Predicting the self-healing performance of microbial self-healing concrete: Static, dynamic intelligent prediction, and formula-based approaches

This study developed an integrated framework for predicting the self-healing performance of microbial self-healing concrete, addressing the limitations of static single-model evaluation, insufficient temporal modeling, and weak physical interpretability. Self-healing experiments were first conducted using three microbial carrier systems: sodium alginate microcapsules (MSA), expanded perlite (MEP), and coral reef sand (MCR). A Bayesian-optimized Stacking model was established for static prediction by integrating heterogeneous base learners. A KAN-GRU dual-tower model was then developed for dynamic prediction by combining nonlinear feature mapping with temporal memory. In addition, the Physics-Informed Robust Recursive Regression (PIR 3 ) procedure was used to derive a semi-empirical formula with explicit physical meaning. The experimental results showed that MSA achieved the best healing performance, with a healing rate above 90% for cracks narrower than 0.7 mm after 28 days. Its repair response and calcium carbonate deposition were superior to those of MEP, MCR, and directly mixed bacterial solutions. Among the prediction models, KAN-GRU achieved the highest accuracy (R 2 = 0.934) and effectively tracked the time-dependent healing process. The static Stacking model showed slightly lower accuracy (R 2 = 0.912) but offered higher computational efficiency and good generalization. The semi-empirical formula required only three basic input parameters and was therefore suitable for rapid engineering assessment. Overall, the proposed framework integrates static prediction, dynamic evolution tracking, and interpretable formula derivation, providing systematic support for the design and life-cycle monitoring of microbial self-healing concrete.