PSI - Issue 5

Rui Teixeira et al. / Procedia Structural Integrity 5 (2017) 951–958 Teixeira,R.; O’Connor, A.; Nogal, M.; Krishnan, N.; Nichols J / Structural Integrity Procedia 00 (2017) 000 – 000

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wind is already over the rated-speed, and therefore the local sensitivity is lower. The Case 7 and 8 confirms the trends identified before. Table 1 – Variation of the sample mean and standard deviation properties function of the parameter modified in the DoE. 0 Case 1 1.16 × 10 −6 (820%) 0.11 × 10 −7 (7.9%) −0.18 × 10 −7 (−12%) 0.12 × 10 −6 (124%) 0.05 × 10 −7 (3.7%) Case 2 −0.17 × 10 −6 (−8.5%) 0.28 × 10 −6 (13.8%) 0.85 × 10 −7 (4.18%) 2.93 × 10 −6 (143%) 0.12 × 10 −6 (5.7%) Case 3 9.63 × 10 −8 (1138%) −0.21 × 10 −8 (−24%) −0.34 × 10 −8 (−40%) 1.07 × 10 −8 (218%) −0.15 × 10 −8 (−18.7%) Case 4 2.3 × 10 −6 (84.3%) −1.1 × 10 −7 (−4%) −5.3 × 10 −7 (−19%) 3.98 × 10 −6 (146%) −3.9 × 10 −7 (−14.3%) Case 5 2.52 × 10 −7 (18.3%) 1.75 × 10 −7 (12.7%) 1.66 × 10 −7 (12.1%) 6.19 × 10 −7 (45.1%) 1.82 × 10 −7 (13.3%) Case 6 1.26 × 10 −6 (370%) −6.2 × 10 −8 (−18.4%) −0.11 × 10 −7 (−3.2%) 2.42 × 10 −7 (71.3%) −0.73 × 10 −7 (−21.5%) Case 7 2.39 × 10 −7 (107%) 1.60 × 10 −8 (7.2%) 0.5 × 10 −8 (2.2%) 3.63 × 10 −7 (163%) 2.74 × 10 −8 (12.3%) Case 8 8.4 × 10 −8 (−9.2%) 3.2 × 10 −8 (3.5%) 9.7 × 10 −8 (10.6%) 1.00 × 10 −6 (110%) 2.4 × 10 −8 (2.6%) 0 0 0 0 0 0 Case 1 2.41 × 10 −7 (495%) 1.79 × 10 −8 (36.6%) −7.4 × 10 −9 (−15.2%) 7.69 × 10 −8 (158%) 1.32 × 10 −8 (27.15%) Case 2 1.9 × 10 −9 (0.40%) 1.55 × 10 −7 (31.8%) 8.88 × 10 −8 (18.2%) 5.35 × 10 −7 (110%) 4.85 × 10 −8 (9.96%) Case 3 3.79 × 10 −8 (483%) −4.4 × 10 −9 (−55.9%) −5.2 × 10 −9 (−66.6%) 6.9 × 10 −8 (88.3%) −5.1 × 10 −9 (−65.1%) Case 4 2.20 × 10 −7 (29.2%) −2.62 × 10 −7 (−34.7%) −3.43 × 10 −7 (−45.5%) 9.89 × 10 −7 (130%) −2.78 × 10 −7 (−36.9%) Case 5 1.29 × 10 −8 (4.42%) 5.56 × 10 −8 (19%) 5.84 × 10 −8 (20%) 6.4 × 10 −9 (2.17%) 8.2 × 10 −8 (28%) Case 6 1.94 × 10 −7 (156%) −6.66 × 10 −8 (−53.3%) −3.4 × 10 −9 (−2.7%) 2.97 × 10 −8 (23.8%) −8.21 × 10 −8 (−65.7%) Case 7 6.41 × 10 −8 (137%) 1.31 × 10 −8 (27.9%) 0.97 × 10 −9 (2.1%) 8.11 × 10 −8 (1.73%) 3.25 × 10 −8 (69.3%) Case 8 −6.97 × 10 −8 (−20.6%) −3.40 × 10 −8 (−10.1%) 2.85 × 10 −7 (8.4%) 2.34 × 10 −7 (69.4%) −9.4 × 10 −8 (−27.8%) The sample standard deviation is a statistical moment that converges slower than the sample mean . The precise analysis of results is then more difficult when the variation of the standard deviation is not very substantial. In this case it is difficult to weight the contribution from the sensitivity itself and from the stochastic convergence of the standard deviation. converges significantly more slowly than the . This convergence depends highly on the sample. In all the case the major variations of standard deviation occur in the same case where the variation of is higher, indicating that an offset of is very likely to be accompanied by a change of the whole population distribution moments. As recommendations from the indicators obtained in the results, when building a Kriging surface, are:  Uncertainty of the short-term damage is quite significant, and standard deviations are in average between 25-30% of the mean over the rated speed. For lower wind speeds, below rated power, where the damage generated is less important for the structure, this value ascends to almost 50%.  and should always be considered in the DoE of a Kriging surrogate surface to assess the reliability of an OWT tower. Making this the dimension of the Kriging surface at least 2.  As the variation of statistical parameters is quite high for low number of simulations, assessing the uncertainty introduced by the wave parameters can be taken as redundant in comparison to the intrinsic uncertainty of the . For severe sea states and states where the wind is not prominent in the results these can be important. Therefore it may be reasonable to model these variables in the DoE or to truncate the Kriging to account for the uncertainty in the regions of interest in the cases where the wave parameters show influence on .  The influence over is limited. The yaw control system was not modeled, still the results obtained indicate that for small wind directions the damage the change in are not relevant. It is important to emphasize that the complexity that affects the OWT is high and other parameters (e.g. structural model, tower diameter or thickness, among others) may be included in the analysis. Nevertheless, these are not the main focus of the Kriging surface as a tool for reliability because they are usually seen as design variables to be set in order to comply with the environmental loading requirements. In particular, the OWT tower thickness and diameter are expected to have a relevant influence in the fatigue life. 0 0 0 0 0