ارزیابی مدل‌های مبتنی‌بر درخت تصمیم غیرپارامتریک برای پیش‌بینی عمق آبشستگی پایه‌های پل

Abstract
The complex nature of bridge pier scour and the influence of various parameters on its estimation highlight the necessity of using a comprehensive nonlinear model. In the present study, four decision-tree-based models along with data from different bridges are employed. The input variables used for modeling the decision trees include upstream flow velocity, median bed particle diameter, upstream flow depth at the pier, pier width, angle of attack of the flow to the pier, pier length, particle diameter for which 84% of the particles are finer, and the pier shape factor, while the output variable is the local scour depth. In this study, modern decision tree methods are applied to calculate and compare bridge pier scour depth. The results indicate that the Extreme Gradient Boosting (XGB) and Random Forest (RF) models, with coefficients of determination of 0.76 and 0.73, respectively, exhibit higher accuracy compared to the four investigated models. The Gradient Boosting (GB) model ranks next with a coefficient of determination of 0.67, while the Decision Tree (DT) model shows the lowest performance. Furthermore, sensitivity analysis performed on the models reveals that pier width and pier length have the greatest influence on scour depth. After these two parameters, upstream flow depth has the most significant effect on scour depth.
 
Extended Abstract
Background and Objective
Water distribution networks represent a critical component of urban infrastructure, ensuring the delivery of safe water at adequate pressure. Rapid urbanization and aging pipelines have increasingly led to failures, pressure deficits, leakage, and reduced network reliability, highlighting the need for efficient design and rehabilitation strategies. The design problem is inherently multi-objective, requiring a balance between minimizing construction costs and maintaining sufficient hydraulic performance. Traditional design approaches are largely heuristic and unable to guarantee near-optimal solutions, whereas evolutionary algorithms have shown superior performance in complex optimization tasks. However, many of these algorithms suffer from drawbacks such as premature convergence, instability, or sensitivity to parameter tuning. The Multi-Objective Grey Wolf Optimizer (MOGWO), inspired by cooperative hunting behavior, has emerged as a robust alternative due to its effective balance between global exploration and local exploitation. This study proposes a novel MOGWO-based framework that minimizes network cost while maximizing resilience, and evaluates its effectiveness on the real-world D-zone distribution network in Mashhad.
 
Methodology
The present study uses four decision tree-based models and data (and information) from multiple bridges. The information used in this study to model the decision trees include the upstream flow velocity, average bed particle diameter, upstream flow depth and base width, angle of water intrusion into the base, base length, and diameter of particles of which 84% are smaller than its diameter, base shape factor, as input variables and local scour depth as output in the model. In this study, new decision tree methods are used to calculate and compare the bridge base scour depth. In this study, data from the US Federal Highway Administration was used to build models and validate decision trees. It was extracted from statistics on several bridges in the US. All information was collected in the field and included information related to the depth of scour around bridge piers in different locations.
 
Findings
The results show that the Extreme Gradient Boosting (XGB) and Random Forest (RF) models with coefficients of determination of 0.76 and 0.73 had higher accuracy than the four models examined, and the Gradient Boosting (GB) model was in the second place after these two models with coefficients of determination of 0.67, and the Decision Tree (DT) model was in the last place. Also, with the sensitivity analysis performed on the models, it was observed that the base width and the base length have the greatest effect on the scour depth. After these two parameters, the upstream flow depth has the greatest effect on the scour depth.
 
Conclusion
Bridge foundation scour is one of the most important issues in bridge safety. Considering the importance of this issue, in the present study, an attempt has been made to use new decision tree-based models to evaluate this issue. Decision tree methods are one of the best evaluation methods due to their simple understanding and ability to work with large and complex data. In future study, it is possible to combine new decision tree-based methods with other data mining or machine learning methods. The results show that the Extreme Gradient Boosting (XGB) and the Random Forest (RF) models had higher accuracy than the four models examined, and the Gradient Boosting (GB) model and the Decision Tree (DT) model were in last place. Also, with the sensitivity analysis performed on the models, it was observed that the base width and the base length have the greatest effect on the scour depth. After these two parameters, the upstream flow depth has the greatest effect on the scour depth.