{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T09:29:54Z","timestamp":1775899794926,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,12]],"date-time":"2023-04-12T00:00:00Z","timestamp":1681257600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52077027"],"award-info":[{"award-number":["52077027"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022021000014"],"award-info":[{"award-number":["2022021000014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Liaoning Province Science and Technology Major Project","award":["52077027"],"award-info":[{"award-number":["52077027"]}]},{"name":"Liaoning Province Science and Technology Major Project","award":["2022021000014"],"award-info":[{"award-number":["2022021000014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Accurate wind power prediction can increase the utilization rate of wind power generation and maintain the stability of the power system. At present, a large number of wind power prediction studies are based on the mean square error (MSE) loss function, which generates many errors when predicting original data with random fluctuation and non-stationarity. Therefore, a hybrid model for wind power prediction named IVMD-FE-Ad-Informer, which is based on Informer with an adaptive loss function and combines improved variational mode decomposition (IVMD) and fuzzy entropy (FE), is proposed. Firstly, the original data are decomposed into K subsequences by IVMD, which possess distinct frequency domain characteristics. Secondly, the sub-series are reconstructed into new elements using FE. Then, the adaptive and robust Ad-Informer model predicts new elements and the predicted values of each element are superimposed to obtain the final results of wind power. Finally, the model is analyzed and evaluated on two real datasets collected from wind farms in China and Spain. The results demonstrate that the proposed model is superior to other models in the performance and accuracy on different datasets, and this model can effectively meet the demand for actual wind power prediction.<\/jats:p>","DOI":"10.3390\/e25040647","type":"journal-article","created":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T02:29:15Z","timestamp":1681352955000},"page":"647","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["An Adaptive Hybrid Model for Wind Power Prediction Based on the IVMD-FE-Ad-Informer"],"prefix":"10.3390","volume":"25","author":[{"given":"Yuqian","family":"Tian","sequence":"first","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8067-9313","authenticated-orcid":false,"given":"Dazhi","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guolin","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7708-2134","authenticated-orcid":false,"given":"Jiaxing","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuming","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongliang","family":"Ni","sequence":"additional","affiliation":[{"name":"China North Vehicle Research Institute, Beijing 100072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"117693","DOI":"10.1016\/j.energy.2020.117693","article-title":"Wind Power Forecasting of an Offshore Wind Turbine Based on High-Frequency Scada Data and Deep Learning Neural Network","volume":"201","author":"Lin","year":"2020","journal-title":"Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1930","DOI":"10.1109\/TSTE.2022.3175916","article-title":"Nonparametric Probabilistic Forecasting for Wind Power Generation Using Quadratic Spline Quantile Function and Autoregressive Recurrent Neural Network","volume":"13","author":"Wang","year":"2022","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1016\/j.renene.2019.01.006","article-title":"A Multi-Objective Wind Speed and Wind Power Prediction Interval Forecasting Using Variational Modes Decomposition Based Multi-Kernel Robust Ridge Regression","volume":"136","author":"Naik","year":"2019","journal-title":"Renew. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.rser.2018.09.046","article-title":"A Review on the Selected Applications of Forecasting Models in Renewable Power Systems","volume":"100","author":"Ahmed","year":"2019","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"117766","DOI":"10.1016\/j.apenergy.2021.117766","article-title":"A Review of Wind Speed and Wind Power Forecasting with Deep Neural Networks","volume":"304","author":"Wang","year":"2021","journal-title":"Appl. Energy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1016\/j.renene.2022.12.124","article-title":"A Cgru Multi-Step Wind Speed Forecasting Model Based on Multi-Label Specific Xgboost Feature Selection and Secondary Decomposition","volume":"203","author":"Jiang","year":"2023","journal-title":"Renew. Energy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"108726","DOI":"10.1016\/j.ijepes.2022.108726","article-title":"A Novel Hybrid Model Based on Laguerre Polynomial and Multi-Objective Runge-Kutta Algorithm for Wind Power Forecasting","volume":"146","author":"Ye","year":"2023","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"116296","DOI":"10.1016\/j.enconman.2022.116296","article-title":"Adaptive Forecasting of Wind Power Based on Selective Ensemble of Offline Global and Online Local Learning","volume":"271","author":"Jin","year":"2022","journal-title":"Energy Convers. Manag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.egyr.2023.02.061","article-title":"Vmd-Cat: A Hybrid Model for Short-Term Wind Power Prediction","volume":"9","author":"Zheng","year":"2023","journal-title":"Energy Rep."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Rajagopalan, S., and Santoso, S. (2009, January 26\u201330). Wind Power Forecasting and Error Analysis Using the Autoregressive Moving Average Modeling. Proceedings of the Paper presented at the General Meeting of the IEEE-Power-and-Energy-Society, Calgary, AB, Canada.","DOI":"10.1109\/PES.2009.5276019"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"117200","DOI":"10.1016\/j.energy.2020.117200","article-title":"A Hybrid Approach Based on Autoregressive Integrated Moving Average and Least-Square Support Vector Machine for Long-Term Forecasting of Net Electricity Consumption","volume":"197","author":"Kaytez","year":"2020","journal-title":"Energy"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yang, Y., and Lu, J. (2022). Foreformer: An Enhanced Transformer-Based Framework for Multivariate Time Series Forecasting. Appl. Intell.","DOI":"10.1007\/s10489-022-04100-3"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"113098","DOI":"10.1016\/j.enconman.2020.113098","article-title":"Deterministic and Probabilistic Multi-Step Forecasting for Short-Term Wind Speed Based on Secondary Decomposition and a Deep Learning Method","volume":"220","author":"Xiang","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1016\/j.cherd.2021.08.013","article-title":"Machine Learning on Sustainable Energy: A Review and Outlook on Renewable Energy Systems, Catalysis, Smart Grid and Energy Storage","volume":"174","author":"Nigam","year":"2021","journal-title":"Chem. Eng. Res. Des."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1016\/j.renene.2020.09.109","article-title":"Wind Speed Forecasting Based on Variational Mode Decomposition and Improved Echo State Network","volume":"164","author":"Hu","year":"2021","journal-title":"Renew. Energy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1007\/s42835-020-00616-1","article-title":"A New Hybrid Approach of Clustering Based Probabilistic Decision Tree to Forecast Wind Power on Large Scales","volume":"16","author":"Khan","year":"2021","journal-title":"J. Electr. Eng. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"116316","DOI":"10.1016\/j.energy.2019.116316","article-title":"A Cascaded Deep Learning Wind Power Prediction Approach Based on a Two-Layer of Mode Decomposition","volume":"189","author":"Yin","year":"2019","journal-title":"Energy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.energy.2022.124750","article-title":"Developing a Wind Power Forecasting System Based on Deep Learning with Attention Mechanism","volume":"257","author":"Tian","year":"2022","journal-title":"Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1820","DOI":"10.1109\/TSTE.2021.3067436","article-title":"Short-Term Multi-Step Ahead Wind Power Predictions Based on a Novel Deep Convolutional Recurrent Network Method","volume":"12","author":"Liu","year":"2021","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1016\/j.renene.2020.03.042","article-title":"Forecasting Energy Consumption and Wind Power Generation Using Deep Echo State Network","volume":"154","author":"Hu","year":"2020","journal-title":"Renew. Energy"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"117446","DOI":"10.1016\/j.apenergy.2021.117446","article-title":"Review of Meta-Heuristic Algorithms for Wind Power Prediction: Methodologies, Applications and Challenges","volume":"301","author":"Lu","year":"2021","journal-title":"Appl. Energy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"108526","DOI":"10.1016\/j.asoc.2022.108526","article-title":"Randomization-Based Machine Learning in Renewable Energy Prediction Problems: Critical Literature Review, New Results and Perspectives","volume":"118","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"121795","DOI":"10.1016\/j.energy.2021.121795","article-title":"A Hybrid Deep Learning Architecture for Wind Power Prediction Based on Bi-Attention Mechanism and Crisscross Optimization","volume":"238","author":"Meng","year":"2022","journal-title":"Energy"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1016\/j.enconman.2018.03.098","article-title":"Wind Speed Forecasting Using Nonlinear-Learning Ensemble of Deep Learning Time Series Prediction and Extremal Optimization","volume":"165","author":"Chen","year":"2018","journal-title":"Energy Convers. Manag."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"107776","DOI":"10.1016\/j.epsr.2022.107776","article-title":"Short-Term Wind Power Forecasting Based on Attention Mechanism and Deep Learning","volume":"206","author":"Xiong","year":"2022","journal-title":"Electr. Power Syst. Res."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zhen, H., Niu, D., Yu, M., Wang, K., Liang, Y., and Xu, X. (2022). A Hybrid Deep Learning Model and Comparison for Wind Power Forecasting Considering Temporal-Spatial Feature Extraction. Sustainability, 12.","DOI":"10.3390\/su12229490"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.rser.2014.03.033","article-title":"A Review of Combined Approaches for Prediction of Short-Term Wind Speed and Power","volume":"34","author":"Tascikaraoglu","year":"2014","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"126906","DOI":"10.1016\/j.energy.2023.126906","article-title":"Explainable Temporal Dependence in Multi-Step Wind Power Forecast Via Decomposition Based Chain Echo State Networks","volume":"270","author":"Wu","year":"2023","journal-title":"Energy"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yang, S., Yang, H., Li, N., and Ding, Z. (2023). Short-Term Prediction of 80-88 Km Wind Speed in near Space Based on Vmd-Pso-Lstm. Atmosphere, 14.","DOI":"10.3390\/atmos14020315"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1793","DOI":"10.1109\/TNNLS.2014.2351391","article-title":"A Novel Empirical Mode Decomposition with Support Vector Regression for Wind Speed Forecasting","volume":"27","author":"Ren","year":"2016","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"126100","DOI":"10.1016\/j.energy.2022.126100","article-title":"Multivariate Wind Speed Forecasting Based on Multi-Objective Feature Selection Approach and Hybrid Deep Learning Model","volume":"263","author":"Lv","year":"2023","journal-title":"Energy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"122020","DOI":"10.1016\/j.energy.2021.122020","article-title":"A High-Accuracy Hybrid Method for Short-Term Wind Power Forecasting","volume":"238","author":"Khazaei","year":"2022","journal-title":"Energy"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"118980","DOI":"10.1016\/j.energy.2020.118980","article-title":"Short-Term Wind Power Forecasting Using the Hybrid Model of Improved Variational Mode Decomposition and Correntropy Long Short-Term Memory Neural Network","volume":"214","author":"Duan","year":"2021","journal-title":"Energy"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"4963","DOI":"10.1109\/TII.2018.2854549","article-title":"Short-Term Wind Speed Forecasting Via Stacked Extreme Learning Machine with Generalized Correntropy","volume":"14","author":"Luo","year":"2018","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"106327","DOI":"10.1016\/j.asoc.2020.106327","article-title":"A New Wind Power Interval Prediction Approach Based on Reservoir Computing and a Quality-Driven Loss Function","volume":"92","author":"Hu","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"114714","DOI":"10.1016\/j.enconman.2021.114714","article-title":"A Novel Asexual-Reproduction Evolutionary Neural Network for Wind Power Prediction Based on Generative Adversarial Networks","volume":"247","author":"Yin","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational Mode Decomposition","volume":"62","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.medengphy.2008.04.005","article-title":"Measuring Complexity Using Fuzzyen, Apen, and Sampen","volume":"31","author":"Chen","year":"2009","journal-title":"Med. Eng. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"11106","DOI":"10.1609\/aaai.v35i12.17325","article-title":"Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting","volume":"35","author":"Zhou","year":"2021","journal-title":"AAAI"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Barron, J.T. (2019, January 15\u201320). A General and Adaptive Robust Loss Function. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00446"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1016\/j.ins.2022.06.090","article-title":"Using Support Vector Regression and K-Nearest Neighbors for Short-Term Traffic Flow Prediction Based on Maximal Information Coefficient","volume":"608","author":"Lin","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.enconman.2020.112824","article-title":"A New Short-Term Wind Speed Forecasting Method Based on Fine-Tuned Lstm Neural Network and Optimal Input Sets","volume":"213","author":"Memarzadeh","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Tao, P., Wu, X., Yang, C., Han, G., Zhou, H., and Hu, Y. (2022). Hourly Electricity Price Prediction for Electricity Market with High Proportion of Wind and Solar Power. Energies, 15.","DOI":"10.3390\/en15041345"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/4\/647\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:15:00Z","timestamp":1760123700000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/4\/647"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,12]]},"references-count":44,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["e25040647"],"URL":"https:\/\/doi.org\/10.3390\/e25040647","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,12]]}}}