# Neural Network System for Predicting Anomalous Data in Applied Sensor Systems
## 3 Results
### Experiment Description
The corresponding autocorrelation function (ACF) and partial autocorrelation function (PACF) diagrams are shown in Figure 6. The final diagrams in Figure 6 allow for the _SARIMAX_ model parameters' following range selections: autoregressive order \(p\in[0,7]\), differencing order  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Number** & **1** & \(\dots\) & **35** & \(\dots\) & **84** & \(\dots\) & **116** & \(\dots\) & **152** & \(\dots\) & **198** & \(\dots\) & **255** & **256** \\ \hline Value & 0.932 & \(\dots\) & 0.948 & \(\dots\) & 0.953 & \(\dots\) & 0.929 & \(\dots\) &\(d=1\), moving average order \(q\in[0,\,7]\), seasonal autoregressive order \(P=1\), seasonal differencing order \(D=1\), seasonal moving average order \(Q=0\), and seasonal period \(s=96\). Clarification: In the context of sensor data registration on board helicopters during flight, the term \"seasonality\" refers to regular and predictable changes in the data caused by time periods within the year (autumn-winter and spring-summer flights), which must be factored for accurate real-time interpretation and analysis. The impact on the sensor readings for gas temperatures before the compressor turbine in helicopter flight during the autumn-winter and spring-summer periods is linked to variations in the external temperature and pressure conditions, leading to changes in the thermodynamic properties of the air entering the engine [51; 52; 53]. In this research, the parameters have been adjusted for helicopter flight conditions during the spring-summer period. In addition to accounting for \"seasonality\", the calibration of the predicting system incorporates actual environmental conditions such as temperature, humidity, and atmospheric pressure. These factors significantly influence the sensor data interpretation accuracy, as they affect the engine's thermodynamic properties and the sensor readings. By integrating these real-time environmental parameters into the calibration process, the system can more precisely adjust for variations and improve the reliability of its predictions under varying flight conditions. Among all the obtained models, the model with SARIMAX parameters \(s=96\), (\(p=6\), \(d=1\), \(q=5\)) (\(P=0\), \(D=1\), \(Q=1\)) was selected for the data cleaning module's routine operation. This model was chosen due to its lowest values for the Akaike information criterion (AIC) [54] and Bayesian information criterion (BIC) [55] compared to other models, and the residual series (the difference between actual and predicted values) exhibits unbiasedness properties, stationarity, and a lack of autocorrelation. Figure 7 presents a 4 min prediction for helicopter flight, with the prediction error having an \(MSE=0.218\%\). In Figure 7, the \"blue curve\" represents the actual data recorded by the sensor, and the \"red curve\" represents the predicted data. Since the proposed SARIMAX model predicts values for the gas temperature from the TV3-117 aircraft engine's in front of the compressor turbine sensor with high accuracy, it can be used to replace missing values with plausible synthetic values. Examples of the reconstructor's performance are shown in Figure 8. In Figure 8, the \"blue curve\" represents the actual data recorded by the sensor, the \"red curve\" represents restored data, the \"red dots\" indicate outliers, and the \"green dots\" represent imputed values. Figure 5: Cluster analysis results: (**a**) the parameter \(T_{G}^{*}\) training sample, (**b**) the parameter \(T_{G}^{*}\) test sample (author’s research, published in [41]). Figure 6: Correlograms of the initial training sample readings of the gas temperature from the TV3-117 aircraft engine’s in front of the compressor turbine sensor: (**a**) ACF and PACF diagrams for the target time series; (**b**) ACF and PACF diagrams for the seasonal differences series; (**c**) ACF and PACF diagrams for the first differences series (author’s research).