## 2 Model Test  
The model test of a flexible riser with buoyancy modules and helical strakes in steady flow was carried out in the towing tank of the Shanghai Ship and Shipping Research Institute (SSSRI). The towing tank is 192 m long, 10 m wide and 4.2 m deep. The test device was mainly composed of a trailer, pretension module and buffer module, as shown in Figure 1. The pipe model was placed horizontally in the pool with its center 1.5 m away from the water surface. The ends of the pipe model were hinged with the pretension module and buffer module. The pretension module applies constant pretension to the pipe model, while the buffer module ensures that the pipe model can move along the axial direction. At the beginning of the test, the pipe model was placed horizontally in the towing tank, and then the trailer drove the pipe model to move forward at a constant speed in the towing tank so as to form a relatively uniform inflow as shown in Figure 2. The accuracy of trailer speed was 0.1%. The experimental current speed ranged from 0.4 m/s to 2.0 m/s. We used brass with good strength and corrosion resistance to simulate the bare pipe. Natural silica gel with great water tightness and low stiffness was selected to simulate the buoyancy modules (Figure 3a). Rubber material was used to make the helical strakes model for its good coating (Figure 3b). The main parameters of the pipe model are shown in Table 1.  
Figure 1: The test device of riser in uniform flow. (1. wave suppression plate; 2. baffle; 3. buffering spring; 4. servo motor; 5. support column; 6. cardan joint; 7. force sensor.) Figure 3: Models of buoyancy modules (**a**) and strakes (**b**). Figure 2: The method to generate uniform flow. F01: 25% of buoyancy modules covered uniformly. The spacing of the buoyancy modules is 90 cm, and at both ends, modules are 26 cm away from the end of the pipe;  
F02: 25% of buoyancy modules covered uniformly + 17.5 D/0.25 D strakes. The buoyancy modules are arranged the same as F01, but there are helical strakes in the bare pipe. F03: 50% of buoyancy modules covered non-uniformly. The spacing of the buoyancy modules in the dense part is 90 cm, while in the sparse part, it is 2 cm. At both ends, modules are 9.5 cm away from the end of the pipe;  
F04: 50% of buoyancy modules covered non-uniformly + 17.5 D/0.25 D strakes. The buoyancy modules are arranged the same as F03, but there are helical strakes in the bare pipe in the sparse part. We used the fiber Bragg grating strain sensors to measure the strain response time history on the surface of the pipe model. Different from the traditional resistive sensors, several fiber Bragg grating sensors can be arranged on one fiber, which is more suitable for array and synchronous measurement. In addition, the fiber Bragg grating sensor also has the advantages of good anti-electromagnetic interference ability, small size, easy installation, low cost, waterproof quality and no loop. The sensors were respectively arranged in the four directions, CF1, CF2, IL1 and IL2, of the pipe model (as shown in Figure 5). The strain information in the four directions of the model was measured. The sensors were evenly arranged, 25 in the IL direction and 19 in the CF direction. The number and spacing of the optical fiber measuring points mainly depended on the maximum modal order that the riser model may excite in the test. To avoid modal confusion when the vortex-induced vibration displacement is reconstructed by the modal analysis method, the number of strain measurement points should be larger than the maximum modal order that the riser model may excite. According to the published vortex-induced vibration test observations [2; 14], the VIV excitation frequencies in the CF and IL directions satisfy the following relationship:  
\[4\leq\frac{U}{f_{CF}D}\leq\ 11 \tag{1}\]