## 4 Experimental Verification
### Model Training and Results  
Firstly, the dataset is substituted into the proposed model for training with the iteration steps is 50, and the learning rate is 0.001. The training process and test results are represented in Figure 14 below. The optimal value is reached in the first 10 steps, and the iterative curve is smooth, which shows that the model has a strong convergence ability (Figure 14a,b). Secondly, the network output is consistent with the target output and the proposed method has no modal leakage, showing that the network has high recognition accuracy. Finally, the test results of a different dataset of the beam are the same, and the training time is the same, indicating that the proposed method is not limited by the type of excitation signal (Figure 14c,d). Figure 11: Different methods to identify the modal parameters of the beam excited by excitation spectrum 1: (**a**) EFDD method; (**b**) FSDD method; (**c**) SSI-COV method; and (**d**) SSI-DATA method. Figure 12: Different methods to identify the modal parameters of the beam excited by excitation spectrum 2: **(a)** EFDD; **(b)** FSDD; **(c)** SSI-COV; and **(d)** SSI-DATA. Figure 13: Different methods to identify the modal parameters of the beam excited by excitation spectrum 3: **(a)** EFDD; **(b)** FSDD; **(c)** SSI-COV; and **(d)** SSI-DATA. Experimental modal analysis is a method of parameter identification based on the measured excitation and response signals of the structure under laboratory conditions. Additionally, the results obtained by the experimental modal analysis are reliable, which is called analysis results. The first five modal frequencies, (16.25 97.5 307.5 617.5 996.3) Hz, of the beam are obtained according to Equation (17). Based on the analysis results (Figure 15a), the relative error of identifying the modal frequency of the beam under non-white noise excitation by different methods is obtained, which is shown in Table 3. The recognition accuracy of the results of the proposed method is the highest, and the results under white and non-white noises excitation are consistent. Therefore, the proposed method can be used for non-white noise excitation, and it has strong anti-noise ability and strong applicability. According to Equation (47), error = (results obtained--analysis results)/analysis results \(\times\) 100%. Figure 14: Training and test results of the beam: (**a**) training loss curve of dataset 1; (**b**) training loss curve of dataset 2; (**c**) test results of dataset 1; and (**d**) test results of dataset 2. Figure 15: Analysis results of experimental structure: (**a**) analysis results of the beam; (**b**) analysis results of the rudder surface. Similarly, the proposed method is used to train and test the rudder surface. The optimal value is reached in the first 15 steps, which shows that the model has a strong convergence ability (Figure 16a,b). The test results of a different dataset of the rudder surface are the same, and the training time is the same, indicating that the proposed method is also applicable to other structures and has research value (Figure 16c,d). Frequency is an important characterization parameter for damage identification, health monitoring, and finite element analysis [1,5]. Therefore, accurate identification frequency has a high application value. Figure 16: Training and test results of the rudder surface: (**a**) training loss curve of dataset 3; (**b**) training loss curve of dataset 4; (**c**) test results of dataset 3; and (**d**) test results of dataset 4.