Realization-Preserving Structure and Order Reduction of Nonlinear Energetic System

Text written in October 2008 for the mor4ansys group.

Ersal, T., Fathy, H. K., and Stein, J. L., 2009, “Realization-Preserving Structure and Order Reduction of Nonlinear Energetic System Models Using Energy Trajectory Correlations”, Journal of Dynamic Systems Measurement and Control, 131(3), pp. 031004 (8p)
http://dx.doi.org/10.1115/1.3072128

I have read another paper written by authors of A Review of Proper Modeling Techniques (http://www-personal.umich.edu/~stein/Publications.pdf).

Actually I have mixed the order of papers. This should be the first paper and the paper Model reduction in vehicle dynamics using importance analysis, about which I have written a week ago, should be the second. The relationships between the papers are similar to theory and application, and it happened that I have read the application paper first and then the theory background. The other way around would be better.
You can request the paper from the authors or the related information is in Chapter 5 of Tulga Ersal’s thesis

http://deepblue.lib.umich.edu/handle/2027.42/57603

This paper describes the method in much more detail. Anyway, what I have written one week ago was correct. The idea is to run a characteristic trajectory for a nonlinear system and then to simplify the model using the energy flow between the components as an indicator. I find the idea very interesting. It would be good, as I have mentioned, to try it for a nonlinear electrical circuit.

A comment. The authors stress the importance to preserve the realization variables. This resembles me adaptive mesh refinement in finite elements. Indeed with this technique one can reach an optimal number of elements, in a way to develop a proper model. However, the dimension of such a model will still be much larger than that obtained by for example implicit moment matching. The elements have a local function support by their nature and I would say that only by using global functions the minimal number of the generalized variables could be reached.


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