Accurate ultra-short-term wind speed forecasting is essential for the reliable integration of wind energy into power grids; nevertheless, it is challenging due to the non-linearity and non-stationarity of wind signals. Therefore, this research introduces a novel multi-phase hybrid framework—VMD-PermEn-DBSCAN-ICEEMDAN—aimed at improving prediction accuracy through the systematic refinement of complex signal components. The process initiates with variational mode decomposition (VMD) to decompose raw wind speed data into intrinsic mode functions (IMFs). Permutation entropy (PermEn) is employed for feature extraction to address the complexity of these components, followed by density-based spatial clustering of applications with noise (DBSCAN) clustering to categorize IMFs exhibiting analogous dynamic patterns. A secondary decomposition phase employing enhanced complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is aimed primarily at high-frequency clusters to reveal hidden fluctuations. These refined features serve as inputs for advanced deep learning models, such as long short-term memory (LSTM) networks, gated recurrent units (GRU), and their hybrid configurations. The framework was assessed utilizing wind speed data from Riyadh, Saudi Arabia, gathered at 5-minute intervals. Experimental findings indicated that the LSTM-GRU hybrid model consistently surpasses independent architectures and conventional machine learning methods, including artificial neural networks, support vector machines, and decision trees. The proposed framework attained a remarkable mean squared error of 0.00081 m2/s2 and a coefficient of determination of 0.99954 for 5-minute forecasts. In addition, the study examined the effects of input lag lengths and forecasting resolutions of up to one hour, validating the model's durability and exceptional performance in ultra-short-term scenarios. The results underscore the effectiveness of integrating adaptive signal decomposition, intelligent clustering, and deep learning for accurate wind speed prediction, offering a dependable resource for energy management and grid stability.
Citation: Musaed Alrashidi. A hybrid VMD-PermEn-DBSCAN-ICEEMDAN deep learning framework for ultra-short-term wind speed prediction[J]. AIMS Mathematics, 2026, 11(5): 12548-12579. doi: 10.3934/math.2026516
Accurate ultra-short-term wind speed forecasting is essential for the reliable integration of wind energy into power grids; nevertheless, it is challenging due to the non-linearity and non-stationarity of wind signals. Therefore, this research introduces a novel multi-phase hybrid framework—VMD-PermEn-DBSCAN-ICEEMDAN—aimed at improving prediction accuracy through the systematic refinement of complex signal components. The process initiates with variational mode decomposition (VMD) to decompose raw wind speed data into intrinsic mode functions (IMFs). Permutation entropy (PermEn) is employed for feature extraction to address the complexity of these components, followed by density-based spatial clustering of applications with noise (DBSCAN) clustering to categorize IMFs exhibiting analogous dynamic patterns. A secondary decomposition phase employing enhanced complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is aimed primarily at high-frequency clusters to reveal hidden fluctuations. These refined features serve as inputs for advanced deep learning models, such as long short-term memory (LSTM) networks, gated recurrent units (GRU), and their hybrid configurations. The framework was assessed utilizing wind speed data from Riyadh, Saudi Arabia, gathered at 5-minute intervals. Experimental findings indicated that the LSTM-GRU hybrid model consistently surpasses independent architectures and conventional machine learning methods, including artificial neural networks, support vector machines, and decision trees. The proposed framework attained a remarkable mean squared error of 0.00081 m2/s2 and a coefficient of determination of 0.99954 for 5-minute forecasts. In addition, the study examined the effects of input lag lengths and forecasting resolutions of up to one hour, validating the model's durability and exceptional performance in ultra-short-term scenarios. The results underscore the effectiveness of integrating adaptive signal decomposition, intelligent clustering, and deep learning for accurate wind speed prediction, offering a dependable resource for energy management and grid stability.
| [1] |
J. Selvaraj, L. Muthuramalingam, V. Karthikeyan, A. Karthick, V. Sathiyaseelan, Optimizing wind energy integration: A review of forecasting techniques and emerging trends, Arch. Computat. Methods Eng., 33 (2026), 4261–4286. https://doi.org/10.1007/s11831-025-10442-1 doi: 10.1007/s11831-025-10442-1
|
| [2] |
D. Kaur, T. T. Lie, N. K. C. Nair, B. Vallès, Wind speed forecasting using hybrid wavelet transform—ARMA techniques, AIMS Energy, 3 (2015), 13–24. https://doi.org/10.3934/energy.2015.1.13 doi: 10.3934/energy.2015.1.13
|
| [3] |
Y. Zhou, S. P. Guan, Y. W. Xue, Hierarchical multi-scale temporal-frequency pattern extraction for accurate wind speed forecasting, Pattern Anal. Applic., 29 (2026), 26. https://doi.org/10.1007/s10044-025-01606-7 doi: 10.1007/s10044-025-01606-7
|
| [4] | S. Ansay, B. Köse, İ. Işıklı, C. Mülayim, B. Ertilav, Forecasting wind speed with autoregressive and long-short term memory neural network models, Journal of AI, 9 (2025) 98–121. |
| [5] | Y. R. Wang, D. C. Wang, Y. Tang, Clustered hybrid wind power prediction model based on ARMA, PSO-SVM, and clustering methods, IEEE Access, 8 (2020), 17071–17079. https://doi.org/10.1109/ACCESS.2020.2968390 |
| [6] |
E. Cadenas, W. Rivera, R. Campos-Amezcua, C. Heard, Wind speed prediction using a univariate ARIMA model and a multivariate NARX model, Energies, 9 (2016), 109. https://doi.org/10.3390/en9020109 doi: 10.3390/en9020109
|
| [7] |
W. Q. Xu, L. K. Ning, Y. Luo, Wind speed forecast based on post-processing of numerical weather predictions using a gradient boosting decision tree algorithm, Atmosphere, 11 (2020), 738. https://doi.org/10.3390/atmos11070738 doi: 10.3390/atmos11070738
|
| [8] |
J. Du, S. Z. Chen, L. L. Pan, Y. B. Liu, A wind speed prediction method based on signal decomposition technology deep learning model, Energies, 18 (2025), 1136. https://doi.org/10.3390/en18051136 doi: 10.3390/en18051136
|
| [9] |
A. Kumar, A. J. Singh, S. Kumar, Forecasting wind speed over multiple horizons: Superiority of deep learning and decomposition-driven hybrid models, Unconventional Resources, 9 (2026), 100296. https://doi.org/10.1016/j.uncres.2025.100296 doi: 10.1016/j.uncres.2025.100296
|
| [10] |
M. Alrashidi, Ultra-short-term solar forecasting with reduced pre-acquired data considering optimal heuristic configurations of deep neural networks, AIMS Mathematics, 9 (2024), 12323–12356. https://doi.org/10.3934/math.2024603 doi: 10.3934/math.2024603
|
| [11] |
P. Pinson, C. Chevallier, G. N. Kariniotakis, Trading wind generation from short-term probabilistic forecasts of wind power, IEEE T. Power Syst., 22 (2007), 1148–1156. https://doi.org/10.1109/TPWRS.2007.901117 doi: 10.1109/TPWRS.2007.901117
|
| [12] | S. S. Soman, H. Zareipour, O. Malik, P. Mandal, A review of wind power and wind speed forecasting methods with different time horizons, In: North American Power Symposium 2010, Arlington, TX, USA, 2010, 1–8. https://doi.org/10.1109/NAPS.2010.5619586 |
| [13] |
F. Li, H. Z. Wang, D. Wang, D. Liu, K. Sun, A review of wind pwer prediction methods based on multi-time scales, Energies, 18 (2025), 1713. https://doi.org/10.3390/en18071713 doi: 10.3390/en18071713
|
| [14] |
F. L. Dias, A. J. Naik, A novel approach to wavelet neural network-based wind power forecasting, Wind, 5 (2025), 14. https://doi.org/10.3390/wind5020014 doi: 10.3390/wind5020014
|
| [15] |
A. E. Kio, J. Xu, N. Gautam, Y. Ding, Wavelet decomposition and neural networks: a potent combination for short term wind speed and power forecasting, Front. Energy Res., 12 (2024), 1277464. https://doi.org/10.3389/fenrg.2024.1277464 doi: 10.3389/fenrg.2024.1277464
|
| [16] | G. N. Pillai, K. V. Shihabudheen, Wind speed forecasting using empirical mode decomposition and regularized ELANFIS, In: 2017 IEEE Symposium Series on Computational Intelligence (SSCI), Honolulu, HI, USA, 2017, 1–7. https://doi.org/10.1109/SSCI.2017.8285324 |
| [17] | Y. Z. Du, K. Zhang, Q. Z. Shao, Z. Chen, A short-term prediction model of wind power with outliers: An integration of long short-term memory, ensemble empirical mode decomposition, and sample entropy, Sustainability, 15 (2023), 6285. https://doi.org/10.3390/su15076285 |
| [18] | Z. Xing, Y. Zhi, R. H. Hao, H. W. Yan, C. Qing, Wind speed forecasting model based on extreme learning machines and complete ensemble empirical mode decomposition, In: 2020 5th Asia Conference on Power and Electrical Engineering (ACPEE), Chengdu, China, 2020,159–163. https://doi.org/10.1109/ACPEE48638.2020.9136553 |
| [19] | B. S. Bommidi, V. Kosana, K. Teeparthi, S. Madasthu, A hybrid approach to ultra short-Term wind speed prediction using CEEMDAN and informer, In: 2022 22nd National Power Systems Conference (Npsc), New Delhi, India, 2022,207–212. https://doi.org/10.1109/NPSC57038.2022.10069064 |
| [20] |
K. Dragomiretskiy, D. Zosso, Variational mode decomposition, IEEE T. Signal Proces., 62 (2014), 531–544. https://doi.org/10.1109/TSP.2013.2288675 doi: 10.1109/TSP.2013.2288675
|
| [21] | N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Snin, Q. A. Zheng, et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. A, 454 (1998), 903–995. https://doi.org/10.1098/rspa.1998.0193 |
| [22] |
X. X. Wang, P. Liu, Q. Y. Liu, Y. Z. Zhang, A hybrid ultra-short-term wind speed prediction model using adaptive VMD and time-series mixer, Int. J. Green Energy, 22 (2025), 2794–2812. https://doi.org/10.1080/15435075.2025.2471997 doi: 10.1080/15435075.2025.2471997
|
| [23] |
J. He, Z. J. Cheng, Z. J. Zhong, L. Z. Liang, J. H. Ye, Wind power prediction based on a hybrid model of iceemdan and moderntcn-informer, IEEE Access, 13 (2025), 145256–145270. https://doi.org/10.1109/ACCESS.2025.3599609 doi: 10.1109/ACCESS.2025.3599609
|
| [24] |
W. Li, C. X. Quan, X. Y. Wang, S. Zhang, Short-term power load forecasting based on a combination of VMD and ELM, Pol. J. Environ. Stud., 27 (2018), 2143–2154. https://doi.org/10.15244/pjoes/78244 doi: 10.15244/pjoes/78244
|
| [25] |
S. J. Wang, C. Liu, K. Liang, Z. Y. Cheng, X. Kong, S. Gao, Wind speed prediction model based on improved vmd and sudden change of wind speed, Sustainability, 14 (2022), 8705. https://doi.org/10.3390/su14148705 doi: 10.3390/su14148705
|
| [26] | X. X. Wang, X. P. Shen, X. Y. Ai, S. J. Li, Short-term wind speed forecasting based on a hybrid model of ICEEMDAN, MFE, LSTM and informer, PLoS One, 18 (2023), e0289161. https://doi.org/10.1371/journal.pone.0289161 |
| [27] |
Z. R. Shu, H. C. Deng, P. W. Chan, X. H. He, Evaluating the intrinsic predictability of wind speed time series via entropy-based approaches, J. Wind Eng. Ind. Aerod., 257 (2025), 105972. https://doi.org/10.1016/j.jweia.2024.105972 doi: 10.1016/j.jweia.2024.105972
|
| [28] |
J. J. Ruiz-Aguilar, I. Turias, J. González-Enrique, D. Urda, D. Elizondo, A permutation entropy-based EMD–ANN forecasting ensemble approach for wind speed prediction, Neural Comput. Applic., 33 (2021), 2369–2391. https://doi.org/10.1007/s00521-020-05141-w doi: 10.1007/s00521-020-05141-w
|
| [29] |
A. Azhar, H. Hashim, A review of wind clustering methods based on the wind speed and trend in Malaysia, Energies, 16 (2023), 3388. https://doi.org/10.3390/en16083388 doi: 10.3390/en16083388
|
| [30] |
P. Zhang, Y. L. Wang, L. K. Liang, X. Li, Q. T. Duan, Short-term wind power prediction using GA-BP neural network based on DBSCAN algorithm outlier identification, Processes, 8 (2020), 157. https://doi.org/10.3390/pr8020157 doi: 10.3390/pr8020157
|
| [31] | S. Q. Wang, C. Chen, Short-term wind power prediction based on DBSCAN clustering and support vector machine regression, In: 2020 5th International Conference on Computer and Communication Systems (ICCCS), Shanghai, China, 2020,941–945. https://doi.org/10.1109/ICCCS49078.2020.9118606 |
| [32] |
H. Liu, C. Chen, Data processing strategies in wind energy forecasting models and applications: A comprehensive review, Appl. Energ., 249 (2019), 392–408. https://doi.org/10.1016/j.apenergy.2019.04.188 doi: 10.1016/j.apenergy.2019.04.188
|
| [33] | A. Taha, N. Nazih, P. Makeen, Wind speed prediction based on variational mode decomposition and advanced machine learning models in zaafarana, Egypt, Sci. Rep., 15 (2025), 15599. https://doi.org/10.1038/s41598-025-98543-6 |
| [34] | H. L. Hu, L. Wang, R. Tao, Wind speed forecasting based on variational mode decomposition and improved echo state network, Renew. Energ., 164 (2021), 729–751. https://doi.org/10.1016/j.renene.2020.09.109 |
| [35] |
C. Bandt, B. Pompe, Permutation entropy: A natural complexity measure for time series, Phys. Rev. Lett., 88 (2002), 174102. https://doi.org/10.1103/PhysRevLett.88.174102 doi: 10.1103/PhysRevLett.88.174102
|
| [36] |
D. T. Mihailović, Permutation entropy and its niche in hydrology: A review, Entropy, 27 (2025), 598. https://doi.org/10.3390/e27060598 doi: 10.3390/e27060598
|
| [37] |
Y. Sun, S. Y. Zhang, A multiscale hybrid wind power prediction model based on least squares support vector regression-regularized extreme learning machine-multi-head attention-bidirectional gated recurrent unit and data decomposition, Energies, 17 (2024), 2923. https://doi.org/10.3390/en17122923 doi: 10.3390/en17122923
|
| [38] |
Z. L. Zhang, Z. T. Xiang, Y. F. Chen, J. Y. Xu, Fuzzy permutation entropy derived from a novel distance between segments of time series, AIMS Mathematics, 5 (2020), 6244–6260. https://doi.org/10.3934/math.2020402 doi: 10.3934/math.2020402
|
| [39] | M. Ester, H. -P. Kriegel, J. Sander, X. W. Xu, A density-based algorithm for discovering clusters in large spatial databases with noise, In: Second International Conference on Knowledge Discovery and Data Mining (KDD'96), 1996,226–231. |
| [40] |
M. A. Colominas, G. Schlotthauer, M. E. Torres, Improved complete ensemble EMD: A suitable tool for biomedical signal processing, Biomed. Signal Proces., 14 (2014), 19–29. https://doi.org/10.1016/J.BSPC.2014.06.009 doi: 10.1016/J.BSPC.2014.06.009
|
| [41] |
B. J. Lu, Z. J. Li, X. B. Zhang, ICEEMDAN–RPE–AITD algorithm for magnetic field signals of magnetic targets, Sci. Rep., 15 (2025), 6509. https://doi.org/10.1038/s41598-025-91068-y doi: 10.1038/s41598-025-91068-y
|
| [42] |
Q. Z. Zhuang, L. Gao, F. Zhang, X. Y. Ren, L. Qin, Y. P. Wang, MIVNDN: ultra-short-term wind power prediction method with MSDBO-ICEEMDAN-VMD-Nons-DC transformer net, Electronics, 13 (2024), 4829. https://doi.org/10.3390/electronics13234829 doi: 10.3390/electronics13234829
|
| [43] |
M. Ayaz, T. Ali, M. Hijji, I. Baig, T. Alhmiedat, E. H. M. Aggoune, Predictive modeling of complex networks using deep learning and fractional dynamics, AIMS Mathematics, 10 (2025), 26717–26743. https://doi.org/10.3934/math.20251175 doi: 10.3934/math.20251175
|
| [44] |
Z. K. Luo, Learning dynamics and convergence of machine learning driven neural ordinary differential equations model for housing price prediction, AIMS Mathematics, 10 (2025), 23803–23820. https://doi.org/10.3934/math.20251058 doi: 10.3934/math.20251058
|
| [45] | T. Zhang, An introduction to support vector machines and other kernel-based learning methods, AI Mag., 22 (2001), 103–104. |
| [46] | K. B. Sahay, S. Srivastava, Short-term wind speed forecasting of lelystad wind farm by using ANN algorithms, In: 2018 International Electrical Engineering Congress (IEECON), Krabi, Thailand, 2018, 1–4. https://doi.org/10.1109/IEECON.2018.8712227 |
| [47] |
U. B. Kahveci, B. Barutçu, Recent hybrid machine learning approaches in wind speed forecasting: A review, J. Econ. Surv., 40 (2025), 242–268. https://doi.org/10.1111/JOES.70005 doi: 10.1111/JOES.70005
|
| [48] |
J. F. Ni, S. Y. Yang, Y. J. Liu, Data cleaning model of mine wind speed sensor based on LOF-GMM and SGAIN, Appl. Sci., 15 (2025), 1801. https://doi.org/10.3390/app15041801 doi: 10.3390/app15041801
|
| [49] | R. Al-Hajj, Probabilistic machine learning-based forecasting of wind speed uncertainty using adaptive kernel density estimation, Math. Biosci. Eng., 22 (2025), 2269–2299. https://doi.org/10.3934/mbe.2025083 |
| [50] |
J. F. Lv, Y. X. Ren, H. J. Zhang, M. Han, A meta-inspired algorithm-based fuzzy model for wind speed prediction using chaotic time series and phase space reconstruction, AIMS Energy, 14 (2026), 1–22. https://doi.org/10.3934/energy.2026001 doi: 10.3934/energy.2026001
|
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Musaed Alrashidi. A hybrid VMD-PermEn-DBSCAN-ICEEMDAN deep learning framework for ultra-short-term wind speed prediction[J]. AIMS Mathematics, 2026, 11(5): 12548-12579. doi: 10.3934/math.2026516
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