{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T18:45:58Z","timestamp":1776710758093,"version":"3.51.2"},"reference-count":33,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T00:00:00Z","timestamp":1750464000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Fundamental Research Funds for the China Institute of Sport Science","award":["24\u201345"],"award-info":[{"award-number":["24\u201345"]}]},{"name":"the Fundamental Research Funds for the China Institute of Sport Science","award":["12302415"],"award-info":[{"award-number":["12302415"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["24\u201345"],"award-info":[{"award-number":["24\u201345"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12302415"],"award-info":[{"award-number":["12302415"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Vertical ground reaction force (vGRF) plays an important role in the study of running-related injuries (RRIs). This study explores the synchronization method between inertial measurement unit (IMU) and vGRF data of running and develops ANN models to accurately predict vGRF. Fifteen runners participated in this study. Acceleration data and vGRF values of eight rearfoot strikers and seven forefoot strikers running at 12, 14, and 16 km\/h were collected by a single IMU and an instrumented treadmill. The sliding time window synchronization (STWS) algorithm was developed to sync IMU data with vGRF data. The wavelet neural network model (WNN) and feed-forward neural network model (FFNN) were adapted to predict vGRF using three-axis or sagittal-axis acceleration data in the stance phase, respectively. One rearfoot striker and one forefoot striker were randomly selected as a test set, while the other participants formed training sets. After synchronization, mean absolute errors for stride time of the IMU and vGRF data were less than 11.2 ms. The coefficient of multiple correlations for vGRF measured curves and predicted curves was more than 0.97. The normalized root mean square errors (NRMSEs) between two curves were 4.6~9.2%, and R2 was 0.93~0.99. For peak vGRF, the NRMSEs were 1.6~8.2%, except for rearfoot strike runners at 16 km\/h using the FFNN model (10.7% and 11.1%). The Bland\u2013Altman plots indicate that the errors for both the WNN and FFNN models are within acceptable limits. The STWS algorithm can effectively achieve the data synchronization between the IMU and the force plate during running. Both WNN and FFNN models demonstrated good accuracy and agreement in predicting vGRF. Using sagittal-axis acceleration data may be an ideal model with good prediction accuracy and less input data. This work provides direction for developing ANN models of personalized monitoring of lower limb load.<\/jats:p>","DOI":"10.3390\/s25133870","type":"journal-article","created":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T04:50:05Z","timestamp":1750654205000},"page":"3870","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Predicting Running Vertical Ground Reaction Forces Using Neural Network Models Based on an IMU Sensor"],"prefix":"10.3390","volume":"25","author":[{"given":"Shangxiao","family":"Li","sequence":"first","affiliation":[{"name":"Research Center for Sports Psychology and Biomechanics, China Institute of Sport Science, Beijing 100061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiahui","family":"Pan","sequence":"additional","affiliation":[{"name":"Research Center for Sports Psychology and Biomechanics, China Institute of Sport Science, Beijing 100061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongmei","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Human Sport Science, Beijing Sport University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shufang","family":"Yuan","sequence":"additional","affiliation":[{"name":"Research Center for Sports Psychology and Biomechanics, China Institute of Sport Science, Beijing 100061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Human Sport Science, Shanghai University of Sport, Shanghai 200438, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8858-8827","authenticated-orcid":false,"given":"Weiya","family":"Hao","sequence":"additional","affiliation":[{"name":"Research Center for Sports Psychology and Biomechanics, China Institute of Sport Science, Beijing 100061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1136\/bjsports-2018-100493","article-title":"Is running associated with a lower risk of all-cause, cardiovascular and cancer mortality, and is the more the better? 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