Supersaturation is the primary variable in sugar crystallization, as it governs sucrose crystal growth and product quality, whereas the purity of the mother liquor is a key indicator of process efficiency. Both variables are difficult to measure online due to technological limitations. This study presents data-driven soft sensors based on Bayesian Gaussian Process Regression (BGPR) for predicting supersaturation and purity in industrial crystallization. A novel covariance matrix was introduced through an extended kernel design, enhancing the flexibility of the BGPR framework. Beyond accurate point predictions, the BGPR framework inherently provides calibrated uncertainty quantification, addressing an issue rarely discussed in the crystallization literature. The proposed soft sensors were trained and validated with real data from an industrial vacuum pan, achieving relative errors below 4% for both variables. The soft sensor requires only three routinely measured variables: temperature, magma brix, and mother liquor brix, which represents a practical advantage since no additional instrumentation is needed. For supersaturation, the uncertainty analysis yielded a Prediction Interval Coverage Probability (PICP) of 93.1%, narrow prediction intervals (MPIW = 0.1024), and a favorable CRPS of 0.0317, confirming robustness. The BGPR soft sensor was compared with five widely used approaches in soft-sensor design: Artificial Neural Networks (ANN), Long Short-Term Memory networks (LSTM), Support Vector Regression (SVR), Random Forest (RF), and Gradient Boosting Regression (GBR). Results showed that BGPR achieves competitive predictive accuracy while additionally providing reliable information on estimation uncertainty. These findings demonstrate the applicability of BGPR-based soft sensors for real-time monitoring of industrial sugar crystallization.
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