# An Innovative Applied Control System of Helicopter Turboshaft Engines Based on Neuro-Fuzzy Networks
## 3 Results
### Neural Network Model Quality Evaluation
The accuracy metric for the developed neuro-fuzzy network (Figure 5) achieves 99.455% following 250 training epochs while addressing the helicopter TE control challenge. This remarkable performance highlights the model's capability to manage the helicopter TE control task across different conditions. Additionally, the loss associated with the neuro-fuzzy network (Figure 5) declines from 2.5 to 0.5% after 250 training epochs in tackling the helicopter TE control task. Such improvements in accuracy and loss indicate a well-optimized model, reinforcing its potential for reliable application in real-world scenarios. The findings suggest that further refinements may enhance the network's adaptability and performance in dynamic operating environments. Figure 12: Accuracy metric diagram. The created neuro-fuzzy network attains a precision score of 0.981, a recall score of 1.0, and an F1-score of 0.990 in the helicopter TE control task under various conditions. These metrics reflect exceptional accuracy and dependability in detecting faults while ensuring zero false negatives. The F1-score also illustrates the model's balanced effectiveness concerning precision and recall. The results obtained were compared (Tables 3 and 4) with four other approaches: 1 is the neural network-based closed three-channel onboard helicopter TE ACS, 2 is the neuro-fuzzy onboard helicopter TE ACS based on ANFIS architecture, 3 is the neuro-fuzzy onboard helicopter TE ACS based on AFNN architecture, and 4 is the traditional helicopter TE ACS. The comparative analysis of various approaches to helicopter TE control reveals that the proposed method demonstrates a high accuracy (99.5%) and F1-score (0.990), confirming its effectiveness and reliability. In contrast, alternative methods show varying results, with Approach 4 having a significantly lower accuracy value of 88.2%. Approaches 1 and 2 exhibit satisfactory outcomes but fall short compared to the proposed solution. Notably, the proposed method achieves a perfect recall value of 1.0, indicating complete identification \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Metric** & **Proposed** & **Alternative** & **Alternative** & **Alternative** & **Alternative** \\  & **Approach** & **Approach 1** & **Approach 2** & **Approach 3** & **Approach 4** \\ \hline True Positives & 96 & 90 & 92 & 99 & 85 \\ True Negatives & 4 & 10 & 8 & 1 & 15 \\ False Positives & 287 & 282 & 284 & 291 & 277 \\ False Negatives & 14 & 20 & 18 & 11 & 25 \\ True Positive Rate & 0.828 & 0.785 & 0.793 & 0.844 & 0.626 \\ False Positive Rate & 0.0101 & 0.0169 & 0.0152 & 0.0097 & 0.0235 \\ False Negative & 0.0098 & 0.0109 & 0.0103 & 0.0093 & 0.0192 \\ Rate & 0.0098 & 0.0109 & 0.0103 & 0.0093 & 0.0192 \\ AUC-ROC & 0.831 & 0.773 & 0.791 & 0.848 & 0.651 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparative analysis results (AUC-ROC analysis). Figure 13: Loss metric diagram. of all positive cases. These results highlight significant advantages in the proposed FTCS for helicopter TE control compared to other examined methods. The comparative analysis (Table 4 and Figure 14) highlights significant performance differences among various approaches to helicopter TE control. The proposed method excels with the highest True Positive Rate (0.828) and True Positives (96), indicating superior fault detection capabilities. In contrast, Alternative Approaches 1 and 2 show lower True Positive Rates (0.785 and 0.793, respectively). The proposed method also maintains a low False Positive Rate (0.0101) compared to Alternatives 1 (0.0169) and 4 (0.0235) while achieving an AUC-ROC score of 0.831, surpassing the other approaches. The proposed approach demonstrates effective fault detection with minimal false alarms, establishing its efficacy in helicopter TE control tasks. Figure 14: The AUC-ROC diagrams: (**a**) the proposed approach; (**b**) the Alternative Approach 1; (**c**) the Alternative Approach 2; (**d**) the Alternative Approach 3; (**e**) the Alternative Approach 4.