# The Method of Restoring Lost Information from Sensors Based on Auto-Associative Neural Networks
## 4 Results
As the information restoration task solution attempt in the sensor failure event, a model experiment was carried out using an ANN, the results of which received 5062 values of the TV3-117 TE indicators (events), of which 4978 values were selected as favorable events and 84 as unfavorable events. Since there are few adverse events when training the model on this set, there is a high probability of the first kind of error (an incorrect value of the indicator is found to be correct). It is possible to train a model with the largest error shift to the second kind zone (the correct value of the indicator is recognized as incorrect). At the same time, the error will remain permissible. In this case, the admissible share of the correct values of the indicators will be calculated according to the universal mathematical GTE model with a free turbine [37, 38, 39]. In this research, it is assumed that the model is trained on favorable events. During training, the main component of the set is highlighted, and the dividing surface shifts to these set boundaries. If the model deviates above some threshold value, the event is considered unfavorable. The feature set, data preprocessing, and gap elimination methods are described in [37, 38, 39]. It is assumed based on works [45, 46] that \(\mathbf{Y}=(y_{1},y_{2},\ldots,y_{p})\) is the feedback set about events, \(X_{i}^{m}=(x_{1i},x_{2i},\ldots,\)\(x_{mi})\) is the \(m\) feature set of the \(i\)-th event; \(\mathbf{Y}^{0}=\left\{y_{i}=0\middle|y_{i}\in\mathbf{Y},\)\(i=\overline{1,p}\right\}\) is the favorable event class; \(\mathbf{Y}^{1}=\left\{y_{i}=1\middle|y_{i}\in\mathbf{Y},\)\(i=\overline{1,p}\right\}\) is the adverse event class. The data amount after gap elimination and processing is \(n=4\) (the neurons' number for input and output layers) and \(v=3\) as the neurons' number for a hidden layer (\"shaft\"); \(\mathbf{Y}^{0}=\left|2893\right|\), \(\mathbf{Y}^{1}=\left|66\right|\). A duplicate set of features \(X_{i}\)\(X_{i}^{m}=\left(x_{1i}^{\prime},\ x_{2i}^{\prime},\ \ldots\ x_{mi}^{\prime}\right)\) was used as a teacher. That is, we obtained \(F:\ X_{i}\to X_{i}^{\prime}\), the classification task solving instead \(F:\ X_{i}\to y_{i}\). The ANN was trained on the set \(\mathbf{Y}^{0}\) and the minimum training deviation for each output neuron was taken as the classification threshold. After ANN training, some test event \(y_{k}\) was evaluated as: \(y_{k}=1\) if a deviation above the threshold occurred in one of the output neurons; \(y_{k}=0\) if the deviation on all output neurons did not exceed a threshold. The sigmoid activation function was used, and the loss function was the difference for each output neuron. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Encoder** & **Decoder** & **Epoch** & **Batch Size** & **Training Data** & **Test Data** & **Optimizer** \\ \hline ReLU & Sigmoid & 200 & 250 & \(5\times 10^{-4}\) & \(1\times 10^{-4}\) & Adam \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Auto-associative neural network training parameters (authors’ research based on [44]). Figure 5: Clustering outcomes: (**a**) original experimental data set (I...VIII—classes); (**b**) training data set (authors’ research, published in [37, 38, 39, 40]). The test set consisted of 132 events (all \(\mathbf{Y}^{1}\) events and, comparatively, 66 \(\mathbf{Y}^{0}\) events). The training set consisted of 2827 events (all other \(\mathbf{Y}^{0}\) events). The accuracy of 100% was achieved on the test set. When adding 12 insignificant features [45; 47], a 99.53% accuracy was achieved where 0.47% was a second-order error (4 valid values of an indicator were recognized as incorrect). It is noted that the results were obtained on the relatively small test set. Objective verification requires access to a larger volume of adverse events and different stages of repeated testing. It is assumed that \(V\) is the hidden layer neuron set.