Extreme Design Events of Non-Gaussian Stochastic Processes

The nature of the ocean is chaotic and, as a result, marine structures face extreme,non-linear load effects. It follows that the prediction of these rare events is a challenge. Attempts to predict extreme loads on offshore structures are generally probabilistic in nature. These purely probabilistic approaches involve a considerable amount of conjecture when enforcing distributions to the process and deciding which single probability of exceedance is suitable. In an attempt to remove these conjectures, a method is developed and proposed in this thesis. Employing the known extreme Gaussian behavior as a foundation, non-Gaussian processes with Gaussian input are transformed into the Gaussian space where extreme characteristics and realizations of extreme events of the transformed non-Gaussian process are produced. This thinking is first applied in the Stochastic Gaussianization Iteration Method (SGIM) where a Gaussian transform is applied to the non-linear process of interest to use Gaussian extreme event prediction tools. The progress and development of this method is discussed and applications in predicting extreme accelerations in hull slamming and estimating extreme tower base bending moments in offshore wind turbines are shown. The SGIM provided the platform for the key method developed in this dissertation: the Matched Upcrossing Equivalent Linear System (MUELS) method. In the MUELS method, the Design Loads Generator (DLG) runs through linear systems that share a mean-upcrossing period with the non-linear system of interest. The DLG provides an ensemble of input time series realizations that lead to extremes of said linear systems, which can then be used as input into the non-linear system of interest. The development of the MUELS method with subsequent applications follow in this dissertation. It is shown that the MUELS method can estimate extreme characteristics, most notably extreme time series realizations, of most non-linear pro-cesses tested in this dissertation. The MUELS method also shows the capability of discovering previously unknown dynamics of a stochastically forced Duffing oscillator.PhDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169929/1/sjedw_1.pd