FATIGUE COUNTS

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FATIGUE COUNTS

Rainflow, zero-crossing, bandwidth, etc.

Michel Olagnon

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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

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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

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Michel Olagnon

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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

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Zero-crossing finds the same large ranges as alltransitions, whereas they are larger with rainflow: rainflow associates high peaks to low valleys and smaller peaks to less deep valleys.

-> Hélène

Michel Olagnon

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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 4m=4 -> damage ~ 346

Michel Olagnon

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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

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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

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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

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RAINFLOW COUNTS

• 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

The new formulae D = (NH-NL)/NH DH + F(, , m) DL

-> Zakoua

Michel Olagnon

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RAINFLOW COUNTS

What does accuracy mean ?

Michel Olagnon

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RAINFLOW COUNTS

Sensitivity to spectral bandwidth secondary wrt aleatory uncertainty.

Michel Olagnon

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RAINFLOW COUNTS

How much conservatism is needed ?How much is too much ?

92%

Michel Olagnon

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West Africa Spectra -> Wide band wave actionMooring responses -> Composite signalsWhat does wide-band mean ?

Michel Olagnon

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

Michel Olagnon

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Which is the widest ?

Michel Olagnon

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= 0.776

= 0.604

Michel Olagnon

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

Michel Olagnon

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

Michel Olagnon

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Do we need double slopes ? Can we use thresholds ?

Michel Olagnon

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Are the components independent ?