Research on Walnut Yield Estimation Based on Interpretable Machine Learning and Stacked Integration Under Different Water–Fertilizer Coupling Regimes

To overcome the limitations of traditional yield estimation methods—which are often subjective, costly, and difficult to implement at scale—this study developed a high-precision, interpretable model for predicting walnut yield by integrating multi-source remote sensing technology with interpretable machine learning. To provide a theoretical foundation for precise water and fertilizer management as well as intelligent production in walnut orchards. By employing interpretable machine learning and a multi-stage integration strategy, the model achieves not only high-precision yield estimation but also elucidates the influence pathways of water–fertilizer coupling on yield formation at a mechanistic level. This advancement offers reliable technical support and a decision-making framework for the precise management of orchards. This study focused on the Xinjiang ‘Wen 185’ walnut, employing field experiments with varying water and fertilizer gradients. A UAV equipped with a multispectral sensor was utilized to capture canopy images, from which vegetation indices and texture features were extracted. This process resulted in a comprehensive dataset that integrated remotely sensed features with management practices. Various machine learning algorithms, including random forest, support vector machine, partial least squares regression, and ridge regression, were applied. An innovative stacked integration model for growth stages was proposed, and the SHAP framework was incorporated to analyze feature contributions and enhance model interpretability. In this study, texture features—particularly those derived from the red-edge band—showed higher predictive importance than traditional vegetation indices. This suggests that they may be more sensitive to canopy structural heterogeneity under the tested conditions. Among the models, random forest showed numerically higher values in terms of R2 and RPD compared to the other individual models under the present dataset, achieving a validation R2 of 0.670 and an RPD of 1.836. The proposed growth stage stacking ensemble (GSSE) model further enhanced prediction accuracy, achieving validation R2 of 0.789, an RMSE of 0.494, and an RPD of 2.296. Additionally, the results revealed that texture may have a potential ability to captured canopy heterogeneity as the primary mechanism underlying yield variation, and the integration of multi-stage spectral information was associated with higher estimation accuracy in this dataset in improving estimation accuracy, with the oil conversion stage contributing up to 60% to the final prediction.