{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T10:27:35Z","timestamp":1774434455675,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T00:00:00Z","timestamp":1770249600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T00:00:00Z","timestamp":1770768000000},"content-version":"vor","delay-in-days":6,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["LQ24F030010"],"award-info":[{"award-number":["LQ24F030010"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62306097"],"award-info":[{"award-number":["62306097"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62202137"],"award-info":[{"award-number":["62202137"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1007\/s40747-025-02212-0","type":"journal-article","created":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T16:59:59Z","timestamp":1770310799000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A flexible linear temporal logic-based data inference architecture for industrial process prediction"],"prefix":"10.1007","volume":"12","author":[{"given":"Xu","family":"Huo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruyu","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2118-6786","authenticated-orcid":false,"given":"Haoyu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qianneng","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiqi","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiufeng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,2,5]]},"reference":[{"key":"2212_CR1","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.psep.2019.11.014","volume":"133","author":"L Zhao","year":"2020","unstructured":"Zhao L, Dai T, Qiao Z, Sun P, Hao J, Yang Y (2020) Application of artificial intelligence to wastewater treatment: a bibliometric analysis and systematic review of technology, economy, management, and wastewater reuse. Process Saf Environ Prot 133:169\u2013182","journal-title":"Process Saf Environ Prot"},{"key":"2212_CR2","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s40747-025-02098-y","volume":"11","author":"Y Zou","year":"2025","unstructured":"Zou Y, Wang H (2025) A three-stage cross-project defect prediction framework based on feature representation and knowledge transfer. Complex Intell Syst 11:459","journal-title":"Complex Intell Syst"},{"key":"2212_CR3","doi-asserted-by":"publisher","first-page":"107071","DOI":"10.1016\/j.compchemeng.2020.107071","volume":"143","author":"S Hwangbo","year":"2020","unstructured":"Hwangbo S, Al R, Sin G (2020) An integrated framework for plant data-driven process modeling using deep-learning with Monte-Carlo simulations. Comput Chem Eng 143:107071","journal-title":"Comput Chem Eng"},{"key":"2212_CR4","doi-asserted-by":"publisher","first-page":"134227","DOI":"10.1016\/j.scitotenv.2019.134227","volume":"698","author":"J Yao","year":"2020","unstructured":"Yao J, Wang P, Wang G, Shrestha S, Xue B, Sun W (2020) Establishing a time series trend structure model to mine potential hydrological information from hydrometeorological time series data. Sci Total Environ 698:134227","journal-title":"Sci Total Environ"},{"key":"2212_CR5","doi-asserted-by":"publisher","first-page":"3511073","DOI":"10.1155\/2022\/3511073","volume":"2022","author":"J Yasenjiang","year":"2022","unstructured":"Yasenjiang J, Xu C, Zhang S, Zhang X (2022) Fault diagnosis and prediction of continuous industrial processes based on hidden Markov model-Bayesian network hybrid model. Int J Chem Eng 2022:3511073","journal-title":"Int J Chem Eng"},{"key":"2212_CR6","doi-asserted-by":"publisher","first-page":"6705","DOI":"10.1007\/s40747-024-01512-1","volume":"40","author":"X Hu","year":"2024","unstructured":"Hu X, Lin S (2024) DFFNet: a lightweight approach for efficient feature-optimized fusion in steel strip surface defect detection. Complex Intell Syst 40:6705\u20136723","journal-title":"Complex Intell Syst"},{"key":"2212_CR7","doi-asserted-by":"publisher","first-page":"3054860","DOI":"10.1155\/2022\/3054860","volume":"2022","author":"C Xu","year":"2022","unstructured":"Xu C, Yasenjiang J, Cui P, Zhang S, Zhang X (2022) Comprehensive monitoring of complex industrial processes with multiple characteristics. Int J Chem Eng 2022:3054860","journal-title":"Int J Chem Eng"},{"issue":"4","key":"2212_CR8","doi-asserted-by":"publisher","first-page":"2938","DOI":"10.1109\/TII.2020.3005532","volume":"17","author":"A Kumar","year":"2021","unstructured":"Kumar A, Jaiswal A (2021) A deep swarm-optimized model for leveraging Industrial data analytics in cognitive manufacturing. IEEE Trans Ind Inform 17(4):2938\u20132946","journal-title":"IEEE Trans Ind Inform"},{"key":"2212_CR9","doi-asserted-by":"publisher","first-page":"1231","DOI":"10.1007\/s11814-018-0028-6","volume":"35","author":"H Kim","year":"2018","unstructured":"Kim H, Gebreselassie AL, Dan S, Shin D (2018) Random forest classifier for real- time chemical leak source tracking using fence-monitoring sensors. Korean J Chem Eng 35:1231\u20131239","journal-title":"Korean J Chem Eng"},{"key":"2212_CR10","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1016\/j.jprocont.2020.07.001","volume":"92","author":"F Griesing-Scheiwe","year":"2020","unstructured":"Griesing-Scheiwe F, Shardt YA, P\u00e9rez-Zu\u00f1iga G, Yang X (2020) Soft sensor design for variable time delay and variable sampling time. J Process Control 92:310\u2013318","journal-title":"J Process Control"},{"key":"2212_CR11","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1016\/j.ins.2019.01.062","volume":"484","author":"W Dai","year":"2019","unstructured":"Dai W, Li D, Zhou P, Chai T (2019) Stochastic configuration networks with block increments for data modeling in process industries. Inf Sci 484:367\u2013386","journal-title":"Inf Sci"},{"key":"2212_CR12","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.ins.2019.04.050","volume":"494","author":"U Yun","year":"2019","unstructured":"Yun U, Lee G, Yoon E (2019) Advanced approach of sliding window based erasable pattern mining with list structure of industrial fields. Inf Sci 494:37\u201359","journal-title":"Inf Sci"},{"key":"2212_CR13","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.chemolab.2018.06.008","volume":"179","author":"Y Wang","year":"2018","unstructured":"Wang Y, Li H (2018) A novel intelligent modeling framework integrating the convolutional neural network with an adaptive time-series window and its application to industrial process operational optimization. Chemometr Intell Lab Syst 179:64\u201372","journal-title":"Chemometr Intell Lab Syst"},{"key":"2212_CR14","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/j.apenergy.2017.12.104","volume":"213","author":"DW Van Der Meer","year":"2018","unstructured":"Van Der Meer DW, Shepero M, Svensson A, Wid\u00b4en J, Munkhammar J (2018) Probabilistic forecasting of electricity consumption, photovoltaic power generation and net demand of an individual building using Gaussian processes. Appl Energy 213:195\u2013207","journal-title":"Appl Energy"},{"key":"2212_CR15","doi-asserted-by":"publisher","first-page":"104098","DOI":"10.1016\/j.conengprac.2019.07.016","volume":"91","author":"W Shao","year":"2019","unstructured":"Shao W, Ge Z, Song Z, Wang K (2019) Nonlinear industrial soft sensor development based on semi-supervised probabilistic mixture of extreme learning machines. Control Eng Pract 91:104098","journal-title":"Control Eng Pract"},{"key":"2212_CR16","doi-asserted-by":"publisher","first-page":"6809569","DOI":"10.1155\/2023\/6809569","volume":"2023","author":"B Liu","year":"2023","unstructured":"Liu B, Nouroddin MK (2023) Application of artificial intelligent approach to predict the normal boiling point of refrigerants. Int J Chem Eng 2023:6809569","journal-title":"Int J Chem Eng"},{"issue":"8","key":"2212_CR17","doi-asserted-by":"publisher","first-page":"5244","DOI":"10.1109\/TII.2019.2952917","volume":"16","author":"D Wu","year":"2020","unstructured":"Wu D, Jiang Z, Xie X, Wei X, Yu W, Li R (2020) LSTM learning with Bayesian and Gaussian processing for anomaly detection in Industrial IoT. IEEE Trans Ind Inform 16(8):5244\u20135253","journal-title":"IEEE Trans Ind Inform"},{"key":"2212_CR18","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/j.compchemeng.2017.02.041","volume":"107","author":"Z Zhang","year":"2017","unstructured":"Zhang Z, Zhao J (2017) A deep belief network based fault diagnosis model for complex chemical processes. Comput Chem Eng 107:395\u2013407","journal-title":"Comput Chem Eng"},{"key":"2212_CR19","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1016\/j.eswa.2018.11.028","volume":"120","author":"NC Petersen","year":"2019","unstructured":"Petersen NC, Rodrigues F, Pereira FC (2019) Multi-output bus travel time prediction with convolutional LSTM neural network. Expert Syst Appl 120:426\u2013435","journal-title":"Expert Syst Appl"},{"issue":"8","key":"2212_CR20","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","volume":"9","author":"S Hochreiter","year":"1997","unstructured":"Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735\u20131780","journal-title":"Neural Comput"},{"key":"2212_CR21","doi-asserted-by":"crossref","unstructured":"Cho K, Van Merri\u00ebnboer B, Gulcehre C, Bahdanau D, Bougares F, Schwenk H, Bengio Y (2014) Learning phrase representations using RNN encoder\u2013decoder for statistical machine translation. arXiv preprint. arXiv:1406.1078","DOI":"10.3115\/v1\/D14-1179"},{"issue":"7553","key":"2212_CR22","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1038\/nature14539","volume":"521","author":"Y LeCun","year":"2015","unstructured":"LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436\u2013444","journal-title":"Nature"},{"key":"2212_CR23","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/j.eswa.2018.07.019","volume":"113","author":"Y Baek","year":"2018","unstructured":"Baek Y, Kim HY (2018) ModAugNet: a new forecasting framework for stock market index value with an overfitting prevention LSTM module and a prediction LSTM module. Expert Syst Appl 113:457\u2013480","journal-title":"Expert Syst Appl"},{"issue":"10","key":"2212_CR24","doi-asserted-by":"publisher","first-page":"3762","DOI":"10.3390\/su10103765","volume":"10","author":"H Chung","year":"2018","unstructured":"Chung H, Shin KS (2018) Genetic algorithm-optimized long short-term memory network for stock market prediction. Sustainability 10(10):3762","journal-title":"Sustainability"},{"key":"2212_CR25","doi-asserted-by":"publisher","first-page":"107738","DOI":"10.1016\/j.compchemeng.2022.107738","volume":"160","author":"LD Hansen","year":"2022","unstructured":"Hansen LD, Stokholm-Bjerregaard M, Durdevic P (2022) Modeling phosphorous dynamics in a wastewater treatment process using Bayesian optimized LSTM. Comput Chem Eng 160:107738","journal-title":"Comput Chem Eng"},{"key":"2212_CR26","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/j.ins.2022.10.078","volume":"616","author":"K Zarzycki","year":"2022","unstructured":"Zarzycki K, \u0141awry\u0144czuk M (2022) Advanced predictive control for GRU and LSTM networks. Inf Sci 616:229\u2013254","journal-title":"Inf Sci"},{"key":"2212_CR27","doi-asserted-by":"crossref","unstructured":"Pnueli A (1977) The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science (SFCS 1977), IEEE, pp 46\u201357","DOI":"10.1109\/SFCS.1977.32"},{"key":"2212_CR28","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/j.tcs.2014.03.033","volume":"560","author":"D Bresolin","year":"2014","unstructured":"Bresolin D, Della Monica D, Montanari A, Sala P, Sciavicco G (2014) Interval temporal logics over strongly discrete linear orders: expressiveness and complexity. Theor Comput Sci 560:269\u2013291","journal-title":"Theor Comput Sci"},{"issue":"3","key":"2212_CR29","doi-asserted-by":"publisher","first-page":"1210","DOI":"10.1109\/TAC.2016.2585083","volume":"62","author":"Z Kong","year":"2017","unstructured":"Kong Z, Jones A, Belta C (2017) Temporal logics for learning and detection of anomalous behavior. IEEE Trans Autom Contr 62(3):1210\u20131222","journal-title":"IEEE Trans Autom Contr"},{"key":"2212_CR30","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.engappai.2017.06.013","volume":"65","author":"K Liu","year":"2017","unstructured":"Liu K, Lin H, Fei Z, Liang J (2017) Spatially\u2013temporally online fault detection using timed multivariate statistical logic. Eng Appl Artif Intell 65:51\u201359","journal-title":"Eng Appl Artif Intell"},{"key":"2212_CR31","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.automatica.2015.03.029","volume":"56","author":"EA Gol","year":"2015","unstructured":"Gol EA, Lazar M, Belta C (2015) Temporal logic model predictive control. Automatica 56:78\u201385","journal-title":"Automatica"},{"key":"2212_CR32","doi-asserted-by":"publisher","first-page":"100865","DOI":"10.1016\/j.nahs.2020.100865","volume":"36","author":"H Han","year":"2020","unstructured":"Han H, Sanfelice RG (2020) Linear temporal logic for hybrid dynamical systems: characterizations and sufficient conditions. Nonlinear Anal Hybrid Syst 36:100865","journal-title":"Nonlinear Anal Hybrid Syst"},{"issue":"5","key":"2212_CR33","doi-asserted-by":"publisher","first-page":"4393","DOI":"10.1109\/TIE.2020.2984976","volume":"68","author":"G Chen","year":"2021","unstructured":"Chen G, Liu M, Kong Z (2021) Temporal-logic-based semantic fault diagnosis with time-series data from industrial internet of things. IEEE Trans Ind Electron 68(5):4393\u20134403","journal-title":"IEEE Trans Ind Electron"},{"key":"2212_CR34","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1016\/j.engappai.2018.04.017","volume":"72","author":"E Bas","year":"2018","unstructured":"Bas E, Grosan C, Egrioglu E, Yolcu U (2018) High order fuzzy time series method based on pi-sigma neural network. Eng Appl Artif Intell 72:350\u2013356","journal-title":"Eng Appl Artif Intell"},{"key":"2212_CR35","doi-asserted-by":"publisher","first-page":"103245","DOI":"10.1016\/j.engappai.2019.103245","volume":"87","author":"S Panigrahi","year":"2020","unstructured":"Panigrahi S, Behera HS (2020) A study on leading machine learning techniques for high order fuzzy time series forecasting. Eng Appl Artif Intell 87:103245","journal-title":"Eng Appl Artif Intell"},{"issue":"2","key":"2212_CR36","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1007\/s41066-022-00331-4","volume":"8","author":"G Goyal","year":"2023","unstructured":"Goyal G, Bisht DC (2023) Adaptive hybrid fuzzy time series forecasting technique based on particle swarm optimization. Granul Comput 8(2):373\u2013390","journal-title":"Granul Comput"},{"key":"2212_CR37","doi-asserted-by":"crossref","unstructured":"Zhou H, Zhang S, Peng J, Zhang S, Li J, Xiong H, Zhang W (2021) Informer: beyond efficient transformer for long sequence time-series forecasting. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 35, pp 11106\u201311115","DOI":"10.1609\/aaai.v35i12.17325"},{"key":"2212_CR38","first-page":"22419","volume":"34","author":"H Wu","year":"2021","unstructured":"Wu H, Xu J, Wang J, Long M (2021) Autoformer: decomposition transformers with auto-correlation for long-term series forecasting. Adv Neural Inf Process Syst 34:22419\u201322430","journal-title":"Adv Neural Inf Process Syst"},{"key":"2212_CR39","unstructured":"Nie Y, Nguyen NH, Sinthong P, Kalagnanam J (2022) A time series is worth 64 words: long-term forecasting with transformers. arXiv preprint. arXiv:2211.14730"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-025-02212-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02212-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02212-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T07:55:41Z","timestamp":1774425341000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-025-02212-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,5]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["2212"],"URL":"https:\/\/doi.org\/10.1007\/s40747-025-02212-0","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,5]]},"assertion":[{"value":"25 August 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2026","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 declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"110"}}