# Mechanical Stress Prediction of an Aircraft Torque Tube Based on the Neural Network Application
## 7 Application of the Neural Network for Stress Prediction
If the R is close to zero, then there is no linear relationship between the outputs and the targets. The training data reached 0.99999, as did the validation, the test data had a value of 0.99931, and the total data stood at 0.99973. These values represent the highly accurate results of the ANN. The results of the stress prediction from the NN are shown in Figure 11, which includes the stresses of the 36 regimes predicted by the neural network and the 36 regimes estimated using the conventional FEM method. When the results from the NN and FEM are compared, it is obvious that the values were matched with high accuracy. In Figure 11, the mechanical stress of the ATT calculated using the ANN is shown by the blue line with circles, and the second red line with dots is the stress calculated using the FEM. Figure 10: Training parameters of the neural network. The main results of this article are presented in Figure 11, where the mechanical stress of the ATT calculated by the ANN and FEM is shown. Figure 11 shows mechanical stress from approximately 360 MPa to 700 MPa; a perfect match can be seen for almost every regime, apart from regime 34, where a small deviation is observable. These results prove the possibility of stress prediction using ANNs as replacements for the FEM. The estimated errors are shown in Figure 12, where the maximal error is only 2%, which is approximately 15 MPa. The stress range for the 36 regimes was almost 350 MPa, so errors of 15 MPa are neglected. The data in Figure 12 demonstrate the high level of accuracy of the neural network for the prediction of the stress on the ATT according to the landing parameters. Although the main task of this research was to develop a new algorithm for mechanical-stress assessment, the scope of further research is briefly outlined in the following paragraph. A novel method using ANN for ATT stress prediction according to the aircraft parameters of temperature and speed can be used in future research as an input for the fatigue-life-counting algorithm (Figure 13). Figure 13 shows an integration of the proposed method into the aircraft-torque-tube-health-monitoring system. The stress calculated by the ANN can be used in the well-known rain-flow method, which is a method used for fatigue-life estimation according to mechanical stress. In Figure 13, the scheme for the cycle-to-failure-counting algorithm for the ATT is shown. As shown in the right part of  
Figure 11: Predicted results of the torque-tube stress calculated by the NN and FEM. Figure 12: Estimated errors of the predicted data by NN and FEM. Figure 13, the stress estimated using a neural network according to the landing parameters (speed, torque-tube temperature, and ambient temperature) was used as an input rain-flow method, as in the lower part of Figure 13. The output from the rain-flow method can be the remaining life of the ATT. The main point of Figure 13 is to present the methodology, which can be used for ATT-life-fatigue prediction for further research with the results from this paper. The methods also show how the respective technologies in ANNs, computer-aided design (CAD), product-lifecycle management (PLM) systems, and computer-aided engineering (CAX) systems could be combined into one method to predict the mechanical stress on specific parts [62; 63].