ACCURACY ANALYSIS FOR KOLMOGOROV ENTROPY USED IN STUDYING THE CHAOTIC DYNAMICS OF CFB REACTORS BASED ON SOLIDS CONCENTRATION FLUCTUATIONS
Abstract
A study on the chaotic dynamics of a high flux circulating fluidized bed (CFB) riser (10-m high and 76-mm i.d.) using the
maximum likelihood estimate of the Kolmogorov entropy (K ML ) is reported. The signals used were measured by using a
solids concentration fiber optic probe, accuracy of which is reported based on statistical analysis. The sensitivity
analysis of the parameters used for computing K ML was conducted to identify optimum settings, based on the standard
error, s(K ML ) and the nature of PDF of the b-values from the reconstructed phase space trajectories. The length of time
series, N, sampling frequency, f s , and number of embedding dimensions, D im , and b , strongly affect the accuracy of K ML
values. A relationship between K ML and b was established, which was obeyed by experimental data from all operating
conditions studied, and for all sampling frequencies. The chaotic dynamics of the CFB was studied by examining the
effect of increasing the local solids concentration at different axial elevations and different operating conditions in a high
flux riser. It was concluded that the K ML method is highly accurate when N > 3,000 data points, for which the effect of
D im is negligible and PDFs of the b-values becomes similar in shape based on σ (b), S k (b) and K u (b).
maximum likelihood estimate of the Kolmogorov entropy (K ML ) is reported. The signals used were measured by using a
solids concentration fiber optic probe, accuracy of which is reported based on statistical analysis. The sensitivity
analysis of the parameters used for computing K ML was conducted to identify optimum settings, based on the standard
error, s(K ML ) and the nature of PDF of the b-values from the reconstructed phase space trajectories. The length of time
series, N, sampling frequency, f s , and number of embedding dimensions, D im , and b , strongly affect the accuracy of K ML
values. A relationship between K ML and b was established, which was obeyed by experimental data from all operating
conditions studied, and for all sampling frequencies. The chaotic dynamics of the CFB was studied by examining the
effect of increasing the local solids concentration at different axial elevations and different operating conditions in a high
flux riser. It was concluded that the K ML method is highly accurate when N > 3,000 data points, for which the effect of
D im is negligible and PDFs of the b-values becomes similar in shape based on σ (b), S k (b) and K u (b).
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