# Tree Based Approaches for Predicting Concrete Carbonation Coefficient
## 3 Materials and Methods  
### Data Used in the Study  
As stated earlier, this work is an extension of previous ones and is intended to predict the carbonation coefficient and strength of concrete using Multiple Linear Regression [23], Artificial Neural Networks and Genetic Programming [11]. Therefore, the same data collated from 17 studies (827 values) found in the literature are used. These encompass data from concrete mixes with different types of binder and binder contents, different water/binder ratios and compressive strengths, as well as types of curing and workability. Approximately half of the data concern concrete in service conditions, i.e., natural exposure, whereas the remaining data concern concrete subjected to accelerated carbonation conditions (laboratory CO2 enriched environment). To ensure that the complete data of all variables could be used to determine the value by default, the missing values in any variable were taken as the mean value of the respective [23]. The checking of the data was carried out, and the outliers (points more than three standard deviations away from the mean value of the respective variable) were removed. Further details of the data can be found in [23], while a summary using variable abbreviations is shown in Table 1. These input parameters are the same as those considered in [23], which were selected according to the analysis of variance technique. For the variable \"Exposure class\" (X), the value of 1 means that the results concern an exposure to an environment that causes concrete to be permanently dry (e.g., building interior) or permanently wet (e.g., totally immersed). The value of 2 is for concrete exposed to environments with moderate humidity (e.g., concrete in open air structures sheltered from rain). Finally, the value of 3 stands for results from concrete exposed to dry-wet cycles (e.g., concrete in open air structures not sheltered from rain) and for concrete with long periods in contact with water (e.g., rainwater drainage systems). Various methods of pre-processing data are used by various researchers, such as rescaling, binarising or standardising the data using Gaussian distribution. One of the commonest problems in pre-processing data is missing values. One way of dealing with this is eliminating the variables with missing values, only using the variables with complete data. Despite its simplicity, this approach has several disadvantages, namely because, on \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Min** & **Max** & **Mean** & **Mode** \\ \hline \hline \multicolumn{1}{c}{Clinker (kg/m\({}^{3}\))—CC} & 66.000 & 529.150 & 292.196 & 362.990 \\ \hline \hline \multicolumn{1}{c}{Clinker/binder ratio (\%)—\(CR\)} & 20.000 & 100.000 & 80.228 & 95 \\ \hline \hline
28-day compressive strength in MPa—\(fc\) & 8.800 & 127.500 & 48.823 & 37.000 \\ \hline \hline \multicolumn{1}{c}{CO2 content—\(CO\)} & 0.020 & 50.000 & 15.490 & 0.040 \\ \hline \hline \multicolumn{1}{c}{Number of curing days—\(d\)} & 7 & 91 & - & 28 \\ \hline \hline \multicolumn{1}{c}{Water/binder ratio—\(w/b\)} & 0.240 & 1.000 & 0.501 & 0.370 \\ \hline \hline \multicolumn{1}{c}{Relative humidity (\%)—\(RH\)} & 50 & 90 & - & 65 \\ \hline \hline \multicolumn{1}{c}{Exposure class—\(X\)} & 1 & 3 & - & 1 \\ \hline \hline \multicolumn{1}{c}{Carbonation coefficient in} & & & & \\ (mm/year\({}^{0.5}\))—\(k\) & 0.180 & 60.420 & 14.585 & 1.730 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of the data used for model development. several occasions, the dataset is reduced to an insufficient size [35]. Therefore, different methods have been developed to deal with missing values. Simple imputation and multiple imputation are the most common approaches [23]. Here, the missing predictor values are replaced by the mean value of the variable under analysis, considering the physical meaning of the mean value for the reliability of the predictions. Based on this approach, the complete data of the variable can be used to estimate the value by default [23].