Purpose With increasing fertilizer use, precise control of granular spreading is essential to reduce environmental impacts and improve agronomic efficiency. This study presents a reliable approach that predict particle trajectories, and the resulting swath width by modeling particle velocity and landing position from centrifugal spreader discs, thereby eliminating the need for time-consuming bin-based field tests. Methods Particle velocity and travel distance data were generated using validated, physics-engine based Extended Discrete Element Method (EDEM) simulations. A realistic spreader geometry, calibrated material properties, and aerodynamic drag were incorporated. The EDEM model was experimentally validated with validation errors ranging between 2% and 6%. Nonlinear polynomial regression models of varying orders and Generalized Additive Models (GAMs) were compared with a non-parametric Random Forest (RF) model to predict particle velocity and position. Results Model performance was assessed using <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{RMSE}\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textrm{AIC}\)</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\textrm{BIC}\)</EquationSource> </InlineEquation>. The results show that Generalized Additive Models (GAMs) consistently outperformed Random Forest (RF) and polynomial regression models, in terms of accuracy with high interpretability. RF ranked as the second-best performing model. The optimal GAM achieved an <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation> = 0.98 (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\textrm{RMSE}\)</EquationSource> </InlineEquation> = 0.27) for velocity prediction and an <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation> = 0.93 (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\textrm{RMSE}\)</EquationSource> </InlineEquation> = 0.27) for position prediction. External validation using an independent EDEM dataset further confirmed the generalizability of the models, yielding an <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation> = 0.98 (<InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\textrm{RMSE}\)</EquationSource> </InlineEquation> = 0.35) for velocity and an <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation> = 0.93 (<InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(\textrm{RMSE}\)</EquationSource> </InlineEquation> = 0.49) for position. In addition, deviance contribution analysis from the GAM models and scaled variable importance from the Random Forest model both identified time, wind flow, disc speed, and traveling speed as the four most influential variables in predicting both response variables. Conclusion GAMs trained using EDEM simulation data provided a robust framework for predicting fertilizer granule trajectories and estimating resulting swath width. These results support future data-driven precision agriculture for improved efficiency for fertilizer application.

A comparative study of centrifugal fertilizer spread using generalized additive model, random forest and polynomial regression

期刊论文
发表日期：

2026年5月23日

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Arezou Lak,
Mehran Mehrandezh,
Denise S. D. Stilling,
Ali Mohammadi

摘要

Purpose

With increasing fertilizer use, precise control of granular spreading is essential to reduce environmental impacts and improve agronomic efficiency. This study presents a reliable approach that predict particle trajectories, and the resulting swath width by modeling particle velocity and landing position from centrifugal spreader discs, thereby eliminating the need for time-consuming bin-based field tests.

Methods

Particle velocity and travel distance data were generated using validated, physics-engine based Extended Discrete Element Method (EDEM) simulations. A realistic spreader geometry, calibrated material properties, and aerodynamic drag were incorporated. The EDEM model was experimentally validated with validation errors ranging between 2% and 6%. Nonlinear polynomial regression models of varying orders and Generalized Additive Models (GAMs) were compared with a non-parametric Random Forest (RF) model to predict particle velocity and position.

Results

Model performance was assessed using \(\textrm{RMSE}\) , \(R^2\) , \(\textrm{AIC}\) , and \(\textrm{BIC}\) . The results show that Generalized Additive Models (GAMs) consistently outperformed Random Forest (RF) and polynomial regression models, in terms of accuracy with high interpretability. RF ranked as the second-best performing model. The optimal GAM achieved an \(R^2\) = 0.98 ( \(\textrm{RMSE}\) = 0.27) for velocity prediction and an \(R^2\) = 0.93 ( \(\textrm{RMSE}\) = 0.27) for position prediction. External validation using an independent EDEM dataset further confirmed the generalizability of the models, yielding an \(R^2\) = 0.98 ( \(\textrm{RMSE}\) = 0.35) for velocity and an \(R^2\) = 0.93 ( \(\textrm{RMSE}\) = 0.49) for position. In addition, deviance contribution analysis from the GAM models and scaled variable importance from the Random Forest model both identified time, wind flow, disc speed, and traveling speed as the four most influential variables in predicting both response variables.

Conclusion

GAMs trained using EDEM simulation data provided a robust framework for predicting fertilizer granule trajectories and estimating resulting swath width. These results support future data-driven precision agriculture for improved efficiency for fertilizer application.