Study on an Interpretable Prediction Model for Pile Bearing Capacity Based on SHAP and BP Neural Networks

To facilitate rapid and precise predictions of pile bearing capacity, a Back Propagation (BP) neural network model has been developed utilizing data sourced from existing literature. The model incorporates several input parameters, including pile length, pile diameter, average effective vertical stress, and undrained shear strength. To enhance the optimization of the BP neural network's hyperparameters, five distinct optimization algorithms were employed: the Sine Cosine Optimization Algorithm (SCA), Snake Optimization Algorithm (SO), Pelican Optimization Algorithm (POA), African Vulture Optimization Algorithm (AVOA), and Chameleon Optimization Algorithm (CSA). The efficacy of the proposed model was validated using a randomly selected, previously unused subset of data and assessed through various evaluation metrics. Furthermore, the prediction outcomes were analyzed in conjunction with the SHAP interpretability method to address the inherent "black box" nature of the model. This analysis allowed for a visualization of the SHAP values associated with the input parameters, thereby elucidating their significance and impact on the predictions of pile capacity. The results indicated that the R² values for the BP-SCA, BP-SO, BP-POA, BP-AVOA, and BP-CSA models were 0.9920, 0.9922, 0.9928, 0.9974, and 0.9943, respectively, with the BP-AVOA model demonstrating the highest accuracy, stability, and predictive performance. The SHAP analysis further revealed that undrained shear strength and average effective vertical stress are the most influential parameters affecting pile bearing capacity, followed by pile length and pile diameter. Overall, the model effectively captures the complex nonlinear relationships among the characteristic parameters, thereby providing a robust foundation for further investigations into pile bearing capacity.