1. Multi-component Sea States
and Unavoidable Fatigue Design Headaches
17/11/2018
Michel Olagnon & Zakoua Guédé

2. Standard Fatigue Design Procedure Michel Olagnon & Zakoua Guédé
Sea states database:
H,T,, probability of occurrence
Discretization of the database, selection of a few representative sea states
Order of magnitude:
102 to 103
Computation of responses and stresses for that subset
Rainflow cycle-counting and damage computation
Simulations
RAOs, QTFs
FE Models
Summation of damages with the probabilities of occurrence
17/11/2018
Michel Olagnon & Zakoua Guédé

3. Michel Olagnon & Zakoua Guédé
Systems database:
H,T,, probability of occurrence
Parameters space:
9 dimensions or more
Sea states database:
H1,T1,1, H2,T2,2, H3,T3,3, joint probability of occurrence
Discretization of the sea states database results from that of the systems, selection of the representative sea states, computation of responses for that subset
Order of magnitude:
106 to 109
Summation of damages with the joint probabilities of occurrence
17/11/2018
Michel Olagnon & Zakoua Guédé

4. At first, we were very happy with our solution
Systems database:
H,T,, probability of occurrence
Order of magnitude:
102 to 103
Discretization of the systems, selection of the representative systems, computation of responses to single systems
Joint probabilities of occurrence
ICA
Order of magnitude:
106 to 109
Combination of damages and summation with the joint probabilities of occurrence
17/11/2018
Michel Olagnon & Zakoua Guédé

5. We were arriving to a swift and neat alternative
Measured sea states
SPOP +
RAO +
????
RAO
Response to each sea state
Response systems
climate
Simulation
Unimodal
formulas
Damage in each sea state
Damage in each « system »
Summation
ICA
Scaling to the foreseen life of the structure
Application of joint probabilities
We were arriving to a swift and neat alternative
17/11/2018
Michel Olagnon & Zakoua Guédé

6. …we had just forgotten something
Joint probabilities of occurrence
17/11/2018
Michel Olagnon & Zakoua Guédé

7. Michel Olagnon & Zakoua Guédé
Joint Probabilities
8040 Measured sea states
SPOP
8038 Main Swells
5464 Secondary Swells
4169 Wind Seas
Metocean Specifications
17/11/2018
Michel Olagnon & Zakoua Guédé

8. Michel Olagnon & Zakoua Guédé
Joint Probabilities
Metocean Specifications
Each sea state contains a Main Swell
Probabilities should be respected, marginaly within each system type, and for combinations of types.
« Unrealistic » combinations should be [merged or] excluded
Components (systems) occur independently
A combination is « unrealistic » if it contradicts the partitionning criteria, for instance ratio of the peak periods between 1/1.2 and 1.2 and directions differing by less than 45°.
17/11/2018
Michel Olagnon & Zakoua Guédé

9. Michel Olagnon & Zakoua Guédé
Joint Probabilities
Metocean specifications
Empirical parameters distributions for each kind of system
Joint probability for system kinds p(MS,SS,WS)
Reconstructed systems climate
17/11/2018
Michel Olagnon & Zakoua Guédé

10. Michel Olagnon & Zakoua Guédé
A combination is « unrealistic » if it contradicts the partitionning criteria.
=> Discretization problem:
Two systems may meet the criteria, but not the representatives of the discretization classes that they belong too, and conversely.
=> Probabilities problem:
What should be done with a rejected combination ? Merge or discard ? How should that be reflected on the target probabilities ?
17/11/2018
Michel Olagnon & Zakoua Guédé

11. Michel Olagnon & Zakoua Guédé
Discretization problem:
Two systems may meet the criteria, but not the representatives of the discretization classes that they belong too, and conversely.
Suit the discretization to the criteria:
Use log-scale (multiplicative) classes for the periods (Log(1.2)/2)
Use half criterion threshold as class width for directions (22.5°) and the log(period).
Reduce bias between actual values and class-representative by centering a class on the modal value
As a result and using 0.5 m class-width for Hs, observed MS fall into 169 classes, SS into 148, WS into 165.
Given the specs, « only » 1.9 million of the 4.2 million combinations are allowed to occur.
17/11/2018
Michel Olagnon & Zakoua Guédé

12. Michel Olagnon & Zakoua Guédé
Main Swell Hs-Tp
17/11/2018
Michel Olagnon & Zakoua Guédé

13. Michel Olagnon & Zakoua Guédé
Secondary Swell Hs-Tp
17/11/2018
Michel Olagnon & Zakoua Guédé

14. Michel Olagnon & Zakoua Guédé
Wind Sea Hs-Tp
17/11/2018
Michel Olagnon & Zakoua Guédé

15. Michel Olagnon & Zakoua Guédé
Assemblage
Start from our 169 MS classes, 148 SS classes, 165 WS classes.
Apply acceptance criteria of the specs to the database, and obtain a corrected database where it is no longer possible to violate criteria
Randomly draw the type of combination amongst MS, MS+SS, MS+WS, MS+SS+WS
Randomly draw each system to be combined according to the distribution of its kind
Apply acceptance criteria of the specs and reject systems that would not have been distinguished in a partitionning process.
17/11/2018
Michel Olagnon & Zakoua Guédé

16. Michel Olagnon & Zakoua Guédé
17/11/2018
Michel Olagnon & Zakoua Guédé

17. Michel Olagnon & Zakoua Guédé
17/11/2018
Michel Olagnon & Zakoua Guédé

18. Probabilities problem Michel Olagnon & Zakoua Guédé
Rejected « impossible » combinations are in contradiction with the independent wave systems assumption.
The independent wave systems assumption itself has not been validated (nor even attempted to).
Yet we need some assumptions since we cannot expect 8000 observations of combinations to provide much help in defining the probabilities of occurrence of the 1.9 million possible combinations given the [nevertheless sensible] discretization.
17/11/2018
Michel Olagnon & Zakoua Guédé

19. Michel Olagnon & Zakoua Guédé
How good are the specs-derived occurrence probabilities for those « only » 1.9 million combinations ?
17/11/2018
Michel Olagnon & Zakoua Guédé

20. Michel Olagnon & Zakoua Guédé
17/11/2018
Michel Olagnon & Zakoua Guédé

21. Michel Olagnon & Zakoua Guédé
How good are the specs-derived occurrence probabilities for those « only » 1.9 million combinations ?
Far from perfect.
A better question:
17/11/2018
Michel Olagnon & Zakoua Guédé

22. That question « concludes » my presentation.
How can we build specifications that would enable swift construction of an accurate sea states climate from a wave systems climate ?
That question « concludes » my presentation.
17/11/2018
Michel Olagnon & Zakoua Guédé

23. Multi-component Sea States
Thank you in advance !
and Unavoidable Fatigue Design Headaches
17/11/2018
Michel Olagnon & Zakoua Guédé