A New Algorithm for Solving the Random Eigenvalue Problem Using Polynomial Chaos Expansion

2005 ◽  
Author(s):  
Debraj Ghosh ◽  
Roger Ghanem
Keyword(s):  
Eigenvalue Problem ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Random Eigenvalue ◽  
Random Eigenvalue Problem

An Enrichment Scheme for Polynomial Chaos Expansion Applied to Random Eigenvalue Problem

2005 ◽  
Author(s):  
Roger Ghanem ◽  
Debraj Ghosh
Keyword(s):  
Eigenvalue Problem ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Eigenvalues And Eigenvectors ◽  
System Parameters ◽  
Statistical Behavior ◽  
Random Eigenvalue ◽  
Clustered Eigenvalues ◽  
Random Eigenvalue Problem

For a system with the parameters modeled as uncertain, polynomial approximations such as polynomial chaos expansion provide an effective way to estimate the statistical behavior of the eigenvalues and eigenvectors, provided the eigenvalues are widely spaced. For a system with a set of clustered eigenvalues, the corresponding eigenvalues and eigenvectors are very sensitive to perturbation of the system parameters. An enrichment scheme to the polynomial chaos expansion is proposed here in order to capture the behavior of such eigenvalues and eigenvectors. It is observed that for judiciously chosen enrichment functions, the enriched expansion provides better estimate of the statistical behavior of the eigenvalues and eigenvectors.

scholarly journals Deep Neural Network and Polynomial Chaos Expansion-Based Surrogate Models for Sensitivity and Uncertainty Propagation: An Application to a Rockfill Dam

Water ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 1830
Author(s):  
Gullnaz Shahzadi ◽  
Azzeddine Soulaïmani
Keyword(s):  
Polynomial Chaos ◽  
Complex Structure ◽  
Uncertainty Propagation ◽  
Surrogate Models ◽  
Polynomial Chaos Expansion ◽  
Soil Parameters ◽  
Chaos Expansion ◽  
Rockfill Dam ◽  
Parametric Studies ◽  
The Impact

Computational modeling plays a significant role in the design of rockfill dams. Various constitutive soil parameters are used to design such models, which often involve high uncertainties due to the complex structure of rockfill dams comprising various zones of different soil parameters. This study performs an uncertainty analysis and a global sensitivity analysis to assess the effect of constitutive soil parameters on the behavior of a rockfill dam. A Finite Element code (Plaxis) is utilized for the structure analysis. A database of the computed displacements at inclinometers installed in the dam is generated and compared to in situ measurements. Surrogate models are significant tools for approximating the relationship between input soil parameters and displacements and thereby reducing the computational costs of parametric studies. Polynomial chaos expansion and deep neural networks are used to build surrogate models to compute the Sobol indices required to identify the impact of soil parameters on dam behavior.

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