# Augmented Data-Driven Approach towards 3D Printed Concrete Mix Prediction
## 2 Methodology
### Augmentation Techniques
#### 2.2.1 Bootstrap Resampling  
Statistical analysis relies on understanding how a statistical property (e.g., mean, proportion) would vary across different random samples drawn from a population. This variability is captured by the sampling distribution, a theoretical concept typically unavailable from a single sample [111]. Traditionally, parametric approaches assume a specific distribution for the data (e.g., normal distribution) and derive the sampling distribution mathematically [112]. Alternatively, non-parametric methods avoid these assump \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Feature**} & \multirow{2}{*}{**Units**} & \multicolumn{6}{c}{**Statistics**} \\ \cline{3-10}  & & & & **Mean** & **STD** & **Min.** & **25 th** & **50 th** & **75 th** & **Max.** \\  & & & & **Peercentile** & **Percentile** & **Percentile** & **Percentile** & **Max.** \\ \hline
1 & Water & (kg/m\({}^{3}\)) & 278.91 & 131.77 & 74.23 & 177.12 & 262.20 & 329.80 & 644.46 \\
2 & Cement & (kg/m\({}^{3}\)) & 525.91 & 282.99 & 0.00 & 290.00 & 565.37 & 683.00 & 1205.00 \\
3 & Silica fume (SF) & (kg/m\({}^{3}\)) & 69.89 & 89.63 & 0.00 & 0.00 & 39.15 & 93.26 & 293.00 \\
4 & Fly ash (FA) & (kg/m\({}^{3}\)) & 317.73 & 382.36 & 0.00 & 0.00 & 177.92 & 489.27 & 1380.00 \\
5 & High-range water-reducing & (kg/m\({}^{3}\)) & 5.73 & 5.06 & 0.00 & 0.98 & 5.30 & 7.60 & 20.00 \\ admixture (HWRA) & & & & & & & & & \\
6 & Nano clay (NC) & (kg/m\({}^{3}\)) & 1.05 & 2.45 & 0.00 & 0.00 & 0.00 & 0.00 & 11.26 \\
7 & Viscosity modifying agent (VMA) & (kg/m\({}^{3}\)) & 3.63 & 8.96 & 0.00 & 0.00 & 0.49 & 2.75 & 55.20 \\
8 & Coarse aggregate (CA) amount & (kg/m\({}^{3}\)) & 221.29 & 417.39 & 0.00 & 0.00 & 0.00 & 343.70 & 1566.30 \\
9 & Coarse aggregate (CA) max. size & (mm) & 1.42 & 2.64 & 0.00 & 0.00 & 0.00 & 1.35 & 10.00 \\
10 & Fine aggregate (FA) amount & (kg/m\({}^{3}\)) & 689.29 & 330.55 & 195.70 & 433.47 & 624.87 & 993.00 & 1229.00 \\
11 & Fine aggregate (FA) max. size & (mm) & 0.45 & 0.23 & 0.18 & 0.30 & 0.40 & 0.48 & 1.00 \\
12 & Fiber tensile strength & (MA) & 1313.90 & 1141.02 & 0.00 & 300.00 & 880.00 & 2500.00 & 3450.00 \\
13 & Fiber elastic modulus & (GTA) & 49.14 & 684.2 & 0.00 & 3.00 & 12.50 & 87.20 & 200.00 \\
14 & Fiber amount & (kg/m\({}^{3}\)) & 19.41 & 36.21 & 0.00 & 1.20 & 9.00 & 21.60 & 157.00 \\
15 & Fiber length & (mm) & 9.03 & 5.77 & 0.00 & 6.00 & 9.00 & 12.00 & 23.00 \\
16 & Fiber diameter & (mm) & 39.51 & 53.99 & 0.00 & 11.20 & 24.00 & 39.00 & 200.00 \\
17 & Cast compressive strength & (MPa) & 56.04 & 38.85 & 18.77 & 36.00 & 42.00 & 53.00 & 170.20 \\
18 & Printed compressive strength-Dir. 1 & (MPa) & 51.42 & 33.59 & 18.20 & 30.60 & 40.43 & 56.00 & 166.50 \\
19 & Printed compressive strength-Dir. 2 & (MPa) & 45.15 & 34.78 & 14.50 & 24.12 & 32.50 & 50.00 & 151.11 \\
20 & Printed compressive strength-Dir. 3 & (MPa) & 36.02 & 27.99 & 10.40 & 18.72 & 24.40 & 47.20 & 148.70 \\
21 & Printed speed & (mm/sec) & 109.83 & 110.01 & 0.83 & 50.00 & 100.00 & 109.31 & 450.00 \\
22 & Slump flow & (mm) & 139.35 & 55.47 & 12.00 & 100.00 & 150.00 & 180.00 & 240.00 \\
23 & Nozzle area & (mm\({}^{3}\)) & 674.15 & 1533.36 & 28.26 & 113.04 & 314.00 & 490.63 & 7850.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistics of the real dataset features. tions [113]. The bootstrap method offers a unique approach. It utilizes the information within a single sample to create an approximation of the sampling distribution through a technique called bootstrap resampling [114]. The key concept is that original data is repeatedly sampled with replacement. This means a data point can be chosen multiple times, and some points may not be chosen at all. Each resampled dataset is called a bootstrap sample. For each bootstrap sample, the statistic of interest is calculated. This generates a collection of statistical values representing a simulated sampling distribution, the bootstrap distribution [115]. In this study, bootstrap resampling is used to generate synthetic data.