Research Papers: Offshore Technology

Bivariate Extreme Value Statistics of Offshore Jacket Support Stresses in Bohai Bay

[+] Author and Article Information
Zhang Jian

Naval Architechture and Offshore
Engineering Department,
Jiangsu University of Science and Technology,
Zhenjiang 212003, China
e-mail: justzj@126.com

Oleg Gaidai

Naval Architechture and Offshore
Engineering Department,
Jiangsu University of Science and Technology,
Zhenjiang 212003, China

Junliang Gao

Naval Architechture and Offshore
Engineering Department,
Jiangsu University of Science and Technology,
Zhenjiang 212003, China
e-mail: gaojunliang880917@163.com

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received May 23, 2017; final manuscript received February 21, 2018; published online April 24, 2018. Assoc. Editor: Marcelo R. Martins.

J. Offshore Mech. Arct. Eng 140(4), 041305 (Apr 24, 2018) (7 pages) Paper No: OMAE-17-1080; doi: 10.1115/1.4039564 History: Received May 23, 2017; Revised February 21, 2018

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.

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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. [CrossRef]
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. [CrossRef]
BMT Fluid Mechanics, 2011, “Global Wave Statistics,” BMT Fluid Mechanics Limited, Teddington, UK, accessed Mar. 16, 2018, http://www.globalwavestatisticsonline.com/
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
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
Wilson, J. , 1984, Dynamics of Offshore Structures, Wiley, New York.
Sarpkaya, T. , and Isaacson, M. , 1981, Mechanics of Wave Forces on Offshore Structures, Van Nostrand Reinhold, New York.
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. [CrossRef]
Naess, A. , and Moan, T. , 2013, Stochastic Dynamics of Marine Structures, Cambridge University Press, Oxford, UK.
Ewans, K. , 2014, “Evaluating Environmental Joint Extremes for the Offshore Industry Using the Conditional Extremes Model,” J. Mar. Syst., 130, pp. 124–130. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Gumbel, E. J. , 1960, “Bivariate Exponential Distributions,” J. Am. Stat. Assoc., 55(292), pp. 698–707. [CrossRef]
Gumbel, E. J. , 1961, “Bivariate Logistic Distributions,” J. Am. Stat. Assoc., 56(294), pp. 335–349. [CrossRef]
Gumbel, E. J. , and Mustafi, C. K. , 1967, “Some Analytical Properties of Bivariate Extremal Distributions,” J. Am. Stat. Assoc., 62(318), pp. 569–588. [CrossRef]
Balakrishnan, N. , and Lai, C.-D. , 2009, Continuous Bivariate Distributions, Springer Science Business Media, New York. [CrossRef]
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.
Nelsen, R. B. , 2006, An Introduction to Copulas (Springer Series in Statistics), Springer Science Business Media, New York.
Kaufmann, E. , and Reiss, R.-D. , 1995, “Approximation Rates for Multivariate Exceedances,” J. Stat. Plann. Inference, 45(1–2), pp. 235–245. [CrossRef]
Hougaard, P. , 1986, “A Class of Multivariate Failure Time Distributions,” Biometrika, 73(3), pp. 671–678.
de Oliveira, J. T. , 1984, “Bivariate Models for Extremes; Statistical Decision,” Statistical Extremes and Applications, Springer, New York, pp. 131–153.
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.
Coles, S. , 2001, An Introduction to Statistical Modeling of Extreme Values (Springer Series in Statistics), Springer-Verlag, London. [CrossRef]
Tawn, J. A. , 1988, “Bivariate Extreme Value Theory: Models and Estimation,” Biometrika, 75(3), pp. 397–415. [CrossRef]
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.
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. [CrossRef]
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.
Naess, A. , and Gaidai, O. , 2009, “Estimation of Extreme Values From Sampled Time Series,” Struct. Saf., 31(4), pp. 325–334. [CrossRef]
Gaidai, O. , and Naess, A. , 2008, “Extreme Response Statistics for Drag Dominated Offshore Structures,” Probab. Eng. Mech., 23(2–3), pp. 180–187. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.


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Fig. 1

Annually averaged spatial distribution of wave height and period in Bohai bay [1]. Star indicates jacket location.

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Fig. 2

An example of offshore jacket platform operating in the Bohai continental shelf

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Fig. 3

Sea state scatter diagram for the Bohai bay area from Ref. [3]. Numbers are fractions of 1000.

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Fig. 4

Finite element model of the jacket

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Fig. 5

Schematic jacket illustration with two stress monitoring location spots

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Fig. 6

Stresses in MPa for two different sea states. Mean stresses are subtracted for each stress.

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Fig. 7

Contour plot of the empirically estimated Ê2(ξ,η) surface (•), optimized Gumbel logistic G2(ξ,η) (∘) and optimized asymmetric logistic A2(ξ,η) (--) surfaces. Negative numbers indicate probability levels on a logarithmic scale.

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Fig. 8

Contour plot of the return periods for optimized Gumbel logistic G2(ξ,η) (∘) and optimized asymmetric logistic A2(ξ,η) (--) surfaces. Boxes indicate return periods in years.

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Fig. 9

Comparison between contour lines for 10 yr return period




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