# Attention-Based Hydrogen Refueling Imputation Model for Efficient Hydrogen Refueling Stations
## 3 Methodology
### Attention-Based Hydrogen Refueling Imputation (AHRI) Model  
Considering the reliability and completeness of time series data is critical for accurate data modeling and analysis, as missing values can lead to significant inaccurate predictions. To overcome this issue, we propose a novel imputation model called the AHRI model. The proposed AHRI model contains the attention-based long short-term memory (LSTM) module [26] to effectively restore the missing values in multivariate time series data. In the AHRI model, the temporal dependencies are captured with the LSTM module, and the primary features are determined via the attention mechanism. Here, the determined features improve the predictive performance and help quickly adapt new data. Figure 2 shows the overview of the proposed AHRI model. Specifically, we temporarily fill in the missing values using linear interpolation and then perform the min-max normalization to guarantee that all data become the same range in [0, 1]. We take the normalized data \(X=[\mathbf{x}_{1},\mathbf{x}_{2},\cdots,\mathbf{x}_{T}]^{t}\) as input, where \(\mathbf{x}_{l}\) consists of 21 independent variables in Table 1. The LSTM module [10] captures temporal dependencies from the normalized data, yielding a set of hidden states \(H=[\mathbf{h}_{1},\mathbf{h}_{2},\cdots,\mathbf{h}_{T}]^{t}\). Next, through the attention \begin{table}
\begin{tabular}{c c c} \hline
**Category** & **Variable** & **Description** \\ \hline Dependent Variable & SoC (\%) & State of charge \\ \hline \multirow{7}{*}{\begin{tabular}{c} Pressure \\ Factor \\ \end{tabular} } & 875 PT1 & Pressure transducer to measure pressure (PT1) \\  & 875 PT3 & Pressure transducer to measure pressure (PT3) \\  & \begin{tabular}{c} Pinlet \\ Psupply \\ \end{tabular} & Pressure at the inlet of the component or system \\ \cline{2-3}  & & 875 TC1 & Thermocouple measurement (TC1) \\  & & 875 TC2 & Thermocouple measurement (TC2) \\  & & 875 TC3 & Thermocouple measurement (TC3) \\  & & \begin{tabular}{c} Tskin \\ Time \\ \end{tabular} & Tank outer surface (shell) temperature \\  & & \begin{tabular}{c} Tline \\ Temperature of hydrogen gas in the pipeline \\ \end{tabular} \\  & \begin{tabular}{c} Tsupply\({}_{G}\) \\ Temperature \\ \end{tabular} & \begin{tabular}{c} Feed gas temperature \\ Temperature \\ \end{tabular} & \begin{tabular}{c} Temperature of the chamber storing hydrogen \\ Gas temperature at the inlet \\ Pressure control device outlet temperature \\ \end{tabular} \\  & \begin{tabular}{c} Trec\({}_{S}\) \\ Temperature of the vessel (solids) \\ \end{tabular} \\  & \begin{tabular}{c} Trec\({}_{G}\) \\ Temperature of the vessel (gas) \\ Nozzle temperature (solids) \\ \end{tabular} \\  & \begin{tabular}{c} Tend1s & Temperature at a specific point \\  & \begin{tabular}{c} Tend2s & Temperature at specific Point \\  & \
\begin{tabular}{c} Tbreak\({}_{S}\) \\ Temperature \\ \end{tabular} &
\begin{tabular}{c} Temperature of a safety device in the system \\ Location of sensor \\ \end{tabular} \\ \hline Flow Factor & FM & Flow rate of hydrogen gas \\ \hline \end{tabular}
\end{table} 
Table 1: Description of variables used in the analysis. Figure 1: Example of preprocessed data. mechanism [9], we measure the attention score \(\mathbf{a}_{t}\) representing the relative importance of each hidden state \(\mathbf{h}_{t}\) in \(H\) and weighs \(\mathbf{h}_{t}\) with \(\mathbf{a}_{t}\) as follows:  
\[\mathbf{f}_{t}=\tanh(W\times\mathbf{h}_{t}+\mathbf{b}), \tag{1}\] \[\mathbf{a}_{t}(i)=\frac{\exp\left(\mathbf{f}_{t}(i)\right)}{\sum_ {j=1}^{T}\exp\left(\mathbf{f}_{j}(i)\right)},\] (2) \[\mathbf{o}_{t}=\mathbf{a}_{t}\odot\mathbf{h}_{t}, \tag{3}\]  
where \(W\) and \(\mathbf{b}\) are the trainable parameters, and \(\odot\) is the element-wise product. Here, the attention mechanism allows the proposed model to prioritize primary features to improve the robustness and reliability of the prediction results.