{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:38:22Z","timestamp":1760146702987,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,4]],"date-time":"2024-12-04T00:00:00Z","timestamp":1733270400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R and D Program of China","doi-asserted-by":"publisher","award":["2021YFF0501101","62173137","23A0426"],"award-info":[{"award-number":["2021YFF0501101","62173137","23A0426"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021YFF0501101","62173137","23A0426"],"award-info":[{"award-number":["2021YFF0501101","62173137","23A0426"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Project of Hunan Provincial Department of Education","award":["2021YFF0501101","62173137","23A0426"],"award-info":[{"award-number":["2021YFF0501101","62173137","23A0426"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["BDCC"],"abstract":"<jats:p>The suspension parameters of heavy-duty freight trains can deviate from their initial design values due to material aging and performance degradation. While traditional multibody dynamics simulation models are usually designed for fixed working conditions, it is difficult for them to adequately analyze the safety status of the vehicle\u2013line system in actual operation. To address this issue, this research provides a suspension parameter estimation technique based on CNN-GRU. Firstly, a prototype C80 train was utilized to build a simulation model for multibody dynamics. Secondly, six key suspension parameters for wheel\u2013rail force were selected using the Sobol global sensitivity analysis method. Then, a CNN-GRU proxy model was constructed, with the actually measured wheel\u2013rail forces as a reference. By combining this approach with NSGA-II (Non-dominated Sorting Genetic Algorithm II), the key suspension parameters were calculated. Finally, the estimated parameter values were applied into the vehicle\u2013line coupled multibody dynamical model and validated. The results show that, with the corrected dynamical model, the relative errors of the simulated wheel\u2013rail force are reduced from 9.28%, 6.24% and 18.11% to 7%, 4.52% and 10.44%, corresponding to straight, curve, and long and steep uphill conditions, respectively. The wheel\u2013rail force simulation\u2019s precision is increased, indicating that the proposed method is effective in estimating the suspension parameters for heavy-duty freight trains.<\/jats:p>","DOI":"10.3390\/bdcc8120181","type":"journal-article","created":{"date-parts":[[2024,12,4]],"date-time":"2024-12-04T10:07:10Z","timestamp":1733306830000},"page":"181","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Suspension Parameter Estimation Method for Heavy-Duty Freight Trains Based on Deep Learning"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7439-1775","authenticated-orcid":false,"given":"Changfan","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Railway Transportation, Hunan University of Technology, Zhuzhou 412007, China"}]},{"given":"Yuxuan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Railway Transportation, Hunan University of Technology, Zhuzhou 412007, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3650-3270","authenticated-orcid":false,"given":"Jing","family":"He","sequence":"additional","affiliation":[{"name":"College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"107617","DOI":"10.1016\/j.aap.2024.107617","article-title":"Enhancing rail safety through real-time defect detection: A novel lightweight network approach","volume":"203","author":"Cao","year":"2024","journal-title":"Accid. Anal. Prev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1016\/j.psep.2024.06.008","article-title":"Predicting the remaining useful life of rails based on improved deep spiking residual neural network","volume":"188","author":"He","year":"2024","journal-title":"Process Saf. Environ. Prot."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.jsr.2021.11.012","article-title":"Impact of mountainous interstate alignments and truck configurations on rollover propensity","volume":"80","author":"Alrejjal","year":"2022","journal-title":"J. Saf. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2456","DOI":"10.1080\/00423114.2022.2113807","article-title":"Dynamic simulation of a heavy-haul freight car under abnormal braking application on tangent and curve","volume":"61","author":"Ramos","year":"2023","journal-title":"Veh. Syst. Dyn."},{"doi-asserted-by":"crossref","unstructured":"Wang, Q., Jiang, X., Zeng, J., Mao, R., Wei, L., and Wu, S. (2024). Innovative method for high-speed railway carbody vibration control caused by hunting instability using underframe suspended equipment. J. Vib. Control, 10775463241272954.","key":"ref_5","DOI":"10.1177\/10775463241272954"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.apm.2024.05.015","article-title":"Adaptive nonlinear damping control of active secondary suspension for hunting stability of high-speed trains","volume":"133","author":"Zhang","year":"2024","journal-title":"Appl. Math. Model."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7561","DOI":"10.1109\/TVT.2024.3351763","article-title":"Prediction of Remaining Useful Life of Railway Tracks based on DMGDCC-GRU Hybrid Model and Transfer Learning","volume":"73","author":"Liu","year":"2024","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"107530","DOI":"10.1016\/j.ress.2021.107530","article-title":"Machine learning for reliability engineering and safety applications: Review of current status and future opportunities","volume":"211","author":"Xu","year":"2021","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_9","first-page":"5003815","article-title":"LLD-MFCOS: A Multi-scale Anchor-Free Detector Based on Label Localization Distillation for Wheelset Tread Defect Detection","volume":"73","author":"Yang","year":"2023","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5496","DOI":"10.1109\/LRA.2023.3285076","article-title":"Danet: Density adaptive convolutional network with interactive attention for 3d point clouds","volume":"8","author":"He","year":"2023","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"122755","DOI":"10.1016\/j.eswa.2023.122755","article-title":"EFRNet-VL: An end-to-end feature refinement network for monocular visual localization in dynamic environments","volume":"243","author":"Wang","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1016\/j.matcom.2021.08.016","article-title":"Passive vehicle suspension system optimization using Harris Hawk Optimization algorithm","volume":"191","author":"Issa","year":"2022","journal-title":"Math. Comput. Simul."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"139","DOI":"10.3901\/JME.2023.12.139","article-title":"Approximate Bayesian Estimation of Suspension Parameters of In-service High-speed Trains Based on Kriging Surrogate Model","volume":"59","author":"He","year":"2023","journal-title":"J. Mech. Eng."},{"doi-asserted-by":"crossref","unstructured":"Zou, H., Wu, Q., and Zou, X. (2022). Research on optimization design of suspension parameters of railway vehicle bogies based on surrogate model. Multimed. Tools Appl., 1\u201319.","key":"ref_14","DOI":"10.1007\/s11042-022-14022-4"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"108950","DOI":"10.1016\/j.ress.2022.108950","article-title":"Machine learning approaches to estimate suspension parameters for performance degradation assessment using accurate dynamic simulations","volume":"230","author":"Pan","year":"2023","journal-title":"Reliab. Eng. Syst. Saf."},{"unstructured":"Zhou, S. (2013). SIMPACK 9 Example Tutorial, Beijing United Publishing Company.","key":"ref_16"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"103375","DOI":"10.1016\/j.advengsoft.2022.103375","article-title":"Multiobjective optimization framework for designing a vehicle suspension system. A comparison of optimization algorithms","volume":"176","author":"Rubio","year":"2023","journal-title":"Adv. Eng. Softw."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"16107","DOI":"10.1109\/TITS.2024.3409716","article-title":"Robust Constraint-Following Control for Bio-Inspired Structure Oriented Active Suspension System of High-Speed Trains","volume":"25","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_19","first-page":"80","article-title":"Multi-objective optimization for dynamics parameters of high-speed trains under side wind","volume":"20","author":"Tian","year":"2020","journal-title":"J. Traffic Transp. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/s40534-021-00252-z","article-title":"Deep learning-based fault diagnostic network of high-speed train secondary suspension systems for immunity to track irregularities and wheel wear","volume":"30","author":"Ye","year":"2022","journal-title":"Railw. Eng. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6721","DOI":"10.1007\/s00521-024-09424-4","article-title":"SRIME: A strengthened RIME with Latin hypercube sampling and embedded distance-based selection for engineering optimization problems","volume":"36","author":"Zhong","year":"2024","journal-title":"Neural Comput. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"109945","DOI":"10.1016\/j.ress.2024.109945","article-title":"On active learning for Gaussian process-based global sensitivity analysis","volume":"245","author":"Chauhan","year":"2024","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"128895","DOI":"10.1016\/j.jhydrol.2022.128895","article-title":"Global sensitivity analysis of bioretention cell design for stormwater system: A comparison of VARS framework and Sobol method","volume":"617","author":"Tansar","year":"2023","journal-title":"J. Hydrol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"112008","DOI":"10.1016\/j.asoc.2024.112008","article-title":"Application of CNN for multiple phase corrosion identification and region detection","volume":"164","author":"Oyedeji","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3085","DOI":"10.1007\/s11042-022-13339-4","article-title":"An efficient two-state GRU based on feature attention mechanism for sentiment analysis","volume":"83","author":"Zulqarnain","year":"2024","journal-title":"Multimed. Tools Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"15217","DOI":"10.1007\/s10462-023-10526-z","article-title":"A comprehensive survey on NSGA-II for multi-objective optimization and applications","volume":"56","author":"Ma","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"119429","DOI":"10.1016\/j.jenvman.2023.119429","article-title":"Combination of coagulation and adsorption technologies for advanced wastewater treatment for potable water reuse: By ANN, NSGA-II, and RSM","volume":"349","author":"Zahmatkesh","year":"2024","journal-title":"J. Environ. Manag."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"130326","DOI":"10.1016\/j.energy.2024.130326","article-title":"Fault diagnosis of hydro-turbine via the incorporation of bayesian algorithm optimized CNN-LSTM neural network","volume":"290","author":"Dao","year":"2024","journal-title":"Energy"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"109600","DOI":"10.1016\/j.ress.2023.109600","article-title":"An efficient sequential anisotropic RBF reliability analysis method with fast cross-validation and parallelizability","volume":"241","author":"Li","year":"2024","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"127284","DOI":"10.1016\/j.neucom.2024.127284","article-title":"An optimized CNN-BiLSTM network for bearing fault diagnosis under multiple working conditions with limited training samples","volume":"574","author":"Song","year":"2024","journal-title":"Neurocomputing"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s10231-023-01356-5","article-title":"Convergence in relative error for the porous medium equation in a tube","volume":"203","author":"Audrito","year":"2024","journal-title":"Ann. Di Mat. Pura Ed Appl."},{"doi-asserted-by":"crossref","unstructured":"Wang, N., Liu, Y., Wang, Z., Wei, Z., Tang, R., Tang, P., and Yu, G. (2024). Locally differentially private frequency distribution estimation with relative error optimization. Front. Comput. 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