Prediction of gas-liquid two-phase pressure increment of a centrifugal pump based on machine learning

Abstract: An accurate and real-time prediction has been urgently required for the pressure increment performance of centrifugal pumps under gas-liquid conditions during transportation. However, there is no appropriate prediction model for the pressure increment of the centrifugal pump at present, due to the complex gas-liquid flow. Machine learning can be widely expected to serve as a new idea for the performance prediction of centrifugal pumps. In this study, a machine learning model and database were established to investigate the effects of the inlet gas volume fraction, the rotational speed, and the liquid flow rate on the two-phase pressure increment performance of the pump. The results show that the inlet gas volume fraction was a direct factor for the deterioration of pump performance. The pump rotational speed and the liquid flow rate were greatly contributed to the improved performance of pump pressure increment. Three parameters were employed as the input features. The 234 sets of sample points from the experiment were divided into the training set (187 sample points) and test set (47 sample points) with the ratio of 8:2. Four models were constructed after pre-processing the data using Linear Regression (LR), BP Neural Network (BPNN), Support Vector Machine (SVM), and Random Forest (RF). The minimum Mean Square Error (MSE) was used to determine the optimal higher-order term regression function of the LR model, the optimal number of iterations, and the number of hidden layer neurons in BPNN. The grid search and 10-fold cross-validation were used to determine the optimal penalty coefficients and kernel parameters of the SVM, the optimal number of decision trees, and the minimum number of samples on leaf nodes in RF. Then, the Mean Relative Error (MRE), the Root Mean Square Error (RMSE), the determination coefficient (R2), and the confidence level were introduced as the evaluation indexes. The prediction ability of different models was evaluated on the training, the test, and the total data set. The results show that the RF model presented the best ability to predict the pressure increment of the pump, followed by the SVM, the BPNN, and the LR model. In the total data set, the MRE, RMSE, and R2 of the predicted pressure increment by RF model were 3.51%, 1.06 kPa, and 0.993, respectively, and the relative error was no more than ±15% under the confidence level of 94.44%. The LR, BPNN, and SVM model failed to represent the characteristics of pump pressure increment, while the RF model performed better to characterize this trend near the pump surging region. It also needed to improve the pressure increment prediction of the RF model around the surging region under a small liquid flow rate. In addition, the importance of input parameters was also evaluated on the pressure increment by RF. Consequently, the rotational speed was the most important parameter on the pressure increment with a value of 52.67%, followed by the inlet gas volume fraction, and the liquid flow rate with 45.41% and 1.92%, respectively. Therefore, the gas-liquid two-phase performance prediction model using RF can be widely expected to better predict the two-phase pressure increment of centrifugal pump. The finding can also provide a strong reference for the design and selection of the centrifugal pump.