{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:24:10Z","timestamp":1760235850488,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2021,9,29]],"date-time":"2021-09-29T00:00:00Z","timestamp":1632873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005416","name":"Norges Forskningsr\u00e5d","doi-asserted-by":"publisher","award":["270791"],"award-info":[{"award-number":["270791"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The ability to optimize power generation in sports is imperative, both for understanding and balancing training load correctly, and for optimizing competition performance. In this paper, we aim to estimate mechanical power output by employing a time-sequential information-based deep Long Short-Term Memory (LSTM) neural network from multiple inertial measurement units (IMUs). Thirteen athletes conducted roller ski skating trials on a treadmill with varying incline and speed. The acceleration and gyroscope data collected with the IMUs were run through statistical feature processing, before being used by the deep learning model to estimate power output. The model was thereafter used for prediction of power from test data using two approaches. First, a user-dependent case was explored, reaching a power estimation within 3.5% error. Second, a user-independent case was developed, reaching an error of 11.6% for the power estimation. Finally, the LSTM model was compared to two other machine learning models and was found to be superior. In conclusion, the user-dependent model allows for precise estimation of roller skiing power output after training the model on data from each athlete. The user-independent model provides less accurate estimation; however, the accuracy may be sufficient for providing valuable information for recreational skiers.<\/jats:p>","DOI":"10.3390\/s21196500","type":"journal-article","created":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T21:26:20Z","timestamp":1633728380000},"page":"6500","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Estimation of Mechanical Power Output Employing Deep Learning on Inertial Measurement Data in Roller Ski Skating"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5215-1834","authenticated-orcid":false,"given":"Md Zia","family":"Uddin","sequence":"first","affiliation":[{"name":"SINTEF Digital, 0373 Oslo, Norway"}]},{"given":"Trine M.","family":"Seeberg","sequence":"additional","affiliation":[{"name":"SINTEF Digital, 0373 Oslo, Norway"}]},{"given":"Jan","family":"Kocbach","sequence":"additional","affiliation":[{"name":"Centre for Elite Sports Research, Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology, 7491 Trondheim, Norway"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9022-4272","authenticated-orcid":false,"given":"Anders E.","family":"Liverud","sequence":"additional","affiliation":[{"name":"SINTEF Digital, 0373 Oslo, Norway"}]},{"given":"Victor","family":"Gonzalez","sequence":"additional","affiliation":[{"name":"SINTEF Digital, 0373 Oslo, Norway"}]},{"given":"\u00d8yvind","family":"Sandbakk","sequence":"additional","affiliation":[{"name":"Centre for Elite Sports Research, Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology, 7491 Trondheim, Norway"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1434-6542","authenticated-orcid":false,"given":"Fr\u00e9d\u00e9ric","family":"Meyer","sequence":"additional","affiliation":[{"name":"Department of Informatics, University of Oslo, 0316 Oslo, Norway"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1123\/ijspp.2016-0749","article-title":"Physiological capacity and training routines of elite cross-country skiers: Approaching the upper limits of human endurance","volume":"12","author":"Sandbakk","year":"2017","journal-title":"Int. J. Sports Physiol. Perform."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2829","DOI":"10.1007\/s00421-011-2261-0","article-title":"The influence of incline and speed on work rate, gross efficiency and kinematics of roller ski skating","volume":"112","author":"Sandbakk","year":"2012","journal-title":"Eur. J. Appl. Physiol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"846","DOI":"10.3389\/fphys.2018.00846","article-title":"Exercise intensity during cross-country skiing described by oxygen demands in flat and uphill terrain","volume":"9","author":"Karlsson","year":"2018","journal-title":"Front. Physiol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1249\/MSS.0000000000002209","article-title":"Oxygen demand, uptake, and deficits in elite cross-country skiers during a 15-km race","volume":"52","author":"Gilgien","year":"2020","journal-title":"Med. Sci. Sport. Exerc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1007\/BF00637393","article-title":"The energy cost of level cross-country skiing and the effect of the friction of the ski","volume":"58","author":"Saibene","year":"1989","journal-title":"Eur. J. Appl. Physiol. Occup. Physiol."},{"key":"ref_6","unstructured":"Allen, H., Coggan, A.R., and McGregor, S. (2019). Training and Racing with a Power Meter, VeloPress."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s12283-013-0136-9","article-title":"Validation of portable 2D force binding systems for cross-country skiing","volume":"16","author":"Ohtonen","year":"2013","journal-title":"Sport. Eng."},{"key":"ref_8","first-page":"127","article-title":"A simulation of cross-country skiing on varying terrain by using a mathematical power balance model","volume":"4","author":"Moxnes","year":"2013","journal-title":"Open Access J. Sport. Med."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1631","DOI":"10.3389\/fphys.2018.01631","article-title":"Propulsive Power in Cross-Country Skiing: Application and Limitations of a Novel Wearable Sensor-Based Method During Roller Skiing","volume":"9","author":"Losnegard","year":"2018","journal-title":"Front. Physiol."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Imbach, F., Candau, R., Chailan, R., and Perrey, S. (2020). Validity of the Stryd Power Meter in Measuring Running Parameters at Submaximal Speeds. Sports, 8.","DOI":"10.3390\/sports8070103"},{"key":"ref_11","first-page":"1","article-title":"Are we ready to measure running power? Repeatability and concurrent validity of five commercial technologies","volume":"21","year":"2020","journal-title":"Eur. J. Sport Sci."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ja\u00e9n-Carrillo, D., Roche-Seruendo, L.E., Cart\u00f3n-Llorente, A., Ram\u00edrez-Campillo, R., and Garc\u00eda-Pinillos, F. (2020). Mechanical Power in Endurance Running: A Scoping Review on Sensors for Power Output Estimation during Running. Sensors, 20.","DOI":"10.3390\/s20226482"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3199","DOI":"10.1016\/j.jbiomech.2015.07.001","article-title":"An inertial sensor-based system for spatio-temporal analysis in classic cross-country skiing diagonal technique","volume":"48","author":"Fasel","year":"2015","journal-title":"J. Biomech."},{"key":"ref_14","unstructured":"Myklebust, H. (2016). Quantification of Movement Patterns in Cross-Country Skiing Using Inertial Measurement Units. [Ph.D. Thesis, Norwegian School of Sport Sciences]."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/s12283-017-0252-z","article-title":"A multi-sensor system for automatic analysis of classical cross-country skiing techniques","volume":"20","author":"Seeberg","year":"2017","journal-title":"Sport. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.3389\/fpsyg.2019.01260","article-title":"Assessment of basic motions and technique identification in classical cross-country skiing","volume":"10","author":"Seeberg","year":"2019","journal-title":"Front. Psychol."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Rindal, O.M.H., Seeberg, T.M., Tj\u00f8nn\u00e5s, J., Haugnes, P., and Sandbakk, \u00d8. (2018). Automatic classification of sub-techniques in classical cross-country skiing using a machine learning algorithm on micro-sensor data. Sensors, 18.","DOI":"10.3390\/s18010075"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Gunjan, V.K., Suganthan, P.N., Haase, J., and Kumar, A. (2021). Deep Learning Algorithms for Human Activity Recognition: A Comparative Analysis BT\u2014Cybernetics, Cognition and Machine Learning Applications, Springer.","DOI":"10.1007\/978-981-33-6691-6"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1527","DOI":"10.1162\/neco.2006.18.7.1527","article-title":"A fast learning algorithm for deep belief nets","volume":"18","author":"Hinton","year":"2006","journal-title":"Neural Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"26146","DOI":"10.1109\/ACCESS.2017.2777003","article-title":"Facial expression recognition using salient features and convolutional neural network","volume":"5","author":"Uddin","year":"2017","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Graves, A., Mohamed, A., and Hinton, G. (2013, January 26\u201331). Speech recognition with deep recurrent neural networks. Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638947"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Mekruksavanich, S., and Jitpattanakul, A. (2021). Lstm networks using smartphone data for sensor-based human activity recognition in smart homes. Sensors, 21.","DOI":"10.3390\/s21051636"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Sherratt, F., Plummer, A., and Iravani, P. (2021). Understanding LSTM network behaviour of IMU-based locomotion mode recognition for applications in prostheses and wearables. Sensors, 21.","DOI":"10.3390\/s21041264"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"16945","DOI":"10.1109\/JSEN.2021.3079564","article-title":"Hand Gesture Recognition based on Trajectories Features and Computation-Efficient Reused LSTM Network","volume":"15","author":"Yang","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Guang, X., Gao, Y., Liu, P., and Li, G. (2021). IMU Data and GPS Position Information Direct Fusion Based on LSTM. Sensors, 21.","DOI":"10.3390\/s21072500"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Curreri, F., Patan\u00e8, L., and Xibilia, M.G. (2021). RNN-and LSTM-Based Soft Sensors Transferability for an Industrial Process. Sensors, 21.","DOI":"10.3390\/s21030823"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1109\/TNNLS.2020.2978267","article-title":"Multiple and complete stability of recurrent neural networks with sinusoidal activation function","volume":"32","author":"Liu","year":"2020","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"384","DOI":"10.3389\/fphys.2021.638499","article-title":"Physiological and Biomechanical Determinants of Sprint Ability Following Variable Intensity Exercise When Roller Ski Skating","volume":"12","author":"Seeberg","year":"2021","journal-title":"Front. Physiol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s00421-010-1372-3","article-title":"Metabolic rate and gross efficiency at high work rates in world class and national level sprint skiers","volume":"109","author":"Sandbakk","year":"2010","journal-title":"Eur. J. Appl. Physiol."},{"key":"ref_30","unstructured":"International Ski Federation (2020). The International Ski Competition Rules (ICR), Book II: Cross-Country, International Ski Federation."},{"key":"ref_31","unstructured":"Chen, Z. (2018). An LSTM Recurrent Network for Step Counting. arXiv."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/19\/6500\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:07:11Z","timestamp":1760166431000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/19\/6500"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,29]]},"references-count":31,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["s21196500"],"URL":"https:\/\/doi.org\/10.3390\/s21196500","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2021,9,29]]}}}