Study of vertical breakwater reliability based on copulas

详细信息    查看全文

• 作者：Sheng Dong ; Jingjing Li ; Xue Li ; Yong Wei
• 关键词：vertical breakwater ; reliability ; Archimedean copula ; goodness of fit ; bivariate logistic Gumbel distribution ; bivariate Lognormal distribution ; multivariate distribution
• 刊名：Journal of Ocean University of China
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：15
• 期：2
• 页码：232-240
• 全文大小：394 KB
• 参考文献：Balas, C. E., and Koc, L., 2002. Risk assessment of vertical breakwaters–A case study in Turkey. China Ocean Engineering, 16(1): 123–134.
  Burcharth, H. F., Sorensen, J. D., and Christian, E., 1994. On the evaluation of failure probability of monolithic vertical wall breakwaters. Proceedings of Wave Barriers in Deepwaters. Yokosuka, Japan, 458–468.
  Castillo, C., Minguez, R., Castillo, E., and Losada, M. A., 2006. An optimal engineering design method with failure rate constraints and sensitivity analysis. Application to composite breakwaters. Coastal Engineering, 53(1): 1–25.CrossRef
  Corbella, S., and Stretch, D. D., 2012. Predicting coastal erosion trends using non-stationary statics and process-based models. Coastal Engineering, 70: 40–49.CrossRef
  Corbella, S., and Stretch, D. D., 2013. Simulating a multivariate sea storm using Archimedean copulas. Coastal Engineering, 76: 68–78.CrossRef
  Dong, H. K., and Woo, S. P., 2005. Neural network for design and reliability analysis of rubble mound breakwaters. Ocean Engineering, 32: 1332–1349.CrossRef
  Dong, S., Gao, J. G., Li, X., and Wei, Y., 2015. A storm surge intensity classification based on extreme water level and concomitant wave height. Journal of Ocean University of China, 14(2): 237–244.CrossRef
  Eryilmaz, S., 2011. Estimation in coherent reliability systems through copulas. Reliability Engineering & System Safety, 96(5): 564–568.CrossRef
  Gumbel, E. J., 1961. Bivariate logistic distributions. Journal of the American Statistical Association, 56: 335–349.CrossRef
  Goda, K., 2010. Statistical modeling of joint probability distribution using copula: Application to peak and permanent displacement seismic demands. Structural Safety, 32(2): 112–123.CrossRef
  Goda, Y., and Takagi, H., 2000. A reliability design method of caisson breakwaters with optimal wave heights. Coastal Engineering Journal, 42(4): 357–387.CrossRef
  Grimaldi, S., and Serinaldi, F., 2006. Asymmetric copula in multivariate flood frequency analysis. Advances in Water Resources, 29(8): 1155–1167.CrossRef
  Hasofer, A. M., and Lind, N. C., 1974. Exact and invariant second-moment code format. Journal of the Engineering Mechanics Division, 100(1): 111–121.
  Hofert, M., 2011. Efficiently sampling nested Archimedean copulas. Computational Statistics and Data Analysis, 55(1): 57–70.CrossRef
  Kaidi, S., Rouainia, M., and Ouahsine, A., 2012. Stability of breakwaters under hydrodynamic loading using a coupled DDA/FEM approach. Ocean Engineering, 55: 62–70.CrossRef
  Kiureghian, A. D., Lin, H. Z., and Hwang, S. J., 1987. Second order reliability approximations. Journal of Engineering mechanics, 113(8): 1208–1225.CrossRef
  Knut, O. R., 1990. Reliability analysis of a coastal dike. Coastal Engineering, 14(1): 43–56.CrossRef
  Liu, Y., and Xie, S. L., 1993. Determination of partial factors for the vertical breakwaters. Port Engineering Technology, (4): 1–5 (in Chinese).
  Ma, M. W., Ren, L. L., Song, S. B., Song, J. L., and Jiang, S. H., 2013. Goodness-of-fit tests for multi-dimensional copulas: Expanding application to historical drought data. Water Science and Engineering, 6(1): 18–30.
  Mase, H., Tsujio, D., Yasuda, T., and Mori, N., 2013. Stability analysis of composite breakwater with wave-dissipating blocks considering increase in sea levels, surges and waves due to climate change. Ocean Engineering, 71: 58–65.CrossRef
  Mehmet, L. K., 2009. Risk assessment of a vertical breakwater using possibility and evidence theories. Ocean Engineering, 36: 1060–1066.CrossRef
  Mehmet, L. K., and Can, E. B., 2012. Reliability analysis of a rubble mound breakwater using theory of fuzzy random variables. Applied Ocean Research, 39: 83–88.
  Nelsen, R. B., 2005. An Introduction to Copulas. 2nd edition. Springer, New York, 17–24.
  Onoufriou, T., and Forbes, V. J., 2001. Developments in structural system reliability assessments of fixed steel offshore platforms. Reliability Engineering & System Safety, 71(2): 189–199.CrossRef
  Qie, L. W., and Li, Y. B., 2004. Reliability index of caisson breakwaters for load variables correlated. China Ocean Engineering, 18(4): 577–584.
  Repko, P. H. A. J. M., Van, G. H. G. V., and Vrijling, J. K., 2004. Bivariate description of offshore wave conditions with physics-based extreme value statistics. Applied Ocean Research, 26: 162–170.CrossRef
  Roberto, M., and Enrique, C., 2009. Reliability-based optimization in engineering using decomposition techniques and FORMS. Structural Safety, 31(3): 214–223.CrossRef
  Suh, K. D., Kim, S. W., Kim, S., and Cheon, S., 2013. Effects of climate change on stability of caisson breakwaters in different water depths. Ocean Engineering, 71: 103–112.CrossRef
  Takayama, T., and Ikeda, N., 1992. Estimation of sliding failure probability of present breakwaters for probabilistic design. Report of the Port and Harbour Research Institute, 31(5): 3–32.
  Tang, X. S., Li, D. Q., Zhou, C. B., and Phoon, K. K., 2013. Modeling bivariate distribution using copulas and its application to component reliability analysis. Engineering Mechanics, 30(12): 8–17, 42 (in Chinese).
  Tarkan, E., 2009. Fuzzy logic approach to conventional rubble mound structures design. Expert Systems with Applications, 36(3): 4162–4170.CrossRef
  Waal, D. J. D., and Gelder, P. H. A. J. M. V., 2005. Modelling of extreme wave heights and periods through copulas. Extremes, 8(4): 345–356.CrossRef
  Xie, S. L., and Liu, Y., 1992. Reliability based design of vertical breakwaters. Proceedings of International Conference on Port Development for the Next Millennium. Hong Kong Institution of Engineers, Hong Kong, 419–423.
  Xie, S. L., and Liu, Y., 1994. Design method of breakwaters based on reliability theory. Acta Oceanologica Sinica, 16(5): 126–129 (in Chinese).
  Yue, S., 2000. The Gumbel logistic model for representing a multivariate storm event. Advances in Water Resources, 24(2): 179–185.CrossRef
  Zeng, X. X., Ren, J. C., Wang, Z., and Marshall, S., 2013. Copulas for statistical signal processing (Part I): Extensions and generalization. Signal Processing, 94: 691–702.CrossRef
  Zhang, W., and Cui, W. C., 1997. Direct integration method about structural reliability. Journal of Shanghai Jiaotong University, 31(2): 114–116 (in Chinese).
  
• 作者单位：Sheng Dong (1)
  Jingjing Li (1)
  Xue Li (1)
  Yong Wei (2) (3)
  
  1. College of Engineering, Ocean University of China, Qingdao, 266100, P. R. China
  2. Pacific Marine Environmental Laboratory, National Oceanic and Atmospheric Administration (NOAA), Seattle, WA, 98115, USA
  3. Joint Institute for the Study of Atmosphere and Ocean, University of Washington, Seattle, WA, 98105, USA
  
• 刊物主题：Oceanography; Meteorology;
• 出版者：Springer Berlin Heidelberg
• ISSN：1993-5021

文摘

The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions. The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions, respectively. The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions, including the bivariate logistic Gumbel distribution, the bivariate lognormal distribution, and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously. We use the fully nested copulas to construct multivariate distributions taking into account related variables. Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater. We show that a bivariate model constructed by Frank copula gives the best reliability analysis, using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater, respectively. The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods. As copulas are suitable for constructing a bivariate or multivariate joint distribution, they have great potential in reliability analysis for other coastal structures. Keywords vertical breakwater reliability Archimedean copula goodness of fit bivariate logistic Gumbel distribution bivariate Lognormal distribution multivariate distribution