# Efficient Seismic Fragility Analysis for Large-Scale Piping System Utilizing Bayesian Approach
## 1 Introduction
Therefore, for the accurate seismic fragility analysis of piping systems, an integrated model that includes both primary and secondary structural frames must be established,  
Figure 1: Comparison between the response spectra obtained from ground motions at the observation posts of USN2 (Ulsan), DKJ (Deokjeongli), and MKL (Myeongkaeli) measured in the 2016 Gyeongju earthquake and the design response spectrum of USNRC RG 1.60.  
and a coupled analysis based on the integrated model must be performed. However, such an approach has a limitation in that it requires a large computational time because numerical analyses must be performed on a relatively complex model. Thus, in the field of nuclear structural analysis and design, this is considered through a decoupled analysis. Specifically, at first, the floor response spectrum for each floor of a building is derived through seismic response analyses of the building structure, which is the primary structural system with respect to the design-input earthquake ground motion. The obtained floor response spectrum is used as the input seismic load of each support location of the piping system, which is a secondary structural system. Owing to the analytical features of this decoupled approach, the seismic response and seismic fragility analyses cannot be performed in consideration of the dynamic characteristics of an integrated model of the building and the piping system, possibly resulting in a large error that is different from the actual phenomenon. In addition, the current seismic fragility analysis method applicable to piping systems is the EPRI (Electric Power Research Institute) separation of variable (SOV) method [18; 19; 20; 21], which basically uses the decoupled analysis approach mentioned above. This method, which is based on a linear analysis, calculates the seismic fragility by separating structure response-related variables, component response-related variables, and component capacity-related variables, and then integrating them into a single log-normal probability distribution. Recently, in contrast to the EPRI SOV method, according to the increase in the seismic intensity, nonlinear seismic response analyses were carried out in order to directly consider the characteristics of the integrated model of a building-piping coupled structural system. Based on these analysis results, a seismic fragility analysis was conducted using the statistical technique of maximum likelihood estimation (MLE) [22; 23]. However, the problem arises that a piping seismic fragility analysis based on the nonlinear seismic response analysis of the building-piping coupled numerical model requires a number of nonlinear analyses to be performed to take into account the uncertainty of the earthquake and the model, which results in a large computational cost. Accordingly, [PERSON] and [PERSON] [24] proposed the equivalent elastic limit state (ELS) concept and related closed-form equation and developed a seismic fragility analysis method based on linear seismic response analysis and this ELS equation. Recently, [PERSON] and [PERSON] [25] proposed a novel closed-form equation by improving the accuracy of the existing ELS equation and developed an effective seismic fragility analysis method that is suitable for the secondary structural system. However, these are still seismic fragility methods based on a linear seismic analysis, and, thus, they are limited by the impossibility of deriving seismic vulnerability by accurately simulating the nonlinear behavior characteristics of the building-piping coupled structural system. Therefore, in this study, based on the existing EPRI SOV seismic fragility analysis method, we propose an efficient piping seismic fragility analysis method using the concept of Bayesian updating. The proposed method is aimed at obtaining a piping seismic fragility curve, while not only reducing the cost of calculating nonlinear seismic response analyses, but also maintaining a similar accuracy in the results, compared to the existing MLE-based method.