Radiation therapy (RT) is commonly used to treat patients with lung cancer. One of the limitations of RT is that irradiation of the surrounding healthy lung tissues during RT may cause damage to the lungs. Radiation-induced pulmonary toxicity may be mitigated by minimizing doses to high-function lung tissues, which we refer to as functional avoidance RT. Lung function can be computed by image registration of treatment planning four-dimensional computed tomography (4DCT), which we refer to as CT ventilation imaging. However, the accuracy of functional avoidance RT is limited by lung function imaging accuracy and artifacts in 4DCT. The goal of this dissertation is to improve the accuracy of functional avoidance RT by overcoming those two limitations. A common method for estimating lung ventilation uses image registration to align the peak exhale and inhale 3DCT images. This approach called the 2-phase local expansion ratio is limited because it assumes no out-of-phase lung ventilation and may underestimate local lung ventilation. Out-of-phase ventilation occurs when regions of the lung reach their maximum (minimum) local volume in a phase other than the peak of inhalation (end of exhalation). This dissertation presents a new method called the N-phase local expansion ratio for detecting and characterizing locations of the lung that experience out-of-phase ventilation. The N-phase LER measure uses all 4DCT phases instead of two peak phases to estimate lung ventilation. Results show that out-of-phase breathing was common in the lungs and that the spatial distribution of out-of-phase ventilation varied from subject to subject. On average, 49% of the out-of-phase regions were mislabeled as low-function by the 2-phase LER. 4DCT and Xenon-enhanced CT (Xe-CT) of four sheep were used to evaluate the accuracy of 2-phase LER and N-phase LER. Results show that the N-phase LER measure was more correlated with the Xe-CT than the 2-phase LER measure. These results suggest that it may be better to use all 4DCT phases instead of the two peak phases to estimate lung function. The accuracy of functional avoidance RT may also be improved by reducing the impact of artifacts in 4DCT. In this dissertation, we propose a a geodesic density regression (GDR) algorithm to correct artifacts in one breathing phase by using artifact-free data in corresponding regions of the other breathing phases. Local tissue density change associated with CT intensity change during respiration is accommodated in the GDR algorithm. Binary artifact masks are used to exclude regions of artifacts from the regression, i.e., the GDR algorithm only uses artifact-free data. The GDR algorithm estimates an artifact-free CT template image and its time flow through a respiratory cycle. Evaluation of the GDR algorithm was performed using both 2D CT time-series images with simulated known motion artifacts and treatment planning 4DCT with real motion artifacts. The 2D results show that there is no significant difference (p-value = 0.95) between GDR regression of artifact data using artifact masks and regression of artifact-free data. In contrast, significant errors (p-value = 0.005) were present in the estimated Jacobian images when artifact masks were not used. We also demonstrated the effectiveness of the GDR algorithm for removing real duplication, misalignment, and interpolation artifacts in 4DCT. Overall this dissertation proposes methods that have the potential to improve functional avoidance RT by accommodating out-of-phase ventilation, and removing motion artifacts in 4DCT using geodesic image regression.

Pile groups are often used to provide support for structures. Capping a pile group further adds to the system's resistance due to the passive earth pressure from surrounding backfill. While ultimate passive earth pressure under static loading conditions can be readily calculated using several different theories, the effects of cyclic and dynamic loading on the passive earth pressure response are less understood. Data derived from the full-scale testing of a pile cap system with a densely compacted sand backfill under static, cyclic, and dynamic loadings was analyzed with particular focus on soil pressures measured directly using pressure plates. Based on the testing and analyses, it was observed that under slow, cyclic loading, the backfill stiffness was relatively constant. Under faster, dynamic loading, the observed backfill stiffness decreased in a relatively linear fashion. During cyclic and dynamic loading, the pile cap gradually developed a residual offset from its initial position, accompanied by a reduction in backfill force. While the pile cap and backfill appeared to move integrally during static and cyclic loadings, during dynamic loading the backfill exhibited out-of-phase movement relative to the pile cap. Observed losses in backfill contact force were associated with both cyclic softening and dynamic out-of-phase effects. Force losses due to dynamic loading increased with increasing frequency (which corresponded to larger displacements). Losses due to dynamic loading were offset somewhat by increases in peak force due to damping. The increase in contact force due to damping was observed to be relatively proportional to increasing frequency. When quantifying passive earth forces with cyclic/dynamic losses without damping, the Mononobe-Okabe (M-O) equation with a 0.75 or 0.8 multiplier applied to the peak ground acceleration can be used to obtain a reasonable estimate of the force. When including increases in resistance due to damping, a 0.6 multiplier can similarly be used.

Loess is a well sorted, fine grained, windblown (aeolian) sediment and deposits as a blanket over large areas, reaching from a few centimetres to several hundreds of meters in height and can drape large landscapes in form of mountains. During a more humid and warmer climate, redox conditions are changed in the loess deposits, with greater seasonal moisture creating greater soil formation (pedogenesis), i.e. palaeosol.  The Chinese Loess Plateau is dominated by the East Asian monsoon climate, and consists of an alternating Loess-palaeosol Formation, spanning back to at least the whole Quaternary period and late Pliocene (~2.8 Ma), and overlays a Red Clay Formation ranging into at least Miocene. This deposit covers therefore the onset of the latest Quaternary Ice Age. The Magnetic Susceptibility (MS) is used to investigate the magnetism of a rock which is inferred to be driven by the pedogenetic activity changes, i.e. during a stronger pedogenesis a higher amount of magnetic minerals forms. In turn the MS measurements becomes as a good indicator of the intensity and duration of the East Monsoon climate. In present study, a newly applied technique in palaeoenvironment is used to investigate the reasons for the out-of-phase response by the MS measurements. The study shows that this is due to viscous relaxation. Thus, the ultrafine superparamagnetic mineral magnetite is giving rise to the out-of-phase response and no other mechanisms. / Lössjord är ett välsorterad, finkornigt, vindblåst (eolisk) sediment som avsätts som ett täcke över stora områden, och kan variera från några centimeter till flera hundra meter i höjd och drapera stora landskap i form av berg. Under ett mer fuktigt och varmare klimat förändras de redoxa förhållandena i lössjordarna, då större säsongsfuktighet skapar en större paleosol-bildning, under en så kallad pedogenes. Den Kinesiska Lössjordsplatån domineras av det östasiatiska monsunklimatet och består av en alternerande Lössjord-paleosol Formation, som sträcker sig tillbaka till åtminstone hela kvartära perioden men även sena Pliocen (~ 2,8 Ma), och överlagrar en Rödlera Formation som sträcker sig minst tillbaka till Miocen. Dessa avlagringar täcker därför övergången till början på den kvartära istiden. Den magnetiska susceptibiliteten (MS) används för att undersöka de magnetiska egenskaperna hos avlagringarna som drivs av de pedogenetiska aktiviteterna, dvs under en starkare pedogenes bildas en högre mängd magnetiska mineraler. I sin tur blir därför MS-mätningarna en bra indikator på intensiteten och varaktigheten av östasiatiska monsunklimatet. I denna studie används en nyligen tillämpad teknik inom paleo-miljö för att undersöka orsakerna bakom ur-fas responsen som fås genom MS-mätningar på avlagringarna. Studien visar att detta beror på viskös relaxation. Således är det ultrafina superparamagnetiska mineralet magnetit som ger upphov till ur-fas responsen och inga andra mekanismer.

[pt] As previsões de falhas por fadiga tornam-se críticas sob condições multiaxiais de carregamento, uma vez que a complexidade do estado de tensões requer uma análise com base em modelos mais avançados do que aqueles adotados para carregamentos uniaxiais. Neste contexto, alguns critérios foram desenvolvidos para tentar prever a falha de componentes submetidos a carregamentos cíclicos multiaxiais. Um exemplo de componente mecânico sujeito a fadiga multiaxial quando em serviço são os eixos virabrequim de unidades geradoras de plantas termoelétricas. Usualmente projetados segundo o critério de Findley, falhas recentes de eixos virabrequim ocorridas no parque termoelétrico nacional, tem provocado o questionamento da eficiência de tal critério. Desta forma, o presente estudo teve como objetivo analisar a aplicabilidade de seis modelos (Papadopoulos, Findley, Matake, McDiarmid, Carpinteri e Spagnoli e Liu e Mahadevan) de fadiga multiaxial de alto ciclo, baseados no plano crítico, para prever a falha de eixos virabrequim de unidades geradoras. Para aplicação dos modelos, adotaram-se diferentes parâmetros de carregamento (tensão média e defasagem de aplicação das tensões normais e cisalhantes) e propriedades de material (resistência à fadiga), partindo de valores encontrados na literatura. Observou-se uma divergência entre os resultados de cada modelo estudado, sendo uns mais conservadores do que os outros, em função do carregamento e propriedades do material. Entretanto, o modelo de Papadopoulos, com base na facilidade de aplicação e sensibilidade de previsão da falha, mostrou-se mais adequado. / [en] The fatigue failure prediction becomes critical under multiaxial loading conditions, since the complexity of the stress state requires analysis based on models more advanced than those adopted for uniaxial loads. In this context, some criteria were developed in an attempt to predict the failure of components subjected to multiaxial cyclic loads. An example of mechanical component subject to multiaxial fatigue is the crankshaft of thermoelectric plants. It is usually projected according to the Findley criterion. However, recent failures of crankshafts occurring in the national thermoelectric park, put on doubt the efficiency of such criterion. In this way, the present study aimed to analyze the applicability of six models (Papadopoulos, Findley, Matake, McDiarmid, Carpinteri e Spagnoli and Liu e Mahadevan) of high cycle multiaxial fatigue, based on the critical plane, to predict failure on crankshaft of generating units. For the models application, different loading parameters (medium stress and out-of-phase stresses) and material properties (fatigue limit) were adopted, starting from values found in the literature. A divergence between the results of each model was observed, some of them were more conservative than the others, depending on the loading and material s properties. However, the Papadopoulos model, based on easy application and failure prediction sensitivity, proved to be more suitable than the others.

This thesis is concerned with nonlinear analyses of BWR stability behaviour, contributing to a deeper understanding in this field. Despite negative feedback-coefficients of a BWR, there are operational points (OP) at which oscillatory instabilities occur. So far, a comprehensive and an in-depth understanding of the nonlinear BWR stability behaviour are missing, even though the impact of the significant physical parameters is well known. In particular, this concerns parameter regions in which linear stability indicators, like the asymptotic decay ratio, lose their meaning. Nonlinear stability analyses are usually carried out using integral (system) codes, describing the dynamical system by a system of nonlinear partial differential equations (PDE). One aspect of nonlinear BWR stability analyses is to get an overview about different types of nonlinear stability behaviour and to examine the conditions of their occurrence. For these studies the application of system codes alone is inappropriate. Hence, in the context of this thesis, a novel approach to nonlinear BWR stability analyses, called RAM-ROM method, is developed. In the framework of this approach, system codes and reduced order models (ROM) are used as complementary tools to examine the stability characteristics of fixed points and periodic solutions of the system of nonlinear differential equations, describing the stability behaviour of a BWR loop. The main advantage of a ROM, which is a system of ordinary differential equations (ODE), is the possible coupling with specific methods of the nonlinear dynamics. This method reveals nonlinear phenomena in certain regions of system parameters without the need for solving the system of ROM equations. The stability properties of limit cycles generated in Hopf bifurcation points and the conditions of their occurrence are of particular interest. Finally, the nonlinear phenomena predicted by the ROM will be analysed in more details by the system code. Hence, the thesis is not focused on rendering more precisely linear stability indicators like DR. The objective of the ROM development is to develop a model as simple as possible from the mathematical and numerical point of view, while preserving the physics of the BWR stability behaviour. The ODEs of the ROM are deduced from the PDEs describing the dynamics of a BWR. The system of ODEs includes all spatial effects in an approximated (spatial averaged) manner, e.g. the space-time dependent neutron flux is expanded in terms of a complete set of orthogonal spatial neutron flux modes. In order to simulate the stability characteristics of the in-phase and out-of-phase oscillation mode, it is only necessary to take into account the fundamental mode and the first azimuthal mode. The ROM, originally developed at PSI in collaboration with the University of Illinois (PSI-Illinois-ROM), was upgraded in significant points: • Development and implementation of a new calculation methodology for the mode feedback reactivity coefficients (void and fuel temperature reactivity) • Development and implementation of a recirculation loop model; analysis and discussion of its impact on the in-phase and out-of-phase oscillation mode • Development of a novel physically justified approach for the calculation of the ROM input data • Discussion of the necessity of consideration of the effect of subcooled boiling in an approximate manner With the upgraded ROM, nonlinear BWR stability analyses are performed for three OPs (one for NPP Leibstadt (cycle7), one for NPP Ringhals (cycle14) and one for NPP Brunsbüttel (cycle16) for which measuring data of stability tests are available. In this thesis, the novel approach to nonlinear BWR stability analyses is extensively presented for NPP Leibstadt. In particular, the nonlinear analysis is carried out for an operational point (OP), in which an out-of-phase power oscillation has been observed in the scope of a stability test at the beginning of cycle 7 (KKLc7_rec4). The ROM predicts a saddle-node bifurcation of cycles, occurring in the linear stable region, close to the KKLc7_rec4-OP. This result allows a new interpretation of the stability behaviour around the KKLc7_rec4-OP. The results of this thesis confirm that the RAM-ROM methodology is qualified for nonlinear BWR stability analyses. / Die vorliegende Dissertation leistet einen Beitrag zum tieferen Verständnis des nichtlinearen Stabilitätsverhaltens von Siedewasserreaktoren (SWR). Trotz der Tatsache, dass in diesem technischen System nur negative innere Rückkopplungskoeffizienten auftreten, können in bestimmten Arbeitspunkten oszillatorische Instabilitäten auftreten. Obwohl relativ gute Kenntnisse über die signifikanten physikalischen Einflussgrößen vorliegen, fehlt bisher ein umfassendes Verständnis des SWR-Stabilitätsverhaltens. Das betrifft insbesondere die Bereiche der Systemparameter, in denen lineare Stabilitätsindikatoren, wie zum Beispiel das asymptotische Decay Ratio (DR), ihren Sinn verlieren. Die nichtlineare Stabilitätsanalyse wird im Allgemeinen mit Systemcodes (nichtlineare partielle Differentialgleichungen, PDG) durchgeführt. Jedoch kann mit Systemcodes kein oder nur ein sehr lückenhafter Überblick über die Typen von nichtlinearen Phänomenen, die in bestimmten System-Parameterbereichen auftreten, erhalten werden. Deshalb wurde im Rahmen der vorliegenden Arbeit eine neuartige Methode (RAM-ROM Methode) zur nichtlinearen SWR-Stabilitätsanalyse erprobt, bei der integrale Systemcodes und sog. vereinfachte SWR-Modelle (ROM) als sich gegenseitig ergänzende Methoden eingesetzt werden, um die Stabilitätseigenschaften von Fixpunkten und periodischen Lösungen (Grenzzyklen) des nichtlinearen Differentialgleichungssystems, welches das Stabilitätsverhalten des SWR beschreibt, zu bestimmen. Das ROM, in denen das dynamische System durch gewöhnliche Differentialgleichungen (GDG) beschrieben wird, kann relativ einfach mit leistungsfähigen Methoden aus der nichtlinearen Dynamik, wie zum Beispiel die semianalytische Bifurkationsanalyse, gekoppelt werden. Mit solchen Verfahren kann, ohne das DG-System explizit lösen zu müssen, ein Überblick über mögliche Typen von stabilen und instabilen oszillatorischen Verhalten des SWR erhalten werden. Insbesondere sind die Stabilitätseigenschaften von Grenzzyklen, die in Hopf-Bifurkationspunkten entstehen, und die Bedingungen, unter denen sie auftreten, von Interesse. Mit dem Systemcode (RAMONA5) werden dann die mit dem ROM vorhergesagten Phänomene in den entsprechenden Parameterbereichen detaillierter untersucht (Validierung des ROM). Die Methodik dient daher nicht der Verfeinerung der Berechnung linearer Stabilitätsindikatoren (wie das DR). Das ROM-Gleichungssystem entsteht aus den PDGs des Systemcodes durch geeignete (nichttriviale) räumliche Mittelung der PDG. Es wird davon ausgegangen, dass die Reduzierung der räumlichen Komplexität die Stabilitätseigenschaften des SWR nicht signifikant verfälschen, da durch geeignete Mittlungsverfahren, räumliche Effekte näherungsweise in den GDGs berücksichtig werden. Beispielsweise wird die raum- und zeitabhängige Neutronenflussdichte nach räumlichen Moden entwickelt, wobei für eine Simulation der Stabilitätseigenschaften der In-phase- und Out-of-Phase-Leistungsoszillationen nur der Fundamentalmode und der erste azimuthale Mode berücksichtigt werden muss. Das ROM, welches ursprünglich am Paul Scherrer Institut (PSI, Schweiz) in Zusammenarbeit mit der Universität Illinois (USA) entwickelt wurde, ist in zwei wesentlichen Punkten erweitert und verbessert worden: • Entwicklung und Implementierung einer neuen Methode zur Berechnung der Rückkopplungsreaktivitäten • Entwicklung und Implementierung eines Modells zur Beschreibung der Rezirkulationsschleife (insbesondere wurde der Einfluss der Rezirkulationsschleife auf den In-Phase-Oszillationszustand und auf den Out-of-Phase-Oszillationszustand untersucht) • Entwicklung einer physikalisch begründeten Methode zur Berechnung der ROM-Inputdaten • Abschätzung des Einflusses des unterkühlten Siedens im Rahmen der ROM-Näherungen Mit dem erweiterten ROM wurden nichtlineare Stabilitätsanalysen für drei Arbeitspunkte (KKW Leibstadt (Zyklus 7) KKW Ringhals (Zyklus 14) und KKW Brunsbüttel (Zyklus 16)), für die Messdaten vorliegen, durchgeführt. In der Dissertationsschrift wird die RAM-ROM Methode ausführlich am Beispiel eines Arbeitspunktes (OP) des KKW Leibstadt (KKLc7_rec4-OP), in dem eine aufklingende regionale Leistungsoszillation bei einem Stabilitätstest gemessen worden ist, demonstriert. Das ROM sagt die Existenz eines Umkehrpunktes (saddle-node bifurcation of cycles, fold-bifurcation) voraus, der sich im linear stabilen Gebiet nahe der Stabilitätsgrenze befindet. Mit diesem ROM-Ergebnis ist eine neue Interpretation der Stabilitätseigenschaften des KKLc7_rec4-OP möglich. Die Resultate der in der Dissertation durchgeführten RAM-ROM Analyse bestätigen, dass das weiterentwickelte ROM für die Analyse des Stabilitätsverhaltens realer Leistungsreaktoren qualifiziert wurde.

[pt] Eixos de virabrequim estão sujeitos a carregamentos multiaxiais quando em serviço. Por se tratar de um estado complexo de tensões, os modelos aplicados na determinação da vida em fadiga de tais componentes devem permitir, também, uma abordagem multiaxial, mais avançados do que aqueles adotados para carregamentos uniaxiais. O objetivo deste trabalho foi prever a falha em serviço de eixos virabrequins de unidades geradoras Diesel ou gás de plantas termoelétricas. Falhas recentemente ocorridas em eixos virabrequins no parque termoelétrico nacional justificam o presente estudo, para garantir eficiência e segurança nas operações industriais. Com base no método de elementos finitos, foram calculadas as tensões atuantes em um eixo virabrequim de unidade geradora a gás, com 10 mancais, duas bielas por mancal e fabricado com aço estrutural DIN 34CrNiMo6. Em sequência, adotando-se estas tensões atuantes calculadas, foram aplicados diversos critérios de fadiga para prever sua falha. Para tal, adotaram-se os modelos de Papadopoulos, Findley, Matake, McDiarmid, Carpinteri e Spagnoli, Liu e Mahadevan, Mises, Sines e Crossland, todos de fadiga de alto ciclo, baseados no plano crítico ou na tensão de von Mises. Propriedades de resistência à fadiga do material foram retiradas da literatura. Os resultados obtidos indicaram que o componente é seguro quando avaliado usando tais critérios. / [en] Crankshaft axles are subject to multiaxial loading when in service. Because the resulting state of stresses is complex, models applied to determining the fatigue life of such components employ a multiaxial approach as well, more advanced than those adopted for uniaxial loads. The objective of this work is to predict the failure in service of crankshafts of diesel or gas generating units of thermoelectric plants. Crankshafts reported recent failures in the national thermoelectric power plant justifies the present study, to guarantee efficiency and safety in such industrial operations. Based on the finite element method, the resulting stresses on a DIN 34CrNiMo6 structural steel gas generating unit crankshaft, with 10 bearings, two connecting rods per bearing were calculated. Using these finite element calculated stresses, several fatigue criteria were applied to predict this cranckshaft structural failure. Models due to Papadopoulos, Findley, Matake, McDiarmid, Carpinteri and Spagnoli, Liu and Mahadevan, Mises, Sines and Crossland, all of high cycle fatigue based on the critical plane or von Mises strain, were adopted. Material fatigue properties used in the analyses were compiled from specidized literature. Obtained results indicated that the component considered is safe regarding fatigue loadings, as evaluated using such criteria.

This thesis is concerned with nonlinear analyses of BWR stability behaviour, contributing to a deeper understanding in this field. Despite negative feedback-coefficients of a BWR, there are operational points (OP) at which oscillatory instabilities occur. So far, a comprehensive and an in-depth understanding of the nonlinear BWR stability behaviour are missing, even though the impact of the significant physical parameters is well known. In particular, this concerns parameter regions in which linear stability indicators, like the asymptotic decay ratio, lose their meaning. Nonlinear stability analyses are usually carried out using integral (system) codes, describing the dynamical system by a system of nonlinear partial differential equations (PDE). One aspect of nonlinear BWR stability analyses is to get an overview about different types of nonlinear stability behaviour and to examine the conditions of their occurrence. For these studies the application of system codes alone is inappropriate. Hence, in the context of this thesis, a novel approach to nonlinear BWR stability analyses, called RAM-ROM method, is developed. In the framework of this approach, system codes and reduced order models (ROM) are used as complementary tools to examine the stability characteristics of fixed points and periodic solutions of the system of nonlinear differential equations, describing the stability behaviour of a BWR loop. The main advantage of a ROM, which is a system of ordinary differential equations (ODE), is the possible coupling with specific methods of the nonlinear dynamics. This method reveals nonlinear phenomena in certain regions of system parameters without the need for solving the system of ROM equations. The stability properties of limit cycles generated in Hopf bifurcation points and the conditions of their occurrence are of particular interest. Finally, the nonlinear phenomena predicted by the ROM will be analysed in more details by the system code. Hence, the thesis is not focused on rendering more precisely linear stability indicators like DR. The objective of the ROM development is to develop a model as simple as possible from the mathematical and numerical point of view, while preserving the physics of the BWR stability behaviour. The ODEs of the ROM are deduced from the PDEs describing the dynamics of a BWR. The system of ODEs includes all spatial effects in an approximated (spatial averaged) manner, e.g. the space-time dependent neutron flux is expanded in terms of a complete set of orthogonal spatial neutron flux modes. In order to simulate the stability characteristics of the in-phase and out-of-phase oscillation mode, it is only necessary to take into account the fundamental mode and the first azimuthal mode. The ROM, originally developed at PSI in collaboration with the University of Illinois (PSI-Illinois-ROM), was upgraded in significant points: • Development and implementation of a new calculation methodology for the mode feedback reactivity coefficients (void and fuel temperature reactivity) • Development and implementation of a recirculation loop model; analysis and discussion of its impact on the in-phase and out-of-phase oscillation mode • Development of a novel physically justified approach for the calculation of the ROM input data • Discussion of the necessity of consideration of the effect of subcooled boiling in an approximate manner With the upgraded ROM, nonlinear BWR stability analyses are performed for three OPs (one for NPP Leibstadt (cycle7), one for NPP Ringhals (cycle14) and one for NPP Brunsbüttel (cycle16) for which measuring data of stability tests are available. In this thesis, the novel approach to nonlinear BWR stability analyses is extensively presented for NPP Leibstadt. In particular, the nonlinear analysis is carried out for an operational point (OP), in which an out-of-phase power oscillation has been observed in the scope of a stability test at the beginning of cycle 7 (KKLc7_rec4). The ROM predicts a saddle-node bifurcation of cycles, occurring in the linear stable region, close to the KKLc7_rec4-OP. This result allows a new interpretation of the stability behaviour around the KKLc7_rec4-OP. The results of this thesis confirm that the RAM-ROM methodology is qualified for nonlinear BWR stability analyses. / Die vorliegende Dissertation leistet einen Beitrag zum tieferen Verständnis des nichtlinearen Stabilitätsverhaltens von Siedewasserreaktoren (SWR). Trotz der Tatsache, dass in diesem technischen System nur negative innere Rückkopplungskoeffizienten auftreten, können in bestimmten Arbeitspunkten oszillatorische Instabilitäten auftreten. Obwohl relativ gute Kenntnisse über die signifikanten physikalischen Einflussgrößen vorliegen, fehlt bisher ein umfassendes Verständnis des SWR-Stabilitätsverhaltens. Das betrifft insbesondere die Bereiche der Systemparameter, in denen lineare Stabilitätsindikatoren, wie zum Beispiel das asymptotische Decay Ratio (DR), ihren Sinn verlieren. Die nichtlineare Stabilitätsanalyse wird im Allgemeinen mit Systemcodes (nichtlineare partielle Differentialgleichungen, PDG) durchgeführt. Jedoch kann mit Systemcodes kein oder nur ein sehr lückenhafter Überblick über die Typen von nichtlinearen Phänomenen, die in bestimmten System-Parameterbereichen auftreten, erhalten werden. Deshalb wurde im Rahmen der vorliegenden Arbeit eine neuartige Methode (RAM-ROM Methode) zur nichtlinearen SWR-Stabilitätsanalyse erprobt, bei der integrale Systemcodes und sog. vereinfachte SWR-Modelle (ROM) als sich gegenseitig ergänzende Methoden eingesetzt werden, um die Stabilitätseigenschaften von Fixpunkten und periodischen Lösungen (Grenzzyklen) des nichtlinearen Differentialgleichungssystems, welches das Stabilitätsverhalten des SWR beschreibt, zu bestimmen. Das ROM, in denen das dynamische System durch gewöhnliche Differentialgleichungen (GDG) beschrieben wird, kann relativ einfach mit leistungsfähigen Methoden aus der nichtlinearen Dynamik, wie zum Beispiel die semianalytische Bifurkationsanalyse, gekoppelt werden. Mit solchen Verfahren kann, ohne das DG-System explizit lösen zu müssen, ein Überblick über mögliche Typen von stabilen und instabilen oszillatorischen Verhalten des SWR erhalten werden. Insbesondere sind die Stabilitätseigenschaften von Grenzzyklen, die in Hopf-Bifurkationspunkten entstehen, und die Bedingungen, unter denen sie auftreten, von Interesse. Mit dem Systemcode (RAMONA5) werden dann die mit dem ROM vorhergesagten Phänomene in den entsprechenden Parameterbereichen detaillierter untersucht (Validierung des ROM). Die Methodik dient daher nicht der Verfeinerung der Berechnung linearer Stabilitätsindikatoren (wie das DR). Das ROM-Gleichungssystem entsteht aus den PDGs des Systemcodes durch geeignete (nichttriviale) räumliche Mittelung der PDG. Es wird davon ausgegangen, dass die Reduzierung der räumlichen Komplexität die Stabilitätseigenschaften des SWR nicht signifikant verfälschen, da durch geeignete Mittlungsverfahren, räumliche Effekte näherungsweise in den GDGs berücksichtig werden. Beispielsweise wird die raum- und zeitabhängige Neutronenflussdichte nach räumlichen Moden entwickelt, wobei für eine Simulation der Stabilitätseigenschaften der In-phase- und Out-of-Phase-Leistungsoszillationen nur der Fundamentalmode und der erste azimuthale Mode berücksichtigt werden muss. Das ROM, welches ursprünglich am Paul Scherrer Institut (PSI, Schweiz) in Zusammenarbeit mit der Universität Illinois (USA) entwickelt wurde, ist in zwei wesentlichen Punkten erweitert und verbessert worden: • Entwicklung und Implementierung einer neuen Methode zur Berechnung der Rückkopplungsreaktivitäten • Entwicklung und Implementierung eines Modells zur Beschreibung der Rezirkulationsschleife (insbesondere wurde der Einfluss der Rezirkulationsschleife auf den In-Phase-Oszillationszustand und auf den Out-of-Phase-Oszillationszustand untersucht) • Entwicklung einer physikalisch begründeten Methode zur Berechnung der ROM-Inputdaten • Abschätzung des Einflusses des unterkühlten Siedens im Rahmen der ROM-Näherungen Mit dem erweiterten ROM wurden nichtlineare Stabilitätsanalysen für drei Arbeitspunkte (KKW Leibstadt (Zyklus 7) KKW Ringhals (Zyklus 14) und KKW Brunsbüttel (Zyklus 16)), für die Messdaten vorliegen, durchgeführt. In der Dissertationsschrift wird die RAM-ROM Methode ausführlich am Beispiel eines Arbeitspunktes (OP) des KKW Leibstadt (KKLc7_rec4-OP), in dem eine aufklingende regionale Leistungsoszillation bei einem Stabilitätstest gemessen worden ist, demonstriert. Das ROM sagt die Existenz eines Umkehrpunktes (saddle-node bifurcation of cycles, fold-bifurcation) voraus, der sich im linear stabilen Gebiet nahe der Stabilitätsgrenze befindet. Mit diesem ROM-Ergebnis ist eine neue Interpretation der Stabilitätseigenschaften des KKLc7_rec4-OP möglich. Die Resultate der in der Dissertation durchgeführten RAM-ROM Analyse bestätigen, dass das weiterentwickelte ROM für die Analyse des Stabilitätsverhaltens realer Leistungsreaktoren qualifiziert wurde.