IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v257y2025ipas0951832025000304.html
   My bibliography  Save this article

A novel hybrid approach combining PDEM and bayesian optimization deep learning for stochastic vibration analysis in train-track-bridge coupled system

Author

Listed:
  • Mao, Jianfeng
  • Li, Zheng
  • Yu, Zhiwu
  • Hu, Lianjun
  • Khan, Mansoor
  • Wu, Jun

Abstract

Train-track-bridge (TTB) system is a highly stochastic dynamical system. Deep learning has been applied to stochastic vibration analysis of TTB systems in recent years. However, most machine learning models consider only a single numerical relationship between input data and output responses. This often results in a strong dependence on training data, leading to a lack of robustness and reliability. In this paper, a novel hybrid method combining the probability density evolution method (PDEM) with an improved Bayesian optimization (BO) deep learning model (IDLM) is proposed for the efficient stochastic vibration analysis of uncertain TTB systems. This approach facilitates information exchange between the train-bridge model and the deep learning model. In this approach, PDEM is integrated into the deep learning framework to achieve a cohesive integration of physical and numerical models. The applicability of the PDEM-IDLM method is verified by comparing the predicted stochastic responses with the results of a validated train-bridge model. Furthermore, a case study investigates the effects of training dataset size, vehicle speed, and noise level, providing additional validation of the robustness of the proposed method.

Suggested Citation

  • Mao, Jianfeng & Li, Zheng & Yu, Zhiwu & Hu, Lianjun & Khan, Mansoor & Wu, Jun, 2025. "A novel hybrid approach combining PDEM and bayesian optimization deep learning for stochastic vibration analysis in train-track-bridge coupled system," Reliability Engineering and System Safety, Elsevier, vol. 257(PA).
    • Handle: RePEc:eee:reensy:v:257:y:2025:i:pa:s0951832025000304
    DOI: 10.1016/j.ress.2025.110827
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832025000304
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2025.110827?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Han, Xiaohui & Dong, Jianping, 2023. "Applications of fractional gradient descent method with adaptive momentum in BP neural networks," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    2. Wang, Hui & Wang, Shuhui & Yang, Ronggang & Xiang, Jiawei, 2024. "An optimized dynamic model improved deep discriminative transfer learning network for fault detection in rotation vector reducers," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    3. Dao, Fang & Zeng, Yun & Qian, Jing, 2024. "Fault diagnosis of hydro-turbine via the incorporation of bayesian algorithm optimized CNN-LSTM neural network," Energy, Elsevier, vol. 290(C).
    4. Chan, Jianpeng & Papaioannou, Iason & Straub, Daniel, 2024. "Bayesian improved cross entropy method with categorical mixture models for network reliability assessment," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    5. Fu, Song & Lin, Lin & Wang, Yue & Guo, Feng & Zhao, Minghang & Zhong, Baihong & Zhong, Shisheng, 2024. "MCA-DTCN: A novel dual-task temporal convolutional network with multi-channel attention for first prediction time detection and remaining useful life prediction," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    6. Zhang, Xinyu & Liu, Chu-An, 2023. "Model averaging prediction by K-fold cross-validation," Journal of Econometrics, Elsevier, vol. 235(1), pages 280-301.
    7. Shang, Yue & Nogal, Maria & Teixeira, Rui & Wolfert, A.R. (Rogier) M., 2024. "Extreme-oriented sensitivity analysis using sparse polynomial chaos expansion. Application to train–track–bridge systems," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    8. Cheng, Yue & Fang, Genshen & Zhao, Lin & Hong, Xu & Ge, Yaojun, 2024. "Uncertainty propagation of flutter analysis for long-span bridges using probability density evolution method," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    9. Li, Long & Xu, Jun & Kuok, Sin-Chi, 2024. "Bayesian sparse grid (BSG) approach for information salvage in reliability assessment of deteriorating structures," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tang, Xueyang & Cai, Xiaopei & Wang, Yuqi & Wang, Pu & Yang, Fei, 2025. "Advanced VTSDREF for vehicle-turnout system dynamic reliability analysis: Integration of hybrid deep learning and adaptive probability density evolution method," Reliability Engineering and System Safety, Elsevier, vol. 256(C).
    2. Tianshu Shao & Xiangdong Xu & Yuelong Su, 2025. "Evaluation and Prediction of Agricultural Water Use Efficiency in the Jianghan Plain Based on the Tent-SSA-BPNN Model," Agriculture, MDPI, vol. 15(2), pages 1-32, January.
    3. Ma, Qiuju & Chen, Zhennan & Chen, Jianhua & Sun, Yubo & Chen, Nan & Du, Mengzhen, 2025. "Assist in real-time risk evaluation induced by electrical cabinet fires in nuclear power plants: A dual AI framework employing BiTCN and TCNN," Reliability Engineering and System Safety, Elsevier, vol. 260(C).
    4. Zhang, Hu & Tian, Wei & Tan, Jingyuan & Yin, Juchao & Fu, Xing, 2024. "Sensitivity analysis of multiple time-scale building energy using Bayesian adaptive spline surfaces," Applied Energy, Elsevier, vol. 363(C).
    5. Zhang, Hui & Zhou, Shenglong & Li, Geoffrey Ye & Xiu, Naihua & Wang, Yiju, 2025. "A step function based recursion method for 0/1 deep neural networks," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    6. Luo, Run & Li, Yadong & Guo, Huiyu & Wang, Qi & Wang, Xiaolie, 2024. "Cross-operating-condition fault diagnosis of a small module reactor based on CNN-LSTM transfer learning with limited data," Energy, Elsevier, vol. 313(C).
    7. Liu, Shaoyang & Wei, Jingfeng & Li, Guofa & He, Jialong & Zhang, Baodong & Liu, Bo, 2025. "A two-stage remaining useful life prediction method based on adaptive feature metric and graph spatiotemporal attention rule learning," Reliability Engineering and System Safety, Elsevier, vol. 257(PA).
    8. Wang, Chen & Zhang, Liming & Chen, Ling & Tan, Tian & Zhang, Cong, 2025. "Remaining useful life prediction of nuclear reactor control rod drive mechanism based on dynamic temporal convolutional network," Reliability Engineering and System Safety, Elsevier, vol. 253(C).
    9. Han, Fucheng & Wang, Wenhua & Zheng, Xiao-Wei & Han, Xu & Shi, Wei & Li, Xin, 2025. "Investigation of essential parameters for the design of offshore wind turbine based on structural reliability," Reliability Engineering and System Safety, Elsevier, vol. 254(PA).
    10. Wang, Wei & Song, Honghao & Si, Shubin & Lu, Wenhao & Cai, Zhiqiang, 2024. "Data augmentation based on diffusion probabilistic model for remaining useful life estimation of aero-engines," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    11. A., Faizanbasha & Rizwan, U., 2025. "Deep learning-stochastic ensemble for RUL prediction and predictive maintenance with dynamic mission abort policies," Reliability Engineering and System Safety, Elsevier, vol. 259(C).
    12. Chen, Haoyu & Huang, Hai & Zheng, Yong & Yang, Bing, 2024. "A load forecasting approach for integrated energy systems based on aggregation hybrid modal decomposition and combined model," Applied Energy, Elsevier, vol. 375(C).
    13. Ren, Xiangyu & Qin, Yong & Li, Bin & Wang, Biao & Yi, Xiaojian & Jia, Limin, 2024. "A core space gradient projection-based continual learning framework for remaining useful life prediction of machinery under variable operating conditions," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    14. Rongjun Cheng & Qinyin Li & Fuzhou Chen & Baobin Miao, 2024. "A Dual-Stage Attention-Based Vehicle Speed Prediction Model Considering Driver Heterogeneity with Fuel Consumption and Emissions Analysis," Sustainability, MDPI, vol. 16(4), pages 1-24, February.
    15. Sotirios Kontogiannis & George Kokkonis & Christos Pikridas, 2025. "Proposed Long Short-Term Memory Model Utilizing Multiple Strands for Enhanced Forecasting and Classification of Sensory Measurements," Mathematics, MDPI, vol. 13(8), pages 1-23, April.
    16. Xinyao, Xu & Xiaolei, Zhou & Qiang, Fan & Hao, Yan & Fangxiao, Wang, 2025. "A global attention based gated temporal convolutional network for machine remaining useful life prediction," Reliability Engineering and System Safety, Elsevier, vol. 260(C).
    17. Wang, Junwei & Xiong, Weili & Ding, Feng & Zhou, Yihong & Yang, Erfu, 2025. "Parameter estimation method for separable fractional-order Hammerstein nonlinear systems based on the on-line measurements," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    18. Long, Jian & Huang, Cheng & Deng, Kai & Wan, Lei & Hu, Guihua & Zhang, Feng, 2024. "Novel hybrid data-driven modeling integrating variational modal decomposition and dual-stage self-attention model: Applied to industrial petrochemical process," Energy, Elsevier, vol. 304(C).
    19. Liang, Tao & Wang, Fuli & Wang, Shu & Li, Kang & Mo, Xuelei & Lu, Di, 2024. "Machinery health prognostic with uncertainty for mineral processing using TSC-TimeGAN," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    20. Haowen Bao & Zongwu Cai & Yuying Sun & Shouyang Wang, 2023. "Penalized Optimal Forecast Combination for Quantile Regressions," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202514, University of Kansas, Department of Economics, revised May 2025.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:257:y:2025:i:pa:s0951832025000304. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.