{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T00:15:31Z","timestamp":1770423331327,"version":"3.49.0"},"reference-count":57,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,26]],"date-time":"2023-12-26T00:00:00Z","timestamp":1703548800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Research and Development Project of Gansu Provincial Science and Technology Department","award":["22YF7GA142"],"award-info":[{"award-number":["22YF7GA142"]}]},{"name":"Key Research and Development Project of Gansu Provincial Science and Technology Department","award":["P2021S012"],"award-info":[{"award-number":["P2021S012"]}]},{"name":"Systematic Major Project of China National Railway Group","award":["22YF7GA142"],"award-info":[{"award-number":["22YF7GA142"]}]},{"name":"Systematic Major Project of China National Railway Group","award":["P2021S012"],"award-info":[{"award-number":["P2021S012"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The rapid growth in the number of electric bicycles (e-bicycles) has greatly improved daily commuting for residents, but it has also increased traffic collisions involving e-bicycles. This study aims to develop an autonomous emergency braking (AEB) system for e-bicycles to reduce rear-end collisions. A framework for the AEB system composed of the risk recognition function and collision avoidance function was designed, and an e-bicycle following model was established. Then, numerical simulations were conducted in multiple scenarios to evaluate the effectiveness of the AEB system under different riding conditions. The results showed that the probability and severity of rear-end collisions involving e-bicycles significantly decreased with the application of the AEB system, and the number of rear-end collisions resulted in a 68.0% reduction. To more effectively prevent rear-end collisions, a low control delay (delay time) and suitable risk judgment criteria (TTC threshold) for the AEB system were required. The study findings suggested that when a delay time was less than or equal to 0.1 s and the TTC threshold was set at 2 s, rear-end collisions could be more effectively prevented while minimizing false alarms in the AEB system. Additionally, as the deceleration rate increased from 1.5 m\/s2 to 4.5 m\/s2, the probability and average severity of rear-end collisions also increased by 196.5% and 42.9%, respectively. This study can provide theoretical implications for the design of the AEB system for e-bicycles. The established e-bicycle following model serves as a reference for the microscopic simulation of e-bicycles.<\/jats:p>","DOI":"10.3390\/s24010137","type":"journal-article","created":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T02:58:12Z","timestamp":1703645892000},"page":"137","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Numerical Analysis of an Autonomous Emergency Braking System for Rear-End Collisions of Electric Bicycles"],"prefix":"10.3390","volume":"24","author":[{"given":"Ying","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China"},{"name":"Key Laboratory of Railway Industry on Plateau Railway Transportation Intelligent Management and Control, Lanzhou 730070, China"}]},{"given":"Haijun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China"},{"name":"Key Laboratory of Railway Industry on Plateau Railway Transportation Intelligent Management and Control, Lanzhou 730070, China"}]},{"given":"Yan","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China"},{"name":"Key Laboratory of Railway Industry on Plateau Railway Transportation Intelligent Management and Control, Lanzhou 730070, China"}]},{"given":"Junyu","family":"Hang","sequence":"additional","affiliation":[{"name":"MOT Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.eist.2018.07.002","article-title":"Where is the politics? E-bike mobility in urban China and civilizational government","volume":"30","author":"Zuev","year":"2019","journal-title":"Environ. Innov. Soc. Transit."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.tbs.2020.10.010","article-title":"Understanding electric bike riders\u2019 intention to violate traffic rules and accident proneness in China","volume":"23","author":"Tang","year":"2021","journal-title":"Travel Behav. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1136\/injuryprev-2012-040618","article-title":"Epidemiological profile of hospitalised injuries among electric bicycle riders admitted to a rural hospital in Suzhou: A cross-sectional study","volume":"20","author":"Du","year":"2014","journal-title":"Inj. Prev. J. Int. Soc. Child Adolesc. Inj. Prev."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, J., Chen, Y., and Chen, D. (2022). Analyzing safety concerns of (e-) bikes and cycling behaviors at intersections in urban area. Sustainability, 14.","DOI":"10.3390\/su14074231"},{"key":"ref_5","first-page":"629","article-title":"Road-side observational survey on 4 unlawful acts among electric bicycle riders in Zhejiang","volume":"37","author":"Zhao","year":"2016","journal-title":"Chin. J. Epidemiol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"101635","DOI":"10.1016\/j.jth.2023.101635","article-title":"Analysis of college students\u2019 phone call behavior while riding e-bikes: An application of the extended theory of planned behavior","volume":"31","author":"Liu","year":"2023","journal-title":"J. Transp. Health"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"49","DOI":"10.3141\/2314-07","article-title":"Traffic safety for electric bike riders in China: Attitudes, risk perception, and aberrant riding behaviors","volume":"2314","author":"Yao","year":"2012","journal-title":"Transp. Res. Rec. J. Transp. Res. Board."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.aap.2018.09.025","article-title":"Investigating factors affecting riders\u2019 behaviors of occupying motorized vehicle lanes on urban streets","volume":"122","author":"Zhang","year":"2019","journal-title":"Accid. Anal. Prev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.aap.2012.12.032","article-title":"The effects of sunshields on red light running behavior of cyclists and electric bike riders","volume":"52","author":"Zhang","year":"2013","journal-title":"Accid. Anal. Prev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.aap.2013.06.011","article-title":"Understanding on-road practices of electric bike riders: An observational study in a developed city of China","volume":"59","author":"Du","year":"2013","journal-title":"Accid. Anal. Prev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.aap.2016.03.007","article-title":"Mobile phone use among motorcyclists and electric bike riders: A case study of Hanoi, Vietnam","volume":"91","author":"Truong","year":"2016","journal-title":"Accid. Anal. Prev."},{"key":"ref_12","unstructured":"Wu, Y., Guo, Y., Li, Z., and Chen, K. (2015, January 11\u201315). Investigating the factors related to the registration of electric bicycle licenses in China. Proceedings of the Transportation Research Board 94th Annual Meeting, Washington, DC, USA."},{"key":"ref_13","first-page":"71","article-title":"Characterizing risky driving behaviors of electric two-wheelers riders to create prevention guidelines in China and in France","volume":"1","author":"Carole","year":"2013","journal-title":"IAFOR J. Soc. Sci."},{"key":"ref_14","first-page":"43","article-title":"Analysis of moped rider violation behavior characteristics at urban signalized intersections","volume":"21","author":"Xu","year":"2011","journal-title":"China Saf. Sci. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1080\/15389588.2023.2176191","article-title":"Effects of forward collision warning and automatic emergency braking on rear-end crashes involving pickup trucks","volume":"24","author":"Cicchino","year":"2023","journal-title":"Traffic Inj. Prev."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Pak, J.M. (2022). Hybrid interacting multiple model filtering for improving the reliability of radar-based forward collision warning systems. Sensors, 22.","DOI":"10.3390\/s22030875"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"106450","DOI":"10.1016\/j.aap.2021.106450","article-title":"Effects of an integrated collision warning system on risk compensation behavior: An examination under naturalistic driving conditions","volume":"163","author":"Yu","year":"2021","journal-title":"Accid. Anal. Prev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"105718","DOI":"10.1016\/j.aap.2020.105718","article-title":"Adverse behavioral adaptation to adaptive forward collision warning systems: An investigation of primary and secondary task performance","volume":"146","author":"Reinmueller","year":"2020","journal-title":"Accid. Anal. Prev."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.trc.2019.12.015","article-title":"Impact on car following behavior of a forward collision warning system with headway monitoring","volume":"111","author":"Zhu","year":"2020","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.trc.2019.08.002","article-title":"DSRC-based rear-end collision warning system\u2014An error-component safety distance model and field test","volume":"107","author":"Zhao","year":"2019","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/j.trc.2018.08.001","article-title":"Effects of crash warning systems on rear-end crash avoidance behavior under fog conditions","volume":"95","author":"Wu","year":"2018","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.trf.2020.08.025","article-title":"Using a multi-user driving simulator system to explore the patterns of vehicle fleet rear-end collisions occurrence under different foggy conditions and speed limits","volume":"74","author":"Huang","year":"2020","journal-title":"Transp. Res. Part F Traffic Psychol. Behav."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Ma, C., Yang, D., Zhou, J., Feng, Z., and Yuan, Q. (2019). Risk riding behaviors of urban e-bicycles: A literature review. Int. J. Environ. Res. Public Health, 16.","DOI":"10.3390\/ijerph16132308"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.trf.2023.04.004","article-title":"Improving drivers\u2019 merging performance in work zone using an in-vehicle audio warning","volume":"95","author":"Duan","year":"2023","journal-title":"Transp. Res. Part F Traffic Psychol. Behav."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.trc.2014.12.003","article-title":"The influence of in-vehicle speech warning timing on drivers\u2019 collision avoidance performance at signalized intersections","volume":"51","author":"Yan","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_26","first-page":"843","article-title":"How do signs and warning influence driving behaviors at flashing light grade crossings?","volume":"14","author":"Yang","year":"2022","journal-title":"J. Transp. Saf. Secur."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1243\/09544070JAUTO983","article-title":"A new lateral impact warning system with grey prediction","volume":"224","author":"Huang","year":"2010","journal-title":"Proc. Inst. Mech. Eng. Part D J. Automob. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"81370","DOI":"10.1109\/ACCESS.2019.2923822","article-title":"ADAS acceptability improvement based on self-learning of individual driving characteristics: A case study of lane change warning system","volume":"7","author":"Sun","year":"2019","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Wang, M., Chen, X., Jin, B., Lv, P., Wang, W., and Shen, Y. (2021). A Novel V2V Cooperative Collision Warning System Using UWB\/DR for Intelligent Vehicles. Sensors, 21.","DOI":"10.3390\/s21103485"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"S21","DOI":"10.1080\/15389588.2019.1623397","article-title":"Forward collision warning based on a driver model to increase drivers\u2019 acceptance","volume":"20","author":"Guillen","year":"2019","journal-title":"Traffic Inj. Prev."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1109\/TITS.2013.2293771","article-title":"Research on a DSRC-based rear-end collision warning model","volume":"15","author":"Xiang","year":"2014","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4390","DOI":"10.1109\/TITS.2018.2884570","article-title":"Real-time feed-forward neural network-based forward collision warning system under cloud communication environment","volume":"20","author":"Lee","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"126294","DOI":"10.1016\/j.physa.2021.126294","article-title":"Stability of heterogeneous traffic considering impacts of platoon management with multiple time delays","volume":"583","author":"Ruan","year":"2021","journal-title":"Physica A"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"An, H., and Jung, J.-i. (2018). Design of a Cooperative Lane Change Protocol for a Connected and Automated Vehicle Based on an Estimation of the Communication Delay. Sensors, 18.","DOI":"10.3390\/s18103499"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1016\/j.jsr.2021.12.023","article-title":"An improved automated braking system for rear-end collisions: A study based on a driving simulator experiment","volume":"80","author":"Hang","year":"2022","journal-title":"J. Saf. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.trc.2014.07.008","article-title":"Applying telecommunications methodology to road safety for rear-end collision avoidance","volume":"50","author":"Benedetto","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1016\/j.sbspro.2011.08.075","article-title":"A collision warning system for rear-end collision: A driving simulator study","volume":"20","author":"Bella","year":"2011","journal-title":"Procedia Soc. Behav. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Huang, Y., Yan, X., Li, X., Duan, K., Rakotonirainy, A., and Gao, Z. (2022). Improving car-following model to capture unobserved driver heterogeneity and following distance features in fog condition. Transportmetrica A, early access.","DOI":"10.1080\/23249935.2022.2048917"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Jiang, R., Hu, M., Zhang, H.M., Gao, Z., Jia, B., Wu, Q., Wang, B., and Yang, M. (2014). Traffic experiment reveals the nature of car-following. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0094351"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.1103\/PhysRevE.62.1805","article-title":"Congested traffic states in empirical observations and microscopic simulations","volume":"62","author":"Treiber","year":"2000","journal-title":"Phys. Rev. E"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/S0001-4575(00)00019-1","article-title":"Extended time-to-collision measures for road traffic safety assessment","volume":"33","author":"Minderhoud","year":"2001","journal-title":"Accid. Anal. Prev."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Huang, Y., Yan, X., Li, X., and Rakotonirainy, A. (2023). Evaluating the safe and eco-driving performances of car-following behaviors in a vehicle platoon under foggy conditions. J. Transp. Saf. Secur., early access.","DOI":"10.1080\/19439962.2023.2201173"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"103655","DOI":"10.1016\/j.trc.2022.103655","article-title":"Anticipated Collision Time (ACT): A two-dimensional surrogate safety indicator for trajectory-based proactive safety assessment","volume":"139","author":"Venthuruthiyil","year":"2022","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"106544","DOI":"10.1016\/j.aap.2021.106544","article-title":"Driver operational level identification of driving risk and graded time-based alarm under near-crash conditions: A driving simulator study","volume":"166","author":"Li","year":"2022","journal-title":"Accid. Anal. Prev."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jsr.2021.09.008","article-title":"A novel traffic conflict risk measure considering the effect of vehicle weight","volume":"80","author":"Wang","year":"2022","journal-title":"J. Saf. Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"105796","DOI":"10.1016\/j.aap.2020.105796","article-title":"A new method of temporal and spatial risk estimation for lane change considering conventional recognition defects","volume":"148","author":"Wu","year":"2020","journal-title":"Accid. Anal. Prev."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.aap.2017.10.015","article-title":"Development of a lane change risk indicator using vehicle trajectory data","volume":"110","author":"Park","year":"2018","journal-title":"Accid. Anal. Prev."},{"key":"ref_48","unstructured":"(2023, November 20). Safety Technical Specification for Electric Bicycle, Available online: https:\/\/www.gov.cn\/xinwen\/2018-01\/17\/5257415\/files\/c627640c4f93478f9f71cb4115c99ea1.pdf."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/j.trb.2015.08.003","article-title":"On some experimental features of car-following behavior and how to model them","volume":"80","author":"Jiang","year":"2015","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1177\/0361198105193400106","article-title":"Analysis and comparison of microscopic traffic flow models with real traffic microscopic data","volume":"1934","author":"Punzo","year":"2005","journal-title":"Transp. Res. Rec. J. Transp. Res. Board."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.aap.2019.05.017","article-title":"Key feature selection and risk prediction for lane-changing behaviors based on vehicles\u2019 trajectory data","volume":"129","author":"Chen","year":"2019","journal-title":"Accid. Anal. Prev."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/j.trf.2020.12.009","article-title":"A comparison of experienced and novice drivers\u2019 rear-end collision avoidance maneuvers under urgent decelerating events","volume":"76","author":"Yang","year":"2021","journal-title":"Transp. Res. Part F Traffic Psychol. Behav."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"2435","DOI":"10.1109\/TITS.2015.2409374","article-title":"Development of a deceleration-based surrogate safety measure for rear-end collision risk","volume":"16","author":"Tak","year":"2015","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1546","DOI":"10.1109\/TITS.2012.2191542","article-title":"Safety benefits of forward collision warning, brake assist, and autonomous braking systems in rear-end collisions","volume":"13","author":"Kusano","year":"2012","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_55","first-page":"100467","article-title":"Connected and automated vehicle platoon maintenance under communication failures","volume":"35","author":"Liu","year":"2022","journal-title":"Veh. Commun."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1109\/TCYB.2019.2962601","article-title":"A secure adaptive control for cooperative driving of autonomous connected vehicles in the presence of heterogeneous communication delays and cyberattacks","volume":"51","author":"Petrillo","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1109\/TVT.2019.2960114","article-title":"Compensation of communication delays in a cooperative ACC system","volume":"69","author":"Xing","year":"2020","journal-title":"IEEE Trans. Veh. Technol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/1\/137\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:42:14Z","timestamp":1760132534000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/1\/137"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,26]]},"references-count":57,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["s24010137"],"URL":"https:\/\/doi.org\/10.3390\/s24010137","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,26]]}}}