{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T16:31:48Z","timestamp":1776184308996,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T00:00:00Z","timestamp":1714348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"China Nuclear Industry Key Laboratory of Simulation Technology","award":["B220631"],"award-info":[{"award-number":["B220631"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Industrial process monitoring is a critical application of multivariate time-series (MTS) anomaly detection, especially crucial for safety-critical systems such as nuclear power plants (NPPs). However, some current data-driven process monitoring approaches may not fully capitalize on the temporal-spatial correlations inherent in operational MTS data. Particularly, asynchronous time-lagged correlations may exist among variables in actual NPPs, which further complicates this challenge. In this work, a reconstruction-based MTS anomaly detection approach based on a temporal-spatial transformer is proposed. It employs a two-stage temporal-spatial attention mechanism combined with a multi-scale strategy to learn the dependencies within normal operational data at various scales, thereby facilitating the extraction of temporal-spatial correlations from asynchronous MTS. Experiments on simulated datasets and real NPP datasets demonstrate that the proposed model possesses stronger feature learning capabilities, as evidenced by its improved performance in signal reconstruction and anomaly detection for asynchronous MTS data. Moreover, the proposed TS-Trans model enables earlier detection of anomalous events, which holds significant importance for enhancing operational safety and reducing potential losses in NPPs.<\/jats:p>","DOI":"10.3390\/s24092845","type":"journal-article","created":{"date-parts":[[2024,4,30]],"date-time":"2024-04-30T04:01:52Z","timestamp":1714449712000},"page":"2845","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Anomaly Detection for Asynchronous Multivariate Time Series of Nuclear Power Plants Using a Temporal-Spatial Transformer"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-1087-7373","authenticated-orcid":false,"given":"Shuang","family":"Yi","sequence":"first","affiliation":[{"name":"College of Electrical Engineering and New Energy, China Three Gorges University, Yichang 443002, China"},{"name":"College of Science, China Three Gorges University, Yichang 443002, China"}]},{"given":"Sheng","family":"Zheng","sequence":"additional","affiliation":[{"name":"College of Science, China Three Gorges University, Yichang 443002, China"}]},{"given":"Senquan","family":"Yang","sequence":"additional","affiliation":[{"name":"China Nuclear Power Operation Technology Corporation, Ltd., Wuhan 430074, China"},{"name":"China Nuclear Industry Key Laboratory of Simulation Technology, Wuhan 430074, China"}]},{"given":"Guangrong","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Science, China Three Gorges University, Yichang 443002, China"}]},{"given":"Jiajun","family":"Cai","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and New Energy, China Three Gorges University, Yichang 443002, China"},{"name":"College of Science, China Three Gorges University, Yichang 443002, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6037","DOI":"10.1016\/j.energy.2011.08.011","article-title":"Sustainability indicators for the assessment of nuclear power","volume":"36","author":"Stamford","year":"2011","journal-title":"Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.rser.2013.01.035","article-title":"Renewable energy and nuclear power towards sustainable development: Characteristics and prospects","volume":"22","author":"Karakosta","year":"2013","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5149","DOI":"10.1016\/j.enpol.2009.07.052","article-title":"Nuclear power for sustainable development: Current status and future prospects","volume":"37","author":"Adamantiades","year":"2009","journal-title":"Energy Policy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1177\/0096340211413358","article-title":"Nuclear power and the public","volume":"67","author":"Ramana","year":"2011","journal-title":"Bull. At. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.pnucene.2010.08.003","article-title":"On-line monitoring applications in nuclear power plants","volume":"53","author":"Hashemian","year":"2011","journal-title":"Prog. Nucl. Energy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.anucene.2017.10.010","article-title":"A survey of the state of condition-based maintenance (CBM) in the nuclear power industry","volume":"112","author":"Cilliers","year":"2018","journal-title":"Ann. Nucl. Energy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.pnucene.2010.12.001","article-title":"Applications of fault detection and diagnosis methods in nuclear power plants: A review","volume":"53","author":"Ma","year":"2011","journal-title":"Prog. Nucl. Energy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"106697","DOI":"10.1016\/j.compchemeng.2019.106697","article-title":"Fault detection and diagnosis in process system using artificial intelligence-based cognitive technique","volume":"134","author":"Arunthavanathan","year":"2020","journal-title":"Comput. Chem. Eng."},{"key":"ref_9","first-page":"1","article-title":"Deep learning for anomaly detection: A review","volume":"54","author":"Pang","year":"2021","journal-title":"ACM Comput. Surv. CSUR"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"109684","DOI":"10.1016\/j.anucene.2023.109684","article-title":"Fault supervision of nuclear research reactor systems using artificial neural networks: A review with results","volume":"185","author":"Khentout","year":"2023","journal-title":"Ann. Nucl. Energy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"112161","DOI":"10.1016\/j.nucengdes.2023.112161","article-title":"Attention-based time series analysis for data-driven anomaly detection in nuclear power plants","volume":"404","author":"Dong","year":"2023","journal-title":"Nucl. Eng. Des."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Deng, A., and Hooi, B. (2021, January 2\u20139). Graph neural network-based anomaly detection in multivariate time series. Proceedings of the AAAI Conference on Artificial Intelligence, Virtually.","DOI":"10.1609\/aaai.v35i5.16523"},{"key":"ref_13","unstructured":"Zong, B., Song, Q., Min, M.R., Cheng, W., Lumezanu, C., Cho, D., and Chen, H. (May, January 30). Deep autoencoding gaussian mixture model for unsupervised anomaly detection. Proceedings of the International Conference on Learning Representations, Vancouver, BC, Canada."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"042050","DOI":"10.1088\/1742-6596\/1213\/4\/042050","article-title":"Temporal convolutional networks for anomaly detection in time series","volume":"1213","author":"He","year":"2019","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Hundman, K., Constantinou, V., Laporte, C., Colwell, I., and Soderstrom, T. (2018, January 19\u201323). Detecting spacecraft anomalies using lstms and nonparametric dynamic thresholding. Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, London, UK.","DOI":"10.1145\/3219819.3219845"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1544","DOI":"10.1109\/LRA.2018.2801475","article-title":"A multimodal anomaly detector for robot-assisted feeding using an LSTM-based variational autoencoder","volume":"3","author":"Park","year":"2018","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Tuli, S., Casale, G., and Jennings, N.R. (2022). Tranad: Deep transformer networks for anomaly detection in multivariate time series data. arXiv.","DOI":"10.14778\/3514061.3514067"},{"key":"ref_18","first-page":"5998","article-title":"Attention is all you need","volume":"30","author":"Vaswani","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"122666","DOI":"10.1016\/j.eswa.2023.122666","article-title":"A comprehensive survey on applications of transformers for deep learning tasks","volume":"241","author":"Islam","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Abdulaal, A., Liu, Z., and Lancewicki, T. (2021, January 14\u201318). Practical approach to asynchronous multivariate time series anomaly detection and localization. Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, Singapore.","DOI":"10.1145\/3447548.3467174"},{"key":"ref_21","unstructured":"Gamboa, J.C.B. (2017). Deep learning for time-series analysis. arXiv."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"120043","DOI":"10.1109\/ACCESS.2021.3107975","article-title":"Deep learning for anomaly detection in time-series data: Review, analysis, and guidelines","volume":"9","author":"Choi","year":"2021","journal-title":"IEEE Access"},{"key":"ref_23","unstructured":"Nie, Y., Nguyen, N.H., Sinthong, P., and Kalagnanam, J. (2022, January 25\u201329). A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. Proceedings of the Eleventh International Conference on Learning Representations, Virtual Event."},{"key":"ref_24","unstructured":"Zhang, Y., and Yan, J. (2023, January 1\u20135). Crossformer: Transformer utilizing cross-dimension dependency for multivariate time series forecasting. Proceedings of the Eleventh International Conference on Learning Representations, Kigali, Rwanda."},{"key":"ref_25","unstructured":"Liu, Y., Hu, T., Zhang, H., Wu, H., Wang, S., Ma, L., and Long, M. (2023). itransformer: Inverted transformers are effective for time series forecasting. arXiv."},{"key":"ref_26","first-page":"100469","article-title":"Digital twin-driven fault diagnosis method for composite faults by combining virtual and real data","volume":"33","author":"Yang","year":"2023","journal-title":"J. Ind. Inf. Integr."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2456","DOI":"10.1109\/TPEL.2022.3207181","article-title":"On Bayesian optimization-based residual CNN for estimation of inter-turn short circuit fault in PMSM","volume":"38","author":"Song","year":"2022","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_28","first-page":"1025","article-title":"Wireless sensor networks for scada and industrial control systems","volume":"3","author":"Nechibvute","year":"2013","journal-title":"Int. J. Eng. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/BF02834632","article-title":"Mahalanobis distance","volume":"4","author":"McLachlan","year":"1999","journal-title":"Resonance"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0169-7439(99)00047-7","article-title":"The mahalanobis distance","volume":"50","author":"Massart","year":"2000","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1038\/s41597-022-01879-1","article-title":"An open time-series simulated dataset covering various accidents for nuclear power plants","volume":"9","author":"Qi","year":"2022","journal-title":"Sci. Data"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.anucene.2011.10.016","article-title":"Introducing PCTRAN as an evaluation tool for nuclear power plant emergency responses","volume":"40","author":"Cheng","year":"2012","journal-title":"Ann. Nucl. Energy"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Jin, Y., Qiu, C., Sun, L., Peng, X., and Zhou, J. (2017, January 1\u20133). Anomaly detection in time series via robust PCA. Proceedings of the 2017 2nd IEEE International Conference on Intelligent Transportation Engineering (ICITE), Singapore.","DOI":"10.1109\/ICITE.2017.8056937"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/9\/2845\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:36:25Z","timestamp":1760106985000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/9\/2845"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,29]]},"references-count":33,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["s24092845"],"URL":"https:\/\/doi.org\/10.3390\/s24092845","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,29]]}}}