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Cadre unifié pour la modélisation des incertitudes statistiques et bornées : application à la détection et isolation de défauts dans les systèmes dynamiques incertains par estimation

Tuan Anh Tran 1
1 LAAS-DISCO - Équipe DIagnostic, Supervision et COnduite
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This thesis deals with state estimation in discrete-time dynamic systems in the context of the integration of statistical and bounded error uncertainties. Motivated by the drawbacks of the interval Kalman filter (IKF) and its improvement (iIKF), we propose a filtering algorithm for linear systems subject to uncertain Gaussian noises, i.e. with the mean and covariance matrix defined by their membership to intervals. This new interval Kalman filter (UBIKF) relies on finding a punctual gain matrix minimizing an upper bound of the set of estimation error covariance matrices by respecting the bounds of the parametric uncertainties. An envelope containing all possible estimates is then determined using interval analysis. The UBIKF reduces not only the computational complexity of the set inversion of the matrices intervals appearing in the iIKF, but also the conservatism of the estimates. We then discuss different frameworks for representing incomplete or imprecise knowledge, including the cumulative distribution functions, the possibility theory and the theory of belief functions. Thanks to the last, a model in the form of a mass function for an uncertain multivariate Gaussian distribution is proposed. A box particle filter based on this theory is developed for non-linear dynamic systems in which the process noises are bounded and the measurement errors are represented by an uncertain Gaussian mass function. Finally, the UBIKF is applied to fault detection and isolation by implementing the generalized observer scheme and structural analysis. Through various examples, the capacity for detecting and isolating sensor/actuator faults of this tool is illustrated and compared to other approaches.
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Tuan Anh Tran. Cadre unifié pour la modélisation des incertitudes statistiques et bornées : application à la détection et isolation de défauts dans les systèmes dynamiques incertains par estimation. Automatique. Université Paul Sabatier - Toulouse III, 2017. Français. ⟨NNT : 2017TOU30292⟩. ⟨tel-01705119v2⟩

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