# The Method of Restoring Lost Information from Sensors Based on Auto-Associative Neural Networks
## 3 Materials and Methods  
This work considers the TV3-117 TE As a research object for the helicopter's TE class. The work considers the following task: it is required to build and train an ANN that provides information monitoring and restoration (in failure case) about the complex nonlinear technical object (the TV3-117 TE example using) operational status in the \(N\) standard sensors presence. In this case, the ANN performs a mirror image of the input data vector onto itself. Information compression is carried out in the hidden layer of the ANN, called the \"shaft\", and information restoration is in the output layer. The fundamental possibility of using compressive mapping forms the principal component method basis [9, 10, 11, 32, 33]. The ANN architecture is shown in Figure 1.  
Figure 1: The proposed auto-associative neural network architecture diagram for lost information restoration in the TV3-117 turboshaft engine sensor failure event [9, 10, 11, 32, 33]. The key point in choosing the ANN structure is determining the optimal number of neurons in the hidden layer [9; 10; 11; 34]. For example, Figure 2 shows the error dependence in information restoration by the ANN [32; 33; 34] in the failure event of one of the sensors (for example, a TV3-117 TE gas generator rotor r.p.m. [35; 36]) on the neuron number in the ANN shaft, calculated according to the expression:  
\[MSE=\frac{1}{n}\cdot\sum[x-dec(enc(x))]^{2}, \tag{1}\]  
where \(x\) is input data, \(enc(x)\) is hidden layer output (encoded data), \(dec(enc(x))\) is reconstructed data, and \(n\) is the example number in the training set. The abscissa axis in Figure 2 shows the relative size of the shaft--the neurons' number ratio in the shaft to the input/output neurons' number (5 neurons). The optimal shaft size in this case is 0.8 (Figure 2). That is, the neurons' number in the shaft (ANN hidden layer) should be 0.8 \(\times\) 5.0 = 4.0. Data for ANN training during flight tests of the TV3-117 TE in a wide range of changes in operating modes (from low throttle to emergency mode) are obtained. Along with the ANN structure chosen, an important stage is an information restoration stage based on this neural network functioning results. This work uses the approach proposed in [10; 11], and it is shown in Figure 3.  
Figure 3: Functional information restoration diagram based on auto-associative neural network [9; 10; 11]. Figure 2: An auto-associative neural network training error dependence diagram example of the neurons’ number in the hidden layer [9; 10; 11]. Signals from the sensors are simultaneously sent to the stack and the tolerance control system, which monitors the measured values from the sensors. If the signals from the sensors are within the tolerance field, they are transmitted further to the control system, which manages the executive mechanisms (EM) affecting the object. If any of the sensor signals goes beyond the tolerance field, then, the tolerance control system removes the last value of this signal from a stack and transfers it to the corresponding input ANN, which restores the information and then transmits it to the automated control system (ACS). The information restoration process from sensors based on an ANN occurs according to the functional scheme presented in Figure 4. The ANN is included directly between the \(S_{1}...S_{n}\) sensors (or in the common information channel) and the ACS. The proposed functional scheme advantages (Figure 4) are the implementation simplicity and the ANN work transparency as part of the management system. To calculate the lost information restoration error from the sensors, the form dependence is used [9]:  
\[e=\left|\frac{real_{value}-nwa_{value}}{max_{value}-min_{value}}\right|\cdot 100 \%, \tag{2}\]  
where \(real_{value}\) is the real value of the parameter; \(nwa_{value}\) is the restored parameter value; \(max_{value}\), \(min_{value}\) are the maximum and minimum values of the parameter.