{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:37:37Z","timestamp":1760146657834,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T00:00:00Z","timestamp":1732665600000},"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>The Portuguese Institute for Quality is responsible for the realization and dissemination of the frequency standard in Portugal. There are several techniques for frequency transfer, but we use a frequency mixer to detect phase variations between two light signals with different wavelengths, traveling along an optical fibre. In this paper, we present the development of a digital twin (DT) that replicates the use of a frequency mixer to improve the frequency transfer problem. A setup was built to train and validate the technique: a frequency mixer was used to determine the phase difference between the two signals, which are caused by temperature gradients in the fibre, together with real-time temperature data from sensors placed along the fibre and on the mixer itself. The DT was trained with two machine learning algorithms, in particular, ARIMA and LSTM networks. To estimate the accuracy of the frequency mixer working as a phasemeter, several sources of uncertainty were considered and included in the DT model, with the goal of obtaining a phase value measurement and its uncertainty in real time. The JCGM 100:2008 and JCGM 101:2008 approaches were used for the estimation of the uncertainty budget. With this work, we merge DT technology with a frequency mixer used for phase detection to provide its value and uncertainty in real time.<\/jats:p>","DOI":"10.3390\/s24237574","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T10:05:56Z","timestamp":1732701956000},"page":"7574","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Digital Twin for a Frequency Mixer Used as a Phase Sensor"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9650-1763","authenticated-orcid":false,"given":"Carlos","family":"Pires","sequence":"first","affiliation":[{"name":"Instituto Portugu\u00eas da Qualidade, Rua Ant\u00f3nio Gi\u00e3o, 2, 2829-513 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0716-9568","authenticated-orcid":false,"given":"Manuel","family":"Abreu","sequence":"additional","affiliation":[{"name":"Physics Department, Faculdade de Ci\u00eancias da Universidade de Lisboa, 1749-016 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1624-4598","authenticated-orcid":false,"given":"Isabel","family":"Godinho","sequence":"additional","affiliation":[{"name":"Instituto Portugu\u00eas da Qualidade, Rua Ant\u00f3nio Gi\u00e3o, 2, 2829-513 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7177-2695","authenticated-orcid":false,"given":"Rui","family":"Agostinho","sequence":"additional","affiliation":[{"name":"Physics Department, Faculdade de Ci\u00eancias da Universidade de Lisboa, 1749-016 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9630-0854","authenticated-orcid":false,"given":"Jo\u00e3o A.","family":"Sousa","sequence":"additional","affiliation":[{"name":"Instituto Portugu\u00eas da Qualidade, Rua Ant\u00f3nio Gi\u00e3o, 2, 2829-513 Caparica, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,27]]},"reference":[{"unstructured":"(2024, July 05). Available online: https:\/\/www.iso.org\/contents\/news\/2022\/05\/metrology-in-digital-era-1.html.","key":"ref_1"},{"doi-asserted-by":"crossref","unstructured":"Sven-Christian Ebenhag, P.O. (2010, January 13\u201316). Fiber based one-way time transfer with enhanced accuracy. Proceedings of the EFTF-2010 24th European Frequency and Time Forum, Noordwijk, The Netherlands.","key":"ref_2","DOI":"10.1109\/EFTF.2010.6533648"},{"unstructured":"Kurtz, S.R. (2001). Mixers as Phase Detectors, WJ Communications, Inc.","key":"ref_3"},{"unstructured":"Poole, I. (2024, September 05). RF Mixing\/Multiplication: Frequency Mixers. Available online: https:\/\/www.electronics-notes.com\/articles\/radio\/rf-mixer\/rf-mixing-basics.php.","key":"ref_4"},{"doi-asserted-by":"crossref","unstructured":"Sun, C., and Shi, V.Z. (2021). A Combination of Physics-based Model and Neural Network Model for Digital Twins. PhysiNet. arXiv.","key":"ref_5","DOI":"10.1002\/int.22798"},{"unstructured":"Larose, D.T. (2015). Data Mining and Predictive Analytics, Wiley. [2nd ed.].","key":"ref_6"},{"unstructured":"(2008). Evaluation of Measurement Data\u2014Guide to the Expression of Uncertainty in Measurement (Standard No. JCGM 100:2008).","key":"ref_7"},{"unstructured":"(2008). Evaluation of Measurement Data\u2014Supplement 1 to the \u201cGuide to the Expression of Uncertainty in Measurement\u201d\u2014Propagation of Distributions Using a Monte Carlo Method (Standard No. JCGM 101:2008).","key":"ref_8"},{"unstructured":"Technologies, A. (2015). 34401A Digital Multimeter User\u2019s Guide, Keysight Technologies. [7th ed.].","key":"ref_9"},{"unstructured":"G\u00e9ron, A. (2019). Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow, O\u2019Reilly Media. [2nd ed.].","key":"ref_10"},{"unstructured":"Mitchell, T.M. (1997). Machine Learning, McGraw-Hill Education.","key":"ref_11"},{"unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning, MIT Press. Available online: www.deeplearningbook.org.","key":"ref_12"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/23\/7574\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:40:40Z","timestamp":1760114440000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/23\/7574"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,27]]},"references-count":12,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["s24237574"],"URL":"https:\/\/doi.org\/10.3390\/s24237574","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2024,11,27]]}}}