# Neural Network System for Predicting Anomalous Data in Applied Sensor Systems
## 3 Results  
### Experiment Description  
The research object in this study is the TV3-117 aircraft engine, which belongs to the helicopter TE class. The sensor in the sensory system consists of 14 T-101 thermocouples, which record the gas temperature before the compressor turbine \(T_{\text{G}}^{*}\) value on board the helicopter (1 value per second) (Table 1) [41]. The preprocessor is implemented using Python libraries as follows. The analyzer uses the standard libraries \"openpyxl\" and \"pandas\". The outlier detector is based on algorithms from the \"adtk\" (Anomaly Detection Toolkit) library [42]. The _SARIMAX_ model, used by the restorer, is implemented in the standard \"statsmodels\" library. The normalizer is implemented using the standard \"sklearn\" library. The predictor is implemented based on the Keras library [43] and the TensorFlow framework [44]. For training the recurrent neural network, subsequences of length \(n=256\) were used, corresponding to 256 s of sensor operation. The RNN hidden state was taken as a column vector of length \(|\mathbf{h}|=32\). The following commonly accepted parameters were used for network training: the loss function was _MSE_ (Mean Square Error), the optimizer was Adam, and the epochs and batch size number were 20 and 32, respectively. The anomaly detector was implemented using the \"MatrixProfile library\" for the Python 3.12.4 programming language [45]. The training dataset (Table 1) homogeneity evaluation using Fisher-Pearson [46] and Fisher-Snedecor [47] criteria is detailed in [41]. According to these criteria, the training dataset of gas temperature readings before the compressor turbine for the TV3-117 aircraft engine is homogeneous, as the calculated values for the Fisher-Pearson and Fisher-Snedecor criteria are below their critical values, i.e., \(\chi_{T_{\text{G}}^{*}}^{2}=4.645<\chi_{critical}^{2}=6.6\) u \(F_{T_{\text{G}}^{*}}=4.645<F_{critical}=6.6\). To assess the representativeness of the training dataset, ref. [41] employed cluster analysis (k-means [48; 49]). Using random sampling, the training and test datasets were divided in a 2:1 ratio (67% and 33%, corresponding to 172 and 84 elements, respectively). The cluster analysis results for the training dataset (Table 1) identified eight classes (classes I...VIII), indicating the presence of eight groups and demonstrating the similarity between the training and test datasets (Figure 5). These results enabled the optimal sample sizes for the determination of gas temperature before the compressor turbine for the TV3-117 aircraft engine: the training dataset comprises256 elements (100%), the validation dataset comprises 172 elements (67% of the training dataset), and the test dataset comprises84 elements (33% of the training dataset). After the processing of data by the preprocessor, the first 172 values (67%) from the sensor (control dataset) were used in two roles: as a dataset for tuning the _SARIMAX_ model parameters used by the reconstructor and as the training dataset for the recurrent neural network in the predictor subsystem. The remaining 84 values (33%) from the sensor (test dataset) were used for the data cleaning module operation simulated under normal conditions. Testing the dataset with ADF and KPSS tests confirmed its non-stationarity. To achieve stationarity, techniques were sequentially applied, including first differencing to remove the trend and seasonal differencing to eliminate seasonality [50].