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The article presents statistical studies of acoustic control signals when diagnosing power transformers of the railway power supply system. Statistical processing of acoustic monitoring data was carried out on the example of transformers with different levels of insulation condition. Comparisons of histograms of the experimental distribution of amplitudes and dominant frequencies of signals with the nearest theoretical distribution laws, performed in the STATISTICA program according to control data obtained from the automated system. The conducted studies have shown a close correlation of defects registered by the acoustic method with the distribution of signals in the form of laws of distribution of random variables. It is shown that for power transformers with mechanical oscillations, both during the passage of the train and at idle, the distribution of amplitudes and dominant frequencies of the recorded signals corresponds to a uniform law. The distribution of amplitudes and dominant frequencies is not centered around a certain average value. For power transformers containing partial discharges, the cause of which is the deterioration of the insulating properties of the windings under the influence of high voltage, the best approximation, both amplitudes and dominant frequencies, showed the Lognormal distribution. The signals are centered around a characteristic mean value. When the train passes, the acoustic system registers both high-frequency signals from the PD and low-frequency signals from body vibrations. There are two components in the distribution law - uniform and lognormal distribution densities. Thus, by the type of distribution of the recorded signals, their amplitude and dominant frequency, it is possible to determine the presence of a defective state of the insulation of power transformers. The study was carried out with the financial support of the Russian Foundation for Basic Research within the framework of the scientific project No. 20-38-90231.

The reliability and longevity of electrical machines, such as motors and generators, are critically determined by the condition of their insulation system. This paper presents a comprehensive analysis of the multifaceted processes leading to the degradation of winding insulation materials. The study reveals the complex and often non-linear interrelationships between key aging factors thermal overloading, electrical surges, mechanical vibrations, and the detrimental impact of the environment (humidity, contaminants). The combined influence of these factors leads to a progressive deterioration of dielectric strength and, consequently, a reduction in the equipment's service life. As a methodological foundation, an innovative approach to insulation condition diagnostics, based on graph modeling, is proposed. The developed graph model serves as a formalized tool for describing cause-and-effect relationships between input parameters (armature current, voltage, and start/stop regimes), external operating conditions, and internal diagnostic parameters, such as insulation resistance, tangent delta, and partial discharge characteristics. Particular attention in the model is paid to the analysis of positive feedback loops, which explain the non-linear, avalanche-like nature of damage development, where one type of defect accelerates the progression of others. The practical significance of the research lies in the transition from traditional planned-preventive maintenance to a predictive model. The proposed graph model enables the early diagnosis of degradation signs and the construction of accurate forecasts for the insulation's remaining useful life. The results of the work pave the way for the development of intelligent monitoring and diagnostic systems, as well as for the optimization of maintenance strategies for power electrical equipment, ultimately enhancing its operational reliability and economic efficiency. The developed graph model will serve as a theoretical basis for creating effective diagnostic systems and predicting the remaining useful life of insulation. Identifying positive feedback loops in degradation processes makes it possible to determine critical control points and develop preventive measures to prevent sudden failures.