A full information expression model for track irregularity based on stochastic harmonic functions in vehicle–turnout structure stochastic vibration analysis

Abstract

Turnout irregularity significantly affects the stochastic vibration behavior of vehicle–turnout structures. This study proposes a fitting formula for the turnout irregularity spectrum and develops a turnout irregularity full information expression model (TIFIEM) using a stochastic harmonic function. The model is applied to vehicle–turnout structure stochastic vibration and reliability analysis. Findings suggest that the Hamming window method, with a window length of 4096 points, is optimal for estimating the turnout irregularity spectrum. It is recommended to fit the power spectral density (PSD) using a 5th-order polynomial for better accuracy. The TIFIEM effectively addresses randomness in amplitude, frequency, and phase. An analysis of 250 irregularity samples is sufficient for the desired accuracy. Additionally, the PSD amplitude at various frequency points follows a Chi-square distribution with 2° of freedom. Regions 3–7 m from the tip of the switch rail on the straight switch rail and 53–54 m on the point rail are most susceptible to wear. When the vehicle passes through the turnout at 300 km/h, the reliability of vehicle–turnout structures at the crossing panel decreases to 95.8%.

Keywords

High-speed railway / Vehicle–turnout coupling dynamics / Turnout irregularity spectrum / Stochastic harmonic function / Probability density evolution method

References

[1] CaiX, TangX, WangY, et al. . Advanced VTCDREM for dynamic reliability evaluation of railway systems: integration of fully probabilistic track irregularities and multifaceted random factors. J Sound Vib, 2024, 584: 118460.

[2] WeiL, ZengJ, LuoR, et al. . Carbody sway behaviour of railway vehicles due to track irregularity from rail alternate side wear. Railw Eng Sci, 2024, 33127-42.

[3] WangY, XiaoH, ZhangZ, et al. . The formation, development and classification of rail corrugation: a survey on Chinese metro. Railw Eng Sci, 2024, 33143-61.

[4] CaiX, TangX, YangF, et al. . Estimation of turnout irregularities using vehicle responses with improved BiLSTM and Gaussian process regression. Measurement, 2023, 221: 113513.

[5] ZengZ, ZhaoY, XuW, et al. . Random vibration analysis of train–bridge under track irregularities and traveling seismic waves using train–slab track–bridge interaction model. J Sound Vib, 2015, 342: 22-43.

[6] ChenG, ZhaiW. Numerical simulation of the stochastic process of railway track irregularities. J Southwest Jiaotong Univ, 1999, 342138-142in Chinese

[7] ChenCJ, LiHC. Track irregularity simulation in frequency domain sampling. J China Railw Soc, 2006, 28338-42in Chinese

[8] ZhouZ, ZhongK, ChenL, et al. . Numerical simulation of track stochastic irregularity and analysis of its effects on environmental vibration. J Railw Sci Eng, 2020, 2861410-1419in Chinese

[9] GaoJ. Comparative analysis of power spectrum density of ballastless track irregularities of Chinese high-speed railway. J Railw Sci Eng, 2015, 124715-723in Chinese

[10] XuL, ZhaoY, ZhuZ, et al. . Vehicle-track random vibrations considering spatial frequency coherence of track irregularities. Veh Syst Dyn, 2014, 60113977-3998.

[11] XuJ, WangP, MaX, et al. . Stiffness characteristics of high-speed railway turnout and the effect on the dynamic train-turnout interaction. Shock Vib, 2016, 1: 1258681

[12] MaX, WangP, WangJ, et al. . Study on impact of over-limit reduced value of switch rail on dynamic characteristics of switch. J China Railw Soc, 2016, 38398-105in Chinese

[13] XuL, LiuX. Matrix coupled model for the vehicle–track interaction analysis featured to the railway crossing. Mech Syst Signal Process, 2021, 152: 107485.

[14] ChiouSB, YenJY. Modeling of railway turnout geometry in the frog area with the vehicle wheel trajectory. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2018, 23261598-1614.

[15] BossoN, BraccialiA, MegnaG, et al. . Effects of geometric track irregularities on vehicle dynamic behaviour when running through a turnout. Veh Syst Dyn, 2023, 613782-798.

[16] XinL, MarkineVL, ShevtsovIY. Numerical procedure for fatigue life prediction for railway turnout crossings using explicit finite element approach. Wear, 2016, 366–367: 167-179.

[17] XinL, MarkineVL, ShevtsovIY. Numerical analysis of the dynamic interaction between wheel set and turnout crossing using the explicit finite element method. Veh Syst Dyn, 2016, 543301-327.

[18] KaewunruenS, RemennikovAM, DindarS. Influence of asymmetrical topology on structural behaviours of bearers and sleepers in turnout switches and crossings. Recent developments in railway track and transportation engineering, 2017ChamSpringer51-60

[19] LinJ, BaiT, XuJ, WangK, HeA, QianY, WangP. Analysis of the wheel-rail dynamic response characteristics and damage to the fixed frog of the No. 3 tram turnout. Eng Fail Anal, 2024, 156: 107872.

[20] LinJ, ZhangYVirtual excitation method for random vibrations, 2004Beijing (in Chinese)Science Press

[21] JieL, ChenJ. Probability density evolution equations—a historical investigation. J Earthq Tsunami, 2013, 3: 209-226.

[22] YuZW, MaoJF. A stochastic dynamic model of train–track–bridge coupled system based on probability density evolution method. Appl Math Model, 2018, 59: 205-232.

[23] YuZW, MaoJF. Probability analysis of train–track–bridge interactions using a random wheel/rail contact model. Eng Struct, 2017, 144: 120-138.

[24] TangX, CaiX, WangY, et al. . An improved solution of the probability density evolution equation for analyzing stochastic structural responses with adaptive time steps and initial conditions. Eng Struct, 2024, 321: 118917.

[25] TangX, CaiX, LiuW, et al. . A novel model for vehicle/turnout nonlinear random vibration analysis based on full probability irregularity spectrum. Nonlinear Dyn, 2024, 1121916983-17005.

[26] LiuL, WeiS, ZhaoY, et al. . Development and validation of GJ-6 track inspection system. Railw Tech Innov, 2015, 2: 53-56in Chinese

[27] LiuXA study of the track irregularity spectrum of railway main lines, 2006BeijingBeijing Jiaotong University2006

[28] YangF, ZhaiW, GaoJ, et al. . PSD of ballastless track irregularities of high-speed railway. Sci Sin Tech, 2014, 447687-696.

[29] WelchP. The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans Audio Electroacoust, 1967, 15270-73.

[30] SchusterA. On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena. Terr Magn, 1898, 3113-41

[31] KaySM, MarpleSL. Spectrum analysis—a modern perspective. Proc IEEE, 1981, 69111380-1419.

[32] LiuYH, LiF, HuangYH. Numerical simulation methods of railway track irregularities. J Traffic Transp Eng, 2006, 6129-33

[33] SunW, ChenJ, LiJ. Stochastic harmonic functions of second kind for spectral representations. J Tongji Univ (Natural Science Edition), 2011, 39111413-1419

[34] LiuY, SunJ, LiW. Dynamic response of flexible wheelset high-speed train passing through turnouts. J Qingdao Univ (Natural Science Edition), 2024, 37169-78in Chinese

[35] WangK. The track of wheel contact points and the calculation of wheel/rail geometric contact parameters. J Southwest Jiaotong Univ, 1984, 1: 89-99in Chinese

[36] Xu J (2015) Simulation and analysis research on the abrasion of curved tip rail of high-speed turnout. Dissertation, Southwest Jiaotong University

[37] MaoJF, XiaoY, YuZW, et al. . Probabilistic model and analysis of coupled train-ballasted track-subgrade system with uncertain structural parameters. J Cent South Univ, 2019, 2872238-2256.

[38] MaoJ, YuZ, JiangL. Stochastic analysis of vehicle-bridge coupled interaction and uncertainty bounds of random responses in heavy haul railways. Int J Str Stab Dyn, 2019, 19121950144.

[39] AndersonJComputational fluid dynamics, 1995New YorkMcGraw-Hill Education

[40] ChenJB, LiJ. Dynamic response and reliability analysis of non-linear stochastic structures. Probab Eng Mech, 2005, 20133-44.

[41] State Administration of Market Regulation, National Standardization Administration (2019) Specification for dynamic performance assessment and testing verification of rolling stock, GB/T 5599-2019 (in Chinese)

Funding

National Key R&D Program of China(2022YFB2602901)

National Natural Science Foundation of China(52178405)

Project of Science and Technology Research and Development Program of China State Railway Group Co., Ltd.(K2022G038)

RIGHTS & PERMISSIONS

The Author(s)