## 4 PCA-IWOA-XGBoost Model Construction and Prediction Result Analysis
### PCA Dimensionality Reduction
\begin{array}{l}F_{1}=0.08x_{1}+0.27x_{2}+0.167x_{3}+0.301x_{4}+0.154x_{5}+0. 183x_{6}+0.075x_{7}-0.069x_{8}-0.105x_{9}+0.202x_{10}-0.231x_{11}\\ F_{2}=-0.039x_{1}+0.247x_{2}-0.09x_{3}+0.221x_{4}-0.017x_{5}+0.224x_{6}-0.279x_{ 7}+0.083x_{8}+0.267x_{9}-0.226x_{10}+0.23x_{11}\\ F_{3}=-191x_{1}+0.021x_{2}+0.279x_{3}-0.033x_{4}+0.417x_{5}-0.322x_{6}-0.177x_{ 3}+0.323x_{8}+0.186x_{9}+0.149x_{10}+0.029x_{11}\\ F_{4}=0.53x_{1}+0.121x_{2}+0.086x_{3}-0.085x_{4}+0.289x_{5}-0.283x_{6}-0.091x_{ 7}-0.409x_{8}+0.067x_{9}-0.259x_{10}+0.079x_{11}\\ F_{5}=0.102x_{1}+0.013x_{2}+0.654x_{3}-0.113x_{4}-0.338x_{5}+0.126x_{6}+0.515x_{ 7}-0.018x_{8}+0.591x_{9}-0.083x_{10}+0.07x_{11}\\ F_{6}=0.759x_{1}+0.042x_{2}-0.489x_{3}-0.035x_{4}-0.02x_{5}-0.02x_{6}+0.175x_{ 7}+0.732x_{8}+0.275x_{9}+0.207x_{10}-0.223x_{11}\\ \end{array}  \tag{29}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(\mathbf{F_{1}}\) & \(\mathbf{F_{2}}\) & \(\mathbf{F_{3}}\) & \(\mathbf{F_{4}}\) & \(\mathbf{F_{5}}\) & \(\mathbf{F_{6}}\) \\ \hline \(x_{1}\) & \(0.08\) & \(-0.039\) & \(-0.191\) & \(0.53\) & \(0.102\) & \(0.759\) \\ \(x_{2}\) & \(0.27\) & \(0.247\) & \(0.021\) & \(0.121\) & \(0.013\) & \(0.042\) \\ \(x_{3}\) & \(0.167\) & \(-0.09\) & \(0.279\) & \(0.086\) & \(0.654\) & \(-0.489\) \\ \(x_{4}\) & \(0.301\) & \(0.221\) & \(-0.033\) & \(-0.085\) & \(-0.113\) & \(-0.035\) \\ \(x_{5}\) & \(0.154\) & \(-0.017\) & \(0.417\) & \(0.289\) & \(-0.338\) & \(-0.02\) \\ \(x_{6}\) & \(0.183\) & \(0.224\) & \(-0.322\) & \(-0.283\) & \(0.126\) & \(-0.02\) \\ \(x_{7}\) & \(0.075\) & \(-0.279\) & \(-0.177\) & \(-0.091\) & \(0.515\) & \(0.175\) \\ \(x_{8}\) & \(-0.069\) & \(0.083\) & \(0.323\) & \(-0.409\) & \(0.018\) & \(0.732\) \\ \(x_{9}\) & \(-0.105\) & \(0.267\) & \(0.186\) & \(0.067\) & \(0.591\) & \(0.275\) \\ \(x_{10}\) & \(0.202\) & \(-0.226\) & \(0.149\) & \(-0.259\) & \(-0.083\) & \(0.207\) \\ \(x_{11}\) & \(-0.231\) & \(0.23\) & \(0.029\) & \(0.079\) & \(0.07\) & \(-0.223\) \\ \hline \end{tabular}
\end{table} 
Table 7: Score coefficients of the first four principal components. Figure 9: Contribution rates and cumulative contribution rates of each principal component. two initial parameters--maximum iteration number and whale population size--a trial-and-error method was used to determine the optimal whale population size. After multiple experiments, it was found that when the maximum iteration number was set to 500, the fitness curve stabilized, so the maximum iteration number for the WOA-XGBoost model was set to 500. With the maximum iteration number fixed, 10 WOA-XGBoost prediction models were constructed, with whale population sizes of 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100. The fitness curves for different whale population sizes are shown in Figure 10. It can be observed that when the whale population size was 90, the corresponding fitness curve was the lowest among all models, indicating the best model performance. Notably, before reaching 500 iterations, the fitness curve of the IWOA-XGBoost model had already stabilized, confirming the reasonableness of the chosen iteration number. With a whale population size of 90 and 500 iterations, the optimized hyperparameters were obtained as follows: learning rate = 0.732, max_depth = 16, n_estimators = 58.