# Review of Structural Modal Tracking in Operational Modal Analysis: Methods and Applications
## 3 Method of Automatic Modal Tracking
### Comparison of Two Representative Tracking Methods  
This section applies two representative methods to field measurements of a super high-rise building, providing a more intuitive comparison of their advantages and limitations. The Shanghai Tower, the tallest building in China (Figure 2a), is located in a coastal region frequently subjected to severe typhoons. As a result of the importance of  
Figure 1: A flowchart of the traditional automatic operational modal analysis process.  
this structure, a comprehensive SHM system has been deployed since its construction (Figure 2b).  
In August 2018, the tower was impacted by three typhoon events, offering unique observational conditions for modal evaluation. Based on the acceleration responses from multiple channels of the SHM system, this paper adopted the automatic SSI-COV method [16] to estimate structural frequencies, with the results shown in Figure 3. They reveal that while the AMPE method can effectively identify low-order frequencies in a brief period, it tends to generate numerous spurious modes under normal environmental excitation and may fail to detect certain physical modes. Critically, both the existence of spurious modes and the absence of physical modes perturb the determination of modal order. This suggests that AMPE may face challenges in providing long-term modal estimation, particularly for higher-order modes. Implementation of accurate and continuous modal tracking aids in monitoring long-term dynamic characteristic variations, thereby enhancing structural assessment capabilities.  
Taking Mode 1 and Mode 6 as examples, Figure 4a presents the tracking results derived from the first representative method (Method 1) [16]. In Method 1, the reference mode is determined by hierarchical clustering, and the new mode is linked only when the MAC ratio and the relative frequency difference satisfy the specified thresholds, which were set to 0.9 and 10% in this study. The analysis revealed significant variation in tracking performance among modes with different orders under uniform threshold conditions. For Mode 6, partial modes were lost during Typhoons Yagi (1814) and Rumbia (1818), despite general stability. Conversely, Mode 1 exhibited over-filtered frequency trajectories under normal wind conditions, obscuring subtle modal variations. While threshold relaxation could mitigate this issue, such an adjustment would inevitably introduce additional noisy poles and spurious modes at other orders. Consequently, unified thresholds may not be applicable for all orders of modes.  
Figure 2: The Shanghai Tower: (**a**) a perspective view [122]; (**b**) the SHM system for acceleration [123].  
Figure 4b illustrates the modal tracking results employing Method 2 [111]. This method dynamically updates reference modes with the most recently estimated modes, while mode linking is established through a similarity matrix derived from the MMOC. A critical implementation constraint involves prespecifying the \(\beta\) of the modes within a targeted frequency band, and \(\beta\) was set to be four within 0.6 Hz in this study. Analytical results demonstrate efficacy in capturing frequency variations during typhoons. However, the mode-missing phenomenon occurs due to misclassification of the orders of reference modes during normal wind. Furthermore, this method is less robust when filtering spurious modes. In summary, distinct modal tracking methods exhibit unique advantages. Strategies capable of tracking rapidly varying modal parameters while remaining sensitive to spurious  
Figure 4: Comparison of modal tracking results between two representative methods: (**a**) Method 1 [16]; (**b**) Method 2 [111].  
Figure 3: The frequency estimation results of the Shanghai Tower using automatic SSI-COV in August 2018.  
modes would facilitate the establishment of more robust methods for long-term continuous modal tracking.