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The article deals with the robust fault detection and isolation based on linear fractional transformation hybrid bond graph. The main objective is to improve the robustness of fault detection step in the presence of parametric uncertainties in hybrid models in order to minimize the false alarms. The scientific interest of the proposed method is the use of only one tool – the bond graph not only for dynamic modelling of uncertain hybrid system but also for generation of adaptive thresholds needed in residual evaluation step. For this task, hybrid bond graph uncertain model approach with controlled junctions in linear fractional transformation form (allowing to represent graphically the parametric uncertainties) is first proposed to represent all the modes of the hybrid system. Second, based on causal and structural properties of the hybrid bond graph, analytical redundancy relations (with nominal and uncertain part) valid for all the modes are then derived systematically from the diagnostic hybrid bond graph. An application to a hydraulic system is used to illustrate this method.

This paper deals with the dimensionality reduction approach to study multi-dimensional constrained global optimization problems where the objective function is non-differentiable over a general compact set D of R n and Hölderian. The fundamental principle is to provide explicitly a parametric representation xi = i(t), 1 ≤ i ≤ n of α-dense curve α in the compact D, for t in an interval I of R, which allows to convert the initial problem to a one-dimensional Hölder unconstrained one. Thus, we can solve the problem by using an efficient algorithm available in the case of functions depending on a single variable. A relation between the parameter α of the curve α and the accuracy of attaining the optimal solution is given. Some concrete α-dense curves in a non-convex feasible region D are constructed. The numerical results show that the proposed approach is efficient.

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