# MEMS-Based Vibration Acquisition for Modal Parameter Identification of Substation Frame
## 4 Modal Analysis of the Substation Frame
### Modal Parameter Identification of the Substation Frame  
The modal parameters of the substation frame include modal frequencies, damping ratios, and mode shapes. For substation frames, which are non-symmetrical structures, various modal orders exist in the parallel truss direction, vertical truss direction, and torsional direction. Therefore, the SSI-Cov method is employed to identify the modal parameters from the response data obtained in both directions.  
Due to the unique characteristics of structural modes, the stabilization diagram results are first examined, as shown in Figure 10. It can be seen that stable poles with corresponding high energy peaks appear near the frequencies of 2.14 Hz and 3.05 Hz in both stabilization diagrams. This indicates that the structure exhibits vibrations in both directions at these modal frequencies, leading to their initial identification as torsional modes. Additionally, a high-energy peak with a stable pole is observed at 4.78 Hz in the parallel truss direction, identifying it as the first-order mode in the parallel direction. Similarly, a high-energy peak with a stable pole is observed at 2.81 Hz in the vertical truss direction, identifying it as the first-order mode in the vertical direction.  
Table 1 lists the identified frequencies and damping ratios for the first four modes of the substation frame. It can be seen that the maximum frequency identification discrepancy between the two methods is 0.02 Hz, occurring in the first-order vertical truss direction, while the maximum damping ratio discrepancy is 0.13%, occurring in the second-order torsional direction. Additionally, the damping ratio for the first-order vertical truss mode is 1.29%, which is significantly higher than that for the first-order parallel truss mode,  
Figure 10: Stabilization diagram: (**a**) parallel truss direction; (**b**) vertical truss direction.  
indicating that the structure exhibits greater energy dissipation capability in the vertical truss direction at the first-order mode.  
Table 2 provides a comparison of the identification results using the SSI-Cov method and the FDD method. It can be seen that, using the same data, the two time-frequency domain algorithms still exhibit differences in their interpretation of frequency and damping ratio. The frequency identification results are generally consistent, with a maximum discrepancy of 0.02 Hz. However, the damping ratio identification results show some variability, with the largest difference occurring in the first-order vertical truss direction, at 0.41%. The variability in the identification results for the other modes is also slightly higher than the differences observed between datasets obtained from different test methods, primarily due to the different time-frequency domains used in the modeling of the two algorithms.  
Nonetheless, an examination of the FDD method's identification results shows that the damping ratio for the first-order vertical truss mode remains the highest, at 0.88%, indicating a strong energy dissipation capability for this mode. Since each mode shape has a spatial structure, the identification results of the substation frame's mode shapes will be discussed separately in the next subsection.