The present work developed a basis to explore numerous damage events utilizing Self-Organizing Map (SOM) introducing Kullback-Leibler (KL) divergence as an appropriate similarity for frequency spectra of damage events. Firstly, we validated the use of KL divergence to frequency spectra of damage events. The experiment using the datasets of damage related sounds showed that the kernel SOM using KL kernel generates accurate cluster map compared to using general kernel functions and the standard SOM. Afterward, we demonstrated our approach can clarify damage process of Solid Oxide Fuel Cells (SOFC) from acoustic emission (AE) events observed by damage test of SOFC. The damage process was inferred by occurrence frequency of AE events upon the cluster map of SOM, where the occurrence density change was obtained by kernel density estimation (KDE). The presented approach can be a common foundation for the domain experts to clarify fracture mechanism of SOFC and/or to monitor SOFC operation.