Title :
Chaotic attractor learning and how to deal with nonlinear singularities
Author :
Bakker, Rembrandt ; Schouten, Jaap C. ; Coppens, Marc-Olivier ; Takens, Roris ; Van den Bleek, Cor M.
Author_Institution :
Dept. of Chem. Reactor Eng., Delft Univ. of Technol., Netherlands
Abstract :
In linear regression it is common practice to use principal component analysis (PCA) to find and remove directions in the input space that are not covered by the observed data. PCA fails to identify these `singular directions´ if the data lie on a lower dimensional nonlinear subspace. Typically, this is the case for data observed from deterministic chaotic systems. In this paper we present a viable nonlinear counterpart for principal component regression, and show why this algorithm can learn stable models for chaotic dynamics where other approaches often fail. The algorithm is applied to an experimental chaotic bubble column, with data highly contaminated with system noise and measurement errors
Keywords :
autoregressive processes; chaos; learning (artificial intelligence); nonlinear dynamical systems; principal component analysis; autoregressive systems; chaotic attractor learning; chaotic bubble column; chaotic dynamics; deterministic chaotic systems; linear regression; lower dimensional nonlinear subspace; measurement errors; nonlinear singularities; observed data; principal component analysis; singular directions; stable models; system noise; Chaos; Chemical reactors; Chemical technology; Mathematics; Neural networks; Noise measurement; Nonlinear dynamical systems; Pollution measurement; Principal component analysis; Space technology;
Conference_Titel :
Adaptive Systems for Signal Processing, Communications, and Control Symposium 2000. AS-SPCC. The IEEE 2000
Conference_Location :
Lake Louise, Alta.
Print_ISBN :
0-7803-5800-7
DOI :
10.1109/ASSPCC.2000.882520