Then, the output models are tested using the testing dataset. The error evaluation is performed in term of MAE as in Equation \ref{eq:5} and RMSE as in Equation \ref{eq:6}. y in the equation denotes as actual value and \(\hat{y}\) is the predicted value.
\[MAE=\frac{1}{n}\sum_{i=1}^{n}\left|y-\hat{y}\right|\label{eq:5}\]
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(y-\hat{y}\right)^{2}}\label{eq:6}\]
The lowest MAE and RMSE of the models are selected to represent G 1(s) and G 2(s ). In the final step,  G 1(s) and G 2(s ) are further verified using validation dataset in parameter fit testing to obtain an optimum value of b pilot and b main. The least error of simulated b is the stopping criteria for the valve’s models. The simulation results are presented in Section \ref{140410}.
Finally, the two models are integrated into Rowen’s model to produce a DLE gas turbine with the actual fuel system model representation. The integration consists of two vital steps. The first one is the replication process of the DLE fuel system setup based on the actual design in Fig. \ref{530751}. The proposed fuel system is integrated into Rowen’s model in Section \ref{171743} to imitate the actual DLE gas turbine fuel system operation. After the integration, the model is simulated using one-day actual load change and ambient temperature signals in the second steps. The simulated signals of pilot and main gas fuel valves, engine fuel flow and turbine temperature are compared with the actual data using MAE and RMSE analysis to measure the model accuracy. The simulated speed signal also analyzed for system stability, which expected to maintain 1.0 p.u throughout the simulation.  The proposed DLE gas turbine model is expected to have 99% accuracy to represent the actual operation for stability study, fault analysis and detection and fault prediction. The results are presented and discussed in the Results and Discussion section.

Results and Discussion

This section is divided into two parts; pilot and main gas fuel valve modelling in Section \ref{140410} and DLE gas turbine model with the integrated fuel system in Section \ref{171743}.

Pilot and Main Gas Fuel Valve Modelling

Pilot valve training dataset is illustrated in Fig. \ref{390141} with the output trend in (a) and an input trend in (b). The valve output follows the trend of the input and no time delay is observed. As the data represent 15 days of the DLE gas turbine operation, the 0% opening indicates the shutdown of the gas turbine and step up to 100% for the start-up. The pilot valve is constant at 55% after the load has reached 50% of the capacity for dry-low emission mode.