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Related papers: A Sparse Polynomial Chaos Expansion-Based Method f…

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We apply the Tensor Train (TT) decomposition to construct the tensor product Polynomial Chaos Expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some…

Numerical Analysis · Mathematics 2015-03-12 Sergey Dolgov , Boris N. Khoromskij , Alexander Litvinenko , Hermann G. Matthies

Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…

Computation · Statistics 2018-10-17 Negin Alemazkoor , Hadi Meidani

This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…

Computation · Statistics 2017-04-05 Negin Alemazkoor , Hadi Meidani

A spline chaos expansion, referred to as SCE, is introduced for uncertainty quantification analysis. The expansion provides a means for representing an output random variable of interest with respect to multivariate orthonormal basis…

Numerical Analysis · Mathematics 2019-11-12 Sharif Rahman

The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…

Systems and Control · Electrical Eng. & Systems 2026-03-24 Le Fang , Wangkun Xu , Fei Teng

In this paper, we discuss a method to find the most influential power system parameters to the probabilistic transient stability assessment problem---finding the probability distribution of the critical clearing time. We perform the…

Systems and Control · Electrical Eng. & Systems 2020-10-23 Raphael L. V. Fortulan , Luís F. C. Alberto

Sub-terahertz (subTHz) antennas will play an important role in the next generations of wireless communication systems. However, when comes to the subTHz frequency spectrum, the antenna fabrication tolerance needs to be accurately considered…

Information Theory · Computer Science 2024-04-09 Aristeides D. Papadopoulos , Yihan Ma , Qi Luo , George C. Alexandropoulos

We consider the effect of multiple stochastic parameters on the time-average quantities of chaotic systems. We employ the recently proposed \cite{Kantarakias_Papadakis_2023} sensitivity-enhanced generalized polynomial chaos expansion,…

Chaotic Dynamics · Physics 2023-11-02 George Papadakis , Kyriakos D. Kantarakias

This paper presents a method for performing Uncertainty Quantification in high-dimensional uncertain spaces by combining arbitrary polynomial chaos with a recently proposed scheme for sensitivity enhancement (1). Including available…

Numerical Analysis · Mathematics 2024-02-09 Nick Pepper , Francesco Montomoli , Kyriakos Kantarakias

Accurate and efficient uncertainty quantification is essential for resilience assessment of modern power systems under high impact and low probability disturbances. Data driven sparse polynomial chaos expansion (DDSPCE) provides a…

Systems and Control · Electrical Eng. & Systems 2026-02-26 Mahsa Ebadat-Parast , Xiaozhe Wang

In this letter, we compare three polynomial chaos expansion (PCE)-based methods for ANCOVA (ANalysis of COVAriance) indices based global sensitivity analysis for correlated random inputs in two power system applications. Surprisingly, the…

Signal Processing · Electrical Eng. & Systems 2023-07-17 Xiaoting Wang , Rong-Peng Liu , Xiaozhe Wang , François Bouffard

Uncertainty quantification (UQ) has received much attention in the literature in the past decade. In this context, Sparse Polynomial chaos expansions (PCE) have been shown to be among the most promising methods because of their ability to…

Methodology · Statistics 2017-03-17 N. Fajraoui , S. Marelli , B. Sudret

A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled,…

Systems and Control · Electrical Eng. & Systems 2021-04-20 Dalong Shi , Xiang Fang , Florian Holzapfel

In this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns. Here, the quantity of interest is the stationary…

Probability · Mathematics 2017-05-17 Katia Bachi , Cédric Chauvière , Hacène Djellout , Karim Abbas

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of…

Numerical Analysis · Mathematics 2018-11-28 Xiu Yang , Xiaoliang Wan , Lin Lin , Huan Lei

Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs. PCEs for models with independent inputs have been extensively explored in…

Systems and Control · Electrical Eng. & Systems 2021-06-02 Zhanlin Liu , Youngjun Choe

Surrogate modeling of costly mathematical models representing physical systems is challenging since it is typically not possible to create a large experimental design. Thus, it is beneficial to constrain the approximation to adhere to the…

Machine Learning · Computer Science 2023-09-06 Lukáš Novák , Himanshu Sharma , Michael D. Shields

We present a regression technique for data-driven problems based on polynomial chaos expansion (PCE). PCE is a popular technique in the field of uncertainty quantification (UQ), where it is typically used to replace a runnable but expensive…

Machine Learning · Statistics 2019-04-02 E. Torre , S. Marelli , P. Embrechts , B. Sudret

We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization. We compare two strategies of the…

Numerical Analysis · Mathematics 2014-06-12 Sergey Dolgov , Boris N. Khoromskij , Alexander Litvinenko , Hermann G. Matthies

Recently, the use of Polynomial Chaos Expansion (PCE) has been increasing to study the uncertainty in mathematical models for a wide range of applications and several extensions of the original PCE technique have been developed to deal with…

Numerical Analysis · Mathematics 2014-06-23 Maria Navarro , Jeroen Witteveen , Joke Blom