Using an evolutionary heterogeneous ensemble of artificial neural network and multivariate adaptive regression splines to predict bearing capacity in axial piles

Accurately estimating the bearing capacity of piles is an onerous task in structural design task that requires a powerful computation model able to elucidate nonlinear impacts of geotechnical factors and the dimension and shape of piles. This study develops a novel heterogeneous ensemble artificial intelligence model, named intelligence multivariate neural network inference model (IMNNIM), to accurately and quickly predict bearing capacity of piles. The IMNNIM was created by integrating the equilibrium optimization algorithm (EO) into a combination of multivariate adaptive regression splines (MARS) and radial basis neural network (RBFNN). The predictive values of the IMNNIM were qualified by dynamically merging prediction information generated by MARS and RBFNN and then adjusting the associated weights and assigned tuning parameter values of the learner members. The performance of the IMNNIM was evaluated using data from 472 driven pile static load test reports. The experimental results using a 10-fold cross-validation method demonstrated the IMNNIM to be the most reliable model for predicting pile-bearing-capacity by achieving the greatest values of MAPE (7.24%), RMSE (90.92kN), MAE (67.98kN), and R² (0.930) and the lowest standard deviation values. A t-test analysis method confirmed the IMNNIM as a superior tool for pile-bearing-capacity estimation.