# 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
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Criterion** & **Proposed Method** & **The Closest Analog [9; 10; 11]** & **Proposed Method Advantages** \\ \hline Restoring lost information & The maximum error in restoring lost information does not exceed 0.50\% (see Table 4) in the TV3-117 TE sensor & The maximum error in restoring lost information does not exceed 0.58\% (see Table 4) & The lost information \\ Restoring lost information & The last ANN information restoration task solving accuracy on the test data set is & The last ANN information restoration task solving accuracy increase on a test data set by 8.8\% is critical when operating complex dynamic objects such as the TV3-117 TE in helicopter flight mode. \\ \hline Accuracy & The lost ANN information restoration task solving accuracy on the test data set is & The last ANN information restoration task solving accuracy increase on a test data set by 8.8\% is critical when operating complex dynamic objects such as the TV3-117 TE in helicopter flight mode. \\ \hline Training rate & The ANN training time using the proposed method of training was 5 min 43 s\(\sim\)343 s (AMD Ryzen 5 5600 processor, 32 KB third-level cache, Zen 3 architecture, 6 cores, 12 threads, 3.5 GHz, RAM—32 GB DDR-4). & The ANN training time using the speed practically does not decrease compared with the classical method of training (the decrease by 9 s, which is insignificant), while the regularization introduction into the classical method of training reduces the risk of overtraining the model. \\ \hline Generalization ability & The determination coefficient was 0.996. & The determination coefficient was 0.850. & An increase in the determination coefficient by 14.7\% indicates a 14.7\% increase in the ANN efficiency to work on new data that it did not see during training. \\ \hline Resource efficiency & Testing was carried out on an AMD Ryzen 5 5600 processor, 32 KB L3 cache, Zen 3 architecture, 6 cores, 12 threads, 3.5 GHz, 32 GB DDR-4 RAM, with an efficiency metric of 0.00270. & Testing was carried out on an AMD Ryzen 5 5600 processor, 32 KB L3 cache, Zen 3 architecture, 6 cores, 12 threads, 3.5 GHz, 32 GB DDR-4 RAM, with an efficiency metric of 0.00288. & The ANN proposed in this work demonstrates a 6.25\% accuracy compared with [9; 10; 11] by the resources expended, which can be significant when operating complex dynamic objects such as the TV3-117 TE in helicopter flight mode. \\ \hline Robustness & The average deviation was 0.00524. & The average deviation was 0.01148. & A decrease in the average deviation by 45.6\% indicates that the ANN proposed in this work is almost two times more robust compared with [9; 10; 11], which indicates the possibility of maintaining high accuracy on different data sets or under different conditions. \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._The generalization ability of an ANN evaluates its ability to correctly process new, previously unseen data. One way to evaluate generalization ability is to use a validation data set that was not used to train it. One measure of generalization ability is the difference between the error on the training data set and the error on the validation data set. If the error on the validation data set is comparable to the error on the training set, this may indicate good generalization ability. To assess the generalization ability, this work uses the determination coefficient \(R^{2}\) as a corresponding metric that evaluates how well the model fits new data and is determined according to the expression:  
\[R^{2}=\frac{\sum_{i}(y_{i}-\hat{y}_{i})^{2}}{\sum_{i}(y_{i}-\overline{y}_{i}) ^{2}}, \tag{21}\]  
where \(y_{i}\) is the actual value of the target variable for the \(i\)-th example, \(\hat{y}_{i}\) is the restored value of the target variable for the \(i\)-th example, and \(\overline{y}_{i}\) is the average value of the target variable across all examples. The determination coefficient \(R^{2}\) ranges from 0 to 1. A value closer to 1 indicates that the model generalizes data better.