# Ensemble-Learning-Based Prediction of Steel Bridge Deck Defect Condition
## 3 Prediction of Steel Bridge Deck Defect Condition Based on Ensemble Learning
### Model Building and Evaluation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Description** & **Data Type** &
\begin{tabular}{c} **Variable** \\ **Type** \\ \end{tabular} & **Mean** & **Std** \\ \hline STATE\_CODE\_001 & The state code and FHWA region code. & Numeric & Input & 30.19 & 14.16 \\ FUNCTIONAL\_CLASS\_026 & The functional classification of inventory & Categorical & Input & 9.64 & 4.01 \\ YEAR\_BUILT\_027 & The year of bridge construction. & Numeric & Input & 1968.27 & 25.64 \\ ADT\_029 & The average daily traffic volume. & Numeric & Input & 9240.39 & 22,197.23 \\ DESIGN\_LOAD\_031 & The live load for which the structure was & Categorical & Input & 3.44 & 2.64 \\ SERVICE\_ON\_042A & Type of service on bridge. & Categorical & Input & 1.58 & 1.47 \\ SERVICE\_UND\_042B & Type of service under bridge. & Categorical & Input & 3.99 & 1.79 \\ STRUCTURE\_TYPE\_043B & Type of design and construction. & Numeric & Input & 2.52 & 2.04 \\ MAIN\_UNIT\_SPANS\_045 & The number of spans in the main unit. & Numeric & Input & 2.45 & 4.79 \\ APPR\_SPANS\_046 & The number of spans in the approach & Numeric & Input & 0.75 & 10.88 \\ MAX\_SPAN\_LEN\_MT\_048 & The length of the maximum span. & Numeric & Input & 22.31 & 21.67 \\ STRUCTURE\_LEN\_MT\_049 & The length of the structure. & Numeric & Input & 69.36 & 241.82 \\ ROADWAY\_WIDTH\_MT\_051 & The most restrictive minimum distance & Numeric & Input & 10.01 & 6.17 \\ DECK\_WIDTH\_MT\_052 & The out-to-out width. & Numeric & Input & 11.18 & 7.18 \\ DECK\_COND\_058 & The overall condition rating of the deck & Categorical & Output & 0.94 & 0.22 \\ SUPERSTRUCTURE\_COND\_059 & The physical condition of all structural & Categorical & Input & 6.23 & 1.18 \\ SUBSTRUCTURE\_COND\_060 & The physical condition of piers, abutments, & Categorical & Input & 6.13 & 1.17 \\ OPERATING\_RATING\_064 & The absolute maximum permissible load & Numeric & Input & 51.45 & 23.26 \\ INVENTORY\_RATING\_066 & The load level. & Numeric & Input & 32.46 & 15.83 \\ DECK\_STRUCTURE\_TYPE\_107 & The type of deck system. & Categorical & Input & 2.14 & 2.41 \\ SURFACE\_TYPE\_108A & The type of wearing surface & Categorical & Input & 3.37 & 2.88 \\ MEMBRANE\_TYPE\_108B & The type of membrane & Categorical & Input & 0.73 & 2.17 \\ DECK\_PROTECTION\_108C & The type of deck protection. & Categorical & Input & 0.82 & 2.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical analysis of characteristic variables. Equation (1). The ROC curve reflects the relationship between the true positive rate (TPR) and the false positive rate (FPR), and the AUC is defined as the area enclosed with the coordinate axis under the ROC curve. The closer the AUC value is to 1, the better the model performance is. The true positive rate (TPR) and the false positive rate (FPR) are shown in Equations (2) and (3), respectively. Accuracy and AUC are the overall descriptions of prediction accuracy for all of the samples. Accuracy is defined as the ratio of the number of correctly classified positive samples to the number of classified positive samples, as shown in Equation (4). Recall is defined as the ratio of the number of correctly classified positive samples to the actual number of positive samples, as shown in Equation (5). There is a mutually constraining relationship between precision and recall; thus, the F1-Score should be used as a comprehensive evaluation index [20]. The F1-score is the summed average of precision and recall, as shown in Equation (6), and a higher F1-score is better. \[\text{Accuracy}= \frac{\text{TP}+\text{TN}}{\text{TP}+\text{FP}+\text{FN}+\text{TN}} \tag{1}\] \[\text{TPR}= \frac{\text{TP}}{\text{TP}+\text{FN}}\] (2) \[\text{FPR}= \frac{\text{FP}}{\text{FP}+\text{TN}}\] (3) \[\text{Precise}= \frac{\text{TP}}{\text{TP}+\text{FP}}\] (4) \[\text{Recall}= \frac{\text{TP}}{\text{TP}+\text{FN}}\] (5) \[\text{F1}-\text{score}\ =\ 2\times\frac{\text{Precise}\times\text{ Recall}}{\text{Precise}+\text{ Recall}} \tag{6}\]