# The Method of Restoring Lost Information from Sensors Based on Auto-Associative Neural Networks
## 2 Related Work Discussion  
Today, the lost information restoration task when complex dynamic object sensors fail is relevant and widespread since sensors are widely used to collect data in various systems, including aviation, medicine, manufacturing, and much more. If a sensor fails or malfunctions [20,21], it can lead to valuable information loss, which can lead to system failures or even accidents. Therefore, lost information restoration in such cases becomes a critical issue to ensure the system's reliable operation and everyone's safety. To solve this task, it is necessary to carefully select and modify the neural network structure, develop effective methods for training them, simulate various sensor failure scenarios, and compare the proposed solutions with existing methods. This will identify improvements and ensure that systems operate reliably while minimizing risks to safety and efficiency. Ref. [22] shows the restoration possibility for the incomplete, damaged, or missing audio signals caused by numerous unforeseen situations, one of which is the sensor failure (audio signal receiver). Restoring incomplete, damaged, or missing audio signals is proposed to be solved as a time series forecasting problem using long short-term memory (LSTM) networks. The LSTM networks' disadvantage in solving the incomplete, damaged, or missing lost information restoration problem when sensors fail is their limited ability to capture long-term dependencies in the data, which can lead to ineffective restoring of the complex dynamic object combined lost information in their operating mode. In [23], a distributive training method is proposed for communication coherence restoration in the controlling multiple agents' process using a linear neural network, the training of which is based on the adaptive control principles, within which the neural network strives to implement an anti-gradient value determined by the distances between agents and their neighbors. This approach's disadvantage is the limited ability of a linear neural network to effectively respond to dynamic changes in the connection profile of a mobile multi-agent system and to ensure reliable restoration of communication under significant speed disturbances, which is critical in the complex dynamic object operation. Ref. [24] researched situations where data are provided in a rounded form, with rounding errors comparable to or greater than measurement errors. Also, this study explored possibilities of achieving greater accuracy than the sampling step and lost information restoration using additional measurement errors. The proposed approach's disadvantage to the complex dynamic object operation is the information restoration accuracy limitation when significant changes in the object or the environment parameters can reduce the system monitoring and control efficiency in real time. In [25], restoring the sign bits task of DCT coefficients in digital images is solved as a mixed integer linear programming problem using two special properties of natural images. The proposed information restoration method accuracy did not exceed 1%. Despite the high accuracy of the proposed method, its disadvantage in the complex objects' operation is its limited applicability in real conditions, for example, helicopter flight mode, which may not be enough for effective monitoring and control of complex dynamic objects. Ref. [26] proposed approximate methods for the complete regression equation restoration in various situations for forecasting models where there are incomplete data based on the binary logistic regression use. The disadvantage of using binary logistic regression to restore lost information when sensors fail on complex dynamic objects may be the insufficient ability of the model to take into account complex relations and dynamic changes in the system, which can lead to insufficient accuracy of data restoration.