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1
Content available Fault diagnosis in nonlinear hybrid systems
Zhirabok A., Shumsky A.
International Journal of Applied Mathematics and Computer Science
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2018
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Vol. 28, no. 4
635--648
EN
The problem of fault diagnosis in hybrid systems is investigated. It is assumed that the hybrid systems under consideration consist of a finite automaton, a set of nonlinear difference equations and the so-called mode activator that coordinates the action of the other two parts. To solve the fault diagnosis problem, hybrid residual generators based on both diagnostic observers and parity relations are used. It is shown that the hybrid nature of the system imposes some restrictions on the possibility of creating such generators. Sufficient solvability conditions of the fault diagnosis problem are found. Examples illustrate details of the solution.
2
Content available Fault detection in nonlinear systems via linear methods
Zhirabok A., Shumsky A., Solyanik S., Suvorov A.
International Journal of Applied Mathematics and Computer Science
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2017
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Vol. 27, no. 2
261--272
EN
The problem of robust linear and nonlinear diagnostic observer design is considered. A method is suggested to construct the observers that are disturbance decoupled or have minimal sensitivity to the disturbances. The method is based on a logic-dynamic approach which allows us to consider systems with non-differentiable nonlinearities in the state equations by methods of linear algebra.
3
Content available An approach to the analysis of observability and controllability in nonlinear systems via linear methods
Zhirabok A., Shumsky A.
International Journal of Applied Mathematics and Computer Science
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2012
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Vol. 22, no. 3
507-522
EN
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.,Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.
4
Content available remote Algebraic approach for model decomposition: Application to fault detection and isolation in discrete-event systems
Berdjag D., Cocquempot V., Christophe C., Shumsky A., Zhirabok A.
International Journal of Applied Mathematics and Computer Science
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2011
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Vol. 21, no 1
109-125
EN
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 decomposition methodology in the general case. The methodology is then detailed for discrete-event model decomposition using pair algebra concepts, and an extension of the output injection technique is used to relax the conservatism of the decomposition.
5
Content available remote Redundancy relations for fault diagnosis in nonlinear uncertain systems
Shumsky A.
International Journal of Applied Mathematics and Computer Science
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2007
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Vol. 17, no 4
477-489
EN
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 a strict feedback form. Algebraic and geometric tools are used for this transformation. The features of the method are made particular for uncertain systems with a linear structure.
6
Content available remote Nonlinear diagnostic filter design: Algebraic and geometric points of view
Shumsky A., Zhirabok A.
International Journal of Applied Mathematics and Computer Science
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2006
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Vol. 16, no 1
115-127
EN
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.
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