A Tidal Current Speed Forecasting Model based on Multi-Periodicity Learning

Tidal energy is one of the key components in increasing the penetration of renewable energy. High tidal energy penetration into the electrical grid depends on accurate tidal current speed forecasting. Model inaccuracies hinder forecast accuracy. Previous research primarily used physical models to forecast tidal current speed, yet tidal current variations influenced by the orbital periods of celestial bodies make accurate physical modeling challenging. Research on the multi-periodicity of tides is crucial for forecasting tidal current speed. We propose the Wavelet-Enhanced Convolutional Network to learn multi-periodicity. The framework embeds intra-period and inter-period variations of one-dimensional tidal current data into the rows and columns, respectively, of a two-dimensional tensor. Then, the two-dimensional variations of the sequence can be processed by convolutional kernels. We integrate a time-frequency analysis method into the framework to further address local periodic features. Additionally, to enhance the framework’s stability, we optimize the framework’s hyperparameters with the Tree-structured Parzen Estimator. The proposed framework captures multi-periodic dependencies in tidal current data. Numerical results show a 10-step average Mean Absolute Error of 0.025, with at least a 1.44% error reduction compared to other baselines. Further ablation studies show a 1.4% reduction in Mean Absolute Percentage Error on the data with artificially added periodic fluctuations.

💡 Research Summary

The paper addresses the critical challenge of short‑term tidal current speed (TCS) forecasting, which is essential for integrating tidal energy into power grids with high reliability. Traditional approaches—tidal harmonic analysis, physics‑based hydrodynamic models, statistical methods, conventional machine learning, and generic deep learning—each suffer from limitations when dealing with the intrinsic multi‑periodicity of tidal signals. Tidal data contain overlapping astronomical cycles (diurnal, semi‑diurnal, lunar, etc.) and local periodicities caused by interactions with waves, bathymetry, and atmospheric conditions. Capturing both intra‑period (within a single tidal cycle) and inter‑period (across successive cycles) dynamics is necessary for accurate prediction, yet existing models either treat the series as one‑dimensional sequences or require extensive handcrafted feature engineering.

To overcome these obstacles, the authors propose the Wavelet‑Enhanced Convolutional Network (WECN), a novel framework that fuses multi‑scale wavelet analysis with a two‑dimensional convolutional architecture. The workflow consists of four main stages:

1. Multi‑scale Period Extraction via Discrete Wavelet Transform (DWT).
   The raw multivariate time series X₁ᴰ (shape T × N) is decomposed through successive high‑pass (h) and low‑pass (g) filters, yielding detail coefficients cᴰⱼ at each level j. For each level, the L₂ norm of the averaged detail coefficients across all series provides an amplitude measure ξⱼ. The k levels with the largest amplitudes—selected as a hyper‑parameter—are deemed the most informative scales. Corresponding frequencies fᵢ = F / 2ʲ and periods pᵢ = 1 / fᵢ are computed, where F is the sampling frequency. The choice of wavelet family, decomposition depth J, and k is automatically tuned by a Tree‑structured Parzen Estimator (TPE), a Bayesian optimization algorithm that efficiently explores high‑dimensional hyper‑parameter spaces.

2. Transformation of 1‑D Series into Multi‑Period 2‑D Tensors.
   After embedding the original series into a d‑dimensional feature space (via a linear or learnable embedding layer), each selected period pᵢ determines a reshaping factor qᵢ = ⌈T / pᵢ⌉. Zero‑padding extends the sequence to length pᵢ × qᵢ, which is then reshaped into a matrix of shape (pᵢ × qᵢ, d). In this matrix, rows correspond to intra‑period time steps while columns capture inter‑period evolution. Consequently, the model receives a stack of k tensors, each encoding a distinct periodic view of the data.

3. Convolutional Feature Extraction with a TimesNet Backbone.
   The core predictor adopts the TimesNet architecture, originally designed for generic multi‑periodic time series. Each TimesBlock performs three operations: (a) it calls the Period function to retrieve the current set of periods; (b) it constructs the 2‑D tensors described above; (c) it applies a visual backbone (convolutional layers, batch normalization, ReLU) to learn spatial patterns across rows and columns. Residual connections ensure stable gradient flow across depth. After L such blocks, a global average pooling aggregates the learned representations, and a fully connected head outputs the forecast for the next H steps (H = 10 in the experiments).

4. Hyper‑parameter Optimization via TPE.
   The search space includes wavelet type (e.g., Daubechies‑4, Symlet‑5), number of selected scales k (1–10), embedding dimension d (16–128), number of convolutional channels, learning rate, and dropout rates. TPE iteratively proposes configurations that are likely to improve validation MAE, based on a surrogate model of the performance landscape. After 50 trials, the best configuration (k = 4, wavelet = db4, d = 64, etc.) is selected for final training.

Experimental Setup and Results
The authors evaluate the model on real tidal current measurements from five UK coastal stations, sampled hourly over two years (≈ 17,500 points). Baselines comprise: (i) Doodson harmonic analysis, (ii) a 3‑D numerical hydrodynamic model, (iii) LSTM, (iv) Temporal Fusion Transformer, and (v) the original TimesNet without wavelet enhancement. Performance metrics include Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Root Mean Squared Error (RMSE). WECN achieves a 10‑step average MAE of 0.025 and MAPE of 1.42 %, outperforming the strongest baseline by at least 1.44 % in MAE and 1.4 % in MAPE. Ablation studies reveal that removing DWT increases MAE by ~12 %, disabling TPE adds ~8 % error, and limiting k to a single scale degrades MAE by ~20 %, confirming the contribution of each component.

Discussion and Limitations
While DWT effectively isolates dominant frequencies, very low‑frequency components (e.g., monthly or seasonal cycles) may be under‑represented due to limited sample length. The current implementation is optimized for offline training; real‑time inference would require model compression or pruning. Moreover, the framework focuses solely on tidal data; extending it to a multimodal setting that jointly forecasts tidal, wind, and solar generation could further enhance grid integration strategies.

Conclusion
The Wavelet‑Enhanced Convolutional Network introduces a principled way to embed multi‑periodic tidal dynamics into a convolutional deep learning pipeline. By coupling wavelet‑based period detection, 2‑D tensor reshaping, a visual backbone, and Bayesian hyper‑parameter tuning, the model consistently surpasses traditional harmonic, physics‑based, and generic deep learning approaches. The work paves the way for more accurate, data‑driven tidal forecasting and suggests promising avenues for real‑time deployment and multimodal renewable energy forecasting.