# WaveConv-sLSTM-KET: A Novel Framework for the Multi-Task Analysis of Oil Spill Fluorescence Spectra
## 3 Results and Discussion
### Model Performance Evaluation
#### 3.3.2 Regression Performance  
As shown in Figure 6, the relationship between oil film thickness and fluorescence intensity varies across different oil types under different laser powers. Combined with the simulated wave environment used in our experiments, the data exhibit high nonlinearity. Table 4 summarizes the regression performance of the four models on the test set. From Table 4, it is evident that the proposed Hybrid framework significantly outperforms the other methods in thickness prediction. The test set's R\({}^{2}\) value being close to 1 indicates a strong correlation between predicted and actual values, demonstrating that the model has effectively learned and can generalize to a broader data range. The lower RMSE suggests that the proposed method has the smallest prediction error for oil film thickness compared to other models. The RPD value of 7.1876 for the Hybrid framework indicates exceptional robustness and stability. An RPD greater than 2 generally signifies a good predictive ability for most applications, while an RPD above 5 indicates a highly reliable model. The transformer model has an RMSE close to that of the Hybrid framework, but its R\({}^{2}\) and RPD values are significantly lower. This suggests that although the transformer can predict thickness to some extent, it lacks extrapolation capabilities and struggles with unseen data. This limitation stems from its feedforward layers, which rely on simple linear transformations. In contrast, the KET module in the proposed framework leverages the nonlinear mapping power of KAN, resulting in predictions that closely correlate with actual values and generalize effectively to other thickness ranges. Traditional regression models like SVM and LR exhibit poor performance on the highly nonlinear fluorescence dataset due to their limited nonlinear modeling capabilities. As a result, they are unable to effectively predict oil film thickness. It is worth noting that our oil film thickness range spans from 50 \(\upmu\)m to 0.5 mm, covering both thin and thick films, with broad sample diversity. The evaluation metrics in Table 4 reflect the model's overall performance rather than its performance for individual oil types. Previous analyses of oil spill spectra revealed that the Raman peak intensity, fluorescence spectral features, and thickness at which Raman peaks disappear vary across oil types, influenced by laser power, wave effects, and intrinsic properties. Traditional methods like fluorescence and Raman suppression often fail to account for these additional factors, reducing their practicality and robustness. The proposed Hybrid framework, with its robust multi-scale feature extraction capabilities, achieves accurate predictions across a wide range of thicknesses and complex scenarios. This demonstrates the model's excellent generalization and adaptability, making it suitable for real-world applications. Figure 11 shows the scatter plots of predictions for the test set of five oils by the two deep learning models. From this figure, it is evident that both models perform differently for each oil type. The Hybrid framework performs best for Mobil Super 1000 X1 Diesel 15W-40, although there is greater prediction variance for the 0.39 mm oil film thickness. This is because at 60 mW laser power, the fluorescence intensity variation for this thickness differs from that under other power conditions, posing challenges for thickness prediction. For the proposed model, the RPD values for regression predictions across all oil types exceed 5, with R\({}^{2}\) values generally above 0.97, indicating a strong extrapolation ability and applicability \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MAE** & **RMSE** & **R\({}^{2}\)** & **RPD** \\ \hline Hybrid framework & 0.0068 & 0.0212 & 0.9806 & 7.1876 \\ Transformer & 0.0266 & 0.0375 & 0.9392 & 4.0542 \\ SVM & 0.4000 & 0.5420 & 0.7028 & 1.8343 \\ LR & 0.5446 & 0.6639 & 0.5541 & 1.4976 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The thickness prediction performance of the model.