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# Fractional Modeling for Quantitative Inversion of Soil-Available Phosphorus Content

by 2,* and 1,*
1
College of Information Engineering, Qujing Normal University, Qujing 655011, China
2
College of Applied Arts and Science, Beijing Union University, Beijing 100083, China
*
Authors to whom correspondence should be addressed.
Mathematics 2018, 6(12), 330; https://doi.org/10.3390/math6120330
Received: 11 November 2018 / Revised: 3 December 2018 / Accepted: 3 December 2018 / Published: 14 December 2018
The study of field spectra based on fractional-order differentials has rarely been reported, and traditional integer-order differentials only perform the derivative calculation for 1st-order or 2nd-order spectrum signals, ignoring the spectral transformation details between 0th-order to 1st-order and 1st-order to 2nd-order, resulting in the problem of low-prediction accuracy. In this paper, a spectral quantitative analysis model of soil-available phosphorus content based on a fractional-order differential is proposed. Firstly, a fractional-order differential was used to perform a derivative calculation of original spectral data from 0th-order to 2nd-order using 0.2-order intervals, to obtain 11 fractional-order spectrum data. Afterwards, seven bands with absolute correlation coefficient greater than 0.5 were selected as sensitive bands. Finally, a stepwise multiple linear regression algorithm was used to establish a spectral estimation model of soil-available phosphorus content under different orders, then the prediction effect of the model under different orders was compared and analyzed. Simulation results show that the best order for a soil-available phosphorus content regression model is a 0.6 fractional-order, the coefficient of determination ( $R 2$ ), root mean square error (RMSE), and ratio of performance to deviation (RPD) of the best model are 0.7888, 3.348878, and 2.001142, respectively. Since the RPD value is greater than 2, the optimal fractional model established in this study has good quantitative predictive ability for soil-available phosphorus content. View Full-Text
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MDPI and ACS Style

Fu, C.; Xiong, H.; Tian, A. Fractional Modeling for Quantitative Inversion of Soil-Available Phosphorus Content. Mathematics 2018, 6, 330. https://doi.org/10.3390/math6120330

AMA Style

Fu C, Xiong H, Tian A. Fractional Modeling for Quantitative Inversion of Soil-Available Phosphorus Content. Mathematics. 2018; 6(12):330. https://doi.org/10.3390/math6120330

Chicago/Turabian Style

Fu, Chengbiao, Heigang Xiong, and Anhong Tian. 2018. "Fractional Modeling for Quantitative Inversion of Soil-Available Phosphorus Content" Mathematics 6, no. 12: 330. https://doi.org/10.3390/math6120330

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