# Additive Manufacturing as an Alternative to Core Sampling in Concrete Strength Assessment
## 3 Results
The fitted slope of 0.97 is our updated transition coefficient, while the intercept (\(-\)4.9 MPa) absorbs the systematic offset induced by porosity, print layering and minor mix fluctuations captured during the campaign. In practice, the in situ compressive strength of a printed element can be estimated simply using the following procedures:  
* Multiplying the routine cube (or coupon) result by 0.97,
* Subtracting \(\approx\) 5 MPa. Because the residual error remains below 2 MPa across the calibrated 0-80 MPa domain, the formula is sufficiently precise for daily quality checks yet slightly conservative--providing an inherent safety buffer. As additional production data become available, the two coefficients can be re-fitted to tighten the prediction band; however, the linear relationship is expected to hold if printing and curing conditions stay within the validated envelope. Immediately after merging the three source-files and removing two incomplete rows, a single aligned data frame containing six representative porosity levels (30-80%) was obtained. The key mechanical responses (elastic strain, core strength, cube strength) and the main print-process descriptors (water-to-cement ratio W/C, layer height, and nozzle travel speed) are consolidated in Table 11; these values constitute the input matrix for all subsequent regression and sensitivity analyses. Figure 12: Predicted versus measured core compressive strength for four regression algorithms—ordinary least squares, Ridge, Lasso, and XGBoost. The dashed line denotes perfect parity; RMSE and R\({}^{2}\) values are reported in each panel. A clear monotonic relationship is evident: as porosity rises from 30% to 80%, both elastic strain and core strength increase almost proportionally, while optimisation efficiency peaks at medium porosity (\(\approx\)60%) before tapering off at the extremes. The modest divergence between \(R_{\text{cube}}\) and \(R_{\text{core}}\) (\(\approx\)4-8 MPa throughout) underpins the near-constant transition coefficient reported earlier. Process variables vary within realistic shop-floor ranges--layer height alternates between 10 mm and 12 mm, and travel speed between 60 mm s\({}^{-1}\) and 100 mm/s\({}^{-1}\)--providing sufficient contrast for the feature-importance study while still reflecting practical print settings. Collectively, the table confirms that the calibrated dataset spans the full operating window targeted by this work, lending confidence to the generality of the derived linear correction. To test whether the transition coefficient can be derived solely from readily measurable mix and print parameters, we expanded the original six-row dataset with five statistically perturbed \"synthetic campaigns\". Each replica introduces \(\pm\)1-2% random noise in porosity, elastic strain, W/C ratio and travel speed--mimicking the scatter that would be expected in routine production while preserving the physical correlations observed in Table 11.  
The full augmented set (n = 36) was split with a stratified 5-fold cross-validation, and four regression pipelines--ordinary least-squares (OLS), Ridge, Lasso and XGBoost--were trained under an identical preprocessing block (numeric standardisation only). The parity plots and error metrics are displayed in Figure 12.  
The visual and numerical evidence in Figure 12 leads to three main observations:  
* Linear behaviour dominates. OLS, Ridge and Lasso all achieve virtually identical accuracy (RMSE \(\approx\) 1.8-1.9 MPa; R\({}^{2}\) > 0.9995), indicating that the mapping from feature space to \(R_{\text{core}}\) is essentially linear within the explored parameter window. * Regularisation has little impact. Adding L\({}_{2}\) (Ridge) or L\({}_{1}\) (Lasso) penalties does not improve generalisation, confirming the absence of multicollinearity or spurious high-variance coefficients after standard scaling. * XGBoost over-fits this miniature set.