Papers on use of nondimensionalization in RSAs?

[Christian Gogu]

Dear All,

I am currently writing a paper which involves using dimensional analysis to reduce the number of variables needed for a response surface approximation (RSA). On a thermal problem we basically managed to reduce the number of variables required from 15 to 2 by a combination of mild simplifying assumptions, nondimensionalization and a global sensitivity analysis. For my introduction I was wondering if anyone has own experience with using dimensional analysis in the context of improving the construction of an RSA (whether reducing the number of variables, improving accuracy or any other improvements)? Any references or a discussion on this are welcome.
Thanks.

Best regards,
Christian Gogu

[eacar]

You can use Sobol's sensitivity equations.
If you are in random variable space, you can use sensitivity derivatives proposed by Wu.

[Christian Gogu]

Yes that's what we did. We used Sobol's global sensitivity analysis on nondimensional parameters characteristic of the problem. We found that in our case combining nondimensionalization and global sensitivity analysis can lead to an even higher reduction in the number of variables.
Maybe to avoid confusion, when I say dimensional analysis previousely, I mean nondimenisonalization.

My question is just for knowing what experience other people could have with using nondimensionalization (alone or in combination with other techniques) to reduce the number of variables needed for an RSA.

[satchi]

Hi Christian,

I would suggest the following paper. This is where I first came across the idea of non-dimensionalization in response surface modeling.

Scaling Laws From Statistical Data and Dimensional Analysis
Journal of Applied Mechanics -- September 2005 -- Volume 72, Issue 5, pp. 648-657 .

The authors web page is
www.mines.edu/~pmendez/

Also see paper by Vignaux.
www.mcs.vuw.ac.nz/~vignaux/docs/maxent.pdf

Satchi