The Nonlinear Gaussian Spectrum of Log-Normal Stochastic Processes and Variables

1999 ◽  
Vol 66 (4) ◽  
pp. 964-973 ◽  
Author(s):  
R. Ghanem
Keyword(s):  
Stochastic Processes ◽  
Polynomial Chaos ◽  
Analytical Investigation ◽  
Polynomial Chaos Expansion ◽  
Stochastic Finite Element Method ◽  
Chaos Expansion ◽  
Mathematical Properties ◽  
Log Normal ◽  
Exponential Operator ◽  
Gaussian Spectrum

A procedure is presented in this paper for developing a representation of lognormal stochastic processes via the polynomial chaos expansion. These are processes obtained by applying the exponential operator to a gaussian process. The polynomial chaos expansion results in a representation of a stochastic process in terms of multidimensional polynomials orthogonal with respect to the gaussian measure with the dimension defined through a set of independent normalized gaussian random variables. Such a representation is useful in the context of the spectral stochastic finite element method, as well as for the analytical investigation of the mathematical properties of lognormal processes.

Stochastic Finite Element Method Using Polynomial Chaos Expansion

2011 ◽  
Vol 199-200 ◽  
pp. 500-504 ◽  
Author(s):  
Wei Zhao ◽  
Ji Ke Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Polynomial Chaos ◽  
Expansion Method ◽  
Polynomial Chaos Expansion ◽  
Polynomial Expansion ◽  
Stochastic Finite Element Method ◽  
Chaos Expansion ◽  
Stochastic Finite Element ◽  
Element Method

We present a new response surface based stochastic finite element method to obtain solutions for general random uncertainty problems using the polynomial chaos expansion. The approach is general but here a typical elastostatics example only with the random field of Young's modulus is presented to illustrate the stress analysis, and computational comparison with the traditional polynomial expansion approach is also performed. It shows that the results of the polynomial chaos expansion are improved compared with that of the second polynomial expansion method.

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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