# Hilbert-Huang-Transform-Based Seismic Intensity Measures for Rocking Response Assessment
## 4 Conclusions  
In the present study, the performance of 12 novel HHT-based IMs in describing the seismic response of typical rocking viaducts is assessed based on optimal IM selection criteria. To this end, a comparative evaluation of the performance between the proposed IM and 26 well-known conventional IMs is presented. Among the proposed IMs, the most optimal ones perform similarly to the conventional ones in describing the rocking rotations and the probability of collapse. Since adopting any of the most optimal IMs introduces considerable uncertainty in fragility assessment, multivariate IMs should be considered. Therefore, all possible bivariate IMs are examined, and fragility curves are provided based on the five most optimal IMs. It is noteworthy that most optimal bivariate IMs consist of one HHT-based parameter. Subsequently, a classification of the seismic response was conducted using discriminant analysis to provide a reliable and rapid estimation of the maximum seismic demand. Based on the performance measures of the classification problem, it is evident that HHT-based IMs result in an enhanced estimation of the seismic performance of the examined structural system.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Classes** & **1** & **2** & **3** & **4** \\ \hline Description & \(0<\theta/\alpha\leq 0.10\) & \(0.10<\theta/\alpha\leq 0.50\) & \(0.5<\theta/\alpha\leq 1\) & \(\theta/\alpha>1\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Adopted classification of the EDP.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Set** & **Accuracy** & **Recall** & **Precision** & **F1 Score** \\ \hline
**Train** & 0.96 (0.97) & 0.92 (0.96) & 0.95 (0.96) & 0.93 (0.96) \\
**Test** & 0.75 (0.85) & 0.75 (0.85) & 0.79 (0.85) & 0.76 (0.85) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average performance measures of the discriminant analysis.  
Rocking-based structural systems can be represented by equivalent rocking blocks [11]. Based on the promising results of this study, the performance of the proposed HHT-based IMs on different rocking structural systems should be further evaluated in future research. Moreover, the rigidity assumption regarding rocking piers leads to a conservative estimation of the seismic response [8]. As such, a more sophisticated model that incorporates the beneficial effect of elasticity could also be adopted.  
Conceptualization, A.E.; methodology, K.E.B., I.E.K., M.T. and A.E.; software, K.E.B., I.E.K., M.T. and A.E.; validation, K.E.B., I.E.K. and A.E.; formal analysis, K.E.B., I.E.K., M.T. and A.E.; investigation, K.E.B., I.E.K., M.T. and A.E.; resources K.E.B., I.E.K., M.T. and A.E.; data curation, I.E.K., K.E.B., M.T. and A.E.; writing--original draft preparation, K.E.B. and I.E.K.; writing--review and editing, K.E.B., I.E.K., M.T. and A.E.; visualization, K.E.B., I.E.K., M.T. and A.E.; supervision, A.E.; project administration, K.E.B. and I.E.K. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare no conflict of interest.