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Identification of a nonlinear circuit
Author(s) -
Timmer J.,
Rust H.,
Horbelt W.,
Voss H.
Publication year - 2002
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/1617-7061(200203)1:1<73::aid-pamm73>3.0.co;2-s
Subject(s) - parameterized complexity , series (stratigraphy) , nonlinear system , identification (biology) , parametric statistics , parametric model , nonparametric statistics , computer science , attractor , algorithm , system identification , differential (mechanical device) , mathematics , control theory (sociology) , artificial intelligence , engineering , data mining , econometrics , measure (data warehouse) , statistics , paleontology , mathematical analysis , physics , botany , control (management) , quantum mechanics , aerospace engineering , biology
The identification of a differential equation underlying a measured time series is a prerequisite for numerous types of applications. In the validation of a proposed parameterized model one often faces the dilemma that it is hard to decide whether possible discrepancies between the measured time series and the simulated model output are caused by an inappropriate model or by wrongly specified parameters in a correct type of model. We propose a combination of parametric modelling based on Bock's multiple shooting algorithm and nonparametric modelling based on optimal transformations as a strategy to test proposed models and if rejected suggest and test new ones. We exemplify this strategy on an experimental time series from a nonlinear chaotically oscillating circuit where we finally obtain an extremely accurate reconstruction of the observed attractor.