Skip to main content
SpringerLink
Log in

Probabilistic model and analysis of coupled train-ballasted track-subgrade system with uncertain structural parameters

基于结构参数不确定的列车-轨道-路基系统耦合振动概率分析

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

Random dynamic responses caused by the uncertainty of structural parameters of the coupled train-ballasted track-subgrade system under train loading can pose safety concerns to the train operation. This paper introduced a computational model for analyzing probabilistic dynamic responses of three-dimensional (3D) coupled train-ballasted track-subgrade system (TBTSS), where the coupling effects of uncertain rail irregularities, stiffness and damping properties of ballast and subgrade layers were simultaneously considered. The number theoretical method (NTM) was employed to design discrete points for the multi-dimensional stochastic parameters. The time-histories of stochastic dynamic vibrations of the TBSS with systematically uncertain structural parameters were calculated accurately and efficiently by employing the probability density evolution method (PDEM). The model-predicted results were consistent with those by the Monte Carlo simulation method. A sensitivity study was performed to assess the relative importance of those uncertain structural parameters, based on which a case study was presented to explore the stochastic probability evolution mechanism of such train-ballasted track-subgrade system.

摘要

列车荷载作用下有砟轨道-路基耦合系统结构参数的不确定性引起的随机振动对行车安全的影响不可忽略。 本文提出了一种基于概率密度演化理论的三维列车-有砟轨道-路基耦合系统随机振动概率仿真分析模型,该模型可同时考虑轨道随机不平顺、道砟层和路基层随机刚度、随机阻尼等耦合效应,为列车-轨道-路基系统随机振动分析提供了一种全新的计算分析方法。 采用数论方法对多维随机参数进行代表性离散数组点设计。 结果表明,与蒙特卡罗模拟方法相比,概率密度演化模型开展随机振动分析更为准确、高效。 基于算例开展了多维随机参数的敏感性分析,系统地评估了不确定结构随机参数的相对重要性,并在此基础上探讨了列车-轨道-路基系统的随机概率演化机制。

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. ZHAI Wan-ming, XIA He, CAI Cheng-biao, GAO Mang-mang, LI Xiao-zhen, GUO Xiang-rong, ZHANG Nan, WANG Kai-yun. High-speed train-track-bridge dynamic interactions-part I: Theoretical model and numerical simulation [J]. International Journal of Rail Transportation, 2013, 1: 1–24. DOI: https://doi.org/10.1080/23248378.2013.791498.

    Google Scholar 

  2. ZHAI Wan-ming. Vehicle-track coupling dynamics (fourth edition) [M]. Beijing, China: Science Press, 2015. (in Chinese)

    Google Scholar 

  3. SUN Y Q, DHANASEKAR M D. A three-dimensional model for the lateral and vertical dynamics of wagon-track systems [J]. Journal of Rail & Rapid Transit, 2003, 217(1): 31–45. DOI:https://doi.org/10.1243/095440903762727339.

    Article  Google Scholar 

  4. ZAKERI J, XIA He, FAN Jun-jie. Dynamic responses of train-track system to single rail irregularity [J]. Latin American Journal of Solids & Structures, 2009, 6(2): 89–104. DOI: https://doi.org/10.1243/095440903762727339.

    Google Scholar 

  5. KARDAS-CINAL E. Spectral distribution of derailment coefficient in non-linear model of railway vehicle-track system with random track irregularities [J]. Nonlinear Dynamics, 2013, 8(3): 1349–1376. DOI: https://doi.org/10.1115/1.4023352.

    Google Scholar 

  6. RECUERO A M, ESCALONA J L. Dynamics of the coupled railway vehicle-flexible track system with irregularities using a multibody approach with moving modes [J]. Vehicle System Dynamics, 2014, 52(1): 45–67. DOI: https://doi.org/10.1080/00423114.2013.857030.

    Article  Google Scholar 

  7. LEI Xiao-yan, WANG Jian. Dynamic analysis of the train and slab track coupling system with finite elements in a moving frame of reference [J]. Journal of Vibration and Control, 2014, 20(9): 1301–1317. DOI: https://doi.org/10.1177/1077546313480540.

    Article  Google Scholar 

  8. YANG Y B, YAU D J, WU S Y. Vehicle-bridge interaction dynamics:with applications to high-speed rail [M]. Singapore: World Scientific Pub Co Inc, 2004.

    Book  Google Scholar 

  9. ZHAI Wan-ming, WANG Kai-yun, CAI Cheng-biao. Fundamentals of vehicle-track coupled dynamics [J]. Vehicle System Dynamics, 2009, 47(11): 1349–1376. DOI: https://doi.org/10.1080/00423110802621561.

    Article  Google Scholar 

  10. XIA H, ZHANG N. Dynamic analysis of railway bridge under high-speed trains [J]. Computers & Structures, 2005, 83(23, 24): 1891–1901. DOI: https://doi.org/10.1016/j.compstruc.2005.02.014.

    Article  Google Scholar 

  11. IYENGAR R N, JAISWAL O R. A new model for non-gaussian random excitations [J]. Probabilistic Engineering Mechanics, 1993, 8(3, 4): 281–287. DOI: https://doi.org/10.1016/0266-8920(93)90022-N.

    Article  Google Scholar 

  12. IYENGAR R N, JAISWAL O R. Random field modeling of railway track irregularities [J]. Journal of Transportation Engineering, 1997, 121(4): 303–308. DOI: https://doi.org/10.1061/(ASCE)0733-947X(1995)121:4(303).

    Article  Google Scholar 

  13. YU Zhi-wu, MAO Jian-feng, GUO Feng-qi, GUO Wei. Non-stationary random vibration analysis of a 3d train-bridge system using the probability density evolution method [J]. Journal of Sound and Vibration, 2016, 366(Supplement C): 173–189. DOI: https://doi.org/10.1016/j.jsv.2015.12.002.

    Article  Google Scholar 

  14. CHEN Jian-bing, SUN Wei-ling, LI Jie, XU Jun. Stochastic harmonic function representation of stochastic processes [J]. Journal of Applied Mechanics, 2013, 80: 1–11. DOI: https://doi.org/10.1115/1.4006936.

    Article  Google Scholar 

  15. XU Lei, ZHAI Wan-ming. Probabilistic assessment of railway vehicle-curved track systems considering track random irregularities [J]. Vehicle System Dynamics, 2018, 56(10): 1552–1576. DOI: https://doi.org/10.1080/00423114.2018.1424916.

    Article  Google Scholar 

  16. XU Lei, ZHANG Qiang, YU Zhi-wu, ZHU Zhi-hui. Vehicle-track interaction with consideration of rail irregularities at three-dimensional space [J]. Journal of Vibration and Control, 2020: 1802499863. DOI: https://doi.org/10.1177/1077546319894816.

  17. MOHAMMADZADEH S, SANGTARASHHA M, MOLATEFI H. A novel method to estimate derailment probability due to track geometric irregularities using reliability techniques and advanced simulation methods [J]. Archive of Applied Mechanics, 2011, 81(11): 1621–1637. DOI: https://doi.org/10.1007/s00419-011-0506-3.

    Article  Google Scholar 

  18. PERRIN G, SOIZE C, DUHAMEL D, FUNFSCHILLING C. Track irregularities stochastic modeling [J]. Probabilistic Engineering Mechanics, 2013, 34: 123–130. DOI: https://doi.org/10.1016/j.probengmech.2013.08.006.

    Article  Google Scholar 

  19. ZHU Meng-yi, CHENG Xiao-hui, MIAO Li-xin, SUN Xin-ya, WANG Shuai. Advanced stochastic modeling of railway track irregularities [J]. Advances in Mechanical Engineering, 2013, 5(6): 401637. DOI: https://doi.org/10.1155/2013/401637.

    Article  Google Scholar 

  20. JIN Z B, QIANG S Z, LI X Z. Perturbation method for trainbridge stochastic structure dynamic analysis [C]// Proceedings of the 3rd International Symposium on Environment Vibrations: Prediction, Monitoring, Mitigation and Evaluation. 2007: 400–405.

  21. MUSCOLINO G, RICCIARDI G, IMPOLLONIA N. Improved dynamic analysis of structures with mechanical uncertainties under deterministic input [J]. Probabilistic Engineering Mechanics, 2000, 15(2): 199–212. DOI: https://doi.org/10.1016/S0266-8920(99)00021-1.

    Article  Google Scholar 

  22. HUANG B, SERESH R F, ZHU L P. Statistical analysis of basic dynamic characteristics of large span cable-stayed bridge based on high order perturbation stochastic FEM [J]. Advances in Structural Engineering, 2013, 16(9): 1499–1512. DOI: https://doi.org/10.1260/1369-4332.16.9.1499.

    Article  Google Scholar 

  23. CAVDAR O, BAYRAKTAR A, ALTUNISIK A. Stochastic seismic analysis of komurhan highway bridge with varying material properties [J]. Civil Engineering and Environmental Systems, 2015, 32(3): 193–205. DOI: https://doi.org/10.1080/10286608.2015.1013796.

    Article  Google Scholar 

  24. XIN Li-feng, LI Xiao-zhen, ZHU Yan, LIU Ming. Uncertainty and sensitivity analysis for train-ballasted track-bridge system [J]. Vehicle System Dynamics, 2020, 58(3): 1–19. DOI: https://doi.org/10.1080/00423114.2019.1584678.

    Article  Google Scholar 

  25. WAN Hua-ping, NI Yi-qing. An efficient approach for dynamic global sensitivity analysis of stochastic train-track-bridge system [J]. Mechanical Systems and Signal Processing, 2019, 117: 843–861. DOI: https://doi.org/10.1016/j.ymssp.2018.08.018.

    Article  Google Scholar 

  26. HUA L K, WANG Y. Applications of number theory to numerical analysis [M]. Berlin, Heridelberg: Springer, 1981.

    MATH  Google Scholar 

  27. LI Jie, CHEN Jian-bing. Probability density evolution method for dynamic response analysis of structures with uncertain parameters [J]. Computational Mechanics, 2004, 34(5): 400–409. DOI: https://doi.org/10.1007/s00466-004-0583-8.

    Article  MATH  Google Scholar 

  28. LI Jie, CHEN Jian-bing. Stochastic dynamic of structures [M]. Singapore: John Wiley & Sons(Asia) Pte Ltd, 2009.

    Book  Google Scholar 

  29. LEI Xiao-yan. High speed railway track dynamics: Models, algorithms and applications [M]. Singapore: Springer, 2016.

    Google Scholar 

  30. CHEN Jian-bing, LI Jie. Dynamic response and reliability analysis of non-linear stochastic structures [J]. Probabilistic Engineering Mechanics, 2005, 20(1): 33–44. DOI: https://doi.org/10.1016/j.probengmech.2004.05.006.

    Article  Google Scholar 

  31. ZENG Qing-yuan, GUO Xiang-rong. Train-bridge time-variant system analysis theory and application [M]. Beijing, China: China Railway Press, 1999. (in Chinese)

    Google Scholar 

  32. YU Zhi-wu, MAO Jian-feng. A stochastic dynamic model of train-track-bridge coupled system based on probability density evolution method [J]. Applied Mathematical Modelling, 2018, 59: 205–232. DOI: https://doi.org/10.1016/j.apm.2018.01.038.

    Article  MathSciNet  MATH  Google Scholar 

  33. YU Zhi-wu, MAO Jian-feng. Probability analysis of traintrack-bridge interactions using a random wheel/rail contact model [J]. Engineering Structures, 2017, 144: 120–138. DOI: https://doi.org/10.1016/j.engstruct.2017.04.038.

    Article  Google Scholar 

  34. JOHNSON K L. Contact mechanics [M]. UK: Cambridge University Press, 1985.

    Book  Google Scholar 

  35. KALKER J J. Three-dmensional elastic bodies in rolling contact [M]. The Netherlands: Kluwer Academic Publishers, 1990.

    Book  MATH  Google Scholar 

  36. CHEN Guo, ZHAI Wan-ming. A new wheel/rail spatially dynamic coupling model and its verification [J]. Vehicle System Dynamics, 2004, 41(4): 301–322. DOI: https://doi.org/10.1080/00423110412331315178.

    Article  Google Scholar 

  37. KALKER J J. On the rolling contact of two elastic bodies in the presence of dry friction [D]. The Netherlands: Delft University, 1967.

    Google Scholar 

  38. FANG Kai-tai. Uniform design: Application of number-theoretic methods in experimental design [J]. Acta Math Appl Sin, 1980, 3(4): 363–372.

    Google Scholar 

  39. FANG Kai-tai, LIN D K. Uniform design in computer and physical experiments [C]// International Workshop on the Grammar of Technology Eevelopment. New York, 2008: 105–125.

  40. ZHOU Yong-dao, FANG Kai-tai. An efficient method for constructing uniform designs with large size [J]. Computational Statistics, 2013, 28(3): 1319–1331. DOI: https://doi.org/10.1007/s00180-012-0359-4.

    Article  MathSciNet  MATH  Google Scholar 

  41. XU Lei, ZHAI Wan-ming. A new model for temporal-spatial stochastic analysis of vehicle-track coupled systems [J]. Vehicle System Dynamics, 2017, 55(3): 427–448. DOI: https://doi.org/10.1080/00423114.2016.1270456.

    Article  Google Scholar 

  42. WEN De-zhi, ZHUO Ren-hong, DING Da-jie, ZHENG Hui, CHENG Jing, LI Zheng-hong. Generation of correlated pseudorandom variables in monte carlo simulation [J]. Acta Physica Sinica, 2012, 61(22): 514–518. DOI: https://doi.org/10.7498/aps.61.220204.

    Google Scholar 

  43. ROSENBLATT M. Remarks on a multivariate transformation [J]. Annals of Mathematical Statistics, 1952, 23(3): 470–472. DOI: https://doi.org/10.1007/978-l-4419-8339-8_8.

    Article  MathSciNet  MATH  Google Scholar 

  44. LI Jie, CHEN Jian-bing. Probability density evolution equations-A historical investigation [J]. Journal of Earthquake and Tsunami, 2009, 3(3): 209–226. DOI: https://doi.org/10.1142/S1793431109000536.

    Article  Google Scholar 

  45. LI Jie, CHEN Jian-bing. The principle of preservation of probability and the generalized density evolution equation [J]. Structural Safety, 2008, 30(1): 65–77. DOI:https://doi.org/10.1016/j.strusafe.2006.08.001.

    Article  MathSciNet  Google Scholar 

Download references

Funding

Projects(51708558, 51878673, U1734208, 52078485, U1934217, U1934209) supported by the National Natural Science Foundation of China; Project(2020JJ5740) supported by the Natural Science Foundation of Hunan Province, China; Project(KF2020-03) supported by the Key Open Fund of State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, China; Project (2020-Special-02) supported by the Science and Technology Research and Development Program of China Railway Group Limited

Author information

Authors and Affiliations

  1. School of Civil Engineering, Central South University, Changsha, 410075, China

    Jian-feng Mao  (毛建锋), Yuan-jie Xiao  (肖源杰), Zhi-wu Yu  (余志武), Erol Tutumluer & Zhi-hui Zhu  (朱志辉)

  2. National Engineering Laboratory for High-Speed Railway Construction, Changsha, 410075, China

    Jian-feng Mao  (毛建锋), Yuan-jie Xiao  (肖源杰), Zhi-wu Yu  (余志武), Erol Tutumluer & Zhi-hui Zhu  (朱志辉)

  3. Key Laboratory of Engineering Structures of Heavy Haul Railway of Ministry of Education, Central South University, Changsha, 410075, China

    Jian-feng Mao  (毛建锋), Yuan-jie Xiao  (肖源杰), Zhi-wu Yu  (余志武), Erol Tutumluer & Zhi-hui Zhu  (朱志辉)

  4. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Erol Tutumluer

Authors
  1. Jian-feng Mao  (毛建锋)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuan-jie Xiao  (肖源杰)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhi-wu Yu  (余志武)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Erol Tutumluer
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhi-hui Zhu  (朱志辉)
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The overarching research goals were developed by MAO Jian-feng and XIAO Yuan-jie, and they established the models, calculated the results and edited the draft of manuscript. YU Zhi-wu and Erol TUTUMLUER provided the concept of manuscript and improved the quality of manuscript. ZHU Zhi-hui helpd to establish the model and verified the calculation. All the authors replied to reviewers’ comments and revised the final version.

Corresponding author

Correspondence to Yuan-jie Xiao  (肖源杰).

Additional information

Conflict of interest

MAO Jian-feng, XIAO Yuan-jie, YU Zhi-wu, Erol TUTUMLUER and ZHU Zhi-hui declared that they have no conflicts of interest to this work.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mao, Jf., Xiao, Yj., Yu, Zw. et al. Probabilistic model and analysis of coupled train-ballasted track-subgrade system with uncertain structural parameters. J. Cent. South Univ. 28, 2238–2256 (2021). https://doi.org/10.1007/s11771-021-4765-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-021-4765-z

Key words

关键词

Search

Navigation