## 2 Materials and Methods
### LSTM-Driven Deterioration Model  
In a previous study [28], a carbonation deterioration model for RC slab bridges was developed using the LSTM algorithm. Building on the same methodology, this study established deterioration models using the procedure illustrated in Figure 3. As described in Section 2.1, data collection involved gathering the necessary data from the bridge inspection reports to train the deterioration model. During data preprocessing, the collected data were classified according to the 9 regions, 3 bridge components, and 12 deterioration types outlined in Table 2 to construct the training dataset, resulting in 324 datasets that spanned a maximum input of 51 years. When training an LSTM model, it is common to label features \begin{table}
\begin{tabular}{c c c} \hline \hline
**Target** & **Region** & **Type of Deterioration Data** \\
**Components** & **Region** & **(Measured by Area, m\({}^{2}\))** & **Bridge Features** \\ \hline \hline \multirow{8}{*}{Slab} & Micro-crack (width \textless{} 0.03 mm) & \multirow{8}{*}{Bergo A} \\  & Region A & Macro-crack (width \textgreater{} 0.03 mm) & \\ \cline{1-1}  & Region B & Crazing (two-way crack) & \\ \cline{1-1}  & Region C & Separation & \\ \cline{1-1}  & Region D & Spalling & Height \\ \cline{1-1}  & & Exfoliation & Width \\ \cline{1-1}  & & Region E & Segregation & Length \\ \cline{1-1}  & Region F & Concrete failure & Service year \\ \cline{1-1}  & Region G & Delamination & \\ \cline{1-1}  & Region H & Efflorescence & \\ \cline{1-1}  & Region I & Leakage & \\ \cline{1-1}  & & Exposed rebar & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data extracted from inspection reports of RC slab bridges. in the data to build the dataset and estimate predicted values as features change. However, in this paper, the dataset was subdivided to improve model accuracy due to the high variation in features and their values relative to the number of data points. Therefore, the 324 datasets imply that the regional (environmental) characteristics and component types are not directly learned by the LSTM but are inherent within the datasets. These 324 training sets were primarily constructed to ensure data continuity. When analyzing the deterioration data from maintenance reports, there were cases in which previously observed deterioration data appeared to be zero for certain years. Typically, this occurs when deteriorations, such as cracks, were detected during inspection in the previous year and repaired, resulting in no further deterioration being observed in the following inspection; hence, it was marked as zero. However, unless the underlying cause of the deterioration is addressed or the component is replaced, the deterioration generally persists. Therefore, these instances were corrected to retain the same values as those of the previous deterioration data. Additionally, if deteriorations were found in subsequent inspections, they were preprocessed and added to the previous data to ensure data accumulation. Figure 3: Deterioration model generation process. Figure 2: Average deterioration areas for slabs, piers, and abutments. As the collected data were aggregated by bridge component units, larger bridges tended to exhibit greater areas of deterioration. To mitigate this issue, the classified data were scaled according to bridge features (height, length, and width), as listed in Table 2, and calculated as follows:  
\[A_{scal(t)}^{(i)}=\frac{\sum_{n}A_{d(t)}^{(i)}}{A_{comp. }},\ if\ \left\{ \begin{array}{l}\mathit{Slab}:&A_{comp.}=L\times W\\ \mathit{Abutment}:&A_{comp.}=H\times W\\ \mathit{Pier}&A_{comp.}=H\end{array} \right. \tag{1}\]  
For instance, if the service year of a bridge is \(t\) and the area of the \(i\)-th deterioration type within a single component is inspected \(n\) times, the total deterioration area \(\sum_{n}A_{d(t)}^{(i)}\) is calculated by summing all deterioration areas. Dividing the total deterioration area by the area of component, \(A_{comp. }\), yields the scaled area of the \(i\)-th deterioration \(A_{scaled(t)}^{(i)}\).