A predictive model for flow index performance of pit drip irrigation emitters using BP-PSO algorithm

It is crucial to accurately obtain the flow index in designing and developing labyrinth drip irrigation emitters. This study designed a pit drip irrigation emitter based on plant biomimetic principles, and created training-testing datasets (160 data points) and external validation datasets (25 data points) through experiments. The improved backpropagation neural network (BP) regression algorithm based on particle swarm optimization (PSO) is used to predict the flow index of the pit drip irrigation emitter. The input parameters include the pit depth l, the inner and outer boundary spacing h, the flow channel angle θ, and the pit aperture j. There were four combinations with the different hidden layer settings, namely BP₁, BP₂, BP₁-PSO, BP₂-PSO. 85% of the training-testing dataset was used to train the developed model (using 5-fold cross-validation), of which 15% was used for testing. The reliability of the prediction model was evaluated using mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), mean absolute percentage error (MAPE), uncertainty at 95%(U₉₅), coefficient of determination (R²), and global performance indicator (GPI). The results indicated that the optimal structures of BP₁ and BP (input-hidden layer-output) were 4-7-1 and 4-4-9-1. The BP₂-PSO model had the best prediction accuracy and stability, MAE, MSE, RMSE, MAPE, U95, R², and GPI values were 1.98 × 10^- 3, 5.49 × 10^- 6, 2.34 × 10^- 3, 4.09 × 10^- 3, 6.46 × 10^- 3, 0.9456, and 3.74 × 10^- 3, respectively. the evaluation values were 6.46 × 10^- 3, 0.9456 and 3.74 × 10^- 3 respectively. The GPI of BP₁, BP₂, BP₁-PSO and BP₂-PSO were 6.35 × 10^- 3, 5.96 × 10^- 3, 4.88 × 10^- 3 and 3.74 × 10^- 3 respectively, indicating good prediction accuracy. The ranking of prediction accuracy was as follows: BP₂-PSO > BP₁-PSO > BP₂ > BP₁. The four models were tested on the external validation dataset, the R² values of all four models were higher than 0.85, indicating good correlation. Through SHAP analysis, the importance of structural parameters to the flow index is ranked as: j > θ > h > l. In order to verify the validity and extensive superiority of BP-PSO model in solving drip irrigation emitter flow index prediction problem, it was compared with six representative machine learning models, including classical models (GR and MLR), integrated models (CatBoost and LSBoost) and hybrid models (MLP-SVM and MLP-DT). The BP₂-PSO and BP₁-PSO models had the highest prediction accuracy in the training-testing process among ten machine learning methods, and BP₂-PSO model had the highest prediction accuracy in the external validation process, which indicated that particle swarm optimization can improve the accuracy of neural network models. The BP₂-PSO model was used to predict the flow index had greater advantages during the design and development stages of pit drip irrigation emitters.