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Probabilistic load flow by generalized polynomial chaos method
2016 IEEE Power and Energy Society General Meeting (PESGM), 2016The probabilistic load flow (PLF) problem is solved by a new approach named generalized polynomial chaos (gPC) method. This method combines the techniques of gPC expansion and Galerkin method and transforms the PLF equations into a set of deterministic equations.
null Hao Wu +4 more
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Generalized polynomial chaos for the convection diffusion equation with uncertainty
International Journal of Heat and Mass Transfer, 2016Abstract In this paper, several numerical algorithms are presented for solving the convection diffusion equation with random diffusivity and periodic boundary conditions. Based on the generalized polynomial chaos expansion and Galerkin projection, the stochastic convection diffusion equation is turned into a set of coupled deterministic equations ...
Ning Li +3 more
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A generalized polynomial chaos based ensemble Kalman filter with high accuracy
Journal of Computational Physics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jia Li 0048, Dongbin Xiu
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Constructing Continuous-Time Chaos-Generating Templates Using Polynomial Approximation
ECMS 2010 Proceedings edited by A Bargiela S A Ali D Crowley E J H Kerckhoffs, 2010Aiming at developing a methodology for constructing continuous-time chaotic dynamical systems as flexible pattern generators, this paper discusses a strategy for binding desired unstable periodic orbits into a chaotic attractor. The strategy is comprised of the following two stages: constructing an interim “chaos-generating template”, and deforming the
Hidetaka Ito +3 more
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Fault detection and diagnosis with parametric uncertainty using generalized polynomial chaos
Computers & Chemical Engineering, 2015Abstract This paper presents a new methodology to identify and diagnose intermittent stochastic faults occurring in a process. A generalized polynomial chaos (gPC) expansion representing the stochastic inputs is employed in combination with the nonlinear mechanistic model of the process to calculate the resulting statistical distribution of measured ...
Yuncheng Du +2 more
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Generalized polynomial chaos based surrogate models for acoustics and vibrations
The Journal of the Acoustical Society of America, 2022This work explores generalized polynomial chaos (GPC) surrogate models and their effectiveness for general acoustics and vibration applications. GPC is primarily known as an uncertainty quantification (UQ) technique and in that context the underlying polynomial-based model has been shown to be effective in mapping input probability distributions to the
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A Goal-Oriented Reduced Basis Methods-Accelerated Generalized Polynomial Chaos Algorithm
SIAM/ASA Journal on Uncertainty Quantification, 2016Summary: The nonintrusive generalized polynomial chaos (gPC) method is a popular computational approach for solving partial differential equations with random inputs. The main hurdle preventing its efficient direct application for high-dimensional input parameters is that the size of many parametric sampling meshes grows exponentially in the number of ...
Jiahua Jiang +2 more
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An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics, 2005Xiaoliang Wan, George Em Karniadakis
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