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APPLICATIONS OF MATHEMATICAL SIMULATION TO THE RELIABILITY AND AVAILABILITY OF COMPLEX SYSTEMS.Summary: Due to the limitations presented by analytical methods to determine the reliability and availability in complex systems, this work is born with the objective of developing mathematical algorithms based on simulation techniques, to help engineers and accountable systems in the task design systems more reliable and with a greater degree of availability, the two issues are closely related to the quality and security of the service offered. The two issues raised (determined on the one hand, the reliability of a complex system, and secondly, if available) are addressed in an original way with the use of concepts from fields as diverse as the simulation Monte CarIo and Events Discretos The mathematical theory of reliability and availability of systems, statistical inference and programming in C / C + +. As a result, three algorithms are obtained, SREMS_AI, SAEDES_AI and SAEDES_A2, which offer as a whole an effective solution to both problems. The process of development has required the four chapters that make up the core of the work:. In Chapter 2 reviews the current status of simulation techniques and introduces key concepts that are then used in the development of algorithms. It discusses their advantages over analytical methods, and introduces the main concepts associated with simulation techniques Mount CarIo (SCM) and Event Discretos (SED). . Chapter 3 is devoted to the techniques and problems related to the generation of pseudo-random values in chapter develops and implements C / C + + algorithm generating numbers pseudo lecuyer_88B. Similarly, functions are implemented in C / C + + intended for the generation of random observations from several continuous distributions (uniform, exponential, k-ErIang, Weibull, normal and log-normal Gamma), which give rise to the library randomVariates. This library is part of the software associated with SREMS_AI, SAEDES_Al and SAEDES_A2, being responsible for generating the random events of the simulation. . In Chapter 4 is conducting the review of the major concepts associated with the theory of reliability and availability of systems: basic structures of systems, fundamental concepts about the same, and different issues that are essential in the further development of algorithms (introduction of the temporary variable, assumption of independence, availability in basic structures, etc..). The chapter also includes a review of published papers in which points to the desirability of using simulation methods for studying the reliability and availability in complex systems. . Finally, in Chapters 5 and 6 is to develop models and algorithms that are proposed in the thesis. It sets out the assumptions of each model alluded, it formalizes the thrust of the methods are explained and with different levels of detail (pseudo-code and source code in C / C + +) each of the three proposed algorithms (SREMS_AI, SAEDES_AI and SAEDES_A2 ). For each algorithm, carried out a series of tests that permitien validation and verification of the same, as well as checking their effectiveness. In addition to the above, the report also includes several annexes which contribute to completing the work. We concluded, finally, that the solutions matemático-i 8 nformáti 2a9 cas outlined in the report represent an original proposal that solved in an effective and efficient dual problem in the goals, thus overcoming the limitations of analytical methods and providing value added to the content of this work.
FAULT DETECTION AND ISOLATION VIA CONTINUOUS TIME STATISTICSAuthor: CASTILLO LOPEZ ANGELA. Year: 2005. University: POLITÉCNICA DE MADRID [ www.upm.es]. Place of defense: E.T.S. ING. INDUSTRIALES. Place of preparation: E.T.S. ING. INDUSTRIALES. Summary: The problem detection and diagnosis of faults in plants modeled using dynamic systems in time continuum is being treated through different procedures which generally can be classified into deterministic and stochastic. The methods developed in this thesis correspond to the line stochastic, are based on the statistical analysis of continuous-time, whereas the effort in this area has traditionally been geared to the development and study of statistics in discrete time. Although the use of computer media force the discretization of signals, it is more natural to address the problem of detection and diagnosis of faults on models with statistical time continuum in time continuum to get detection and diagnosis in real time (on - line). Schemes detection and diagnosis presented here basically to waste generation from the model of the system, which is supposed available, and its subsequent analysis. The statistical tools used to extract information about the residue of failure are contrasted assumptions; contrasts can be built from different statistical different, thus giving rise to different patterns of detection and diagnosis, which will be characterized from the point of view of their convenience for the detection of different types of bugs. The Bayes rule, commonly used in grading patterns, it is also helpful in stage of diagnosis, isolation of the bug. The validation of the methods presented is given through various examples of simulation, in particular considers the case bugs in the source voltage of a circuit.
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