Monitoring of cane sugar crystallization process by multiscale time-series analysis

Abstract

This work presents a proposal for the indirect monitoring of cane sugar crystallization using the multiscale analysis of temperature, pH, and torque time series. The time series were obtained at different crystallizer operating conditions; an experimental design considering four cooling profiles and three seed sizes was performed. Three multiscale methodologies (i.e., Detrended Fluctuation Analysis (DFA), R/S analysis, and Power Spectral Density (PSD)) were applied, identifying that the analyzed time series exhibit fractal behavior in three characteristic scale intervals, which suggests that the time series fluctuations may be a response to the interactions between transport phenomena inherent in the cane sugar crystallization process. By calculating the dynamic fractal dimension for the different characteristic scale intervals, correlations between the fractal dimension (FD) and the experimental measures of the key variables were identified, i.e., average crystal size,% volume, and formed mass crystal with FD calculated by temperature, pH, and torque time-series, respectively. Temperature, pH, and torque measurements are inexpensive, easy to implement, and can be obtained in real-time. The results suggest that multiscale time series analysis captured during the cane sugar crystallization has a high potential for indirect online monitoring with low economic and computational costs.