Bayesian multivariate track geometry degradation modeling and its use in condition-based inspection

Abstract

Effective maintenance of railway infrastructure is crucial for safe and comfortable transportation. Among the various degradation modes, track geometry deformation due to repeated loading significantly impacts operational safety. Detecting and maintaining acceptable track geometry involve the use of track recording vehicles (TRVs) that inspect and record geometric parameters. This study aims to develop a novel track geometry degradation model that considers multiple indicators and their correlations, accounting for both imperfect manual and mechanized tamping. A multivariate Wiener model is formulated to capture the characteristics of track geometry degradation. To address data limitations, a hierarchical Bayesian approach with Markov Chain Monte Carlo (MCMC) simulation is employed. This research contributes to the analysis of a multivariate predictive model, which considers the correlation between the degradation rates of multiple indicators, providing insights for rail operators and new track-monitoring systems. The model’s performance is validated through a real-world case study on a commuter track in Queensland, Australia, using actual data and independent test datasets. Additionally, the study demonstrates the application of the proposed multivariate degradation model in developing a condition-based inspection policy for track geometry, potentially reducing the number of TRVs runs while maintaining abnormal detection levels and failure rates.

Keywords

Track geometry degradation / Multivariate degradation model / Multivariate wiener process / Bayesian approach / Degradation prediction

References

[1] Arcieri G, Hoelzl C, Schwery O, et al. . Bridging POMDPs and Bayesian decision making for robust maintenance planning under model uncertainty: an application to railway systems. Reliab Eng Syst Saf, 2023, 239: 109496.

[2] Lee JS, Yeo IH, Bae Y. A stochastic track maintenance scheduling model based on deep reinforcement learning approaches. Reliab Eng Syst Saf, 2024, 241: 109709.

[3] Sedghi M, Kauppila O, Bergquist B, et al. . A taxonomy of railway track maintenance planning and scheduling: a review and research trends. Reliab Eng Syst Saf, 2021, 215: 107827.

[4] Wu Q, Azad AK, Cole C, et al. . Identify severe track geometry defect combinations for maintenance planning. Int J Rail Transp, 2022, 10(1): 95-113.

[5] Higgins C, Liu X. Modeling of track geometry degradation and decisions on safety and maintenance: a literature review and possible future research directions. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2018, 232(5): 1385-1397.

[6] Soleimanmeigouni I, Ahmadi A, Kumar U. Track geometry degradation and maintenance modelling: a review. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2018, 232(1): 73-102.

[7] Wang Y, Wang P, Wang X, et al. . Position synchronization for track geometry inspection data via big-data fusion and incremental learning. Transp Res Part C Emerg Technol, 2018, 93: 544-565.

[8] Saleh A, Remenyte-Prescott R, Prescott D, et al. . Intelligent and adaptive asset management model for railway sections using the iPN method. Reliab Eng Syst Saf, 2024, 241: 109687.

[9] Rebello S, Cholette ME, Truong-Ba H et al (2022) Railway track geometry degradation modelling and prediction for maintenance decision support. In: 15th World Congress on Engineering Asset Management, Bonito, pp 422–432

[10] Soleimanmeigouni Iman, Ahmadi AlirezaKumar U, Ahmadi A, Verma AK, Varde P. A survey on track geometry degradation modelling. Current trends in reliability, availability, maintainability and safety, 2016, Cham. Springer International Publishing3-12.

[11] Letot C, Soleimanmeigouni I, Ahmadi A, et al. . An adaptive opportunistic maintenance model based on railway track condition prediction. IFAC-PapersOnLine, 2016, 49(28): 120-125.

[12] Meier-Hirmer C, Riboulet G, Sourget F, et al. . Maintenance optimization for a system with a gamma deterioration process and intervention delay: application to track maintenance. Proc Inst Mech Eng Part O J Risk Reliab, 2009, 223(3): 189-198

[13] Mishra M, Odelius J, Thaduri A, et al. . Particle filter-based prognostic approach for railway track geometry. Mech Syst Signal Process, 2017, 96: 226-238.

[14] Quiroga LM, Schnieder E. Monte Carlo simulation of railway track geometry deterioration and restoration. Proc Inst Mech Eng Part O J Risk Reliab, 2012, 226(3): 274-282

[15] Sharma S, Cui Y, He Q, et al. . Data-driven optimization of railway maintenance for track geometry. Transp Res Part C Emerg Technol, 2018, 90: 34-58.

[16] Wordofa DH (2022) Development of track geometry degradation model & review of recovery models. In: 2022 Joint Rail Conference, April 20–21, Virtual, Online, JRC2022–79370

[17] Vale C, Lurdes SM. Stochastic model for the geometrical rail track degradation process in the Portuguese railway Northern Line. Reliab Eng Syst Saf, 2013, 116: 91-98.

[18] Caetano LF, Teixeira PF. Predictive maintenance model for ballast tamping. J Transp Eng, 2016, 142(4): 04016006.

[19] Liao Y, Han L, Wang H, et al. . Prediction models for railway track geometry degradation using machine learning methods: a review. Sensors, 2022, 22(19): 7275.

[20] Khajehei H, Ahmadi A, Soleimanmeigouni I, et al. . Prediction of track geometry degradation using artificial neural network: a case study. Int J Rail Transp, 2022, 10(1): 24-43.

[21] Cinlar E. Introduction to stochastic processes, 2013, New York. Dover Publications

[22] Ross SM. Introduction to probability models, 201411New York. Academic Press

[23] Mercier S, Meier-Hirmer C, Roussignol M. Bivariate Gamma wear processes for track geometry modelling, with application to intervention scheduling. Struct Infrastruct Eng, 2012, 8(4): 357-366.

[24] Khajehei H, Ahmadi A, Soleimanmeigouni I, et al. . Allocation of effective maintenance limit for railway track geometry. Struct Infrastruct Eng, 2019, 15(12): 1597-1612.

[25] Soleimanmeigouni I, Ahmadi A, Nissen A, et al. . Prediction of railway track geometry defects: a case study. Struct Infrastruct Eng, 2020, 16(7): 987-1001.

[26] Soleimanmeigouni I, Xiao X, Ahmadi A, et al. . Modelling the evolution of ballasted railway track geometry by a two-level piecewise model. Struct Infrastruct Eng, 2018, 14(1): 33-45.

[27] Prescott D, Andrews J. Investigating railway track asset management using a Markov analysis. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2015, 229(4): 402-416.

[28] He Q, Li H, Bhattacharjya D, et al. . Track geometry defect rectification based on track deterioration modelling and derailment risk assessment. J Oper Res Soc, 2015, 66(3): 392-404.

[29] Bressi S, Santos J, Losa M. Optimization of maintenance strategies for railway track-bed considering probabilistic degradation models and different reliability levels. Reliab Eng Syst Saf, 2021, 207: 107359.

[30] Arasteh-Khouy I, Larsson-Kråik PO, Nissen A, et al. . Cost-effective track geometry maintenance limits. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2016, 230(2): 611-622.

[31] Lasisi A, Attoh-Okine N. Principal components analysis and track quality index: a machine learning approach. Transp Res Part C Emerg Technol, 2018, 91: 230-248.

[32] An R, Sun Q, Wang F, et al. . Improved railway track geometry degradation modeling for tamping cycle prediction. J Transp Eng Part A Syst, 2018, 144(7): 04018025.

[33] Rios ID, Ruggeri F, Wiper MP. Bayesian analysis of stochastic process models, 2012, Hoboken. Wiley.

[34] Andrade AR, Teixeira PF. A Bayesian model to assess rail track geometry degradation through its life-cycle. Res Transp Econ, 2012, 36(1): 1-8.

[35] Andrade AR, Teixeira PF. Hierarchical Bayesian modelling of rail track geometry degradation. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2013, 227(4): 364-375.

[36] Andrade AR, Teixeira PF. Statistical modelling of railway track geometry degradation using Hierarchical Bayesian models. Reliab Eng Syst Saf, 2015, 142: 169-183.

[37] Jiang D, Chen T, Xie J, et al. . A mechanical system reliability degradation analysis and remaining life estimation method—with the example of an aircraft hatch lock mechanism. Reliab Eng Syst Saf, 2023, 230: 108922.

[38] Stan Development Team (2024) Stan reference manual, v2.36.0. https://mc-stan.org

[39] Fonnesbeck CJ, Patil A, Huard D et al (2017) PyMC documentation. http://github.com/pymc-devs/pymc

[40] Lewandowski D, Kurowicka D, Joe H. Generating random correlation matrices based on vines and extended onion method. J Multivar Anal, 2009, 100(9): 1989-2001.

[41] Gelman A. Prior distributions for variance parameters in hierarchical models (comment onarticle by Browne and Draper). Bayesian Anal, 2006, 1(3): 515-533.

[42] Homan MD, Gelman A. The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J Mach Learn Res, 2014, 15(1): 1593-1623. DOI:

[43] Truong-Ba H, Cholette ME, Borghesani P, et al. . Condition-based inspection policies for boiler heat exchangers. Eur J Oper Res, 2021, 291(1): 232-243.

Funding

Australian Research Council(LP200100382)

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