## 1 Introduction  
Power transmission is one of the significant activities in human communities, delivering electrical energy from power generators to the user. Substations are the key nodes in the power network. However, previous post-earthquake investigations have shown that the electrical equipment in substations is vulnerable to seismic occurrences [1, 2, 3]. In view of this, scholars have undertaken seismic studies on various kinds of electrical equipment from different aspects to mitigate earthquake-induced damage. As shown in Figure 1, seismic studies on power systems develop continually from performance evaluation to system resilience. At the earliest, some researchers analyzed and evaluatedthe seismic performance of much equipment, such as power transformers [4; 5], bushings [6; 7], surge arresters [8], and other post equipment [9; 10; 11; 12; 13]. Based on the seismic response analysis, some effective seismic mitigation measures were proposed for electrical equipment to improve their seismic performance, e.g., a double friction pendulum [14], wire ropes [15; 16], multiple tuned mass dampers [17], friction dampers, and prestressed tendons [18]. Nonetheless, the majority of the prior seismic investigations have been on transformer and post-type apparatus. Indeed, suspension equipment requires both design and protection. While [PERSON] et al. assessed the seismic performance of a suspended 800 kV converter valve and proposed a restraint method for its protection [19], there is a deficiency of seismic studies concerning suspended filter capacitors, which possess a markedly different structure from the converter valve. On top of response analysis and seismic mitigation analysis, recent years have seen the increase in seismic vulnerability and failure risk assessments on electrical equipment. Since Anagnos developed the empirical seismic fragility database of electrical equipment by damage statistics in 1999 [20], many scholars started the evaluations for substation equipment by simulation or tests. [PERSON] et al., [PERSON] et al., and [PERSON] et al., respectively, assessed the failure probability of power transformers and disconnect switches in succession [21; 22; 23]. [PERSON] et al. assessed the seismic failure risk of the post electrical equipment on supporting structures in 2023 [24; 25]. [PERSON] et al. also completed the seismic risk analysis for substation equipment using a reliability-based approach [26]. In addition, some detection measures were implemented to electrical equipment to complete the real assessment [27; 28]. Further, some circuit and system analysis approaches were applied to the entire substations and the system vulnerability simulation model was proposed [29; 30]. However, the assessment work at substation system levels always concentrates on the global situation, which ignores the detailed response laws of standalone equipment [31; 32]. The oversimplification of the equipment brings a large error. In current seismic studies, the seismic performance and vulnerability of some single equipment such as the suspended filter capacitor are still unclear and worth looking into. Seismic vulnerability analysis plays a critical role in the performance assessment on engineering structures [33; 34; 35; 36]. Incremental dynamic analysis (IDA) is the most commonly used vulnerability analysis approach for assessing different types of structures. The general vulnerability analysis reflects the whole structural dynamic performance whereas it lacks the consideration of some sorts of uncertainty factors and influence. Research in recent decades have revealed that material uncertainty is one of the critical factors that influences  
Figure 1: Seismic studies on power systems and the location of the study of this paper. the structural seismic vulnerability [37; 38; 39; 40], in addition to other uncertainties such as the structural parameter uncertainty [41]. For instance, [PERSON] et al. found that material strength uncertainty would increase the seismic fragility and failure risk of structures [7; 29].