## 7 Conclusions  
In this study, a seismic fragility analysis method, composed of PCA and a K-means clustering algorithm, has been developed for the damage probability assessment of high-pier bridges under pulse-like ground motions. Meanwhile, the correlation coefficient and the condition number have been adopted as judgment indices to identify those _IMs_ with weak correlation and multicollinearity. A comprehensive system has been established to determine the optimal combination of _IMs_ that meets the requirements for the PCA method. Based on this system, an optimal combination of _IMs_, without weak correlation and multicollinearity, was obtained from the 29 initial candidate seismic _IMs_. Meanwhile, using a PCA algorithm, the principal components of the optimal combination of _IMs_ were calculated. Then, the K-means clustering algorithm was applied to classify the original group of selected 100 pulse-like ground motions into four classes, based on the first three principal components. After that, the original class, first class, second class, and third class pulse-like ground motions were scaled using PGA, ranging from 0.1 g to 1.0 g, with a 0.1 g increment. Furthermore, by establishing a 3D finite element model of the exemplar high-pier bridge via the OpenSees platform, the increment nonlinear dynamic time-history analyses of the exemplary high-pier bridge were conducted to record the maximum cross-section curvatures of high piers under the various scale classes of pulse-like ground motions. Finally, according to the IDA method's analysis procedures, the seismic fragility curves of the exemplar high-pier bridge under various classes of pulse-like ground motions were developed and compared. The results show that the fragility curves of the slight and moderate damage stages under the first class and the third class pulse-like ground motions were basically identical, and the damage probability values were all larger than those of the original class pulse-like ground motions; in the extensive and collapse damage stages, the fragility curves of the original class pulse-like ground motions were almost equal to the third class pulse-like ground motions, and all were smaller than the damage probability under the first class pulse-like ground motions, apart from the collapse damage stage of the pier top cross-sections (cross-sections 5-5 and 10-10); the fragility curves of the second class pulse-like ground motions were the smallest of the various class pulse-like ground motions. It can be seen that the selection of pulse-like ground motions has a significant impact on the calculation of the damage probability of high-pier bridges. Therefore, it is important to utilize the PCA and K-means approach to classify the selected ground motions, which can also improve the analytical precision and accuracy of damage probability calculations. Moreover, the damage probabilities under various classes of ground motions for the high-pier top cross-section were all greater than the high-pier bottom cross-section. In addition, the lower pier was more prone to failure, compared to the higher pier under original class, first class, second class, and third class ground motions. Therefore, the high-pier top cross-section and the lower pier should be considered more closely in the seismic design of multi-span high-pier continuous rigid-frame bridges. However, this study applies the IDA method to perform seismic fragility analysis for the case study of a high-pier bridge, which requires scaling the selected ground motions and increasing the computational effort. Therefore, further research will be focused on combining machine-learning methods, which offer good small-sample prediction capability, with the PCA and K-means approach to develop a new seismic fragility analysis method that can reduce the computational effort needed, while ensuring calculation accuracy. Conceptualization, J.Z. ; methodology, J.Z. ; software, J.Z. ; writing--original draft preparation, J.Z. ; funding acquisition, J.Z. ; writing--review and editing, H.J.