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Probability Distribution Functions of Maximum Wheel Unloading Rate Based on Extremal Index

Zi-Ji Zhou

https://orcid.org/0000-0002-3410-4196

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, P. R. China

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Nan Zhang

https://orcid.org/0000-0003-0215-2465

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, P. R. China

E-mail Address: nzhang@bjtu.edu.cn

Corresponding author.

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, and

Zhang-Ming Wang

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, P. R. China

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https://doi.org/10.1142/S0219455423500153Cited by:2 (Source: Crossref)

Abstract

To study the probabilistic distribution of maximum wheel unloading rate of high-speed trains and its temporal correlation when a train passes over a bridge, a method for the estimation of the extremal index is proposed. Using the time series threshold theory, the maximum value cumulative distribution function (CDF) when the wheel unloading rate is regarded as a time series is derived and validated. This approach can also address dependent series, which the traditional probability distribution function formulas could not. Then, the difference between treating the wheel unloading rate as a time series and independent series is investigated using Monte Carlo simulations. Finally, the influence of the number of calculation steps on the threshold is studied, and the differences between thresholds calculated by different extremal indices when considering the number of trains running during the service period of the bridge are explored. The maximum value CDFs of the wheel unloading rate for different track irregularities, bridge lengths, and vehicle speeds are investigated for a three-span simply-supported bridge. The results show that the differences in the maximum value probability density functions (PDFs) obtained by considering the wheel unloading rate as time series and independent random series cannot be ignored. However, when studying a high-confidence level problem, such as the threshold of the wheel unloading rate, the difference between the two approaches is small enough. As the number of calculation steps increases, the extremal index will gradually decrease. When considering a long-distance high-speed rail line, its shorter segment can be used to study the threshold of the wheel unloading rate.

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References

1. G. I. Schueeller , Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis — recent advances. Struct. Eng. Mech. 32(1) (2009) 1–20. Crossref, Web of Science, Google Scholar
2. W. Wang, Y. Zhang and H. J. Ouyang , Influence of random multi-point seismic excitations on the safety performance of a train running on a long-span bridge, Int. J. Struct. Stab. Dyn. 20(4) (2020) 2050054. Link, Web of Science, Google Scholar
3. A. Naess, B. J. Leira and O. Batsevych , System reliability analysis by enhanced Monte Carlo simulation, Struct. Saf. 31(5) (2009) 349–355. Crossref, Web of Science, Google Scholar
4. Y. B. Yang et al., State-of-the-art of the vehicle-based methods for detecting the various properties of highway bridges and railway tracks. Int. J. Struct. Stab. Dyn. 20(4) (2020) 2041004. Link, Web of Science, Google Scholar
5. B. P. Alduse et al., Effect of uncertainties in wind speed and direction on the fatigue damage of long-span bridges, Eng. Struct. 100 (2015) 468–478. Crossref, Web of Science, Google Scholar
6. V. Poliakov et al., Running safety of a high-speed train within a bridge zone, Int. J. Struct. Stab. Dyn. 20(13) (2020). Google Scholar
7. S. Mohammadzadeh, M. Sangtarashha and H. Molatefi , A novel method to estimate derailment probability due to track geometric irregularities using reliability techniques and advanced simulation methods, Arch. Appl. Mech. 81(11) (2011) 1621–1637. Crossref, Web of Science, Google Scholar
8. J. Li and J. B. Chen , Probability density evolution method for dynamic response analysis of structures with uncertain parameters, Comput. Mech. 34(5) (2004) 400–409. Crossref, Web of Science, Google Scholar
9. Z. W. Yu and J. F. Mao , Probability analysis of train $-$ $-$ track $-$ $-$ bridge interactions using a random wheel/rail contact model, Eng. Struct. 144(1) (2017) 120–138. Google Scholar
10. Z. W. Yu and A. Mao , A stochastic dynamic model of train–track–bridge coupled system based on probability density evolution method, Appl. Math. Model. 59 (2018) 205–232. Crossref, Web of Science, Google Scholar
11. J. H. Lin, Y. H. Zhang and Y. Zhao , Pseudo-excitation method and some recent developments, Procedia Eng. 14 (2011) 2453–2458. Crossref, Google Scholar
12. X. Z. Li, Y. Zhu and Z. B. Jin , Nonstationary random vibration performance of train–bridge coupling system with vertical track irregularity, Shock Vib. 2016 (2016) 1–19. Crossref, Web of Science, Google Scholar
13. Y. Zhu, X. Z. Li and Z. B. Jin , Three-dimensional random vibrations of a high-speed-train–bridge time-varying system with track irregularities, Proc. Inst. Mech. Eng. F J. Rail Rapid Transit 230(8) (2016) 1851–1876. Google Scholar
14. Y. Zhao, Y. H. Zhang and J. H. Lin , Random Vibration Analysis Method of Train Structure Interaction (Science Press, 2018). Google Scholar
15. X. H. He, K. Shi and T. Wu , An efficient analysis framework for high-speed train–bridge coupled vibration under non-stationary winds, Struct. Infrastruct. Eng. 16(9) (2020) 1326–1346. Crossref, Web of Science, Google Scholar
16. L. Hu and Y. L. Xu , Extreme value of typhoon-induced non-stationary buffeting response of long-span bridges, Probabilistic Eng. Mech. 36 (2014) 19–27. Crossref, Web of Science, Google Scholar
17. N. Zhang, Z. J. Zhou and Z. Z. Wu , Safety evaluation of a vehicle–bridge interaction system using the pseudo-excitation method, Railw. Eng. Sci. 30(1) (2022) 1–16. Crossref, Google Scholar
18. W. M. Zhai et al., High-speed train–track–bridge dynamic interactions Part II: Experimental validation and engineering application, Int. J. Rail Transp. 1(1–2) (2013) 25–41. Crossref, Google Scholar
19. N. Zhang and H. Xia , Dynamic analysis of coupled vehicle–bridge system based on inter-system iteration method, Comput. Struct. 114–115 (2013) 26–34. Crossref, Web of Science, Google Scholar
20. S. Resnick , Extreme Values, Extreme Value, Regular Variation, and Point Processes (Springer-Verlag, New York, 1987). Crossref, Google Scholar
21. M. R. Leadbetter, G. Lindgren and H. Rootzén , Extremes and Related Properties of Random Sequences and Processes (Springer, New York, 1983). Crossref, Google Scholar
22. D. J. Shi , Practical Extreme Value Statistical Method (Tianjin Science and Technology Press, 2006). Google Scholar
23. Z. J. Zhou, N. Zhang and Q. K. Sun , Research on probability statistics of train running safety indices based on pseudo-excitation method, Proc. Inst. Mech. Eng. F: J. Rail Rapid Transit 236(7) (2022) 863–873. Google Scholar
24. L. Xu, W. M. Zhai and J. M. Gao , A probabilistic model for track random irregularities in vehicle/track coupled dynamics, Appl. Math. Model. 51 (2017) 145–158. Crossref, Web of Science, Google Scholar
25. H. Xia, N. Zhang and W. W. Guo , Dynamic Interaction of Train–Bridge Systems in High-Speed Railways: Theory and Applications, (Beijing Jiaotong University Press, 2018). Crossref, Google Scholar