## 2 Materials and Methods
### LSTM-Driven Deterioration Model
Additionally, if the target component is a deck, \(A_{comp. }\) is calculated as the product of total length (\(L\)) and width (\(W\)). For abutments, \(A_{comp. }\) is calculated as the product of mean height (\(H\)) and width (\(W\)). In the case of piers, pier types are much more varied than other components, including circular, rectangular, multi-columnal, and pi-shaped forms. As a result, it is challenging to uniformly calculate component areas, so we defined \(A_{comp. }=H\) to simplify the data preprocessing procedure. Ideally, surface area should be calculated and scaled according to each pier type, and this should be defined based on user requirements. The scaled datasets were classified based on the bridge service life according to each data inspection point, thereby defining them as a time-series dataset. However, this dataset could be directly used for LSTM training owing to several reasons. The first was the presence of outliers. Bridge deterioration typically increases proportionally with the service life, except in the case of special or poorly maintained bridges. However, the measured data can be affected by human errors owing to the perspective and subjectivity of the inspectors. Therefore, this study employed the interquartile range, isolation forest, and Bayesian neural network (BNN) to remove outliers. Notably, the BNN calculates the probability distribution of the data and selects the deterioration data within the 1-\(\sigma\) range for training. The second reason was the presence of missing values in the time-series dataset owing to instances of no inspections because of inspection intervals, which led to data gaps that required compensation. Because linear interpolation can disturb the feature characteristics, this study employed the BNN model to probabilistically fill in these data gaps. The third reason was data duplication, as the data were not classified by bridges. Therefore, surveys of multiple bridges in the same year resulted in multiple deterioration data points for a single time step. In such cases, the mean value of these multiple data points for each time step was calculated and used as a substitute. The dataset obtained through the aforementioned processes was used for the LSTM training, as shown in Figure 4. The TensorFlow library of Python was used for model building. Two LSTM layers were used as the learning model with the number of LSTM input data nodes set to 15. Hyperbolic tangent was employed as the activation function for each layer and a dropout layer of 0.5 was added to each layer to prevent overfitting. During the learning process, the dataset was divided into training and validation sets. The validation data comprised data for the past decade from the initial dataset, whereas the training set included the remaining data. After model training was completed, the predictions for the past decade were compared with the samples in the validation set. However, the validation set contained observed values rather than true values, which introduced significant errors. Thus, a comparison was conducted using the average data values, and the average accuracy across all deterioration models was 76.8%. The trained model was subsequently used to predict the deterioration data for each service year over the next 100 years. For example, if data were available up to the 35 th service year, the LSTM model used the deterioration data from years 21-35 to predict deterioration in the 36 th year. These data were then incorporated with those from years 22-36, and the LSTM model was used again to predict the data for the 37 th year. Thisprocess was iterated to generate predictions for up to 100 years through each deterioration model. Finally, 324 datasets were generated, each containing deterioration data for up to 100 years. Regression analysis was then performed to derive the deterioration curve. In this study, a power-type trend equation (Equation (2)) was used to describe the increase in the deterioration area over time (\(t\)), resulting in 324 deterioration models (\(d^{1\sim 324}\)).