Sequential sampling strategy for extreme event statistics in nonlinear dynamical systems
Name
11138.full.pdf
Description
Published version
Size
1.04 MB
Format
Adobe PDF
Checksum (MD5)
f2a7aac3d6b3b5a99467ce98f6cc2dec
Author(s)
Mohamad, Mustafa A
Sapsis, Themistoklis P
Date Issued
2018
Journal
Proceedings of the National Academy of Sciences of the United States of America
Publisher
Proceedings of the National Academy of Sciences
Version
Final published version
Abstract
© 2018 National Academy of Sciences. All rights reserved. We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems from a 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 uses Gaussian process regression to perform Bayesian inference on the parameter-Toobservation map describing the quantity of interest. We then approximate the desired pdf along with uncertainty bounds using 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 uses only information from the inferred map, it has minimal computational cost. Moreover, the special form of the metric emphasizes the tails of the pdf. The method is practical for systems where the dimensionality of the parameter space is of moderate size and for problems where each sample is very expensive to obtain. We apply the method to estimate the extreme event statistics for a very high-dimensional system with millions of degrees of freedom: An offshore platform subjected to 3D irregular waves. It is demonstrated that the developed approach can accurately determine the extreme event statistics using a limited number of samples.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1073/PNAS.1813263115
