Algorithm 1: Proposed Algorithm.

Inputs: Stabilization diagram (frequency, damping ratio, and mode shape), damping ratio limits (${\zeta }_{min}$ and ${\zeta }_{max}$), stabilization criteria ($li{m}_f$, $li{m}_{\zeta }$ and $li{m}_{MAC}$), and similarity measure threshold ($li{m}_D$). Output: Global modes Classify as stable all poles that satisfy the stabilization criteria and as not stable all remaining poles Classify as spurious all poles with damping ratio lower than ${\zeta }_{min}$ or higher than ${\zeta }_{max}$ (Hard Validation Criteria—HVC) or that do not appear with a complex conjugated pair Extract the number of stable poles ($n_{me}$) Create a matrix of zeros $D\in {ℝ}^{n_{me}\times n_{me}}$ For $m$ in $\left[1,n_{me}\right]$: 5.1. For $n$ in $\left[1,n_{me}\right]$: Compute the distance between the poles $m$ and $n$ ($d_{m,n}$) using the relative distance between the natural frequencies of both poles and assign the result to the matrix $D$ in the position ($m,n$) Apply agglomerative hierarchical clustering taking the distance matrix $D$ as the method’s similarity measure and consider the informed threshold ($li{m}_D$) Extract the number of clusters obtained ($n_c$) For $c$ in $\left[1,n_c\right]$: 8.1. If cluster $c$ has more than one pole of each order, remove all poles of each order but one, and keep the one with the damping ratio closest to the cluster’s damping ratio median 8.2. Store the number of poles and each modal parameter (natural frequency, damping ratio, mode shapes and order) of the cluster $c$ Create a histogram of the number of poles in each cluster Extract the mean size of the clusters Select the clusters whose size is bigger than the mean size Create a boxplot of the frequency and of the damping ratio Remove the outliers: - If ${\omega }_n<Q_1{}_{freq}-1.5 IQ{R}_{freq}$ or ${\omega }_n>Q_3{}_{freq}+1.5 IQ{R}_{freq}$, remove the pole $n$ because it is a frequency outlier - If ${\zeta }_n<Q_1{}_{\zeta }-1.5 IQ{R}_{\zeta }$ or ${\omega }_{\zeta }>Q_3{}_{\zeta }+1.5 IQ{R}_{\zeta }$, remove the pole $n$ because it is a damping ratio outlier Being $Q_1$ is the first quartile, $Q_3$ the third quartile, and $IQR$ the difference between the upper and lower quartiles Extract the parameters that represent the clusters: mean frequency, mean damping ratio, and mean mode shape Extract the number of global modes ($n_{gm}$) For $i$ in $\left[1,n_{gm}\right]$: 16.1. Extract the number of poles ($n_p$) 16.2. Create a matrix of zeros $D_{MAC-i}\in {ℝ}^{n_p\times n_p}$ 16.3. For $m$ in $\left[1,n_p\right]$: 16.3.1. For $n$ in $\left[1,n_p\right]$: Compute the MAC value between the poles $m$ and $n$ and assign the result to the matrix $D_{MAC-i}$ in the position ($m,n$) 16.4. Extract the minimum value of the matrix $D_{MAC-i}$ ($mi{n}_i$) 16.5. If $mi{n}_i<li{m}_{MAC}$: 16.6. Create a matrix of zeros $D_i\in {ℝ}^{n_p\times n_p}$ 16.7. For $m$ in $\left[1,n_p\right]$: 16.8. For $n$ in $\left[1,n_p\right]$: 16.9. Compute the distance between the poles $m$ and $n$ according to Equation (14) and assign the result to the matrix $D_i$ in the position ($m,n$) 16.10. Apply agglomerative hierarchical clustering taking the distance matrix $D_i$ as the method’s similarity measure and considering the informed MAC limit ($1/li{m}_{MAC}$) 16.11. Select the poles from the biggest cluster to represent the global mode $i$ 16.12. Extract the parameters that represent the modal globe: mean frequency, mean damping ratio, and mean mode shape