# Frost Resistance Prediction of Concrete Based on Dynamic Multi-Stage Optimisation Algorithm
## 3 Data Processing and Analysis  
### Data Acquisition  
This study uses 7090 datasets, of which 1215 data are derived from the daily experiments of the research group. The laboratory data are measured by the research group through a series of freeze-thaw cycle experiments on concrete samples with different mix proportions through strict experimental procedures. All samples are tested under the same experimental conditions to ensure the consistency and comparability of the data. Another 5875 pieces of data are derived from published related research papers. This part of the data is carefully screened during the collection process, retaining only research results that are consistent with the objectives of this study, with clear data sources and standardised experimental methods. In addition, nine input variables such as cement and water, as well as two prediction indices of relative dynamic elastic modulus and mass loss rate required for this study, are retained. The collected data are divided into two datasets for data processing and analysis. One is relative dynamic elastic modulus (RDEM) as the prediction index, and the other is mass loss rate (MLR) as the prediction index. The input indices are defined as C (cement), W (water), FA (fly ash), S (fine aggregate), G (coarse aggregate), WRA (water reducer), GGBS (mineral powder), GC (gas content), and NFTC (freeze-thaw cycle times). These features are selected based on the widely recognised influencing factors in existing research on concrete frost resistance and engineering practices, covering raw material composition, admixture usage, and environmental acting factors. Tables 1 and 2 show the descriptive statistics of variables in the dataset. The statistical indicators, such as minimum value, maximum value, mean value, and standard deviation in the table, reveal the core characteristics of the dataset and comprehensively reflect the variability, concentration trend, and overall distribution range of the data. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **Unit** & **Minimum** & **Maximum** & **Mean** &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} \\ \hline C & kg/m\({}^{3}\) & 110.00 & 533.00 & 266.02 & 82.64 \\ FA & kg/m\({}^{3}\) & 0.00 & 266.00 & 67.49 & 41.69 \\ GGBS & kg/m\({}^{3}\) & 0.00 & 190.00 & 16.85 & 31.19 \\ S & kg/m\({}^{3}\) & 530.00 & 994.00 & 743.48 & 80.88 \\ G & kg/m\({}^{3}\) & 777.32 & 1703.00 & 1133.50 & 153.58 \\ WRA & kg/m\({}^{3}\) & 0.00 & 11.51 & 1.54 & 2.50 \\ GC & kg/m\({}^{3}\) & 0.06 & 9.40 & 4.32 & 1.90 \\ W & kg/m\({}^{3}\) & 81.00 & 200.00 & 148.85 & 26.93 \\ NFTC & times & 0.00 & 400.00 & 138.06 & 92.65 \\ RDEM & \% & 43.33 & 107.41 & 88.05 & 12.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dataset descriptive statistics of relative dynamic elastic modulus. To show the relationship among the variables in the dataset, the scatter plot matrices of relative dynamic elastic modulus and mass loss rate are drawn, respectively, as shown in Figures 6 and 7. A scatter plot matrix is a data visualisation tool used to exhibit binary relationships between multiple variables in a single view; it can help identify relationships between variables, distribution patterns of data, and potential outliers [29]. The diagonal graph shows the frequency distribution histogram of the data distribution of a single variable. The upper half of the diagonal shows the joint probability density plot of the two variables. The darker colour indicates denser data points in this area, and the sparse area far away from the main density area may indicate outliers. The graph in the lower half of the diagonal shows a scatter plot of the relationship of the two variables. To ensure the accuracy of the model and avoid the problem of multicollinearity, the correlation between input variables should be less than 0.8 [30].