Research On Inverse Method Of Centrifugal Pump Blade And Performance Prediction Based On Gaussian Process Regression

With the development of computer computing speed,CFD technology and modern flow testing technique,the research on the complex flow in centrifugal pump is more and more in-depth.The research on centrifugal pump can be summarized as direct problem and inverse problem,in which the direct problem belongs to the flow analysis problem and the inverse problem belongs to the design problem.The inverse problem is always the key and difficult problems in the field of fluid machinery for the complex relationship among blade shape,hydraulic performance and internal flow structure.In this research,according to Bayesian theory of posterior probability obtained from known prior probability,the inverse methods for centrifugal pump blade based on the single output Gaussian process regression(SOGPR)and the multi-output Gaussian process regression(MOGPR)were proposed,respectively.The training sample set consists of the blade shape parameters and the distribution of flow parameters.The hyperparameters in the inverse problem models were trained by using the maximum likelihood estimation and the gradient descent algorithm.The blade shape corresponding to the objective blade load can be achieved by the trained inverse problem models.Finally,the prediction model of centrifugal pump performance was constructed based on the MOGPR inverse problem model,and its prediction performance was analyzed.The main contents and conclusions are as follows:(1)The machine learning technology was introduced into the field of hydraulic machinery optimization design,and the inverse method of centrifugal pump blade based on Gaussian process regression was proposed.The MH48-12.5 low specific speed centrifugal pump was selected to analyze and compare the accuracy,generalization ability and reliability of the proposed inverse problem models.The prototype blade shape corresponding to the objective blade load can be calculated exactly by the trained SOGPR and MOGPR inverse problem model,respectively,and the uncertainty of solution is very small.(2)The LOO cross-validation was carried out respectively on both models,and the results were compared and analyzed.The blade shapes within the sample space can be achieved exactly and efficiently by both of the SOGPR and MOGPR inverse problem models according to the given objective blade load distributions.Both inverse problem models are robust to calculate the inverse problem of pump blade.The RMSE values of the MOGPR inverse problem model are generally lower than the SOGPR inverse problem model.The research shows that the accuracy of the MOGPR inverse problem model to calculate inverse problem of pump blade is better than the SOGPR inverse problem model.(3)The extrapolation characteristics of both models were tested and compared.The extrapolation blade obtained by the MOGPR inverse problem model almost approaches its objective blade shape,and the blade shape is continuous and smoother.However,the extrapolation blade shape acquired by the SOGPR inverse problem model is messy,which is unable to achieve the inverse design.The correlation matrix of MOGPR model can constrain the relationship between blade shape parameters,so that the feature information of blade shape can be captured well in the process of solving the inverse problem.The extrapolation characteristic of the MOGPR inverse problem model is much better than the SOGPR inverse problem model.(4)Based on the MOGPR inverse problem model with better performance,the prediction model of centrifugal pump performance was constructed.The blade shape parameters were taken as model input,and the head and hydraulic efficiency of centrifugal pump were taken as model output.The influence of the number of training samples on the accuracy of the prediction model was analyzed.With the increase of the number of training samples,the prediction accuracy of the MOGPR performance prediction model is gradually improved,and the uncertainty of the prediction results is gradually reduced.The ability for MOGPR to learn the correlation between output variables in the prediction process was analyzed.The correlation between output variables learned by the correlation matrix of MOGPR model is basically consistent with the results of Pearson correlation coefficient.Based on the performance prediction model,the influence of blade inlet and outlet angle and blade wrap angle on the head and hydraulic efficiency of centrifugal pump was analyzed.The head and hydraulic efficiency of centrifugal pump are weakly affected by the change of blade inlet angle,but greatly affected by the change of blade outlet angle and blade wrap angle.The centrifugal pump performance prediction model based on MOGPR can achieve more accurate prediction under a small number of sample training,which can improve the efficiency of hydraulic machinery optimization design.