# A Hybrid Deep Learning Model Based on FFT-STL Decomposition for Ocean Wave Height Prediction
## 3 Experimental Results and Analysis
### Data Analysis and Modeling  
Observational data for 2021 and 2022 were selected as a training dataset. Initially, a Fast Fourier Transform (FFT) was applied to the raw time series to extract both the underlying time-domain signal and its corresponding frequency spectrum. The FFT analysis revealed a dominant frequency of approximately 0.12175 Hz, as shown in Figure 6. Given the inverse relationship between frequency and period, this dominant frequency corresponds to a fundamental cycle of approximately 8 days, a value that is both reasonable and physically meaningful for subsequent analysis. Figure 5: Comparison of original and smoothed wave data. Figure 6: Dominant frequency spectrum analysis. Based on the derived period, the STL model was refined by setting the seasonal window parameter to reflect an 8-day cycle specifically, as shown in Figure 7. This adjustment enabled the significant wave height time series to be decomposed into three distinct components: a long-term trend capturing the underlying wave behavior over extended periods, seasonal fluctuations representing the recurring periodic patterns, and the remainder embodying the irregular or noise-like variations. To further verify the effectiveness of STL decomposition, the Dickey-Fuller enhanced test was performed on the remaining component \(R(t)\), and the \(p\)-value obtained by the test was 0.00, which was significantly lower than the conventional significance level. Based on this, the null hypothesis that the remaining sequence contains a unit root was rejected, and it was clearly confirmed that the remainder is stationary. The stationarity of the residual is a key indicator in STL decomposition. This feature shows that STL decomposition successfully separates the system trend component and the seasonal component, and the final residual contains only random component noise, which strongly proves the effectiveness of STL decomposition in this data processing. To model the decomposed trend component, we use a bidirectional long short-term memory network. The network contains 132,737 trainable parameters, corresponding to a memory footprint of about 518.5 KB. We use a two-layer bidirectional architecture to enhance the extraction of temporal features by capturing forward and backward dependencies in the sequence. The first BiLSTM layer consists of 128 units (64 units in each direction) with a total of 33,792 parameters, designed to capture local temporal patterns within a 24-step input window. The second BiLSTM layer is a fully connected structure with 128 units, resulting in a total of 98,816 parameters. This layer performs spatiotemporal feature compression, thereby achieving a high-level abstraction from sequence input to latent representation. The output layer uses a fully connected neuron to generate the final prediction. To mitigate overfitting and enhance generalization, we use a two-layer dropout regularization scheme with a dropout rate of 0.1. The resulting network maintains a sparse connectivity rate of about 0.3%. The bidirectional design of the BiLSTM network helps to comprehensively model both past and future temporal dependencies, thus enhancing its ability to capture the long-term patterns inherent in the trend component of the wave height time series. Before building the model, the dataset was reasonably divided. All observations were divided into training subsets and test subsets at a ratio of 80% and 20%, respectively. Among them, the training subset is used for model calibration, and the model performs parameter learning and optimization on this part of the data, while the test subset is reserved and  
Figure 7: Data decomposition results through STL (42040 station). is specifically used to evaluate the performance of the model on unknown data to ensure that the generalization ability of the model is effectively tested. The model training process lasts for 100 training cycles.