Accurately predict the efficiency of centrifugal pumps at different rotational speeds is important but still intractable in practice. To enhance the prediction performance, this work proposes a hybrid modeling method by combining both the process data and knowledge of centrifugal pumps. First, according to the process knowledge of centrifugal pumps, the efficiency curve is divided into two stages. Then, the affinity law of pumps and a Gaussian process regression (GPR) model are explored and utilized to predict the efficiency at their suitable flow stages, respectively. Furthermore, a probability index is established through the prediction variance of a GPR model and Bayesian inference to select a suitable training set to improve the prediction accuracy. Experimental results show the superiority of the hybrid modeling method, compared with only using mechanism or data-driven models.

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The present paper presents a multilayer hybrid model for sensorless measurement of pump operating status, with the objective of enabling safe and stable operations while reducing energy losses. The model takes easily measurable variables such as rotational frequency and valve opening as input features to predict the performance parameters of the centrifugal pump. By integrating Just-in-time learning (JITL) with Gaussian process regression (GPR) and leveraging the unique probability features of GPR, a JGPR is developed to extract valuable feature information. The JGPR sequentially predicts the flow rate, coefficient for dynamic head, and shaft power. The predicted values are extended to other input features, which can accurately capture the characteristics of the centrifugal pump and effectively replace the process of acquiring process parameters through sensors. Finally, the mechanism model is integrated into the multilayer JGPR model to calculate the performance parameters of centrifugal pump. The validation results indicate a strong agreement between predicted and experimental results, with predicted meeting performance parameters all engineering requirements. Compared to a single model, the multilayer hybrid model significantly improves the reliability of predictions, demonstrating the feasibility of using this approach to predict performance parameters. This research provides valuable insights into the measurement of sensorless pump operating states, enabling safe and efficient operation in complex conditions.