This paper presents a generic Monte Carlo-based approach for bivariate extreme response prediction for fixed offshore structures, particularly jacket type. The bivariate analysis of extremes is often poorly understood and generally not adequately considered in most practical measurements/situations; that is why it is important to utilize the recently developed bivariate average conditional exceedance rate (ACER) method. According to the current literature study, there is not yet a direct application of the bivariate ACER method to coupled offshore jacket stresses. This study aims at being first to apply bivariate ACER method to jacket critical stresses, aiming at contributing to safety and reliability studies for a wide class of fixed offshore structures. An operating jacket located in the Bohai bay was taken as an example to demonstrate the proposed methodology. Satellite measured global wave statistics was used to obtain realistic wave scatter diagram in the jacket location area. Second-order wave load effects were taken into account, while simulating jacket structural response. An accurate finite element ANSYS model was used to model jacket response dynamics, subject to nonlinear hydrodynamic wave and sea current loads. Offshore structure design values are often based on univariate statistical analysis, while actually multivariate statistics is more appropriate for modeling the whole structure. This paper studies extreme stresses that are simultaneously measured/simulated at two different jacket locations. Due to less than full correlation between stresses in different critical jacket locations, application of the multivariate (or at least bivariate) extreme value theory is of practical engineering interest.

References

References
1.
Lv
,
X.
,
Yuan
,
D.
,
Ma
,
X.
, and
Tao
,
J.
,
2014
, “
Wave Characteristics Analysis in Bohai Sea Based on ECMWF Wind Field
,”
Ocean Eng.
,
91
, pp.
159
171
.
2.
Wang
,
Z.
,
Wu
,
K.
,
Zhou
,
L.
, and
Wu
,
L.
,
2012
, “
Wave Characteristics and Extreme Parameters in the Bohai Sea
,”
China Ocean Eng.
,
26
(
2
), pp.
341
350
.
3.
BMT Fluid Mechanics, 2011, “
Global Wave Statistics
,” BMT Fluid Mechanics Limited, Teddington, UK, accessed Mar. 16, 2018, http://www.globalwavestatisticsonline.com/
4.
DNV,
2011
, “Modelling and Analysis of Marine Operations,” Det Norske Veritas, Norway, Oslo, Standard No.
DNV-RP-H103
.https://rules.dnvgl.com/docs/pdf/DNV/codes/docs/2011-04/RP-H103.pdf
5.
DNV,
2010
, “Environmental Conditions and Environmental Loads,” Det Norske Veritas, Norway, Oslo, Standard No.
DNV-RP-C205
.https://rules.dnvgl.com/docs/pdf/dnv/codes/docs/2010-10/rp-c205.pdf
6.
Wilson
,
J.
,
1984
,
Dynamics of Offshore Structures
,
Wiley
,
New York
.
7.
Sarpkaya
,
T.
, and
Isaacson
,
M.
,
1981
,
Mechanics of Wave Forces on Offshore Structures
,
Van Nostrand Reinhold
,
New York
.
8.
Naess
,
A.
, and
Moan
,
T.
,
2005
, “
Probabilistic Design of Offshore Structures
,”
Handbook of Offshore Engineering
, Vol.
1
,
S. K.
Chakrabarti
, ed.,
Elsevier
,
Amsterdam, The Netherlands
, pp.
197
277
.
9.
Naess
,
A.
, and
Moan
,
T.
,
2013
,
Stochastic Dynamics of Marine Structures
,
Cambridge University Press
, Oxford, UK.
10.
Ewans
,
K.
,
2014
, “
Evaluating Environmental Joint Extremes for the Offshore Industry Using the Conditional Extremes Model
,”
J. Mar. Syst.
,
130
, pp.
124
130
.
11.
Heffernan
,
J. E.
, and
Tawn
,
J. A.
,
2004
, “
A Conditional Approach for Multivariate Extreme Values
,”
J. R. Stat. Soc.: Ser. B
,
66
(
3
), pp.
497
546
.
12.
Jensen
,
J. J.
, and
Capul
,
J.
,
2006
, “
Extreme Response Predictions for Jack-Up Units in Second-Order Stochastic Waves by FORM
,”
Probab. Eng. Mech.
,
21
(
4
), pp.
330
337
.
13.
Zhao
,
Y. G.
, and
Ono
,
T.
,
1999
, “
A General Procedure for First/Second Order Reliability Method (FORM/SORM)
,”
Struct. Saf.
,
21
(
2
), pp.
95
112
.
14.
Gumbel
,
E. J.
,
1960
, “
Bivariate Exponential Distributions
,”
J. Am. Stat. Assoc.
,
55
(
292
), pp.
698
707
.
15.
Gumbel
,
E. J.
,
1961
, “
Bivariate Logistic Distributions
,”
J. Am. Stat. Assoc.
,
56
(
294
), pp.
335
349
.
16.
Gumbel
,
E. J.
, and
Mustafi
,
C. K.
,
1967
, “
Some Analytical Properties of Bivariate Extremal Distributions
,”
J. Am. Stat. Assoc.
,
62
(
318
), pp.
569
588
.
17.
Balakrishnan
,
N.
, and
Lai
,
C.-D.
,
2009
,
Continuous Bivariate Distributions
,
Springer Science Business Media
,
New York
.
18.
Sklar
,
M.
,
1959
,
Fonctions De Repartition Dimensions Et Leurs Marges
, Vol.
8
,
Publications of the Institute of Statistics of the University of Paris
,
Paris, France
, pp.
229
231
.
19.
Nelsen
,
R. B.
,
2006
,
An Introduction to Copulas
(Springer Series in Statistics),
Springer Science Business Media
,
New York
.
20.
Kaufmann
,
E.
, and
Reiss
,
R.-D.
,
1995
, “
Approximation Rates for Multivariate Exceedances
,”
J. Stat. Plann. Inference
,
45
(
1–2
), pp.
235
245
.
21.
Hougaard
,
P.
,
1986
, “
A Class of Multivariate Failure Time Distributions
,”
Biometrika
,
73
(
3
), pp.
671
678
.
22.
de Oliveira
,
J. T.
,
1984
, “
Bivariate Models for Extremes; Statistical Decision
,”
Statistical Extremes and Applications
,
Springer
,
New York
, pp.
131
153
.
23.
de Oliveira
,
J.
T.,
1982
, “Bivariate Extremes: Models and Statistical Decision,” Center for Stochastic Processes, University of North Carolina, Chapel Hill, NC, Technical Report No. 14.
24.
Coles
,
S.
,
2001
,
An Introduction to Statistical Modeling of Extreme Values
(Springer Series in Statistics),
Springer-Verlag
,
London
.
25.
Tawn
,
J. A.
,
1988
, “
Bivariate Extreme Value Theory: Models and Estimation
,”
Biometrika
,
75
(
3
), pp.
397
415
.
26.
Naess
,
A.
,
2011
, “A Note on the Bivariate ACER Method,” Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway, Preprint Statistics No. 01/2011.
27.
Naess
,
A.
, and
Karpa
,
O.
,
2015
, “
Statistics of Bivariate Extreme Wind Speeds by the ACER Method
,”
J. Wind Eng. Ind. Aerodyn.
,
139
, pp.
82
88
.
28.
Karpa
,
O.
, and
Naess
,
A.
,
2015
, “
Statistics of Extreme Wind Speeds and Wave Heights by the Bivariate ACER Method
,”
ASME J. Offshore Mech. Arct. Eng.
,
137
(
2
), p. 021602.
29.
Naess
,
A.
, and
Gaidai
,
O.
,
2009
, “
Estimation of Extreme Values From Sampled Time Series
,”
Struct. Saf.
,
31
(
4
), pp.
325
334
.
30.
Gaidai
,
O.
, and
Naess
,
A.
,
2008
, “
Extreme Response Statistics for Drag Dominated Offshore Structures
,”
Probab. Eng. Mech.
,
23
(
2–3
), pp.
180
187
.
31.
Naess
,
A.
,
Gaidai
,
O.
, and
Haver
,
S.
,
2007
, “
Estimating Extreme Response of Drag Dominated Offshore Structures From Simulated Time Series of Structural Response
,”
Ocean Eng.
,
34
(16), pp.
2188
2197
.
32.
Song
,
L.
,
Fu
,
S.
,
Cao
,
J.
,
Ma
,
L.
, and
Wu
,
J.
,
2016
, “
An Investigation Into the Hydrodynamics of a Flexible Riser Undergoing Vortex-Induced Vibration
,”
J. Fluids Struct.
,
63
, pp.
325
350
.
33.
Wei
,
W.
,
Fu
,
S.
,
Moan
,
T.
,
Lu
,
Z.
, and
Deng
,
S.
,
2017
, “
A Discrete-Modules-Based Frequency Domain Hydroelasticity Method for Floating Structures in Inhomogeneous Sea Conditions
,”
J. Fluids Struct.
,
74
, pp.
321
339
.
34.
Naess
,
A.
, and
Gaidai
,
O.
,
2008
, “
Monte Carlo Methods for Estimating the Extreme Response of Dynamical Systems
,”
J. Eng. Mech.
,
134
(
8
), pp. 628–636.
You do not currently have access to this content.