Natural Gradient Boosting for Probabilistic Prediction of Soaked CBR Values Using an Explainable Artificial Intelligence Approach

Abstract

The California bearing ratio (CBR) value of subgrade is the most used parameter for dimensioning flexible and rigid pavements. The test for determining the CBR value is typically conducted under soaked conditions and is costly, labour-intensive, and time-consuming. Machine learning (ML) techniques have been recently implemented in engineering practice to predict the CBR value from the soil index properties with satisfactory results. However, they provide only deterministic predictions, which do not account for the aleatoric uncertainty linked to input variables and the epistemic uncertainty inherent in the model itself. This work addresses this limitation by introducing an ML model based on the natural gradient boosting (NGBoost) algorithm, becoming the first study to estimate the soaked CBR value from this probabilistic perspective. A database of 2130 soaked CBR tests was compiled for this study. The NGBoost model showcased robust predictive performance, establishing itself as a reliable and effective algorithm for predicting the soaked CBR value. Furthermore, it produced probabilistic CBR predictions as probability density functions, facilitating the establishment of reliable confidence intervals, representing a notable improvement compared to conventional deterministic models. Finally, the Shapley additive explanations method was implemented to investigate the interpretability of the proposed model.