TY - JOUR

T1 - Bounding the first excursion probability of linear structures subjected to imprecise stochastic loading

AU - Faes, Matthias G.R.

AU - Valdebenito, Marcos A.

AU - Moens, David

AU - Beer, Michael

N1 - Funding Information: The Research Foundation Flanders is gratefully acknowledged for the support of Matthias Faes under Grant No. 12P3519N . Marcos Valdebenito acknowledges the support of ANID ( National Agency for Research and Development , Chile) under its program FONDECYT, Grant No. 1180271 ; Universidad Tecnica Federico Santa Maria under its program PAC (Programa Asistente Cientifico 2017); and the Alexander von Humboldt Foundation through its program Humboldt Research Fellowship for Experienced Researchers.

PY - 2020/10/15

Y1 - 2020/10/15

N2 - This paper presents a highly efficient and accurate approach to determine the bounds on the first excursion probability of a linear structure that is subjected to an imprecise stochastic load. Traditionally, determining these bounds involves solving a double loop problem, where the aleatory uncertainty has to be fully propagated for each realization of the epistemic uncertainty or vice versa. When considering realistic structures such as buildings, whose numerical models often contain thousands of degrees of freedom, such approach becomes quickly computationally intractable. In this paper, we introduce an approach to decouple this propagation by applying operator norm theory. In practice, the method determines those epistemic parameter values that yield the bounds on the probability of failure, given the epistemic uncertainty. The probability of failure, conditional on those epistemic parameters, is then computed using the recently introduced framework of Directional Importance Sampling. Two case studies involving a modulated Clough-Penzien spectrum are included to illustrate the efficiency and exactness of the proposed approach.

AB - This paper presents a highly efficient and accurate approach to determine the bounds on the first excursion probability of a linear structure that is subjected to an imprecise stochastic load. Traditionally, determining these bounds involves solving a double loop problem, where the aleatory uncertainty has to be fully propagated for each realization of the epistemic uncertainty or vice versa. When considering realistic structures such as buildings, whose numerical models often contain thousands of degrees of freedom, such approach becomes quickly computationally intractable. In this paper, we introduce an approach to decouple this propagation by applying operator norm theory. In practice, the method determines those epistemic parameter values that yield the bounds on the probability of failure, given the epistemic uncertainty. The probability of failure, conditional on those epistemic parameters, is then computed using the recently introduced framework of Directional Importance Sampling. Two case studies involving a modulated Clough-Penzien spectrum are included to illustrate the efficiency and exactness of the proposed approach.

KW - First excursion probability

KW - Imprecise probabilities

KW - Interval analysis

KW - Linear structure

KW - Stochastic loading

UR - http://www.scopus.com/inward/record.url?scp=85088393269&partnerID=8YFLogxK

U2 - 10.1016/j.compstruc.2020.106320

DO - 10.1016/j.compstruc.2020.106320

M3 - Article

AN - SCOPUS:85088393269

VL - 239

JO - Computers & structures

JF - Computers & structures

SN - 0045-7949

M1 - 106320

ER -