Nonparametric CART and M5 Methods Application on Bridge Piers Scour Depth Computation

Bridge pier scouring is one of the most important fields in hydraulics and river engineering, especially due to loss of life and property caused by bridge failure. Many experimental equations have been previously proposed to evaluate bridge pier scouring, most of which could not accurately simulate scoring depth because of complexity of the phenomenon. The present study, in this regard, compares two nonparametric CART and M5’ models having tree-structure and dividing the problem space into several branches. CART model offers a scalar quantity for each branch while M5’ model could provide equations as a result of bridge scour for different branches. Mixture densimetric particle Froude number, pier shape factor and ratio of flow depth to pier width were taken into account as input parameters in this research. Pier shape factor has been chosen as the first decision variable in both models that reflects the importance of this parameter on scour depth, corresponded to previous equations from the literature. Statistical analysis on proposed models and previous equations indicated that the nonparametric models could predict scour depth around piers with more precision. Discrepancy ratio was one of the statistical tests used in this research, indicating more than 65% accuracy for the tree-based models against other equations having less than 50% accuracy. Same results were observed from other statistical tests such as RMSE and R2. Finally, in comparison with CART model, M5’ was recommended for estimating of scour depth according to its simple structure. Also based on sensitivity analysis on M5’ model, pier width, flow depth and velocity had the highest impact on scour depth, respectively.