## 1 Introduction  
In nuclear power plants (NPPs), a primary system, usually a building or non-building structure, and many secondary systems, usually composed of equipment, are connected to each other. In the design or seismic fragility assessment of equipment installed in a structure, an in-structure response spectrum (ISRS) is used as the input motion for the equipment. The ISRS represents the peak acceleration response of a single-degree-of-freedom oscillator located in a structure excited by ground motions. The ISRS is computed for different natural frequencies of the oscillator and plotted in the form of acceleration versus natural frequency. The procedure for calculating ISRS is presented in Figure 1. The ISRS is important in the safety evaluation of equipment located in an NPP structure because various equipment has different natural frequencies and the uncertainty in natural frequency is necessary to be considered in the probabilistic safety assessment [1]. The ISRS is usually computed based on the response acceleration at individual equipment locations obtained using a structural model decoupled from the equipment. Relatively heavy equipment was considered in the analysis by adding only the mass of the equipment to the structural model. However, the ISRS computed based on decoupled analysis may have excessive conservatism compared with coupled analysis, particularly when the equipment and structure interact in resonance [2]. Therefore, excessive conservatism in the ISRS by decoupled analysis leads to a conservative design of the equipment, which increases rigidity and causes more frequent vibrations, making the components of the equipment more vulnerable to fatigue failure [3]. In addition, the ISRS obtained from the decoupled analysis has a limitation in that it can yield inaccurate equipment responsesthat may be non-conservative [4]. ASCE/SEI 4-16, which addresses the seismic analysis of NPPs, requires a coupled analysis when the structural response differs by more than 10% and provides graphical criteria based on the mass and frequency ratios between the primary and secondary systems to determine whether a coupled analysis is required [5]. The USNRC allows decoupled analysis under several conditions, such as highly flexible support connecting the structure and equipment [6]. Apart from the dynamic characteristics of the primary structure, soil parameter uncertainty may influence significantly the ISRS [7]. In the case of more general building structures, the influence of the inelastic structural behavior on the ISRS was investigated [8]. To obtain the ISRS through flexible analysis, it is necessary to analyze many coupled systems, each comprising the same primary system and a single degree of freedom (SDOF) oscillator representing the secondary system. The natural frequency of the oscillator differs for each coupled system and corresponds to the frequency in the abscissa of the ISRS. The fundamental methodology of the coupled analysis considering the equipment-structure interaction was established in the past. [PERSON] (1996), and [PERSON] and [PERSON] (1995) proposed an analytical method for transforming the eigenvalues and eigenvectors of multi-degree-of-freedom (MDOF) subsystems to obtain the modal characteristics of the coupled system [3;4]. [PERSON] et al. (2015) and [PERSON] et al. (2015), [PERSON] et al. (2022) developed and validated a direct-spectra-to-spectra method to compute the ISRS directly from the response spectrum of the ground motion based on the modal combination of the coupled system [9; 10; 11]. These methods have the disadvantage of being limited to modal analysis. As the modal characteristics of the coupled system change, the response of the entire system must be recalculated correspondingly. On the other hand, [PERSON] (1989) derived a transfer function between the acceleration response of the decoupled primary structure and that of the secondary system comprising a coupled system [12].