Stochastic Modeling and Error Analysis of Infrared Sensors in Axle-Box Heating Control Systems

The paper presents the theoretical and applied foundations of stochastic modeling and analysis of measurement errors in infrared sensors used within automated systems for monitoring the heating of railway axle-box assemblies. The necessity of accounting for random disturbances arising from environmental influences, sensor installation angles, variations in the sensor-to- object distance, dynamic effects, and background radiation-factors that significantly affect the accuracy of temperature measurements-is substantiated. Based on the Central Limit Theorem, a stochastic model of the random error component is developed, in which the total error is represented as a normally distributed random variable with a variance of σ² = 0.0475 (σ ≈ 0.22 °C). To verify the adequacy of the proposed model, operational data from the KTSM‑02BT, DISK-B, and FUES-EPOS systems operating on the railway network of “O‘zbekiston temir yo‘llari” JSC during 2022–2024 were analyzed. A statistical assessment of 249,765 train passages revealed a 62 % increase in the number of registered malfunctions, including a rise in false alarms caused by solar radiation and sensor miscalibration. The experimental results confirmed the stochastic nature of measurement errors and demonstrated close agreement between the empirical variance and theoretical estimates of the model. The developed stochastic model and its empirical validation improve the reliability of temperature monitoring, reduce the number of false detections, and enhance the overall robustness and accuracy of automated diagnostic systems for monitoring the technical condition of railway axle-box assemblies.