# A Hybrid Deep Learning Model Based on FFT-STL Decomposition for Ocean Wave Height Prediction
## 3 Experimental Results and Analysis
### Model Comparison  
This study develops a hybrid forecasting model based on the seasonal trend using Loess, which decomposes the time series into trend, seasonal and remainder components. These components are modeled using BiLSTM, SARIMAX, and 1D-CNN, respectively. To evaluate the effectiveness of the Hybrid-STL model, we use independent BiLSTM, and 1D-CNN models as benchmarks and conduct a comparative analysis in terms of computational efficiency and forecast precision. After calculation, the results are shown in Table 1. In terms of mean square error, the Hybrid-STL model performs best, only 0.0087, indicating that the average square of the error between its predicted value and the true value is extremely small, and it can  
Figure 11: Predicted results of CNN. Figure 12: Comparison of predicted wave height and actual wave height (42040 station). Figure 10: The changing remainder of training loss and validation loss for CNN model. accurately fit the data characteristics. The MSE of the BiLSTM model is 0.0554, which is nearly 6 times higher than that of the Hybrid-STL model, indicating that its prediction error is relatively large. The MSE of the 1D-CNN model is 0.02992, which is between the first two. The fitting effect is inferior to the Hybrid-STL model, but better than the BiLSTM model. The mean absolute error measures the average of the absolute values of the errors between the predicted value and the true value. The MAE of the Hybrid-STL model is 0.0783, which once again proves its advantage in prediction accuracy. The MAE of the BiLSTM model is 0.1478, and the MAE of the 1D-CNN model is 0.1534. The MAE values of the latter two are higher than that of the Hybrid-STL model, and the MAE value of the 1D-CNN model is even slightly higher than that of the BiLSTM model, which shows that the 1D-CNN model performs relatively worse in terms of direct measurement of absolute error. Based on the three prediction accuracy indicators, the Hybrid-STL model is significantly better than the BiLSTM and 1D-CNN models in capturing data features and accurately predicting wave heights, while the BiLSTM and 1D-CNN models have certain limitations in prediction accuracy. Although the 1D-CNN model performs slightly better than the BiLSTM model in MSE and RMSE, it performs poorly in the MAE indicator. From the perspective of runtime, the 1D-CNN model has the highest training efficiency, taking only 4.2 s per epoch, thanks to the high efficiency of its convolutional structure in feature extraction, which can process data quickly; the BiLSTM model takes 16.1 s per epoch, because its recurrent neural network structure needs to process sequence information, the computational complexity is high, resulting in a longer runtime; the Hybrid-STL model takes 24 s per epoch, which is the longest among the three models, which may be due to its integration of multiple analysis methods and model structures, requiring more computing resources and time for data decomposition, feature extraction and prediction. The Hybrid-STL model, with its absolute advantage in prediction accuracy, can provide more reliable and accurate results for wave height prediction, especially for fields such as marine engineering and disaster warning that require extremely high prediction accuracy. Although its operating efficiency is relatively low, it can be compensated by optimizing algorithms and improving hardware performance in the pursuit of high-precision prediction scenarios. The BiLSTM model is at an intermediate level in both prediction accuracy and operating efficiency, and is suitable for general prediction tasks that require a relatively balanced balance between accuracy and efficiency. Although the 1D-CNN model has excellent operating efficiency, its prediction accuracy is average and has certain application value in scenarios that require high prediction speed and relatively low accuracy.