Hybrid machine learning models for predicting crack stress thresholds in granitic rocks: A metaheuristic hyperparameter optimization framework

Abstract Accurate estimation of crack initiation stress (σ ci ) and crack damage stress (σ cd ) is fundamental for evaluating brittle rock failure, assessing the stability of underground excavations, and improving the safety and design of geotechnical engineering projects. However, direct laboratory determination of these crack stress thresholds is time-consuming, expensive, and often impractical for large-scale engineering applications. This study therefore investigates the applicability of hybrid machine learning (ML) models that integrate Artificial Neural Networks (ANN) and Decision Trees (DT) with Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) for predicting crack stress thresholds in granitic rocks. Unlike previous studies that applied ML mainly to general rock mechanical properties, this study develops and evaluates four hybrid machine learning (ML) models including PSO-ANN, GA-ANN, PSO-DT, and GA-DT, using an experimental dataset of 107 granitic rock samples, where the metaheuristic algorithms optimize the machine learning models to improve prediction accuracy. Among all tested models, the PSO-optimized ANN (PSO-ANN) consistently demonstrates high performance, achieving coefficient of determination (R²) values of 0.931 for σ ci and 0.956 for σ cd predictions with minimal error metrics, significantly outperforming traditional and non-optimized ML counterparts. Model robustness was evaluated through 5-fold cross-validation, confirming stable performance across different data partitions. Sensitivity analysis identifies Uniaxial Compressive Strength (UCS) as the most influential input parameter, followed by Young’s modulus, while Poisson’s ratio shows marginal impact. Taylor diagram evaluations further validate the predictive robustness and generalizability of the PSO-ANN model. The proposed hybrid models demonstrated promising predictive performance for the investigated granitic rock dataset. These models may serve as efficient tools for preliminary estimation of crack thresholds and can complement laboratory investigations. However, further validation using larger, more diverse, and independent datasets is required before application in design-critical rock engineering.