Predicting the photosynthetic rate of protected grape using grey wolf optimizer-back propagation

The photosynthetic rate of the protected grape can be accurately predicted under multiple environmental features. There is also a correlation between the environmental factors and the photosynthetic rate in the protected grape. In this study, the photosynthetic rate of the protected grape was predicted using the grey wolf optimizer - back propagation (GWO-BP). 1) Nina Queen Grape was taken as the research target. Its photosynthetic data was collected under controlled environmental conditions from June to September 2024, thereby covering the key growth stages of the crop. And then the data was normalized to unify the data scale. 2) Four key factors on photosynthetic rate were screened out, including carbon dioxide concentration, air temperature, air humidity, and light intensity, according to random forest Gini importance and maximum information coefficient. A BP neural network model was constructed with a 4-12-1 structure. 3) Xavier uniform and zero initialization were used to initialize the weights and thresholds of the BP model. And then the adaptive moment estimation (ADAM) was introduced to dynamically adjust the learning rate. The momentum gradient descent and adaptive learning rate were combined to determine the learning rates for different parameters. The first- and second-order moment estimation of the gradient was calculated to accelerate the convergence for the stability of the convergence. 4) The GWO was used to optimize the initial weights and thresholds, because the BP model was easy to falling into a local optimum. The weights and thresholds of the BP neural network were initialized by Xavier uniform and zero initialization. And then the adaptive moment estimation was introduced to dynamically adjust the learning rate. The better performance was then achieved to compare with the four models of BP, support vector regression (SVR), random forest (RF), and extreme learning machine (ELM). The results show that the BP model shared the determination coefficients (R²) of 0.832 and 0.834 on the validation and test set, respectively, which were better than the conventional model. But the prediction presented a large deviation in the extreme value area of the photosynthetic rate. The validation set R² of the GWO-BP model increased to 0.920 after GWO optimization, while the root mean square error and mean absolute error decreased by 31.2% and 25.1%, respectively; The test set R² reached 0.918, while the root mean square error and the mean absolute error decreased by 29.8% and 22.5%, respectively; Huber loss function was reduced from 0.01 to less than 0.006, indicating the low prediction errors. As such, the GWO effectively avoided the local optimum in the BP model, particularly for the global search and convergence stability of the model. There was a better prediction performance in the extreme value area. A dependable technical solution was provided to accurately capture the coupling relationship between the photosynthetic rate of the protected grape and multiple environmental factors. The findings can also provide a strong reference to accurately predict the photosynthetic rate of the protected grape.