Horizontal Visibility Graph Analysis for Flow Regime Recognition in a Gas–Solid Fluidized Bed

Flow regime recognition is crucial for the design and control of gas–solid fluidized beds. This study utilizes and validates the horizontal visibility graph (HVG) method for converting pressure fluctuation time series into complex networks to characterize flow regime transitions. Key topological properties, including global efficiency, average path length, and graph diameter, were extracted. These metrics exhibit significant, quantifiable changes at the critical transition velocity from the bubbling to turbulent regimes ( U c = 0.1155 m/s). For instance, the average path length and graph diameter increased by approximately 60% and 80%, respectively. When 13 HVG network properties were used as input features in machine learning algorithms, classifiers such as back propagation and random forest achieved near-perfect recognition between bubbling, transition, and turbulent regimes (accuracy >95%, macro-F1 >94.5%). The method provides a complementary, quantitatively grounded, network-based framework for flow regime analysis, offering a promising tool for the advanced monitoring of fluidized bed systems.