Calibrated probabilistic prediction of compressive strength in palm oil fuel ash-modified concrete using conformal learning

Machine-learning models have increasingly been used to predict the compressive strength of palm oil fuel ash (POFA) concrete; however, most existing studies remain limited to deterministic point predictions and do not quantify predictive uncertainty. This limitation restricts their practical use in risk-informed mix design and engineering specification, where the reliability of a predicted strength value is as important as its accuracy. To address this gap, the present study develops a internally coverage-assessed probabilistic prediction framework for estimating the compressive strength of POFA concrete. A benchmark dataset of 407 experimental observations compiled from 18 source studies is partitioned into training ( n = 244, 60%), calibration ( n = 61, 15%), and test ( n = 102, 25%) sets. After 5-fold cross-validated hyperparameter tuning on training data exclusively, four point-prediction models are benchmarked. Three uncertainty quantification (UQ) frameworks are evaluated: Natural Gradient Boosting (NGBoost) with Normal and LogNormal distributions, split conformal prediction with three base models, and Mondrian conformal prediction stratified by water-to-binder (W/B) ratio. All prediction interval coverage probabilities (PICP) are accompanied by 95% Wilson score confidence intervals. SHAP is applied directly to NGBoost’s internal log-scale parameter with 5-seed Kernel Explainer stability verification. XGBoost achieves the highest point-prediction accuracy (R²=0.9749, RMSE = 4.402 MPa, validated across 10 random splits: mean R²=0.9774 ± 0.0043). NGBoost-Normal is significantly overconfident (PICP = 0.804, Wilson CI = [0.717, 0.869], ECE = 0.058 at nominal 90%). The conformal results demonstrated an accuracy–coverage divergence that is theoretically consistent with conformal prediction: XGBoost, the most accurate base model, produced the narrowest conformal intervals and the lowest coverage (PICP = 0.873, Wilson CI = [0.794, 0.924]), whereas the Hybrid stacking model produced wider intervals and higher internal coverage (PICP = 0.931, Wilson CI = [0.865, 0.966], ECE = 0.022). Direct sigma SHAP, stable across 5 Kernel Explainer seeds (max CV = 0.133), reveals W/B Ratio dominates prediction uncertainty; Cement and POFA rise substantially in uncertainty importance relative to CS prediction ranks, while Curing Age collapses. Internal conformal calibration improved interval reliability relative to direct NGBoost intervals; however, overlap-controlled external validation on 147 non-overlapping Kazemi records showed that nominal coverage was not preserved under dataset/source shift. Therefore, the framework is interpreted as an internally calibrated UQ baseline and transferability diagnostic rather than a deployment-ready design tool.