A.V. Volosova1, S.V. Skryl2, V.I. Terekhov3, A.I. Kanev4, M.V. Vinogradova5

1–5 Bauman Moscow State Technical University (Moscow, Russia)
1 volosova@bmstu.ru, 2 skryl@bmstu.ru, 3 terekchow@bmstu.ru, 4 aikanev@bmstu.ru, 5 vinogradova.m@bmstu.ru

The sustainable development of high-availability systems directly depends on ensuring their security. Timely detection and elimination of threats of various levels of complexity is one of the main tasks of security systems. The successful solution of this task is directly related to the adequate mathematical modeling of possible threats. The mathematical model of a threat should take into account the heterogeneity of features, the change in the geometry of the state space, and the presence of control. In modern methods of information geometry, the Riemannian space is often used to model threats, which allows for the binary detection of threats, but does not provide for classification and assessment of the level of danger. The purpose of the article is to build adequate mathematical models of threats based on the tools of the Riemannian space for the simultaneous solution of the tasks of detection, classification and determination of the level of threat danger. The paper proposes a method of building adequate mathematical models of threats based on the tools of the Riemannian space. The method allows to solve the problem of detection, classification and detection of modern threats. The method of mathematical modeling of threats based on the tools of the Romanov space allows to improve the quality of security of high-availability systems due to the possibilities of accurate detection of threats. The effectiveness of the method is demonstrated on the examples of detection of single flying objects and swarms of various configurations.

Volosova A.V., Skryl S.V., Terekhov V.I., Kanev A.I., Vinogradova M.V. Possibilities of adequate mathematical modeling of threats in riemannian space // Highly Available Systems. 2026. V. 22. № 3. P. 99−111. DOI: https://doi.org/10.18127/j20729472-202603-09

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