Efficient computation of extreme excursion probabilities for dynamical systems
Abstract
We develop a novel computational method for evaluating the extreme excursion probabilities arising for random initialization of nonlinear dynamical systems. The method uses a Markov chain Monte Carlo or a Laplace approximation approach to construct a biasing distribution that in turn is used in an importance sampling procedure to estimate the extreme excursion probabilities. The prior and likelihood of the biasing distribution are obtained by using Rice's formula from excursion probability theory. We use Gaussian mixture biasing distributions and approximate the nonGaussian initial excitation by the method of moments to circumvent the linearity and Gaussianity assumptions needed by excursion probability theory. We demonstrate the effectiveness of this computational framework for nonlinear dynamical systems of up to 100 dimensions.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 DOI:
 10.48550/arXiv.2001.11904
 arXiv:
 arXiv:2001.11904
 Bibcode:
 2020arXiv200111904R
 Keywords:

 Mathematics  Numerical Analysis;
 Mathematics  Dynamical Systems;
 Mathematics  Probability