# Attention-Based Hydrogen Refueling Imputation Model for Efficient Hydrogen Refueling Stations
## 4 Results
### Comparative Assessment  
We compare the proposed AHRI model with regression, multiple, and autoencoder-based imputation methods. In this test, we generate 20 erroneous samples by randomly excluding elements of the observed samples at error rates of 20% and 40%, respectively. Here, if even one value of the independent variable is discarded, the corresponding value of the dependent variable is also omitted. Then, imputation methods fill in missing values with their estimated values. In Table 2, the proposed method outperforms the existing algorithms significantly in both metrics. Figure 3 shows the qualitative results, in which the proposed imputation model can effectively fill in the missing values while maintaining the overall flow similar to the observed SoC values. Table 3 shows the imputation results of the proposed model with two error rates for each test sample. Specifically, when 20% of the elements are missing, the proposed imputation model yields 0.08 RMSE, representing that the estimated data are close to the original data, and 0.92 R\({}^{2}\), indicating that the overall flow is similar to the original one. Moreover, when 40% of the elements are missing, obtaining 0.14 RMSE and 0.82 R\({}^{2}\) indicates that the estimated data flow is relatively similar to the real observed data. It demonstrates that the proposed imputation model can effectively fill in the erroneous data, even though almost half of the elements are missing. Figure 3: Qualitative comparison of imputation results with the error rate of 20%. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multirow{2}{*}{\begin{tabular}{c} **Regression** \\ **Imputation** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Multiple** \\ **Imputation** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Autoencoders** \\ **Imputation** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Proposed** \\ **AHRI** \\ \end{tabular} } \\ \cline{3-4} \cline{6-6}  & RMSE (\(\downarrow\)) & 0.32 & 0.28 & 0.15 & **0.06** \\  & R\({}^{2}\) (\(\uparrow\)) & 0.70 & 0.76 & 0.85 & **0.95** \\ \hline \multirow{2}{*}{**Model**} & RMSE (\(\downarrow\)) & 0.41 & 0.35 & 0.27 & **0.14** \\  & R\({}^{2}\) (\(\uparrow\)) & 0.65 & 0.69 & 0.77 & **0.82** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of imputation results according to error rates. **Temporal Dependency:** In method I of Table 4, each LSTM module is replaced with a fully connected layer. Note that the LSTM module allows the model to capture temporal dependencies, specifically long-term dependencies. The gaps between I and III indicate that temporal dependencies are important for the hydrogen data imputation. **Attention:** Method II employs LSTM modules only without the attention mechanism in Equations (1)-(3). By comparing II and III, we observe that the attention mechanism improves imputation performance significantly by capturing the dependencies of variables and determining the primary features. Moreover, the performance R\({}^{2}\) gaps between I and II shows that the model with the attention mechanism (method I) maintains an overall data flow more similar to the real observed data even though it cannot capture the temporal dependencies due to an absence of LSTM modules. **Robustness against different infrastructures:** We evaluate the robustness of the proposed model against the infrastructures in which the different hydrogen supply models may be built and their independent variables also differ. Unfortunately, the public hydrogen refueling data are unavailable except for [11], obtained from the same HRS. Thus, supposing that the number of independent variables in a certain infrastructure may differ from those in [11], we randomly remove the independent variables of [11] for this test. Table 5 lists the imputation results according to the number of independent variables. Although reducing the number of variables degrades performance, the degradation is acceptable, considering that all independent variables in [11] affect SoC.