Parametric modelling of time series of pressure fluctuations in gas-solid fluidized beds

Applying parametric models on time series of pressure fluctuations recorded in a fluidized bed, this paper shows that the bed dynamics can be expressed in analogy with a mechanical system of a certain degree. Thus, the pressure signal is assumed to be an output of a linear time-invariant system driven by a forcing function. The forcing function represents a number of apparently random events (e.g. formation of bubbles at the air-distributor, bubble eruptions at the surface of the bed) and may thereby be approximated as white noise. Parametric models are advocated for characterization of the dynamics of fluidized beds when, for various reasons, long data records are not available or when the quality of the recorded signal is poor. An autoregressive model (AR) of the time series is proposed, and it is shown that the order of the model identifies a mechanical equivalent of certain fluidization behaviour. The model is applied to four fluidization time series, previously investigated. The result indicates that fluidized beds behave like single second-order systems or multiple higher-order mechanical systems acting in parallel. Parametric methods are also used for estimation of power spectra of pressure fluctuations. The information obtained is presented in the form of Bode plots to accentuate the behaviour of fluidized beds as linear dynamical systems. The results are compared with the corresponding information obtained by nonparametric methods, now predominantly used. Data requirements (number of samples, sampling frequency) for the use of parametric models are discussed. (c) 2005 Elsevier Ltd. All rights reserved.