## 3 Analysis of the Practical Engineering Data and Results
### Establishment of Predicting Models Based on ANFIS, ANN, PCA-ANN, and PCA-ANFIS Models  
Using practical engineering data on carbonation depth in concrete structures from Table 1, this study employed principal component analysis (PCA) to establish the traditional ANFIS model, the ANN model, the PCA-ANN model, and the PCA-ANFIS model for carbonation depth forecasting. The data in Table 3 after dimension reduction by PCA were used as the input vector for the PCA-ANFIS model and the PCA-ANN model, while the data in Table 1 formed the input vector for the ANFIS model and the ANN model, with carbonation depth as the output vector in both cases. For both models, 45 subsamples were retained as training data, with the remaining five subsamples used as checking data. The predicted results were influenced by the parameter set for the ANFIS models and PCA-ANFIS models, including the type of fuzzy-based rule, the number of membership functions (MFs), and the membership function types [26]. For the ANFIS model and the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Principal** & **Eigenvalues \(\lambda_{i}\)** & **VCP** & **CVCP (\%)** \\ \hline
1 & 2.28 & 41.31 & 41.31 \\
2 & 1.29 & 19.71 & 61.02 \\
3 & 0.99 & 15.40 & 76.42 \\
4 & 0.88 & 13.81 & 90.23 \\
5 & 0.46 & 7.82 & 98.05 \\
6 & 0.11 & 1.95 & 100.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analysis results of PCA. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**NO.** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** \\ \hline Y1 & 2.41 & 2.10 & 3.23 & 2.92 & 2.87 & 2.56 & 2.55 & 1.90 & 1.92 & 2.23 & \(-\)0.69 & \(-\)0.69 & 0.83 \\ Y2 & 0.15 & \(-\)0.84 & 0.78 & \(-\)0.21 & 0.54 & 0.10 & \(-\)0.45 & 1.52 & 0.39 & 1.38 & 1.05 & 2.15 & 0.17 \\ Y3 & \(-\)1.28 & 0.60 & \(-\)1.19 & 0.69 & \(-\)1.23 & 1.04 & 0.65 & \(-\)1.16 & 1.14 & \(-\)0.74 & 0.77 & 1.54 & 1.10 \\ Y4 & 0.16 & \(-\)0.31 & \(-\)0.96 & \(-\)1.43 & \(-\)0.53 & \(-\)0.54 & \(-\)0.99 & \(-\)1.72 & \(-\)0.18 & 0.29 & \(-\)0.92 & \(-\)0.02 & 0.43 \\ NO. & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 & 25 & 26 \\ \hline Y1 & \(-\)2.02 & \(-\)1.70 & \(-\)1.67 & \(-\)0.70 & \(-\)0.39 & 0.53 & 0.84 & 0.72 & 0.72 & \(-\)0.76 & \(-\)0.30 & 0.02 & \(-\)0.63 \\ Y2 & \(-\)0.78 & 0.21 & 0.49 & \(-\)2.05 & \(-\)1.06 & \(-\)0.29 & 1.80 & \(-\)0.19 & \(-\)0.19 & \(-\)2.13 & \(-\)0.93 & 1.16 & \(-\)1.18 \\ Y3 & \(-\)0.25 & \(-\)2.13 & 0.77 & \(-\)0.34 & \(-\)2.22 & 0.99 & \(-\)0.11 & 1.08 & 1.08 & \(-\)0.67 & 0.05 & \(-\)1.05 & 0.01 \\ Y4 & \(-\)0.58 & \(-\)0.12 & 0.24 & 0.96 & 1.43 & 1.12 & 2.49 & 1.00 & 1.00 & \(-\)0.68 & \(-\)0.48 & 0.89 & \(-\)0.03 \\ NO. & 27 & 28 & 29 & 30 & 31 & 32 & 33 & 34 & 35 & 36 & 37 & 38 & 39 \\ \hline Y1 & \(-\)0.62 & \(-\)0.31 & \(-\)1.99 & \(-\)1.99 & \(-\)1.37 & \(-\)2.29 & \(-\)2.29 & \(-\)2.61 & 0.89 & \(-\)0.59 & \(-\)0.59 & \(-\)0.59 & \(-\)0.59 \\ Y2 & \(-\)0.08 & 0.91 & 0.81 & 0.81 & 1.13 & 1.75 & 1.20 & \(-\)0.34 & 1.85 & 1.04 & \(-\)0.94 & \(-\)0.94 & \(-\)0.39 \\ Y3 & 0.79 & \(-\)1.09 & 0.69 & 0.69 & 0.96 & \(-\)1.37 & \(-\)1.76 & \(-\)0.27 & \(-\)0.50 & 1.59 & 0.18 & 0.18 & 0.57 \\ Y4 & 0.87 & 1.34 & \(-\)0.27 & \(-\)0.27 & \(-\)0.64 & \(-\)0.28 & \(-\)0.73 & \(-\)1.65 & 0.54 & 1.76 & 0.13 & 0.13 & 0.58 \\ NO. & 40 & 41 & 42 & 43 & 44 & 45 & 46 & 47 & 48 & 49 & 50 & \\ \hline Y1 & \(-\)0.15 & \(-\)0.05 & \(-\)0.15 & \(-\)2.50 & \(-\)2.49 & 0.74 & 0.74 & 0.44 & \(-\)0.17 & \(-\)0.10 & \(-\)0.17 & & \\ Y2 & \(-\)0.44 & \(-\)0.39 & \(-\)0.44 & \(-\)0.09 & 1.01 & \(-\)1.20 & \(-\)1.20 & \(-\)0.40 & \(-\)1.76 & \(-\)1.73 & \(-\)1.76 & & \\ Y3 & 0.26 & 0.30 & 0.26 & 0.10 & 0.88 & 0.19 & 0.19 & \(-\)1.70 & \(-\)0.11 & \(-\)0.08 & \(-\)0.11 & & \\ Y4 & \(-\)1.06 & \(-\)1.12 & \(-\)1.06 & \(-\)1.15 & \(-\)0.25 & \(-\)0.17 & \(-\)0.17 & 1.10 & 0.63 & 0.59 & 0.63 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of data after dimension reduction by the PCA method. ANN model, six nodes were used in the input layer, and one node was used in the output layer.