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Area of Science:

  • Computational mechanics
  • Statistical modeling
  • Applied mathematics

Background:

  • Evaluating extreme event statistics in nonlinear dynamical systems is challenging with limited data.
  • High-dimensional systems, like offshore platforms, require efficient statistical estimation methods.

Purpose of the Study:

  • To develop a sequential strategy for improving probability density function (pdf) estimates from sparse data.
  • To enable accurate extreme event statistics evaluation for computationally expensive, high-dimensional systems.

Main Methods:

  • Utilizes Gaussian process regression for Bayesian inference on parameter-to-observation maps.
  • Employs a sequential optimization procedure to select the next-best data point, minimizing uncertainty.
  • Focuses on improving pdf estimation, particularly in the tails, for scalar quantities of interest.

Main Results:

  • Accurate estimation of extreme event statistics was achieved using a limited number of samples.
  • The method demonstrated effectiveness on a high-dimensional system (offshore platform under irregular waves).
  • The sequential approach significantly reduces computational cost by minimizing sample evaluations.

Conclusions:

  • The developed method provides a practical and efficient solution for extreme event statistics evaluation in data-scarce, high-dimensional scenarios.
  • Gaussian process regression and sequential design offer a powerful combination for complex system analysis.
  • This approach is valuable for engineering applications where sample acquisition is costly.