Improved Inverse First-Order Reliability Method for Analyzing Long-Term Response Extremes of Floating Structures

Abstract

Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an approach for the long-term extreme-response analysis of floating structures. A modified gradient-based retrieval algorithm in conjunction with the inverse first-order reliability method (IFORM) is proposed to enable the use of convolution models in long-term extreme analysis of structures with an analytical formula of response amplitude operator (RAO). The proposed algorithm ensures convergence stability and iteration accuracy and exhibits a higher computational efficiency than the traditional backtracking method. However, when the RAO of general offshore structures cannot be analytically expressed, the convolutional integration method fails to function properly. A numerical discretization approach is further proposed for offshore structures in the case when the analytical expression of the RAO is not feasible. Through iterative discretization of environmental contours (ECs) and RAOs, a detailed procedure is proposed to calculate the long-term response extremes of offshore structures. The validity and accuracy of the proposed approach are tested using a floating offshore wind turbine as a numerical example. The long-term extreme heave responses of various return periods are calculated via the IFORM in conjunction with a numerical discretization approach. The environmental data corresponding to N-year structural responses are located inside the ECs, which indicates that the selection of design points directly along the ECs yields conservative design results.

Keywords

Long-term response analysis / Floating structures / Inverse first-order reliability method / Convolution model / Gradient-based retrieval algorithm / Environmental contour method

References

[1] BaarholmGS, MoanT. Estimation of nonlinear long-term extremes of hull girder loads in ships. Marine Structures, 2000, 13(6): 495-516

[2] BattjesJA. Long-term wave height distributions at seven stations around the British Isles. Deutsche Hydrographische Zeitschrift, 1972, 25(4): 179-189

[3] BeshbichiOE, RødstølH, XingY, OngMC. Prediction of long-term extreme response of two-rotor floating wind turbine concept using the modified environmental contour method. Renewable Energy, 2022, 189: 1133-1144

[4] BruserudK, HaverS, MyrhaugD. Joint description of waves and currents applied in a simplified load case. Marine Structures, 2018, 58: 416-433

[5] CastellonDF, FenerciA, ØisethO, PetersenW. Investigations of the long-term extreme buffeting response of longspan bridges using importance sampling Monte Carlo simulations. Engineering Structures, 2022, 273: 114986-114986

[6] ChenDS, FengXY, LiZQ, ChenJF. Long-term extreme responses of torsional moments at two-directional hinges for moored very large floating structures. Ocean Engineering, 2023, 290: 116330-116330

[7] ClarindoG, Guedes SoaresC. Environmental contours of sea states by the I-FORM approach derived with the Burr-Lognormal statistical model. Ocean Engineering, 2024, 291: 116315

[8] DuX, SudjiantoA, ChenW. An integrated framework for optimization under uncertainty using inverse reliability strategy. Journal of Mechanical Design, 2004, 126(4): 562-570

[9] EwansK, JonathanP. Evaluating environmental joint extremes for the offshore industry using the conditional extremes model. Journal of Marine Systems, 2014, 130: 124-130

[10] FarnesKA, MoanT. Extreme dynamic, non-linear response of fixed platforms using a complete long-term approach. Applied Ocean Research, 1993, 15(6): 317-326

[11] FontaineE, OrseroP, LedouxA, NerzicR, PrevostoM, QuiniouV. Reliability analysis and response based design of a moored FPSO in West Africa. Structural Safety, 2013, 41: 82-96

[12] GiskeFIG, KvåleKA, LeiraBJ, ØisethO. Long-term extreme response analysis of a long-span pontoon bridge. Marine Structures, 2018, 58: 154-171

[13] GiskeFIG, LeiraBJ, ØisethO. Full long-term extreme response analysis of marine structures using inverse FORM. Probabilistic Engineering Mechanics, 2017, 50: 1-8

[14] HaverS. Wave climate off northern Norway. Applied Ocean Research, 1985, 7(2): 85-92

[15] HaverS, WintersteinSR. Environmental contour lines: A method for estimating long term extremes by a short term analysis. Transactions-Society of Naval Architects and Marine Engineers, 2008, 116: 116-127

[16] KrogstadHE. Height and period distributions of extreme waves. Applied Ocean Research, 1985, 7(3): 158-165

[17] LiH, FoschiRO. An inverse reliability method and its application. Structural Safety, 1998, 20(3): 257-270

[18] LiL, YuanZM, GaoY, ZhangXS, TezdoganT. Investigation on long-term extreme response of an integrated offshore renewable energy device with a modified environmental contour method. Renewable Energy, 2019, 132: 33-42

[19] LiQ, GaoZ, MoanT. Modified environmental contour method to determine the long-term extreme responses of a semi-submersible wind turbine. Ocean Engineering, 2017, 142: 563-576

[20] LiaoZK, ZhaoYL, DongS. Estimating design loads for floating structures using environmental contours. Journal of Marine Science and Application, 2022, 21(3): 114-127

[21] Longuet-HigginsMS. On the joint distribution of the periods and amplitudes of sea waves. Journal of Geophysical Research, 1975, 80(18): 2688-2694

[22] LystadTM, FenerciA, ØisethO. Buffeting response of longspan bridges considering uncertain turbulence parameters using the environmental contour method. Engineering Structures, 2020, 213: 110575

[23] MackayE, HauteclocqueGD. Model-free environmental contours in higher dimensions. Ocean Engineering, 2023, 273: 113959-113959

[24] NaessA. Technical note: On the long-term statistics of extremes. Applied Ocean Research, 1984, 6(4): 227-228

[25] NaessA, MoanTStochastic dynamics of marine structures, 2012, Cambridge, Cambridge University Press

[26] Ochi MK (1998) Ocean waves: the stochastic approach. Cambridge University Press

[27] SagriloL, NaessA, DoriaAS. On the long-term response of marine structures. Applied Ocean Research, 2011, 33(3): 208-214

[28] VanemE. Joint statistical models for significant wave height and wave period in a changing climate. Marine Structures, 2016, 49: 180-205

[29] Vázquez-HernándezAO, EllwangerGB, SagriloLVS. Long-term response analysis of FPSO mooring systems. Applied Ocean Research, 2011, 33(4): 375-383

[30] WangYG. A novel environmental contour method for predicting long-term extreme wave conditions. Renewable Energy, 2020, 162: 926-933

[31] Winterstein SR, Ude TC, Cornell CA, Bjerager P, Haver S (1993) Environmental parameters for extreme response Inverse FORM with omission factors. ICOSSAR-93, Innsbruck, 551–557

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Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature