{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T15:26:41Z","timestamp":1777994801171,"version":"3.51.4"},"reference-count":33,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,23]],"date-time":"2022-09-23T00:00:00Z","timestamp":1663891200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The intelligent electrical power system is a comprehensive symmetrical system that controls the power supply and power consumption. As a basis for intelligent power supply control, load demand forecasting in power system operation management has attracted considerable research attention in energy management. In this study, we proposed a novel unsupervised multi-dimensional feature learning forecasting model, named MultiDBN-T, based on a deep belief network and transformer encoder to accurately forecast short-term power load demand and implement power generation planning and scheduling. In the model, the first layer (pre-DBN), based on a deep belief network, was designed to perform unsupervised multi-feature extraction feature learning on the data, and strongly coupled features between multiple independent observable variables were obtained. Next, the encoder layer (D-TEncoder), based on multi-head self-attention, was used to learn the coupled features between various locations, times, or time periods in historical data. The feature embedding of the original multivariate data was performed after the hidden variable relationship was determined. Finally, short-term power load forecasting was conducted. Experimental comparison and analysis of various sequence learning algorithms revealed that the forecasting results of MultiDBN-T were the best, and its mean absolute percentage error and root mean square error were improved by more than 40% on average compared with other algorithms. The effectiveness and accuracy of the model were experimentally verified.<\/jats:p>","DOI":"10.3390\/sym14101999","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T01:23:16Z","timestamp":1664414596000},"page":"1999","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An Unsupervised Multi-Dimensional Representation Learning Model for Short-Term Electrical Load Forecasting"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8333-7415","authenticated-orcid":false,"given":"Weihua","family":"Bai","sequence":"first","affiliation":[{"name":"School of Computer Science, Zhaoqing University, Zhaoqing 526061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaxian","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Computer Science, Zhaoqing University, Zhaoqing 526061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jialing","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Computer Science, Zhaoqing University, Zhaoqing 526061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenwei","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Computer Science, Zhaoqing University, Zhaoqing 526061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keqin","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Computer Science, State University of New York, New Paltz, NY 12561, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"120069","DOI":"10.1016\/j.energy.2021.120069","article-title":"A novel genetic LSTM model for wind power forecast","volume":"223","author":"Shahid","year":"2021","journal-title":"Energy"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Phan, Q.T., Wu, Y.K., and Phan, Q.D. (2021). A hybrid wind power forecasting model with XGBoost, data preprocessing considering different NWPs. Appl. Sci., 11.","DOI":"10.3390\/app11031100"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"103269","DOI":"10.1016\/j.est.2021.103269","article-title":"A novel method for state of energy estimation of lithium-ion batteries using particle filter and extended Kalman filter","volume":"43","author":"Lai","year":"2021","journal-title":"J. Energy Storage"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1016\/j.renene.2021.03.030","article-title":"Artificial Neural Networks based wake model for power prediction of wind farm","volume":"172","author":"Ti","year":"2021","journal-title":"Renew. Energy"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kasihmuddin, M.S.M., Jamaludin, S.Z.M., Mansor, M.A., Wahab, H.A., and Ghadzi, S.M.S. (2022). Supervised Learning Perspective in Logic Mining. Mathematics, 10.","DOI":"10.3390\/math10060915"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Mohd Jamaludin, S.Z., Mohd Kasihmuddin, M.S., Md Ismail, A.I., Mansor, M.A., and Md Basir, M.F. (2020). Energy based logic mining analysis with hopfield neural network for recruitment evaluation. Entropy, 23.","DOI":"10.3390\/e23010040"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Jamaludin, S.Z.M., Romli, N.A., Kasihmuddin, M.S.M., Baharum, A., Mansor, M.A., and Marsani, M.F. (J. King Saud Univ.-Comput. Inf. Sci., 2022). Novel Logic Mining Incorporating Log Linear Approach, J. King Saud Univ.-Comput. Inf. Sci., in press.","DOI":"10.1016\/j.jksuci.2022.08.026"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1109\/TSG.2017.2753802","article-title":"Short-term residential load forecasting based on LSTM recurrent neural network","volume":"10","author":"Kong","year":"2019","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Luo, H., Zhou, P., Shu, L., Mou, J., Zheng, H., Jiang, C., and Wang, Y. (2022). Energy performance curves prediction of centrifugal pumps based on constrained PSO-SVR model. Energies, 15.","DOI":"10.3390\/en15093309"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"113917","DOI":"10.1016\/j.enconman.2021.113917","article-title":"Application of hybrid model based on empirical mode decomposition, novel recurrent neural networks and the ARIMA to wind speed prediction","volume":"233","author":"Liu","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wei, N., Li, C., Duan, J., Liu, J., and Zeng, F. (2019). Daily natural gas load forecasting based on a hybrid deep learning model. Energies, 12.","DOI":"10.3390\/en12020218"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1016\/j.egyr.2019.06.003","article-title":"Short-term load forecasting of urban gas using a hybrid model based on improved fruit fly optimization algorithm and support vector machine","volume":"5","author":"Lu","year":"2019","journal-title":"Energy Rep."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wenlong, H., and Yahui, W. (2020, January 22\u201324). Load forecast of gas region based on ARIMA algorithm. Proceedings of the 2020 Chinese Control And Decision Conference (CCDC), Hefei, China.","DOI":"10.1109\/CCDC49329.2020.9164623"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Musbah, H., and El-Hawary, M. (2019, January 5\u20138). SARIMA model forecasting of short-term electrical load data augmented by fast fourier transform seasonality detection. Proceedings of the IEEE Canadian Conference of Electrical and Computer Engineering (CCECE), Edmonton, AB, Canada.","DOI":"10.1109\/CCECE.2019.8861542"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1016\/j.rser.2017.02.023","article-title":"A review and analysis of regression and machine learning models on commercial building electricity load forecasting","volume":"73","author":"Yildiz","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"117857","DOI":"10.1016\/j.energy.2020.117857","article-title":"Short-term load forecasting for microgrid energy management system using hybrid HHO-FNN model with best-basis stationary wavelet packet transform","volume":"203","author":"Tayaba","year":"2020","journal-title":"Energy"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Panapakidis, I., Katsivelakis, M., and Bargiotas, D. (2022). A Metaheuristics-Based Inputs Selection and Training Set Formation Method for Load Forecasting. Symmetry, 14.","DOI":"10.3390\/sym14081733"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"185059","DOI":"10.1109\/ACCESS.2020.3029943","article-title":"Machine learning based energy management model for smart grid and renewable energy districts","volume":"8","author":"Ahmed","year":"2020","journal-title":"IEEE Access"},{"key":"ref_19","first-page":"190","article-title":"Forecasting of energy consumption and production using recurrent neural networks","volume":"18","author":"Shabbir","year":"2020","journal-title":"Adv. Electr. Electron. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Shirzadi, N., Nizami, A., Khazen, M., and Nik-Bakht, M. (2021). Medium-term regional electricity load forecasting through machine learning and deep learning. Designs, 5.","DOI":"10.3390\/designs5020027"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Fan, G.-F., Guo, Y.-H., Zheng, J.-M., and Hong, W.-C. (2019). Application of the weighted K-nearest neighbor algorithm for short-term load forecasting. Energies, 12.","DOI":"10.3390\/en12050916"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Madrid, E.A., and Antonio, N. (2021). Short-term electricity load forecasting with machine learning. Information, 12.","DOI":"10.3390\/info12020050"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5271","DOI":"10.1109\/TSG.2017.2686012","article-title":"Deep learning for household load forecasting\u2014A novel pooling deep RNN","volume":"9","author":"Shi","year":"2018","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wang, X., Gao, X., Wang, Z., Ma, C., and Song, Z. (2021). A Combined Model Based on EOBL-CSSA-LSSVM for Power Load Forecasting. Symmetry, 13.","DOI":"10.3390\/sym13091579"},{"key":"ref_25","unstructured":"Zhou, T., Ma, Z., Wen, Q., Wang, X., Sun, L., and Jin, R. (2022). FEDformer: Frequency enhanced decomposed transformer for long-term series forecasting. arXiv, preprint."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"106583","DOI":"10.1016\/j.ijepes.2020.106583","article-title":"A multi-energy load prediction model based on deep multi-task learning and ensemble approach for regional integrated energy systems","volume":"126","author":"Xuan","year":"2021","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"106542","DOI":"10.1016\/j.ijepes.2020.106542","article-title":"Multi-energy net load forecasting for integrated local energy systems with heterogeneous prosumers","volume":"126","author":"Zhou","year":"2021","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2703","DOI":"10.1109\/TSG.2022.3166600","article-title":"A Transformer-Based Method of Multi-Energy Load Forecasting in Integrated Energy System","volume":"13","author":"Wang","year":"2022","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Phyo, P.P., and Byun, Y.C. (2021). Hybrid Ensemble Deep Learning-Based Approach for Time Series Energy Prediction. Symmetry, 13.","DOI":"10.3390\/sym13101942"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1798","DOI":"10.1109\/TPAMI.2013.50","article-title":"Representation learning: A review and new perspectives","volume":"35","author":"Bengio","year":"2013","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1109\/JPROC.2021.3058954","article-title":"Toward causal representation learning","volume":"109","author":"Locatello","year":"2021","journal-title":"Proc. IEEE"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Hinton, G.E. (2012). A practical guide to training restricted Boltzmann machines. Neural Networks: Tricks of the Trade, Springer.","DOI":"10.1007\/978-3-642-35289-8_32"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.compchemeng.2017.02.041","article-title":"A deep belief network based fault diagnosis model for complex chemical processes","volume":"107","author":"Zhang","year":"2017","journal-title":"Comput. Chem. Eng."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/1999\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:38:25Z","timestamp":1760143105000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/1999"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,23]]},"references-count":33,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["sym14101999"],"URL":"https:\/\/doi.org\/10.3390\/sym14101999","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,23]]}}}