TY - JOUR

T1 - Distribution-free P-box processes based on translation theory

T2 - Definition and simulation

AU - Faes, Matthias G.R.

AU - Broggi, Matteo

AU - Chen, Guan

AU - Phoon, Kok Kwang

AU - Beer, Michael

N1 - Funding Information: Matthias Faes acknowledges the partial financial support of the Research Foundation Flanders (FWO), Belgium under grant number 12P3519N as well as the Alexander von Humboldt foundation, Germany under the Humboldt Research Fellowship framework

PY - 2022/7

Y1 - 2022/7

N2 - Typically, non-deterministic models of spatial or time dependent uncertainty are modelled using the well-established random field framework. However, while tailored for exactly these types of time and spatial variations, stochastic processes and random fields currently have only limited success in industrial engineering practice. This is mainly caused by its computational burden, which renders the analysis of industrially sized problems very challenging, even when resorting to highly efficient random field analysis methods such as EOLE. Apart from that, also the methodological complexity, high information demand and rather indirect control of the spatial (or time) variation has limited its cost–benefit potential for potential end-users. This data requirement was recently relaxed by some of the authors with the introduction of imprecise random fields, but so far the method is only applicable to parametric p-box valued stochastic processes and random fields. This paper extends these concepts by expanding the framework towards distribution-free p-boxes. The main challenges addressed in this contribution are related to both the non-Gaussianity of realisations of the imprecise random field in between the p-box bounds, as well as maintaining the imposed auto-correlation structure while sampling from the p-box. Two case studies involving a dynamical model of a car suspension and the settlement of an embankment are included to illustrate the presented concepts.

AB - Typically, non-deterministic models of spatial or time dependent uncertainty are modelled using the well-established random field framework. However, while tailored for exactly these types of time and spatial variations, stochastic processes and random fields currently have only limited success in industrial engineering practice. This is mainly caused by its computational burden, which renders the analysis of industrially sized problems very challenging, even when resorting to highly efficient random field analysis methods such as EOLE. Apart from that, also the methodological complexity, high information demand and rather indirect control of the spatial (or time) variation has limited its cost–benefit potential for potential end-users. This data requirement was recently relaxed by some of the authors with the introduction of imprecise random fields, but so far the method is only applicable to parametric p-box valued stochastic processes and random fields. This paper extends these concepts by expanding the framework towards distribution-free p-boxes. The main challenges addressed in this contribution are related to both the non-Gaussianity of realisations of the imprecise random field in between the p-box bounds, as well as maintaining the imposed auto-correlation structure while sampling from the p-box. Two case studies involving a dynamical model of a car suspension and the settlement of an embankment are included to illustrate the presented concepts.

KW - Imprecise probability

KW - Probability box

KW - Random field

KW - Scarce data

KW - Stochastic process

UR - http://www.scopus.com/inward/record.url?scp=85130091780&partnerID=8YFLogxK

U2 - 10.1016/j.probengmech.2022.103287

DO - 10.1016/j.probengmech.2022.103287

M3 - Article

AN - SCOPUS:85130091780

VL - 69

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

SN - 0266-8920

M1 - 103287

ER -