# Review of Structural Modal Tracking in Operational Modal Analysis: Methods and Applications
## 2 Method of Automatic Modal Parameter Estimation  
In a complete AOMA process, AMPE serves as the prerequisite for subsequent modal tracking. This section provides a concise review of AMPE methods. First-generation modal estimation methods introduce substantial uncertainty through manual interpretation, including the least-squares complex frequency domain (LSCF) approach [64], SSI [65], the ERA [66], and so on. Consequently, AMPE frameworks have been developed to address this issue and improve automation. Among the modal analysis techniques in the time and frequency domains, SSI has received considerable attention, owing to its rigorous mathematical basis for linear systems [67] and its demonstrated effectiveness in long-term monitoring implementations [68, 69, 70]. Most AMPE methods focus on the automatic interpretation of stabilization diagrams. In these diagrams, the poles representing physical modes possess consistent values and hence form vertical lines across different orders, whereas spurious modes exhibit random dispersion [71]. [PERSON] et al. [72] divided the AMPE process based on stabilization diagrams into four steps, which were establishing the stabilization diagram, cleaning the stabilization diagram, interpreting the stabilization diagram, and removing the outliers in the estimation results. Existing research and contributions primarily concentrate on cleaning the stabilization diagram based on the mode validation criteria and interpreting the stabilization diagram based on clustering techniques. In the step of cleaning the stabilization diagram, the mode validation criteria are generally employed to filter noisy poles exhibiting anomalous frequency, damping ratio, or mode shape characteristics. Meanwhile, the criteria are also combined with \(k\)-means clustering [73] and modified fuzzy \(c\)-means (FCM) clustering [74] to remove certain spurious modes. [PERSON] et al. [17] systematically categorized these criteria into three hard validation criteria and multiple soft validation criteria. Table 1 synthesizes the common soft mode validation criteria adopted in modal analysis, with detailed definitions available in the corresponding references. The symbol \(\surd\) signifies that the criterion has been employed, while the symbol--denotes that no adoption has been found. The content related to modal tracking will be elaborated in detail in Section 3. It has been proven that the majority of these criteria play important roles in AMPE [30]. Specifically, they are widely utilized to ascertain whether the poles in a stabilization diagram, generated by the discrete state-space model, correspond to physical or spurious modes. It is noteworthy that due to the influence of environmental noise and systematic error, estimated physical mode values may vary in a large range. It is unfeasible to use ideal values as thresholds to divide physical and spurious modes. In actual applications, the thresholds of soft mode validation criteria appropriate for each stabilization diagram are either manually defined or automatically computed. Following stabilization diagram cleaning, the retained candidate modes need to be automatically separated into distinct groups to extract the physical modes. Current studies extensively employ clustering algorithms to interpret stabilization diagrams, including hierarchical clustering [80; 81; 82], FCM clustering [83; 84], \(k\)-means clustering [85], ordering points to identify the clustering structure (OPTICS) [86], the density-based spatial clustering of applications with noise (DBSCAN) algorithm [87; 88], fast density peak clustering (FDPC) [89], potential-based hierarchical agglomerative clustering [90], and so on. While these clustering techniques enhance operational efficiency and interpretability, threshold selection during clustering introduces subjectivity that may compromise estimation accuracy. For instance, FCM clustering requires the user to set the number of clusters, and DBSCAN requires joint optimization of the minimum point density and the searching radius.