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## Random field representation methods

version 1.2.0.0 (16.2 KB) by
Implementation of EOLE, OSE and K-L (Discrete, Galerkin & Nyström) methods for 1D random fields

Updated 22 Jan 2020

Different covariance kernels are defined to illustrate three series expansion methods for the representation of 1D random fields: the 'expansion optimal linear estimator (EOLE)', the orthogonal series expansion (OSE)' and the 'Karhunen-Loève (K-L)' methods. The solution of the K-L eigenvalue problem is computed with the Discrete, Nyström and Galerkin methods. The main references are: "Stochastic finite element methods and reliability" by Sudret and Der Kiureghian, and "Stochastic finite elements: a spectral approach" by Ghanem and Spanos.
Several references to equations and useful comments are written in order to provide a better understanding of the codes. The programs estimate the corresponding eigenvalues and eigenvectors of the covariance kernel, and plot several random field realizations, together with the covariance approximation.

Any suggestions, corrections and/or improvements are kindly accepted :-)

### Cite As

Felipe Uribe (2021). Random field representation methods (https://www.mathworks.com/matlabcentral/fileexchange/52372-random-field-representation-methods), MATLAB Central File Exchange. Retrieved .

Diogo Cecílio

Dear Felipe Uribe,

i have the same question as Ji Bao in KL expansion Galekin method about the eigenvector normalization. Could you explain better how this normalization it's done? Thank you very much!

Diogo Cecílio

i forgot to mention it is in KL expansion Galekin method! tank you again!

How to generate random field in 2D using this?

Ji Bao

Felipe Uribe

Dear all,
It has been a while since I checked the codes and comments. I just created an update of the KL expansion folder.
Thank you for the interest !

Ji Bao

Hi Felipe,

1st, I think in KL expansion Galekin method, the eigenvectors obtained should be normalized in terms of B matrix, otherwise, your variance error will be out of bound.
2nd, in the KL expansion discrete integration. As mentioned by Kiureghian. D. (in the paper 'The finite element method in structural reliability'), there should be any variance errors for this method. However, the main error in your code comes from the trapezoid integral method. If you change the way to normalize the eigenvector, there should not be any error for the discrete integration method.

zhang hongbo

do you have any reference for your functions?

Slimane Grine

Hamed Nikbakht

Did you compare your EOLE simulation results with FERUM implementation by any chance?

Thanks,

##### MATLAB Release Compatibility
Created with R2017b
Compatible with any release
##### Platform Compatibility
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