1. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS First results

2. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS A few topics: A. How conservative is the narrow-band approximation for a unimodal spectrum ? B. How good are MC simulations wrt exact WAFO calculations ? C. How good are the various formulas ? D. What is a “conservative climate” ?

3. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS A. How conservative is the narrow-band approximation for a unimodal spectrum ? It may be noted that M 0 and M 2 are normalizing factors, and thus normalized damage for a Pierson-Moskowitz depends only on m, for a Jonswap on m and , etc. Sensitivity to spectral bandwidth. Sensitivity to spectral shape. Sensitivity to cut-off frequency.

4. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS Sensitivity to spectral bandwidth.

5. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS Sensitivity to spectral bandwidth.

6. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS Sensitivity to amplitude filtering.

7. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS Sensitivity to cut-off frequency. (without M 0 correction)

8. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS Sensitivity to cut-off frequency. (with M 0 correction)

9. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS Sensitivity to cut-off frequency. A simple way to find a reasonable cut-off frequency for waves : For amplitudes less than 0.2 H S, we see no change in the damage when filtering them out. Assuming a global steepness of the sea state of 6% (wind sea), waves of 0.2 H S break for periods smaller than T Z / 3.5. It is thus reasonable to cut the spectrum at about 4 f p of the wind sea. In the case of a Pierson-Moskowitz spectrum, the resulting  is 0.66, i.e. same as for white noise.

10. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS B. How good are MC simulations wrt exact WAFO calculations ? Sensitivity to the number of simulations. Sensitivity to alea modeling (random phases/complex spectrum). Sensitivity to stationarity (high- or low-frequency consisting of impulse-like responses from time to time).

11. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS Sensitivity to the number/length of simulations.

12. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS Sensitivity to the number/length of simulations.

13. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS C. How good are the various formulas ? vs. , the normalized low-frequency standard-deviation vs. , the normalized low-frequency number of cycles vs. the bandwidth of the high-frequency signal.

14. Zakoua Guédé & Michel Olagnon RAINFLOW COUNTS The new formulae D = (N H -N L )/N H D H + F( , , m) D L M L distributed as the maximum of N H /N l maxima of the global signal : D = (1-  ) D H + Z 1 (m,  ) ((1-  2 )/(1-  2 )) m/2 D L M L distributed as the highest N H /N l maxima of the global signal : D = (1-  ) D H + Z 2 (m,  ) ((1-  2 )/(1-  2 )) m/2 D L M L distributed as the highest N H /N l narrow-band maxima of the global signal : D = (1-  ) D H + Q(m/2+1, -Ln(  )) / (1-  2 ) m/2 D L D DNB = (1-  ) D H + (1+  /  (1-  2 )) m D L