Recent Advances in Polynomial Chaos Expansion: Theory, Applications and Software

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F23%3APU150154" target="_blank" >RIV/00216305:26110/23:PU150154 - isvavai.cz</a>

Výsledek na webu

<a href="http://tces.vsb.cz/Home/" target="_blank" >http://tces.vsb.cz/Home/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.35181/tces-2023-0015" target="_blank" >10.35181/tces-2023-0015</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Recent Advances in Polynomial Chaos Expansion: Theory, Applications and Software

Popis výsledku v původním jazyce

The paper is focused on recent advances in uncertainty quantification using polynomial chaos expansion (PCE). PCE is a well-known technique for approximation of costly mathematical models with random inputs – surrogate model. Although PCE is a widely used technique and it has several advantages over various surrogate models, it has still several limitations and research gaps. This paper reviews some of the recent theoretical developments in PCE. Specifically a new active learning method optimizing the experimental design and an extension of analytical statistical analysis using PCE will be reviewed. These two topics represent crucial tools for efficient applications: active learning leads generally to a significantly more efficient construction of PCE and improved statistical analysis allows for analytical estimation of higher statistical moments directly from PCE coefficients. Higher statistical moments can be further used for the identification of probability distribution and estimation of design quantiles, which is a crucial task for the probabilistic analysis of structures. Selected applications of the theoretical methods are briefly presented in a context of civil engineering as well as some preliminary results of further research. A part of the paper also presents UQPy package containing state-of-the-art implementation of the PCE theory

Název v anglickém jazyce

Recent Advances in Polynomial Chaos Expansion: Theory, Applications and Software

Popis výsledku anglicky

The paper is focused on recent advances in uncertainty quantification using polynomial chaos expansion (PCE). PCE is a well-known technique for approximation of costly mathematical models with random inputs – surrogate model. Although PCE is a widely used technique and it has several advantages over various surrogate models, it has still several limitations and research gaps. This paper reviews some of the recent theoretical developments in PCE. Specifically a new active learning method optimizing the experimental design and an extension of analytical statistical analysis using PCE will be reviewed. These two topics represent crucial tools for efficient applications: active learning leads generally to a significantly more efficient construction of PCE and improved statistical analysis allows for analytical estimation of higher statistical moments directly from PCE coefficients. Higher statistical moments can be further used for the identification of probability distribution and estimation of design quantiles, which is a crucial task for the probabilistic analysis of structures. Selected applications of the theoretical methods are briefly presented in a context of civil engineering as well as some preliminary results of further research. A part of the paper also presents UQPy package containing state-of-the-art implementation of the PCE theory

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

20102 - Construction engineering, Municipal and structural engineering

Projekt

<a href="/cs/project/GA22-00774S" target="_blank" >GA22-00774S: Pravděpodobnostní posouzení v mostním inženýrství za užití náhradního metamodelu (MAPAB)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series

ISSN

1804-4824

e-ISSN

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Svazek periodika

23

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

7

Strana od-do

47-53

Kód UT WoS článku

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EID výsledku v databázi Scopus

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