# An Innovative Applied Control System of Helicopter Turboshaft Engines Based on Neuro-Fuzzy Networks
## 3 Results  
### Input Data Preprocessing  
The software product Matlab 2014b was used to conduct the computational experiment in the research. For the computational experiment, the aviation engine TV3-117 was selected as the research object, which is part of the powerplant for the Mi-8 MTV helicopter [55; 56]. The parameters of the TV3-117 engine (\(n_{TC}\), \(n_{FT}\), \(T_{G}^{*}\), etc.) required for the computational experiment were derived solely from flight data recorded during the testing of the Mi-8 MTV helicopter. Data registration was performed onboard using D-2M and D-1M sensors, along with 14 paired thermocouples T-101 [51] (data recording occurred over a 320 s interval during an actual flight with a sampling period of 1 s). These data were provided upon an official request from the authors' team to the Ministry of Internal Affairs of Ukraine and are intended for implementation in the project \"Theoretical and Applied Aspects of Aviation Development\", officially registered in Ukraine under number 0123U104884. The variation in parameters for the TV3-117 engine illustrates the complexity of the time series (Figure 6) [57], and the diagrams indicate the need to account for the current values of the parameters and the accumulation of data in the model's memory [58; 59]. Figure 6 shows an increase in the parameters within the interval from 21 to 62 s of approximately 1.5 to 1.8 times due to the engine's transitional operating mode. As mentioned in the Introduction, the engine operates in steady modes about 85% of the time and only about 15% in transitional modes. Following [40; 41; 42; 45; 46; 47; 51; 54], 256 values for \(n_{TC}\), \(n_{FT}\), \(T_{G}^{*}\), etc., were selected, as illustrated in Figure 6. Based on the parameters \(n_{TC}\), \(n_{FT}\), \(T_{G}^{*}\), etc., the selected values, the control error values, and the control error rate are obtained (Table 1), constituting the training dataset. Figure 6: The TV3-117 turboshaft engine parameters in a dynamic time series using digitized oscillograms: the black curve is the gas generator rotor r.p.m; the violet curve is the free turbine rotor speed; the light blue curve is the gas temperature in the front of the compressor turbine. The training dataset homogeneity was assessed according to the Fisher-Pearson [60; 61; 62] and Fisher-Snedecor [63; 64; 65] criteria at a significance level of \(\alpha\) = 0.01 (Table 2). The significance level of 0.01 was chosen in the control task for helicopter gas turbine engines to ensure high reliability in statistical conclusions, which is particularly crucial in aviation safety. This stringent criterion minimizes type I error likelihood, contributing to more accurate and safer engine control across various operating modes. The training and test datasets' representativeness was assessed through cluster analysis, which involved dividing the input dataset \(x=(e(t),\frac{de(t)}{dt})\) (Table 1) into \(k\) predetermined clusters [66]. Each cluster groups objects that are more similar to each other than to objects in different clusters [67]. This process continues until minimal change occurs in the centroids or the iteration's specified number is completed [68; 69; 70; 71]. Cluster analysis of the training data (Table 1) revealed eight clusters (I...VIII). The training and test sets were formed in a 2:1 ratio (67 and 33%, respectively) based on random selection. Both datasets showed the presence of eight clusters, indicating a similar composition. The distances between clusters were nearly identical across both sets, confirming their similarity (Figure 7).