# Mechanical Stress Prediction of an Aircraft Torque Tube Based on the Neural Network Application
## 7 Application of the Neural Network for Stress Prediction  
In order to create a new method for life prediction, the stress of the torque tube during landing is an essential part. Instead of calculating the stress for every landing, the neural network was developed. It can be used to predict the maximal stress during each landing of an aircraft. Once the stress is calculated according to the speed and temperatures, it is possible to use for example rain-flow method and count the cycles to failure of the torque tube [53]. As mentioned above, the NN was used for stress prediction during the training phase of the NN while the results from the FEM analyses were used. The inputs for the NN are in Table 2; in addition to the parameters defining the regime, the stress from the FEM analysis was also used for the NN training [54; 55]. An example of the training dataset is in Table 2; a total of 36 training regimes were used for the training of the NN. The training data obtained in the FEM analyses were normalized for the NN. Three of the thirty-six training inputs are shown as examples in Table 2. The input layer consists of three neurons. The first input is the brake temperature, the second input is the outside temperature, and the third is the landing speed. The structure of the output layer is one neuron represented by the stress in MPa. The NN for the stress prediction of the torque tube was developed in MATLAB software, in the form of feedforward network back propagation. The SCG algorithm--scaled conjugate gradient was used as a training function. An activation function is a hyperbolic tangent sigmoid-transfer function [56; 57]. The network designed for the stress prediction of the torque tube in Figure 9 consists of one input and output layer and three hidden layers [58; 59; 60]. In the input layer, the brake temperature, outside temperature, and landing speed (Figure 9) are present during the training and during the life of the NN [60; 61]. On the other hand, during training in the output layer, the stress is from the FEM analysis for the specific braking regime and during life, the network predicts the stress based on the trained weights and biases. It should be emphasized that Figure 9 presents a principal ANN architecture used for ATT-stress prediction. In accordance with the architecture, the ANN mathematical model was designed in MATLAB software for stress prediction. The architecture of the NN for the study presented in Figure 9 was programmed and trained in MATLAB. The ANN's elapsed training time was 0.03 s and, once it was trained,  
Figure 9: An architecture of the neural network for stress prediction. the NN predicted the stress for 36 operational regimes in 0.016648 s; thus, for one regime, in the prediction only took 0.00046 s. The statistical parameters of the training NN are shown in Figure 10[58; 61]. Figure 10 consists of four plots, the first of which approximates the training data, and it is visualized by the blue line. In total, 70% of the data were devoted to the ANN training process, while 15% of the data were used for the validation (second plot with green line), and the remaining 15% of the data were test data for the ANN (plot with red line). All the values are summarized in the fourth plot, with a black line. As can be seen in Figure 10, all four lines reached a highly accurate fit. Figure 10 is also called a regression plot, which shows the relationship between the outputs of the network and the targets. If the training were perfect, the network outputs and the targets would be exactly equal, but this relationship is rarely perfect in practice. The dashed line in each plot represents the perfect result of outputs = targets. The solid line represents the best-fitting linear-regression line between the outputs and the targets. The R-value is an indication of the relationship between the outputs and targets; it is the coefficient of correlation. If R = 1, this indicates that there is an exact linear relationship between the outputs and the targets.