We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a very small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the ‘next-best’ data point (set of parameters) that when evaluated results in improved estimates of the probability density function (pdf) for a scalar quantity of interest. The approach utilizes Gaussian process regression to perform Bayesian inference on the parameter-to-observation map describing the quantity of interest. We then approximate the desired pdf along with uncertainty bounds utilizing the posterior distribution of the inferred map. The ‘next-best’ design point is sequentially determined through an optimization procedure that selects the point in parameter space that maximally reduces uncertainty between the estimated bounds of the pdf prediction. Since the optimization process utilizes only information from the inferred map it has minimal computational cost. Moreover, the special form of the criterion emphasizes the tails of the pdf. The method is applied to estimate the extreme event statistics for a very high-dimensional system with millions degrees of freedom: an offshore platform subjected to three-dimensional irregular waves. It is demonstrated that the developed approach can accurately determine the extreme event statistics using orders of magnitude smaller number of samples compared with traditional approaches.

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