Multistep ahead wind forecast using variational mode decomposition and gated recurrent deep learning unit

A research team led by Pardeep Singla, Komal Duhan, Sandeep Sharma, Sumit Saroha, Manoj Duhan, and Manoj Arora has introduced an advanced decomposition-based predictive framework that substantially increases the precision of multistep ahead wind speed forecasting. Described in an evaluation published in Discover Energy, the architecture couples Variational Mode Decomposition with a Gated Recurrent Unit neural network optimized through systematic grid searching. Wind speed dynamics present notorious operational challenges for contemporary electrical power networks due to their intermittent, volatile, and highly nonstationary behavior. By preprocessing raw wind speed time series through adaptive variational decomposition, the researchers demonstrated that complex, nonlinear signals can be separated into discrete sub-frequency modes that recurrent deep learning predictors can learn with marked stability. When evaluated against standard benchmark architectures, the combined methodology yielded notable error reductions across one-step, two-step, and three-step prediction horizons, demonstrating significant potential for improving operational reliability and integration planning within wind energy generation infrastructures.

The integration of wind power into broader electrical grids requires accurate forecasting to allow grid operators to balance resource allocations, maintain power system security, and curtail economic losses associated with unexpected supply variations. The researchers observed that conventional statistical methods, including autoregressive integrated moving average models, support vector regression, and artificial neural networks, frequently encounter difficulties when mapping the volatile temporal trajectories typical of atmospheric airflow. Although deep learning architectures such as Long Short-Term Memory networks and Gated Recurrent Units capture nonlinear temporal dependencies far more effectively than classical models, standalone networks struggle when processing highly nonstationary raw sequences. Prior academic efforts to stabilize input series turned to empirical signal decomposition strategies, including Empirical Mode Decomposition and its noise-assisted extensions. However, those techniques remain susceptible to mode mixing, where disparate frequency components bleed across decomposed bands, as well as heightened noise sensitivity that compromises predictive consistency across differing geographic sites and forecasting horizons.

To overcome these persistent structural limitations, the authors developed a three-stage computational pipeline configured around Variational Mode Decomposition. Unlike recursive filtering procedures, Variational Mode Decomposition operates as an adaptive, non-recursive variational framework that concurrently estimates modal functions and their corresponding center frequencies to minimize aggregate estimated spectral bandwidth. In the proposed workflow, candidate decomposition parameters were systematically tested, ultimately establishing eight intrinsic mode functions alongside a quadratic penalty parameter set to two thousand to minimize spectral overlap between adjacent sub-bands while keeping total reconstruction error low. The decomposed sub-series were subsequently routed into individual Gated Recurrent Unit networks. The researchers selected Gated Recurrent Units over standard Long Short-Term Memory architectures because their consolidated update gating mechanism simplifies internal state management, curtails overall parameter counts, speeds up network training, and mitigates empirical overfitting while maintaining robust capacity for learning temporal dependencies across extended sequence horizons.

Hyperparameter optimization for the recurrent predictors was executed through an exhaustive grid search using validation set mean squared error as the objective function, replacing arbitrary trial-and-error tuning with reproducible optimization protocols. To structure the predictive inputs, the authors evaluated lag observations spanning from 5 to 20 past increments, identifying an optimal input window of 15 sequential time lags. The grid search converged on 90 hidden recurrent units drawn from an evaluated range of 60 to 150 units, a gradient threshold of 0.01 selected from candidates between 0.05 and 0.1, an optimized learning rate of 0.001 from a search space spanning 0.001 to 0.01, and an established default drop factor of 0.2. In the final stage of the modeling pipeline, individual forecasts generated for each decomposed intrinsic mode function were aggregated through linear reconstruction to synthesize the complete wind speed forecast across the designated evaluation horizons.

The empirical validation of the architecture relied on meteorological datasets retrieved from the National Solar Radiation Database for two climatologically distinct Indian wind energy hubs: Muppandal, situated in Kanyakumari, and Jaisalmer, situated in Rajasthan. Because these records represent modeled satellite reanalysis data rather than direct on-site anemometer readings, they provided standardized environmental time series recorded at 15-minute sampling intervals across July 2019. Each location dataset encompassed 2,980 contiguous samples, partitioned into an 80 percent training corpus of 2,384 points and a 20 percent testing corpus of 596 points. The statistical properties of the two environments varied dramatically, enabling rigorous cross-regional generalizability testing. The Jaisalmer desert site featured an operational range between 0.3 and 9.8 meters per second, a higher mean speed of 5.4623 meters per second, elevated standard deviation of 2.5329, near-zero skewness of negative 0.1852, and platykurtic kurtosis of 1.9516, indicating broad fluctuations with fewer extreme spikes. Muppandal presented a coastal profile spanning 2.0 to 9.1 meters per second, a lower mean of 4.4968 meters per second, reduced standard deviation of 1.4305, positive right-skewness of 0.8978, and a leptokurtic kurtosis of 3.2999 characterized by frequent low winds and heavier tail distributions.

Across all evaluated forecasting horizons, the optimized decomposition framework consistently outperformed standalone networks and alternative empirical decomposition combinations across root mean square error, mean absolute error, mean absolute percentage error, and coefficient of determination metrics. For single-step forecasting in Jaisalmer, the proposed hybrid model registered a root mean square error of 0.228, a mean absolute error of 0.161, a mean absolute percentage error of 6.92 percent, and a coefficient of determination of 0.995. In contrast, the standalone Gated Recurrent Unit registered values of 0.440, 0.303, 11.43 percent, and 0.981, while standalone Long Short-Term Memory models recorded 0.623, 0.423, 17.75 percent, and 0.963, respectively. Intermediate hybrid models using empirical mode decomposition exhibited notable instability; for example, the empirical mode decomposition hybrid with Long Short-Term Memory produced an inferior mean absolute error of 0.351 compared to the standalone Gated Recurrent Unit in Jaisalmer, illustrating how mode mixing impairs model consistency.

For the coastal Muppandal site, single-step predictions produced by the proposed model achieved a root mean square error of 0.084, a mean absolute error of 0.065, a mean absolute percentage error of 1.52 percent, and a coefficient of determination of 0.992. Percentage improvement analyses highlighted substantial gains across both testing environments. Relative to standalone Long Short-Term Memory models, the proposed framework reduced single-step root mean square error by 63.40 to 73.50 percent, mean absolute error by 61.93 to 75.28 percent, and mean absolute percentage error by 61.01 to 78.09 percent. Compared to standalone Gated Recurrent Units, root mean square error decreased by 48.18 to 61.64 percent, mean absolute error fell by 46.86 to 63.48 percent, and mean absolute percentage error dropped by 39.45 to 67.52 percent. Substantial margins persisted over empirical mode decomposition benchmarks, where root mean square error decreased by 46.47 to 66.66 percent over the empirical Long Short-Term Memory variant and by 34.67 to 52.80 percent over the empirical Gated Recurrent Unit variant.

When the evaluation was extended to two-step and three-step ahead predictions, forecasting errors inevitably expanded across all candidate models due to compounding prediction errors and recursive uncertainty propagation through time. Nevertheless, the rate of error accumulation remained markedly attenuated in the variational hybrid architecture. In two-step ahead forecasting for Jaisalmer, the proposed model maintained a root mean square error of 0.289, a mean absolute error of 0.215, a mean absolute percentage error of 9.09 percent, and a coefficient of determination of 0.992. These metrics surpassed the variational Long Short-Term Memory network, which achieved a root mean square error of 0.327, as well as the empirical Gated Recurrent Unit and empirical Long Short-Term Memory models, which registered root mean square errors of 0.386 and 0.485, respectively. Standalone networks exhibited marked degradation at the two-step mark, with the Gated Recurrent Unit recording a root mean square error of 0.545 and the Long Short-Term Memory network deteriorating to 0.803.

To confirm that these empirical advantages reflected genuine structural enhancements rather than stochastic sampling artifacts, the investigators applied the Diebold-Mariano statistical hypothesis test across both regional datasets and all prediction horizons. Critical test statistics were compared against standard two-tailed normal critical values of plus or minus 1.96 for the 95 percent confidence interval and plus or minus 2.58 for the 99 percent confidence interval. The computed test values demonstrated that the superior predictive performance of the proposed model achieved statistical significance over competing benchmark models across the majority of comparisons at the stringent 99 percent confidence level. In a minor subset of comparisons, such as two-step and three-step ahead forecasts against the variational Long Short-Term Memory network on the Jaisalmer data, the test statistic failed to surpass the 99 percent threshold but retained statistical significance at the 95 percent confidence level, affirming that the variational framework delivers statistically verifiable gains across disparate testing contexts.

Because sudden shifts in wind velocity exert severe mechanical and electrical stress on utility grids, the research team also assessed the architecture’s capacity to detect dynamic ramp events, defined as temporal differences between consecutive observations exceeding a threshold scaled to 0.3 times the standard deviation of wind speed differences. During ramp analysis on the Jaisalmer dataset, the proposed framework achieved a recall of 0.866, a leading precision score of 0.7821, an overall F1-score of 0.8218, and a reduced ramp root mean square error of 0.0723, compared to higher errors ranging between 0.098 and 0.101 for empirical decomposition alternatives. On the noisier Muppandal dataset, where overall precision dipped to between 0.50 and 0.62 across models, the proposed framework maintained superior detection capabilities, securing an F1-score of 0.7267 and a ramp error of 0.0725. Detailed 24-point visual analyses revealed occasional staircase-like tracking over brief coastal intervals, indicating that the model prioritizes aggregate global stability over localized high-frequency sensitivity.

Subject of Research: Multistep ahead wind speed forecasting using variational mode decomposition and gated recurrent unit deep learning architectures

Article Title: Multistep ahead wind forecast using variational mode decomposition and gated recurrent deep learning unit

Article References: Singla, P., Duhan, K., Sharma, S., Saroha, S., Duhan, M., & Arora, M. (2026). Multistep ahead wind forecast using variational mode decomposition and gated recurrent deep learning unit. Discover Energy, 6(1), Article 75. https://doi.org/10.1007/s43937-026-00172-1

Image Credits: AI Generated

DOI: 10.1007/s43937-026-00172-1

Keywords: wind speed forecasting, variational mode decomposition, gated recurrent units, renewable energy, deep learning, time series forecasting, ramp event detection, grid search optimization, Multistep, ahead, wind, forecast