scholarly journals Sparse grid quadrature on products of spheres

2015 ◽  
Vol 70 (3) ◽  
pp. 485-517
Author(s):  
Markus Hegland ◽  
Paul Leopardi
Keyword(s):  
Sparse Grid ◽  
Sparse Grid Quadrature ◽  
Products Of Spheres

Propagation of Parametric Uncertainties in a Nonlinear Aeroelastic System Using an Improved Adaptive Sparse Grid Quadrature Routine

2018 ◽  
Vol 4 (4) ◽  
Author(s):  
Harshini Devathi ◽  
Sunetra Sarkar
Keyword(s):  
Basis Functions ◽  
Sparse Grid ◽  
Parametric Uncertainties ◽  
Relative Importance ◽  
Stochastic Response ◽  
Aeroelastic System ◽  
Accelerated Convergence ◽  
Aerodynamic Parameters ◽  
Stall Flutter ◽  
Sparse Grid Quadrature

A novel uncertainty quantification routine in the genre of adaptive sparse grid stochastic collocation (SC) has been proposed in this study to investigate the propagation of parametric uncertainties in a stall flutter aeroelastic system. In a hypercube stochastic domain, presence of strong nonlinearities can give way to steep solution gradients that can adversely affect the convergence of nonadaptive sparse grid collocation schemes. A new adaptive scheme is proposed here that allows for accelerated convergence by clustering more discretization points in regimes characterized by steep fronts, using hat-like basis functions with nonequidistant nodes. The proposed technique has been applied on a nonlinear stall flutter aeroelastic system to quantify the propagation of multiparametric uncertainty from both structural and aerodynamic parameters. Their relative importance on the stochastic response is presented through a sensitivity analysis.

Sparse-grid quadrature nonlinear filtering

Automatica ◽  
2012 ◽  
Vol 48 (2) ◽  
pp. 327-341 ◽  
Author(s):  
Bin Jia ◽  
Ming Xin ◽  
Yang Cheng
Keyword(s):  
Nonlinear Filtering ◽  
Sparse Grid ◽  
Sparse Grid Quadrature
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