## 3 Numerical Simulations and Experimental Verification
### Experimental Validation of a Cantilever Beam  
To further validate the effectiveness of the method proposed in this paper, an actual beam structure of free boundary is used for the experiment, as shown in Figure 13. Bruel & Kjaer RT Pro Photon 7.41 data acquisition system, PCB 208C02 force sensor (with a sensitivity of 112,410 mV/kN, a measurement range of 0.4448 kN, a low frequency response (\(-\)5%)  
Figure 12: Typical plot of the Modal Assurance Criterion (MAC) for the identified mode shapes and exact mode shapes of 6-DOF chain model of a railway vehicle.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & \multicolumn{2}{c}{**Natural Frequency (rad/s) \([\Omega]\)**} & \multicolumn{3}{c}{**Damping Ratio (\%)**} \\ \cline{2-7}  & **Exact** & **MSSI** & **Error (\%)** & **Exact** & **MSSI** & **Error (\%)** \\ \hline \(1\) & 2.79 & 2.79 & 0.00 & 4.89 & 4.89 & 0.01 \\ \hline \(2\) & 3.71 & 3.71 & 0.00 & 6.62 & 6.62 & 0.01 \\ \hline \(3\) & 16.55 & 16.53 & 0.09 & 16.65 & 16.62 & 0.16 \\ \hline \(4\) & 19.27 & 19.25 & 0.12 & 18.78 &of 0.001 Hz, and an upper frequency limit of 36,000 Hz), and Polytec OFV-5000 Modular Vibrometer (having a frequency range of DC-24 MHz with velocities up to \(\pm\)10 m/s and displacements from the picometer to meter range) are used for measuring response signal. The simulated nonstationary excitation through Teledyne LeCroy T3 AFG40 signal generator is imported into the Modal Shop K20070E01 vibration exciter, and the vibration shaker excites the cantilever beam structure. A typical white noise with an approximately consistent-power spectral density was synchronized with the shaker voltage time history and recorded, as shown in Figure 14, as provided from the waveform source panel in the RT Pro Photon 7.41 data acquisition system. Currently, an OMA-based roving different directions of sensor head of laser doppler vibrometer is performed to measure the actual modal properties of the beam structure by the data acquisition device, including four channels, only twenty measurement positions on the actual aluminum alloy beam were marked, as shown in Figure 15, and the shaker excitation impacts acted as the third location of the beam.  
Figure 14: Power spectrum associated with stationary white noise.  
Figure 13: Schematic diagram of the experimental setup.  
The length, width, and height of the beam structure used for this paper are 512.8, 25.5, and 3.0 mm, respectively, the mass is 104.97 g, and the material is 5052-0 aluminum alloy. In addition, the \"exact\" modal parameters are obtained from the data of auto power spectrum of stationary response and cross power spectrum of stationary excitation and response by using ME'Scope software. Note that \"exact\" stationary excitation is a built-in stationary white noise generated from Briel & Kjaer RT Pro Photon 7.41 data acquisition system is imported into the Modal Shop K20070E01 electrodynamic shaker to excite the cantilever beam structure. The natural frequencies of the first four modes are about 10.85, 70.32, 176.31, and 290.31 Hz, as listed in Table 6. Finally, the modal parameters obtained are used to compare the identification results of MSSI, as shown in Table 6 and Figure 16. It is observed that the frequency errors are less than 15%, Figure 1