## 4 Dynamic Model Updating Examples
### Proof Examples: Dynamic Model Updating of a Thin Plate
#### 4.1.2 Updating Based on the Impact Modal Test Data  
The thin plate was suspended via a flexible cord with nine acceleration sensors evenly arranged, as shown in Figure 5. Excitation of the thin plate was achieved using an impact hammer, and the roving hammer method was employed to excite each of the fifteen response points five times. The translational acceleration responses in the thickness direction were measured at each point to obtain the smooth frequency response function data. The analytical bandwidth ranged from 100 to 1200 Hz. The stability tolerances of vibration vector, frequency, and damping were 2%, 1%, and 5%, respectively, and the model size was 100. Then, a clear stabilization diagram was obtained based on the poly-reference least squares complex exponential method [37], as shown in Figure 6. The first ten modes are marked by the red letter \"s\" and violaceous line in Figure 6.  
The natural frequencies and corresponding modal damping ratios are detailed in Table 6. Compared with Table 2, the FRE values were larger, as were the \(RMSE_{FRE}\) and \(CV\). Figure 5: Overview of the impact modal test of the thin plate. (**a**) Screenshot of the frequency response function and experimental model. (**b**) Impact modal test instrument. (**c**) Suspension of the thin plate. (**d**) Location of the sensors. Figure 6: Stabilization diagram and the mode shapes of the thin plate in the impact modal test. Unlike the simulated \"experimental\" data, the modes obtained in the impact modal test were complex. Since all the modal damping ratios in Table 6 were less than 0.7%, the realization method was used by multiplying the modulus of each element of the complex mode shape vector by the sign of the cosine of its phase angle [10]. As shown in Figure 6, the first ten real mode shapes were obtained. Then, the following updating process was the same as Section 4.1.1. After pre-analysis, two uncorrelated mode pairs were specified for the MUUM method: (A7, E6) and (A6, E7). Then, both the MUUM and CMPES methods were used to update the initial FE model based on the experimental modal results. As listed in Table 7, the updated results in terms of \(RMSE_{FRE}\) were the same with the value of 2.55% in both methods. For the thin plate, the discrepancies of MAC values between the FE and experimental results were affected by factors such as noncoincidence of impact and response points and added mass of acceleration sensors. The \(RSME_{MAC}\) of the updated model obtained by the CMPES method was only a little smaller (from 0.2038 to 0.1902) than that of the initial analysis, but it was better than the one (0.2082) obtained by the MUUM method. The \(CV\) of the updated model obtained by the CMPES method was also less than the MUUM method, which was 0.1552 and 0.1784, respectively. As mentioned in Section 2, the updated results are usually susceptible to the CMPES based on existing methods. For the MUUM method, since the constant groups of correlated and uncorrelated mode pairs are specified by pre-analysis, noticeable differences among updated models may occur by different groups. To compare the robustness of the two methods, three different groups of correlated and uncorrelated mode pairs for the MUUM method were selected from full-factorial design