A Python module that implements tools for the simulation and identification of random fields using the Karhunen-Loeve expansion representation.

This folder contains:

• a Python module named randomfields,

• 4 Python scripts implementing basic examples, showing the ways the module functionalities can be used. NB: simulation scripts must be run before their corresponding identification counterpart because the simulation scripts generate input randomfield data (dumped to ascii file) for identification.

The present Python module and its examples rely on:

• OpenTURNS (>= 1.4)

• Numpy (>= 1.6)

• Scipy (>= 0.9)

• Matplotlib (>= 1.0)

The example scripts can be run from this folder for testing. They'll import the randomfields module from the local folder.

In order to make the randomfields module installation systemwide, you may either:

• copy the randomfields module (directory) in the "site-package" directory of your Python distribution (e.g. /usr/local/lib/python2.7/site-package). NB: You might need admin rights to do so.

• append the parent directory of the randomfields module (directory) to your PYTHONPATH environment variable.

The randomfields module uses Python docstrings. Use either "help(object)" in a classic Python shell or "object?" in an improved Python (IPython) shell.

This module was implemented by Phimeca Engineering SA, EdF and Institut Navier (ENPC). It is shipped as is without any warranty of any kind.

Contributions are welcome.

• Implement other Galerkin schemes such as the Haar wavelet Galerkin scheme proposed by Phoon et al. (2002). More advanced (smoother) wavelets could also be used.

• Call for data: if you have any, please contribute, possibly along with an identification example.

• Any other idea within the scope of the module is welcome!

• Phoon, K.; Huang, S. & Quek, S. Implementation of Karhunen-Loeve expansion for simulation using a wavelet-Galerkin scheme Prob. Eng. Mech., 2002, 17, 293-303

• Ghanem, R. & Spanos, P. Stochastic Finite Elements: A Spectral Approach (Revised edition) Dover Publications Inc., 2003, 224

• Sudret, B. & Der Kiureghian, A. Stochastic Finite Element Methods and Reliability, A State-of-the-Art report University of California, Berkeley, 2000

• Desceliers, C.; Soize, C. & Ghanem, R. Identification of chaos representations of elastic properties of random media using experimental vibration tests Comput. Mech., 2007, 39, 831-838