## 4 PCA-IWOA-XGBoost Model Construction and Prediction Result Analysis
### PCA Dimensionality Reduction
Based on the cumulative contribution rate results, the first six principal components were selected for analysis, with their score coefficients shown in Table 7.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Serial**} & \multirow{2}{*}{**Date**} & \multirow{2}{*}{**Location**} & \multirow{2}{*}{\(\mathbf{x_{1}}\)} & \multirow{2}{*}{\(\mathbf{x_{2}}\)} & \multirow{2}{*}{\(\mathbf{x_{3}}\)} & \multirow{2}{*}{\(\mathbf{x_{4}}\)} & \multirow{2}{*}{\(\mathbf{x_{5}}\)} & \multirow{2}{*}{\(\mathbf{x_{6}}\)} & \multirow{2}{*}{\(\mathbf{x_{7}}\)} & \multirow{2}{*}{\(\mathbf{x_{8}}\)} & \multirow{2}{*}{\(\mathbf{x_{9}}\)} & \multirow{2}{*}{\(\mathbf{x_{10}}\)} & \multirow{2}{*}{\(\mathbf{x_{11}}\)} & \multicolumn{2}{c}{**Total**} \\
**Number** & & & & & & & & & & & & & & & \\ \hline
1 & 1970-01-05 & Tonghai & 2 & 7.7 & 13 & 10 & 8 & 2 & 120 & 1 & 2 & 1 & 2 & 15,621 \\
2 & 1970-12-03 & Xiji & 2 & 5.2 & 12 & 7 & 8 & \(-\)1 & 142 & 1 & 3 & 2 & 2 & 117 \\
3 & 1976-04-06 & Helinger & 2 & 6.1 & 18 & 7 & 7 & 0 & 55 & 2 & 2 & 2 & 2 & 28 \\
4 & 1976-07-28 & Tangshan & 2 & 7.8 & 12 & 11 & 8 & 3 & 401 & 2 & 1 & 3 & 1 & 242,769 \\  
anzhihua & 1 & 4.9 & 9 & 6 & 7 & \(-\)1 & 171 & 4 & 2 & 2 & 2 & 22 \\
25 & 2008-05-12 & Dangiong & 1 & 8 & 14 & 11 & 8 & 3 & 27 & 4 & 3 & 3 & 2 & 69,227 \\
26 & 2008-08-30 & Vushu & 1 & 5.9 & 10 & 8 & 7 & 1 & 325 & 4 & 4 & 2 & 2 & 41 \\
27 & 2008-10-06 & Yingjiang & 1 & 6.3 & 8 & 8 & 9 & \(-\)1 & 3 & 4 & 3 & 2 & 2 & 10 \\
28 & 2010-04-14 & Ya’an & 1 & 6.8 & 14 & 9 & 7 & 2 & 9 & 4 & 3 & 2 & 2 & 2698 \\
29 & 2011-03-10 & Yiliang & 1 & 5.5 & 10 & 8 & 7 & 1 & 59 & 5 & 2 & 2 & 2 & 25 \\
30 & 2012-04-20 & Lushan & 1 & 6.7 & 13 & 9 & 7 & 2 & 87 & 5 & 3 & 3 & 1 & 196 \\
31 & 2012-09-07 & Zhangxian & 1 & 5.4 & 14 & 8 & 7 & 1 & 177 & 5 & 2 & 2 & 2 & 81 \\
32 & 2013-04-20 & Ludian & 1 & 6.7 & 13 & 9 & 8 & 1 & 95 & 5 & 3 & 2 & 2 & 196 \\
33 & 2013-07-22 & Kangding & 1 & 6.3 & 20 & 8 & 8 & 0 & 87 & 5 & 3 & 3 & 2 & 95 \\
34 & 2014-08-03 & Kaoshiung & 1 & 6.2 & 12 & 9 & 9 & 0 & 220 & 5 & 1 & 4 & 1 & 617 \\
35 & 2014-11-22 & Jiuzhahiogu & 1 & 6.1 & 18 & 8 & 9 & \(-\)1 & 11 & 5 & 3 & 2 & 2 & 10 \\
36 & 2016-02-06 & Yangbi & 2 & 6.4 & 15 & 9 & 8 & 1 & 943 & 5 & 3 & 2 & 2 & 117 \\
37 & 2017-08-08 & Luding & 2 & 6.7 & 20 & 9 & 8 & 1 & 15 & 5 & 3 & 2 & 2 & 25 \\
38 & 2021-05-21 & Jishishan & 2 & 6.1 & 8 & 8 & 8 & 0 & 70 & 5 & 3 & 2 & 2 & 3 \\
39 & 2022-09-05 & Wushi & 1 & 6.5 & 16 & 9 & 8 & 1 & 40 & 5 & 3 & 3 & 2 & 93 \\
40 & 2023-As shown in Table 7, the principal component score coefficient matrix reveals distinct composite characteristics of each factor group. \(F_{1}\) is mainly composed of epicentral intensity and \(\beta\), representing seismic destruction potential. \(F_{2}\) reflects the combined influence of epicentral intensity and fortification level, indicating structural resilience. \(F_{3}\) is associated with focal depth, while \(F_{4}\) relates to the earthquake occurrence time, possibly capturing temporal patterns. \(F_{5}\) is influenced by population density and terrain, representing geographical and demographic factors. \(F_{6}\) combines building code and focal depth, reflecting construction and source coupling. Overall, the first three principal components effectively capture key dimensions such as seismic intensity, defense capacity, and source conditions, providing a compact and meaningful input set for the subsequent modeling. The first six extracted principal components were used as input variables for IWOA to optimize the XGBoost model for predicting earthquake fatalities. The expressions for the principal components can be obtained from Table 7, as follows:  
\[