{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T17:34:30Z","timestamp":1775756070503,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2021,11,19]],"date-time":"2021-11-19T00:00:00Z","timestamp":1637280000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Nowadays, the use of wearable inertial-based systems together with machine learning methods opens new pathways to assess athletes\u2019 performance. In this paper, we developed a neural network-based approach for the estimation of the Ground Reaction Forces (GRFs) and the three-dimensional knee joint moments during the first landing phase of the Vertical Drop Jump. Data were simultaneously recorded from three commercial inertial units and an optoelectronic system during the execution of 112 jumps performed by 11 healthy participants. Data were processed and sorted to obtain a time-matched dataset, and a non-linear autoregressive with external input neural network was implemented in Matlab. The network was trained through a train-test split technique, and performance was evaluated in terms of Root Mean Square Error (RMSE). The network was able to estimate the time course of GRFs and joint moments with a mean RMSE of 0.02 N\/kg and 0.04 N\u00b7m\/kg, respectively. Despite the comparatively restricted data set and slight boundary errors, the results supported the use of the developed method to estimate joint kinetics, opening a new perspective for the development of an in-field analysis method.<\/jats:p>","DOI":"10.3390\/s21227709","type":"journal-article","created":{"date-parts":[[2021,11,21]],"date-time":"2021-11-21T21:00:50Z","timestamp":1637528450000},"page":"7709","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Machine Learning-Based Estimation of Ground Reaction Forces and Knee Joint Kinetics from Inertial Sensors While Performing a Vertical Drop Jump"],"prefix":"10.3390","volume":"21","author":[{"given":"Serena","family":"Cerfoglio","sequence":"first","affiliation":[{"name":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2772-4837","authenticated-orcid":false,"given":"Manuela","family":"Galli","sequence":"additional","affiliation":[{"name":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, Italy"},{"name":"E4Sport Laboratory, Politecnico di Milano, 23900 Lecco, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2640-1764","authenticated-orcid":false,"given":"Marco","family":"Tarabini","sequence":"additional","affiliation":[{"name":"E4Sport Laboratory, Politecnico di Milano, 23900 Lecco, Italy"},{"name":"Dipartimento di Meccanica, Politecnico di Milano, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2240-5394","authenticated-orcid":false,"given":"Filippo","family":"Bertozzi","sequence":"additional","affiliation":[{"name":"Department of Biomedical Sciences for Health, Universit\u00e0 degli Studi di Milano, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6532-6464","authenticated-orcid":false,"given":"Chiarella","family":"Sforza","sequence":"additional","affiliation":[{"name":"Department of Biomedical Sciences for Health, Universit\u00e0 degli Studi di Milano, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0649-3665","authenticated-orcid":false,"given":"Matteo","family":"Zago","sequence":"additional","affiliation":[{"name":"Department of Biomedical Sciences for Health, Universit\u00e0 degli Studi di Milano, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1519\/SSC.0000000000000331","article-title":"Drop jump: A technical model for scientific application","volume":"39","author":"Pedley","year":"2017","journal-title":"Strength Cond. J."},{"key":"ref_2","first-page":"81","article-title":"Drop jump and muscle damage markers","volume":"3","author":"Eiras","year":"2009","journal-title":"Serb. J. Sport. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.ptsp.2018.08.002","article-title":"Vertical drop jump landing depth influences knee kinematics in female recreational athletes","volume":"33","author":"Augustsson","year":"2018","journal-title":"Phys. Ther. Sport"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"202","DOI":"10.5312\/wjo.v7.i4.202","article-title":"Use of clinical movement screening tests to predict injury in sport","volume":"7","author":"Chimera","year":"2016","journal-title":"World J. Orthop."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.gaitpost.2016.03.003","article-title":"Reliability of knee biomechanics during a vertical drop jump in elite female athletes","volume":"46","author":"Mok","year":"2016","journal-title":"Gait Posture"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1177\/0363546512472043","article-title":"Comparison of drop jumps and sport-specific sidestep cutting: Implications for anterior cruciate ligament injury risk screening","volume":"41","author":"Kristianslund","year":"2013","journal-title":"Am. J. Sports Med."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1177\/0363546511429776","article-title":"A Prospective Evaluation of the Landing Error Scoring System (LESS) as a Screening Tool for Anterior Cruciate Ligament Injury Risk","volume":"40","author":"Smith","year":"2012","journal-title":"Am. J. Sports Med."},{"key":"ref_8","first-page":"1","article-title":"Do knee abduction kinematics and kinetics predict future anterior cruciate ligament injury risk? A systematic review and meta-analysis of prospective studies","volume":"21","author":"Creaby","year":"2020","journal-title":"BMC Musculoskelet. Disord."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1177\/1747954120952577","article-title":"Influence of age and sex on drop jump landing strategies in \u00e9lite youth soccer players","volume":"16","author":"Lucarno","year":"2020","journal-title":"Int. J. Sports Sci. Coach."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1843","DOI":"10.1002\/jor.23414","article-title":"Mechanisms, Prediction, and Prevention of ACL Injuries: Cut Risk With Three Sharpened and Validated Tools","volume":"34","author":"Hewett","year":"2016","journal-title":"J. Orthop. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1177\/0363546504269591","article-title":"Biomechanical measures of neuromuscular control and valgus loading of the knee predict anterior cruciate ligament injury risk in female athletes: A prospective study","volume":"33","author":"Hewett","year":"2005","journal-title":"Am. J. Sports Med."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1833","DOI":"10.1007\/s11517-019-02000-2","article-title":"Intelligent prediction of kinetic parameters during cutting manoeuvres","volume":"57","author":"Mundt","year":"2019","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"665","DOI":"10.2519\/jospt.2009.3004","article-title":"Reliability and validity of observational risk screening in evaluating dynamic knee valgus","volume":"39","author":"Ekegren","year":"2009","journal-title":"J. Orthop. Sports Phys. Ther."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1007\/s40279-014-0168-8","article-title":"What is normal? Female lower limb kinematic profiles during athletic tasks used to examine anterior cruciate ligament injury risk: A systematic review","volume":"44","author":"Fox","year":"2014","journal-title":"Sports Med."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"998","DOI":"10.2519\/jospt.2015.5612","article-title":"Association between anatomical characteristics, knee laxity, muscle strength, and peak knee valgus during vertical drop-jump landings","volume":"45","author":"Nilstad","year":"2015","journal-title":"J. Orthop. Sports Phys. Ther."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1115\/1.4004413","article-title":"A wearable system to assess risk for anterior cruciate ligament injury during jump landing: Measurements of temporal events, jump height, and sagittal plane kinematics","volume":"133","author":"Dowling","year":"2011","journal-title":"J. Biomech. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1007\/s11517-016-1537-2","article-title":"Validation of inertial measurement units with an optoelectronic system for whole-body motion analysis","volume":"55","author":"Mecheri","year":"2017","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Teufl, W., Miezal, M., Taetz, B., Frohlichi, M., and Bleser, G. (2019). Validity of inertial sensor based 3D joint kinematics of static and dynamic sport and physiotherapy specific movements. PLoS ONE, 14.","DOI":"10.1371\/journal.pone.0213064"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wang, L., Cheng, L., and Zhao, G. (2009). Machine Learning for Human Motion Analysis: Theory and Practice, IGI Global.","DOI":"10.4018\/978-1-60566-900-7"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6891","DOI":"10.3390\/s140406891","article-title":"IMU-based joint angle measurement for gait analysis","volume":"14","author":"Seel","year":"2014","journal-title":"Sensors"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Schmidt, M., Jaitner, T., Nolte, K., Rheinl\u00e4nder, C., Wille, S., and Wehn, N. (2014, January 24\u201326). A wearable inertial sensor unit for jump diagnosis in multiple athletes. Proceedings of the icSPORTS 2014\u20142nd International Congress on Sports Sciences Research and Technology Support, Rome, Italy.","DOI":"10.5220\/0005145902160220"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Adesida, Y., Papi, E., and McGregor, A.H. (2019). Exploring the role of wearable technology in sport kinematics and kinetics: A systematic review. Sensors, 19.","DOI":"10.3390\/s19071597"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3389\/fbioe.2020.00041","article-title":"Estimation of Gait Mechanics Based on Simulated and Measured IMU Data Using an Artificial Neural Network","volume":"8","author":"Mundt","year":"2020","journal-title":"Front. Bioeng. Biotechnol."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Teufl, W., Miezal, M., Taetz, B., Fr\u00f6hlich, M., and Bleser, G. (2018). Validity, test-retest reliability and long-term stability of magnetometer free inertial sensor based 3D joint kinematics. Sensors, 18.","DOI":"10.3390\/s18071980"},{"key":"ref_25","unstructured":"Mundt, M., Koeppe, A., Bamer, F., Potthast, W., and Pforzheim, A.C. (2018, January 10\u201314). Prediction of joint kinetics based on joint kinematics using neural networks. Proceedings of the 36th Conference of the International Society of Biomechanics in Sports, Auckland, New Zealand."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Stetter, B.J., Ringhof, S., Krafft, F.C., Sell, S., and Stein, T. (2019). Estimation of knee joint forces in sport movements using wearable sensors and machine learning. Sensors, 19.","DOI":"10.3390\/s19173690"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Lim, H., Kim, B., and Park, S. (2019). Prediction of lower limb kinetics and kinematics during walking by a single IMU on the lower back using machine learning. Sensors, 20.","DOI":"10.3390\/s20010130"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1021\/ci00010a022","article-title":"Model-Free Mapping Devices","volume":"32","author":"Maggiora","year":"1992","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"ref_29","first-page":"43","article-title":"Introduction to multi-layer feed-forward neural networks","volume":"39","author":"Svozil","year":"1997","journal-title":"Comput. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Argent, R., Bevilacqua, A., Keogh, A., Daly, A., and Caulfield, B. (2021). The importance of real-world validation of machine learning systems in wearable exercise biofeedback platforms: A case study. Sensors, 21.","DOI":"10.3390\/s21072346"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Karatsidis, A., Bellusci, G., Schepers, H.M., de Zee, M., Andersen, M.S., and Veltink, P.H. (2017). Estimation of ground reaction forces and moments during gait using only inertial motion capture. Sensors, 17.","DOI":"10.3390\/s17010075"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1016\/j.jbiomech.2013.02.024","article-title":"Impact Differences in Ground Reaction Force and Center of Mass Between the First and Second Landing Phases of a Drop Vertical Jump and their Implications for Injury Risk Assessment","volume":"46","author":"Bates","year":"2013","journal-title":"J. Biomech."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.gaitpost.2009.04.004","article-title":"A six degrees-of-freedom marker set for gait analysis: Repeatability and comparison with a modified Helen Hayes set","volume":"30","author":"Collins","year":"2009","journal-title":"Gait Posture"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Winter, D.A. (2009). Biomechanics and Motor Control of Human Movement, Wiley. [4th ed.].","DOI":"10.1002\/9780470549148"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Crenna, F., Rossi, G.B., and Berardengo, M. (2021). Filtering biomechanical signals in movement analysis. Sensors, 21.","DOI":"10.3390\/s21134580"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1080\/00207179008934126","article-title":"Non-linear system identification using neural networks","volume":"51","author":"Chen","year":"1990","journal-title":"Int. J. Control"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Boussaada, Z., Curea, O., Remaci, A., Camblong, H., and Bellaaj, N.M. (2018). A nonlinear autoregressive exogenous (NARX) neural network model for the prediction of the daily direct solar radiation. Energies, 11.","DOI":"10.3390\/en11030620"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"102060","DOI":"10.1016\/j.isci.2021.102060","article-title":"Battery lifetime prediction and performance assessment of different modeling approaches","volume":"24","author":"Hosen","year":"2021","journal-title":"iScience"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1166\/jctn.2013.2736","article-title":"Comparative analysis of system identification techniques for nonlinear modeling of the neuron-microelectrode junction","volume":"10","author":"Khan","year":"2013","journal-title":"J. Comput. Theor. Nanosci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.5194\/gmd-7-1247-2014","article-title":"Root mean square error (RMSE) or mean absolute error (MAE)?\u2014Arguments against avoiding RMSE in the literature","volume":"7","author":"Chai","year":"2014","journal-title":"Geosci. Model Dev."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3389\/fphys.2018.00218","article-title":"Estimation of vertical ground reaction forces and sagittal knee kinematics during running using three inertial sensors","volume":"9","author":"Wouda","year":"2018","journal-title":"Front. Physiol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"9","DOI":"10.3389\/fbioe.2020.00009","article-title":"A Machine Learning and Wearable Sensor Based Approach to Estimate External Knee Flexion and Adduction Moments During Various Locomotion Tasks","volume":"8","author":"Stetter","year":"2020","journal-title":"Front. Bioeng. Biotechnol."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Zago, M., Tarabini, M., Spiga, M.D., Ferrario, C., Bertozzi, F., Sforza, C., and Galli, M. (2021). Machine-learning based determination of gait events from foot-mounted inertial units. Sensors, 21.","DOI":"10.3390\/s21030839"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7709\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:32:56Z","timestamp":1760167976000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7709"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,19]]},"references-count":43,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["s21227709"],"URL":"https:\/\/doi.org\/10.3390\/s21227709","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,19]]}}}