Solution of the Diagnostic Problem in the Cases of Precise and Inaccurate Trajectory Measurements
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SOLUTION OF THE DIAGNOSTIC PROBLEM IN THE CASES OF PRECISE AND INACCURATE TRAJECTORY MEASUREMENTS M. V. Shamolin
UDC 519.234
Abstract. We consider the problem of differential diagnostics of the functional status of control objects that have a module structure and a finite set of possible malfunctions and reduce this problem to two separate problems that can be solved separately: the inspection problem (ascertainment of malfunction criteria in the system) and the diagnostic problem (search of malfunctions). We prove the feasibility of solution of the problem of differential diagnostics in the cases of precise and inaccurate trajectory measurements at the level of mathematical models. Keywords and phrases: diagnostics, controlled system, aircraft, basic malfunction, diagnostic space, inspection problem, diagnostic problem. AMS Subject Classification: 62G05, 68U01
CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Diagnostic Problem: The Case of Exact Trajectory Measurements 2. Case of Inaccurate Trajectory Measurements . . . . . . . . . . . . 3. Statistical Solution of the Problem of Differential Diagnostics . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Introduction The phenomenon where a trajectory of a dynamical reaches a certain prescribed surface may serve as a criterion for the presence of a malfunction in the system. A malfunction can occur at any time instant during the motion of the system at any point inside a given inspection surface (see [1, 2, 15]). Initial information for the solution of the inspection problem is a mathematical model of the motion of an object examined, a bounded domain of initial conditions, and an a priori list of mathematical models of the motion with possible malfunctions. Using this information. one can choose an inspection surface. We will solve the diagnostic problem by tracing the trajectory of the object after the moment when it reaches the inspection surface. It is necessary that the diagnostics is performed during the motion of the object, its duration is sufficiently small (for example, a half or quarter of period of fast oscillations of the object), and it does not require additional instrumentation. These circumstances do not allow one to use cumbersome algorithms of identification theory, so we must construct new algorithms of continuous express diagnostics. Acknowledgment. This work was partially supported by the Russian Foundation for Basic Research (project No. 15-01-00848-a). Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 150, Geometry and Mechanics, 2018.
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Diagnostic Problem: The Case of Exac
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