AUTOMATION, ІОТ, ROBOTICS AND INFORMATION-MEASUREMENT SYSTEMS

Linear Dynamic Systems State Diagnosis Using Separate Evaluation Method

Authors

A. Yu. Volovyk ORCID 0000-0002-8772-9843
Vinnytsia National Technical University ROR
A. Yu. Savytskyi ORCID 0009-0000-3490-6300
Vinnytsia National Technical University ROR
DOI https://doi.org/10.31649/1997-9266-2026-187-4-194-203

Keywords

discrete linear dynamic system separate evaluation method analytical redundancy

Abstract

To ensure  high level of performance and operational reliability of  modern, highly integrated technical systems, the timely detection and identification of malfunctions, failures, and sudden disturbances is critical. Their rapid identification  makes it possible to promptly implement appropriate corrective actions, aimed at restoring system functionality and preventing the development of emergency situations. This paper addresses the problem of synthesizing a specialized filter designed to detect and localize failures, malfunctions, or disturbances in a class of linear stationary discrete-time systems. The fundamental principle of the algorithm is the concept of analytical redundancy based on a mathematical model of the system under observation. The diagnostic algorithm was designed so  that pre-formed residual differences, in the form of signatures, would allow the effects of target-type faults to be distinguished from the faults or disturbances influence of other classes. This resulted in the creation of an “extrapolator-corrector” device structure containing two parallel filters implemented in a form that is algorithmically equivalent to a Kalman filter. It is noteworthy that one of the subsystems provides a fault-free state vector estimate, while the other, which has a degenerate structure, is designed to generate a fault estimate. The resulting difference vector components are uniquely associated with a given fault type. The application of this algorithm reduces computational costs but introduces additional constraints and reduces the accuracy of the estimation results, due to computational issues related to the system’s pseudo-inverse matrices. Since this solution is approximate and non-unique, the resulting structure exhibits characteristics of quasi-optimality. In general terms, the convergence and stability of the obtained estimates are briefly discussed. The results of the method performance test are presented using an illustrative numerical example. The analysis of the results is presented in comparison with the abilities of the classical Kalman filter, which clearly demonstrates the effectiveness of the developed approach and its advantages. The computational experiment results confirmed the overall effectiveness of the method. The synthesized filter enables to generate state estimates of satisfactory quality and perform correctly when diagnosing unexpected malfunctions, failures, and sudden disturbances. Based on the conclusions drawn, it can be stated that this work introduces an element of scientific novelty into the field of fault detection and classification in linear discrete dynamic systems. Directions for further research have been identified.

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How to Cite

[1]
“Linear Dynamic Systems State Diagnosis Using Separate Evaluation Method”, Вісник ВПІ, no. 4, pp. 194–203, Oct. 2026, doi: 10.31649/1997-9266-2026-187-4-194-203.

Author Biographies

A. Yu. Volovyk, Vinnytsia National Technical University

Dr. Sc. (Eng.), Professor of the Chair of Information Radioelectronic Technologies and Systems

A. Yu. Savytskyi, Vinnytsia National Technical University

Cand. Sc. (Eng.), Associate Professor, Associate Professor of the Chair of Information Radioelectronic Technologies and Systems

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