Study of the reliabillity and safety of an N-dimensional system by the method of stepwise ortohogonalization

DOI: 10.31673/2412-9070.2025.051282

Abstract

In the context of digital transformation, ensuring the reliability and security of information and communication systems is becoming increasingly critical, as their stable operation determines the continuity of managing safety-critical objects and the protection of the information environment. This paper proposes a stepwise orthogonalization method for analyzing complex N-dimensional systems operating under stochastic feedback loops. Unlike traditional approaches, such as the Gaussian elimination method, the proposed solution accounts for the incompatibility of events arising in control loops, making it suitable for studying multi-loop structures with a high level of uncertainty.
The method combines tools of linear algebra and logic-probabilistic analysis, thus establishing a methodological link between deterministic and stochastic approaches. The algorithm relies on the sequential elimination of unknown variables and the substitution of compatible events with incompatible ones, which allows constructing expressions for evaluating the probabilities of information flows within the system. Its applicability is demonstrated using a graph with n vertices, modeling the distribution of information flows in environments with multiple control circuits. A key outcome of the method is the ability to accurately consider the influence of ε-events associated with the passage of signals through graph edges.
The proposed approach provides opportunities to assess the reliability and security of N-dimensional systems both at the level of individual information flows and the entire infrastructure. The step wise orthogonalization method helps identify hidden stochastic dependencies, evaluate the probability of critical component failures, and determine their impact on overall system performance. The study emphasizes that this method can be effectively applied in practical safety management tasks, particularly in the design of information and communication networks, as well as in the integration of modern technologies such as MEC, NFV, and URLLC.
The obtained results confirm the efficiency of the stepwise orthogonalization method as a tool for reducing risks, improving reliability, and ensuring the resilience of complex systems under conditions of uncertainty. Future research may focus on extending the applicability of the method to more complex topologies, multiparametric scenarios, and systems with advanced adaptive control mechanisms.

Keywords: information and communication system; N-dimensional system; orthogonalization; stochastic connection; system of event equations; logical-probabilistic analysis; event graph; control loop; flow probability.