When underground openings are constructed, groundwater inflow can occur, which might lead to ground settlements, namely in clay. In these types of construction projects, it is beneficial to be able to quantify risks related to these settlements. A framework developed by Sundell et al. (2019, Risk Analysis, Vol. 39, 105-124) deals with this, in which one part is a statistical settlement model. However, since their model only considers primary compression, a model that accounts for secondary compression (or creep) is necessary to better represent real conditions.In this thesis, an adaptation of Sundell’s et al. (2019) model that includes creep settlement was developed and applied on a focus area of the tunnel project Stockholm Bypass. First, distributions of parameters were created based on data from the project and complementary data from literature. Thereafter, a stochastic model based on an existing creep model was coupled with the Monte Carlo method.A cell where 8 m groundwater drawdown had previously been measured was simulated with the stochastic model. Results from this show wide settlement distribution. Moreover, a scenario with a sudden groundwater drawdown of 6 m was simulated over the entire focus area. Results from the scenario show larger settlements over a larger influence area when creep effects were included compared with simulations without creep effects.The proposed model was also verified against two other creep settlement models. The verification indicates an overestimation in initial settlements, but an underestimation of the excess pore pressure. The proposed model long-term settlement results were within 0.1 m of the compared models. A sensitivity analysis shows that different size of distributions of the permeable parameters and the creep parameters used in the model had low impact on settlement distribution in the presented model. / Undermarksanläggningar kan orsaka grundvattendränering, vilket kan leda till marksättningar. I dessa projekt är det fördelaktigt att kunna kvantifiera riskerna för dessa marksättningar. Ett ramverk utvecklat av Sundell et al. (2019, Risk Analysis, Vol. 39, 105-124) behandlar detta, och inbegriper bland annat en statistisk sättningsmodell. Eftersom modellen endast beaktar primärkonsolidering av jorden, är en modell som även behandlar sekundärkonsolidering (krypning) nödvändig för att bättre representera verkliga förhållanden.I denna uppsats utvecklades och tillämpades en anpassning av Sundells et al. (2019) modell till att inkludera krypsättningar på ett fokusområde i tunnelprojektet Förbifart Stockholm. Först skapades fördelningar av parametrar baserade på data från projektet samt kompletterande data från litteratur. Därefter byggdes en stokastisk modell baserat på en existerande krypmodell kopplat med Monte Carlo-metoden.Med den stokastiska modellen simulerades en punkt där 8 m grundvattensänkning hade skett. Resultatet från denna simulering visar att den beräknade sättningen är varierande. Därutöver simulerades hela fokusområdet för ett scenario med en konstant grundvattensänkning på 6 meter. Resultatet visar större sättningar över ett större påverkansområde när krypeffekter inkluderas jämfört med när de inte gjorde det.Den föreslagna modellen verifierades också mot två andra krypsättningsmodeller. Verifieringen antyder på en överskattning i de initiala sättningarna, men en underskattning av porövertrycket. Den föreslagna modellens långsiktiga sättningar låg inom 0,1 m jämfört med de andra modellernas sättningar. Genom en sensitivitetsanalys erhölls att storleken på variationskoefficienten hos permeabilitetsparametrar samt krypparametrar använda i modellen inte hade någon större påverkan på fördelningen av sättningar i den presenterade modellen.

<p>This thesis contains two parts. In the first part, which contains Chapter 2 and Chapter 3, we consider scheduling problems with learning effect and time-dependent processing time on a single machine. In Chapter 2, we investigate the earliness-tardiness objective, as well as the objective without due date assignment consideration. By reducing them to a special linear assignment problem, we solve them in near-linear time. As a consequence, we improve the time complexity for some previous algorithms for scheduling problems with learning effect and/or time-dependent processing time. In Chapter 3, we investigate the total number of tardy jobs objective. By reducing them to a linear assignment problem, we solve them in polynomial time. For some important special cases, where there is only learning effect OR time-dependent processing time, we reduce the time complexity to quadratic time. In the second part, which contains Chapter 4 and Chapter 5, we investigate the bicriteria scheduling problems in a supply chain. We separate the objectives in two parts, where the delivery cost is one of them. We present efficient algorithms to identify all the Pareto-optimal solutions for various scenarios. In Chapter 4, we study the cases without due date assignment; while in Chapter 5 we study the cases with due date assignment consideration.</p>

In modern communication systems, it’s important to detect and use available radio frequencies effectively. However, current methods face challenges with complexity and noise interference. We’ve developed a new approach using advanced artificial intelligence (AI) based computing techniques to improve efficiency and accuracy in this process. Our method shows promising results, requiring only minimal additional resources in exchange of improved performance compared to older techniques. / Master of Science / In modern communication systems, it’s important to detect and use available radio frequencies effectively. However, current methods face challenges with complexity and noise interference. We’ve developed a new approach using advanced artificial intelligence (AI) based computing techniques to improve efficiency and accuracy in this process. Our method shows promising results, requiring only minimal additional resources in exchange of improved performance compared to older techniques.

High harmonic generation (HHG) is an extreme non-linear phenomenon where strong laser fields interact with a medium to produce coherent and high-frequency harmonics of the incident light. It has emerged as a rapidly growing research area in bulk materials since its first observation in ZnO crystals in 2011. Over the past decade, pioneering studies have already been made in understanding the details of the microscopic mechanism behind this phenomenon, like the role of intra- and inter-band transitions, the contribution of the modulus and the phase of the dipole moment to even and odd harmonic peaks, the role of the oscillating dipoles, effects of broken symmetry, etc. However, the role of electron-electron correlations in the HHG from strongly correlated materials is much less understood. In these materials the interactions between electrons play a significant role, leading to complex and intriguing physical behaviors. In this dissertation, on the example of ZnO, perovskites BaTiO3 and BiFeO3, and transition-metal oxide VO2 I will study the role of electron-electron interaction effects in the HH spectra by using the time-dependent density-functional theory (TDDFT) approach with the exchange-correlation kernel obtained with dynamical mean- field theory (DMFT). In DMFT, one takes into account time-resolved on-site electron-electron interactions (neglected in most of other approaches) that are crucial for a larger part of strongly correlated materials. As I demonstrate, correlation effects significantly modify the HH spectrum, e.g., through the ultrafast modification of the spectrum of the system, as it was found for ZnO. As the next step, I explored the effects of electron-electron correlations in the HH spectrum of BaTiO3 perturbed by intense, few-cycle mid-infrared laser excitations. The correlation effects in this system lead to the emergence of "super-harmonics" - periodic enhancements and suppressions of specific harmonic orders that depend on the correlation strength. I extended my analysis to the case of BiFeO3, where in addition to correlation effects the effects of memory in HHG were analyzed. I have found that both correlation effects and memory lead to an extension of the harmonic cutoff. In my final part, I explored the effect of electron correlations on the HH spectrum of VO2 and compared my findings with the experiment. The obtained results may shed light on the often important role of electron correlations in the HH spectra of solids, providing valuable insights into ultrafast dynamics in complex materials, and contributing to advancements in nonlinear optics and strong-field physics, with the potential for novel photonic devices and imaging techniques in the attosecond and femtosecond regimes.

Les mémoires non volatiles intégrées représentent une part importante du marché des semi-conducteurs. Bien qu'il s'adresse à de nombreuses applications différentes, ce type de mémoire fait face à des problèmes pour poursuivre la réduction continue de la résolution des technologies CMOS. En effet, l'introduction récente de high-k et de métal pour la grille des transistors menace la compétitivité de la solution Flash. En conséquence, de nombreuses solutions émergentes sont étudiées. L'Antifuse dans le cadre des mémoires OTP est utilisée pour l'identification de puces, la configuration de circuits, la réparation de système ou le stockage de données sécurisées. La programmation Antifuse repose sur la dégradation de l'oxyde de grille de son condensateur sous haute tension. Des travaux antérieurs ont déjà apporté quelques connaissances sur les mécanismes physiques impliqués sur des technologies à oxyde de grille SiO2. De nouveaux défis découlent de l'introduction des nouveaux matériaux de grille. Un examen complet est nécessaire sur les mécanismes de dégradation des oxydes impliqués dans la programmation Antifuse. L'utilisation intensive de la haute tension suggère également d'étendre notre connaissance sur la fiabilité dans cette gamme de tension. Les états pré et post-claquage de l'oxyde de grille sous des mécanismes à haute tension sont donc étudiés dans ce manuscrit se concentrant sur les technologies CMOS les plus avancées. Une loi en puissance type TDDB a été étendue vers les hautes tensions pour être utilisée comme un modèle de temps de programmation Antifuse. L'extension de la fiabilité TDDB nous donne également un élément clé pour modéliser la durée de vie du transistor de sélection. Des paramètres de programmation tels que l'amplitude de la tension, la compliance du courant ou la température sont également étudiés et leur impact sur le rendement en courant de lecture est abordé. Cette étude nous permet de rétrécir agressivement la surface globale de la cellule sans perte de performance ni de dégradation de la fiabilité. Un processus de caractérisation Antifuse est proposé pour être retravaillé et un modèle de programmation de tension-température-dépendante est inventé. Ce manuscrit a également mis l'accent sur la modélisation de courant de cellule programmée comme la fuite d’un oxyde de grille post-claquage. Un modèle compact MOSFET dégradé est proposé et comparé à l'état de l’art. Un bon accord est trouvé pour s'adapter à la large gamme de caractérisations I (V) de la cellule programmée. L'activation de ce modèle dans un environnement de design nous a permis de simuler la dispersion des distributions de courants de cellules programmées au niveau de la taille du produit à l'aide de runs Monte-Carlo. Enfin, cette thèse s'achève autour d'une étude d'investigation OxRAM comme une solution émergente. En combinant le dispositif Antifuse avec le mécanisme de commutation résistif de l'OxRAM, une solution hybride est proposée en perspective. / Embedded Non Volatile Memories represent a significant part of the semiconductor market. While it addresses many different applications, this type of memory faces issues to keep the CMOS scaling down roadmap. Indeed, the recent introduction of high-k and metal for the CMOS gate is threatening the Flash’s competitiveness. As a consequence many emerging solutions are being. The Antifuse as part of the OTP memories is fully CMOS compliant, Antifuse memories are used for Chip ID, chip configuration, system repairing or secured data storage to say the least. The Antifuse programming relies on the gate oxide breakdown of its capacitor under high voltage. Previous work already brought some knowledge about the physical mechanisms involved but mainly on SiO2 gate oxide technologies. New challenges arise from the introduction of the new gate materials. A full review is needed about the oxide breakdown mechanisms involved in the Antifuse programming. The extensive use of high voltage also suggests to extend our knowledge about reliability within this voltage range. Pre and post gate oxide breakdown under high voltage mechanisms are then deeply investigated in this manuscript focusing on the most advanced CMOS technologies. Fowler Nordheim Tunneling has been confirmed as the main mechanism responsible for the gate oxide leakage conduction under high voltage during the wearout phase even-though defect contribution has been evidenced to mainly contribute under low voltage , e.g. the virgin Antifuse leakage current. A TDDB based power law has been extended toward high voltage to be used as a robust Antifuse programming time model. Extending the TDDB reliability under high electric field also gives us key element to model the selection MOSFET time to failure. Programming parameters such as voltage amplitude, current compliance or temperature are also investigated and their impact on the Read Current Yield are tackled. This study allows us to aggressively shrink the bitcell overall area without losing performance nor degrading the reliability. This study also reveals a worst case scenario for the programming parameters when temperature is very low. As a consequence, the early Antifuse characterization process is proposed to be rework and a programming voltage-temperature-dependent solution is invented. This manuscript also focused on the Antifuse programmed cell current modeling as gate oxide post-breakdown conduction. A remaining MOSFET compact model is proposed and compared to the state of the art. Good agreement is found to fit the wide range of read current. Enabling this model within a CAD environment has allowed us to simulate the Read Current Yield dispersion at product size level using Monte-Carlo runs. Finally, this thesis wraps up around an OxRAM investigation study as a serious emerging eNVM solution. Combining the Antifuse device with the resistive switching mechanism of the OxRAM, a hybrid solution is proposed as a perspective.

Cette thèse porte sur la description théorique de processus dynamiques ultra-rapides de molécules polyatomiques et de leur contrôle par impulsions laser. Nous avons d’abord étudié la photochimie de l’aniline à l’aide de calculs de structure électronique. Nous avons d´écrit plusieurs régions clé des surfaces d’énergie potentielle et analysé ces résultats en relation avec les données expérimentales existantes. La photochimie de la pyrazine a été étudiée par des calculs de dynamiques quantique basés sur un Hamiltonien modèle incluant les quatre états électroniques excités de plus basse énergie et seize modes de vibration. Nous montrons que l’état sombre Au(nπ∗) joue un rôle important dans la dynamique de la molécule après photo-excitation. Un modèle simplifié à deux états et quatre modes a été utilisé pour étudier le contrôle par laser de la dynamique de la pyrazine photo-excitée. Nous proposons un mécanisme visant à augmenter la durée de vie de l’état B2u(ππ∗) en utilisant l’effet Stark induit par une impulsion laser intense non-résonante. / The central subject of this thesis is the theoretical description of ultrafast dynamical processes in molecular systems of chemical interest and of their control by laser pulses. We first use electronic structure calculations to study the photochemistry of aniline. A umber of previously unknown features of the potential energy surfaces of the low-lying elec-tronic states are reported, and analyzed in relation with the experimental results available. We use quantum dynamics simulations, based on a model Hamiltonian including the four lowest excited electronic states and sixteen vibrational modes, to investigate the photochem-istry of pyrazine. We show that the dark Au(nπ∗) state plays an important role in the ultrafast dynamics of the molecule after photoexcitation. The laser control of the excited state dynamics of pyrazine is studied using a simplified two-state four-mode model Hamiltonian. We propose a control mechanism to enhance the lifetime of the bright B2u(ππ∗) state using the Stark effect induced by a strong non-resonant laser pulse. We finally focus on the laser control of the tunneling dynamics of the NHD2 molecule, using accurate full-dimensional potential energy and dipole moment surfaces. We use simple effective Hamiltonians to explore the effect of the laser parameters on the dynamics and design suitable laser fields to achieve the control. These laser fields are then used in MCTDH quantum dynamics simulations. Both enhancement and suppression of tunneling are achieved in our model.

Les MOSFET en SiC sont appelées à remplacer les IGBT en Silicium pour des applications de demandant une plus forte vitesse de commutation. Cependant, les MOSFET en SiC ont encore quelques problèmes de fiabilité, tels que la robustesse de la diode interne ou bien la robustesse de l'oxyde de grille. Cette dernière est liée à l’oxyde de grille des composants du type MOSFET. Des instabilités de la tension de seuil sont aussi signalées. Cette thèse aborde ces deux sujets sur des MOSFET commerciaux 1200 V. L'étude de la diode interne met en évidence que les caractéristiques I-V (de la diode intrinsèque) demeurent stables après l'application d'un stress. Cependant, une dérive surprenante de la tension de seuil apparaît. Des tests complémentaires, en stressant le canal à la place de la diode, avec les mêmes contraintes n'ont pas montré de dérive significative de la tension de seuil. Donc, l'application d'un stress en courant quand le composant est en mode d'accumulation semble favoriser l'apparition des instabilités de la tension de seuil. La robustesse de l'oxyde de grille concerne les instabilités de la tension de seuil, mais aussi l'estimation de la durée de vie à des conditions d'opération nominales. Les résultats obtenus montrent que la durée de vie de l'oxyde de grille n'est plus un problème. Pourtant, le suivi du courant de grille pendant les tests ainsi que les caractérisations de la capacité de grille mettent en évidence des translations de la courbe C(V) à cause des phénomènes d’injection des porteurs et de piégeage, mais aussi la possible présence d’ions mobiles. Aussi, une bonne analyse des dégradations et dérives liées à l’oxyde de grille doit être réalisée. / SiC power MOSFETs are called to replace Si IGBT for some medium and high power applications (hundreds of kVA). However, even if crystallographic defects have been drastically reduced, SiC MOSFETs are always concerned by some robustness issues such as the internal diode robustness or the robustness of the gate oxide. The last one especially affects MOSFETs devices and is linked to the apparition of instabilities in the threshold voltage. This thesis focuses on these two issues. The study of the internal diode robustness highlighted that the I-V curve (of the intrinsic diode) remains stable after the application of a current stress in static mode, but also with the DUT placed in a converter with inductive switchings. These are the most stressful conditions. However, a surprising drift in the threshold voltage has been observed when some devices operates under these conditions; in static mode or in a converter. Complementary tests stressing the channel instead of the internal diode in the same temperature and dissipated power, have not resulted in a drift of the threshold voltage. Thus, the application of a current stress when the device is in accumulation regime could favour the apparition of instabilities in the threshold voltage. The study of the gate oxide focus in the instabilities of the threshold voltage, but also on the expected lifetime of the oxide at nominal conditions. Results obtained shown that the expected lifetime (TDDB) of the oxide is no longer a problem. Indeed, tests realized in static mode, but also in a converter under inductive switching conditions resulted in expected lifetimes well above 100 years. However, the monitoring of the gate current during the test and gate capacitance characterizations C(V) highlighted a shift in the capacitance due to carrier injection and trapping phenomena and probably to the presence of mobile-ions. Still regarding the instabilities of the threshold voltage, classic tests resulted in no significant variations of the threshold voltage at 150 _C. However, at 200 _C the drift observed for some manufacturers is higher than +30%. This is unacceptable for high-temperature applications and evidence that the quality of the gate oxide and the SiC=SiO2 interface must continue to be improved, together with the manufacturing methods to minimize the presence of mobile ions in the substrate.

Thesis (MScEng (Civil Engineering))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: Strain Hardening Cement-based Composite (SHCC) is part of the High Performance Fibre Reinforced Cement-based Composite (HPFRCC) family and is a relative new concrete composite. This Fibre Reinforced Cement-based Composite (FRCC) contains randomly distributed short fibres and when subjected to a uni-axial tensile load multiple cracking occurs. The multiple cracking generates fine cracks which are normally smaller than 100 μm and achieve a strain capacity of more than 5 %. There are limited publications regarding the research of sustained tensile tests on SHCC and especially the cracking behaviour of SHCC under quasi-static uni-axial as well as sustained tensile loads. The cracking behaviour is described as the average crack width, number of cracks and descriptive statistical properties which could be used to represent the distribution of the multiple fine cracks under uni-axial tension. There are two types of tests that were under consideration to determine the cracking behaviour of SHCC. The first is quasi-static uniaxial tensile tests and the second is sustained tensile tests. The latter was dependant on the uni-axial tensile tests in terms of the sustained load applied. The sustained loads ranged from 40 % to 80 % of the ultimate tensile resistance recorded from the uni-axial tensile tests that correspond with a strain rate of 0.001 /s. Different strain rates were used for the uni-axial tensile tests to determine the effect on the cracking behaviour. The cracking behaviour was determined with the aid of a non-contact optical 3D digital deformation measuring device called ARAMIS. The content of this thesis gives a background study of the cracking behaviour and relevant research performed on SHCC under certain loads as well as some literature about the timedependant effects of a cement-based composite. The functioning of the device called ARAMIS is explained as well as the resulting effects of this device on the preparation of the test specimens. The experimental framework for the uni-axial and sustained tensile tests is discussed. Thereafter, the experimental results of the tests are depicted and discussed. The results shed some light on the basic material properties such as the average ultimate stress and average ultimate strain, Young’s modulus, etc. for the quasi-static tensile tests as well as shrinkage and creep of SHCC. The cracking behaviour such as the average crack width, number of cracks, the variance and skewness of the distribution of the crack widths in the test specimens for the quasi-static uni-axial and sustained tensile tests are depicted and discussed. The cracking behaviour when subjected to uni-axial tensile tests with different strain rates is significantly governed by the formation of new cracks and the average crack width remains small with increase in strain. There is no significant difference for the cracking behaviour found when subjected to different strain rates. However, when SHCC is subjected to a sustained load then the average crack width is dependant on the number of cracks that form over time as well as the load level. The formation of fewer and wider cracks was observed for specimens loaded at average 40 % of the ultimate tensile resistance stress, however at loading percentages of higher than 65 % more cracks developed which resulted in a smaller average crack width. / AFRIKAANSE OPSOMMING: Vervorming Verharding Sement gebaseerde samestelling “Strain Hardening Cement-based Composite” (SHCC) is deel van die familie van “High Performance Fibre Reinforced Cement-based Composite” (HPFRCC) en is ʼn relatiewe nuwe beton samestelling. Hierdie vesel versterkte sement gebaseerde beton bevat willekeurig verspreide kort vesels en veelvoudige klein krake vorm onder monotoniese trekkragte. Hierdie veelvoudige klein krake is minder as 100 μm wyd en lei tot ʼn vervorming van meer as 5 %. Daar is ʼn tekort aan navorsing oor die kruip van SHCC sowel as die kraak gedrag van hierdie sement gebaseerde samestelling onderhewig aan trek. Die kraak gedrag word beskryf as die gemiddelde kraakwydte, aantal krake en ʼn paar beskrywende statistiese parameters. Hierdie kraak gedrag parameters kan gebruik word om ʼn verdeling te kan weergee van die veelvoudige klein krake onder ʼn trek belasting. Twee tipes toetse was uitgevoer om die kraak gedrag te beskryf. Die eerste tipe toets was monotoniese trek toetse en die tweede tipe was kruip toetse. Die tweede toets was afhanklik van die monotoniese trek toetse in terme van die belasting wat gebruik was vir die kruip toetse. Die belasting was gevarieer vanaf 40 % tot 80 % van die breekbelasting wat bepaal is met die monotoniese trektoetse wat ooreenstem met ʼn vervorming tempo van 0.001 /s. Verskillende vervorming tempo’s vir die monotoniese trektoetse was uitgevoer om te bepaal wat die effek is op die kraak gedrag. Die kraak gedrag was bepaal met behulp van ʼn geen-kontak optiese 3D digitale deformasie meet instrument genoem ARAMIS. Die inhoud van die tesis bevat ʼn kort opsoming oor ʼn agtergrond studie van die kraak gedrag en relevante navorsing oor vesel versterkte sement gebaseerde beton, sowel as literatuur oor die tydafhanklike effekte van ʼn sement gebaseerde samestelling. Die beheer en gebruik van die meet instrument ARAMIS word verduidelik, sowel as die effek van hierdie masjien op die voorbereiding vir die eksperimente. Die eksperimentele uiteensetting vir die monotoniese en kruip toetse word beskryf. Daarvolgens is die resultate van die eksperimentele toetse getoon en verduidelik. Die resultate verduidelik die basiese materiaal eienskappe, byvoorbeeld die gemiddelde breekspanning met die ooreenkomstige breekvervorming, Young’s modulus en so voorts vir die monotoniese trektoetse, sowel as eienskappe met betrekking tot krimp en kruip van SHCC. Die kraak gedrag naamlik die gemiddelde kraakwydte, aantal krake per meter, variansie en die skuinsheid van die ontwikkelde krake met die toets proefstukke vir die monotoniese en kruip trek toetse word weergegee en verduidelik. Die kraak gedrag van SHCC wanneer getoets word met verskillende monotoniese trektoets tempo’s word beheer deur die ontwikkeling van nuwe krake en die gemiddelde kraakwydte is beduidend laag met toenemende vervorming. Daar is geen beduidende verskil in die kraak gedrag ten opsigte van die verskillende monotoniese trek tempo’s nie. In teendeel, wanneer SHCC belas word met ʼn konstante las oor tyd word die gemiddelde kraakwydte beheer deur die ontwikkeling van nuwe krake sowel as die belasting wat aangewend is. Onder ʼn belasting van so laag as 40 % van die breekbelasting vorm daar minder krake, maar met ʼn groter gemiddelde kraakwydte. Wanneer belas word met meer as 65 % van die breekbelasting vorm meer krake wat lei tot ʼn kleiner gemiddelde kraakwydte.

區間型資料一般定義為由一個連續型變數的上限及下限所構成，本文中，我們特別引進了一種與時間相關的區間型資料，在Irpino (2006, Pattern Recognition Letters, 27, 504-513)，他提出每個觀測值皆是由某個時段的起始值及終點值之有方向性的區間所組成，譬如某一支股票在某一周的開盤價和收盤價。過去已經有許多方法運用在區間型資料，但尚未有方法來處理有方向性的區間型資料，然而Irpino 延伸主成分方法來處理有方向性的區間資料。Irpino提出的方法以幾何學的觀點來說，可視為定義在多維度空間上對有方向性線段(一般都稱作“spaghetti”)的分析，在本文中我們有更作進一步的延伸，不僅引入股票的開盤價及收盤價，且引入當周的最高價及最低價來探索Irpino所遺漏的資訊。此外，我們也嘗試用貝他分配來取代Irpino所使用的均勻分配來檢測是否有明顯的改善。延伸的方法需要計算大量複雜的式子，包含了平均數，變異數，共變異數等，最後利用相關係數矩陣進行主成分分析。然而最後的結論為若考慮資訊的價值，以加入最高值和最小值的延伸方法是較好的選擇。 / Interval data are generally defined by the upper and the lower value assumed by a unit for a continuous variable. In this study, we introduce a special type of interval description depending on time. The original idea (Irpino, 2006, Pattern Recognition Letters, 27, 504-513) is that each observation is characterized by an oriented interval of values with a starting and a closing value for each period of observation: for example, the beginning and the closing price of a stock in a week. Several factorial methods have been discovered in order to treat interval data, but not yet for oriented intervals. Irpino presented an extension of principle component analysis to time dependent interval data, or, in general, to oriented intervals. From a geometrical point of view, the proposed approach can be considered as an analysis of oriented segments (nicely called “spaghetti”) defined in a multidimensional space identified by periods. In this paper, we make further extension not only provide the opening and the closing value but also the highest and the lowest value in a week to find out more information that cannot simply obtained from the original idea. Besides, we also use beta distribution to see if there is any improvement corresponding to the original ones. After we make these extensions, many complicated computations should be calculated such as the mean, variance, covariance in order to obtain correlation matrix for PCA. With regard to the value of information, the extended idea with the highest prices and the lowest price is the best choice.

Dans le contexte de la modélisation aléatoire des événements récurrents, un modèle statistique particulier est exploré. Ce modèle est fondé sur la théorie des processus de comptage et est construit dans le cadre d'analyse de défaillances dans les réseaux d'eau. Dans ce domaine nous disposons de données sur de nombreux systèmes observés durant une certaine période de temps. Les systèmes étant posés à des instants différents, leur âge est utilisé en tant qu'échelle temporelle dans la modélisation. Le modèle tient compte de l'historique incomplet d'événements, du vieillissement des systèmes, de l'impact négatif des défaillances précédentes sur l'état des systèmes et des covariables. Le modèle est positionné parmi d'autres approches visant à l'analyse d'événements récurrents utilisées en biostatistique et en fiabilité. Les paramètres du modèle sont estimés par la méthode du Maximum de Vraisemblance (MV). Une covariable dépendante du temps est intégrée au modèle. Il est supposé qu'elle est extérieure au processus de défaillance et constante par morceaux. Des méthodes heuristiques sont proposées afin de tenir compte de cette covariable lorsqu'elle n'est pas observée. Des méthodes de simulation de données artificielles et des estimations en présence de la covariable temporelle sont proposées. Les propriétés de l'estimateur (la normalité, le biais, la variance) sont étudiées empiriquement par la méthode de Monte Carlo. L'accent est mis sur la présence de deux directions asymptotiques : asymptotique en nombre de systèmes n et asymptotique en durée d'observation T. Le comportement asymptotique de l'estimateur MV constaté empiriquement est conforme aux résultats théoriques classiques. Il s'agit de l'asymptotique en n. Le comportement T-asymptotique constaté empiriquement n'est pas classique. L'analyse montre également que les deux directions asymptotiques n et T peuvent être combinées en une unique direction : le nombre d'événements observés. Cela concerne les paramètres classiques du modèle (les coefficients associés aux covariables fixes et le paramètre caractérisant le vieillissement des systèmes). Ce n'est en revanche pas le cas pour le coefficient associé à la covariable temporelle et pour le paramètre caractérisant l'impact négatif des défaillances précédentes sur le comportement futur du système. La méthodologie développée est appliquée à l'analyse des défaillances des réseaux d'eau. L'influence des variations climatiques sur l'intensité de défaillance est prise en compte par une covariable dépendante du temps. Les résultats montrent globalement une amélioration des prédictions du comportement futur du processus lorsque la covariable temporelle est incluse dans le modèle. / In the context of stochastic modeling of recurrent events, a particular model is explored. This model is based on the counting process theory and is built to analyze failures in water distribution networks. In this domain the data on a large number of systems observed during a certain time period are available. Since the systems are installed at different dates, their age is used as a time scale in modeling. The model accounts for incomplete event history, aging of systems, negative impact of previous failures on the state of systems and for covariates.The model is situated among other approaches to analyze the recurrent events, used in biostatistics and in reliability. The model parameters are estimated by the Maximum Likelihood method (ML). A method to integrate a time-dependent covariate into the model is developed. The time-dependent covariate is assumed to be external to the failure process and to be piecewise constant. Heuristic methods are proposed to account for influence of this covariate when it is not observed. Methods for data simulation and for estimations in presence of the time-dependent covariate are proposed. A Monte Carlo study is carried out to empirically assess the ML estimator's properties (normality, bias, variance). The study is focused on the doubly-asymptotic nature of data: asymptotic in terms of the number of systems n and in terms of the duration of observation T. The asymptotic behavior of the ML estimator, assessed empirically agrees with the classical theoretical results for n-asymptotic behavior. The T-asymptotics appears to be less typical. It is also revealed that the two asymptotic directions, n and T can be combined into one unique direction: the number of observed events. This concerns the classical model parameters (the coefficients associated to fixed covariates, the parameter characterizing aging of systems). The presence of one unique asymptotic direction is not obvious for the time-dependent covariate coefficient and for a parameter characterizing the negative impact of previous events on the future behavior of a system.The developed methodology is applied to the analysis of failures of water networks. The influence of climatic variations on failure intensity is assessed by a time-dependent covariate. The results show a global improvement in predictions of future behavior of the process when the time-dependent covariate is included into the model.