# The Method of Restoring Lost Information from Sensors Based on Auto-Associative Neural Networks
## 4 Results
### The Obtained Results in Comparison with the Most Approximate Analog
A value closer to 0 or negative may indicate that the model is underfitted or overfitted. To evaluate the ANN resources using efficiency, this work uses the _Efficiency_ metric, which takes into account the predictions' accuracy and the resources spent amount on training and/or prediction. One such metric could be the relationship between accuracy and resource utilization (for example, computational or time resources). It is assumed that \(Acc_{1}\) and \(Acc_{2}\) are the two ANN compared accuracies, and \(Res_{1}\) and \(Res_{2}\)--resources used (the ANN training time parameter was used in this work since both networks were tested with an identical amount of memory--32 GB DDR-4). Then, the resource use efficiency assessment is determined by the expression:  
\[Efficiency_{1}=\frac{Acc_{1}}{Res_{1}},\ \ \ Efficiency_{2}=\frac{Acc_{2}}{Res_{2}}. \tag{22}\]  
Thus, by comparing the effectiveness of two ANNs, it is possible to determine which of them demonstrates higher accuracy by the resources expended. ANN robustness assessment can be achieved by analyzing its performance on different data sets or under different conditions. One of the approaches to solving the problem of robustness assessment is to research the change in the ANS reconstruction accuracy when varying the input data or model parameters. This work uses a traditional method for the ANN robustness assessment, which is based on determining the standard deviation of the lost information restoration accuracy on various subsamples or data sets--the smaller the standard deviation, the more resistant the ANN is to changes in data or conditions. The standard deviation of the lost information restoration accuracy is determined according to the expression:  
\[\sigma=\sqrt{\frac{\sum_{i=1}^{N}\left(Acc_{i}-\overline{Acc}\right)^{2}}{n}}, \tag{23}\]  
where \(Acc_{i}\) is the ANN accuracy on the \(i\)-th data set or with the \(i\)-th parameters variation, \(\overline{Acc}\) is the average accuracy value for all observations, and \(n\) is the subsamples' number. In this work, for each ANS, the accuracy was determined on \(n=8\) different subsamples of 32 values in each training sample with a total volume of 256 values. It is assumed that \(Acc_{1i}\) and \(Acc_{2i}\) are the accuracy values of the first and second ANS on the \(i\)-th subsample, respectively (Table 7). Then the average accuracy for each neural network is, respectively, \(\overline{Acc_{1}}=0.988\) and \(\overline{Acc_{2}}=0.901\), and the average deviation--0.00524 and 0.01148. Thus, the results obtained during the comparative analysis (Table 6) of the proposed method for restoring lost information with the closest one, which is based on the ANN with the traditional method of teaching [9; 10; 11], developed by [PERSON] and [PERSON], indicate that that the proposed method is more effective compared with [9; 10; 11] in performing the lost information restoration task during the sensor failure event in the operating mode of complex dynamic objects, for example, a TV3-117 TE in helicopter flight mode.