Fig. 4: Construction and comprehensive validation of an aPCE surrogate model.
a Characterization of input variables and polynomial basis. The top panel shows the kernel density estimation (KDE) plots showing the probability density function (PDF) of each input variable, and the bottom panel displays Stieltjes orthogonal polynomials derived from the empirical distributions. b Age-specific prediction verification. Parity plots compare model predictions (Pv) against experimentally measured true values (Tv) across 7, 14, and 28 curing days. Blue markers denote Pv-Tv pairs; yellow/blue bars indicate sample count distributions; red dashed line represents ideal 1:1 correspondence. c Comprehensive comparison of predicted versus actual results across the entire curing timeline. Dataset-wide comparison of Pv and Tv, including a ± 20% error band (shaded) and the ideal fit line. d Model performance evaluated using multiple statistical metrics (where a, k, r, v, m represent crack surface repair rate, crack water seepage repair rate, crack resistivity-based repair rate, crack ultrasonic velocity repair rate, and crack anti-chloride repair rate, respectively). e Global sensitivity analysis through the Sobol index. The main Sobol index (Si) represents individual contributions to output variance; the total Sobol index (STi) includes interaction effects.
