[tel-01097469] Développement d’une méthodologie conjointe d’analyse structurelle et de sûreté de fonctionnement des propriétés d’un système complexe.

This thesis concerns the development of methods and tools of a joint analysis of structural properties and dependability. More specifically, the study focuses on structured systems such as linear, bilinear or switched systems. These systems must verify important structural properties (observability, controllability, etc) for the accomplishment of their missions. The structure of a system can be represented by a graph consisting of vertices and edges. Vertices represent the system variables and edges represent the relationships between these variables. The verification of structural properties depends mainly on four elementary graphical conditions which are connectivity, linking, distance and complete matching conditions. These conditions are combined according to the structural property which gives a generic aspect of our approach. Moreover, we have developed algorithms with their proofs to express these conditions and so the structural properties that depend on this conditions as boolean expressions based on the edges of the system graph. In the graphical representation of a structured system, the relationships between its variables are provided by physical laws and components that can be cleverly associated to edges of the graph. Thus, each edge of the graph is related to one or more external components (sensors/actuators), or internal components. A failure on one or several components can cause structural changes in the system, and can make a structural property unsatisfied. Thanks to a association edge-components, structural properties can be reformulated as boolean expressions based on the operating state of the components. In this thesis, we focus on the probabilistic assessment of structural properties. Using Boolean expressions associated to structural properties, their reliability and/or availability can be calculated knowing the dependability characteristics of the involved components. The calculation of reliability and availability of the structural properties is performed using some dependability tools, such as reliability diagrams blocks, Markov chains, Bayesian networks and dynamic Bayesian networks. Through this study, the calculation of reliability and/or availability of structural properties allows us to verify if, during the mission time of the system, the studied structural property remain satisfied and/or respect a level of performance required in the system specification. When this level of performance is not respected, it is necessary to take some measures to maintain on the the system components such as increase their reliability and availability or provide hardware redundancy.



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