multivariate adaptive regression splines

The mechanical characteristics of rocks and rock masses are considered as the determining factors in making plans in the mining and civil engineering projects. Two factors that determine how rocks responds in varying stress conditions are P-wave velocity (PWV) and its isotropic properties. Therefore, achieving a high-accurate method to estimate PWV is a very important task. This work investigates the use of different intelligent models such as multivariate adaptive regression splines (MARS), classification and regression tree (CART), group method of data handling (GMDH), and gene expression programming (GEP) for the prediction of PWV. The proposed models are then evaluated using several error statistics, i.e. squared correlation coefficient (R2) and root mean squared error (RMSE). The values of R2 obtained from the CART, MARS, GMDH, and GEP models are 0.983, 0.999, 0.995, and 0.998, respectively. Furthermore, the CART, MARS, GMDH, and GEP models predict PWV with the RMSE values of 0.037, 0.007, 0.023, and 0.020, respectively. According to the aforementioned amounts, the models presented in this work predict PWV with a good performance. Nevertheless, the results obtained reveal that the MARS model yields a better prediction in comparison to the GEP, GMDH, and CART models. Accordingly, MARS can be offered as an accurate model for predicting the aims in other rock mechanics and geotechnical fields.

Intake structures have been widely used for flow diversion in the irrigation and drainage networks. In this paper, the multivariate adaptive regression splines (MARS), artificial neural network (ANN), and support vector machine (SVM) techniques were utilized for prediction of discharge coefficient (Cd) of lateral intakes. The experimental data pertaining to dimensionless parameters on Cd were collected to develop the models. The results indicated that the best performance in modeling is related to the MARS model with R2=0.98 and RMSE=0.023 and the MARS model outperforms the ANN and SVM models. The tangent sigmoid and radial basic functions were found to be the most efficient transfer and kernel functions for ANN and SVM, respectively. Moreover, Froude number (Fr1) and the ratio of the weir height to the upstream flow depth (P/d1) were the most effective factors for predicting Cd. Evaluation of the performance of applied models in term of developed discrepancy ratio (DDR) index shows that the minimum data dispersivity is related to the MARS model.