Hinging Hyperplanes for Non-Linear Identification
1995 (English)Report (Other academic)
The hinging hyperplane method is an elegant and efficient way of identifying piecewise linear models based on the data collected from an unknown linear or nonlinear system. This approach provides "a powerful and efficient alternative to neural networks with computing times several orders of magnitude less than fitting neural networks with a comparable number of parameters", as stated in . In this report, the hinging hyperplane approach is discussed from the system identification viewpoint. The bottleneck of this approach, namely, the hinge finding scheme, is investigated. The behavior of the hinge finding algorithm is very dependent on the initial values provided. Several methods for analyzing low dimensional cases are suggested. Although not general, these methods provide some interesting insights into the mechanisms of the hinge finding algorithm. Information from linear models produced by the multiple model least-squares is used to facilitate implementation. The possibility of using binary-tree structured models is also discussed. In addition, an extension of the hinging hyperplane idea leads to a hinge smoothing method in which the hinging hyperplanes are smoothed at the hinge. As a result a neural net like basis function is obtained. Finally, the hinging hyperplane method is used for modeling three real systems.
Place, publisher, year, edition, pages
Linköping: Linköping University , 1995. , 23 p.
LiTH-ISY-R, ISSN 1400-3902 ; 1713
Hinging hyperplanes, Non-linear identification
IdentifiersURN: urn:nbn:se:liu:diva-55196ISRN: LiTH-ISY-R-1713OAI: oai:DiVA.org:liu-55196DiVA: diva2:315780