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

Many recent research results have concluded that the multiple-input multiple-output (MIMO) wireless communication architecture is a promising approach to achieve high bandwidth efficiencies. MIMO wireless channels can be simply defined as a link for which both the transmitting and receiving ends are equipped with multiple antenna elements. This advanced communication technology has the potential to resolve the bottleneck in traffic capacity for future wireless networks. Applying MIMO techniques to mobile communication systems, the problem of channel fading between the transmitters and receivers, which results in received signal strength fluctuations, is inevitable. The time-varying nature of the mobile channel affects various aspects of receiver design. This thesis provides some analytical methodologies to investigate the variation of MIMO eigenmodes. Although the scope is largely focussed on the temporal variation in this thesis, our results are also extended to frequency variation. Accurate analytical approximations for the level crossing rate (LCR) and average fade duration (AFD) of the MIMO eigenmodes in an independent, identically distributed (i.i.d.) flat-fading channel are derived. Furthermore, since several channel metrics (such as the total power gain, eigenvalue spread, capacity and Demmel condition number) are all related to the eigenmodes, we also derive their LCRs and AFDs using a similar approach. The effectiveness of our method lies in the fact that the eigenvalues and corresponding channel metrics can be well approximated by gamma or Gaussian variables. Our results provide a comprehensive, closed-form analysis for the temporal behavior of MIMO channel metrics that is simple, robust and rapid to compute. An alternative simplified formula for the LCR for MIMO eigenmodes is also presented with applications to different types of autocorrelation functions (ACF). Our analysis has been verified via Monte Carlo computer simulations. The joint probability density function (PDF) for the eigenvalues of a complex Wishart matrix and a perturbed version of it are also derived in this thesis. The latter version can be used to model channel estimation errors and variations over time or frequency. Using this PDF, the probabilities of adaptation error (PAE) due to feedback delay in some adaptive MIMO schemes are evaluated. In particular, finite state Markov chains (FSMC) have been used to model rate-feedback system and dual-mode antenna selection schemes. The PDF is also applied to investigate MIMO systems that merge singular value decomposition (SVD)-based transceiver structure and adaptive modulation. A FSMC is constructed to investigate the modulation state entering rates (MSER), the average stay duration (ASD), and the effects of feedback delay on the accuracy of modulation state selection in mobile radio systems. The system performance of SVD-based transceivers is closely related to the quality of the channel information at both ends of the link. Hence, we examine the effect of feedback time delay, which causes the transmitter to use outdated channel information in time-varying fading channels. In this thesis, we derive an analytical expression for the instantaneous signal to interference plus noise ratio (SINR) of eigenmode transmission with a feedback time delay. Moreover, this expression implies some novel metrics that gauge the system performance sensitivity to time-variations of the steering vectors (eigenvectors of the channel correlation matrix) at the transmitter. Finally, the fluctuation of the channel in the frequency domain is of interest. This is motivated by adaptive orthogonal frequency division multiplexing (OFDM) systems where the signalling parameters per subcarriers are assigned in accordance with some channel quality metrics. A Gaussian distribution has been suggested to approximate the number of subcarriers using certain signalling modes (such as outage/transmission and diversity/multiplexing), as well as the total data rates, per OFDM realization. Additionally, closed-form LCRs for the channel gains (including the individual eigenmode gains) over frequency are also derived for both single-input single-output (SISO) and MIMO-OFDM systems. The corresponding results for the average fade bandwidth (AFB) follow trivially, These results may be useful for system design, for example by calculating the feedback overheads based on subcarrier aggregation.

Orientador: Michel Daoud Yacoub / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-06T02:52:07Z (GMT). No. of bitstreams: 1 Fraidenraich_Gustavo_M.pdf: 1838522 bytes, checksum: 4099008fa7bbc89eb2642a891bd64509 (MD5) Previous issue date: 2006 / Resumo: Neste trabalho, uma nova distribuição de probabilidade amplamente geral, a distribuição a-?-?-µ, é proposta. Esta distribuição contempla como casos particulares várias outras distribuições conhecidas na literatura, tais como Rayleigh, Rice, Nakagami-m, Hoyt, Weibull, a-? (Gamma Generalizada) ?-µ e ?-µ. Por conta de sua generalidade, todos os mais importantes ambientes de desvanecimento de curto prazo são modelados por esta distribuição. Além de prover a função densidade de probabilidade para o modelo a-?-?-µ, os momentos e a função cumulativa de probabilidade também são encontrados. Este modelo geral é então especializado para quatro casos particulares, para os quais distribuições mais simples, mas ainda gerais, são encontradas: a a-?-µ, a-?-µ, ?-? Simétrica e ?-? Assimétrica. Para esses casos, estimadores práticos baseados nos momentos são deduzidos. A aplicabilidade destes estimadores é verificada utilizando medidas de campo realizadas na Unicamp com um equipamento construído no laboratório Wisstek para este ?m. Em seguida, estatísticas de ordem superior, em particular a taxa de cruzamento de nível e a duração média de desvanecimento, são encontradas de forma exata para os ambientes Hoyt e Weibull em sistemas de diversidade com M ramos desbalanceados, não idênticos e independentes utilizando os combinadores por ganho igual e por razão máxima. Neste trabalho, o resultado geral é validado através de simulações e redução das expressões gerais para casos em que os resultados já são conhecidos. Além disso, para alguns destes casos particulares, as expressões gerais são simplificadas e reduzidas a fórmulas fechadas. Estendendo esse último campo de investigação e seguindo um pioneiro trabalho da literatura, o qual abordou o caso Rayleigh, a taxa de cruzamento de nível e a duração média de desvanecimento são obtidas para ambientes Hoyt com dois ramos correlacionados. Nesta investigação, reformula-se a metodologia da literatura e obtém-se um procedimento geral para a análise da taxa de cruzamento de nível e duração média de desvanecimento em ambientes com apenas um cluster, com aplicação direta aos canais Rice, Weibull, ?-? Simétrica e ?-? Assimétrica. Finalmente, este trabalho propõe, de forma precursora, uma distribuição para a fase do canal Nakagami-m. Ao contrário do que, convencionalmente e por simplicidade, se postulava, a distribuição de fase é não uniforme e dependente de m, o que torna o modelo compatível com aqueles aproximados por Nakagami-m, nomeadamente Hoyt e Rice / Abstract: In this work, a new, very general probability density function, the a-?-?-µ distribution, is proposed. This distribution comprises, as particular cases, several other well known distributions such as Rayleigh, Rice, Nakagami-m, Hoyt, Weibull, a-? (Generalized Gamma) ?-µ and ?-µ. Due to its generality, all of the most important short fading environments can be modeled by this distribution. Besides providing the probability density function for the a-?-?-µ model, the moments and the cumulative distribution function are also found. This general model is then specialized into four particular cases, for which new simpler, though still general, distributions, are found: the a-?-µ, a-?-µ, Symmetrical ?-?, and Asymmetrical ?-?. For these cases, practical moment-based estimators are derived. The applicability of these estimators is verified using field measurements obtained through an experiment conducted at the University of Campinas (Unicamp) with an equipment specially built for this end in the Wisstek laboratory. Higher order statistics, more specifically the level crossing rates and average fade durations, are then obtained in an exact form for the Hoyt and Weibull fading environments. The results are applicable to M unbalanced, non-identical, and independent channels using equal gain and maximal ratio combining techniques. The general results are thoroughly validated by means of simulation and also by reducing the general solution to some particular cases for which the solutions are known. Moreover, new closed form expressions are also achieved for some of these particular cases. Extending this field of investigation and following a pioneering work in the literature, which approached the Rayleigh case, the level crossing rate and average fade duration are obtained considering two correlated, unbalanced, and non-identical branches in a Hoyt fading environment. In this investigation, the methodology found in the literature is reformulated and generalized so as to comprise several other cases. The general procedure developed for this analysis can now be applied to other fading environment for which one cluster of mutipaths exists, i.e., Rice, Weibull, Symmetrical ?-?, and Asymmetrical ?-?. Finally, this work proposes, in a pioneering way, the phase distribution for the Nakagami-m channel. Contrary to what conventionally, and for simplicity, was usually postulated, the phase distribution is non-uniform and dependent on m, rendering this model compatible with those approximated by Nakagami-m, namely Hoyt and Rice / Mestrado / Telecomunicações e Telemática / Mestre em Engenharia Elétrica