## 2 Model Riser and Data Sets  
The NDP model riser experiment was carried out by the Norwegian Marine Technology Research Institute (Marintek) in 2003, by horizontally towing a flexible cylinder in the Ocean Basin test facility. The experimental setup is schematically described in Figure 1, which shows that a horizonal cylinder is attached to the test rig and towed by a crane and gondola. Towing both ends of the cylinder at the same speed by the crane in one direction simulates a uniform current flow, with one end fixed and towing the other end using the gondola to traverse a circular arc simulates a linearly sheared current flow. The maximum towing speed is 2.4 m/s, which simulates a flow field with Reynoldsnumber around 70,000. The key physical and hydrodynamic properties of the model cylinder are listed in Table 1. More details related to the design and setup of the experiment may be found in references of [PERSON] et al. (2013) and [PERSON] (2014). The riser response was measured using 24 strain sensors (one sensor failed for some test runs; hence, in some cases, only 23 strain sensors were available) and eight accelerometers for the cross-flow (CF) direction; similarly, in the inline (IL) direction, measurements from 40 strain sensors and eight accelerometers were available. It is assumed that all the measurements are accurate; the effects of noise and error in response measurements on fatigue damage estimates were not accounted for in the present study. We note, however, that accurate measurements are essential to any experimental study; results and conclusions drawn for this and other studies would be contaminated by measurement inaccuracies or noise ([PERSON], 2014; [PERSON], 2014). Among the six data sets available at the VIV data repository ([PERSON], 2014), four of them were obtained from tests on bare/unstraked risers. Table 2 summarizes current characteristics, root-mean-square (RMS) values of the CF displacement (normalized with respect to the outer diameter of the cylinder cross-section, \(D\)), and the time duration of each data set. The durations vary from 18 s to 60 s, which ensure over 100 cycles of CF oscillations for each data set. Because of the large RMS values of the CF displacement, the riser response is thought to be associated with VIV and, as such, these four tests are well suited for this study. Note that, in Table 2, the RMS values of the CF displacement are calculated based on the entire length of record and the largest value from all the eight accelerometers is reported. Figure 1: Schematics of the experimental setup: (**a**) test rig in vertical view; and (**b**) simulated current profiles in plan view, left is uniform current flow and right is linearly sheared current flow. Given CF and IL measurements at the same cross-section of a riser, [PERSON] et al. [18] computed the fatigue damage at several points along the outer circumference, and noted that the maximum fatigue damage for that cross-section location was usually equal to the larger of the CF fatigue damage and the IL fatigue damage. For the four NDP data sets, fatigue damage rates (per year) at the locations of the twenty-four CF strain sensors and the forty IL strain sensors are calculated based on stress time series, computed as the product of the available strain time series with the Young's modulus of the riser material, along with the use of Miner's rule [19]. A rainflow cycle-counting algorithm (details may be found in the literature [20; 21]), and S-N curve data lead to fatigue damage computed as follows:  
\[d=\frac{n}{N}=\frac{n}{aS^{-b}}, \tag{1}\]  
where \(d\) is the cumulative fatigue damage resulting from the stress/strain time series. In addition, \(N\) represents the number of cycles to failure for a constant-amplitude stress range, \(S\). The actual variable-amplitude stress time series causes fatigue damage equivalent to that of \(n\) cycles of constant amplitude, \(S\); \(n\) and \(S\) are computed as products of the rainflow cycle-counting procedure.