'Lumping' of Fatigue Load Cases

Garrad Hassan & Partners Ltd. 

Mungo Morris 

‘Lumping’ of Fatigue Load Cases 

Introduction 

An investigation was carried out to determine the minimum number of load cases required to 

calculate the fatigue loading of offshore wind turbines whilst maintaining acceptable 

accuracy. The study was prompted by the observation that the three dimensions of the wave 

height / wave period / wind speed scatter diagram could potentially require a very large 

number of load cases to be examined. During this study, the meteorological data was binned 

into progressively larger bin sizes and the changes in the fatigue loads were calculated 

relative to a set of baseline results which were themselves calculated using a high level of bin 

resolution. 

Turbine model and environmental data 

The model used for the calculations was that of a variable speed, pitch regulated 2MW 

generic offshore turbine. The fundamental properties of the turbine are presented in Table 1: 

Rotor configuration 

3-bladed upwind 

Rotor Diameter 

65m 

Hub Height 

60m 

1 st Tower fundamental fore-aft frequency 0.48Hz (1.38P) 

2 nd Tower fundamental fore-aft frequency 3.12Hz (8.96P) 

1 st Tower fundamental side-side frequency 0.47Hz (1.35P) 

2 nd Tower fundamental side-side frequency 2.91Hz (8.36P) 

Table 1 

The environmental data was taken from the NESS database of wind and sea state for a 

position off the Dutch coast. 

Baseline study 

The data within the 3-dimensions of the wind speed / significant wave height / wave period 

scatter diagram were initially binned with windspeed, wave height and period bin widths of 

2m/s, 0.5m and 0.5s respectively. This resulted in a 14 × 13 × 16 matrix of probability values, 

of which there were 204 non-zero elements. This was considered the baseline case, at the 

highest practical definition, against which results from coarser bin resolutions were compared. 

In addition to calculating the probability of occurrence of each bin, mean values of wave 

height and period where calculated for each bin. The ‘damage equivalent load mean wave 

height’ differs from the arithmetic mean because the fatigue damage is proportional to the 

load created by the waves, to the power of the inverse SN slope m: 

Damage ∝ 

where Hs is the significant wave height. 

S 

m 

∝ 

Hs 

m


Mungo Morris 

Consequently the equation for the DEL mean wave height is: 

Hs = 

⎛ 

⎜ 

⎝ 

1 

N 

N 

∑ i = 1 

In contrast, for the wave period, the fatigue damage is approximately proportional to the 

number of cycles, and the appropriate mean is therefore the arithmetic mean of the wave 

periods within each bin * . In addition, the mean wind speed within each bin was not calculated 

– all values that fell between 5 and 7m/s, for example, were considered to have a mean wind 

speed of 6m/s. This is consistent with the normal approach for simulating wind speed 

distributions for onshore turbines. 

Damage equivalent loads were calculated at key points in the turbine structure for inverse SN 

slope values of 4, 6, 8 and 10 and assuming a frequency of 1Hz. 

Having calculated the initial fatigue loads using the probability distribution of the 204 

simulations, the same process was then repeated for increasingly larger bin sizes of wave 

height and period. In all cases, the wind speed bin size was kept at 2m/s to reflect the current 

practice for onshore wind distribution simulation. The full range of bin sizes covered are 

shown in Figure.1. 

Hs 

m 

i 

1 

m 

⎞ 

⎟ 

⎠ 

3 

2.5 

Wave period bin size [s] 

2 

1.5 

1 

0.5 

0 

0 0.5 1 1.5 2 2.5 3 

Significant wave height bin size [m] 

Figure 1. Bin size combinations 

When comparing the fatigue loads generated by these ‘coarser’ bin sizes with the original 

base-line loads, it became apparent that the reduction in resolution in bin sizes had very little 

effect on the final fatigue loads generated. 

* In Hindsight it would have been more correct to have averaged (1/Period), but this would not change 

the conclusions significantly.


Mungo Morris 

To confirm the above observations, three bin resolutions were considered in greater detail 

(See Table 2 and Figure 2). The final set of simulations, Series 3, is the extreme case which 

features only one simulation per wind speed – i.e. the height and period bin size covers the 

whole range of data resulting in one DEL mean value of wave height and period for all 

simulations. 

Wind speed bin 

width (m/s) 

Wave height bin 

width (m) 

Wave period bin 

width (s) 

Number of 

simulations 

Series 1 2 0.5 0.5 204 

Series 2 2 2.5 2.5 39 

Series 3 2 6.0 6.5 14 

Table 2: Simulation types 

Figure 2: Comparison of bin sizes 

. 

The results of this analysis are presented in tables 3 to 5 below. Due to the large quantity of 

data generated, the decision was taken to analyse only the loads which were likely to be 

affected by waves running in a fore–aft direction.


Mungo Morris 

Inverse SN slope 

4 6 8 10 

Blade 1 Root My 228.34 348.69 465.42 571.40 

Blade 1 Root Fx 12.09 17.88 23.44 28.61 

Blade 1 Flapwise moment 234.48 358.66 475.99 582.70 

Blade 1 Flapwise force 13.10 19.47 25.08 30.08 

Rotating hub Fx 22.36 35.61 46.59 55.88 

Tower Base My 2419.55 3550.89 4590.65 5508.01 

Tower Base Fx 189.26 285.18 387.43 495.88 

Tower Top My 246.41 336.75 429.09 517.14 

Tower Top Fx 25.09 40.11 53.11 64.55 

Table 3: Series 1 - Fatigue loads for wave height and period bin sizes of 0.5m and 0.5s 

respectively (in kNm) 


4 6 8 10 

Blade 1 Root My 228.38 348.74 465.46 571.41 

Blade 1 Root Fx 12.09 17.88 23.45 28.62 




Tower Base My 2424.67 3544.61 4566.12 5468.30 

Tower Base Fx 191.04 285.12 382.86 486.14 

Tower Top My 246.42 336.76 429.06 517.10 

Tower Top Fx 25.10 40.12 53.13 64.61 




4 6 8 10 

Blade 1 Root My 228.35 348.70 465.43 571.40 

Blade 1 Root Fx 12.09 17.88 23.44 28.60 




Tower Base My 2411.54 3541.25 4595.88 5543.22 

Tower Base Fx 192.69 282.88 372.23 461.06 

Tower Top My 246.49 336.83 429.06 516.94 

Tower Top Fx 25.04 40.03 53.01 64.45 



Table 6 shows the percentage changes between results for series 2 and series 1, and between 

series 3 and series 1. The applicable values of inverse SN slope for each load are highlighted. 

It can be seen that the variation in DEL, even when all the wave heights and periods are


Mungo Morris 

condensed into single values at each wind speed, never exceeds 2% (Tower Base Fx), and 

many other loads are almost unaffected. 

Series 2 Series 3 

4 6 8 10 4 6 8 10 

Blade 1 Root My 0.02 0.02 0.01 0.00 0.00 0.00 0.00 0.00 

Blade 1 Root Fx -0.01 0.01 0.03 0.04 -0.01 -0.02 -0.02 -0.01 

Blade 1 Flap moment 0.00 0.00 0.01 0.01 -0.01 -0.01 0.00 -0.01 

Blade 1 Flap force 0.00 0.00 -0.01 -0.01 0.00 -0.02 -0.02 -0.02 

Rotating hub Fx 0.00 -0.04 -0.06 -0.06 -0.02 -0.04 -0.05 -0.05 

Tower Base My 0.21 -0.18 -0.53 -0.72 -0.33 -0.27 0.11 0.64 

Tower Base Fx 0.94 -0.02 -1.18 -1.96 1.81 -0.81 -3.92 -7.02 

Tower Top My 0.01 0.00 -0.01 -0.01 0.03 0.02 -0.01 -0.04 

Tower Top Fx 0.03 0.02 0.04 0.09 -0.19 -0.20 -0.19 -0.16 

Table 6: Variation in load from original base-line case (percent) 

A possible explanation for the very small changes in fatigue loads is that the wave loading 

itself makes a very small contribution to the total fatigue loading. To check this possibility, 

two simulations, one with waves present and one without waves, were run and damage 

equivalent loads calculated. If there was negligible difference between the loads generated by 

both runs then this would be evidence that the wave action had an insignificant affect on the 

fatigue loads. These simulations were performed at a wind speed of 6.56m/s (the mode of the 

wind speed distribution) and, in one case, with a significant wave height of 1.0m and a peak 

spectral period of 3.9s. The percentage increases in tower loads due to the inclusion of the 

waves is presented in table 7. 


4 6 8 10 

Tower Base My 8.11% 9.83% 10.11% 10.19% 

Tower Base Fx 279.64% 270.51% 243.94% 229.54% 

Tower Top My 0.02% 0.01% 0.00% 0.00% 

Tower Top Fx -0.12% -0.04% -0.01% 0.00% 

Table 7: Fatigue load increase due to presence of wave 

It can be seen from Table 7 that, although all tower top loads are little affected by the 

presence of the wave in the simulation, the tower base loads are strongly affected – the foreaft 

tower base force in particular. From Table 6 one can see that this is the same load that 

varied by only 1.8% when all 204 initial simulations were ‘lumped’ into 1 value of wave 

height and period for all simulations. One must therefore conclude that, despite having a 

strong influence on the fatigue loading of the turbine, the effect of waves can be simply and 

accurately modelled by using large bin size means of the wave height and period in all 

simulations.

'Lumping' of Fatigue Load Cases

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?