Modeling topological nature of gas–liquid mixing process inside rectangular channel using RBF-NN combined with CEEMDAN-VMD

•CEEMDAN-VMD-RBF-NN is proposed to predict topological nature of bubbles in RC.•CEEMDAN-VMD is used to decompose the topological time series of bubbles twice.•Optimal prediction accuracy of topological nature of bubbles is improved by 5.84%.•Optimal prediction accuracy of topological time series of bubbles is up to 97.93%. In this work, signal processing techniques (i.e., complete ensemble empirical mode decomposition with adaptive noise-variational mode decomposition) and neural network algorithms (i.e., RBF neural network) are used for predicting the topological nature of gas-liquid mixtures in rectangular channels. Specifically, the indicator first Betti number is introduced to describe the topological structure of the gas-liquid mixing process. Firstly, the original topological nature time series were secondary decomposed by the complete ensemble empirical mode decomposition with adaptive noise and variational mode decomposition to reduce the randomness and volatility of the original signal. Then the decomposed signals are fed into RBF neural network for modeling and prediction. The important specific and quantitative results are that the prediction accuracy of topological nature time series can be improved by 0.46%∼5.84% with the hybrid model proposed. Moreover, the prediction accuracy of each working condition is more than 95%, and the prediction accuracy under C1 condition is the highest, reaching 97.93%. The conclusion from the above is that the hybrid model can improve the prediction accuracy and efficiency, reduce the number of experiments and shorten the design cycle. The gap it filled in the literature is that the prediction of gas–liquid mixing topological nature time series in rectangular channels. In addition, it is of great significance to engineering design in the fields of heat energy and chemical engineering.