Heidelberg 1999 – scientific programme

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KY: Kybernetik

KY 3: Datenerfassung | Datenanalyse

KY 3.1: Talk

Tuesday, March 16, 1999, 11:00–11:45, ZO 3

Data-Based Modeling of Nonlinear Dynamical Systems A Lagrangian Approach — •Josef Wagenhuber — Siemens AG, Corporate Technology, Information & Communications 4, Otto-Hahn-Ring 6, D-81730 Munich, Germany

We present a new algorithm for the adaptation of parameters or weights of a continous dynamical system, given by differential equations, to a discrete set of integral data, e.g. a fininite time series of measurements.This method works about a factor equal to the dimension of the system’s state space faster than conventional sensitivity analysis and does not assume a continuous measurement signal.Representing a process by a system of differential equations allows the incorporation of a-priori knowledge, which especially in technical applications is given by differential relationships between certain process variables, whereas a system representation using discrete, recurrent equations renders the inclusion of a-priori knowledge more diffcult. This algorithm can also be generalized to the modeling of spatio-temporal systems. It computes the gradient of the model-data mismatch defined by an arbitrary differentiable objective function directly without an additional calculation of sensitivities using an abstract formalism of Lagrange multipliers in function spaces. In order to illustrate the capabilities of this algorithm for dynamic modeling we shortly review the results of an already published application of this method to the modeling of an industrially important chemical reaction performed in a laboratory-scale reactor.

Keywords: Nonlinear Dynamics, System Identification, Neural Networks, Process Modeling, Time Series eigentliche Text, genau einmal