Work

Uncertainty-aware estimation of compressive strength for fly ash concrete with enhanced probabilistic prediction performance by incorporating the associated mortar strength

Year: 2026

Type: article

Abstract: Machine learning (ML) has been widely utilized to estimate the compressive strength ( f c ) of fly ash (FA) concrete due to its high efficiency and accuracy. However, the inherent variability in concrete materials introduces significant uncertainty in f c value, which traditional deterministic ML models cannot quantify. To address this engineering problem, this study proposes to adopt natural gradient boosting (NGBoost), a renowned probabilistic ML model, to estimate f c for FA concrete. Normal distribution-based prediction interval is determined to quantify model uncertainty. Furthermore, the associated mortar strength of the FA concrete is incorporated into NGBoost as an additional feature to evaluate its impact on prediction performance and to explore underlying mechanisms. Results demonstrate that including mortar strength (Model 2) improves the generalization performance of NGBoost compared to excluding it (Model 1). Shapley additive explanations (SHAP) reveal that for the deterministic interpretation, adding mortar strength does not significantly alter the variation trends between original features and their corresponding SHAP values. Mortar strength itself exhibits a strong positive correlation with its SHAP value, allowing Model 2 to capture variations in f c more accurately with an improved coefficient of determination (R 2 ) of 0.921 on the testing dataset. For the probabilistic interpretation, incorporating mortar strength inevitably introduces some uncertainty, with its mean absolute SHAP value of 0.12 MPa in Model 2, but it significantly reduces uncertainties for other features, decreasing their corresponding values by 0.17–0.33 MPa. Consequently, Model 2 attains better probabilistic prediction performance, with a negative log-likelihood of 3.802 on the testing dataset. This study offers a new perspective for observing the reduction and redistribution of uncertainty in ML models and provides a new method for the probabilistic prediction of the strength of FA concrete.

Source: Scientific Reports

DOI: 10.1038/s41598-026-74474-8