# Research on Prediction Method of Bolt Tightening for Aviation Components Based on Neural Network
## 3 Aviation Component Bolt Tightening
### RBF Neural Network  
In 1985, [PERSON] [16] proposed the RBF method to solve the multivariable interpolation problem, the method was then applied to the design of neural networks by [PERSON] and [PERSON] in 1988. Then, RBF neural networks were formed. Different from other neural networks, an RBF neural network consists of an input layer, a hidden layer, and an output  
Figure 14: Two-bolt tightening sequences of the aviation component under different conditions. (a) 0.1 mm gap value; (b) 0.08 mm gap value. layer. Therefore, the structure of a RBF neural network is simple. The RBF neural network regards the learning process as finding the surface that can best fit the sample points in high-dimensional space, so that the original linear indivisible problem becomes linear divisible. This surface is then used to interpolate the test data. The Gauss function has the advantages of simple expression, radial symmetry, and good smoothness; therefore, the Gauss function was chosen as the activation function for the hidden layer. The hidden layer output and neural network output can be expressed as follows:  
\[\varphi(x_{i},c_{i})=\exp(-\frac{\|x_{i}-c_{i}\|^{2}}{2\sigma^{2}}) \tag{7}\]  
\[f(x)=\sum_{i=1}^{d}\omega_{i}\bullet\varphi(x,c_{j}) \tag{8}\]  
where \(c_{j}\) is the center point of the j neuron; \(\sigma\) is the width of the Gaussian basis function; \(\|x_{i}-c_{i}\|\) is the Euclidean distance from the sample point to the center point; and \(\omega_{j}\) is the weight of the j neuron. The inputs of the neural network surrogate model in this paper are the bolt tightening sequence, the gap value between the aviation component front section cabin and the control cabin front section, and the axis inclination angle between the aviation component front section cabin and the control cabin front section. The network parameters were set as follows: the target value of the network fitting error was 0.0001, and the expansion constant was 0.29. A RBF model was established using MATLAB programming. A total of 200 groups of data were simulated through the finite element method, of which 160 groups were used as training samples, and 40 groups were test samples. The evenness and average value of the residual preload of the bolts were taken as evaluation parameters to select the best tightening sequence. The inputs and outputs of the model were defined. The Latin hypercube method was used to sample data, to ensure the uniformity of data sampling. After the neural network surrogate model of the bolt tightening system of the aviation component had been established, the best tightening process was selected based on this. The selection standard was that the average value of the residual preload of the bolt was the largest and the most uniform. With the help of the genetic algorithm, we could find the best tightening sequence from the surrogate model. Therefore, taking the maximum and average residual preload of the bolts as the optimization objective, the optimal sequence was obtained using the genetic algorithm. Then, the optimal tightening sequence of the aviation component bolts in the design domain was obtained. The neural network prediction process is shown in Figure 15.  
Figure 15: Neural network prediction flowchart. Under the conditions of a 0.1 mm gap, 0.2\({}^{\circ}\) axis inclination angle, and 0.08 mm gap and 0.15\({}^{\circ}\) axis inclination angle, a comparison of the simulation values and the prediction values of the aviation component optimal tightening sequences predicted by the neural network surrogate model is shown in Figures 16 and 17. As shown in Figures 16 and 17, the basic change curves of the prediction and simulation value were the same. Under the condition of a 0.1 mm gap value, the error between the simulation value and the prediction value of Bolt 1 was the largest, which was 308 N, 0.4% of itself. Under the condition of a 0.08 mm gap value, the error between the simulation value and the prediction value of Bolt 4 was the largest, which was 363 N, 0.5% of itself.