Integration of physical load and statistical degradation models in predicting the resource of the upper structure of the railway track for new operating conditions

In the modern practice of managing the resource of the upper structure of the railway track, two fundamentally different approaches to forecasting are used: physical modeling, taking into account the passages of rolling stock with defective wheelsets, and statistical modeling of track degradation with a horizon of up to 15 years. These approaches were developed independently and did not have a methodological connection, which limited the possibilities of forecasting for new operating conditions that did not have an accumulated array of degradation data.

The article proposes a method of bilateral integration of the physical load model (micro-level) and the statistical degradation model of the Unified Corporate Automated System for Monitoring the Degradation of the Infrastructure of Russian Railways, UCASMD (macro-level). The integration is performed in two directions: bottom-up – calculation of the degradation function coefficient from the physical equivalence coefficient and the observed proportion of defective wheelsets – and top-down – refinement of physical parameters from accumulated diagnostic data of reference sections.

The inverse-variance weighting principle is applied to determine the optimal balance between the two models. It is shown that the characteristic duration of accumulated data at which the contributions of the physical and statistical models are equal is (3.5 ± 0.8) years: below this threshold the forecast is predominantly physical, above it – predominantly statistical. The method was validated on four sections of the Eastern polygon of Russian Railways carrying 14,200-tonne freight trains. The average deviation of the hybrid forecast from actual data was 8–12 %, which outperforms the accuracy of the individual models (15–25 % for the statistical model, 12–18 % for the physical model without calibration). The proposed approach substantially extends the applicability of upper track structure resource forecasting to conditions where accumulated diagnostic data are limited or unavailable.

1. Kogan A. Ya. Track dynamics and its interaction with rolling stock. Moscow: Transport; 1997. 326 p. (In Russ.).

2. Verigo M. F., Kogan A. Ya. Interaction of track and rolling stock. Moscow: Transport; 1986. 559 p. (In Russ.).

3. Software implementation of the calculation algorithms for the track degradation forecasting method. Proceedings of the Scientific and Technical Council. Moscow: VNIIZhT; 2026. 28 p. (In Russ.).

4. Dolgy A. I., Vinogradov S. A. Conceptual model of the integrated platform for strategic planning and infrastructure management of Russian Railways. Moscow: NIAS; 2026. 84 p. (In Russ.).

5. Romanov A. V., Kiselev A. A. On the distribution law of the dynamic wheel-rail contact force. Proceedings of Petersburg Transport University. 2025;22(4):926–937. (In Russ.).

6. Adadurov A. S., Tsomayev P. I., Podgrebennyy I. M., Ivanov A. N. Results of modelling the impact of a freight car wheel with two sub-rejection wheel flats on the railway track. Proceedings of Petersburg Transport University. 2026;23(2):40–48. (In Russ.).

7. Krasnov O. G. Prediction of rail wear and contact-fatigue damage under intensified freight traffic conditions. Specialty 2.9.2 ‘Railway Track, Railway Surveying and Design’: dissertation for the degree of Doctor of Engineering; Russian University of Transport. Moscow: RUT (MIIT); 2022. (In Russ.).

8. Adadurov A. S., Suslov O. A. Experimental study of digital accelerometers and systems for detecting wheel tread defects of rolling stock. Railway Engineering. 2019;(47):40–45. (In Russ.).

9. Adadurov A. S., Fedorova V. I., Nerezkov A. V., Suslov O. A. Implementation results of the accelerometric universal monitoring post and further prospects for detecting wheel tread defects of railway cars. Modern Technologies. System Analysis. Modelling. 2021;(69):192–199. (In Russ.).

10. Miner M. A. Cumulative damage in fatigue. Journal of Applied Mechanics. 1945;12:A159–A164.

11. Hartung J., Knapp G., Sinha B. K. Statistical Meta-Analysis with Applications. Hoboken, NJ: Wiley; 2008. 264 p. (Ch. 3 “Weighted estimators and inverse-variance weighting”).

12. Bernardo J. M., Smith A. F. M. Bayesian Theory. Chichester: Wiley; 2000. 586 p.

13. Cramér H. Mathematical Methods of Statistics. Princeton, NJ: Princeton University Press; 1946. 575 p. (Central limit theorem, Ch. 17).

14. Results of track maintenance operations for 12 Months of 2025. Key objectives for 2026: Report of the Track and Structures Department, Central Infrastructure Directorate of Russian Railways. Moscow; 2026. 12 p. (In Russ.).

15. Order No. 766/r of Russian Railways, dated 18.08.2023. Development strategy of the Central Infrastructure Directorate of Russian Railways. Moscow: Russian Railways; 2023. 53 p. (In Russ.).