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

authored by: Peihua Ni, Danko J. Jerez, Vasileios C. Fragkoulis, Matthias G.R. Faes, Marcos A. Valdebenito, Michael Beer
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.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): KU Leuven
Universidad Adolfo Ibanez
University of Liverpool
Tongji University
Type: Article
Journal: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume: 8
ISSN: 2376-7642
Publication date: 03.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Civil and Structural Engineering, Building and Construction, Safety, Risk, Reliability and Quality
Electronic version(s): https://doi.org/10.1061/AJRUA6.0001217 (Access: Closed)