This work investigates numerically two different methods of moments applied to Hermite derived probability distribution model and variations of Weibull distribution fitted to the short-term time series peaks sample of stochastic response parameters of a simplified jack-up platform model which represents a source of high non-Gaussian responses. The main focus of the work is to compare the results of short-term extreme response statistics obtained by the so-called linear method of moments (L-moments) and the conventional method of moments using either Hermite or Weibull models as the distribution model for the peaks. A simplified mass-spring system representing a three-legged jack-up platform is initially employed in order to observe directly impacts of the linear method of moments (L-moments) in extreme analysis results. Afterward, the stochastic response of the three-legged jack-up platform is analyzed by means of 3D finite element model. Bias and statistical uncertainty in the estimated extreme statistics parameters are computed considering as the “theoretical” estimates those evaluated by fitting a Gumbel to a sample of episodical extreme values obtained from distinct short-term realizations (or simulations). Results show that the variability of the extreme results, as a function of the simulation length, determined by the linear method of moments (L-moments) is smaller than their corresponding ones derived from the conventional method of moments and the biases are more or less the same.

References

References
1.
Karunakaran
,
D. N.
,
1993
, “
Nonlinear Dynamic Response and Reliability Analysis of Drag-Dominated Offshore Platforms
,” D.Sc. thesis, University of Trondheim, Trondheim, Norway.
2.
Cassidy
,
M. J.
,
Taylor
,
P. H.
,
Eatock Taylor
,
R.
, and
Houlsby
,
G. T.
,
2002
, “
Evaluation of Long-Term Extreme Response Statistics of Jack-up Platforms
,”
Ocean Eng.
,
29
(
13
), pp.
1603
1631
.10.1016/S0029-8018(01)00110-X
3.
Nascimento
,
L. S.
,
Sagrilo
,
L. V. S.
, and
Ellwanger
,
G. B.
,
2010
, “
Extreme Value Analysis of Jack-Up Dynamic Response Parameters
,”
Mar. Syst. Ocean Technol.
,
6
(
2
), pp.
75
86
.
4.
Winterstein
,
S. R.
,
1988
, “
Nonlinear Vibration Models for Extremes and Fatigue
,”
J. Eng. Mech.
,
114
(
10
), pp.
1772
1790
.10.1061/(ASCE)0733-9399(1988)114:10(1772)
5.
Naess
,
A.
, and
Gaidai
,
O.
,
2009
, “
Estimation of Extreme Values From Sampled Time Series
,”
Struct. Saf.
,
31
(
4
), pp.
325
334
.10.1016/j.strusafe.2008.06.021
6.
Hosking
,
J. R. M.
,
1990
, “
L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics
,”
J. R. Stat. Soc. B
,
52
(
1
), pp.
105
124
.
7.
Brebbia
,
C. A.
, and
Walker
,
S.
,
1979
,
Dynamic Analysis of Offshore Structures
,
1st ed.
,
Butterworth
,
London, UK
.
8.
Najafian
,
G.
,
2010
, “
Comparison of Three Different Methods of Moments for Derivation of Probability Distribution Parameters
,”
Appl. Ocean Res.
,
32
(
3
), pp.
298
307
.10.1016/j.apor.2010.06.001
9.
Ang
,
A.-S.
, and
Tang
,
W.
,
1984
,
Probability Concepts in Engineering Planning and Design
, Vol.
2
,
Wiley
,
New York
.
10.
Greenwood
,
J. A.
,
Landwehr
,
J. M.
,
Matalas
,
N. C.
, and
Wallis
,
J. R.
,
1979
, “
Probability Weighted Moments: Definition and Relation to Parameters of Several Distributions Expressable in Inverse Form
,”
Water Res. Res.
,
15
(
5
), pp.
1049
1054
.10.1029/WR015i005p01049
11.
Winterstein
,
S. R.
, and
MacKenzie
,
C. A.
,
2011
, “
Extremes of Nonlinear Vibration: Models Based on Moments, L-moments, and Maximum Entropy
,”
International Conference on Ocean
, Offshore, and Artic Engineering, Rotterdam, The Netherlands, June 19–24,
ASME
Paper No. OMAE2011-49867, pp.
617
626
.10.1115/OMAE2011-49867
12.
Jensen
,
J. J.
, and
Capul
,
J.
,
2006
, “
Extreme Response Predictions for Jack-ups Units in Second Order Stochastic Waves by Form
,”
Probab. Eng. Mech.
,
21
(
4
), pp.
330
337
.10.1016/j.probengmech.2005.11.007
13.
Cassidy
,
M. J.
,
Eatock Taylor
,
R.
, and
Houlsby
,
G. T.
,
2001
, “
Analysis of Jack-up Units Using a Constrained new Wave Methodology
,”
Appl. Ocean Res.
,
23
(
4
), pp.
221
234
.10.1016/S0141-1187(01)00005-0
14.
Paz
,
M.
,
1997
,
Structural Dynamic: Theory and Computation
,
International Thomson Publishing
,
New York
.
15.
Ang
,
A.-S.
, and
Tang
,
W.
,
1975
,
Probability Concepts in Engineering Planning and Design
, Vol.
1
,
Wiley
,
New York
.
16.
Nascimento
,
L. S.
,
2009
, “
Extreme Response Analysis of Jack-ups Response Parameters
,” M.Sc. dissertation, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.
You do not currently have access to this content.