A methodology for evaluating the reliability and risk of structures under complex service environments

The theoretical basis and numerical implementation of NESSUS (Numerical Evaluation of Stochastic Structures Under Stress), a computer code for probabilistic structural analysis of aerospace components, are described, with an emphasis on the use of NESSUS for reliability and risk assessment. Topics addressed include the structure of probabilistic models of fatigue-crack initiation, risk/cost evaluation, fatigue-fracture analysis, and fatigue-crack initiation. Numerical results from typical applications are presented in graphs and briefly characterized. The usefulness of NESSUS predictions for establishing inspection and retirement schedules and for component certification is indicated

Mutual Information, Information-Theoretic Thresholds and the Condensation Phenomenon at Positive Temperature

There is a vast body of recent literature on the reliability of communication through noisy channels, the recovery of community structures in the stochastic block model, the limiting behavior of the free entropy in spin glasses and the solution space structure of constraint satisfaction problems. At first glance, these topics ranging across several disciplines might seem unrelated. However, taking a closer look, structural similarities can be easily identified. Factor graphs exploit these similarities to model the aforementioned objects and concepts in a unified manner. In this contribution we discuss the asymptotic average case behavior of several quantities, where the average is taken over sparse Erd\H{o}s-R\'enyi type (hyper-) graphs with positive weights, under certain assumptions. For one, we establish the limit of the mutual information, which is used in coding theory to measure the reliability of communication. We also determine the limit of the relative entropy, which can be used to decide if weak recovery is possible in the stochastic block model. Further, we prove the conjectured limit of the quenched free entropy over the planted ensemble, which we use to obtain the preceding limits. Finally, we describe the asymptotic behavior of the quenched free entropy (over the null model) in terms of the limiting relative entropy.Comment: 95 page

Static reliability and resilience in dynamic systems

Two systems are modeled in this thesis. First, we consider a multi-component stochastic monotone binary system, or SMBS for short. The reliability of an SMBS is the probability of correct operation. A statistical approximation of the system reliability is provided for these systems, inspired in Monte Carlo Methods. Then, we are focused on the diameter constrained reliability model (DCR), which was originally developed for delay sensitive applications over the Internet infrastructure. The computational complexity of the DCR is analyzed. Networks with an efficient (i.e., polynomial time) DCR computation are offered, termed Weak graphs. Second, we model the effect of a dynamic epidemic propagation. Our first approach is to develop a SIR-based simulation, where unrealistic assumptions for SIR model (infinite, homogeneous, fully-mixed population) are discarded. Finally, we formalize a stochastic rocess that counts infected individuals, and further investigate node-immunization strategies, subject to a budget nstraint. A combinatorial optimization problem is here introduced, called Graph Fragmentation Problem. There, the impact of a highly virulent epidemic propagation is analyzed, and we mathematically prove that Greedy heuristic is suboptimal

Random Information Spread in Networks

Let G=(V,E) be an undirected loopless graph with possible parallel edges and s and t be two vertices of G. Assume that vertex s is labelled at the initial time step and that every labelled vertex copies its labelling to neighbouring vertices along edges with one labelled endpoint independently with probability p in one time step. In this paper, we establish the equivalence between the expected s-t first arrival time of the above spread process and the notion of the stochastic shortest s-t path. Moreover, we give a short discussion of analytical results on special graphs including the complete graph and s-t series-parallel graphs. Finally, we propose some lower bounds for the expected s-t first arrival time.Comment: 17 pages, 1 figur