## 6 Results and Discussion
From Tables 4 and 5, in the case of 30 hidden nodes, the MSE is 23.487 with the sigmoid-function-based PCA-ELM model, whereas it is 42.206 with the hyperbolic-tangent-function-based PCA-ELM model. In the case of 100 hidden neurons, the MSE is 22.379 with the sigmoid-function-based PCA-ELM model, whereas it is 668.565 with the hyperbolic-tangent-function-based PCA-ELM model. This shows that the prediction model using the sigmoid function is more reliable from the lower range of hidden nodes. The Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Root Mean Square Error (RMSE) are determined from the predicted values. An extensive comparison of these values for various numbers of hidden nodes and both activation functions --hyperbolic tangent and sigmoid functions--is illustrated in Figure 5. Notations used in Figure 5 represent _activation function-number of neurons_, where 'H', 'S' represent the hyperbolic tangent function and sigmoid function, respectively. For example, H-3--represents a hyperbolic tangent activation function with 3 hidden neurons, and S-3--a sigmoid activation function with 3 hidden neurons. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter/Model** & **S-3** & **S-30** & **S-50** & **S-80** & **S-100** \\ \hline training sum of squares error & 0.094 & 0.022 & 0.015 & 0.018 & 0.015 \\ training time (in milliseconds) & 0 & 0 & 2 & 2 & 2 \\ training relative error & 0.045 & 0.012 & 0.01 & 0.013 & 0.01 \\ testing sum of squares error & 0.158 & 0.018 & 0.023 & 0.034 & 0.023 \\ testing relative error & 0.278 & 0.018 & 0.017 & 0.027 & 0.017 \\ MSE & 160.063 & 23.487 & 14.714 & 33.224 & 22.379 \\ MAE & 8.0185 & 3.531 & 2.969 & 4.282 & 3.626 \\ MAPE & 1.436 & 0.621 & 0.526 & 0.767 & 0.639 \\ RMSE & 12.655 & 4.841 & 3.835 & 5.764 & 4.730 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Sigmoid-function-based PCA–ELM model for a various number of hidden neurons. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter/Model** & **H-3** & **H-30** & **H-50** & **H-80** & **H-100** \\ \hline training sum of squares error & 0.288 & 0.021 & 0.008 & 0.125 & 2.268 \\ training time (in milliseconds) & 2 & 2 & 6 & 5 & 9 \\ training relative error & 0.037 & 0.002 & 0.001 & 0.025 & 0.288 \\ testing sum of squares error & 0.386 & 0.272 & 0.415 & 0.733 & 1.939 \\ testing relative error & 0.135 & 0.019 & 0.135 & 0.094 & 0.678 \\ MSE & 107.124 & 42.206 & 61.051 & 110.047 & 668.565 \\ MAE & 7.249 & 3.200 & 3.141 & 6.609 & 21.095 \\ MAPE & 1.300 & 0.572 & 0.557 & 1.180 & 3.668 \\ RMSE & 10.350 & 6.496 & 7.813 & 10.490 & 25.857 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Hyperbolic-tangent-function-based PCA–ELM model for a various numbers of hidden neurons. The developed PCA-ELM network's workings have been tested in three aspects:  
* The performance of the conventional ELM has been compared with that of PCA-ELM. * The PCA-ELM network was compared by varying the range of hidden neurons. * The two PCA-ELM networks using the hyperbolic tangent function and sigmoid function are developed and compared. The PCA-ELM network was built using the hyperbolic tangent function, and the range of neurons is varied. As the range of neurons increased, the error also increased, and the efficiency of the model decreased, whereas in the PCA-ELM network using a sigmoid function when the range of hidden neurons is varied, as the range is increased, the error decreased. The number of hidden neurons is varied from 3, 30, 50, 80, and 100. In addition, the training time for a neural network model is crucial, and a conventional ELM network is challenging. So, by using the PCA technique, the large boiler data are reduced to minimal data without losing any of their features, and those acquired principal components are integrated into the ELM network; this PCA-ELM is accurate and fast compared to the conventional ELM network. This can be observed from training time in the comparison Table 6.