Symbolic Regression-Dimensionless Learning Data-Driven\nCoupled Modeling of the Interpretable Bed Expansion Ratio in a Liquid–Solid\nFluidized Bed

In\nthe chemical industry, liquid–solid fluidized beds are\ncommonly encountered because of their diverse real-world applications,\nincluding but not limited to heterogeneous catalysis, mineral leaching,\ncrystallization, and so on. In liquid–solid fluidized beds,\nthere are various parameters (i.e., bed expansion ratio, voidage,\ndrag coefficient), which are key performance indicators and have received\nmuch attention. It is necessary to develop an efficient method that\ncan accurately model these parameters. For this purpose, this study\nproposes a symbolic regression-dimensionless learning data-driven\ncoupled modeling method to develop an interpretable bed expansion\nratio correlation. First, 2815 fluidization data points with eight\nindependent features from different granular beds (i.e., glass bead,\nsea sand, polystyrene ball, metal ball, catalyst bead, calcite) are\ncollected. Then, statistical analysis, data nondimensionalization,\nand relative importance analysis are performed for feature selection\nand dimensionality reduction. The dimensionless data set and raw data\nset are employed to train the symbolic regression model and dimensionless\nlearning data-driven model, respectively. Compared to traditional\nblack-box models, both symbolic regression and dimensionless learning\ndata-driven modeling can generate explicit function expressions with\nstrong interpretability and high prediction accuracy. Furthermore,\nthe symbolic regression is coupled with a dimensionless learning data-driven\nmodel to mine bed expansion ratio correlation, which has higher prediction\naccuracy and universality (<i>R</i><sup>2</sup> > 0.97).\nIt is believed that the developed symbolic regression-dimensionless\nlearning data-driven coupled model has good generalization ability.