Research On Optimization Design Of Centrifugal Pump Impeller Based On Multi-output Gaussian Process Regression

Hydraulic optimization design of pumps has always been a hot topic in the field of fluid machinery,and which has strong application value in engineering.Because of the complex internal flow and large hydraulic loss in centrifugal pump,and the complicated relationship between the blade shape,hydraulic performance and the internal flow,it is more difficult to perform the optimization design of pumps.With the rapid development of computational fluid dynamics(CFD)technology in recent years,the design theory of pumps has been further developed.However,there are many problems in the optimization of hydraulic model of pump s,such as large amount of calculation and difficulty in optimiz ation.In this study,machine learning technology was introduced into the field of the optimization design of hydraulic machinery,and an optimization design method of centrifugal pump impeller based on multi-output Gaussian process regression(MOGPR)was proposed under the Bayesian framework of the transformation of known p rior distribution to posterior distribution.Based on the MOGPR model,the backward impeller design model and the forward performance prediction model of centrifugal pump were constructed respectively.Finally,the performance prediction model was combined with the multi-objective optimization algorithm to optimize the performance of centrifugal pump on the basis of the initial design.The main research contents and conclusions of this paper are as follows:(1)The hydraulic design method of centrifugal pum p based on the MOGPR model was established.Based on the existing excellent hydraulic models,the gradient descent method was used to train the response relationship between the performance parameters such as head,flow rate and the geometric parameters of centrifugal pump impeller.The hydraulic design of the impeller of M125-100 centrifugal pump was carried out by using the proposed MOGPR surrogate model design method,and a set of initial geometry parameters of the impeller were obtained.The model obtai ned by the MOGPR design method was compared with the original model,and the geometric parameters of the two impellers are basically the same,and the hydraulic performance is also highly consistent.The correlation analysis of the impeller geometry parame ters was carried out based on the correlation matrix of the MOGPR model.Finally,the internal law between the specific speed and the impeller geometry parameters in the model data was discussed.(2)The proposed MOGPR and NSGA-Ⅱ mixture model was used to further optimize the initial MOGPR design.On the basis of the initial MOGPR design,Latin hypercube design and CFD numerical simulation was used to construct the initial sample set.The relationship between the geometric shape of the impeller and the CFD numerical results of the sample set was trained,and the surrogate model for hydraulic performance prediction of the pump was established.The surrogate model of the pump performance prediction was constructed to evaluate the fitness function of offspring by the MOGPR method.CFD numerical simulation was performed for two optimization schemes,namely,the tradeoff optimal design and the optimal head constraint design on the Pareto non-dominated optimal solution set,and the numerical simulation results were compared with the algorithm results.The surrogate optimization algorithm based on MOGPR and NSGA-Ⅱ has high optimization efficiency and global optimization ability.(3)The accuracy of the forward and backward surrogate models was verified.The LOO cross validation test was used and the results were analyzed.The results show that both of the two models have good prediction accuracy and generalization ability.This method is suitable for regressi on problems with the characteristics of high dimensionality,small sample size and nonlinearity.(4)The hydraulic performance and internal flow field of the centrifugal pump were compared and analyzed between the optimal design and the initial design.Compared with the initial design model,the hydraulic performance of the two optimization design models has been greatly improved,and the hydraulic efficiency has been improved more obviously.The internal flow field of the optimal head constraint design and the initial design were compared and analyzed.After optimization,the turbulent kinetic energy in the impeller is reduced obviously,the flow structure is greatly improved,and the flow separation and secondary flow in the impeller are effectively suppressed.The optimization design method of centrifugal pump based on MOGPR can design a better hydraulic model than the original design.