{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T19:27:35Z","timestamp":1770492455936,"version":"3.49.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"23","license":[{"start":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T00:00:00Z","timestamp":1624838400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T00:00:00Z","timestamp":1624838400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Spanish Ministry of Economy and Business","award":["RTC-2015-3358-5"],"award-info":[{"award-number":["RTC-2015-3358-5"]}]},{"name":"Aragon government RIS3 program","award":["LMP_16_18"],"award-info":[{"award-number":["LMP_16_18"]}]},{"DOI":"10.13039\/501100007041","name":"Universidad de Zaragoza","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100007041","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents a fault detection system for photovoltaic standalone applications based on Gaussian Process Regression (GPR). The installation is a communication repeater from the Confederaci\u00f3n Hidrogr\u00e1fica del Ebro (CHE), public institution which manages the hydrographic system of Arag\u00f3n, Spain. Therefore, fault-tolerance is a mandatory requirement, complex to fulfill since it depends on the meteorology, the state of the batteries and the power demand. To solve it, we propose an online voltage prediction solution where GPR is applied in a real and large dataset of two years to predict the behavior of the installation up to 48\u00a0hour. The dataset captures electrical and thermal measures of the lead-acid batteries which sustain the installation. In particular, the crucial aspect to avoid failures is to determine the voltage at the end of the night, so different GPR methods are studied. Firstly, the photovoltaic standalone installation is described, along with the dataset. Then, there is an overview of GPR, emphasizing in the key aspects to deal with real and large datasets. Besides, three online recursive multistep GPR model alternatives are tailored, justifying the selection of the hyperparameters: Regular GPR, Sparse GPR and Multiple Experts (ME) GPR. An exhaustive assessment is performed, validating the results with those obtained by Long Short-Term Memory (LSTM) and Nonlinear Autoregressive Exogenous Model (NARX) networks. A maximum error of 127\u00a0mV and 308\u00a0mV at the end of the night with Sparse and ME, respectively, corroborates GPR as a promising tool.<\/jats:p>","DOI":"10.1007\/s00521-021-06254-6","type":"journal-article","created":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T19:07:21Z","timestamp":1624907241000},"page":"16577-16590","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Online voltage prediction using gaussian process regression for fault-tolerant photovoltaic standalone applications"],"prefix":"10.1007","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9376-543X","authenticated-orcid":false,"given":"Jos\u00e9 Miguel","family":"Sanz-Alcaine","sequence":"first","affiliation":[]},{"given":"Eduardo","family":"Sebasti\u00e1n","sequence":"additional","affiliation":[]},{"given":"Iv\u00e1n","family":"Sanz-Gorrachategui","sequence":"additional","affiliation":[]},{"given":"Carlos","family":"Bernal-Ruiz","sequence":"additional","affiliation":[]},{"given":"Antonio","family":"Bono-Nuez","sequence":"additional","affiliation":[]},{"given":"Milutin","family":"Pajovic","sequence":"additional","affiliation":[]},{"given":"Philip V.","family":"Orlik","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,6,28]]},"reference":[{"key":"6254_CR1","first-page":"4636","volume":"5","author":"S Vazquez","year":"2011","unstructured":"Vazquez S, Lukic S, Galvan E, Franquelo LG, Carrasco JM, Leon JI (2011) Recent advances on energy storage systems. Proc Industrial Electron Conf. 5:4636\u20134640","journal-title":"Proc Industrial Electron Conf."},{"key":"6254_CR2","doi-asserted-by":"publisher","first-page":"3028","DOI":"10.1016\/j.jclepro.2017.11.107","volume":"172","author":"M Taki","year":"2016","unstructured":"Taki M, Rohani A, Soheili-Fard F, Abdeshahi A (2016) Assessment of energy consumption and modeling of output energy for wheat production by neural network (MLP and RBF) and Gaussian process regression (GPR) models. J Clean Prod 172:3028\u20133041","journal-title":"J Clean Prod"},{"key":"6254_CR3","doi-asserted-by":"publisher","first-page":"1607","DOI":"10.1109\/TIE.2012.2222852","volume":"60","author":"M Sechilariu","year":"2013","unstructured":"Sechilariu M, Wang B, Locment F (2013) Building integrated photovoltaic system with energy storage and smart grid communication. IEEE Trans Ind Electron 60:1607\u20131618","journal-title":"IEEE Trans Ind Electron"},{"key":"6254_CR4","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1109\/TSG.2015.2392100","volume":"7","author":"W Yu","year":"2016","unstructured":"Yu W, Xue Y, Luo J, Ni M, Tong H, Huang T (2016) An UHV grid security and stability defense system: Considering the risk of power system communication. IEEE Trans Smart Grid 7:491\u2013500","journal-title":"IEEE Trans Smart Grid"},{"key":"6254_CR5","first-page":"1935","volume":"6","author":"J Qui\u00f1onero-candela","year":"2005","unstructured":"Qui\u00f1onero-candela J, Rasmussen CE, Herbrich R (2005) A unifying view of sparse approximate Gaussian process regression. J Mach Learn Res 6:1935\u20131959","journal-title":"J Mach Learn Res"},{"key":"6254_CR6","volume-title":"Gaussian processes for machine learning","author":"CE Rasmussen","year":"2006","unstructured":"Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT Press"},{"key":"6254_CR7","doi-asserted-by":"publisher","first-page":"2391","DOI":"10.1109\/TIE.2015.2509916","volume":"63","author":"A El Mejdoubi","year":"2016","unstructured":"El Mejdoubi A, Oukaour A, Chaoui H, Gualous H, Sabor J, Slamani Y (2016) State-of-charge and state-of-health lithium-ion batteries\u2019 diagnosis according to surface temperature variation. IEEE Trans Ind Electron 63:2391\u20132402","journal-title":"IEEE Trans Ind Electron"},{"key":"6254_CR8","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1109\/TII.2012.2222650","volume":"9","author":"HT Lin","year":"2013","unstructured":"Lin HT, Liang TJ, Chen SM (2013) Estimation of battery state of health using probabilistic neural network. IEEE Trans Ind Informatics 9:679\u2013685","journal-title":"IEEE Trans Ind Informatics"},{"key":"6254_CR9","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1016\/j.jpowsour.2014.07.016","volume":"269","author":"JN Hu","year":"2014","unstructured":"Hu JN, Hu JJ, Lin HB, Li XP, Jiang CL, Qiu XH, Li WS (2014) State-of-charge estimation for battery management system using optimized support vector machine for regression. J Power Sources 269:682\u2013693","journal-title":"J Power Sources"},{"key":"6254_CR10","doi-asserted-by":"publisher","first-page":"4311","DOI":"10.1109\/TIE.2017.2764869","volume":"65","author":"GO Sahinoglu","year":"2018","unstructured":"Sahinoglu GO, Pajovic M, Sahinoglu Z, Wang Y, Orlik PV, Wada T (2018) Battery state-of-charge estimation based on regular\/recurrent gaussian process regression. IEEE Trans Ind Electron 65:4311\u20134321","journal-title":"IEEE Trans Ind Electron"},{"key":"6254_CR11","first-page":"827","volume":"6","author":"M Pajovic","year":"2017","unstructured":"Pajovic M, Sahinoglu Z, Wang Y, Orlik PV, Wada T (2017) Online data-driven battery voltage prediction. Proc Int Conf Ind Informatics. 6:827\u2013834","journal-title":"Proc Int Conf Ind Informatics."},{"key":"6254_CR12","first-page":"80","volume":"12","author":"D Liu","year":"2012","unstructured":"Liu D, Pang J, Zhou J, Peng Y (2012) Data-driven prognostics for lithium-ion battery based on Gaussian process regression. Proc Progn Syst Heal Manag Conf. 12:80\u201384","journal-title":"Proc Progn Syst Heal Manag Conf."},{"issue":"11","key":"6254_CR13","doi-asserted-by":"publisher","first-page":"12775","DOI":"10.1109\/TVT.2020.3024019","volume":"69","author":"X Cong","year":"2020","unstructured":"Cong X, Member S, Zhang C, Member S, Jiang J (2020) A hybrid method for the prediction of the remaining useful life of lithium - ion batteries with accelerated capacity degradation. IEEE Trans Vehic Tech 69(11):12775\u201312785","journal-title":"IEEE Trans Vehic Tech"},{"key":"6254_CR14","doi-asserted-by":"publisher","first-page":"39474","DOI":"10.1109\/ACCESS.2019.2905740","volume":"7","author":"J Liu","year":"2019","unstructured":"Liu J, Chen Z (2019) Remaining useful life prediction of lithium-ion batteries based on health indicator and gaussian process regression model. IEEE Access 7:39474\u201339484","journal-title":"IEEE Access"},{"key":"6254_CR15","doi-asserted-by":"publisher","first-page":"1225","DOI":"10.1109\/TTE.2019.2944802","volume":"5","author":"K Liu","year":"2019","unstructured":"Liu K, Hu X, Wei Z, Li Y, Jiang Y (2019) Modified gaussian process regression models for cyclic capacity prediction of lithium-ion batteries. IEEE Trans Transp Electrif 5:1225\u20131236","journal-title":"IEEE Trans Transp Electrif"},{"issue":"4","key":"6254_CR16","doi-asserted-by":"publisher","first-page":"3170","DOI":"10.1109\/TIE.2020.2973876","volume":"68","author":"K Liu","year":"2020","unstructured":"Liu K, Shang Y, Ouyang Q, Widanage WD (2020) A data-driven approach with uncertainty quantification for predicting future capacities and remaining useful life of lithium-ion battery. IEEE Trans Ind Electron 68(4):3170\u20133180","journal-title":"IEEE Trans Ind Electron"},{"key":"6254_CR17","doi-asserted-by":"publisher","first-page":"3767","DOI":"10.1109\/TII.2019.2941747","volume":"16","author":"K Liu","year":"2020","unstructured":"Liu K, Li Y, Hu X, Lucu M, Widanage WD (2020) Gaussian process regression with automatic relevance determination kernel for calendar aging prediction of lithium-ion batteries. IEEE Trans Ind Informatics 16:3767\u20133777","journal-title":"IEEE Trans Ind Informatics"},{"issue":"8","key":"6254_CR18","first-page":"514","volume":"8","author":"CKI Williams","year":"1996","unstructured":"Williams CKI, Rasmussen CE (1996) Gaussian processes for regression. Adv Neural Inf Process Syst 8(8):514\u2013520","journal-title":"Adv Neural Inf Process Syst"},{"key":"6254_CR19","unstructured":"Duvenaud DK (2014) Automatic model construction with Gaussian processes (Doctoral thesis)."},{"key":"6254_CR20","first-page":"3011","volume":"11","author":"CE Rasmussen","year":"2010","unstructured":"Rasmussen CE, Nickisch H (2010) Gaussian processes for machine learning (GPML) toolbox. J Mach Learn Res 11:3011\u20133015","journal-title":"J Mach Learn Res"},{"key":"6254_CR21","doi-asserted-by":"crossref","unstructured":"Kohonen T (2001) Self-organizing maps, 3rd ed.","DOI":"10.1007\/978-3-642-56927-2"},{"key":"6254_CR22","unstructured":"Kohonen T (1997) Exploration of very large databases by self-organizing maps. IEEE Int Conf Neural Networks - Conf Proc."},{"key":"6254_CR23","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1109\/IJCNN.1989.118292","volume":"2","author":"J Kangas","year":"1989","unstructured":"Kangas J, Kohonen T, Laaksonen J, Simula O, Venta O (1989) Variants of self-organizing maps. Int Joint Conf Neur Net 2:517\u2013522","journal-title":"Int Joint Conf Neur Net"},{"key":"6254_CR24","unstructured":"Vesanto Juha, Himberg Johan, Alhoniemi Esa PJ (2000) Self-Organizing Map in Matlab: Som Toolbox"},{"key":"6254_CR25","first-page":"577","volume":"9","author":"K Wagstaff","year":"2001","unstructured":"Wagstaff K, Cardie C, Rogers S, Schr\u00f6dl S (2001) Constrained K-means clustering with background knowledge. Int Conf Mach Learn ICML. 9:577\u2013584","journal-title":"Int Conf Mach Learn ICML."},{"key":"6254_CR26","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1016\/S0031-3203(02)00060-2","volume":"36","author":"A Likas","year":"2003","unstructured":"Likas A, Vlassis N, J. Verbeek J, (2003) The global k-means clustering algorithm. Pattern Recognit 36:451\u2013461","journal-title":"Pattern Recognit"},{"key":"6254_CR27","doi-asserted-by":"crossref","unstructured":"Sanz-Gorrachategui I, Pastor-Flores P, Guillen-Asensio A, Artal-Sevil JS, Bono-Nuez A, Martin-Del-Brio B, Bernal-Ruiz C (2020) Unsupervised clustering of battery waveforms in off-grid PV installations. Int Conf Ecol Veh Renew Energies - Conf Proc.","DOI":"10.1109\/EVER48776.2020.9242942"},{"key":"6254_CR28","unstructured":"Bauer M, Van Der Wilk M, Rasmussen CE (2016) Understanding probabilistic sparse Gaussian Process approximations. Adv Neural Inf Process Syst 1533\u20131541"},{"key":"6254_CR29","doi-asserted-by":"crossref","unstructured":"Ozcan G, Pajovic M, Sahinoglu Z, Wang Y, Orlik PV, Wada T (2016) Online battery state-of-charge estimation based on sparse gaussian process regression. IEEE Power Energy Soc Gen Meet - Conf Proc","DOI":"10.1109\/PESGM.2016.7741980"},{"key":"6254_CR30","first-page":"333","volume":"14","author":"K Chalupka","year":"2013","unstructured":"Chalupka K, Williams CKI, Murray I (2013) A framework for evaluating approximation methods for Gaussian process regression. J Mach Learn Res 14:333\u2013350","journal-title":"J Mach Learn Res"},{"key":"6254_CR31","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1016\/0304-3975(85)90224-5","volume":"38","author":"TF Gonzalez","year":"1985","unstructured":"Gonzalez TF (1985) Clustering to minimize the maximum intercluster distance. Theor Comput Sci 38:293\u2013306","journal-title":"Theor Comput Sci"},{"key":"6254_CR32","doi-asserted-by":"publisher","first-page":"1191","DOI":"10.1080\/00207179008934126","volume":"51","author":"S Chen","year":"1990","unstructured":"Chen S, Billings SA, Grant PM (1990) Non-linear system identification using neural networks. Int J Control 51:1191\u20131214","journal-title":"Int J Control"},{"key":"6254_CR33","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1109\/3477.558801","volume":"27","author":"HT Siegelmann","year":"1997","unstructured":"Siegelmann HT, Horne BG, Giles CL (1997) Computational capabilities of recurrent NARX neural networks. IEEE Trans Syst Man, Cybern Part B Cybern 27:208\u2013215","journal-title":"IEEE Trans Syst Man, Cybern Part B Cybern"},{"key":"6254_CR34","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1016\/j.neunet.2005.06.042","volume":"18","author":"A Graves","year":"2005","unstructured":"Graves A, Schmidhuber J (2005) Framewise phoneme classification with bidirectional LSTM and other neural network architectures. Neural Netw 18:602\u2013610","journal-title":"Neural Netw"},{"key":"6254_CR35","doi-asserted-by":"publisher","first-page":"2222","DOI":"10.1109\/TNNLS.2016.2582924","volume":"28","author":"K Greff","year":"2017","unstructured":"Greff K, Srivastava RK, Koutnik J, Steunebrink BR, Schmidhuber J (2017) LSTM: A search space odyssey. IEEE Trans Neural Networks Learn Syst 28:2222\u20132232","journal-title":"IEEE Trans Neural Networks Learn Syst"},{"key":"6254_CR36","doi-asserted-by":"crossref","unstructured":"Guillen-Asensio A, Sanz-Gorrachategui I, Pastor-Flores P, Artal-Sevil JS, Bono-Nuez A, Martin-Del-Brio B, Bernal-Ruiz C (2020) Battery state prediction in photovoltaic standalone installations. Int Conf Ecol Veh Renew Energies - Conf Proc.","DOI":"10.1109\/EVER48776.2020.9243111"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-021-06254-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-021-06254-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-021-06254-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T18:14:47Z","timestamp":1635963287000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-021-06254-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,28]]},"references-count":36,"journal-issue":{"issue":"23","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["6254"],"URL":"https:\/\/doi.org\/10.1007\/s00521-021-06254-6","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,28]]},"assertion":[{"value":"28 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 June 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 June 2021","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 conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}