{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T04:17:27Z","timestamp":1783138647618,"version":"3.54.6"},"reference-count":41,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T00:00:00Z","timestamp":1709856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004761","name":"Natural Science Foundation of Hainan Province","doi-asserted-by":"publisher","award":["2019RC144"],"award-info":[{"award-number":["2019RC144"]}],"id":[{"id":"10.13039\/501100004761","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Electric vehicles with hub motors have integrated the motor into the wheel, which increase the unsprung mass of the vehicle, and intensifies the vibration of the underspring components. The motor excitation during driving also intensifies the wheel vibration. The coupling effect between the two makes the performance of electric vehicles deteriorate. The article employed a disc-type permanent-magnet motor as the hub motor, taking into consideration the increase in sprung mass caused by the hub motor and the adverse effects of vertical vibration from motor excitation. Based on random road-surface excitation, and considering the secondary excitation caused by wheel motor drive and vehicle-road coupling, a coupled-dynamics model of a semi-active-suspension vehicle-road system for vertical vehicle motion is investigated under multiple excitations. Using body acceleration, suspension deflection, and dynamic tire load as evaluation indicators, a BP neural network PID controller based on the sparrow search algorithm optimization is proposed for the semi-active-suspension system. Compared with PID control and particle swarm optimization (PSO-BPNN-PID), the research findings indicate that the optimized semi-active suspension significantly improves the ride comfort of hub-motor electric vehicles, and meets the requirements for control performance under different vehicle driving conditions.<\/jats:p>","DOI":"10.3390\/s24061757","type":"journal-article","created":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T10:10:52Z","timestamp":1709892652000},"page":"1757","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Optimization of the Semi-Active-Suspension Control of BP Neural Network PID Based on the Sparrow Search Algorithm"],"prefix":"10.3390","volume":"24","author":[{"given":"Mei","family":"Li","sequence":"first","affiliation":[{"name":"Mechanical and Electrical Engineering College, Hainan University, Haikou 570100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Xu","sequence":"additional","affiliation":[{"name":"Mechanical and Electrical Engineering College, Hainan University, Haikou 570100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zelong","family":"Wang","sequence":"additional","affiliation":[{"name":"Mechanical and Electrical Engineering College, Hainan University, Haikou 570100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuaihang","family":"Liu","sequence":"additional","affiliation":[{"name":"Mechanical and Electrical Engineering College, Hainan University, Haikou 570100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.rser.2015.04.130","article-title":"A review on the state-of-the-art technologies of electric vehicle, its impacts and prospects","volume":"49","author":"Yong","year":"2015","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.trd.2018.02.009","article-title":"Forecasting electricity demand of electric vehicles by analyzing consumers\u2019 charging patterns","volume":"62","author":"Moon","year":"2018","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"He, S., Fan, X., Wang, Q., Chen, X., and Zhu, S. (2022). Review on torque distribution scheme of four-wheel hub motor electric vehicle. Machines, 10.","DOI":"10.3390\/machines10080619"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"6623","DOI":"10.1016\/j.jsv.2014.07.016","article-title":"Vibration of vehicle\u2013pavement coupled system based on a Timoshenko beam on a nonlinear foundation","volume":"333","author":"Ding","year":"2014","journal-title":"J. Sound Vib."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.soildyn.2016.01.016","article-title":"An analytical method for evaluating highway embankment responses with consideration of dynamic wheel\u2013pavement interactions","volume":"83","author":"Lu","year":"2016","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1080\/10298436.2018.1562189","article-title":"Dynamics of vehicle\u2013pavement system based on a viscoelastic Euler\u2013Bernoulli beam model","volume":"21","author":"Snehasagar","year":"2020","journal-title":"Int. J. Pavement Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"021001","DOI":"10.1115\/1.4006784","article-title":"A nonlinear vehicle-road coupled model for dynamics research","volume":"8","author":"Li","year":"2013","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1177\/10775463211048266","article-title":"Modal analysis and dynamic shimmy behavior of vehicle-road system","volume":"29","author":"Wei","year":"2023","journal-title":"J. Vib. Control"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.engstruct.2019.04.042","article-title":"Decoupled technique for dynamic response of vehicle-pavement systems","volume":"191","author":"Krishnanunni","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s42154-021-00139-z","article-title":"Review and development of electric motor systems and electric powertrains for new energy vehicles","volume":"4","author":"Cai","year":"2021","journal-title":"Automot. Innov."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2864","DOI":"10.1109\/TTE.2021.3074970","article-title":"Hub motor vibration control for distributed-driven electric vehicles: A review","volume":"7","author":"Zhao","year":"2021","journal-title":"IEEE Trans. Transp. Electrif."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1016\/j.jsv.2018.12.012","article-title":"Coupling effect between road excitation and an hub switched reluctance motor on vehicle ride comfort and active suspension control","volume":"443","author":"Shao","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"115426","DOI":"10.1016\/j.jsv.2020.115426","article-title":"Coupling effects in hub motor and optimization for active suspension system to improve the vehicle and the motor performance","volume":"482","author":"Wu","year":"2020","journal-title":"J. Sound Vib."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4655","DOI":"10.1109\/TVT.2015.2461635","article-title":"The influence of the magnetic force generated by the hub motor on the vertical and lateral coupling dynamics of electric vehicles","volume":"65","author":"Tan","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1034","DOI":"10.1080\/00423114.2015.1037313","article-title":"State of the art survey: Active and semi-active suspension control","volume":"53","author":"Tseng","year":"2015","journal-title":"Veh. Syst. Dyn."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1109\/TCST.2017.2699158","article-title":"A bioinspired dynamics-based adaptive tracking control for nonlinear suspension systems","volume":"26","author":"Pan","year":"2017","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.procs.2019.02.025","article-title":"Networked control for active suspension system","volume":"150","author":"Youness","year":"2019","journal-title":"Procedia Comput. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9263","DOI":"10.1109\/TCYB.2021.3052816","article-title":"Robust optimal control for the vehicle suspension system with uncertainties","volume":"52","author":"Bai","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Truong, N.L.V., and Hai, P.T. (2017, January 21\u201323). Analytical design of PID controller for enhancing ride comfort of active vehicle suspension system. Proceedings of the 2017 International Conference on System Science and Engineering (ICSSE), Ho Chi Minh City, Vietnam.","DOI":"10.1109\/ICSSE.2017.8030886"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.isatra.2014.05.025","article-title":"Adaptive control of nonlinear uncertain active suspension systems with prescribed performance","volume":"54","author":"Huang","year":"2015","journal-title":"ISA Trans."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.ymssp.2018.08.022","article-title":"Practical multi-objective control for automotive semi-active suspension system with nonlinear hydraulic adjustable damper","volume":"117","author":"Ma","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.jsv.2018.08.009","article-title":"An approach for minimizing the number of objective functions in the optimization of vehicle suspension systems","volume":"435","author":"Papaioannou","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"9458","DOI":"10.1109\/TIE.2019.2893847","article-title":"Adaptive neural network control for active suspension systems with time-varying vertical displacement and speed constraints","volume":"66","author":"Liu","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1016\/j.asoc.2018.06.002","article-title":"Dynamic neural network-based feedback linearization control of full-car suspensions using PSO","volume":"70","author":"Pedro","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Han, S.-Y., Dong, J.-F., Zhou, J., and Chen, Y.-H. (2022). Adaptive fuzzy PID control strategy for vehicle active suspension based on road evaluation. Electronics, 11.","DOI":"10.3390\/electronics11060921"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.17485\/ijst\/2016\/v9i1\/83806","article-title":"Neural network based vibration control for vehicle active suspension system","volume":"9","author":"Kalaivani","year":"2016","journal-title":"Indian J. Sci. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.advengsoft.2018.04.009","article-title":"Vibration control of an active vehicle suspension systems using optimized model-free fuzzy logic controller based on time delay estimation","volume":"127","author":"Mustafa","year":"2019","journal-title":"Adv. Eng. Softw."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2285","DOI":"10.1007\/s11831-021-09663-x","article-title":"A review of multi-objective optimization: Methods and algorithms in mechanical engineering problems","volume":"29","author":"Pereira","year":"2021","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"102722","DOI":"10.1016\/j.advengsoft.2019.102722","article-title":"Integrated optimization for mechanical elastic wheel and suspension based on an improved artificial fish swarm algorithm","volume":"137","author":"Xu","year":"2019","journal-title":"Adv. Eng. Softw."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s11831-022-09804-w","article-title":"Advances in sparrow search algorithm: A comprehensive survey","volume":"30","author":"Gharehchopogh","year":"2023","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"112104","DOI":"10.1016\/j.measurement.2022.112104","article-title":"Accelerometer-based human fall detection using sparrow search algorithm and back propagation neural network","volume":"204","author":"Wang","year":"2022","journal-title":"Measurement"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"39973","DOI":"10.1016\/j.ijhydene.2022.09.141","article-title":"Sparrow search algorithm applied to temperature control in PEM fuel cell systems","volume":"47","author":"Xu","year":"2022","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Huang, Y., Luo, W., and Lan, H. (2022). Adaptive pre-aim control of driverless vehicle path tracking based on a SSA-BP neural network. World Electr. Veh. J., 13.","DOI":"10.3390\/wevj13040055"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"51","DOI":"10.3901\/JME.2021.12.051","article-title":"Modeling and Dynamic Analysis of Mechanic-electro-road Coupling System of Electric Vehicles","volume":"57","author":"Li","year":"2021","journal-title":"J. Mech. Eng."},{"key":"ref_35","unstructured":"Yang, W.H. (2016). Research on Dynamic Characteristics and Vibration Control of Electric Vehicle Driven by Hub Motors with Semi-active Suspension. [Ph.D. Thesis, Wuhan Niversity of Science and Technology]."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.conengprac.2005.01.007","article-title":"On the automatic tuning and adaptation of PID controllers","volume":"14","author":"Clarke","year":"2006","journal-title":"Control Eng. Pract."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Permatasari, D.A., and Maharani, D.A. (2018, January 13\u201314). Backpropagation neural network for tuning PID pan-tilt face tracking. Proceedings of the 2018 3rd International Conference on Information Technology, Information System and Electrical Engineering (ICITISEE), Yogyakarta, Indonesia.","DOI":"10.1109\/ICITISEE.2018.8720968"},{"key":"ref_38","first-page":"2831","article-title":"Recent Versions and Applications of Sparrow Search Algorithm","volume":"30","author":"Awadallah","year":"2023","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1080\/21642583.2019.1708830","article-title":"A novel swarm intelligence optimization approach: Sparrow search algorithm","volume":"8","author":"Xue","year":"2020","journal-title":"Syst. Sci. Control Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"90958","DOI":"10.1109\/ACCESS.2022.3201867","article-title":"Nonlinear damping curve control of semi-active suspension based on improved particle swarm optimization","volume":"10","author":"Li","year":"2022","journal-title":"IEEE Access"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.neucom.2018.04.055","article-title":"Variable universe fuzzy control for vehicle semi-active suspension system with MR damper combining fuzzy neural network and particle swarm optimization","volume":"306","author":"Pang","year":"2018","journal-title":"Neurocomputing"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/6\/1757\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:11:05Z","timestamp":1760105465000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/6\/1757"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,8]]},"references-count":41,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["s24061757"],"URL":"https:\/\/doi.org\/10.3390\/s24061757","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,8]]}}}