# Gas Turbine Off-Design Performance Adaption Based on Cluster Sampling
## 3 Results and Discussion
### Comparison of the Prediction Using Random Sampling and Cluster Sampling  
In the previous section, the performance adaption processes of two ten-point sampling datasets were completed using the PSO algorithm, and the performance models after adaption based on data points of the random sampling set and the cluster sampling set were obtained, which were denoted as Model 1 and Model 2, respectively. This section compares and discusses the accuracy of these two models using the remaining data points (excluding the sampling points). The prediction errors of the two models based on different sampling methods at the remaining data points are shown in Figure 7.  
As can be seen from Figure 7, the cluster sampling correction results are better than the random sampling results in terms of power prediction and compressor outlet pressure prediction. The prediction accuracy of the compressor outlet temperature is similar in both methods, and both are relatively high and around 0.3%; the prediction accuracy of the turbine outlet temperature is also similar in both methods. Table 4 lists the mean error and maximum error of each measured variable in the dataset. According to Table 4, it can be seen that, overall, the models obtained using random sampling correction and cluster sampling correction have average errors of less than 1.2% for each prediction variable, and the overall average error of cluster sampling is better than that of random sampling. For the power and compressor outlet pressure prediction results, random sampling is slightly worse than the results of cluster sampling, which is reflected in both the average and maximum errors. The average error of power increased by 0.559% and that of the compressor outlet pressure increased by 0.302%. Their maximum errors increased by 1.193% and 1.041%, respectively. For the compressor outlet temperature, the prediction accuracy of both methods is similar, with random sampling results slightly higher than cluster sampling results, but they are generally at the same level of accuracy. For the turbine outlet temperature, the average prediction accuracy is 0.586% for Model 1 and 0.650% for Model 2, basically in the same accuracy level. The maximum error of Model 1 is 3.027%, which can be relatively high, while Model 2 using cluster sampling is 2.037%, improving by 0.685% in comparison with random sampling. In both cases, most prediction errors are below 1.5%, 93.6% for random sampling and 96.0% for cluster sampling. It can be seen that cluster sampling seems to have a certain effect on reducing the maximum error and the average error. This may be due to cluster sampling taking into account multiple clustering conditions and selecting the center points of the conditions, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Measurements** & **Before Adaption** & **After Adaption** \\ \hline Power & 3.316\% & 0.497\% \\ Compressor Outlet Temperature & 3.716\% & 0.316\% \\ Compressor Outlet Pressure & 3.359\% & 0.469\% \\ Turbine Outlet Temperature & 1.396\% & 1.159\% \\ Four Measurements & 2.947\% & 0.610\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Predicted errors before and after adaption. Figure 6: Convergence process based on the clustering sample. which considers the full range of accuracy and also maintains a certain representativeness for each clustering condition. Figure 7: Comparison of the prediction errors of four different measurements between the two models. To analyze the accuracy improvement created by cluster sampling, the data set was divided into two parts. In Section 3.2, it was mentioned that the k-means algorithm was used to divide the dataset into 10 categories. Cluster sampling selects the points closest to the cluster centers from each cluster to form a sample set, while random sampling picks points directly from the data.