## 1 Introduction  
As the pertinent section of the rocket structure (Figures 1 and 2) is mostly connected by bolted flanges, the connection surface cannot maintain the overall continuity of the spacecraft. Therefore, it has specific nonlinear characteristics, which lead to a complex dynamic response under different operating conditions and types of equipment. These nonlinear response characteristics will undoubtedly affect the overall safety and reliability of the structure, so it is necessary to study the mechanical model of bolted flange connection structures to describe such structural responses. Figure 1: Schematic diagram of rocket’s inter-stage separation system [1]. [PERSON] et al. introduced the fine finite-element model of a bolted connection structure into the actual engineering structure for analysis and verified its validity, comparing it with the beam model of the bolted connection structure [3]. [PERSON] et al. investigated the micro-slip mechanical behavior of the connection surface to develop the framework of an equivalent prediction model and the parameter identification of a bolted connection structure [4]. [PERSON] and [PERSON] developed a mechanistic analysis model of the stop flange and illustrated the applicability of bilinear stiffness [5]. [PERSON] and [PERSON] analyzed the nonlinear behavior of the bolted flange connection structure under tension-bending-torsion conditions through a fine finite-element model [6]. [PERSON] et al. provided a model of the bolted flange connection structure by introducing different stiffnesses to the tension and compression, which explains the mechanism of the transverse and longitudinal coupling vibration of the interstage segment of the spacecraft [7]. Based on this, [PERSON] et al. investigated the bending-torsion-shear coupling of the structure, in which the shear pins are equipped with the spacecraft docking surface, and then analyzed the effect of different parameters on the internal forces of the structure, such as the lateral inclination angle of the shear pin [8]. [PERSON] et al. carried out a simulation analysis and destructive tests, looking at the failure of a bolted flange connection structure of a projectile body under impact loading [9]. [PERSON] et al. developed a simplified model of the bolted joined cylindrical shell structure based on the Sanders shell theory to investigate nonlinear mechanical properties [10; 11]. Then, they proposed a micro-slip model to simulate contact friction [12; 13]. To simulate the dynamic response of a launch vehicle's nonlinear bolted flange connection structure, [PERSON] et al. suggested a simplified dynamic modeling method based on a static structural analysis [14]. [PERSON] et al. investigated the near-resonant response of a dual-joint structure model driven by harmonic excitation considering the nonlinear stiffness [15]. The present research focuses on the simplified modeling and static/dynamic analysis of the connection structure in the rocket body to study the nonlinear mechanical characteristics of the overall structure. The bolt preload influences the stiffness properties and dynamic characteristics of the connection structure and is a key indicator of structural safety in practical applications. Therefore, research on the detection of bolt preload is very important for the connection structure of the rocket body. However, the research on the characteristics of the bolt preload is not sufficient. Since it is difficult to practically measure the bolt preload in real time, its failure can-not be detected directly. Therefore, bolt-loosening detection was studied in this work by performing an eigenvalue decomposition based on variational modal decomposition (VMD) and singular value decomposition (SVD). The VMD of the acceleration response data obtained from the finite-element analysis was applied to obtain the intrinsic mode function (IMF). The SVD eigenvalue was decomposed after Hilbert-Huang Transform (HHT), and the feature matrix was comprehensively obtained by combining the permutation entropy.