E2E-FANet: A Highly Generalizable Framework for Waves prediction Behind Floating Breakwaters via Exogenous-to-Endogenous Variable Attention

Accurate prediction of waves behind floating breakwaters (FB) is crucial for optimizing coastal engineering structures, enhancing safety, and improving design efficiency. Existing methods demonstrate limitations in capturing nonlinear interactions between waves and structures, while exhibiting insufficient capability in modeling the complex frequency-domain relationships among elevations of different wave gauges. To address these challenges, this study introduces the Exogenous-to-Endogenous Frequency-Aware Network (E2E-FANet), a novel end-to-end neural network designed to model relationships between waves and structures. The E2E-FANetarchitecture incorporates a Dual-Basis Frequency Mapping (DBFM) module that leverages orthogonal cosine and sine bases to extract wave features from the frequency domain while preserving temporal information. Additionally, we introduce the Exogenous-to-Endogenous Cross-Attention (E2ECA) module, which employs cross attention to model the interactions between endogenous and exogenous variables. We incorporate a Temporal-wise Attention (TA) mechanism that adaptively captures complex dependencies in endogenous variables. These integrated modules function synergistically, enabling E2E-FANet to achieve both comprehensive feature perception in the time-frequency domain and precise modeling of wave-structure interactions. To comprehensively evaluate the performance of E2E-FANet, we constructed a multi-level validation framework comprising three distinct testing scenarios: internal validation under identical wave conditions, generalization testing across different wave conditions, and adaptability testing with varying relative water density (RW) conditions. These comprehensive tests demonstrate that E2E-FANet provides accurate waves behind FB predictions while successfully generalizing diverse wave conditions.

A Novel Framework for Significant Wave Height Prediction based on Adaptive Feature Extraction Time-Frequency Network

Precise forecasting of significant wave height (Hs) is essential for the development and utilization of wave energy. The challenges in predicting Hs arise from its non-linear and non-stationary characteristics. The combination of decomposition preprocessing and machine learning models have demonstrated significant effectiveness in Hs prediction by extracting data features. However, decomposing the unknown data in the test set can lead to data leakage issues. To simultaneously achieve data feature extraction and prevent data leakage, a novel Adaptive Feature Extraction Time-Frequency Network (AFE-TFNet) is proposed to improve prediction accuracy and stability. It is encoder-decoder rolling framework. The encoder consists of two stages: feature extraction and feature fusion. In the feature extraction stage, global and local frequency domain features are extracted by combining Wavelet Transform (WT) and Fourier Transform (FT), and multi-scale frequency analysis is performed using Inception blocks. In the feature fusion stage, time-domain and frequency-domain features are integrated through dominant harmonic sequence energy weighting (DHSEW). The decoder employed an advanced long short-term memory (LSTM) model. Hourly measured wind speed (Ws), dominant wave period (DPD), average wave period (APD) and Hs from three stations are used as the dataset, and the four metrics are employed to evaluate the forecasting performance. Results show that AFE-TFNet significantly outperforms benchmark methods in terms of prediction accuracy. Feature extraction can significantly improve the prediction accuracy. DHSEW has substantially increased the accuracy of medium-term to long-term forecasting. The prediction accuracy of AFE-TFNet does not demonstrate significant variability with changes of rolling time window size. Overall, AFE-TFNet shows strong potential for handling complex signal forecasting.