Estimating Rapeseed Nutrient Content Using Fractional-Order Differentiation of UAV-Based Hyperspectral Data

Nutrient elements are crucial for the growth, yield, and quality of rapeseed. Rapid and non-destructive monitoring of canopy nutrient status in rapeseed is of great significance for precise nutrient diagnosis and growth assessment. Although spectral remote sensing technology has become an efficient alternative to traditional laboratory methods, conventional approaches often struggle to effectively and finely extract specific feature information when faced with the complex canopy spectral environment of rapeseed, limiting the accuracy of synchronous monitoring for multiple nutrient elements.

By exploring the hyperspectral response mechanism of nutrient elements in rapeseed, this study aimed to construct quantitative estimation models for six nutrient elements in rapeseed leaves, namely boron (B), nitrogen (N), phosphorus (P), potassium (K), calcium (Ca), and sulfur (S), and improve their estimation accuracy, while analyzing the impact of different modeling methods on nutrient estimation, thereby providing a reference for precision nutrient management.

Based on hyperspectral data acquired during key growth stages of rapeseed and corresponding leaf nutrient concentrations, this study employed fractional-order differentiation (FOD) to enhance spectral feature signals and systematically compared the estimation accuracy of leaf nutrient contents using three machine learning algorithms: partial least squares regression (PLSR), support vector regression (SVR), and random forest regression (RFR).

Compared with the original spectral models, the models based on FOD spectra showed a 13%-30% increase in R², with the smallest performance difference between the training and test sets (average ΔR² =0.09). In particular, high-order FOD (>1.0) effectively highlighted subtle features like the red-edge slope and eliminated baseline drift, making the R² of the optimal models for N and B reach 0.89 and 0.87, respectively. Among the three algorithms, RFR exhibited the most robust performance (test-set R² of for different nutrients ranging from 0.48 to 0.89), with its selected sensitive bands (e.g., protein and chlorophyll absorption regions) closely align with crop physiological mechanisms. Spatial mapping revealed heterogeneous distribution characteristics of nutrients, confirming the model's ability to interpret field micro-environments.

This study proposed and validated a coupled methodological framework of FOD-RFR, which was capable of effectively deciphering subtle spectral features of multiple nutrients throughout the entire growth cycle of rapeseed, enabling non-destructive simultaneous estimation with significantly improved accuracy. This framework not only achieved differentiated collaborative estimation of multiple nutrients in rapeseed but also provided valuable insights and references for the remote sensing monitoring of complex biochemical parameters in field crops.