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

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.

Keywords

coupled train-ballast-subgrade system / structural parameter uncertainty / stochastic dynamic analysis / probability density evolution method / wheel-rail interaction

References

[1] ZhaiW-M, XiaH, CaiC-B, GaoM-M, LiX-Z, GuoX-R, ZhangN, WangK-Y. High-speed train-track-bridge dynamic interactions-part I: Theoretical model and numerical simulation [J]. International Journal of Rail Transportation, 2013, 1: 1-24

[2] ZhaiW-MVehicle-track coupling dynamics (fourth edition) [M], 2015, Beijing, China, Science Press(in Chinese)

[3] SunY Q, DhanasekarM 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

[4] ZakeriJ, XiaH, FanJ-J. Dynamic responses of train-track system to single rail irregularity [J]. Latin American Journal of Solids & Structures, 2009, 6(2): 89-104

[5] Kardas-CinalE. 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

[6] RecueroA M, EscalonaJ 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

[7] LeiX-Y, WangJ. 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

[8] YangY B, YauD J, WuS YVehicle-bridge interaction dynamics:with applications to high-speed rail [M], 2004, Singapore, World Scientific Pub Co Inc

[9] ZhaiW-M, WangK-Y, CaiC-B. Fundamentals of vehicle-track coupled dynamics [J]. Vehicle System Dynamics, 2009, 47(11): 1349-1376

[10] XiaH, ZhangN. Dynamic analysis of railway bridge under high-speed trains [J]. Computers & Structures, 2005, 83(2324): 1891-1901

[11] IyengarR N, JaiswalO R. A new model for non-gaussian random excitations [J]. Probabilistic Engineering Mechanics, 1993, 8(34): 281-287

[12] IyengarR N, JaiswalO R. Random field modeling of railway track irregularities [J]. Journal of Transportation Engineering, 1997, 121(4): 303-308

[13] YuZ-W, MaoJ-F, GuoF-Q, GuoW. 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(SupplementC): 173-189

[14] ChenJ-B, SunW-L, LiJ, XuJ. Stochastic harmonic function representation of stochastic processes [J]. Journal of Applied Mechanics, 2013, 80: 1-11

[15] XuL, ZhaiW-M. Probabilistic assessment of railway vehicle-curved track systems considering track random irregularities [J]. Vehicle System Dynamics, 2018, 56(10): 1552-1576

[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] MohammadzadehS, SangtarashhaM, MolatefiH. 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

[18] PerrinG, SoizeC, DuhamelD, FunfschillingC. Track irregularities stochastic modeling [J]. Probabilistic Engineering Mechanics, 2013, 34: 123-130

[19] ZhuM-Y, ChengX-H, MiaoL-X, SunX-Y, WangS. Advanced stochastic modeling of railway track irregularities [J]. Advances in Mechanical Engineering, 2013, 5(6): 401637

[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] MuscolinoG, RicciardiG, ImpolloniaN. Improved dynamic analysis of structures with mechanical uncertainties under deterministic input [J]. Probabilistic Engineering Mechanics, 2000, 152199-212

[22] HuangB, SereshR F, ZhuL 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

[23] CavdarO, BayraktarA, AltunisikA. Stochastic seismic analysis of komurhan highway bridge with varying material properties [J]. Civil Engineering and Environmental Systems, 2015, 32(3): 193-205

[24] XinL-F, LiX-Z, ZhuY, LiuM. Uncertainty and sensitivity analysis for train-ballasted track-bridge system [J]. Vehicle System Dynamics, 2020, 58(3): 1-19

[25] WanH-P, NiY-Q. An efficient approach for dynamic global sensitivity analysis of stochastic train-track-bridge system [J]. Mechanical Systems and Signal Processing, 2019, 117: 843-861

[26] HuaL K, WangYApplications of number theory to numerical analysis [M], 1981, Berlin, Heridelberg, Springer

[27] LiJ, ChenJ-B. Probability density evolution method for dynamic response analysis of structures with uncertain parameters [J]. Computational Mechanics, 2004, 34(5): 400-409

[28] LiJ, ChenJ-BStochastic dynamic of structures [M], 2009, Singapore, John Wiley & Sons(Asia) Pte Ltd

[29] LeiX-YHigh speed railway track dynamics: Models, algorithms and applications [M], 2016, Singapore, Springer

[30] ChenJ-B, LiJ. Dynamic response and reliability analysis of non-linear stochastic structures [J]. Probabilistic Engineering Mechanics, 2005, 20(1): 33-44

[31] ZengQ-Y, GuoX-RTrain-bridge time-variant system analysis theory and application [M], 1999, Beijing, China, China Railway Press(in Chinese)

[32] YuZ-W, MaoJ-F. A stochastic dynamic model of train-track-bridge coupled system based on probability density evolution method [J]. Applied Mathematical Modelling, 2018, 59: 205-232

[33] YuZ-W, MaoJ-F. Probability analysis of traintrack-bridge interactions using a random wheel/rail contact model [J]. Engineering Structures, 2017, 144: 120-138

[34] JohnsonK LContact mechanics [M], 1985, UK, Cambridge University Press

[35] KalkerJ JThree-dmensional elastic bodies in rolling contact [M], 1990, The Netherlands, Kluwer Academic Publishers

[36] ChenG, ZhaiW-M. A new wheel/rail spatially dynamic coupling model and its verification [J]. Vehicle System Dynamics, 2004, 41(4): 301-322

[37] KalkerJ JOn the rolling contact of two elastic bodies in the presence of dry friction [D], 1967, The Netherlands, Delft University

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

[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] ZhouY-D, FangK-T. An efficient method for constructing uniform designs with large size [J]. Computational Statistics, 2013, 28(3): 1319-1331

[41] XuL, ZhaiW-M. A new model for temporal-spatial stochastic analysis of vehicle-track coupled systems [J]. Vehicle System Dynamics, 2017, 55(3): 427-448

[42] WenD-Z, ZhuoR-H, DingD-J, ZhengH, ChengJ, LiZ-H. Generation of correlated pseudorandom variables in monte carlo simulation [J]. Acta Physica Sinica, 2012, 61(22): 514-518

[43] RosenblattM. Remarks on a multivariate transformation [J]. Annals of Mathematical Statistics, 1952, 23(3): 470-472

[44] LiJ, ChenJ-B. Probability density evolution equations-A historical investigation [J]. Journal of Earthquake and Tsunami, 2009, 3(3): 209-226

[45] LiJ, ChenJ-B. The principle of preservation of probability and the generalized density evolution equation [J]. Structural Safety, 2008, 30(1): 65-77