Operator Norm-Based Statistical Linearization to Bound the First Excursion Probability of Nonlinear Structures Subjected to Imprecise Stochastic Loading

Peihua Ni, Danko J. Jerez, Vasileios C. Fragkoulis, Matthias G.R. Faes, Marcos A. Valdebenito, Michael Beer

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

This paper presents a highly efficient approach for bounding the responses and probability of failure of nonlinear models subjected to imprecisely defined stochastic Gaussian loads. Typically, such computations involve solving a nested double-loop problem, where the propagation of the aleatory uncertainty has to be performed for each realization of the epistemic parameters. Apart from near-trivial cases, such computation is generally intractable without resorting to surrogate modeling schemes, especially in the context of performing nonlinear dynamical simulations. The recently introduced operator norm framework allows for breaking this double loop by determining those values of the epistemic uncertain parameters that produce bounds on the probability of failure a priori. However, the method in its current form is only applicable to linear models due to the adopted assumptions in the derivation of the involved operator norms. In this paper, the operator norm framework is extended and generalized by resorting to the statistical linearization methodology to account for nonlinear systems. Two case studies are included to demonstrate the validity and efficiency of the proposed approach.

Original languageEnglish
Article number04021086
JournalASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume8
Issue number1
DOIs
StatePublished - 1 Mar 2022

Keywords

  • Imprecise probabilities
  • Operator norm theorem
  • Statistical linearization
  • Uncertainty quantification

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