{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T23:05:36Z","timestamp":1771023936832,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,12]],"date-time":"2024-12-12T00:00:00Z","timestamp":1733961600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20201043"],"award-info":[{"award-number":["BK20201043"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["KM202210853002"],"award-info":[{"award-number":["KM202210853002"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["2024JCCXJD01"],"award-info":[{"award-number":["2024JCCXJD01"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"name":"R&amp;D Program of Beijing Municipal Education Commission","award":["BK20201043"],"award-info":[{"award-number":["BK20201043"]}]},{"name":"R&amp;D Program of Beijing Municipal Education Commission","award":["KM202210853002"],"award-info":[{"award-number":["KM202210853002"]}]},{"name":"R&amp;D Program of Beijing Municipal Education Commission","award":["2024JCCXJD01"],"award-info":[{"award-number":["2024JCCXJD01"]}]},{"name":"Fundamental Research Funds for Central Universities","award":["BK20201043"],"award-info":[{"award-number":["BK20201043"]}]},{"name":"Fundamental Research Funds for Central Universities","award":["KM202210853002"],"award-info":[{"award-number":["KM202210853002"]}]},{"name":"Fundamental Research Funds for Central Universities","award":["2024JCCXJD01"],"award-info":[{"award-number":["2024JCCXJD01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Interval prediction is to predict the range of power prediction intervals, which can guide electricity production and usage better. To improve further improve the performance of the prediction interval, this paper aims to investigate he wind power interval prediction method based on the lower and upper bound evaluation (LUBE). Firstly, an improved loss function is proposed, which transforms multi-objective optimization problems into single-objective optimization with guidance of mathematical derivation. Afterward, the interval prediction results can be further improved through a combination of graph convolutional network (GCN) and gate recurrent unit (GRU). Then, the tree-structured Parzen estimator (TPE) optimization algorithm optimizes the GCN cell to find the optimal parameter configuration and maximize the performance of the model. Finally, in the experimental part, the proposed GCN-GRU with improved loss function is compared with some current mainstream neural networks. The results show that for any type of network, the improved loss function can obtain prediction intervals with better performance. Especially for the prediction interval based on GCN-GRU, the prediction interval normalized average width (PINAW) and prediction interval relative deviation (PIRD) can reach 6.75% and 46.99%, respectively, while ensuring the given prediction interval nominal confidence (PINC).<\/jats:p>","DOI":"10.3390\/sym16121643","type":"journal-article","created":{"date-parts":[[2024,12,12]],"date-time":"2024-12-12T03:52:49Z","timestamp":1733975569000},"page":"1643","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Interval Forecast Method for Wind Power Based on GCN-GRU"],"prefix":"10.3390","volume":"16","author":[{"given":"Wenting","family":"Zha","sequence":"first","affiliation":[{"name":"School of Electrical and Control Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xueyan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electrical and Control Engineering, Beijing Polytechnic College, Beijing 100042, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yijun","family":"Du","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1366-8686","authenticated-orcid":false,"given":"Yingyu","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Electrical and Control Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"119464","DOI":"10.1016\/j.renene.2023.119464","article-title":"Parametric study of the effects of clump weights on the performance of a novel wind-wave hybrid system","volume":"219","author":"Zhang","year":"2023","journal-title":"Renew. Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1080\/15435070903228050","article-title":"Piecewise Support Vector Machine Model for Short-Term Wind-power Prediction","volume":"6","author":"Liu","year":"2009","journal-title":"Int. J. Green Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1016\/j.renene.2013.08.011","article-title":"Short-term wind speed forecasting using wavelet transform and support vector machines optimized by genetic algorithm","volume":"62","author":"Liu","year":"2014","journal-title":"Renew. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/j.isatra.2022.01.024","article-title":"Ultra-short-term power forecast method for the wind farm based on feature selection and temporal convolution network","volume":"129","author":"Zha","year":"2022","journal-title":"ISA Trans."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Li, J., Geng, D., Zhang, P., Meng, X., Liang, Z., and Fan, G. (2019, January 7\u20139). Ultra-Short Term Wind Power Forecasting Based on LSTM Neural Network. Proceedings of the 2019 IEEE 3rd International Electrical and Energy Conference (CIEEC), Beijing, China.","DOI":"10.1109\/CIEEC47146.2019.CIEEC-2019625"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1016\/j.renene.2020.10.119","article-title":"Wind power forecasting\u2014A data-driven method along with gated recurrent neural network","volume":"163","author":"Kisvari","year":"2021","journal-title":"Renew. Energy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"484","DOI":"10.35833\/MPCE.2018.000792","article-title":"Performance Improvement of Artificial Neural Network Model in Short-Term Forecasting of Wind Farm Power Output","volume":"8","author":"Medina","year":"2020","journal-title":"J. Mod. Power Syst. Clean Energy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"12467","DOI":"10.1109\/ACCESS.2020.2966275","article-title":"A Reliability Assessment Approach for Electric Power Systems Considering Wind Power Uncertainty","volume":"8","author":"Yang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.rser.2014.01.033","article-title":"Review on probabilistic forecasting of wind power generation","volume":"32","author":"Zhang","year":"2014","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_10","first-page":"4710","article-title":"An Interval Prediction Approach of Wind Power Based on Skip-GRU and Block-Bootstrap Techniques","volume":"59","author":"Quan","year":"2023","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1109\/TPWRS.2008.922526","article-title":"Statistical Analysis of Wind Power Forecast Error","volume":"23","author":"Bludszuweit","year":"2008","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2240016","DOI":"10.1142\/S0219455422400168","article-title":"Tail-Weighted Wind Speed Distribution by Mixture Model with Constrained Maximum Likelihood","volume":"22","author":"Huang","year":"2022","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1109\/TSTE.2012.2232944","article-title":"Prediction Intervals for Short-Term Wind Farm Power Generation Forecasts","volume":"4","author":"Khosravi","year":"2013","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.renene.2019.11.143","article-title":"A novel wind power probabilistic forecasting approach based on joint quantile regression and multi-objective optimization","volume":"149","author":"Hu","year":"2020","journal-title":"Renew. Energy"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Li, D., Hussain, A., Yu, X., Liu, S., Yu, X., and Zhang, K. (2021, January 18\u201321). Wind Power Prediction Based on Kalman Filter and Non-parametric Kernel Density Estimation. Proceedings of the 2021 IEEE\/IAS Industrial and Commercial Power System Asia (I&CPS Asia), Chengdu, China.","DOI":"10.1109\/ICPSAsia52756.2021.9621598"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"51556","DOI":"10.1109\/ACCESS.2018.2870430","article-title":"Probability Interval Prediction of Wind Power Based on KDE Method With Rough Sets and Weighted Markov Chain","volume":"6","author":"Yang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1109\/TNN.2010.2096824","article-title":"Lower Upper Bound Estimation Method for Construction of Neural Network-Based Prediction Intervals","volume":"22","author":"Khosravi","year":"2011","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kavousi-Fard, A., Khosravi, A., and Nahavadi, S. (2014, January 6\u201311). A novel fuzzy multi-objective framework to construct optimal prediction intervals for wind power forecast. Proceedings of the 2014 International Joint Conference on Neural Networks (IJCNN), Beijing, China.","DOI":"10.1109\/IJCNN.2014.6889459"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1109\/TSTE.2017.2774195","article-title":"Direct Interval Forecast of Uncertain Wind Power Based on Recurrent Neural Networks","volume":"9","author":"Shi","year":"2018","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Shen, Y., Lu, X., Yu, X., Zhao, Z., and Wu, D. (2016, January 27\u201329). Short-term wind power intervals prediction based on generalized morphological filter and artificial bee colony neural network. Proceedings of the 35th Chinese Control Conference (CCC), Chengdu, China.","DOI":"10.1109\/ChiCC.2016.7554714"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.renene.2020.03.098","article-title":"The short-term interval prediction of wind power using the deep learning model with gradient descend optimization","volume":"155","author":"Li","year":"2020","journal-title":"Renew. Energy"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhang, D.W., Zhang, Z.C., Chen, Z.G., Zhou, Y., Li, F., and Chi, C. (2023). Wind power interval prediction based on variational mode decomposition and the fast gate recurrent unit. Front. Energy Res., 10.","DOI":"10.3389\/fenrg.2022.1022578"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"61739","DOI":"10.1109\/ACCESS.2021.3073995","article-title":"A Novel Efficient DLUBE Model Constructed by Error Interval Coefficients for Clustered Wind Power Prediction","volume":"9","author":"Peng","year":"2021","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Hu, Y., Qiao, Y.L., Chu, J.C., Yuan, L., and Pan, L. (2019). Joint Point-Interval Prediction and Optimization of Wind Power Considering the Sequential Uncertainties of Stepwise Procedure. Energies, 12.","DOI":"10.3390\/en12112205"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2814","DOI":"10.1109\/TII.2022.3160696","article-title":"Probabilistic Wind Power Forecasting Using Optimized Deep Auto-Regressive Recurrent Neural Networks","volume":"19","author":"Arora","year":"2023","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1503","DOI":"10.3233\/IFS-141433","article-title":"A new hybrid method to forecast wind turbine output power in power systems","volume":"28","author":"Soleymani","year":"2015","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"108009","DOI":"10.1016\/j.asoc.2021.108009","article-title":"Integrating a softened multi-interval loss function into neural networks for wind power prediction","volume":"113","author":"Hu","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1109\/TNN.2008.2005605","article-title":"The Graph Neural Network Model","volume":"20","author":"Scarselli","year":"2009","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Nishio, M., Nishizawa, M., Sugiyama, O., Kojima, R., Yakami, M., Kuroda, T., and Togashi, K. (2018). Computer-aided diagnosis of lung nodule using gradient tree boosting and Bayesian optimization. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0195875"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/12\/1643\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:53:04Z","timestamp":1760115184000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/12\/1643"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,12]]},"references-count":29,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["sym16121643"],"URL":"https:\/\/doi.org\/10.3390\/sym16121643","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,12]]}}}