Symbolic Regression-Dimensionless Learning Data-Driven Coupled Modeling of the Interpretable Bed Expansion Ratio in a Liquid–Solid Fluidized Bed

In the chemical industry, liquid–solid fluidized beds are commonly encountered because of their diverse real-world applications, including but not limited to heterogeneous catalysis, mineral leaching, crystallization, and so on. In liquid–solid fluidized beds, there are various parameters (i.e., bed expansion ratio, voidage, drag coefficient), which are key performance indicators and have received much attention. It is necessary to develop an efficient method that can accurately model these parameters. For this purpose, this study proposes a symbolic regression-dimensionless learning data-driven coupled modeling method to develop an interpretable bed expansion ratio correlation. First, 2815 fluidization data points with eight independent features from different granular beds (i.e., glass bead, sea sand, polystyrene ball, metal ball, catalyst bead, calcite) are collected. Then, statistical analysis, data nondimensionalization, and relative importance analysis are performed for feature selection and dimensionality reduction. The dimensionless data set and raw data set are employed to train the symbolic regression model and dimensionless learning data-driven model, respectively. Compared to traditional black-box models, both symbolic regression and dimensionless learning data-driven modeling can generate explicit function expressions with strong interpretability and high prediction accuracy. Furthermore, the symbolic regression is coupled with a dimensionless learning data-driven model to mine bed expansion ratio correlation, which has higher prediction accuracy and universality (R2 > 0.97). It is believed that the developed symbolic regression-dimensionless learning data-driven coupled model has good generalization ability.