{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T09:54:33Z","timestamp":1762509273152,"version":"3.41.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,4,12]],"date-time":"2025-04-12T00:00:00Z","timestamp":1744416000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,12]],"date-time":"2025-04-12T00:00:00Z","timestamp":1744416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des Autom Embed Syst"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s10617-025-09293-7","type":"journal-article","created":{"date-parts":[[2025,4,12]],"date-time":"2025-04-12T21:30:40Z","timestamp":1744493440000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Physics-informed neural networks for monitoring dynamic systems: ring bearing system study case"],"prefix":"10.1007","volume":"29","author":[{"given":"Josafat","family":"Leal Filho","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matheus","family":"Wagner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ant\u00f4nio Augusto","family":"Fr\u00f6hlich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,4,12]]},"reference":[{"key":"9293_CR1","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.asoc.2016.12.014","volume":"52","author":"MS Hossain","year":"2017","unstructured":"Hossain MS et al (2017) Artificial neural networks for vibration based inverse parametric identifications: a review. Appl Soft Comput 52:203\u2013219","journal-title":"Appl Soft Comput"},{"key":"9293_CR2","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/j.compstruc.2014.01.013","volume":"138","author":"L Facchini","year":"2014","unstructured":"Facchini L, Betti M, Biagini P (2014) Neural network based modal identification of structural systems through output-only measurement. Comput Struct 138:183\u2013194","journal-title":"Comput Struct"},{"issue":"8","key":"9293_CR3","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1016\/j.engappai.2004.08.010","volume":"17","author":"B Xu","year":"2004","unstructured":"Xu B et al (2004) Direct identification of structural parameters from dynamic responses with neural networks. Eng Appl Artif Intell 17(8):931\u2013943","journal-title":"Eng Appl Artif Intell"},{"issue":"3","key":"9293_CR4","doi-asserted-by":"publisher","first-page":"650","DOI":"10.3390\/buildings13030650","volume":"13","author":"S Moradi","year":"2023","unstructured":"Moradi S et al (2023) Novel physics-informed artificial neural network architectures for system and input identification of structural dynamics pdes. Buildings 13(3):650","journal-title":"Buildings"},{"key":"9293_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2021.116196","volume":"508","author":"Z Lai","year":"2021","unstructured":"Lai Z, Mylonas C, Nagarajaiah S, Chatzi E (2021) Structural identification with physics-informed neural ordinary differential equations. J Sound Vib 508:116196","journal-title":"J Sound Vib"},{"issue":"18","key":"9293_CR6","doi-asserted-by":"publisher","first-page":"710","DOI":"10.1016\/j.ifacol.2016.10.249","volume":"49","author":"SL Brunton","year":"2016","unstructured":"Brunton SL, Proctor JL, Kutz JN (2016) Sparse identification of nonlinear dynamics with control (sindyc). IFAC-PapersOnLine 49(18):710\u2013715","journal-title":"IFAC-PapersOnLine"},{"issue":"1","key":"9293_CR7","doi-asserted-by":"publisher","first-page":"10166","DOI":"10.1038\/s41598-023-36799-6","volume":"13","author":"A Sholokhov","year":"2023","unstructured":"Sholokhov A, Liu Y, Mansour H, Nabi S (2023) Physics-informed neural ode (pinode): embedding physics into models using collocation points. Sci Rep 13(1):10166","journal-title":"Sci Rep"},{"key":"9293_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111466","volume":"468","author":"J O\u2019Leary","year":"2022","unstructured":"O\u2019Leary J, Paulson JA, Mesbah A (2022) Stochastic physics-informed neural ordinary differential equations. J Comput Phys 468:111466","journal-title":"J Comput Phys"},{"key":"9293_CR9","unstructured":"Djeumou F, Neary C, Goubault E, Putot S, Topcu U (2022) Neural networks with physics-informed architectures and constraints for dynamical systems modeling. In: Learning for Dynamics and Control Conference. PMLR, pp 263\u2013277"},{"key":"9293_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijfatigue.2022.107270","volume":"166","author":"D Chen","year":"2023","unstructured":"Chen D, Li Y, Liu K, Li Y (2023) A physics-informed neural network approach to fatigue life prediction using small quantity of samples. Int J Fatigue 166:107270","journal-title":"Int J Fatigue"},{"key":"9293_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2020.106458","volume":"245","author":"FA Viana","year":"2021","unstructured":"Viana FA, Nascimento RG, Dourado A, Yucesan YA (2021) Estimating model inadequacy in ordinary differential equations with physics-informed neural networks. Comput Struct 245:106458","journal-title":"Comput Struct"},{"key":"9293_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2023.110544","volume":"200","author":"Q Ni","year":"2023","unstructured":"Ni Q, Ji J, Halkon B, Feng K, Nandi AK (2023) Physics-informed residual network (piresnet) for rolling element bearing fault diagnostics. Mech Syst Signal Process 200:110544","journal-title":"Mech Syst Signal Process"},{"key":"9293_CR13","doi-asserted-by":"crossref","unstructured":"Szanda\u0142a T (2021) Review and comparison of commonly used activation functions for deep neural networks. Bio-inspired neurocomputing, pp 203\u2013224","DOI":"10.1007\/978-981-15-5495-7_11"},{"key":"9293_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2021.104295","volume":"103","author":"S Shen","year":"2021","unstructured":"Shen S, Lu H, Sadoughi M, Hu C, Nemani V, Thelen A, Webster K, Darr M, Sidon J, Kenny S (2021) A physics-informed deep learning approach for bearing fault detection. Eng Appl Artif Intell 103:104295","journal-title":"Eng Appl Artif Intell"},{"key":"9293_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2023.110123","volume":"190","author":"X Yin","year":"2023","unstructured":"Yin X, Huang Z, Liu Y (2023) Bridge damage identification under the moving vehicle loads based on the method of physics-guided deep neural networks. Mech Syst Signal Process 190:110123","journal-title":"Mech Syst Signal Process"},{"key":"9293_CR16","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1016\/j.jmsy.2020.09.005","volume":"57","author":"J Wang","year":"2020","unstructured":"Wang J, Li Y, Zhao R, Gao RX (2020) Physics guided neural network for machining tool wear prediction. J Manuf Syst 57:298\u2013310","journal-title":"J Manuf Syst"},{"issue":"9","key":"9293_CR17","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s00158-022-03348-0","volume":"65","author":"S Kim","year":"2022","unstructured":"Kim S, Choi J-H, Kim NH (2022) Data-driven prognostics with low-fidelity physical information for digital twin: physics-informed neural network. Struct Multidiscip Optim 65(9):255","journal-title":"Struct Multidiscip Optim"},{"key":"9293_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.engfracmech.2021.108130","volume":"258","author":"X-C Zhang","year":"2021","unstructured":"Zhang X-C, Gong J-G, Xuan F-Z (2021) A physics-informed neural network for creep-fatigue life prediction of components at elevated temperatures. Eng Fract Mech 258:108130","journal-title":"Eng Fract Mech"},{"key":"9293_CR19","unstructured":"Raissi M, Perdikaris P, Karniadakis GE (2017) Physics informed deep learning (part I): Data-driven solutions of nonlinear partial differential equations. Preprint at arxiv:1711.10561"},{"key":"9293_CR20","unstructured":"Raissi M, Perdikaris P, Karniadakis GE (2017) Physics informed deep learning (part II): Data-driven discovery of nonlinear partial differential equations. Preprint at https:\/\/arxiv.org\/abs\/1711.10566"},{"key":"9293_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2020.103996","volume":"96","author":"RG Nascimento","year":"2020","unstructured":"Nascimento RG, Fricke K, Viana F (2020) A tutorial on solving ordinary differential equations using python and hybrid physics-informed neural network. Eng Appl Artif Intell 96:103996","journal-title":"Eng Appl Artif Intell"},{"key":"9293_CR22","doi-asserted-by":"publisher","unstructured":"Filho JL, Wagner M, Frohlich AA (2023) Physics-informed neural networks for monitoring dynamic systems: Wind turbine study case. In: 2023 XIII Brazilian symposium on computing systems engineering (SBESC), pp 1\u20136. https:\/\/doi.org\/10.1109\/SBESC60926.2023.10324156","DOI":"10.1109\/SBESC60926.2023.10324156"},{"key":"9293_CR23","unstructured":"Chen RT, Rubanova Y, Bettencourt J, Duvenaud DK (2018) Neural ordinary differential equations. Advances in neural information processing systems. vol 31"},{"issue":"12","key":"9293_CR24","doi-asserted-by":"publisher","first-page":"1238","DOI":"10.3390\/machines10121238","volume":"10","author":"R Wang","year":"2022","unstructured":"Wang R, Wang Y, Cao X, Yang S, Guo X (2022) Nonlinear analysis of rotor-bearing-seal system with varying parameters muszynska model based on cfd and rbf. Machines 10(12):1238","journal-title":"Machines"},{"issue":"1","key":"9293_CR25","first-page":"8819676","volume":"2020","author":"M Desouki","year":"2020","unstructured":"Desouki M, Sassi S, Renno J, Gowid SA (2020) Dynamic response of a rotating assembly under the coupled effects of misalignment and imbalance. Shock Vib 2020(1):8819676","journal-title":"Shock Vib"},{"key":"9293_CR26","unstructured":"Ribeiro F (2022) Machinery Fault Database (MaFaulDa)-multivariate time-series acquired by sensors on a SpectraQuest\u2019s machinery fault simulator (MFS) alignment-balance-vibration-ABVT"},{"issue":"3","key":"9293_CR27","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1080\/00031305.2014.917055","volume":"68","author":"PH Westfall","year":"2014","unstructured":"Westfall PH (2014) Kurtosis as peakedness, 1905\u20132014. rip. Am Stat 68(3):191\u2013195","journal-title":"Am Stat"},{"issue":"11","key":"9293_CR28","first-page":"43","volume":"67","author":"B Kocha\u0144ski","year":"2022","unstructured":"Kocha\u0144ski B (2022) Does kurtosis measure the peakedness of a distribution? Wiadomo\u015bci Statystyczne. Pol Stat 67(11):43\u201361","journal-title":"Pol Stat"},{"issue":"1","key":"9293_CR29","doi-asserted-by":"publisher","first-page":"52","DOI":"10.5395\/rde.2013.38.1.52","volume":"38","author":"H-Y Kim","year":"2013","unstructured":"Kim H-Y (2013) Statistical notes for clinical researchers: assessing normal distribution (2) using skewness and kurtosis. Restor Dent Endod 38(1):52\u201354","journal-title":"Restor Dent Endod"}],"container-title":["Design Automation for Embedded Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10617-025-09293-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10617-025-09293-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10617-025-09293-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T21:02:27Z","timestamp":1750971747000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10617-025-09293-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,12]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["9293"],"URL":"https:\/\/doi.org\/10.1007\/s10617-025-09293-7","relation":{},"ISSN":["0929-5585","1572-8080"],"issn-type":[{"type":"print","value":"0929-5585"},{"type":"electronic","value":"1572-8080"}],"subject":[],"published":{"date-parts":[[2025,4,12]]},"assertion":[{"value":"21 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 April 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have declared no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"3"}}