## 5 Fatigue Damage Estimation Based on a Small Number of Sensors  
The estimation of fatigue damage rates over the entire length of the NDP model riser based on measurements from a large number of sensors was discussed in the previous section (Section 4). However, actual deepwater drilling risers are seldom instrumented as densely as the NDP model riser due to the high cost of sensor deployment, maintenance, data retrieval, etc. Accordingly, it is of interest to discuss estimation of fatigue damage rates over the riser length based on measurements from a much smaller number of sensors than before. Using strain measurements from eight sensors as inputs, the riser response is reconstructed at the locations of all of the twenty-four sensors (including the eight input sensors). By iterating over numerous different combinations of any eight strain sensors as inputs (from among all the twenty-four available sensors on the riser), optimal locations for the eight sensors along the riser are identified by cross-validation, wherein estimated strains and fatigue damage rates at the twenty-four locations are compared with strains and fatigue damage rates based on actual recorded measurements there. In principle, all the possible combinations of eight sensors chosen from twenty-four available sensors could be considered as selections; however, this would result in an exceedingly large number of combinations to be evaluated. Thus, only thirty-four arrangements or combinations of eight sensors are selected for the fatigue damage analysis. Figure 10 shows the locations of the eight sensors for these thirty-four selected combinations. The first group (identified as G1) comprises sixteen combinations,  
Figure 9: Alternative parameters that might be used to evaluate the reconstructed riser response; these include the variability factor (ratio of the fatigue damage rates), the ratio of RMS values of strains, and the ratio of RMS values of displacements. each of which includes eight contiguous sensors; the second group (G2) has six combinations wherein six sensors are located near the top end (i.e., near the higher current end in the case of the sheared current data sets) and the remaining two sensors are near the middle, at a location around one-fourth of the riser's length from the bottom (low-current) end, or at the bottom end. Note that the malfunctioning strain sensor (no. 21) is not selected as an input sensor in these studies. Four other groups (G3 to G6) are also considered as shown in Figure 10.  
Note that not all the five empirical methods discussed earlier are employed in this study that uses only eight strain sensors to estimate fatigue damage; there are reasons for this. First, for the modified WWA method, only two or three modes could be represented if eight sensors are available; this would make it difficult to account for all the important frequencies (the first and higher harmonics) of the riser response. Second, for the POD and MPR methods, the accuracy of the interpolation (from information at the discrete locations of the input sensors to all other locations) controls the accuracy of the reconstructed riser response at target locations without sensors. If the target location has no available sensors nearby or if it is spatially outside the range of the suite of input sensors, the reconstructed riser response will be inaccurate. Given these limitations, the modified WWA, POD and MPR methods are not employed in this study that considers only eight input sensors; only the WWA and the hybrid methods are employed to estimate fatigue damage rates at the twenty-four locations along the NDP model riser using measurements from eight sensors. The base-10 logarithms of the 24 variability factors estimates from the WWA method based on eight sensors in each of the thirty-four combinations are presented as box-and-whisker plots in Figure 11a,b, which summarize results for the two uniform current data sets and the two sheared current data sets, respectively.