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

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

Článek recenzovaný mimo WoS a Scopus

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

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

Uncertainty quantification; polynomial chaos expansion; active learning; statistical analysis.

Uncertainty quantification; polynomial chaos expansion; active learning; statistical analysis.

NOVÁK, L.; NOVÁK, D.

2024

31.12.2023

VSB - Technical University of Ostrava

Ostrava, Czech Republic

1804-4824

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

23

2

Česká republika

47

53

7

http://tces.vsb.cz/Home/