# Neural Network System for Predicting Anomalous Data in Applied Sensor Systems
## 5 Conclusions  
The scientific novelty of the obtained results lies in the development of a neural network system for predicting anomalous data in sensor systems, which, through a preprocessor, predictor, reconstructor, and anomaly detector, enables anomaly prediction in sensor data with an accuracy of up to 98.2%. The scientific novelty in this article was achieved as follows:  
1. A preprocessor model based on the _SARIMAX_ model was developed, allowing for the determination of autocorrelation and partial autocorrelation in the training dataset while accounting for dynamic changes (e.g., seasonal variations) and external regressors and trends, enabling time series prediction with an accuracy of up to 97.9%.
2. A predictor model based on a modified LSTM network with additional Dropout and Dense layers was developed, enabling sensor-derived value prediction. An example of the prediction of TV3-117 aircraft engine gas temperature before the compressor turbine values for one minute of helicopter flight experimentally confirmed that the prediction error did not exceed 0.218%.
3. A reconstructor model was developed, which, by utilizing the distribution of prediction errors, allowed for the restoration of missing time series values and outlier replacement with plausible synthetic values with an accuracy of up to 98.73%.
4. An anomaly detector model was developed that, through the application of the concept of dissonance, allowed for sensor data anomaly prediction. This enabled the detection of two anomalies based on two minutes of activity from the TV3-117 aircraft engine gas temperature before the compressor turbine sensor during flight: a brief sensor malfunction and a sharp temperature drop due to changes in airflow, with type I and type II errors below 1.12 and 1.01%, respectively, and a detection time of less than 1.611 s, confirming the system's high efficiency.
5. An AUC-ROC value of 0.818 indicated that the developed system has a strong capability to distinguish between normal and anomalous data, making it a reliable tool for accurately detecting anomalies while effectively minimizing both false positives and missed detections.  
**Author Contributions:** Conceptualization, S.V., V.V. and V.L.; methodology, S.V., M.N. and V.V.; software, V.V. and V.L.; validation, V.V. and V.L.; formal analysis, S.V.; investigation, M.N.; resources, M.N., V.S. and O.M.; data curation, S.V., M.N., V.V. and V.L.; writing--original draft preparation, S.V.; writing--review and editing, S.V.; visualization, V.V.; supervision, V.S. and O.M.; project administration, V.S. and O.M.; funding acquisition, M.N. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Data Availability Statement:** Data are contained within the article.  
**Acknowledgments:** This research was supported by the Ministry of Internal Affairs of Ukraine as \"Theoretical and applied aspects of the aviation sphere development\" under Project No. 0123U104884 and by the Ministry of Education and Science of Ukraine \"Methods and means of identification of combat vehicles based on deep learning technologies for automated control of target distribution\" under Project No. 0124U000925.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Nomenclature**  
\(c\): is the constant;  
\(\varphi_{1}\),..., \(\varphi_{p}\):  
\(\theta_{1}\),..., \(\theta_{q}\):  
\(\varepsilon_  
\[T_{occurmed,i} \text{is the time when the $i$-th anomaly actually occurred;}\] \[\text{TP}_{\text{\emph{replaced}}} \text{is the number of outliers that were correctly replaced by the}\] \[\text{reconstruct with predicted values;}\] \[\text{FP}_{\text{\emph{replaced}}} \text{is the number of normal data incorrectly replaced by the reconstructor}\] \[\text{with predicted values.}\]