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 Vestnik SamU. Estestvenno-Nauchnaya Ser., 2020, Volume 26, Issue 1, Pages 52–68 (Mi vsgu623)

Mathematics

Problems of differential and topological diagnostics. Part 4. The case of exact trajectorial measurements

M. V. Shamolin

Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russian Federation

Abstract: Proposed work is the fourth in the cycle, therefore, the diagnostic problem is formulated for the case of exact trajectorial measurements, the diagnostic theorem is stated and proved, and two diagnostic algorithms that follow from this theorem are presented. Techniques for an a priori counting of constants, which should be stored in a program for the computer-aided diagnostics whenever the first diagnostic algorithm is used, and other algorithmic parameters are considered. If the second algorithm is applied, the constants should not be stored; this algorithm is based on the search for the minimum value of the diagnostic functional among the values of this functional that were obtained in the process of diagnostics for the a priori chosen set of reference malfunctions. Various extensions of the diagnostic theorem are considered, namely, the problem of whether the diagnostic algorithms thus obtained are applicable when the dimension of the diagnostic vector being used is lower than that of the state vector or when the uninterrupted express-diagnostics with no checking surface is carried out, the problem of selecting the “minimum” diagnostic time, the diagnostics of malfunctions occurring in the neighborhoods of reference non-degenerate malfunctions and not envisaged in the a priori list. We consider other functionals solving the diagnostic problem. Finally, we state the extended diagnostic problem that is solved by using the proposed algorithms.

Keywords: diagnostic problem, diagnostic algorithms, extended diagnostic problem.

DOI: https://doi.org/10.18287/2541-7525-2020-26-1-52-68

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UDC: 517+531.01
Revised: 18.02.2020
Accepted:28.02.2020

Citation: M. V. Shamolin, “Problems of differential and topological diagnostics. Part 4. The case of exact trajectorial measurements”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 26:1 (2020), 52–68

Citation in format AMSBIB
\Bibitem{Sha20} \by M.~V.~Shamolin \paper Problems of differential and topological diagnostics. Part~4. The case of exact trajectorial measurements \jour Vestnik SamU. Estestvenno-Nauchnaya Ser. \yr 2020 \vol 26 \issue 1 \pages 52--68 \mathnet{http://mi.mathnet.ru/vsgu623} \crossref{https://doi.org/10.18287/2541-7525-2020-26-1-52-68} 

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This publication is cited in the following articles:
1. M. V. Shamolin, “Zadachi differentsialnoi i topologicheskoi diagnostiki. Chast 5. Zadacha diagnostirovaniya (sluchai traektornykh izmerenii s oshibkoi)”, Vestn. SamU. Estestvennonauchn. ser., 26:3 (2020), 30–39
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