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Redundancy relations for fault diagnosis in nonlinear uncertain systems

Alexey Shumsky — 2007

International Journal of Applied Mathematics and Computer Science

The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand sides are polynomials. The method involves a nonlinear transformation of the initial system model into...

An approach to the analysis of observability and controllability in nonlinear systems via linear methods

Alexey ZhirabokAlexey Shumsky — 2012

International Journal of Applied Mathematics and Computer Science

The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g.,...

Nonlinear diagnostic filter design: algebraic and geometric points of view

Alexey ShumskyAlexey Zhirabok — 2006

International Journal of Applied Mathematics and Computer Science

The problem of diagnostic filter design is studied. Algebraic and geometric approaches to solving this problem are investigated. Some relations between these approaches are established. New definitions of fault detectability and isolability are formulated. On the basis of these definitions, a procedure for diagnostic filter design is given in both algebraic and geometric terms.

Algebraic approach for model decomposition: Application to fault detection and isolation in discrete-event systems

Denis BerdjagVincent CocquempotCyrille ChristopheAlexey ShumskyAlexey Zhirabok — 2011

International Journal of Applied Mathematics and Computer Science

This paper presents a constrained decomposition methodology with output injection to obtain decoupled partial models. Measured process outputs and decoupled partial model outputs are used to generate structured residuals for Fault Detection and Isolation (FDI). An algebraic framework is chosen to describe the decomposition method. The constraints of the decomposition ensure that the resulting partial model is decoupled from a given subset of inputs. Set theoretical notions are used to describe the...

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