# Seismic Vulnerability Assessment of Hybrid Mold Transformer Based on Dynamic Analyses
## 5 Conclusions  
In the present study, the seismic vulnerability of the mold transformer, which plays a crucial role in buildings, was assessed by dynamic analyses incorporating experimental results. In total, 1120 dynamic analysis cases were analyzed to describe the major characteristics of a prototype mold transformer. The truncated incremental dynamic analysis (TIDA) approach was used to estimate the seismic fragility curves with a set of 20 natural ground motions and three cases of uncertain modeling parameters including the effective translational stiffness, effective rotational stiffness, and the coil mass. The primary conclusions that may be drawn from this study are as follows:  
1. The proposed analytical model showed good agreement with the data obtained from the shaking table test in terms of the shapes of acceleration-time history response, peak amplitude of acceleration response in tri-axial directions, the results of Fourier-transform (FT) analyses of acceleration response in frequency domain, the shapes of displacement-time history response, and the maximum displacement with a wide range of PGA.
2. Based on the shaking table test series results, three potential damage states were adopted to evaluate the seismic vulnerability: the failure of the spacers (DS1), the excessive movement in Y-direction (DS2), and the loosening of the linked bolts between the bottom beam and bed beam (DS3). Simultaneously, the limit values corresponding to the damage state for each performance level were also determined partly based on the test results and partly based on judgment.
3. The fragility curves were developed using the TIDA approach based on the analytical results, acceptance criteria from the test results, and the maximum likelihood estimator method, and they provided an overview of the failure probability of the hybrid mold transformers according to different PGAs and performance levels. Accordingly, for a given value of the probability of exceedance, the critical PGA for each performance level corresponding to specific damage states can be definitively determined.
4. The critical PGA values corresponding to 40% probability of exceedance, which may play an important role in the seismic vulnerable evaluation and seismic design purposes, were also determined from the fragility curves. The values for the cases of DS1 corresponding to the OP and PR performance levels were 0.15 g and 0.4 g, respectively; the values for the cases of DS2 corresponding to the OP and PR performance levels were 0.3 g and 0.45 g, respectively; and the values for the cases of DS2 corresponding to the OP, PR, and LS performance levels were 0.2 g, 0.6 g, and 1.2 g, respectively.  
Methodology, N.H.D.; Investigation, J.-Y.K. and S.-J.L.; Writing--Original Draft Preparation, N.H.D.; Writing--Review & Editing, K.-K.C.; Supervision, K.-K.C.  
**Funding:** This research was supported by a grant (No. 19 AUDP-C146352-02) from the Architecture & Urban Development Research Program funded by the Ministry of Land, Infrastructure and Transport of the Korean Government.  
**Acknowledgments:** We gratefully acknowledge the supports of Ministry of Land, Infrastructure and Transport of the Korean Government under a grant No. 19 AUDP-C146352-02 from the Architecture & Urban Development Research Program, and Soongsil University for supporting us.  
**Conflicts of Interest:** The authors declare no conflicts of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Damage States** & **Performance Levels** & **Median \(\theta\)** & **Standard Deviation \(\beta\)** \\ \hline DS1 & OP & 0.16 & 0.28 \\  & PR & 0.42 & 0.31 \\  & OP & 0.34 & 0.40 \\ DS2 & PR & 0.50 & 0.40 \\  & OP & 0.22 & 0.37 \\ DS3 & PR & 0.66 & 0.40 \\  & LS & 1.29 & 0.40 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Values of limit states of the mold transformer.