Non Linear Prediction of Fluidized Bed Pressure Fluctuation Signal
Advancing the chemical engineering fundamentals
Particulate Systems (T2-3P)
Keywords: Chaotic Attractor, Fluidized Bed, Pressure Fluctuation
Non linear time series techniques have been applied to pressure fluctuation of a fluidized bed. A great advantage of pressure signals is that they include the effect of many different dynamic phenomena taking place in the bed, such as bubble formation, bubble coalescence and bubble passage. Attractor reconstruction is usually the first step in the analysis of dynamical systems. The method of delays reconstructs the attractor dynamics by using time delay and embedding dimension to carry out analysis in the reconstructed state space. A number of methods have been developed in determining the time delay and the minimum embedding dimension. In the present study, several methods have been tested in order to determine the best possible attractor reconstruction. After reconstructing the attractor, determinism test was performed to verify if the studied time series indeed originates from a deterministic system. In fact, it is desired to verify whether the series is deterministic and whether it contains enough relevant information to make predictions. If both conditions are fulfilled, a sufficiently long segment of data should be enough to predict the next segment. Several state space based prediction methods, i.e., nearest neighbors, delta-epsilon and polynomial based methods were used to predict next segment of pressure fluctuation. The quality of a non linear prediction could be assessed by comparison of the predicted data for last segment of known sample time series of pressure signal with its original benchmark. Chaotic invariants (i.e., fractal dimension, entropy and Lyapunov exponent spectrum) of measured and predicted time series of pressure signals were compared next. Fractal dimensions deal with the position of the points in phase space, Liapunov exponents estimate the departure rate of nearby trajectories and entropy gauges the way information is lost. Since prediction errors of pressure fluctuations grow exponentially with time at short time scales and the exponent separation rate between predicted and measured values is proportional to the maximal Lyapunou exponent, usually long-term predictability of pressure fluctuations is impossible.
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Presented Monday 17, 13:30 to 15:00, in session Particulate Systems (T2-3P).
