{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T05:28:36Z","timestamp":1772342916113,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T00:00:00Z","timestamp":1742947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>Digital twin (DT) technology has become a key enabler for prognostics and health management (PHM) in complex industrial systems, yet scaling predictive models for multi-component degradation (MCD) scenarios remains challenging, particularly when transferring insights from predictive models of smaller systems developed with limited data to larger systems. To address this, a physics-informed neural network (PINN) framework that integrates a standardized scaling methodology, enabling scalable DT analytics for MCD prognostics, was developed in this paper. Our approach employs a systematic DevOps workflow that features containerized PINN DT analytics deployed on a Kubernetes cluster for dynamic resource optimization, a real-time DT platform (PTC ThingWorx\u2122), and a custom API for bidirectional data exchange that connects the cluster to the DT platform. A key contribution of this paper is the scalable DT model, which facilitates transfer learning of degradation patterns across heterogeneous hydraulic systems. Three (3) hydraulic system configurations were modeled, analyzing multi-component filter degradation under pump speeds of 700\u2013900 RPM. Trained on limited data from a reference system, the scaled PINN model achieved 88.98% accuracy for initial degradation detection at 900 RPM\u2014outperforming an unscaled baseline of 64.13%\u2014with consistent improvements across various speeds and thresholds. This work advances PHM analytics by reducing costs and development time, providing a scalable framework for cross-system DT deployment.<\/jats:p>","DOI":"10.3390\/computers14040121","type":"journal-article","created":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T04:17:14Z","timestamp":1742962634000},"page":"121","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Scalable Data Transformation Models for Physics-Informed Neural Networks (PINNs) in Digital Twin-Enabled Prognostics and Health Management (PHM) Applications"],"prefix":"10.3390","volume":"14","author":[{"given":"Atuahene Kwasi","family":"Barimah","sequence":"first","affiliation":[{"name":"Department of Applied Science, School of Computing, Engineering and Built Environment, Glasgow Caledonian University, Glasgow G4 0BA, UK"}]},{"given":"Ogwo Precious","family":"Onu","sequence":"additional","affiliation":[{"name":"Department of Applied Science, School of Computing, Engineering and Built Environment, Glasgow Caledonian University, Glasgow G4 0BA, UK"}]},{"given":"Octavian","family":"Niculita","sequence":"additional","affiliation":[{"name":"Department of Applied Science, School of Computing, Engineering and Built Environment, Glasgow Caledonian University, Glasgow G4 0BA, UK"}]},{"given":"Andrew","family":"Cowell","sequence":"additional","affiliation":[{"name":"Department of Applied Science, School of Computing, Engineering and Built Environment, Glasgow Caledonian University, Glasgow G4 0BA, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9131-5918","authenticated-orcid":false,"given":"Don","family":"McGlinchey","sequence":"additional","affiliation":[{"name":"Department of Applied Science, School of Computing, Engineering and Built Environment, Glasgow Caledonian University, Glasgow G4 0BA, UK"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"103316","DOI":"10.1016\/j.compind.2020.103316","article-title":"Digital Twin for maintenance: A literature review","volume":"123","author":"Errandonea","year":"2020","journal-title":"Comput. Ind."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"103469","DOI":"10.1016\/j.compind.2021.103469","article-title":"Digital twin paradigm: A systematic literature review","volume":"130","author":"Semeraro","year":"2021","journal-title":"Comput. Ind."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"110801","DOI":"10.1016\/j.rser.2021.110801","article-title":"Towards the future of smart electric vehicles: Digital twin technology","volume":"141","author":"Bhatti","year":"2021","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"101297","DOI":"10.1016\/j.aei.2021.101297","article-title":"A review of digital twin in product design and development","volume":"48","author":"Lo","year":"2021","journal-title":"Adv. Eng. Inform."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"14","DOI":"10.36001\/phme.2024.v8i1.4099","article-title":"Towards Physics-Informed PHM for Multi-component degradation (MCD) in complex systems","volume":"8","author":"Barimah","year":"2024","journal-title":"PHM Soc. Eur. Conf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1007\/s10409-021-01148-1","article-title":"Physics-Informed Neural Networks (PINNs) for Fluid Mechanics: A Review","volume":"37","author":"Cai","year":"2021","journal-title":"Acta Mech. Sin."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1109\/TPWRS.2022.3162473","article-title":"Applications of Physics-Informed Neural Networks in Power Systems\u2014A Review","volume":"38","author":"Huang","year":"2022","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_8","first-page":"27","article-title":"Study of various maintenance approaches types of failure and failure detection techniques used in hydraulic pumps: A review","volume":"X","author":"Srivyas","year":"2017","journal-title":"Ind. Eng. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"032003","DOI":"10.1088\/2631-8695\/acefae","article-title":"From Data to Insight, Enhancing Structural Health Monitoring Using Physics-Informed Machine Learning and Advanced Data Collection Methods","volume":"5","author":"Rizvi","year":"2023","journal-title":"Eng. Res. Express"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4","DOI":"10.36001\/phme.2024.v8i1.3969","article-title":"Design of Digital Twins for In-Service Support and Maintenance","volume":"8","author":"Barimah","year":"2024","journal-title":"PHM Soc. Eur. Conf."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, Z. (2020). Digital Twin Technology. Industry 4.0\u2014Impact on Intelligent Logistics and Manufacturing, IntechOpen.","DOI":"10.5772\/intechopen.80974"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Rasheed, A., San, O., and Kvamsdal, T. (2019). Digital Twin: Values, Challenges and Enablers. arXiv.","DOI":"10.1109\/ACCESS.2020.2970143"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Singh, M., Fuenmayor, E., Hinchy, E.P., Qiao, Y., Murray, N., and Devine, D. (2021). Digital Twin: Origin to Future. Appl. Syst. Innov., 4.","DOI":"10.3390\/asi4020036"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"113524","DOI":"10.1016\/j.dss.2021.113524","article-title":"Digital Twin: Generalization, Characterization and Implementation","volume":"145","author":"VanDerHorn","year":"2021","journal-title":"Decis. Support Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1016\/j.jmsy.2022.06.015","article-title":"Digital Twin Modeling","volume":"64","author":"Tao","year":"2022","journal-title":"J. Manuf. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"06022001","DOI":"10.1061\/(ASCE)ME.1943-5479.0001034","article-title":"Digital Twin: From Concept to Practice","volume":"38","author":"Agrawal","year":"2022","journal-title":"J. Manag. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"108952","DOI":"10.1109\/ACCESS.2020.2998358","article-title":"Digital Twin: Enabling Technologies, Challenges and Open Research","volume":"8","author":"Fuller","year":"2020","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Olesen, J.F., and Shaker, H.R. (2020). Predictive Maintenance for Pump Systems and Thermal Power Plants: State-of-the-Art Review, Trends and Challenges. Sensors, 20.","DOI":"10.3390\/s20082425"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Saad, A., Faddel, S., and Mohammed, O. (2020). IoT-Based Digital Twin for Energy Cyber-Physical Systems: Design and Implementation. Energies, 13.","DOI":"10.3390\/en13184762"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"030801","DOI":"10.1115\/1.4049537","article-title":"Digital Twin-Driven Remaining Useful Life Prediction for Gear Performance Degradation: A Review","volume":"21","author":"He","year":"2021","journal-title":"J. Comput. Inf. Sci. Eng."},{"key":"ref_21","first-page":"4","article-title":"Industrial Internet of Things Monitoring Solution for Advanced Predictive Maintenance Applications","volume":"7","author":"Civerchia","year":"2017","journal-title":"J. Ind. Inf. Integr."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/j.jmsy.2020.06.017","article-title":"Review of Digital Twin about Concepts, Technologies, and Industrial Applications","volume":"58","author":"Liu","year":"2021","journal-title":"J. Manuf. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1007\/978-3-030-82529-4_35","article-title":"Automation of IoT-Based Services Using Digital Twin","volume":"Volume 298","author":"Anghel","year":"2022","journal-title":"Lecture Notes in Networks and Systems"},{"key":"ref_24","first-page":"98","article-title":"Digital Twin-Based Services: A Taxonomy (Extended Abstract)","volume":"14","author":"Papadonikolaki","year":"2023","journal-title":"IET Conf. Proc."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Talasila, P., Gomes, C., Mikkelsen, P.H., Arboleda, S.G., Kamburjan, E., and Larsen, P.G. (2023, January 28\u201331). Digital twin as a service (DTaaS): A platform for digital twin developers and users. Proceedings of the 2023 IEEE Smart World Congress (SWC), Portsmouth, UK.","DOI":"10.1109\/SWC57546.2023.10448890"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Georgakopoulos, D., and Bamunuarachchi, D. (2021, January 13\u201315). Digital twins-based application development for digital manufacturing. Proceedings of the 2021 IEEE 7th International Conference on Collaboration and Internet Computing (CIC), Atlanta, GA, USA.","DOI":"10.1109\/CIC52973.2021.00025"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Steinmetz, C., Schroeder, G.N., Rettberg, A., Rodrigues, R.N., and Pereira, C.E. (2021, January 1\u20135). Enabling and supporting car-as-a-service by digital twin modeling and deployment. Proceedings of the 2021 Design, Automation & Test in Europe Conference & Exhibition (DATE), Grenoble, France.","DOI":"10.23919\/DATE51398.2021.9474248"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/MCC.2015.51","article-title":"Containerization and the PaaS Cloud","volume":"2","author":"Pahl","year":"2017","journal-title":"IEEE Cloud Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations","volume":"378","author":"Raissi","year":"2019","journal-title":"J. Comput. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"108362","DOI":"10.1016\/j.anucene.2021.108362","article-title":"Uncertainty Quantification and Software Risk Analysis for Digital Twins in the Nearly Autonomous Management and Control Systems: A Review","volume":"160","author":"Lin","year":"2021","journal-title":"Ann. Nucl. Energy"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.1016\/j.ymssp.2005.09.012","article-title":"A Review on Machinery Diagnostics and Prognostics Implementing Condition-Based Maintenance","volume":"20","author":"Jardine","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.ymssp.2014.05.029","article-title":"Significance, Interpretation, and Quantification of Uncertainty in Prognostics and Remaining Useful Life Prediction","volume":"52","author":"Sankararaman","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Williams, C.K., and Rasmussen, C.E. (2006). Gaussian Processes for Machine Learning, MIT Press.","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Barimah, A.K., Niculita, O., McGlinchey, D., and Cowell, A. (2023). Data-quality assessment for digital twins targeting multi-component degradation in industrial internet of things (IIoT)-enabled smart infrastructure systems. Appl. Sci., 13.","DOI":"10.3390\/app132413076"},{"key":"ref_35","unstructured":"Knight, E., Russell, M., Sawalka, D., and Yendell, S. (2013). ValveModeling. Control Valve Wiki."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2664","DOI":"10.1080\/01431161.2019.1694725","article-title":"Analysis of various optimizers on deep convolutional neural network model in the application of hyperspectral remote sensing image classification","volume":"41","author":"Bera","year":"2020","journal-title":"Int. J. Remote Sens."},{"key":"ref_37","unstructured":"Gal, Y., and Ghahramani, Z. (2016, January 19\u201324). Dropout as a bayesian approximation: Representing model uncertainty in deep learning. Proceedings of the International Conference on Machine Learning, PMLR, New York, NY, USA."}],"container-title":["Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-431X\/14\/4\/121\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:00:19Z","timestamp":1760029219000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-431X\/14\/4\/121"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,26]]},"references-count":37,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["computers14040121"],"URL":"https:\/\/doi.org\/10.3390\/computers14040121","relation":{},"ISSN":["2073-431X"],"issn-type":[{"value":"2073-431X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,26]]}}}