## 3 Results and Discussion
### Performance of Combined Model  
In this section, the performance of the proposed combined model is evaluated through multiple aspects, including basic metrics comparison, error distribution analysis, and cross validation. Taking ten modification models as an example, following the training of these ten modification models, an accuracy comparison between the basic and combined models is conducted on the test set, as detailed in Table 1.  
Figure 5: Results of operating classification with different numbers of clusters. (**a**) Five clusters, showing a broad categorization of operating conditions; (**b**) ten clusters, providing a more detailed distinction of operating states. Table 1 presents a comparison of accuracy between the basic model and the combined model across different clustered operational conditions and the overall dataset. The first ten rows compare the accuracy of the basic and combined models for each cluster, showing improvements in MAPE and R2 for all clusters. In terms of MaxAPE, most categories exhibited a decrease in maximum error, while a few categories showed an increase. The last column summarizes changes in metrics across the entire dataset, revealing a 32.66% reduction in MAPE and an increase in R2. Due to the inherent randomness in maximum errors, the combined model experiences an increase in MaxAPE. However, the error distribution, as shown in the violin diagram of the absolute percentage error predicted by both models in Figure 6, demonstrates that the combined model improves the prediction accuracy of the basic model. This figure illustrates that the combined model reduces errors overall and confines them more to the lower error regions. Specifically, the combined model controls the error at 75% of prediction points to 0.2946%, while the basic model's corresponding value is 0.4647%, representing a 36.56% reduction. This demonstrates the enhanced accuracy of the combined model compared to the basic model. The improvement of these metrics indicates an advancement in the model's ability to predict gas turbine power output, thereby enhancing its reliability and practicality in real-world applications. Accurate prediction data are essential in various scenarios, including power dispatch, equipment performance monitoring, and aiding operators in making more precise decisions. Figure 7 compares the predicted values of the combined model and basic model with the actual values. For data clarity, the points are sorted according to the actual output values. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Cluster Label**} & \multicolumn{2}{c}{**MAPE**} & \multicolumn{2}{c}{**MaxAPE**} & \multicolumn{2}{c}{**R2**} \\ \cline{2-7}  & **Basic Model** & **Combined Model** & **Basic Model** & **Combined Model** & **Basic Model** & **Combined Model** \\ \hline
0 & 0.2376\% & 0.1684\% & 2.378\% & 2.346\% & 0.9426 & 0.9717 \\
1 & 0.5278\% & 0.3734\% & 2.245\% & 2.033\% & 0.9046 & 0.9442 \\
2 & 0.3652\% & 0.2320\% & 1.278\% & 1.387\% & 0.9483 & 0.9778 \\
3 & 0.4644\% & 0.3003\% & 2.393\% & 2.758\% & 0.9347 & 0.9658 \\
4 & 0.2592\% & 0.1867\% & 1.757\% & 1.363\% & 0.9665 & 0.9827 \\
5 & 0.2898\% & 0.1614\% & 2.026\% & 0.9473\% & 0.9763 & 0.9933 \\
6 & 0.2198\% & 0.1741\% & 0.7762\% & 0.7487\% & 0.9882 & 0.9920 \\
7 & 0.2924\% & 0.2122\% & 1.909\% & 1.700\% & 0.9544 & 0.9705 \\
8 & 0.4226\% & 0.3289\% & 1.820\% & 1.858\% & 0.9840 & 0.9903 \\
9 & 0.3345\% & 0.1998\% & 2.235\% & 1.721\% & 0.9441 & 0.9784 \\ Total & 0.3491\% & 0.2346\% & 2.393\% & 2.758\% & 0.9966 & 0.9982 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Accuracy comparison of basic model and combined model. Figure 6: The violin plot of absolute percentage error by combined and basic models. From Figure 7a, it is observed that both the basic model and the combined model follow the actual value changes.