Optimisation of Ensemble Learning Algorithms for Geotechnical Applications: A Mathematical Approach to Relative Density Prediction

The challenge of predicting relative dry density ( D r ) in granular materials is addressed through advanced mathematical modelling and machine learning (ML) techniques. A novel approach to optimise ensemble learning algorithms is presented, with a focus placed on the mathematical foundations of these methods. An experimental dataset obtained from a mobile pluviator was utilised to develop and analyse various ML models. The mathematical analysis was centred on the optimisation and comparative performance of ensemble methods, with particular emphasis given to gradient boosting regression (GBR), AdaBoost regression, and extreme gradient boosting (XGBoost). The mathematical formulation of the GBR model was rigorously examined and optimised using advanced tuning functions, achieving exceptional performance metrics (mean squared error [MSE] = 11.91, mean absolute error [MAE] = 1.93, R 2 = 0.997). Through sensitivity analysis, it was revealed that the distance between the shutter plate and the top sieve is the most significant factor affecting D r prediction. A computational platform was developed within the Google Colab environment, demonstrating the practical application of the mathematical models. This research contributes to applied mathematics by showcasing advanced algorithmic approaches to solving complex geotechnical engineering problems while providing a rigorous mathematical foundation for future developments.