The effect of gypsum on the physical and chemical characteristics of sodic soils is nonlinear and controlled by multiple factors. The support vector machine (SVM) is able to solve practical problems such as small samples, nonlinearity, high dimensions, and local minima points. This paper reports the use of the SVM regression method to predict changes in the chemical properties of sodic soils under different gypsum application rates in a soil column experiment and to evaluate the effect of gypsum reclamation on sodic soils. The research results show that (1) the SVM soil solute transport model using the Matlab toolbox represents the change in Ca2+ and Na+ in the soil solution and leachate well, with a high prediction accuracy. (2) Using the SVM model to predict the spatial and temporal variations in the soil solute content is feasible and does not require a specific mathematical model. The SVM model can take full advantage of the distribution characteristics of the training sample. (3) The workload of the soil solute transport prediction model based on the SVM is greatly reduced by not having to determine the hydrodynamic dispersion coefficient and retardation coefficient, and the model is thus highly practical.
The support vector machine (SVM) method was developed based on the Vapnik statistical learning theory and in particular the statistical Vapnik-Chervonenkis Dimension theory and the Structural Risk Minimization Inductive Principle [
The soil was sampled from the Changsheng Experimental Station of the Bayannur League Institute of Water Resources in the northwest of China. The soil had typical sodic soil characteristics, that is, a high pH and exchangeable sodium percentage and low hydraulic conductivity. The soil texture was clay and its physical and chemical properties are listed in Table
Physical and chemical properties of the soil.
Exchangeable cations/cmolc·kg−1 | Soil bulk |
| ||||
---|---|---|---|---|---|---|
Na+ | K+ |
|
|
CEC | Density/g·cm−3 | |
8.65 | 0.60 | 0.50 | 1.27 | 11.02 | 1.45 | 9.15 |
Soluble cations/mmoLc·l−1 | Soluble anions/mmolc·l−1 | ||||||
---|---|---|---|---|---|---|---|
Na+ | K+ |
|
|
Cl− |
|
|
|
303.15 | 5.18 | 3.33 | 3.33 | 193.33 | 50.00 | 51.67 | 20.00 |
Particle size distribution/% |
| ||
---|---|---|---|
2.0–0.02 | 0.02–0.002 | <0.002 | dS·m−1 |
23.2 | 0.95 | 42.1 | 0.95 |
The experimental device (Figure
Experimental treatments of
Experimental treatments |
|
|
|
|
---|---|---|---|---|
Concentration of CaSO4/g·L−1 | 0.5 | 1.0 | 1.5 | 2.0 |
Concentration of |
7.35 | 14.71 | 22.06 | 29.41 |
Experimental device of Ca2+ penetration.
The experimental procedure was as follows. The tested soil samples were poured homogeneously into the Plexiglass column at a dry soil bulk density of 1.45 g·cm−3 to a depth of 10 cm. The soil columns were saturated with distilled water from the bottom up at a saturation rate of 2 cm per hour. Once the soils were saturated, the surface water was quickly drained with a vacuum pump and the Ca2+ solution that had been configured in the Mariotte bottle was immediately supplied. The Ca2+ and Na+ concentrations of the leachate were measured once every 24 hours. The Ca2+ and Na+ concentrations in the soil solution and soil colloid were measured after the penetration experiment.
The soil samples were air-dried and passed through a 1 mm sieve. The EC, pH, soluble anions, and soluble cations were measured using 1 : 5 water extracts. The soluble cations were measured using an atomic absorption spectrophotometer (AAS-3620); soluble anions were determined by anion chromatography (ICS-900); soil pH was determined with the glass electrode method. The salt content was measured using a 1 cm conductivity cell, dip-type probe. Exchangeable cations were determined in a 1 M ammonium acetate (pH = 7) extract. Following this extraction and washing with 96% alcohol, the cation exchange capacity was determined by the removal of ammonium ions by distillation. Na+ and K+ were determined by flame emission spectroscopy (FP6400) in the extract, and Ca2+ and Mg2+ were determined by atomic absorption spectrophotometer (AAS-3620). Particle size distribution was determined with the hydrometer method. The concentrations of Na+ and Ca2+ in the leachate were measured using an atomic absorption spectrophotometer (AAS-3620).
The SVM method was initially introduced to solve classification problems but can be extended to deal with regression problems [
A linear and separable sample set (
This is the decision-making function
Equation (
Consider the following linear regression problem.
The regression hyperplane
Equation (
This problem can be solved by modifying (
The partition hyperplane
Letting
The algorithm is further improved by allowing fitting error through the introduction of slack variables
Provided that the optimal solution to (
In the objective function of (
Setting the solution to (
The dual problem is then written as follows:
The solution to (
As
For a wide range of nonlinear problems, the SVM maps samples to the high-dimensional Hilbert space by skillfully using nuclear transform methods and processing using linear methods. If the mapping is
The complete algorithm of the SVM for dealing with nonlinear regression problems is as follows. Select parameters Construct the following optimization problem:
Find the optimal solution Construct the decision function
where
The SVM method is applied to predict the reclamation effect of a desulfurization byproduct (gypsum) on sodic soils. The main factors influencing the reclamation process must first be determined, and then the sample datasets of observations are selected for training the SVM. Predictions can then be made according to the parameters obtained from the training.
The measured values for the Ca2+ concentrations in the leachate are shown in Figure
Changes in the measured values of Ca2+ in the leachate with leaching times ((a)
The measured values for the Na+ concentrations in the leachate are shown in Figure
Change in the measured values of Na+ in the leachate with leaching time ((a)
An SVM model of the variations in Ca2+ concentration in sodic soils in a penetration test was constructed and used for data prediction. The training process and analytical results are as follows.
The measured Ca2+ concentrations of the soil leachate from 0 h to 480 h in 0.5 g·L−1, 1.0 g·L−1, and 2.0 g·L−1 treatments of gypsum and from 240 h to 480 h in a 1.5 g·L−1 treatment of gypsum were used as the input data. The measured Ca2+ concentrations of the leachate from 0 h to 240 h in a 1.5 g·L−1 gypsum treatment were used as the inspection data. The data were normalized, and the prediction model based on the SVM was constructed in Matlab with the following parameters: kernel function rbf (shaped as in (
The SVM model was applied to predict the data. The prediction results and measured data are shown in Figure
Comparison of the measured values and predicted results for the Ca2+ concentration of the soil leachate in a penetration experiment.
Regression analysis of the measured values and predicted results for the Ca2+ concentration of the soil leachate in a penetration experiment.
The measured Na+ concentrations of the soil leachate from 0 h to 480 h in 0.5 g·L−1, 1.0 g·L−1, and 2.0 g·L−1 treatments of gypsum and from 240 h to 480 h in a 1.5 g·L−1 treatment of gypsum were used as the input data. The measured Na+ concentrations of the leachate from 0 h to 240 h in a 1.5 g·L−1 gypsum treatment were used as the inspection data. The data were normalized, and the prediction model based on the SVM was constructed in Matlab with the following parameters: kernel function rbf (shaped as in (
The SVM model was applied to predict the data. The prediction results and measured data are shown in Figure
Comparison of the measured values and predicted results for the Na+ concentration of the soil leachate in a penetration experiment.
Regression analysis of the measured values and predicted results for the Na+ concentration of the soil leachate in a penetration experiment.
The SVM method is a type of lumped parameter prediction method and has broad applicability in determining small changes in a parameter system [
describes the difference between the measured values (
The application presented in the current paper was compared to a very well-known machine learning tool, the artificial neural network (ANN) model. The SVM can take full advantage of the distribution characteristics of the training sample, constructs a discriminant function according to the training sample, and does not need much prior information, which favors it over other nonlinear methods [
Statistical parameters indicative of model performance.
Model |
|
|
||
---|---|---|---|---|
The root mean square error (RMSE) | The mean absolute error (MAE) | The root mean square error (RMSE) | The mean absolute error (MAE) | |
Support vector machine (SVM) | 0.27 | 0.21 | 15.91 | 12.84 |
Artificial neural network (ANN) | 0.52 | 0.39 | 26.15 | 18.81 |
The simulation and prediction model of solute transport was constructed using Matlab toolbox based on nonlinear SVM theory, and the transport and transformation law of Ca2+ and Na+ in Ca2+ penetration process was carried out to simulate and predict. The following conclusions can be drawn from our findings. The change of Ca2+ and Na+ in leachate can be reflected by SVM soil solute transport model by using Matlab toolbox, and the prediction accuracy is high. Using SVM model to predict the spatial and temporal variations of soil solute content is feasible, and it does not require a specific mathematical model. SVM model can take full advantage of the distribution characteristics of training samples and does not require too much of a priori information and use skills. The workload of soil solute transport prediction model based on SVM was greatly reduced without determination of the hydrodynamic dispersion coefficient and retardation coefficient, and the SVM model has a strong practicality.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported by the National Natural Science Foundation of China (50749032), Beijing Higher Education Young Elite Teacher Project, and the Fundamental Research Funds for the Central Universities, China (2652012072).