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Double fault distinguishability in linear systems

100%
Kościelny J., Łabęda-Grudziak Z.
International Journal of Applied Mathematics and Computer Science
|
2013
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tom 23
|
nr 2
395-406
EN
This paper develops a new approach to double fault isolation in linear systems with the aid of directional residuals. The method of residual generation for computational as well as internal forms is applied. Isolation of double faults is based on the investigation of the coplanarity of the residual vector with the planes defined by the individual pairs of directional fault vectors. Additionally, the method of designing secondary residuals, which are structured and directional, is proposed. These transformations allow achieving various isolation properties. It is shown that double fault distinguishability can be improved by decomposing the observed residual vector along the response directions. The described methods are illustrated with a simple computational example.
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A new approach to multiple fault diagnosis: A combination of diagnostic matrices, graphs, algebraic and rule-based models. The case of two-layer models

100%
Ligęza A., Kościelny J.
International Journal of Applied Mathematics and Computer Science
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2008
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tom 18
|
nr 4
465-476
EN
The diagnosis of multiple faults is significantly more difficult than singular fault diagnosis. However, in realistic industrial systems the possibility of simultaneous occurrence of multiple faults must be taken into account. This paper investigates some of the limitations of the diagnostic model based on the simple binary diagnostic matrix in the case of multiple faults. Several possible interpretations of the diagnostic matrix with rule-based systems are provided and analyzed. A proposal of an extension of the basic, single-level model based on diagnostic matrices to a two-level one, founded on causal analysis and incorporating an OR and an AND matrix is put forward. An approach to the diagnosis of multiple faults based on inconsistency analysis is outlined, and a refinement procedure using a qualitative model of dependencies among system variables is sketched out.
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Fault isolability with different forms of the faults-symptoms relation

81%
Kościelny J., Syfert M., Rostek K., Sztyber A.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 4
815-826
EN
The definitions and conditions for fault isolability of single faults for various forms of the diagnostic relation are reviewed. Fault isolability and unisolability on the basis of a binary diagnostic matrix are analyzed. Definitions for conditional and unconditional isolability and unisolability on the basis of a fault information system (FIS), symptom sequences and directional residuals are formulated. General definitions for conditional and unconditional isolability and unisolability in the cases of simultaneous evaluation of diagnostic signal values and a sequence of symptoms are provided. A comprehensive example is discussed.
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