## 1 Introduction  
Vortex-Induced Vibrations (VIV) of long flexible structures with bluff cross-sections are encountered in a great variety of physical problems, ranging from Aeolian vibrations hanging in the air to the vibrations of slender marine structures in deepwaters, e.g., cables and risers placed in ocean currents. The interaction between fluid flow and slender bodies results in the periodic hydrodynamic forces that are induced due to VIV. If the vibration period is close to the natural period of the system, it can lead to the fast accumulation of fatigue damage to the risers and amplified drag loads on the riser systems. In recent years, Steel Lazy Wave Riser (SLWR) has become an attractive deepwater riser system design due to its functionality in improved fatigue life. When subjected to external flow, both the buoyancy elements and the bare riser section may experience VIV. The vortex shedding frequency of the buoyancy element is lower than that of the bare riser section due to its larger diameter. Moreover, these two vortex-shedding processes will interact with each other and influence the VIV responses. There have been extensive experimental studies on VIV responses, as reviewed by [PERSON] [1], [PERSON] and [PERSON] [2], and [PERSON] et al. [3]. Model tests with rigid cylinders are normally carried out either on elastic supports or with forced motions [4; 5; 6]. Prototype Reynolds numbers can be achieved in some of the tests with a rigid cylinder section [7; 8; 9]. Test results demonstrated that VIV responses are affected by the Reynolds number and surface roughness, especially in the critical Reynolds number range. However, no complete hydrodynamic database at the prototype Reynoldsnumber exists considering the large parameter space. High mode VIV tests with flexible pipes have been carried out by [PERSON] et al. [10], [PERSON] et al. [11] and [PERSON] et al. [12], which further revealed the complexity of the response, such as dual resonance, multi-mode vibration, unsteady lock-in, higher harmonic fluid forces and traveling wave dominant response. However, our understanding of the VIV responses of a riser with staggered buoyancy elements remains limited. Several model tests were carried out to investigate the interaction between VIV responses of the bare riser sections and the buoyancy elements [13; 14; 15]. It was observed that such interactions were influenced by many parameters, such as buoyancy element dimensions and their arrangement (i.e., spacing between two buoyancy elements) [16]. In these tests with flexible riser models, accelerations and bending strains along the length of the tested model were measured. However, the hydrodynamic forces along the riser models were not directly measured. Large differences were observed while predicting VIV responses of the riser with staggered buoyancy elements using the default hydrodynamic coefficients for both bare and the buoyancy elements [17]. A forced motion test of a rigid cylinder with staggered buoyancy elements was carried out to extract hydrodynamic coefficients on buoyancy elements and bare pipe sections by [PERSON] et al. [18]. In their tests, hydrodynamic force coefficients subjected to pure CF motions were obtained. It was shown that the hydrodynamic coefficients of the buoyancy elements differed significantly from the bare section. It is also known that the hydrodynamic coefficients of a cylinder oscillating in both in-line (IL) and CF directions will differ from those from pure CF motions ([19; 20]). Hence, it is of interest to extract hydrodynamic coefficients directly from the VIV test with flexible pipe models. The inverse analysis is one such method which uses measured response data to calculate the external VIV loads by assuming that the mechanical properties (stiffness, mass, etc.) are known. The hydrodynamic coefficients are then calculated from the estimated forces [21]. The obtained hydrodynamic coefficients provide valuable insights for better understanding the behavior of a flexible cylinder.