zakoua guédé & michel olagnon rainflow counts first results
TRANSCRIPT
Zakoua Guédé & Michel Olagnon
ww
w.i
fre
me
r.fr
lfre
mer
RAINFLOW COUNTS
First results
Zakoua Guédé & Michel Olagnon
ww
w.i
fre
me
r.fr
lfre
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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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lfre
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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
ww
w.i
fre
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r.fr
lfre
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RAINFLOW COUNTS
Sensitivity to spectral bandwidth.
Zakoua Guédé & Michel Olagnon
ww
w.i
fre
me
r.fr
lfre
mer
RAINFLOW COUNTS
Sensitivity to spectral bandwidth.
Zakoua Guédé & Michel Olagnon
ww
w.i
fre
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r.fr
lfre
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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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w.i
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lfre
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RAINFLOW COUNTS
Sensitivity to cut-off frequency.(with M0 correction)
Zakoua Guédé & Michel Olagnon
ww
w.i
fre
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r.fr
lfre
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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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lfre
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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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w.i
fre
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r.fr
lfre
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RAINFLOW COUNTS
Sensitivity to the number/length of simulations.
Zakoua Guédé & Michel Olagnon
ww
w.i
fre
me
r.fr
lfre
mer
RAINFLOW COUNTS
Sensitivity to the number/length of simulations.
Zakoua Guédé & Michel Olagnon
ww
w.i
fre
me
r.fr
lfre
mer
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
ww
w.i
fre
me
r.fr
lfre
mer
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