Zakoua Guédé & Michel Olagnon

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RAINFLOW COUNTS

First results

Zakoua Guédé & Michel Olagnon

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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” ?

Zakoua Guédé & Michel Olagnon

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RAINFLOW COUNTS

A. How conservative is the narrow-band approximation for a unimodal spectrum ?

It may be noted that M0 and M2 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.

Zakoua Guédé & Michel Olagnon

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RAINFLOW COUNTS

Sensitivity to spectral bandwidth.

Zakoua Guédé & Michel Olagnon

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RAINFLOW COUNTS

Sensitivity to spectral bandwidth.

Zakoua Guédé & Michel Olagnon

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RAINFLOW COUNTS

Sensitivity to amplitude filtering.

Zakoua Guédé & Michel Olagnon

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RAINFLOW COUNTS

Sensitivity to cut-off frequency.(without M0 correction)

Zakoua Guédé & Michel Olagnon

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RAINFLOW COUNTS

Sensitivity to cut-off frequency.(with M0 correction)

Zakoua Guédé & Michel Olagnon

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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 HS, 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 HS break for periods smaller than TZ/ 3.5. It

is thus reasonable to cut the spectrum at about 4 fp of

the wind sea.

In the case of a Pierson-Moskowitz spectrum, the

resulting is 0.66, i.e. same as for white noise.

Zakoua Guédé & Michel Olagnon

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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).

Zakoua Guédé & Michel Olagnon

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RAINFLOW COUNTS

Sensitivity to the number/length of simulations.

Zakoua Guédé & Michel Olagnon

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RAINFLOW COUNTS

Sensitivity to the number/length of simulations.

Zakoua Guédé & Michel Olagnon

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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.

Zakoua Guédé & Michel Olagnon

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RAINFLOW COUNTS

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 + Q(m/2+1, -Ln()) / (1-2)m/2 DL

• DDNB = (1-) DH + (1+ /(1-2))m DL