Prediction of Coefficient of Restitution of Limestone in Rockfall Dynamics Using Adaptive Neuro-Fuzzy Inference System and Multivariate Adaptive Regression Splines

Rockfalls are a type of landslide that poses significant risks to roads and infrastructure in mountainous regions worldwide. The main objective of this study is to predict the coefficient of restitution (COR) for limestone in rockfall dynamics using an adaptive neuro-fuzzy inference system (ANFIS) and Multivariate Adaptive Regression Splines (MARS). A total of ۹۳۱ field tests were conducted to measure kinematic, tangential, and normal CORs on three surfaces: asphalt, concrete, and rock. The ANFIS model was trained using five input variables: impact angle, incident velocity, block mass, Schmidt hammer rebound value, and angular velocity. The model demonstrated strong predictive capability, achieving root mean square errors (RMSEs) of ۰.۱۳۴, ۰.۱۹۳, and ۰.۲۱۷ for kinematic, tangential, and normal CORs, respectively. These results highlight the potential of ANFIS to handle the complexities and uncertainties inherent in rockfall dynamics. The analysis was also extended by fitting a MARS model (degree ۲, ۸ basis functions) to the same dataset. The MARS model achieved MAE ≈ ۰.۰۹۵ and RMSE ≈ ۰.۱۱۸—marginally improving over ANFIS—while delivering a fully explicit algebraic form and an intrinsic ranking of variable importance.

کلیدواژه ها:

Coefficient of restitution ، adaptive neuro-fuzzy inference system ، Rockfall ، Field test ، Multivariate Adaptive Regression Splines (MARS)