## 1 Introduction  
Risers are an indispensable component of offshore oil and gas exploitation structures, connecting the wellhead at the sea bottom and the offshore platform at sea surface, and they are utilized to transport the exploited oil and gas (production riser) or to guide the drilling equipment (drilling riser). Nowadays, high-grade steel risers predominate. However, in order to exploit resources in deeper water and harsher environments, different risers are being produced using different materials, such as aluminum (AI) risers, titanium (Ti) risers and fiber-reinforced polymer (FRP) composite risers. For the AI riser and the Ti riser, the design process and working conditions are similar to those of high-grade steel risers, since all their materials are isotropic. In contrast, FRP composite risers, which are a laminated structure with anisotropic materials, have a different design process and design considerations [1; 2]. Many studies, including static analysis and testing, dynamic response, durability under working condition, and so on, have been conducted since the 1950s [3] on the most traditional risers. In the 1980s, the concept of FRP composite risers appeared [4], and since then, more studies and projects have been conducted, such as static and fatigue tests [5; 6], verification field tests [7], and pressure integrity tests [8], as well as studies about the optimized design of FRP composite risers by considering the possibilities of different design methodologies, different materials for liner and composite laminate, different laminate stacking sequences, different reinforced fiber angles and different lamina thicknesses [1; 2; 9; 10; 11; 12]. Compared to other structures, risers are vulnerable to vortex-induced vibration (VIV), i.e., the motions induced on risers interacting with an external flow, which is the main cause of fatigue failure in risers. For metal risers, studies of VIV have been conducted for more than four decades using laboratory and field tests and experiments [13; 14; 15; 16; 17]. In addition to the riser (the vertical pipeline), the VIV of the flexible pipeline lying parallel to the bottom floor were also investigated, and the effects of sea-bottom proximity under steady flow and/or wave-induced current on the fatigue life and VIV amplitude and frequency of suspended spans of flexible pipelines were discussed [18; 19; 20; 21]. Meanwhile, the framework for the theoretical analysis of VIV for risers was firstly built by [PERSON] (the lift-oscillator model) [22], and this model was then developed for flexible risers [23]; more recently, wake oscillator models were modified and developed according to different parameters and situations [24; 25; 26; 27; 28; 29]. Currently, computational fluid dynamics (CFD) with different models and methodologies has been applied to solve the VIV problems of risers [17; 30; 31]. In contrast, for FRP composite risers, the studies of VIV response were comparatively fewer, but still produced inspired results. A global-local analysis methodology was built to investigate the VIV responses of composite risers under semi-empirical fluid load models [32]; [PERSON] and [PERSON] et al. compared the dynamic performance of composite and steel risers using ABQUS and SHEAR7 [33; 34], and [PERSON] et al. [35] simulated the VIV response for FRP composite risers by CFD with different modeling methods. From the previous studies, the VIV of specific risers with fixed design factors were understood, as well as the effect of single design variable on their response for VIV. However, the combination of multiple parameters and the significant sequence of each parameter on risers' VIV characteristics have rarely been considered. To explore the significant sequence of different parameters on risers' VIV characteristics, grey relational analysis (GRA) is an effective tool which is small sample, small amount of calculation and no requirement for independency [36].