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

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

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

Michel Olagnon

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

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

Simple Summation: add independent damages... …yet: 10 + 1 = 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

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

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

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

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

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

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

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

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

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

Which is the widest ? Michel Olagnon

 = 0.776  = 0.604 Michel Olagnon

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

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

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

Are the components independent ? Michel Olagnon