Chaotic and statistical tests on fiber optic dynamic data taken from the riser section of a circulating fluidized bed

Dynamical tests have been applied to fiber optic data taken from a cold-flow circulating fluidized bed to characterize flow conditions, identify three characteristic scales (macro, meso, and micro), and understand the contribution these scales have on the raw data. The characteristic variable analyzed is the raw voltage signal obtained from a fiber-optic probe taken at various axial and radial positions under different loading conditions. These experiments were carried out with the bed material of cork particles with a medium particle size of 812 μm. The characterization was accomplished through analysis of the distribution of the signal through the third and fourth moments of skewness and excess kurtosis. A generalization of the autocorrelation function known as the average mutual information function was analyzed by examining the function's first minimum, identifying the point at which successive elements are no longer correlated. Further characterization was accomplished through the correlation dimension, a measure of the complexity of the chaotic attractor in deterministic chaos theory. Lastly, the amount of disorder of the system is described by a Kolmogorov-type entropy estimate. All six aforementioned tests were also implemented on ten levels of detail coefficients resulting from a discrete wavelet transformation of the same signal as used above. Through this analysis it is possible to identify and describe micro (particle level), meso (clustering or turbulence level), and macro (physical or dimensional level) length scales even though some literature considers these scales inseparable as is discussed. This investigation also used detail wavelet coefficients in conjunction with ANOVA to show which scales have the most impact on the raw signal resulting from local hydrodynamic conditions.