Binomial-Bivariate Log-Normal Compound Model and its Application on Probability Estimation of Extreme Sea State

Abstract

Extreme value analysis is an indispensable method to predict the probability of marine disasters and calculate the design conditions of marine engineering. The rationality of extreme value analysis can be easily affected by the lack of sample data. The peaks over threshold (POT) method and compound extreme value distribution (CEVD) theory are effective methods to expand samples, but they still rely on long-term sea state data. To construct a probabilistic model using short-term sea state data instead of the traditional annual maximum series (AMS), the binomial-bivariate log-normal CEVD (BBLCED) model is established in this thesis. The model not only considers the frequency of the extreme sea state, but it also reflects the correlation between different sea state elements (wave height and wave period) and reduces the requirement for the length of the data series. The model is applied to the calculation of design wave elements in a certain area of the Yellow Sea. The results indicate that the BBLCED model has good stability and fitting effect, which is close to the probability prediction results obtained from the long-term data, and reasonably reflects the probability distribution characteristics of the extreme sea state. The model can provide a reliable basis for coastal engineering design under the condition of a lack of marine data. Hence, it is suitable for extreme value prediction and calculation in the field of disaster prevention and reduction.

Keywords

Bivariate compound extreme value distribution / Double-threshold sampling / Extreme sea state / Short-term data / Probabilistic prediction

References

[1] Chen YP, Li JX, Pan SQ, Gan M, Pan Y, Xie DM, Clee S. Joint probability analysis of extreme wave heights and surges along China’s coasts. Ocean Engineering, 2019, 177: 97-107

[2] Cheng YJ, Pang L, Dong S. Study on the estimation of very long return-period significant wave height during hurricane in the region of South China Sea. Journal of Ocean University of China, 2019, 49(S2): 125-132

[3] Cheng YJ, Yan ZD, Pang L, Liu WW (2018) Probability analysis on the typhoon induced sea states of the South China Sea. 2018 OCEANS-MTS/IEEE Kobe Techno-Oceans (OTO), Kobe, Japan, 1–10. DOI: https://doi.org/10.1109/OCEANSKOBE.2018.8559105

[4] Coles SG, Tawn JA. Modelling extreme multivariate events. Journal of the Royal Statistical Society, Series B, Methodological, 1991, 53(2): 377-392

[5] Galambos J. The theory and applications of reliability with Bayesian and nonparametric methods, 1977, New York: Academic Press, 151-164

[6] Gumbel EJ, Mustafi CK. Some analytical properties of bivariate extremal distributions. Publications of the American Statistical Association, 1967, 62(318): 569-588

[7] Gupta S, Manohar CS. Multivariate extreme value distributions for random vibration applications. Journal of Engineering Mechanics, 2005, 131(7): 712-720

[8] Hua YJ, Zhang ZY. Comparative research on extreme risk of stock market based on BMM and POT model. Journal of Industrial Engineering/Engineering Management, 2009, 23(4): 104-115 (in Chinese)

[9] Jia Y, Sasani M. Modeling joint probability of wind and flood hazards in Boston. Natural Hazards Review, 2021, 22(4): 04021047

[10] Joe H. Families of min-stable multivariate exponential and multivariate extreme value distributions. Statistics Probability Letters, 1989, 9(1): 75-82

[11] Leadbetter MR, Lindgren G, Rootzen H. Extreme and related properties of random sequences and series, 1983, New York: Springer-Verlag, 1-141

[12] Li CW, Song Y. Correlation of extreme waves and water levels using a third-generation wave model and a 3D flow model. Ocean Engineering, 2006, 33(5–6): 635-653

[13] Li FJ, Bicknell C, Lowry R, Li Y. A comparison of extreme wave analysis methods with 1994–2010 offshore Perth dataset. Coastal Engineering, 2012, 69: 1-11

[14] Liu DF, Li HJ. Prediction of extreme significant wave height from daily maxima. China Ocean Engineering, 2001, 15(1): 97-106 (in Chinese)

[15] Liu DF, Wen SQ, Wang LP. Poisson-Gumbel mixed compound extreme value distribution and its application. Chinese Science Bulletin, 2002, 47(17): 1356-1360 (in Chinese)

[16] Liu DF, Dong S. Stochastic engineering oceanography, 2004, Qingdao: China Ocean University Press, 107-117 (in Chinese)

[17] Liu DF, Wang LP, Pang L. Theory of multivariate compound extreme value distribution and its application to extreme sea state prediction. Chinese Science Bulletin, 2006, 23(51): 2926-2930

[18] Liu DF, Pang L, Xie BT, Wu YK. Study on typhoon disaster zoning and Fortification Criteria in China—double nested multi-objective joint probability model and its application. Science in China Series E Technological Sciences, 2007, 51(7): 1038-1048

[19] Liu SS. The selection and application of the threshold of POT model, 2014, Changchun: Jilin University, 12 28. (in Chinese)

[20] Liu JC, Lence BJ, Isaacson M. Direct joint probability method for estimating extreme sea levels. Journal of Waterway Port Coastal and Ocean Engineering, 2010, 136(1): 66-76

[21] Ma FS, Liu DF. Compound extreme value distribution theory and its applications. Acta Mathematicae Applacatae Sinica, 1979, 2(4): 366-375 (in Chinese)

[22] Pang L, Chen X, Li YL (2013) Long-term probability prediction on the extreme sea states induced by typhoon of the South China sea. 2013 Advanced Materials Research, Guilin, China, 726–731, 833–841. DOI: https://doi.org/10.4028/www.scientific.net/AMR.726-73L833

[23] Pang L, Xu F, Gong X, Zhan YF. Study of the influence of tropical cyclone on offshore wind turbine egenerator system. Periodical of Ocean University of China, 2015, 45(10): 109-113

[24] Park J, Smarsly K, Law KH, Hartmann D (2013) Multivariate analysis and prediction of wind turbine response to varying wind field characteristics based on machine learning. ASCE International Workshop on Computing in Civil Engineering, Los Angeles, 113–120. DOI: https://doi.org/10.1061/9780784413029.015

[25] Pei B, Pang WC, Testik F, Ravichandran N (2012) Joint distributions of hurricane wind and storm surge for the city of charleston in South Carolina. ATC & SEI Conference on Advances in Hurricane Engineering 2012, Miami, 703–714. DOI:https://doi.org/10.1061/9780784412626.062

[26] Shi DJ, Sun BK. Moment estimation in a nested logistic model. Systems Engineering-Theory & Practice, 2001, 21(1): 53-60 (in Chinese)

[27] Simão ML, Sagrilo LVS, Videiro PM. A multi-dimensional long-term joint probability model for environmental parameters. Ocean Engineering, 2022, 255: 111470

[28] Sun LL. Measurements and application of the extreme risk of financial data, 2014, Chongqing: Chongqing University, 19-20 (in Chinese)

[29] Tawn JA. Modelling multivariate extreme value distributions. Biometrika, 1990, 77(2): 245-253

[30] Wang LP. Multivariate compound extreme value distribution theory and its engineering applications, 2005, Qingdao: Ocean University of China, 68-72 (in Chinese)

[31] Xi D Z, Lin N, Nadal-Caraballo NC. A joint-probability model for tropical cyclone rainfall hazard assessment. GEO-EXTREME 2021: Climatic Extremes and Earthquake Modeling, 2021, 329: 1-10

[32] Yan ZD, Pang L, Dong S. Analysis of extreme wind speed estimates in the Northern South China Sea. Journal of Applied Meteorology and Climatology, 2020, 59(10): 1625-1635

[33] Yang X, Wang J, Weng SG. Joint probability study of destructive factors related to the “Triad” phenomenon during typhoon events in the coastal regions: Taking Jiangsu Province as an example. Journal of Hydrologic Engineering, 2020, 25(11): 05020038