## 2 Materials and Methods
### Model Updating Procedure  
The actual structures are complex, and it is difficult to calculate the resonance and antiresonant frequencies theoretically. Therefore, the finite element method is used for calculation and combined with RBF neural network to update the structural parameters. The flowchart of the proposed method is shown in Figure 3, and the procedure of the proposed method for model updating is described as follows:  
Figure 2: RBF neural network architecture.  
Figure 3: Flowchart of the proposed method.  
Step 1: Construct the initial finite element model of the structure;  
Step 2: According to the structural characteristics, determine the updating parameters and estimate the corresponding value range;  
Step 3: Select an appropriate uniform design table according to the number of updating parameters and the corresponding value range, and arrange it according to its affiliated usage table;  
Step 4: Use the finite element method to calculate the dynamic response, obtain FRF curves, identify the resonance and antiresonant frequencies, and take them as the characteristic quantities of the objective function;  
Step 5: Take the characteristic quantities in Step 4 as the input vector, and the corresponding updating parameters as the output vector; the RBF neural network is used for training and the mapping relationship between them is constructed;  
Step 6: The characteristic quantities of the target value (or measured value) are inputted into the trained neural network, and the updated parameters are obtained by using the generalization of the RBF neural network.  
The RBF neural network is adopted as the optimization algorithm, and the number of samples and the value range of updating parameters are the main factors affecting the accuracy of the method. Due to the large scale of the finite element model of the actual complex structure and the time-consuming calculation, it is crucial to determine a reasonable number and representative sample points to reduce the calculation time and improve the accuracy of the neural network model [28]. The uniform design [36] hassome advantages such as uniform dispersion and good representativeness of test points, and obtaining more information with fewer points. Therefore, the method is used to determine the samples, code-named \(U_{n}(q^{s})\) or \(U_{n}^{*}(q^{s})\), and each uniform design table has its usage table. The symbol \(U\) represents uniform design, \(n\) represents the number of tests, \(q\) represents the number of each factor level, and \(s\) represents the number of factors. Finally, \({}^{*}\) denotes that the uniform design table has better uniformity, which should be preferred.  
In use, the appropriate alternative uniform design table should be determined firstly according to the number of the updating parameters (i.e., the symbol \(s\)) and the range of each updating parameter (i.e., the symbol \(q\)). Each updating parameter value range should cover the corresponding initial value and target value, and then compare the deviation of the same number of factors (i.e., the symbol \(s\)) in the corresponding use table. Because the smaller the discrepancy value, the better the uniformity, the uniformity design table corresponding to the minimum is selected as the sample in the finite element analysis.