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This thesis is concerned with the utilisation of spatial information in processing of high-frequency sidescan SONAR imagery, and particularly in how such information can be used in developing techniques to assist in mapping functions. Survey applications aim to generate maps of the seabed, but are time consuming and expensive; automatic processing is required to improve efficiency. Current techniques have had some success, but utilise little of the available spatial information. Previously, inclusion of such knowledge was prohibitively expensive; recent improvements in numerical simulations techniques has reduced the costs involved. This thesis attempts to exploit these improvements into a method for including spatial information in SONAR processing and in general to image and signal analysis. Bayesian techniques for inclusion of prior knowledge and structuring complex problems are developed and applied to problems of texture segmentation, object detection and parameter extraction. It is shown through experiments on groundtruth and real datasets that the inclusion of spatial context can be very effective in improving poor techniques or, conversely in allowing simpler techniques to be used with the same objective outcome (with obvious computational advantages). The thesis also considers some of the implementation problems with the techniques used, and develops simple modifications to improve common algorithms.

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Complex networks is a vibrant research field and has received much attention over the last decade. Central to this area is the question of how networks around us are constructed. The essential notion of network research is that these systems are assembled in a decentralised way, thus no central agent is planning the network beforehand. Despite this lack of central coordination, many networks present intriguing universalities, such as broad degree distributions, in the form of power-laws. The subject of study in this thesis is a class of networks that are constructed by a node intrinsic variable, called fitness. The way these networks grow could be called a rich-get-richer mechanism. The fitter a node is, the more likely it is to acquire new connections inside the network. Several aspects that are directly connected to these networks are explored in this thesis. In the first part, the properties of growing networks that are driven by fitness are investigated and it is shown that the introduction of growth leads to a topological structure that is different from its static counterpart. In the subsequent chapter, percolation on fitness driven networks is studied. The results give insights into possible mechanisms that can stabilise systems. Furthermore, the theory can be used to identify vulnerable structures around us. In the following chapter, the world trade network is discussed. This numerical investigation highlights possible improvements to the methodology to make statistical analysis more robust. That chapter is followed by an analysis of time-varying networks. Time-varying networks represent an interesting construct that allows a formulation of stochastic processes on the same time-scale as the evolution of the network itself. This possibility is highly relevant to the investigation of epidemics, for instance. In the last chapter, a study of a system of clusters and their self-organised formation is presented.

[pt] Este trabalho apresenta um dos procedimentos adotados na avaliação do desempenho da estimação de parâmetros. Este procedimento consiste na determinação de limites inferiores no erro médio quadrático da estimação. São examinados os limites de Cramér-Rao e Ziv-Zakai abordando-se especialmente sua aplicação ao problema da estimação de parâmetros de um processo aleatório gaussiano. Em exemplo ilustrativo os resultados obtidos são aplicados a estimação dos parâmetros da densidade espectral de potência de um processo, supondo-se para esta densidade, um modelo racional simples. / [en] This work presents one of the possible approaches of evaluating the parameter estimation performance. This approach is based on the determination of lover bounds for estimate mean square error. The Cramér-Rao and Ziv-Zakai bounds are studied mainly in the case of gaussian random process parameter estimation. The results are applied as an example to the estimation of the power spectral density parameters of a random process. A simple rational model is used to represent this spectral density.

In the thesis, the reliability analysis of structural components and structural details subject to random loading and random resistance degradation is addressed. The study concerns evaluation of the probability of failure due to an overload of a component or structural detail, in consideration of random (environmental) loads and their combination, uncertain resistance parameters, statistical and phenomenological uncertainty and random resistance degradation mechanisms. Special attention is devoted to resistance degradation, as it introduces an additional level of difficulty in the solution of time variant reliability problems. The importance of this study arrives from the ageing of existing infrastructure in a world wide scale and from the lack of standards and codes for the ongoing safety management of general structures past their original design lives. In this context, probabilistic-based risk assessment and reliability analysis provide a framework for the safety management of ageing structures in consideration of inherent load and resistance uncertainty, current state of the structure, further resistance degradation, periodic inspections, in the absence of past experience and on an individual basis. In particular, the critical problem of resistance degradation due to fatigue is addressed. The formal solution of time variant reliability problems involves integration of local crossing rates over a conditional failure domain boundary, over time and over random resistance variables. This solution becomes very difficult in the presence of resistance degradation, as crossing rates become time dependent, and the innermost integration over the failure domain boundary has to be repeated over time. Significant simplification is achieved when the order of integrations is changed, and crossing rates are first integrated over the random failure domain boundary and then over time. In the so-called ensemble crossing rate or Ensemble Up-crossing Rate (EUR) approximation, the arrival rate of the first crossing over a random barrier is approximated by the ensemble average of crossings. This approximation conflicts with the Poisson assumption of independence implied in the first passage failure model, making results unreliable and highly conservative. Despite significant simplification of the solution, little was known to date about the quality of the EUR approximation. In this thesis, a simulation procedure to obtain Poissonian estimates of the arrival rate of the first up-crossing over a random barrier is introduced. The procedure is used to predict the error of the EUR approximation. An error parameter is identified and error functions are constructed. Error estimates are used to correct original EUR failure probability results and to compare the EUR with other common simplifications of time variant reliability problems. It is found that EUR errors can be quite large even when failure probabilities are small, a result that goes against previous ideas. A barrier failure dominance concept is introduced, to characterize those problems where an up-crossing or overload failure is more likely to be caused by a small outcome of the resistance than by a large outcome of the load process. It is shown that large EUR errors are associated with barrier failure dominance, and that solutions which simplify the load part of the problem are more likely to be appropriate in this case. It is suggested that the notion of barrier failure dominance be used to identify the proper (simplified) solution method for a given problem. In this context, the EUR approximation is compared with Turkstra’s load combination rule and with the point-crossing formula. It is noted that in many practical structural engineering applications involving environmental loads like wind, waves or earthquakes, load process uncertainty is larger than resistance uncertainty. In these applications, barrier failure dominance in unlikely and EUR errors can be expected to be small. The reliability problem of fatigue and fracture under random loading is addressed in the thesis. A solution to the problem, based on the EUR approximation, is constructed. The problem is formulated by combining stochastic models of crack propagation with the first passage failure model. The solution involves evaluation of the evolution in time of crack size and resistance distributions, and provides a fresh random process-based approach to the problem. It also simplifies the optimization and planning of non-destructive periodic inspection strategies, which play a major role in the ongoing safety management of fatigue affected structures. It is shown how sensitivity coefficients of a simplified preliminary First Order Reliability solution can be used to characterize barrier failure dominance. In the fatigue and fracture reliability problem, barrier failure dominance can be caused by large variances of resistance or crack growth parameters. Barrier failure dominance caused by resistance parameters leads to problems where overload failure is an issue and where the simplified preliminary solution is likely to be accurate enough. Barrier failure dominance caused by crack growth parameters leads to highly non-linear problems, where critical crack growth dominates failure probabilities. Finally, in the absence of barrier failure dominance, overload failure is again the issue and the EUR approximation becomes not just appropriate but also accurate. The random process-based EUR solution of time-variant reliability problems developed and the concept of barrier failure dominance introduced in the thesis have broad applications in problems involving general forms of resistance degradation as well as in problems of random vibration of uncertain structures. / PhD Doctorate

In the paper asymptotic expansions for second-order moments of integral functionals of a class of random functions are considered. The random functions are assumed to be $\epsilon$-correlated, i.e. the values are not correlated excluding a $\epsilon$-neighbourhood of each point. The asymptotic expansions are derived for $\epsilon \to 0$. With the help of a special weak assumption there are found easier expansions as in the case of general weakly correlated functions.

Práce je věnována generování náhodných struktur dvousložkových vláknových kompozitních materiálů a statistickým metodám analýzy náhodnosti těchto struktur. Byly vyvinuty čtyři algoritmy a vygenerované struktury byly statisticky porovnány s reálnými daty.

The paper is dedicated to the modeling and the simulation of random processes and fields. Using the concept and the theory of weakly correlated functions a consistent representation of sufficiently smooth random processes will be derived. Special applications will be given with respect to the simulation of road surfaces in vehicle dynamics and to the confirmation of theoretical results with respect to the zeros of random polynomials.

This dissertation focuses on extending solution methods in the area of stochastic optimization. Attention is focused to three specific problems in the field. First, a solution method for mixed integer programs subject to chance constraints is discussed. This class of problems serves as an effective modeling framework for a wide variety of applied problems. Unfortunately, chance constrained mixed integer programs tend to be very challenging to solve. Thus, the aim of this work is to address some of these challenges by exploiting the structure of the deterministic reformulation for the problem. Second, a stochastic program for integrating renewable energy sources into traditional energy systems is developed. As the global push for higher utilization of such green resources increases, such models will prove invaluable to energy system designers. Finally, a process for transforming clinical medical data into a model to assist decision making during the treatment planning phase for palliative chemotherapy is outlined. This work will likely provide decision support tools for oncologists. Moreover, given the new requirements for the usage electronic medical records, such techniques will have applicability to other treatment planning applications in the future.