Skip to main content

Advertisement

SpringerLink
Log in

Probabilistic modeling of long-term joint wind and wave load conditions via generative adversarial network

  • ORIGINAL PAPER
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

Offshore structures, such as oil and gas platforms and offshore wind turbines, are subjected to wind and wave loads simultaneously during their service lifetime. Since the wind and wave states are of significant randomness and dependence, the probabilistic modeling of joint wind and wave conditions plays an essential role in the safety design of offshore structures. Currently, three different methods can be adopted to establish the joint probabilistic model, which, however, are somewhat inconvenient in applications. The recently emerged generative adversarial networks has been demonstrated to be effective in dealing with high-dimensional random variables in several fields. In this study, the implicit joint probabilistic model of joint wind and wave load conditions is developed based on the Wasserstein generative adversarial network with gradient penalty. Long-term metocean reanalysis data of the site in the South China Sea is used to train and validate the model. After one million training steps, high-quality samples that are quite similar to the original data can be generated by the developed model. In addition, statistical comparisons of the generated samples obtained by the C-vine copula approach and the developed generative adversarial network model are performed as well, which demonstrates the effectiveness and superiority of the developed model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  • Aas K, Czado C, Frigessi A, Bakken H (2009) Pair-copula constructions of multiple dependence. Insur Math Econ 44(2):182–198

    Article  Google Scholar 

  • Abirami S, Chitra P (2022) Regional spatio-temporal forecasting of particulate matter using autoencoder based generative adversarial network. Stoch Environ Res Risk Assess 36(5):1255–1276

    Article  Google Scholar 

  • Ang AH-S, Tang WH (2007) Probability concepts in engineering: emphasis on applications to civil and environmental engineering. Willey, Hoboken

    Google Scholar 

  • Arjovsky M, Bottou L (2017) Towards principled methods for training generative adversarial networks. arXiv preprint arXiv:1701.04862

  • Arjovsky M, Chintala S, Bottou L (2017) Wasserstein generative adversarial networks. In: Doina P, Yee Whye T (eds) The 34th international conference on machine learning. PMLR, pp 214–223

  • Cheng ZS, Svangstu E, Moan T, Gao Z (2019) Long-term joint distribution of environmental conditions in a Norwegian fjord for design of floating bridges. Ocean Eng 191:106472

    Article  Google Scholar 

  • Dee DP, Uppala SM, Simmons AJ, Berrisford P, Poli P, Kobayashi S, Andrae U, Balmaseda MA, Balsamo G, Bauer P, Bechtold P, Beljaars ACM, van de Berg L, Bidlot J, Bormann N, Delsol C, Dragani R, Fuentes M, Geer AJ, Haimberger L, Healy SB, Hersbach H, Holm EV, Isaksen L, Kallberg P, Kohler M, Matricardi M, McNally AP, Monge-Sanz BM, Morcrette JJ, Park BK, Peubey C, de Rosnay P, Tavolato C, Thepaut JN, Vitart F (2011) The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorol Soc 137(656):553–597

    Article  Google Scholar 

  • Ding Y, Chen J, Shen J (2020) Conditional generative adversarial network model for simulating intensity measures of aftershocks. Soil Dyn Earthq Eng 139:106281

    Article  Google Scholar 

  • Ding YJ, Chen J, Shen JX (2021) Prediction of spectral accelerations of aftershock ground motion with deep learning method. Soil Dyn Earthq Eng 150:106951

    Article  Google Scholar 

  • Dißmann J, Brechmann EC, Czado C, Kurowicka D (2013) Selecting and estimating regular vine copulae and application to financial returns. Comput Stat Data Anal 59:52–69

    Article  Google Scholar 

  • Ditlevsen O (2002) Stochastic model for joint wave and wind loads on offshore structures. Struct Saf 24(2):139–163

    Article  Google Scholar 

  • DNVGL (2019) Environmental conditions and environmental loads, DNVGL recommended practice: DNVGL-RP-C205. DNVGL

  • Fazeres-Ferradosa T, Taveira-Pinto F, Vanem E, Reis MT, Neves LD (2018) Asymmetric copula-based distribution models for met-ocean data in offshore wind engineering applications. Wind Eng 42(4):304–334

    Article  Google Scholar 

  • Genest C, Quessy J-F, Rémillard B (2007) Asymptotic local efficiency of Cramér-von Mises tests for multivariate independence. Ann Stat 35(1):166–191

    Article  Google Scholar 

  • Gong Y, Dong S, Wang Z (2022) Forecasting of typhoon wave based on hybrid machine learning models. Ocean Eng 266:112934

    Article  Google Scholar 

  • Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, Cambridge

    Google Scholar 

  • Goodfellow IJ, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y (2014) Generative adversarial nets. In: Proceedings of the 27th international conference on neural information processing systems. MIT Press, Montreal, Canada, , vol 2, pp 2672–2680

  • Gui J, Sun Z, Wen Y, Tao D, Ye J (2021) A review on generative adversarial networks: algorithms, theory, and applications. IEEE Trans Knowl Data Eng. https://doi.org/10.1109/TKDE.2021.3130191

    Article  Google Scholar 

  • Gulrajani I, Ahmed F, Arjovsky M, Dumoulin V, Courville AC (2017) Improved training of wasserstein gans. Adv Neural Inf Process Syst 25:5767–5777

    Google Scholar 

  • IEC (2019) Wind energy generation systems-part 1: design requirements, 4th edn, IEC International Standard: 61400-1. International Electrotechnical Commision (IEC), Switzerland

  • Karimirad M (2014) Offshore energy structures: for wind power, wave energy and hybrid marine platforms. Springer

    Book  Google Scholar 

  • Kim SG, Chae YH, Seong PH (2020) Development of a generative-adversarial-network-based signal reconstruction method for nuclear power plants. Ann Nucl Energy 142:107410

    Article  CAS  Google Scholar 

  • Kingma DP, Ba J (2015). Adam: a method for stochastic optimization. arXiv:1412.6980

  • Lei X, Sun L, Xia Y (2020) Lost data reconstruction for structural health monitoring using deep convolutional generative adversarial networks. Struct Health Monit 20(4):2069–2087

    Article  Google Scholar 

  • Lei Y, Zheng XY, Zheng HD (2021) Dynamic responses of the state-of-the-art floating system integrating a wind turbine with a steel fish farming cage: model tests vs. numerical simulations. In: ASME 2021 40th international conference on ocean, offshore and arctic engineering

  • Li X, Zhang W (2020) Long-term assessment of a floating offshore wind turbine under environmental conditions with multivariate dependence structures. Renew Energy 147:764–775

    Article  Google Scholar 

  • Li L, Cheng Z, Yuan Z, Gao Y (2018) Short-term extreme response and fatigue damage of an integrated offshore renewable energy system. Renew Energy 126:617–629

    Article  Google Scholar 

  • Liao ZK, Huang WN, Dong S, Li HJ (2022) Modelling trivariate distribution of directional ocean data in the Barents Sea seasonal ice zone. Ocean Eng 260:111745

    Article  Google Scholar 

  • Mazarakos T, Konispoliatis D, Katsaounis G, Polyzos S, Manolas D, Voutsinas S, Soukissian T, Mavrakos SA (2019) Numerical and experimental studies of a multi-purpose floating TLP structure for combined wind and wave energy exploitation. Mediterr Mar Sci 20(4):745–763

    Article  Google Scholar 

  • Nelsen RB (2006) An introduction to copulas, 2nd edn. Springer, New York

    Google Scholar 

  • Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin Z, Gimelshein N, Antiga L, Desmaison A, Köpf A, Yang E, DeVito Z, Raison M, Tejani A, Chilamkurthy S, Steiner B, Fang L, Bai J, Chintala S (2019) Pytorch: an imperative style, high-performance deep learning library. In: 33rd conference on neural information processing systems, Vancouver, pp 8026–8037

  • Shen JX, Chen J, Ding G (2020) Random field model of sequential ground motions. Bull Earthq Eng 18(11):5119–5141

    Article  Google Scholar 

  • Silva-González F, Heredia-Zavoni E, Montes-Iturrizaga R (2013) Development of environmental contours using Nataf distribution model. Ocean Eng 58:27–34

    Article  Google Scholar 

  • Song YP, Basu B, Zhang ZL, Sørensen JD, Li J, Chen JB (2021) Dynamic reliability analysis of a floating offshore wind turbine under wind-wave joint excitations via probability density evolution method. Renew Energy 168:991–1014

    Article  Google Scholar 

  • Song YP, Chen JB, Sørensen JD, Li J (2022) Multi-parameter full probabilistic modeling of long-term joint wind-wave actions using multi-source data and applications to fatigue analysis of floating offshore wind turbines. Ocean Eng 247:110676

    Article  Google Scholar 

  • Stewart GM, Robertson A, Jonkman J, Lackner MA (2016) The creation of a comprehensive metocean data set for offshore wind turbine simulations. Wind Energy 19(6):1151–1159

    Article  Google Scholar 

  • Tang XS, Li DQ, Zhou CB, Phoon KK (2015) Copula-based approaches for evaluating slope reliability under incomplete probability information. Struct Saf 52:90–99

    Article  Google Scholar 

  • Tao JJ, Chen JB, Ren XD (2020) Copula-based quantification of probabilistic dependence configurations of material parameters in damage constitutive modeling of concrete. J Struct Eng 146(9):04020194

    Article  Google Scholar 

  • Tomasicchio GR, Vicinanza D, Belloli M, Lugni C, Latham J-P, Iglesias Rodriguez JG, Jensen B, Vire A, Monbaliu J, Taruffi F, Pustina L, Leone E, Russo S, Francone A, Fontanella A, Di Carlo S, Muggiasca S, Decorte G, Rivera-Arreba I, Ferrante V, Battistella T, Guanche Garcia R, Martìnez Dìaz A, ElsÄsser B, Via-Estrem L, Xiang J, Andersen MT, Kofoed JP, Kramer MB, Musci E, Lusito L (2020) Physical model tests on spar buoy for offshore floating wind energy converion. Ital J Eng Geol Environ 58:129–143

    Google Scholar 

  • Vanem E (2010) Long-term time-dependent stochastic modelling of extreme waves. Stoch Environ Res Risk Assess 25(2):185–209

    Article  Google Scholar 

  • Vanem E (2016) Joint statistical models for significant wave height and wave period in a changing climate. Mar Struct 49:180–205

    Article  Google Scholar 

  • Vanem E (2019) Environmental contours for describing extreme ocean wave conditions based on combined datasets. Stoch Environ Res Risk Assess 33(4–6):957–971

    Article  Google Scholar 

  • Vanem E, Zhu T, Babanin A (2022) Statistical modelling of the ocean environment—a review of recent developments in theory and applications. Mar Struct 86:103297

    Article  Google Scholar 

  • Wang ZW, Zhang WM, Zhang YF, Liu Z (2021) Circular-linear-linear probabilistic model based on vine copulas: an application to the joint distribution of wind direction, wind speed, and air temperature. J Wind Eng Ind Aerodyn 215:104704

    Article  Google Scholar 

  • Wang Y, Liu Z, Wang H (2022) Proposal and layout optimization of a wind-wave hybrid energy system using GPU-accelerated differential evolution algorithm. Energy 239:121850

    Article  Google Scholar 

  • Wei K, Shen Z, Ti Z, Qin S (2020) Trivariate joint probability model of typhoon-induced wind, wave and their time lag based on the numerical simulation of historical typhoons. Stoch Environ Res Risk Assess 35(2):325–344

    Article  Google Scholar 

  • Xia P, Bai H, Zhang T (2022) Multi-scale reconstruction of porous media based on progressively growing generative adversarial networks. Stoch Environ Res Risk Assess 36(11):3685–3705

    Article  Google Scholar 

  • Xiong J, Chen J (2019) A generative adversarial network model for simulating various types of human-induced loads. Int J Struct Stab Dyn 19(08):1950092

    Article  Google Scholar 

  • Zheng X, Lei Y (2018) Stochastic response analysis for a floating offshore wind turbine integrated with a steel fish farming cage. Appl Sci 8(8):1229

    Article  Google Scholar 

Download references

Acknowledgements

The financial supports from the Natural Science Foundation of Jiangsu Province (Grant No. BK20220357), the Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No. 22KJB560005), and the Fundamental Research Funds for the Central Universities of China (Nos. JZ2022HGQA0168, PA2022GDSK0063) are highly appreciated.

Funding

Funding is provided by Natural Science Foundation of Jiangsu Province (Grant No. BK20220357), Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No. 22KJB560005), Fundamental Research Funds for the Central Universities (Grant Nos. JZ2022HGQA0168, PA2022GDSK0063).

Author information

Authors and Affiliations

  1. College of Civil Engineering, Nanjing Tech University, No. 30 Puzhu Road (S), Nanjing, 211816, People’s Republic of China

    Yupeng Song

  2. School of Civil and Hydraulic Engineering, Hefei University of Technology, No. 193 Tunxi Road, Hefei, 230009, People’s Republic of China

    Xu Hong

  3. School of Civil Engineering, Zhengzhou University, No. 100 Science Avenue, Zhengzhou, 450001, People’s Republic of China

    Jiecheng Xiong

  4. Faculty of Architecture, Civil and Transportation Engineering, Beijing University of Technology, No. 100 Pingleyuan, Beijing, 100124, People’s Republic of China

    Jiaxu Shen

  5. College of Civil Engineering, Tongji University, No. 1239 Siping Road, Shanghai, 200092, People’s Republic of China

    Zekun Xu

Authors
  1. Yupeng Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xu Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiecheng Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiaxu Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zekun Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Yupeng Song: methodology, formal analysis, writing original draft, review & editing Xu Hong: methodology, formal analysis, review & editing Jiecheng Xiong: methodology, review & editing Jiaxu Shen: methodology, review & editing Zekun Xu: methodology, review & editing

Corresponding author

Correspondence to Xu Hong.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, Y., Hong, X., Xiong, J. et al. Probabilistic modeling of long-term joint wind and wave load conditions via generative adversarial network. Stoch Environ Res Risk Assess 37, 2829–2847 (2023). https://doi.org/10.1007/s00477-023-02421-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-023-02421-4

Keywords

Search

Navigation