Dissertations / Theses on the topic 'Non-stationary distribution'

As environmental change is happening at an unprecedented pace, a comprehensive and holistic approach is needed in order to mitigate the increasing negative effect of extreme natural events occurring based on the natural and anthropogenic variations. Of all the geophysical phenomena, flooding is one of the most catastrophic events, leading to quite a few losses and damages across the World. Recent extraordinary flood events happened in north – western England, precisely sequences of the severe floods in the county of Cumbria, Lancashire and Manchester in 2004, 2009 and 2015, have brought many concerns not only for the residents but also for the community of hydrologists in UK. These extreme events in these areas comparing with their typical river discharge values have raised an important question of whether any significant changes in the magnitude of river flows can be detected as a result of natural/human - induced clime change. If so, whether they can be attributed to any meteorological predictors such as rainfall frequency analysis. The results, performed for 39 river gauging stations based on annual maxima (AM) approach, indicate that around 92% of the river gauging stations show non – stationary behaviour; whereas only in 8%, stationarity is dominant. More importantly, annual rainfall is deemed as the best explanatory variable to express the variability of our data much better than other covariates for a vast majority of stations (around 60%).

Brushless Direct Current (BLDC) motors are one of the motor types rapidly gaining popularity. BLDC motors are being increasingly used in critical high performance industries such as appliances, automotive, aerospace, consumer, medical, industrial automation equipment and instrumentation. Fault detection and condition monitoring of BLDC machines is therefore assuming a new importance. The objective of this research is to advance the field of rotor and load fault diagnosis in BLDC machines operating in a variety of operating conditions ranging from constant speed to continuous transient operation. This objective is addressed as three parts in this research. The first part experimentally characterizes the effects of rotor faults in the stator current and voltage of the BLDC motor. This helps in better understanding the behavior of rotor defects in BLDC motors. The second part develops methods to detect faults in loads coupled to BLDC motors by monitoring the stator current. As most BLDC applications involve non-stationary operating conditions, the diagnosis of rotor faults in non-stationary conditions forms the third and most important part of this research. Several signal processing techniques are reviewed to analyze non-stationary signals. Three new algorithms are proposed that can track and detect rotor faults in non-stationary or transient current signals.

Muchos tipos de señales que encontramos a diario pertenecen a la categoría de sinusoides no estacionarias. Una gran parte de esas señales son sonidos que presentan una gran variedad de características: acústicos/electrónicos, sonidos instrumentales harmónicos/impulsivos, habla/canto, y la mezcla de todos ellos que podemos encontrar en la música. Durante décadas la comunidad científica ha estudiado y analizado ese tipo de señales. El motivo principal es la gran utilidad de los avances científicos en una gran variedad de áreas, desde aplicaciones médicas, financiera y ópticas, a procesado de radares o sonar, y también a análisis de sistemas. La estimación precisa de los parámetros de sinusoides no estacionarias es una de las tareas más comunes en procesado digital de señales, y por lo tanto un elemento fundamental e indispensable para una gran variedad de aplicaciones. Las transformaciones de tiempo y frecuencia clásicas son solamente apropiadas para señales con variación lenta de amplitud y frecuencia. Esta suposición no suele cumplirse en la práctica, lo que conlleva una degradación de calidad y la aparición de artefactos. Además, la resolución temporal y frecuencial no se puede incrementar arbitrariamente debido al conocido principio de incertidumbre de Heisenberg. \\ El principal objetivo de esta tesis es revisar y mejorar los métodos existentes para el análisis de sinusoides no estacionarias, y también proponer nuevas estrategias y aproximaciones. Esta disertación contribuye sustancialmente a los análisis sinusoidales existentes: a) realiza una evaluación crítica del estado del arte y describe con gran detalle los métodos de análisis existentes, b) aporta mejoras sustanciales a algunos de los métodos existentes más prometedores, c) propone varias aproximaciones nuevas para el análisis de los modelos sinusoidales existentes i d) propone un modelo sinusoidal muy general y flexible con un algoritmo de análisis directo y rápido.
Many types of everyday signals fall into the non-stationary sinusoids category. A large family of such signals represent audio, including acoustic/electronic, pitched/transient instrument sounds, human speech/singing voice, and a mixture of all: music. Analysis of such signals has been in the focus of the research community for decades. The main reason for such intense focus is the wide applicability of the research achievements to medical, financial and optical applications, as well as radar/sonar signal processing and system analysis. Accurate estimation of sinusoidal parameters is one of the most common digital signal processing tasks and thus represents an indispensable building block of a wide variety of applications. Classic time-frequency transformations are appropriate only for signals with slowly varying amplitude and frequency content - an assumption often violated in practice. In such cases, reduced readability and the presence of artefacts represent a significant problem. Time and frequency resolu

Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (page 49).
In this thesis, I look at multiple Variational Inference algorithm, transform Kalman Variational Bayes and Stochastic Variational Inference into streaming algorithms and try to identify if any of them work with non-stationary distributions. I conclude that Kalman Variational Bayes can do as good as any other algorithm for stationary distributions, and tracks non-stationary distributions better than any other algorithm in question.
by Arsen Mamikonyan.
M. Eng.

Les inondations constituent le risque naturel prédominant dans le monde et les dégâts qu'elles causent sont les plus importants parmi les catastrophes naturelles. Un des principaux facteurs expliquant les inondations sont les précipitations extrêmes. En raison des changements climatiques, l'occurrence et l'intensité de ces dernières risquent fort probablement de s'accroître. Par conséquent, le risque d'inondation pourrait vraisemblablement s'intensifier. Les impacts de l'évolution des précipitations extrêmes sont désormais un enjeu important pour la sécurité du public et pour la pérennité des infrastructures. Les stratégies de gestion du risque d'inondation dans le climat futur sont essentiellement basées sur les simulations provenant des modèles numériques de climat. Un modèle numérique de climat procure notamment une série chronologique des précipitations pour chacun des points de grille composant son domaine spatial de simulation. Les séries chronologiques simulées peuvent être journalières ou infra-journalières et elles s'étendent sur toute la période de simulation, typiquement entre 1961 et 2100. La continuité spatiale des processus physiques simulés induit une cohérence spatiale parmi les séries chronologiques. Autrement dit, les séries chronologiques provenant de points de grille avoisinants partagent souvent des caractéristiques semblables. De façon générale, la théorie des valeurs extrêmes est appliquée à ces séries chronologiques simulées pour estimer les quantiles correspondants à un certain niveau de risque. La plupart du temps, la variance d'estimation est considérable en raison du nombre limité de précipitations extrêmes disponibles et celle-ci peut jouer un rôle déterminant dans l'élaboration des stratégies de gestion du risque. Par conséquent, un modèle statistique permettant d'estimer de façon précise les quantiles de précipitations extrêmes simulées par un modèle numérique de climat a été développé dans cette thèse. Le modèle développé est spécialement adapté aux données générées par un modèle de climat. En particulier, il exploite l'information contenue dans les séries journalières continues pour améliorer l'estimation des quantiles non stationnaires et ce, sans effectuer d'hypothèse contraignante sur la nature de la non-stationnarité. Le modèle exploite également l'information contenue dans la cohérence spatiale des précipitations extrêmes. Celle-ci est modélisée par un modèle hiérarchique bayésien où les lois a priori des paramètres sont des processus spatiaux, en l'occurrence des champs de Markov gaussiens. L'application du modèle développé à une simulation générée par le Modèle régional canadien du climat a permis de réduire considérablement la variance d'estimation des quantiles en Amérique du Nord
Precipitation extremes plays a major role in flooding events and their occurrence as well as their intensity are expected to increase. It is therefore important to anticipate the impacts of such an increase to ensure the public safety and the infrastructure sustainability. Since climate models are the only tools for providing quantitative projections of precipitation, flood risk management for the future climate may be based on their simulations. Most of the time, the Extreme value theory is used to estimate the extreme precipitations from a climate simulation, such as the T-year return levels. The variance of the estimations are generally large notably because the sample size of the maxima series are short. Such variance could have a significant impact for flood risk management. It is therefore relevant to reduce the estimation variance of simulated return levels. For this purpose, the aim of this paper is to develop a non-stationary and regional statistical model especially suited for climate models that estimates precipitation extremes. At first, the non-stationarity is removed by a preprocessing approach. Thereafter, the spatial correlation is modeled by a Bayesian hierarchical model including an intrinsic Gaussian Markov random field. The model has been used to estimate the 100-year return levels over North America from a simulation by the Canadian Regional Climate Model. The results show a large estimation variance reduction when using the regional model

Le but de la these est d'effectuer l'inference statistique d'une classe generale de modeles de series temporelles non lineaires. Notre contribution consiste d'abord a determiner des conditions assurant l'existence d'une loi stationnaire, l'existence des moments de cette loi stationnaire et la forte melangeance de tels modeles. Nous etablissons ensuite les proprietes asymptotiques de l'estimateur du minimum de distance d'hellinger du parametre d'interet. La robustesse de cet estimateur est egalement envisagee. Nous examinons aussi, via la methode des moindres carres, les proprietes asymptotiques des estimateurs des coefficients des modeles autoregressifs a seuils

There are many sources of waveforms or signals existing around us. They can be natural phenomena such as sound, light and invisible like electromagnetic fields, voltage, etc. Getting an insight into these waveforms helps explain the mysteries surrounding our world and the signal spectral analysis (i.e. the Fourier transform) is one of the most significant approaches to analyze a signal. Nevertheless, Fourier analysis cannot provide a time-dependent spectrum description for spectrum-varying signals-non-stationary signal. In these cases, time-frequency distribu- tions are employed instead of the traditional Fourier transform. There have been a variety of methods proposed to obtain the time-frequency representations (TFRs) such as the spectrogram or the Wigner-Ville distribution. The time-frequency distributions (TFDs), indeed, offer us a better signal interpretation in a two-dimensional time-frequency plane, which the Fourier transform fails to give. Nevertheless, in the case of incomplete data, the time-frequency displays are obscured by artifacts, and become highly noisy. Therefore, signal time-frequency features are hardly extracted, and cannot be used for further data processing. In this thesis, we propose two methods to deal with compressed observations. The first one applies compressive sensing with a novel chirp dictionary. This method assumes any windowed signal can be approximated by a sum of chirps, and then performs sparse reconstruction from windowed data in the time domain. A few improvements in computational complexity are also included. In the second method, fixed kernel as well as adaptive optimal kernels are used. This work is also based on the assumption that any windowed signal can be approximately represented by a sum of chirps. Since any chirp's auto-terms only occupy a certain area in the ambiguity domain, the kernel can be designed in a way to remove the other regions where auto-terms do not reside. In this manner, not only cross-terms but also missing samples’ artifact are mitigated significantly. The two proposed approaches bring about a better performance in the time-frequency signature estimations of the signals, which are sim- ulated with both synthetic and real signals. Notice that in this thesis, we only consider the non-stationary signals with frequency changing slowly with time. It is because the signals with rapidly varying frequency are not sparse in time-frequency domain and then the compressive sensing techniques or sparse reconstructions could not be applied. Also, the data with random missing samples are obtained by randomly choosing the samples’ positions and replacing these samples with zeros.

Thesis (Ph. D.)--University of California, San Diego, 2009.
Title from first page of PDF file (viewed June 23, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 114-116).

L’estuaire du Wouri, situé au coeur du Golfe de Guinée et ouvert sur l’océan Atlantique est soumis à un large éventail d’influence atmosphérique, océanique, continentale et anthropique à différentes échelles de temps (court et long-terme) contrôlant son évolution. La première partie de cette thèse, axée sur des archives remontant au 20ème siècle, a permis de reconstituer l’histoire de l’évolution du littoral estuarien du Wouri. Parallèlement, pour déterminer les tendances d’évolution des hauteurs d’eau, quantifier et qualifier la cinématique du trait de côte et des fonds dans l’estuaire, un travail d’inventaire, de numérisation et d’analyse des documents historiques a été réalisé. Ceci a permis d’enregistrer une évolution du niveau moyen à un rythme d’environ 25mm/an en 17 ans (2002 – 2019). Les résultats ont révélé une prédominance des variations dominées par l’érosion en aval et inversement par l’accrétion en amont, sur la période de 64 ans (1948-2012). Ces tendances sont accentuées par la présence de facteurs amplificateurs (pression anthropique et changement climatique). Afin d’étudier les processus hydrodynamiques et sédimentaires à court terme, une modélisation numérique de la propagation de la marée et la distribution des salinités et des sédiments fins a été réalisée à l’aide de TELEMAC 3D (calibré et validé grâce aux mesures in-situ acquises au cours de l’année 2019). La marée a montré une asymétrie dominée par le jusant dans sa partie inférieure et inversement par le flot dans sa partie supérieure. La distribution de la salinité a permis de caractériser l’estuaire de bien mélangé en vive-eau, particulièrement en étiage à stratifié en morte eau, particulièrement en période de crue. Les variations saisonnières, du régime fluvial ont montré une migration longitudinale de la position de la zone de turbidité maximale : déplacement en amont pendant les étiages et en aval pendant les crues avec pour conséquence une exportation massive de sédiments dans la partie intermédiaire et aval de l’estuaire. Dans un contexte actuel du changement climatique associé aux forts impacts anthropiques, cette étude souligne la nécessité de l’utilisation des archives historiques, de données in-situ couplées à un modèle numérique pour mieux comprendre l’évolution passée et actuelle de l’hydrodynamique et de la dynamique sédimentaire
The Wouri estuary, located in the heart of the Gulf of Guinea and open to the Atlantic Ocean, is subject to a wide range of atmospheric, oceanic, continental and anthropic influences at different time scales (short and long term) controlling its evolution. The first part of this thesis, based on archives dating back to the 20th century, allows us to reconstruct the history of the evolution of the Wouri estuary coastline. At the same time, in order to determine the evolution trends of the water levels, to quantify and qualify the kinematics of the coastline and the bottoms in the estuary, an inventory, digitization and analysis of historical documents was carried out. This allowed to record an evolution of the average level at a rate of about 25mm/year in 17 years (2002 - 2019). The results revealed a predominance of variations dominated by erosion downstream and conversely by accretion upstream, over the 64-year period (1948-2012). These trends are accentuated by the presence of amplifying factors (anthropogenic pressure and climate change). In order to study the hydrodynamic and sedimentary processes in the short term, a numerical modeling of the tidal propagation and the distribution of salinities and fine sediments was performed using TELEMAC 3D (calibrated and validated thanks to in-situ measurements acquired during 2019). The tide showed an asymmetry dominated by the ebb in its lower part and inversely by the flood in its upper part. The distribution of salinity allowed to characterize the estuary from well mixed in spring tide, particularly in low water to stratified in neap tide, particularly in flood period. Seasonal variations of the river regime have shown a longitudinal migration of the position of the maximum turbidity zone : upstream during low water and downstream during high water with a massive export of sediments in the intermediate and downstream part of the estuary. In a current context of climate change associated with strong anthropogenic impacts, this study highlights the need to use historical archives, in-situ data coupled with a numerical model to better understand the past and present evolution of hydrodynamics and sediment dynamics

High Performance Liquid Chromatography (HPLC) is a widely used tech-nique both for detecting and purifying substances in academy and in the industry. In order to facilitate the use of, and knowledge in HPLC, character-ization of stationary phases is of utmost importance. Tailor made characteri-zation methods and workflows are steadily increasing the speed and accura-cy in which new separation systems and methods are developed. In the field fundamental separation science and of preparative chromatography there is always the need for faster and more accurate methods of adsorption isotherm determination. Some of that demand are met with the steadily increase of computational power, but the practical aspects on models and methods must also be further developed. These nonlinear characterization methods will not only give models capable of describing the adsorption isotherm but also actual values of local adsorption energies and monolayer saturation capacity of an individual interaction sites etc.The studies presented in this thesis use modern alkali stable stationary phas-es as a model phase, which will give an insight in hybrid materials and their separation mechanism. This thesis will include an update and expansion in using the Elution by Characteristic Points (ECP) method for determination of adsorption isotherms. The precision is even further increased due to the ability to use slope data as well as an increase in usability by assigning a set of guidance rules to be applied when determine adsorption isotherms having inflection points. This thesis will further provide the reader with information about stationary phase characterization and the power of using existing tech-niques; combine them with each other, and also what the expansion of meth-ods can revile in terms of precision and increased usability. A more holistic view of what benefits that comes with combining a non-linear characteriza-tion of a stationary phase with more common linear characterization meth-ods are presented.

Tato práce se zabývá využitím distribucí neboli zobecněných funkcí k řešení nestacionárních okrajových problémů v mechanice kontinua. Nejprve je zavedena teorie distribucí a jejich definice jako spojitých lineárních funkcionálů na prostoru testovacích funkcí. Druhá část teoretické kapitoly představuje Laplaceovu integrální transformaci. Následující kapitola se věnuje řešení průhybu nosníků pod vlivem nespojitého časově proměnlivého zatížení. Jejím výsledkem je vytvoření obecného modelu řešení průhybových čar nosníků vužitím distribucí. Poslední kapitola se zabývá řešením nestacionárního proudění v trubicích spojených hydraulickými prvky.

Dans cette thèse, nous abordons l'estimation non paramétrique de la fonction de dépendance des distributions multivariées à valeurs extrêmes. Dans une première partie, on adopte l’hypothèse classique stipulant que les variables aléatoires sont indépendantes et identiquement distribuées (i.i.d). Plusieurs estimateurs non paramétriques sont comparés pour une fonction de dépendance trivariée de type logistique dans deux différents cas. Dans le premier cas, on suppose que les fonctions marginales sont des distributions généralisées à valeurs extrêmes. La distribution marginale est remplacée par la fonction de répartition empirique dans le deuxième cas. Les résultats des simulations Monte Carlo montrent que l'estimateur Gudendorf-Segers (Gudendorf et Segers, 2011) est plus efficient que les autres estimateurs pour différentes tailles de l’échantillon. Dans une deuxième partie, on ignore l’hypothèse i.i.d vue qu’elle n'est pas vérifiée dans l'analyse des séries temporelles. Dans le cadre univarié, on examine le comportement extrêmal d'un modèle autorégressif Gaussien stationnaire. Dans le cadre multivarié, on développe un nouveau théorème qui porte sur la convergence asymptotique de l'estimateur de Pickands vers la fonction de dépendance théorique. Ce fondement théorique est vérifié empiriquement dans les cas d’indépendance et de dépendance asymptotique. Dans la dernière partie de la thèse, l'estimateur Gudendorf-Segers est utilisé pour modéliser la structure de dépendance des concentrations extrêmes d’ozone observées dans les stations qui enregistrent des dépassements de la valeur guide et limite de la norme Tunisienne de la qualité d'air NT.106.04
In this thesis, we investigate the nonparametric estimation of the dependence function for multivariate extreme value distributions. Firstly, we assume independent and identically distributed random variables (i.i.d). Several nonparametric estimators are compared for a trivariate dependence function of logistic type in two different cases. In a first analysis, we suppose that marginal functions are generalized extreme value distributions. In a second investigation, we substitute the marginal function by the empirical distribution function. Monte Carlo simulations show that the Gudendorf-Segers (Gudendorf and Segers, 2011) estimator outperforms the other estimators for different sample sizes. Secondly, we drop the i.i.d assumption as it’s not verified in time series analysis. Considering the univariate framework, we examine the extremal behavior of a stationary Gaussian autoregressive process. In the multivariate setting, we prove the asymptotic consistency of the Pickands dependence function estimator. This theoretical finding is confirmed by empirical investigations in the asymptotic independence case as well as the asymptotic dependence case. Finally, the Gudendorf-Segers estimator is used to model the dependence structure of extreme ozone concentrations in locations that record several exceedances for both guideline and limit values of the Tunisian air quality standard NT.106.04

This thesis deals with the problem of the instantaneous frequency (IF) estimation of sinusoidal signals. This topic plays significant role in signal processing and communications. Depending on the type of the signal, two major approaches are considered. For IF estimation of single-tone or digitally-modulated sinusoidal signals (like frequency shift keying signals) the approach of digital phase-locked loops (DPLLs) is considered, and this is Part-I of this thesis. For FM signals the approach of time-frequency analysis is considered, and this is Part-II of the thesis. In part-I we have utilized sinusoidal DPLLs with non-uniform sampling scheme as this type is widely used in communication systems. The digital tanlock loop (DTL) has introduced significant advantages over other existing DPLLs. In the last 10 years many efforts have been made to improve DTL performance. However, this loop and all of its modifications utilizes Hilbert transformer (HT) to produce a signal-independent 90-degree phase-shifted version of the input signal. Hilbert transformer can be realized approximately using a finite impulse response (FIR) digital filter. This realization introduces further complexity in the loop in addition to approximations and frequency limitations on the input signal. We have tried to avoid practical difficulties associated with the conventional tanlock scheme while keeping its advantages. A time-delay is utilized in the tanlock scheme of DTL to produce a signal-dependent phase shift. This gave rise to the time-delay digital tanlock loop (TDTL). Fixed point theorems are used to analyze the behavior of the new loop. As such TDTL combines the two major approaches in DPLLs: the non-linear approach of sinusoidal DPLL based on fixed point analysis, and the linear tanlock approach based on the arctan phase detection. TDTL preserves the main advantages of the DTL despite its reduced structure. An application of TDTL in FSK demodulation is also considered. This idea of replacing HT by a time-delay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the time-delay in the presence of additive Gaussian noise. Based on the above analysis, the behavior of the first and second-order TDTLs has been analyzed in additive Gaussian noise. Since DPLLs need time for locking, they are normally not efficient in tracking the continuously changing frequencies of non-stationary signals, i.e. signals with time-varying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequency-modulated (FM) signals widely used in communication systems. Part-II of this thesis is dedicated for the IF estimation of non-stationary signals. For such signals the classical spectral techniques break down, due to the time-varying nature of their spectra, and more advanced techniques should be utilized. For the purpose of instantaneous frequency estimation of non-stationary signals there are two major approaches: parametric and non-parametric. We chose the non-parametric approach which is based on time-frequency analysis. This approach is computationally less expensive and more effective in dealing with multicomponent signals, which are the main aim of this part of the thesis. A time-frequency distribution (TFD) of a signal is a two-dimensional transformation of the signal to the time-frequency domain. Multicomponent signals can be identified by multiple energy peaks in the time-frequency domain. Many real life and synthetic signals are of multicomponent nature and there is little in the literature concerning IF estimation of such signals. This is why we have concentrated on multicomponent signals in Part-H. An adaptive algorithm for IF estimation using the quadratic time-frequency distributions has been analyzed. A class of time-frequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are time-only or one-dimensional, rather than the time-lag (two-dimensional) kernels. Hence this class has been named as the T -class. If the parameters of these TFDs are properly chosen, they are more efficient than the existing fixed-kernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The T-distributions has been used in the IF adaptive algorithm and proved to be efficient in tracking rapidly changing frequencies. They also enables direct amplitude estimation for the components of a multicomponent

The use of the Advanced Censored Closure (ACC) technique, recently proposed by the authors for predicting the peak response of linear structures vibrating under random processes, is extended to the case of non-linear oscillators driven by stationary white noise. The proposed approach requires the knowledge of mean upcrossing rate and spectral bandwidth of the response process, which in this paper are estimated through the Stochastic Averaging method. Numerical applications to oscillators with non-linear stiffness and damping are included, and the results are compared with those given by Monte Carlo Simulation and by other approximate formulations available in the literature.

Due essentially to the di culties associated with obtaining explicit forms of stationary marginal distributions of non-linear stationary processes, appropriate characterizations of such processes are worked upon little. After discussing an elaborate motivation behind this thesis and presenting preliminaries in Chapter 1, we characterize, in Chapter 2, the stationary marginal distributions of certain non-linear multivariate stationary processes. To do so, we show that the stationary marginal distributions of these processes belong to speci c skew-distribution families, and for a given skew-distribution from the corresponding family, a process, with stationary marginal distribution identical to that given skew-distribution, can be found. While conventional time series analysis greatly depends on the assumption of stationarity, measurements taken from many physical systems, which consist of both periodicity and randomness, often exhibit cyclostationarity (i.e., a periodic structure in their  rst- and second-order moments). Identifying the hourly global horizontal irradiances (GHIs), collected at a solar monitoring station of Saudi Arabia, as a cyclostationary process and considering the signi cant impact of that on the energy production in Saudi Arabia, Chapter 3 provides a temporal model of GHIs. Chapter 4 extends the analysis to a spatio-temporal cyclostationary modeling of 45 di erent solar monitoring stations of the Kingdom. Both the proposed models are shown to produce better forecasts, more realistic simulations, and reliable photovoltaic power estimates in comparison to a classical model that fails to recognize the GHI data as cyclostationary. Chapter 5 extends the notion of cyclostationarity to a novel and exible class of processes, coined evolving period and amplitude cyclostationary (EPACS) processes, that allows periods and amplitudes of the mean and covariance functions to evolve and, therefore, accommodates a much larger class of processes than the cyclostationary processes. Thereafter, we investigate its properties, provide methodologies for statistical inference, and illustrate the presented methods using a simulation study and a real data example, from the heavens, of the magnitudes of the light emitted from the variable star R Hydrae. Finally, Chapter 6 summarizes the  ndings of the thesis and discusses its signi - cance and possible future extensions.

Robustness of a system has been defined in various ways and a lot of work has been done to model the robustness of a system, but quantifying or measuring robustness has always been very difficult. In this research, we develop a framework for robust system architecture. We consider a system of a linear estimator (multiple tap filter) and then attempt to model the system performance and robustness in a graphical manner, which admits an analysis using the differential geometric concepts. We compare two different perturbation models, namely the gradient with biased perturbations (sub-optimal model) of a surface and the gradient with unbiased perturbations (optimal model), and observe the values to see which of them can alternately be used in the process of understanding or measuring robustness. In this process we have worked on different examples and conducted many simulations to find if there is any consistency in the two models. We propose the study of robustness measures for estimation/prediction in stationary and non-stationary environment using differential geometric tools in conjunction with probability density analysis. Our approach shows that the gradient can be viewed as a random variable and therefore used to generate probability densities, allowing one to draw conclusions regarding the robust- ness. As an example, one can apply the geometric methodology to the prediction of time varying deterministic data in imperfectly known non-stationary distribution. We also compare stationary to non-stationary distribution and prove that robustness is reduced by admitting residual non-stationarity. We then research and develop a robust iterative handoff algorithm, relating generally to methods, devices and systems for reselecting and then handing over a mobile communications device from a first cell to a second cell in a cellular wireless communications system (GPRS, W-CDMA or OFDMA). This algorithm results in significant decrease in amount of power and/or result is a decrease of break in communications during an established voice call or other connection, in the field, thereby outperforming prior art.

Monitoring of engineered systems consists of characterizing the normal behavior of the system and tracking departures from it. Techniques to monitor a system can be split into two classes based on their use of inputs and outputs of the system. Systems-based monitoring refers to the case when both inputs and outputs of a system are available and utilized. Conversely, symptomatic monitoring refers to the case when only outputs of the system are available. This thesis extended symptomatic and systems-based monitoring of biomedical systems via the use of non-stationary signal processing and advanced monitoring methods. Monitoring of various systems of the human body is encumbered by several key hurdles. First, current biomedical knowledge may not fully comprehend the extent of inputs and outputs of a particular system. In addition, regardless of current knowledge, inputs may not be accessible and outputs may be, at best, indirect measurements of the underlying biological process. Finally, even if inputs and outputs are measurable, their relationship may be highly nonlinear and convoluted. These hurdles require the use of advanced signal processing and monitoring approaches. Regardless of the pursuit of symptomatic or system-based monitoring, the aforementioned hurdles can be partially overcome by using non-stationary signal analysis to reveal the way frequency content of biomedical signals change over time. Furthermore, the use of advanced classification and monitoring methods facilitated reliable differentiation between various conditions of the monitored system based on the information from non-stationary signal analysis. The human brain was targeted for advancement of symptomatic monitoring, as it is a system responding to a plethora internal and external stimuli. The complexity of the brain makes it unfeasible to realize system-based monitoring to utilize all the relevant inputs and outputs for the brain. Further, measurement of brain activity (outputs), in the indirect form of electroencephalogram (EEG), remains a workhorse of brain disorder diagnosis. In this thesis, advanced signal processing and pattern recognition methods are employed to devise and study an epilepsy detection and localization algorithm that outperforms those reported in literature. This thesis also extended systems-based monitoring of human biomedical systems via advanced input-output modeling and sophisticated monitoring techniques based on the information from non-stationary signal analysis. Explorations of system-based monitoring in the NMS system were driven by the fact that joint velocities and torques can be seen NMS responses to electrical inputs provided by the central nervous system (CNS) and the electromyograph (EMG) provides an indirect measurement of CNS excitations delivered to the muscles. Thus, both inputs and outputs of this system are more or less available and one can approach its monitoring via the use of system-based approaches.
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Το πρόβλημα που αντιμετωπίζει η διατριβή αφορά στη μοντελοποίηση μη-στασίμων τυχαίων ταλαντώσεων επί τη βάσει μετρήσεων του σήματος της ταλάντωσης, μέσω μοντέλων FS-TAR/TARMA. Οι στόχοι της διατριβής περιλαμβάνουν την αποτίμηση της εφαρμοσιμότητας των μεθόδων FS-TAR/TARMA για την μοντελοποίηση και ανάλυση της ταλάντωσης χρονικά μεταβαλλόμενών κατασκευών, καθώς και τη σύγκρισή τους με εναλλακτικές παραμετρικές μεθόδους του πεδίου του χρόνου. Ιδιαίτερη βαρύτητα δίνεται και στην αντιμετώπιση θεμάτων που σχετίζονται με την εκτίμηση μοντέλων FS-ΤAR/TARMA, καθώς και στην θεωρητική ασυμπτωτική ανάλυση των ιδιοτήτων των εκτιμητριών που χρησιμοποιούνται. Η διατριβή αρχικά παρουσιάζει μια συγκριτική ανασκόπηση της βιβλιογραφίας στο θέμα της μοντελοποίησης μη-στασίμων ταλαντώσεων μέσω παραμετρικών μεθόδων του πεδίου του χρόνου, η οποία και επιδεικνύει τα πλεονεκτήματα των μεθόδων FS-TAR/TARMA. Στη συνέχεια αντιμετωπίζεται μια σειρά προβλημάτων που εμφανίζονται κατά την εκτίμηση (των παραμέτρων) και την επιλογή της δομής του μοντέλου. Η αποτελεσματικότητα των μεθόδων FS-TAR/TARMA για την μοντελοποίηση και ανάλυση μη-στάσίμων ταλαντώσεων επιδεικνύεται και πειραματικά μέσω εφαρμογής στην οποία πραγματοποιείται επιτυχής εξαγωγή των δυναμικών χαρακτηριστικών μιας εργαστηριακής χρονικά μεταβαλλόμενης κατασκευής. Στη συνέχεια, η διατριβή εστιάζει στην αναζήτηση ακριβέστερων εκτιμητριών, καθώς και στην ασυμπτωτική ανάλυση των ιδιοτήτων των εκτιμητριών «γενικών» (όχι αναγκαστικά περιοδικά μεταβαλλόμενων) μοντέλων FS-TAR/TARMA. Συγκεκριμένα, εξετάζονται οι περιπτώσεις των εκτιμητριών σταθμισμένων ελαχίστων τετραγώνων [Weighted Least Squares (WLS)], μέγιστης πιθανοφάνειας [Maximum Likelihood (ML)], καθώς και μια εκτιμήτρια πολλαπλών σταδίων [Multi Stage (MS)], η οποία αναπτύσσεται στην παρούσα διατριβή και είναι ασυμπτωτικά ισοδύναμη με την εκτιμήτρια ML ενώ ταυτόχρονα χαρακτηρίζεται από μειωμένη υπολογιστική πολυπλοκότητα. Στη διατριβή αποδεικνύεται η συνέπεια (consistency) των εκτιμητριών αυτών και εξάγεται η ασυμπτωτική κατανομή (asymptotic distribution) τους. Παράλληλα, αναπτύσσεται μια συνεπής εκτιμήτρια του ασυμπτωτικού πίνακα συνδιασποράς και μια μέθοδος για τον έλεγχο εγκυρότητας των μοντέλων FS-TAR/TARMA. Η ορθότητα των αποτελεσμάτων της ασυμπτωτικής ανάλυσης επιβεβαιώνεται μέσω μελετών Monte Carlo.
The thesis studies the problem of non-stationary random vibration modeling and analysis based on available measurements of the vibration signal via Functional Series Time-dependent AutoRegressive / AutoRegressive Moving Average (FS-TAR/ TARMA) models. The aims of the thesis include the assessment of the applicability of FS-TAR/TARMA methods for the modeling and analysis of non-stationary random vibration, as well as their comparison with alternative time-domain parametric methods. In addition, significant attention has been paid to the FS-TAR/TARMA estimation problem and to the theoretical asymptotic analysis of the estimators. A critical overview and comparison of time-domain, parametric, non-stationary random vibration modeling and analysis methods is firstly presented, where the high potential of FS-TAR/TARMA methods is demonstrated. In the following, a number of issues concerning the FS-TAR/TARMA model (parameter) estimation and model structure selection are considered. The effectiveness of the FS-TARMA methods for non-stationary random vibration modeling and analysis is experimentally demonstrated, through their application for the recovery of the dynamical characteristics of a time-varying bridge-like laboratory structure. In the sequel, the thesis focuses on the asymptotic analysis of “general” (that is not necessarily periodically evolving) FS-TAR/TARMA estimators. In particular, the Weighted Least Squares (WLS) and Maximum Likelihood (ML) estimators are both investigated, while a Multi Stage (MS) estimator, that approximates the ML estimator at reduced complexity, is developed. The consistency of the considered estimators is established and their asymptotic distribution is extracted. Furthermore, a consistent estimator of the asymptotic covariance matrix is formulated and an FS-TAR/TARMA model validation method is proposed. The validity of the theoretical asymptotic analysis results is assessed through several Monte Carlo studies.

In Geostatistical modelling of the spatial distribution of rock attributes, the multivariate distribution of a Random Function defines the range of possible values and the spatial relationships among them. Under a decision of stationarity, the Random Function distribution and its statistics are inferred from data within a spatial domain deemed statistically homogenous. Assuming stationary multiGaussianity allows spatial prediction techniques to take advantage of this simple parametric distribution model. These techniques compute the local distributions with surrounding data and global spatially invariant statistics. They often fail to reproduce local changes in the mean, variability and, particularly, the spatial continuity, that are required for geologically realistic modelling of rock attributes. The proposed alternative is to build local Random Function models that are deemed stationary only in relation to the locations where they are defined. The corresponding location-dependent distributions and statistics are inferred by weighting the samples inversely proportional to their distance to anchor locations. These distributions are locally Gaussian transformed. The transformation models carry information on the local histogram. The distance weighted experimental measures of spatial correlation are able to adapt to local changes in the spatial continuity and are semi-automatically fitted by locally defined variogram models. The fields of local variogram and transformation parameters are used in locally stationary spatial prediction algorithms. The resulting attribute models are rich in non-stationary spatial features. This process implies a higher computational demand than the traditional techniques, but, if data is abundant enough to allow a reliable inference of the local statistics, the proposed locally stationary techniques outperform their stationary counterparts in terms of accuracy and precision. These improved models have the potential of providing better decision support for engineering design.
Mining Engineering