# Frost Resistance Prediction of Concrete Based on Dynamic Multi-Stage Optimisation Algorithm
## 6 Results and Discussion
The Wilcoxon signed-rank test, a non-parametric testing method, is selected to conduct pairwise comparisons of the prediction performance differences between DMSOA-CatBoost and AOA-CatBoost, as well as SCA-CatBoost. The tests are performed at a significance level of \(\alpha=0.05\). As shown in Tables 9 and 10, DMSOA-CatBoost is significantly superior to AOA-CatBoost and SCA-CatBoost on both datasets, with all \(p\)-values less than 0.05. This indicates that DMSOA-CatBoost has a statistically significant predictive advantage, and the significance results effectively support the superiority of the proposed method. In the field of machine learning for frost resistance prediction, traditional machine learning models often encounter challenges when faced with complex and dynamically changing datasets, including the need to effectively process large amounts of frequently changing data and the need to deal with possible high-dimensional features and nonlinear relationships. When standard CatBoost is faced with ultra-large-scale datasets or complex scenarios that require fine tuning owing to its huge parameter space and high sensitivity, the parameter optimisation process may no longer become intuitive and efficient, which may easily lead to model overfitting or underfitting. The introduction of DMSOA, with its superior development, detection, and local optimal avoidance ability, not only allows one to determine the best hyperparameters but also to adjust the strategy of feature combination and boundary counting, thus improving the adaptability and robustness of the model in changeable environments and significantly improving the predicting accuracy of concrete frost resistance. Combining the efficient search ability of DMSOA with the high-performance learning algorithm of CatBoost, application of the DMSOA-CatBoost optimisation model can accurately predict the frost resistance of concrete and provide a reliable support and decision-making basis for engineering practice. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Statistic (W)** & \(p\)**-Value** &
\begin{tabular}{c} **Significance** \\ **(\(\alpha=0.05\))** \\ \end{tabular} \\ \hline DMSOA-CatBoost & & 0 & 0.009 & ✓ \\ vs SCA-CatBoost & & & \\ DMSOA-CatBoost & & & \\ vs AOA-CatBoost & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Wilcoxon signed-rank test results (MLR). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **R\({}^{2}\)** & **MSE** & **RMSE** & **MAE** & **CC** & **SDR** \\ \hline SCA-CatBoost & 0.861 & 0.190 & 0.436 & 0.243 & 0.933 & 0.914 \\ AOA-CatBoost & 0.872 & 0.178 & 0.422 & 0.233 & 0.937 & 0.919 \\ DMSOA-CatBoost & 0.885 & 0.167 & 0.403 & 0.225 & 0.941 & 0.924 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Evaluation of different optimised models (MLR). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Statistic (W)** & \(p\)**-Value** &
\begin{tabular}{c} **Significance** \\ **(\(\alpha=0.05\))** \\ \end{tabular} \\ \hline DMSOA-CatBoost & & 0 & 0.014 & ✓ \\ DMSOA-CatBoost & & 5 & 0.020 & ✓ \\ vs. AOA-CatBoost & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Wilcoxon signed-rank test results (RDEM). Moreover, the research group has made achievements in the prediction of different properties of concrete and the recommendation of proportion and made a complete software system. Figure 24 presents the main interface of system function selection, including frost resistance, strength, electric flux and other properties. Figure 25 presents the interface of frost resistance prediction, which also provides the prediction of relative dynamic elastic modulus and mass loss rate. The prediction model is DMSOA-CatBoost. It provides an efficient and accurate tool for engineers and researchers to optimise the design and preparation process of concrete, which not only improves engineering quality but also substantially reduces material waste and engineering costs whilst contributing to the development of concrete technology.