Fractional-order derivative coupled machine learning models for quantitative prediction of soil Ni content

Abstract

To explore the effects of fractional-order derivative (FOD) implementation strategies and key parameters on Vis–NIR hyperspectral modeling for soil nickel (Ni) content prediction, this study focused on contaminated farmland soil in Mojiang Hani Autonomous County, Yunnan Province, China. Twelve modeling pipelines were designed, combining two FOD implementation strategies (fixed-window FOD and full-history FOD), two feature band selection strategies (the correlation coefficient method and full-spectrum bands), and four regression algorithms (PLSR, SVR, BPNN, and GRNN). The results showed the following: (1) The impact of fixed-window FOD on hyperspectral preprocessing and subsequent modeling performance was non-monotonic with window size; appropriate window sizes helped mitigate potential information redundancy and imbalance associated with full-history FOD while reducing preprocessing time. (2) Compared with integer-order derivative (IOD) preprocessing, FOD preprocessing (both fixed-window and full-history) was more effective in improving the predictive performance of models for soil Ni prediction. (3) The optimal model under fixed-window FOD (GRNN, window size = 80, order = 0.95) achieved RPD = 2.74, R² = 0.87, and RMSE = 97.76 mg/kg on the validation set. For full-history FOD, the best model (BPNN, order = 0.7) yielded RPD = 2.56, R² = 0.85, and RMSE = 104.66 mg/kg.