Non-conventional modeling of extreme significant wave height through random sets
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Non-conventional modeling of extreme significant wave height through random sets ZHANG Yi1*, LAM Jasmine Siu Lee2 1
Division of Infrastructure Systems and Maritime Studies, School of Civil and Environmental Engineering, N1-B1a-25, Nanyang Technological University, Singapore 639798, Singapore 2 Division of Infrastructure Systems and Maritime Studies, School of Civil and Environmental Engineering, N1-01b-43, Nanyang Technological University, Singapore 639798, Singapore Received 5 February 2013; accepted 22 January 2014 ©The Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg 2014
Abstract The analysis and design of offshore structures necessitates the consideration of wave loads. Realistic modeling of wave loads is particularly important to ensure reliable performance of these structures. Among the available methods for the modeling of the extreme significant wave height on a statistical basis, the peak over threshold method has attracted most attention. This method employs Poisson process to characterize time-varying properties in the parameters of an extreme value distribution. In this paper, the peak over threshold method is reviewed and extended to account for subjectivity in the modeling. The freedom in selecting the threshold and the time span to separate extremes from the original time series data is incorporated as imprecision in the model. This leads to an extension from random variables to random sets in the probabilistic model for the extreme significant wave height. The extended model is also applied to different periods of the sampled data to evaluate the significance of the climatic conditions on the uncertainties of the parameters. Key words: offshore engineering, extreme value distribution, wave height, peak over threshold, random set, Pareto distribution Citation: Zhang Yi, Lam Jasmine Siu Lee. 2014. Non-conventional modeling of extreme significant wave height through random sets. Acta Oceanologica Sinica, 33(7): 125–130, doi: 10.1007/s13131-014-0508-4
1 Introduction The modeling of extreme significant wave height (Hs) poses many statistical challenges. A common problem in dealing with the whole set of natural observations is that they usually present high serial correlation and large variations in magnitude for different reference periods. This does not seem to conform the hypothesis of a stationary stochastic process, and hence make the statistical characterization of extremes difficult as the essential assumption in the statistical approach requires the data to be independent and identically distributed (Bermudez and Kotz, 2010). Several authors have modeled the non-stationary behaviors in extreme Hs (Méndez et al., 2006; Ruggiero et al., 2010). Among the available methods, the peak over threshold (POT) method has attracted the most attention. Compared with other methods, this approach is found quite efficient in the utilization of data for a limited data set (Muraleedharan et al., 2007). But through the implementation of the POT method, some subjective uncertainties may turn to
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