# Enhancing Reliability Analysis with Multisource Data:
## 3 Results Attained by Using the Proposed WIM and NBI Synthesis Method  
### Correlating Operating LR with Attributes Available in the NBI to Characterize Resistance  
There is no strong linear relationship between the bridge CR and LR in the Georgia's bridge inventory. The goodness of fit measure (or R2 value) is less than 0.5. Thus, a supervised Machine Learning (ML) algorithm implementing a XGBoost model [21] is used to search for a relationship between the two variables--changes in CR and changes in the maximum load carrying capacity (or operating LR), in conjunction with other predictor variables--bridge attributes available in the NBI. This is achieved by predicting operating LR using the six variables shown in Figure 3.  
Figure 3: SHAP value plot of attributes from NBI Database using (a) XGBoost and (b) CatBoost algorithms.  
XGBoost is a decision-tree-based ensemble ML algorithm that uses a gradient boosting framework. This algorithm minimizes loss by employing the mean squared error between two iterative steps. The bridge inspection (or NBI) data collected between 1992 and 2021 are analyzed. Figure 3 presents a plot showing SHAP values. The plot consists of solid dots showing data points, where each dot has three main characteristics. First, the vertical location shows the feature importance, ranked in downward descending order. Second, a different shade of gray exhibits whether the variable has high or low impact on the prediction outcome. Black and white dots indicate a high and low impact variable, respectively, and its position shows the strength of impact on the prediction of the target variable (i.e., the operating LR). Finally, the horizontal axis shows the positive and negative impact of the predictors (e.g., variables such as condition rating) on the target variable. Ultimately, a SHAP plot illustrates the impact of predictors on the target variable prediction.  
The results shown in Figure 3a are generated using the GridSearch and cross-validation methods to identify hyperparameters such as the maximum depth [of trees] of 7, the learning rate of 0.3, the estimator parameter of 150, alpha of 1.0, min_split_loss of 4.0, lambda of 1.0, subsample of 0.8, min_child_weight of 5.0 for the XGBoost model. For the CatBoost model, the maximum depth [of trees] of 7, num_trees of 2000, l2_leaf_reg of 0.2, and the learning rate of 0.1 are used. Two metrics are used to evaluate the model accuracy: The RMSE value is 8.16 and R2-score is 0.77 for the test data set for the XGBoost model, both of which are considered good scores for a regression model. The CatBoost yields an R2-score of 0.70 and an RMSE of 9.21.  
Figure 3 shows that there is a strong relationship between the condition ratings (particularly substructure CR) and operating LR, and that older, wider, and longer bridges are more likely to drive the operating LR down. The gradient boosting regression analysis confirms that the operating LR well captures the changes in bridge conditions, and the probability of exposure to traffic and weathering. Verifying such correlation is significant to establish the maximum load capacity for a reliability analysis of bridges.