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A Bluff-and-Fix Algorithm for Polynomial Chaos Methods [PDF]
Computational Science – ICCS 2020, 2020 Stochastic Galerkin methods can be used to approximate the solution to a differential equation in the presence of uncertainties represented as stochastic inputs or parameters. The strategy is to express the resulting stochastic solution using [Formula: see text] terms of a polynomial chaos expansion and then derive and solve a deterministic, coupled ...
Lyman L, Iaccarino G.
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HIERARCHICAL ADAPTIVE POLYNOMIAL CHAOS EXPANSIONS [PDF]
Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2015), 2015 Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be required, which leads to a large polynomial basis whereas usually only a few of the basis functions are in fact ...
Mai, Chu V., Sudret, Bruno
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Projection Pursuit Adaptation on Polynomial Chaos Expansions
Computer Methods in Applied Mechanics and Engineering, 2022 The present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos expansions (PCE) were recently proposed to construct low-dimensional approximations adapted to specific quantities
Xiaoshu Zeng, Roger Ghanem
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A conditional stochastic projection method applied to a parametric vibrations problem
Journal of Civil Engineering and Management, 2014 Parametric vibrations can be observed in cable-stayed bridges due to periodic excitations caused by a deck or a pylon. The vibrations are described by an ordinary differential equation with periodic coefficients.
Wlodzimierz Brzakala, Aneta Herbut
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MECHANICAL STRUCTURAL RELIABILITY ANALYSIS BASED ON POLYNOMIAL CHAOS EXPANSIONS
Jixie qiangdu, 2022 Reliability is one of important index in the analysis and evaluation of mechanical structure. Aiming at the problems of various failure modes and low efficiency of reliability evaluation for complex mechanical structures, the reliability analysis method ...
WANG ZhiMing +4 more
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Vehicle parameter sensitivity with polynomial chaos
Revista Iberoamericana de Automática e Informática Industrial RIAI, 2015 It is interesting to analyze the parameter sensitivity of mathematical models that describe physical systems, and it deserves particular attention the sensitivity study of models with uncertainty in the parameter values.
Eduardo Haro +2 more
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From wind to loads: wind turbine site-specific load estimation with surrogate models trained on high-fidelity load databases [PDF]
Wind Energy Science, 2018 We define and demonstrate a procedure for quick assessment of site-specific lifetime fatigue loads using simplified load mapping functions (surrogate models), trained by means of a database with high-fidelity load simulations.
N. Dimitrov +3 more
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Performance Evaluation of Generalized Polynomial Chaos [PDF]
, 2003 In this paper we review some applications of generalized polynomial chaos expansion for uncertainty quantification. The mathematical framework is presented and the convergence of the method is demonstrated for model problems. In particular, we solve the first-order and second-order ordinary differential equations with random parameters, and examine the
Dongbin Xiu +3 more
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A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters
Complexity, 2018 The generalized Polynomial Chaos Expansion Method (gPCEM), which is a random uncertainty analysis method by employing the orthogonal polynomial bases from the Askey scheme to represent the random space, has been widely used in engineering applications ...
Rugao Gao, Keping Zhou, Yun Lin
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IEEE Access, 2019 The problem of characterizing the sensitivity indices of structural performance considering random and interval uncertainty variables simultaneously is analyzed.
Chan Qiu +3 more
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