1. Rainflow, zero-crossing, bandwidth, etc.
FATIGUE COUNTS
Rainflow, zero-crossing, bandwidth, etc.
Michel Olagnon

2. RAINFLOW COUNTS The on-going study:
1. West-Africa spectra are different from those that we are used to. We need first to check our analysis methods in such cases.
2. It seems impossible to calculate through all combinations of the values of a dozen parameters describing sea states. We need ways to combine the damages created by the components of the sea states at the final stage only.
3. How do we select the calculation cases from the climate description and from the combination formulas ?
Michel Olagnon

3. RAINFLOW COUNTS
Time domain analysis in a composite signal context (Hélène Pineau - Actimar)
Spectral domain - Simple summation and alternatives (Michel Olagnon - Ifremer)
Preliminary results with combination formulas (Zakoua Guédé - Ifremer)
Michel Olagnon

4. Michel Olagnon

5. With respect to counting all transitions, zero-crossing removes most of the small ranges, and rainflow turns medium-small ranges into smaller ones and, as we will see better on the next figure, into enlargement of the largest ones.
Michel Olagnon

6. Zero-crossing finds the same large ranges as all
transitions, whereas they are larger with rainflow:
rainflow associates high peaks to low valleys and smaller peaks to less deep valleys.
-> Hélène
Michel Olagnon

7. Simple Summation: add independent damages...
…yet:
= 11 cycles range 2,
m=4 -> damage ~ 176
9 cycles range 1.78 in average, 1 cycle range 4
m=4 -> damage ~ 346
Michel Olagnon

8. Simple summation is not conservative, yet it would be nice to still be able to compute separately damage for each component and to have a (non-linear) way to make the combination.
Michel Olagnon

9. RAINFLOW COUNTS Separate the turning points into two sets:
* The maximum (and resp. minimum) over each interval where the low frequency signal is positive (resp. negative)
* The other turning points
Michel Olagnon

10. RAINFLOW COUNTS The Simple Summation formula D = DH + DL
The Combined Spectrum formula D = NH+L((DH/NH)2/m + (DL/NL)2/m)m/2
The DNB formula D = (NH-NL)/NH DH + NL((DH/NH)1/m + (DL/NL)1/m)m
The new formulae D = (NH-NL)/NH DH + Z(L/H+L ,NL/NH, m) DL
The CNB (Jiao-Moan) formula
D = F1(L/H+L ,NL/NH, m) DH + F2(L/H+L ,NL/NH, , m) DL
The “exact” formula D = WAFO (Combined Spectrum)
Michel Olagnon

11. RAINFLOW COUNTS -> Zakoua
The new formulae D = (NH-NL)/NH DH + F(, , m) DL
ML distributed as the maximum of NH/Nl maxima of the global signal : D = (1-)DH + Z1(m, ) ((1-2)/(1-2))m/2 DL
ML distributed as the highest NH/Nl maxima of the global signal : D = (1-)DH + Z2(m, ) ((1-2)/(1-2))m/2 DL
ML distributed as the highest NH/Nl narrow-band maxima of the global signal: D = (1-)DH + 1/ Q(m/2+1, -Ln()) / (1-2)m/2 DL
ML distributed as the sum of two Rayleigh variables (Igor).
DDNB = (1-) DH + (1+  /(1-2))m DL
-> Zakoua
Michel Olagnon

12. What does accuracy mean ?
RAINFLOW COUNTS
What does accuracy mean ?
Michel Olagnon

13. Sensitivity to spectral bandwidth secondary wrt aleatory uncertainty.
RAINFLOW COUNTS
Sensitivity to spectral bandwidth secondary wrt aleatory uncertainty.
Michel Olagnon

14. How much conservatism is needed ?
RAINFLOW COUNTS
How much conservatism is needed ?
How much is too much ?
92%
Michel Olagnon

15. West Africa Spectra -> Wide band wave action
Mooring responses -> Composite signals
What does wide-band mean ?
Michel Olagnon

16. Is this a wideband spectrum ?
If yes, is it because of the ears or of the tail ?
Michel Olagnon

17. Which is the widest ?
Michel Olagnon

18.  = 0.776
 = 0.604
Michel Olagnon

19. Effect on the rainflow ranges distribution when removing the spectrum tail: very similar to removing the smallest cycles.
Michel Olagnon

20. What kind of S-N curve slopes are we designing for ?
Michel Olagnon

21. Do we need double slopes ? Can we use thresholds ?
Michel Olagnon

22. Are the components independent ?
Michel Olagnon