Riprap stones are frequently applied to protect rivers and channels against erosion processes. Many empirical equations have been proposed in the past to estimate the unit discharge at the failure circumstance of riprap layers. However, these equations lack general impact due to the limited range of experimental variables. To overcome these shortcomings, support vector machine (SVM), multivariate adaptive regression splines (MARS), and random forest (RF) techniques have been applied in this study to estimate the approach densimetric Froude number at the incipient motion of riprap stones. Riprap stone size, streambank slope, uniformity coefficient of riprap layer stone, specific density of stones, and thickness of riprap layer have been considered as controlling variables. Quantitative performances of the artificial intelligence (AI) models have been assessed by many statistical measures including: coefficient of correlation (R), root mean square error (RMSE), mean absolute error (MAE), and scatter index (SI). Statistical performance of AI models indicated that SVM model with radial basis function (RBF) kernel had better performance (SI = 0.37) than MARS (SI = 0.75) and RF (SI = 0.63) techniques. The proposed AI models performed better than existing empirical equations. From a parametric study the results demonstrated that the erosion-critical stone-referred Froude number (F_s,c) is mainly controlled by the streambank slope.

经常使用裂石来保护河流和河道免受侵蚀。过去已经提出了许多经验方程式，以估计裂石层破坏情况下的单位流量。但是，由于实验变量的范围有限，这些方程式缺乏通用影响。为了克服这些缺点，在本研究中应用了支持向量机（SVM），多元自适应回归样条（MARS）和随机森林（RF）技术来估计裂石初始运动时的接近弗洛德数。抛石的大小，河岸坡度，抛石层石的均匀性系数，石的比重和抛石层的厚度均被视为控制变量。人工智能（AI）模型的量化性能已通过许多统计方法进行了评估，包括：相关系数（R），均方根误差（RMSE），平均绝对误差（MAE）和散射指数（SI）。AI模型的统计性能表明，具有径向基函数（RBF）内核的SVM模型具有比MARS（SI = 0.75）和RF（SI = 0.63）技术更好的性能（SI = 0.37）。所提出的AI模型比现有的经验方程式表现更好。通过参数研究，结果表明，以腐蚀为关键的石材称为Froude数（AI模型的统计性能表明，具有径向基函数（RBF）内核的SVM模型具有比MARS（SI = 0.75）和RF（SI = 0.63）技术更好的性能（SI = 0.37）。所提出的AI模型比现有的经验方程式表现更好。通过参数研究，结果表明，以腐蚀为关键的石材称为Froude数（AI模型的统计性能表明，具有径向基函数（RBF）内核的SVM模型具有比MARS（SI = 0.75）和RF（SI = 0.63）技术更好的性能（SI = 0.37）。所提出的AI模型比现有的经验方程式表现更好。通过参数研究，结果表明，以腐蚀为关键的石材称为Froude数（F _s，c）主要由河岸坡度控制。