  First-passage probability estimation of high-dimensional nonlinear stochastic
systems is a significant task to be solved in many science and engineering
fields, but remains still an open challenge. The present paper develops a novel
approach, termed 'fractional moments-based mixture distribution', to address
such challenge. This approach is implemented by capturing the extreme value
distribution (EVD) of the system response with the concepts of fractional
moments and mixture distribution. In our context, the fractional moment itself
is by definition a high-dimensional integral with a complicated integrand. To
efficiently compute the fractional moments, a parallel adaptive sampling scheme
that allows for sample size extension is developed using the refined Latinized
stratified sampling (RLSS). In this manner, both variance reduction and
parallel computing are possible for evaluating the fractional moments. From the
knowledge of low-order fractional moments, the EVD of interest is then expected
to be reconstructed. Based on introducing an extended inverse Gaussian
distribution and a log extended skew-normal distribution, one flexible mixture
distribution model is proposed, where its fractional moments are derived in
analytic form. By fitting a set of fractional moments, the EVD can be recovered
via the proposed mixture model. Accordingly, the first-passage probabilities
under different thresholds can be obtained from the recovered EVD
straightforwardly. The performance of the proposed method is verified by three
examples consisting of two test examples and one engineering problem.
