## 3 Case Study
### Elman Neural Network for Bridge Condition Prediction  
The data are classified based on the features mentioned above. Out of the datasets from Texas, 5600 are eligible; 70% of the data are used for training, 20% for validation, and 10% for testing. The data with selected features and completed classification are used as ENN inputs to predict the long-term performance of a given bridge. Assuming the prediction for Year 60 results, the Elman neural network predicts these results by adding the predicted values of \(t_{59}\) to the original ENN inputs from \(t_{1}\)-\(t_{58}\). In this study, this iteration of the one-step prediction process lasts for 60 cycles, as shown in the figure, and the total number of long-term predictions (LTP) for the ENN of the bridge is 10, as shown in Figure 5. \begin{table}
\begin{tabular}{l l l} \hline \hline
**No.** & **Characteristic Binding** & **Accuracy** \\ \hline
1 & Age + Average daily truck traffic + Kind of material & 88.8\% \\
2 & Age + Average daily truck traffic + Kind of material + Skew & 85.2\% \\
3 & Age + Average daily truck traffic + Kind of material + Skew + Deck & 88.3\% \\  & structure type & \\
4 & Age + Average daily truck traffic + Kind of material + Skew + Deck & 93.8\% \\  & structure type + Type of bridge & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Different ways of combining bridge features. Figure 4: Pareto chart of importance of bridge features. Before analyzing these prediction results, a filtering process of the predicted condition is required to further improve the quality of the long-term predictions. The filtering process adheres to the guideline that the condition of the previous year should be greater than or equal to the condition of the following year. That is, if the bridge does not undergo maintenance, the condition rating should not improve, as bridge degradation is a continuous, gradual, and slow progression. Therefore, if the predicted bridge condition rating is 5.45 in Year 53 and 5.47 in Year 54 for LTP10 in Figure 5, this does not correspond to the actual rule of bridge deterioration, so this prediction dataset for LTP10 should be discarded. The results of the bridge condition prediction are removed from the deterioration curves with the highest and lowest predicted conditions, because these two curves deviate significantly, as shown in Figure 6.  
Figure 5: Ten prediction results using Elman neural network. Figure 6: Worst and best bridge deterioration curves predicted by Elman neural network. After completing network training and optimization analysis, the selected prediction curve for the condition rating of the bridge is shown in Figure 7. The transition probability matrix of the Markov chain is calculated using the selected bridge deterioration curve. Owing to the straightforward process of the genetic algorithm, the optimal solution of the objective function can be found through the continuous iteration of the function. Therefore, a genetic algorithm will be used. The genetic algorithm is an optimization search algorithm inspired by the principles of natural selection and genetics. It is a stochastic search technique commonly used to solve various optimization problems. Specifically, the process of the genetic algorithm involves initializing the population, evaluating fitness, selecting, crossing over, mutating, and repeating the process. The advantage of the genetic algorithm is that it can conduct a global search in the solution space and is well-suited for optimization problems with high complexity and a large search space. To calculate the transition probability matrix of the bridge condition over a span of 60 years, the following steps are taken: first, the 60-year range is divided into 10 intervals of 6 years each, and the transition probability matrix for each interval is calculated.