University of Tennessee
Knoxville TN 37996-2210
M.B. Kennel, C.S. Daw
Oak Ridge National Laboratory
Knoxville TN 37932-6472
Morgantown Energy Technology Laboratory
Morgantown WV 26507-0880
We present advanced, nonlinear statistical methods for analysis of dynamic pressure time series signals from fluidized beds for the purpose of reliably diagnosing fluidization conditions. These general algorithms, which transcend linear or spectral techniques, can monitor fluidization-state stationarity, diagnose process state, or signal adverse conditions such as agglomeration. We can reliably compare states when the natural character of the dynamics is already complex, fluctuating, possibly chaotic and noisy -- as in fluidized bed reactors -- and provide a statistical confidence limit on the degree of match or mismatch.
As recognized by developments in nonlinear dynamics and "chaotic signal processing", multidimensional state-space vectors reconstructed from the observed scalar time series yield interesting signatures of the overall condition of the dynamics.
One of our approaches is to compute empirical correlation integrals of this multidimensional state space and compare conditions with a nonparametric test such as the Kolmogorov-Smirnov statistic. We test correlation integrals from unknown fluidization conditions against a library of correlation integrals from known fluidization conditions and obtain a quantification of and statistical confidence on the degree of similarity. Another novel test statistic examines the full geometry of the signal in state space, which yields even more precise diagnostics, at the cost of somewhat increased computational effort. Both methods accurately discriminate different fluidization conditions generated in our laboratory experiments and correctly match "unknown" states to known examples.
We demonstrate two example applications: classification of the fluidization state in a bed of Group D glass beads, and detection of an anomalous agglomerated state in a bed of Group B-D polyethylene particles. This method is generic, as we show it works with different signal types, such as acoustic (sound-level) measurements, and with other fluidized particles.
For classification, we first generate a library of processed signals from a range of fluidization conditions from minimum fluidization to vigorous complex slugging. We then record new signals from several test conditions and demonstrate that the algorithms accurately classify the fluidization regime and reject incorrect alternatives at a high statistical confidence level. Power spectra are far less useful for classification.
For diagnosis, we record differential pressure signals from the bed of PE particles with and without an agglomerated mass in the bed. We show that the advanced test detects the influence of the agglomerate at a highly significant level over a range of fluidization conditions.
We discuss practical application issues such as library data-base management, intermittent versus continuous statistical analysis, and the feasibility and relevance of these tests for on-line process monitoring and control.
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