## 4 Fatigue Damage Estimation Based on a Large Number of Sensors  
The CF strains on the NDP model riser were measured using twenty-four strain sensors (only twenty-three sensors were available for the NDP2420 data set, since strain sensor no. 21 had failed). In the results described here, we select one sensor at a time as the target sensor, and use measurements from the remaining twenty-three (or twenty-two) sensors to reconstruct strains at the location of the target sensor by employing the various empirical methods described above. Such analysis for each empirical method, applied with sensor no. 4 as the target sensor, was presented in the previous section (Section 3). The variability factor, which represents the ratio of the fatigue damage rate based on the reconstructed strain (at the target sensor) to that based directly on the measured strain there, is used as a criterion to compare the empirical methods. Figure 8 presents variability factors estimated at the twenty-four locations for the two uniform current data sets (red color) and the two sheared current data sets (blue color), by employing each of the five empirical methods. The lowest and highest values of the variability factor estimated for each data set using each empirical method, are also indicated in the figure legends--for example, Figure 8a states that the twenty-four variability factors estimated by the WWA method on the NDP2120 uniform current data set ranged from 0.25 to 6.58. Figure 7: The hybrid (MPR + modified WWA) procedure applied with twenty-three input sensors (sensor no. 4 is the target) for the NDP2350 (sheared current) data set: (**a**) PSDs of the strains measured at the twenty-three sensors; (**b**) summation of the strain PSDs and the frequency components that preserve 99% energy; (**c**) strain PSD at the target sensor, reconstructed (using modes that preserve 99% energy) versus measured; and (**d**) RMS curvatures, reconstructed (using modes that preserve 99% energy) vs. measured. Figure 8: _Cont._  
Some general conclusions that may be drawn by studying Figure 8 are summarized here. 1. With the WWA method, a large number of modes can be interpreted from a suite of measurements. The modified WWA method can better account for the effects of traveling waves and localized curvature changes but fewer modes can be interpreted or used in reconstruction of strains at any target location. As a consequence, in this study where a large number of sensors (twenty-three) are available, fatigue damage rates estimated over the entire riser length by the WWA and the modified WWA methods are generally of comparable accuracy (see Figure 8a,b). 2. Fatigue damage rates estimated by the POD and MPR methods are quite similar since both methods are affected by the quality of the unavoidable interpolation--it may be noted that the presence of sensors close to a target location leads to good estimation of the fatigue damage there; however, when nearby sensors are not present, as is the case for sensor no. 9 indicated by the red ellipses in Figure 8c,d, fatigue damage estimates are less accurate. 3. The fatigue damage rates for the two uniform current data sets estimated either by the POD or the MPR method are less accurate than those estimated by the WWA or the modified WWA method; one likely reason for this is due to the strong non-stationary response characteristics indicated particularly in the two uniform current data sets (see [PERSON] et al. [35]) that more directly affect the accuracy of the POD and the MPR methods. With the WWA and the modified WWA methods, the modal weights are solved for at each time instant (see Equation (7)); the POD and the MPR methods, on the other hand, assume that the riser response is described by a stationary process and decomposition of the measured response is based on the entire record (see Equations (11) and (16)).