# The Method of Restoring Lost Information from Sensors Based on Auto-Associative Neural Networks
## 4 Results
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Auto-Associative Neural Network Structure**} & \multicolumn{2}{c}{**TV3-117 Turboshaft Engine Parameter Restoration Error,\%**} \\  & \(G_{\text{T}}\) & \(n_{TC}\) & \(n_{\text{FT}}\) & \(T_{G}^{*}\) \\ \hline
4-3-4 as part of the proposed improved functional diagram (Figure 14) & 0.31 & 0.28 & 0.19 & 0.31 \\
5-4-5 as part of a basic functional diagram developed by ([PERSON] and [PERSON] [9; 10; 11]) & 0.33 & 0.31 & 0.24 & 0.42 \\ \hline \end{tabular}
\end{table} 
Table 3: Auto-associative neural network information restoration results in sensor failure cases. Tables 3 and 4 analysis shows that the use of the ANN architecture 4-3-4 with the proposed improved method of its training as part of an improved functional diagram for information restoration (Figure 14) allows for 10% more accurate lost information restoration in the single failure (break) event of complex dynamic sensor objects (the TV3-117 TE example use) in comparison with the ANN architecture 5-4-5 as part of the basic functional information restoring diagram developed by [PERSON] and [PERSON] [9; 10; 11]. Also, the use of the ANN architecture 4-3-4 with the proposed improved method of training it as part of an improved functional diagram for information restoring (Figure 14) allows for 14% more accurate restoration of lost information in the double (multiple) sensors failure event of complex dynamic objects (the TV3-117 TE example use) compared with the ANN architecture 5-4-5 as part of the basic functional diagram for information restoring developed by [PERSON] and [PERSON] [9; 10; 11]. Increasing the lost information restoration accuracy by 10 to 14% is critical in the complex dynamic objects' operation (for example, a TV3-117 TE in helicopter flight mode). Analysis of the results given in Tables 3 and 4 shows that even though the information restoration accuracy in the double sensor failures deteriorates somewhat, the ANN ensures satisfactory quality use of information restoration, i.e., the ACS measuring channel performance preservation. Summarizing the obtained results, an engineering methodology for creating, training, and testing ANNs for restoring lost information from sensors is proposed, which includes the following steps: data preprocessing (normalization, calibration, digitization); statistical processing to detect gross measurement errors; data scaling; the ANN architecture and structure choosing; shaft size determination based on the covariance analysis results using the principal components method; activation functions selection, training algorithm; and the developed ANN effectiveness training, testing, and evaluating for lost information restoration from sensors. Recall is the fraction of the correctly classified parameters compared with the total count of parameters belonging to the true class [51]:  
\[Recall=\frac{TP}{TP+FN}, \tag{16}\]  
where \(FN\) is the false negative results. After calculating the \"precision\" and \"recall\" metrics values, a situation may occur in which the classifier's recall is low and the precision is high. Therefore, it is necessary to introduce an additional metric, which is the harmonic mean of precision and recall, the so-called F-measure. This metric is calculated as follows [51]:  
\[F-measure=2\cdot\frac{Precision\cdot Recall}{Precision+Recall}. \tag{17}\]  
The ROC (receiver operating characteristic) curve shows the trade-off between characteristics such as TPR (the real anomalies percentage that is correctly predicted by the classifier) and FPR (the real normal data percentage that is predicted as anomalous by the classifier). They are calculated as follows [51; 52]:  
\[TPR=\frac{TP}{TP+FN}, \tag{18}\]  
\[FPR=\frac{FP}{TN+FP}, \tag{19}\]  
where \(TN\) is the false negative result. The area under the ROC curve is represented by the AUC metric, whose values range from 0.5 to 1. An AUC of 1 indicates that the model is ideal, and an AUC of 0.5 indicates that the model is guessing at random.