Hyperspectral estimation of chlorophyll density in winter wheat using fractional-order derivative combined with machine learning
Authors: Yang Chenbo , Feng Meichen , Bai Juan , Sun Hui , Bi Rutian , Song Lifang , Wang Chao , Zhao Yu , Yang Wude , Xiao Lujie , Zhang Meijun , Song Xiaoyan 
Published: January 2025

Chlorophyll density (ChD) can reflect the photosynthetic capacity of the winter wheat population, therefore achieving real-time non-destructive monitoring of ChD in winter wheat is of great significance for evaluating the growth status of winter wheat. Derivative preprocessing has a wide range of applications in the hyperspectral monitoring of winter wheat chlorophyll. In order to research the role of fractional-order derivative (FOD) in the hyperspectral monitoring model of ChD, this study based on an irrigation experiment of winter wheat to obtain ChD and canopy hyperspectral reflectance. The original spectral reflectance curves were preprocessed using 3 FOD methods: Grünwald-Letnikov (GL), Riemann-Liouville (RL), and Caputo. Hyperspectral monitoring models for winter wheat ChD were constructed using 8 machine learning algorithms, including partial least squares regression, support vector regression, multi-layer perceptron regression, random forest regression, extra-trees regression (ETsR), decision tree regression, K-nearest neighbors regression, and gaussian process regression, based on the full spectrum band and the band selected by competitive adaptive reweighted sampling (CARS). The main results were as follows: For the 3 types of FOD, GL-FOD was suitable for analyzing the change process of the original spectral curve towards the integer-order derivative spectral curve. RL-FOD was suitable for constructing the hyperspectral monitoring model of winter wheat ChD. Caputo-FOD was not suitable for hyperspectral research due to its insensitivity to changes in order. The 3 FOD calculation methods could all improve the correlation between the original spectral curve and Log(ChD) to varying degrees, but only the GL method and RL method could observe the change process of correlation with order changes, and the shorter the wavelength, the smaller the order, and the higher the correlation. The bands screened by CARS were distributed throughout the entire spectral range, but there was a relatively concentrated distribution in the visible light region. Among all models, CARS was used to screen bands based on the 0.3-order RL-FOD spectrum, and the model constructed using ETsR reached the best accuracy and stability. Its R2c, RMSEc, R2v, RMSEv, and RPD were 1.0000, 0.0000, 0.8667, 0.1732, and 2.6660, respectively. In conclusion, based on the winter wheat ChD data set and the corresponding canopy hyperspectral data set, combined with 3 FOD calculation methods, 1 band screening method, and 8 modeling algorithms, this study constructed hyperspectral monitoring models for winter wheat ChD. The results showed that based on the 0.3-order RL-FOD, combined with the CARS screening band, ETsR modeling has the highest accuracy, and hyperspectral estimation of winter wheat ChD can be realized. The results of this study can provide some reference for the rapid and nondestructive estimation of ChD in winter wheat.