On-Line Recognition of Critical States in Chemical Reaction Systems
The behavior of a continuous chemical reactor may change in an unpredictable way, if some system parameter being subject to a slow drift passes a bifurcation point. Then, for instance, the temperature suddenly increases or starts oscillating, which may cause a loss of production or even reactor accidents.
A hybrid approach for the on-line recognition of bifurcation points in chemical reaction systems is presented. The method does not require any global mathematical model of the underlying process, but it creates local ones and adapts it to measurements by means of a least-squares-optimization. The local models consist of compositions of so-called normal forms, which are differential equations of minimal dimension, and neural networks.
The models are constructed in a way that system stability as well as the type of the bifurcation being about to happen can be easily read off on model parameters.
KeywordsNormal Form Hopf Bifurcation Bifurcation Point Static Bifurcation Unstable Steady State
Unable to display preview. Download preview PDF.
- Carr, J. (1981): Applications of Centre Manifold Theory. (Applied Mathematical Science, vol. 35 ) Springer, New YorkGoogle Scholar
- Guckenheimer, J., Holmes, P. (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York.Google Scholar
- Hertz, J., Krogh, A., Palmer, R. G. (1991): Introduction to the Theory of Neural Computation, first edition, Addison-Wesley, Redwood City, California.Google Scholar
- Seydel, R. (1993): BIFPACK: A program package for calculating bifurcations. Technical report, Universitat Ulm.Google Scholar
- Mihatsch, O. (1995): Recognition of critical states in chemical reaction systems using a normal form approach combined with neural nets. Report TUM-M9505, Technische Universitat München. [submitted to Chaos, Solitons and Fractals]Google Scholar