# The Method of Restoring Lost Information from Sensors Based on Auto-Associative Neural Networks
## 4 Results
### Results Generalizations  
1. Further advancements have been made in refining the neural network approach for restoring lost data in the sensor failure event in intricate dynamic systems, which, through an auto-associative neural network (autoencoder) use, makes it possible to restore lost data with 99% accuracy. This is evidenced by the metrics of precision, recall, and F-measure, the values of which for normal data are 0.989, 0.987, and 0.988, respectively, and for abnormal data--0.967, 0.967, and 0.968, respectively. 2. The basic training algorithm of an auto-associative neural network (autoencoder) has been improved by adding regularization to the loss function and updating the weights, which reduces the model overtraining risk when it adapts too much to the training data and loses the ability for new data generalization. It has been experimentally proven based on an improved training algorithm that an auto-associative neural network (autoencoder) indicates a minimal risk of model overtraining since the maximum value of the resulting loss function does not exceed 0.025 (2.5%). 3. For the first time, a hypothesis on updating weights in an auto-associative neural network (autoencoder) using gradient descent with regularization was formulated and proven, which confirms the basic training algorithm improving the feasibility of an auto-associative neural network (autoencoder) and, as a result, the model complexity controlling and reducing its risk of retraining. 4. The functional diagram of the system for restoring lost information has been improved, which is based on an additional neural network to identify the complex dynamic object parameters, and significant accuracy and efficiency of the lost information restoration process in the event of complex dynamic object sensor failures are achieved. This is explained by a decrease in the maximum error values in restoring lost information, namely: - A single sensor failure (break) example used for the TV3-117 turboshaft engine-- it was established that the maximum error in restoring its parameters does not exceed 0.39%, while the maximum error in restoring its parameters using the basic functional diagram of the system for restoring lost information, developed by [PERSON] and [PERSON], is 0.42% [9; 10; 11], which is almost 10% more and can be critical during the complex dynamic object parameter identification, such as the TV3-117 turboshaft engine, under operating conditions; - A double (multiple) failure example used for the TV3-117 turboshaft engine sensors (breaks)--it was established that the maximum error in restoring its parameters does not exceed 0.50%, while the maximum error in restoring its parameters using the basic functional diagram of the system for restoring lost information, developed by [PERSON] and [PERSON], is 0.58% [9; 10; 11], which is \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Subsample Number** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & \(\overline{Acc}\) \\ \hline
**Proposed Method (ANN 1)** & 0.991 & 0.982 & 0.984 & 0.981 & 0.985 & 0.994 & 0.995 & 0.992 & 0.988 \\ \hline
**The closest Analog**[9; 10; 11] **(ANN 2)** & 0.914 & 0.913 & 0.906 & 0.889 & 0.893 & 0.888 & 0.915 & 0.889 & 0.901 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Indicators of calculation result accuracy for the proposed auto-associative network with a famous network in the restoration of lost information method, developed by [PERSON] and [PERSON] in [9; 10; 11], with a training sample of 256 elements divided into 8 subsamples of 32 elements each. almost 14% more and can be critical during the complex dynamic object parameter identification, such as the TV3-117 turboshaft engine, under operating conditions. 5.