With the aim of improving the shortcomings of the traditional single hidden layer back propagation (BP) neural network structure and learning algorithm, this paper proposes a centrifugal pump performance prediction method based on the combination of the Levenberg–Marquardt (LM) training algorithm and double hidden layer BP neural network. MATLAB was used to establish a double hidden layer BP neural network prediction model to predict the head and efficiency of a centrifugal pump. The average relative error of the head between the experimental and prediction obtained by the double hidden layer BP neural network model was 4.35%, the average relative error of the model prediction efficiency and the experimental efficiency was 2.94%, and the convergence time was 1/42 of that of the single hidden layer. The double hidden layer BP neural network model effectively solves the problems of low learning efficiency and easy convergence into local minima—issues that were common in the traditional single hidden layer BP neural network training. Furthermore, the proposed model realizes hydraulic performance prediction during the design process of a centrifugal pump.

Traditional centrifugal pump performance prediction (CPPP) employs the semi-theoretical and semi-empirical approaches; however, it can lead to many prediction errors. Considering the superiority of deep learning when applied to nonlinear systems, in this paper, a method combining hydraulic loss and convolutional neural network (HLCNN) is applied to CPPP. Head and efficiency were selected as two variables for demonstrating the energy performance of the centrifugal pump in order to reflect the prediction ability of the proposed model. The evaluation results indicate that the predicted head and efficiency are accurate, compared with the experimental results. Furthermore, the HLCNN prediction model was compared against machine learning methods and the computational fluid dynamic method. The proposed HLCNN model obtained a better AREmean, root mean square error, sum of squares due to error, and mean absolute error for centrifugal pump energy performance. The research revealed that the HLCNN model achieves accurate energy performance prediction in the design of centrifugal pumps, reducing the development time and costs.

When a pump is propelled by a propeller, the nozzle flooding of the jet wake area will produce a turbulent quasi-sequence structure and have a certain impact on the outflow field structure and thrust characteristics of the water jet propulsion pump. In this paper, a method that combined numerical simulation with vortex dynamics is adopted, which analyzes the dynamic characteristics and influence on the thrust characteristics of the water jet propulsion pump. A large eddy simulation turbulence model and a dimensionless water jet propulsion pump velocity coefficient were used to reveal flow structure and relation, with the pump operation parameters of the wake vortex ring. The thrust with a trailing vortex ring is 7.0% higher than that without a trailing vortex ring. Vortex dynamics and mathematical statistics are combined to quantitatively analyze the dynamic characteristics of the jet tail vortex ring. Finally, the formation time of the vortex ring is obtained in exponential relation with dimensionless transmission velocity and vorticity coefficient, which has nonlinear relation with vortex intensity coefficient and helicity coefficient. BP Neural Network combined with the LM algorithm is used to establish the mathematical relationship between the thrust and the physical characteristic parameters of the vortex ring.