significantly complex, and, thus, requires a formulation that do not contain unrealistic experimental conditions such as 2-dimensional confinement and steadiness of the thermal field with respect to changes in internal parameters. One of the most adopted is the variational formulation based on quadratic error forms for the reconstruction of the internal heat conduction distribution and convection coefficient for a 3-dimensional problem. Within this framework, the ill conditioned nature of the problem manifests itself on the optimization surface by producing problematic topologies such as contour and multiple local minima, saddle points, plateaux around the solution pit and so on. To be able to apply th method a numerical model was written based on a finite difference discretization of the governing differential equation and boundary conditions. An error functional was defined by comparing experimental and numerical measurement temperatures. Numerical simulations aiming at mapping the corresponding optimization surfaces andatidentifing the associated problematic structures or pathologies, resulting in the reconstruction of convection coefficient.
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An evaluation of deterministic prediction of ocean waves using pressure data to assist a Wave Energy Converter / En utvärdering av användandet av tryckdata för att deterministiskt förutspå havsvågor för att assistera ett vågkraftverkBassili, Niclas, Eriksson, Douglas January 2020 (has links)
Currently, existing devices for extracting electrical power from ocean waves all suffer from problems with low efficiency due to a lack of information about the incoming waves in advance. The complex dynamic nonlinear characteristics of the ocean make the prediction of these incoming waves a great challenge. This paper aims to investigate a deterministic short-term wave-by-wave prediction system, that can accurately predict the wave height and timing of the incoming waves, based on measurements from a submerged pressure sensor. The complete prediction process contains three steps, namely reconstruction, assimilation, and prediction. A nonlinear Weakly Dispersive Reconstruction method (WDM) is firstly employed to accurately calculate the surface elevation from the measured pressures. Afterwards, a variational assimilation method is used to convert the time series surface elevation to a spatial wavefield, to obtain initial conditions for the prediction. Lastly, a High Order Spectral Method (HOSM) deterministically predicts the evolution of the 2D irregular wavefield based on the acquired initial conditions. To verify the performance of this proposed prediction system, tests were conducted with data from irregular sea states with varying wave parameters, generated by simulations as well as model experiments in the controlled environment of a wave tank. The results show that the surface elevation can be predicted within 5% from the reference, for a future period of about 10 seconds for wavefields commonly experienced by a wave energy converter. Based on the results, a prediction is possible, but the accuracy heavily depends on the current sea state and the chosen prediction distance.The results have been compared against similar tests made using radar data and proven to be a viable alternative for certain sea states. In conclusion, pressure measurements, as a mean to sample an ocean wavefield, is shown to be a good option when combined with nonlinear reconstruction and prediction methods to assist the power harvesting capabilities of a wave energy converter. / Nuvarande enheter för att extrahera elektrisk energi från havsvågor lider av stora problem med låg effektivitet på grund av brist på information om de inkommande vågorna. Det komplexa ickelinjära dynamiska beteendet hos havsvågor gör förutsägelsen av dem till en stor utmaning. Det här arbetet syftar till att undersöka ett deterministiskt kortsiktigt system för att förutspå våg för våg, som noggrant kan förutspå våghöjd och tidpunkt för de inkommande vågorna, baserat på mätdata från en dränkbar trycksensor. Den kompletta förutsägelseprocessen innehåller tre steg, rekonstruktion, assimilering och förutsägelse. En ickelinjär weakly dispersive reconstruction method används först för att med hög noggrannhet beräkna ythöjningen från det uppmätta trycket. Därefter, används en variational assimilation method för att konvertera en tidsserie av ythöjningen till ett rumsligt vågfält, för att erhålla initialvillkor för förutsägelsen. Slutligen används en High Order Spectral Method för att deterministiskt förutspå utvecklingen av det tvådimensionella oregelbundna vågfältet baserat på de förvärvade initialvillkoren. För att verifiera prestandan av det föreslagna förutsägelsesystemet, så genomfördes tester med data från olika oregelbundna havstillstånd med varierande parametrar, genererade av simuleringar, såväl som modellexperiment utförda i en kontrollerad miljö i form av en vågtank. Resultaten från testerna visar att ythöjningen förutspås inom 5% från referensen, för en period på 10 sekunder framåt i tiden, för vågor som ett vågkraftverk vanligtvis utsätts för. Baserat på resultatet, så är det möjligt att förutspå inkommande vågor, men noggrannheten beror kraftigt på det aktuella havstillståndet och det valda avståndet för förutsägelsen. Resultaten har jämförts mot liknande tester gjorda med radardata och visat sig vara ett genomförbart alternativ för vissa havstillstånd. Sammanfattningsvis visas det att tryckmätningar, som ett medel för att mäta ett havsvågfält, är ett bra alternativ när de kombineras med ickelinjära rekonstruktions- och förutsägelsemetoder för att hjälpa till att öka ett vågkraftverks energigenerering.
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Antenna characterization using phaseless near-field antenna measurementsBrown, Trevor 12 September 2016 (has links)
This thesis focuses on the application of electromagnetic inverse source techniques to characterize antennas using phaseless (amplitude-only) near-field (NF) measurement data. Removing the need to measure phase reduces the overall cost of the measurement apparatus since simple power meters can be used instead of expensive vector network analyzers. It has also been shown in the literature that a phaseless approach can improve the accuracy of the calculated far-field (FF) pattern in the presence of probe positioning errors compared to the amplitude-and-phase approach. A brief discussion on the state-of-the-art methods for characterizing antennas using phaseless near-field measurement data is presented. Two general approaches used most often to perform near-field to far-field (NF-FF) transformations, namely modal expansion and source reconstruction, are explained in detail for scenarios with and without phase information. A phaseless source reconstruction method (SRM) is the primary focus of this work. The SRM is an application of an electromagnetic inverse source technique and therefore, the complexities of solving the associated ill-posed inverse source problem are discussed. The application of the SRM to spherical and planar measurement geometries are presented along with the concerns regarding regularization resulting from discretizing the ill-posed system. A multiplicative regularization (MR) scheme originally developed for inverse scattering is adapted to suit the nonlinear cost functional for the phaseless planar measurement case and the mathematical framework is derived in detail. The resulting MR-SRM is fully automated and incorporates adaptive regularization. The developed algorithms are evaluated using several examples with synthetic phaseless NF data demonstrating the benefits and limitations of the source reconstruction method and the multiplicative regularization scheme. The application of the SRM to antenna diagnostics using phaseless NF data is also shown. Finally, the developed planar algorithms are tested with experimentally collected phaseless measurement data to demonstrate their potential as suitable antenna characterization techniques that can be of interest to the antenna measurement community. / October 2016
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