Nonlinear Dynamics Isolated by Delaunay Triangulation Criteria
2004 (English)Report (Other academic)
Inspired by an idea by Q. Zhang, we show that Delaunay triangulation of data points sampled from a system with an additive nonlinearity gives a criterion by which a linear projection can be found that isolates the nonlinear dependence, leaving out the linear one. This isolation means the nonlinear modeling can be confined to a regressor space of lower dimensionality, which in turn means over-parameterization can be avoided. Monte Carlo simulations indicate that a particular criterion built on triangle asymmetries has a minimum that coincides with the sampled system nonlinear part. The criterion is however complex to compute and non-convex, which makes it difficult to optimize globally.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2004. , 17 p.
LiTH-ISY-R, ISSN 1400-3902 ; 2598
Identification, Delaunay triangulation, Nonlinear modeling, Monte Carlo simulation
IdentifiersURN: urn:nbn:se:liu:diva-55981ISRN: LiTH-ISY-R-2598OAI: oai:DiVA.org:liu-55981DiVA: diva2:316755