ESTIMATION OF SOIL HEAVY METAL COMBINING FRACTIONAL ORDER DERIVATIVE

Abstract. It is important for the sustainable development of soil and monitoring the soil quality to obtain the heavy metal contents. Visible and near-infrared (Vis–NIR) spectroscopy provides an alternative method for soil heavy metal estimation. A total of 80 soil samples collected in Xuzhou city of China were utilized as data sets for calibration and validation to establish the relationship between the soil reflectance and soil heavy metal content. To amplify the weak spectral characteristic, improve the estimation ability, and explore the characteristic band regions, the preprocessing method of fractional order derivative (FOD) (intervals of 0.25, range of 0–2) and the wavebands selection method of interval partial least squares regression (IPLS) are introduced in this paper. Combining these two methods, for Chromium (Cr), the best estimation model yields Rp2 and RMSRp values of 0.97 and 2.20, respectively, when fractional order is 0.5. This paper explores the potential that FOD conducts the most appropriate order to preprocess spectra and IPLS selects the feature band regions in estimating soil heavy metal of Cr. The results show that FOD and IPLS can strengthen the soil information and improve the accuracy and stability of soil heavy metal estimation effectively.

Download Full-text

Development of a soil heavy metal estimation method based on a spectral index: Combining fractional-order derivative pretreatment and the absorption mechanism

The Science of The Total Environment ◽

10.1016/j.scitotenv.2021.151882 ◽

2021 ◽

pp. 151882

Author(s):

Lihan Chen ◽

Jian Lai ◽

Kun Tan ◽

Xue Wang ◽

Yu Chen ◽

...

Keyword(s):

Heavy Metal ◽

Spectral Index ◽

Fractional Order ◽

Estimation Method ◽

Order Derivative ◽

Absorption Mechanism ◽

Fractional Order Derivative ◽

Soil Heavy Metal

Download Full-text

Combination of fractional order derivative and memory-based learning algorithm to improve the estimation accuracy of soil organic matter by visible and near-infrared spectroscopy

CATENA ◽

10.1016/j.catena.2018.10.051 ◽

2019 ◽

Vol 174 ◽

pp. 104-116 ◽

Cited By ~ 15

Author(s):

Yongsheng Hong ◽

Songchao Chen ◽

Yaolin Liu ◽

Yong Zhang ◽

Lei Yu ◽

...

Keyword(s):

Organic Matter ◽

Infrared Spectroscopy ◽

Soil Organic Matter ◽

Fractional Order ◽

Near Infrared Spectroscopy ◽

Near Infrared ◽

Learning Algorithm ◽

Order Derivative ◽

Estimation Accuracy ◽

Fractional Order Derivative

Download Full-text

Estimation of Heavy Metals in Agricultural Soils Using Vis-NIR Spectroscopy with Fractional-Order Derivative and Generalized Regression Neural Network

Remote Sensing ◽

10.3390/rs13142718 ◽

2021 ◽

Vol 13 (14) ◽

pp. 2718

Author(s):

Xitong Xu ◽

Shengbo Chen ◽

Liguo Ren ◽

Cheng Han ◽

Donglin Lv ◽

...

Keyword(s):

Neural Network ◽

Heavy Metals ◽

Heavy Metal ◽

Mathematical Models ◽

Fractional Order ◽

Agricultural Soils ◽

Nir Spectroscopy ◽

Generalized Regression Neural Network ◽

Fractional Order Derivative ◽

Band Combination

With the development of industrialization and urbanization, heavy metal contamination in agricultural soils tends to accumulate rapidly and harm human health. Visible and near-infrared (Vis-NIR) spectroscopy provides the feasibility of fast monitoring of the variation of heavy metals. This study explored the potential of fractional-order derivative (FOD), the optimal band combination algorithm and different mathematical models in estimating soil heavy metals with Vis-NIR spectroscopy. A total of 80 soil samples were collected from an agriculture area in Suzi river basin, Liaoning Province, China. The spectra for mercury (Hg), chromium (Cr), and copper (Cu) of the samples were obtained in the laboratory. For spectral preprocessing, FODs were allowed to vary from 0 to 2 with an increment of 0.2 at each step, and the optimal band combination algorithm was applied to the spectra after FOD. Then, four mathematical models, namely, partial least squares regression (PLSR), adaptive neural fuzzy inference system (ANFIS), random forest (RF) and generalized regression neural network (GRNN), were used to estimate the concentration of Hg, Cr and Cu. Results showed that high-order FOD had an excellent effect in highlighting hidden information and separating minor absorbing peaks, and the optimal band combination algorithm could remove the influence of spectral noise caused by high-order FOD. The incorporation of the optimal band combination algorithm and FOD is able to further mine spectral information. Furthermore, GRNN made an obvious improvement to the estimation accuracy of all studied heavy metals compared to ANFIS, PLSR, and RF. In summary, our results provided more feasibility for the rapid estimation of Hg, Cr, Cu and other heavy metal pollution areas in agricultural soils.

Download Full-text

Combining Fractional Order Derivative and Spectral Variable Selection for Organic Matter Estimation of Homogeneous Soil Samples by VIS–NIR Spectroscopy

Remote Sensing ◽

10.3390/rs10030479 ◽

2018 ◽

Vol 10 (3) ◽

pp. 479 ◽

Cited By ~ 25

Author(s):

Yongsheng Hong ◽

Yiyun Chen ◽

Lei Yu ◽

Yanfang Liu ◽

Yaolin Liu ◽

...

Keyword(s):

Organic Matter ◽

Variable Selection ◽

Fractional Order ◽

Nir Spectroscopy ◽

Soil Samples ◽

Order Derivative ◽

Fractional Order Derivative ◽

Spectral Variable ◽

Homogeneous Soil ◽

Selection For

Download Full-text

GENERALIZED THEORY OF MAGNETO-THERMO-VISCOELASTIC SPHERICAL CAVITY PROBLEM UNDER FRACTIONAL ORDER DERIVATIVE: STATE SPACE APPROACH

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.11.86 ◽

2020 ◽

Vol 9 (11) ◽

pp. 9769-9780

Author(s):

S.G. Khavale ◽

K.R. Gaikwad

Keyword(s):

State Space ◽

Fractional Order ◽

Order Derivative ◽

Laplace Inversion ◽

State Space Approach ◽

Spherical Region ◽

Fractional Order Derivative ◽

Numerical Laplace Inversion ◽

Mathcad Software ◽

Space Approach

This paper is dealing the modified Ohm's law with the temperature gradient of generalized theory of magneto-thermo-viscoelastic for a thermally, isotropic and electrically infinite material with a spherical region using fractional order derivative. The general solution obtained from Laplace transform, numerical Laplace inversion and state space approach. The temperature, displacement and stresses are obtained and represented graphically with the help of Mathcad software.

Download Full-text

Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

Advances in Difference Equations ◽

10.1186/s13662-020-03087-w ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Choonkil Park ◽

R. I. Nuruddeen ◽

Khalid K. Ali ◽

Lawal Muhammad ◽

M. S. Osman ◽

...

Keyword(s):

Fractional Derivative ◽

Fractional Order ◽

Mathematical Physics ◽

Order Derivative ◽

Conformable Fractional Derivative ◽

Fractional Order Derivative ◽

De Vries ◽

Fifth Order ◽

2D And 3D

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

Download Full-text