# Neural Network System for Predicting Anomalous Data in Applied Sensor Systems
## 3 Results
### Results of Data Anomaly Prediction  
Figure 11 illustrates an example of two anomalies detected during the data cleaning module's simulation, corresponding to two minutes of the TV3-117 aircraft engine gas temperature before the compressor turbine sensor activity under helicopter flight conditions. The first anomaly is a \"Top 1 dissonance\" found in the test dataset, indicating a temporary malfunction of the sensor. The second anomaly is a \"Top 10 dissonance\" and points to a rapid decrease in gas temperature before the compressor turbine due to increased airflow speed and changes in external air pressure. In both cases, the detected anomalies require a response from the helicopter's flight commander (human operator). These anomalies prompt an immediate assessment by the flight commander to determine the appropriate corrective actions or adjustments needed. Such proactive responses help maintain optimal engine performance and ensure operational safety by addressing potential issues before they escalate. The system's ability to accurately detect and classify anomalies in real time significantly enhances the reliability and responsiveness of the monitoring process. To better interpret the anomaly detection results, it is important to discuss both healthy and unhealthy conditions in detail. By examining the baseline or normal operational parameters alongside the detected anomalies, one can more accurately assess the system's performance and sensitivity. Healthy conditions may include stable engine performance with consistent sensor readings and normal gas temperatures before the compressor turbine, indicative of optimal operation. Unhealthy conditions, on the other hand, might involve irregular sensor data, such as sudden temperature drops or fluctuating readings due to sensor malfunctions, increased airflow speeds, or changes in external air pressure. To perform cross-validation (k-fold cross-validation), the training dataset is partitioned into \(k\) subsets (folds): \(D_{1}\), \(D_{2}\), \(\ldots\), \(D_{k}\). For each \(i\)-th fold (\(i=1,2,\ldots,k\)), one subset serves as the validation set while the remaining \(k-1\) folds are utilized for training. The model is trained on the \(k-1\) subsets and assessed on the remaining subset. In each \(i\)-th iteration, the model is trained on data \(D_{train}^{(i)}\)(and evaluated on data \(D_{val}^{(i)}\)), where  
\[D_{train}^{(i)}=\underset{j\
eq i}{\cup}D_{j},\ D_{val}^{(i)}=D_{i} \tag{33}\]  
Subsequently, the metric (in this research, _MSE_) is computed on the validation set for each \(i\)-th fold:  
\[\text{Metric}_{i}=\text{evaluate}\Big{(}M^{(i)},D_{val}^{(i)}\Big{)}. \tag{34}\]  
Figure 11: Diagrams of anomalies detected during the data cleaning module’s simulation: (**a**) “Top 1 anomaly” (sensor activity over 12 min of helicopter flight); (**b**) “Top 10 anomaly” (sensor activity over 12 min of helicopter flight) (author’s research). where \(M^{(i)}\) represents a model trained on \(D_{val}^{(i)}\). Upon completion of all \(k\) iterations, the mean metric value is computed across all folds:  
\[\text{Average Metric}=\frac{1}{k}\cdot\sum_{i=1}^{k}\text{Metric}_{i}. \tag{35}\]  
In assessing the effectiveness of the computational experiment, a cross-validation procedure (k-fold cross-validation) was performed. For this, \(k=5\) equal subsets (folds) of 51 elements each randomly chosen from the training sample. The following metric values were obtained: Metric(\(k_{1}\)) = 0.224%, Metric(\(k_{2}\)) = 0.228%, Metric(\(k_{3}\)) = 0.227%, Metric(\(k_{4}\)) = 0.226%, and Metric(\(k_{5}\)) = 0.229%. The average metric was calculated as 0.227%, which differs from \(MSE_{\text{min}}\) = 0.218% by 3.96%. This indicates that the average value of the metric (mean square error) after cross-validation is close to the \(MSE_{\text{min}}\) obtained from one fold (in this case, \(k_{3}\)). The 3.96% difference reflects how much the average metric deviates from the best individual result achieved during the cross-validation iterations.