# Using ANFIS and BPNN Methods to Predict the Unfrozen Water Content of Saline Soil in Western Jilin, China

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{0}), salt content (S), and temperature (T) are used as input parameters for predicting the unfrozen water content (W

_{u}). The results of the ANFIS and BPNN models are compared. The results show that although both methods are suitable for predicting the unfrozen water content of saline soil in the Zhenlai area, western Jilin, the prediction accuracy of the ANFIS model is higher.

## 1. Introduction

_{u}) of saline soil in the Zhenlai area of Western Jilin by NMR, under different temperature (T), salt content (S) and initial water content (W

_{0}). There is currently little research on the prediction of the unfrozen water content of saline soil. In this study, BPNN and adaptive network fuzzy inference system (ANFIS) prediction models of the unfrozen water content are established, and the best prediction model is selected. The prediction models are established and calculated using MATLAB software.

## 2. Test of Unfrozen Water Content

#### 2.1. Samples Preparation

- The physical and chemical properties of the saline soil samples were tested;
- Salt was removed from the saline soil samples with deionized distilled water;
- The samples were prepared using deionized distilled water and soluble salt (a salt mixture of sodium sulfate and sodium carbonate, with a ratio of 2.8:1). After the salt in the saline soil was washed out, the sample was prepared according to the preset salt content and water content (Table 1);
- After the samples were well prepared, the samples were placed in a sealed fresh-keeping bag for 24 h, so that the solution was evenly distributed in the samples;
- The sample was prepared to the following size: 25 mm in diameter with a height of 50 mm, and about 70 g in weight.

#### 2.2. Test Result

#### 2.2.1. Varied Initial Water Content and Fixed Salt Content

_{0}) is different (Figure 2). During the freezing process, the sample went through three stages. This trend of change is consistent with those introduced in the literature [32,33,34].

_{u}) decreases with decreasing temperature until it gradually stabilizes. When the temperature is from −0.2 °C to −5 °C, the process is in the first stage (the high-temperature stage). In this stage, the water in the sample does not completely change phase. The content of unfrozen water is stable and is greater than 16%. When the temperature ranges from −10 °C to −5 °C, the process is in the second stage (mutation stage). The unfrozen water in the samples begins to crystallize into ice, and its content decreases rapidly with the decrease of temperature. When the temperature ranges from −20 °C to −10 °C, the process is in the third stage (stable stage). At this stage, the content of unfrozen water gradually tends to be stable with the drop of temperature.

#### 2.2.2. Fixed Initial Water Content and Varied Salt Content

_{0}) is in the same, and the salt content (S) is different (Figure 3).

#### 2.2.3. Freezing and Melting Process

## 3. Numerical Simulation

_{u}) of saline soil is mainly affected by initial water content (W

_{0}), salinity (S), temperature (T), and so on. Therefore, the relationship between them can be expressed by Equation (1).

_{u}= f(W

_{0}, S, T),

_{0}), salinity (S), and temperature (T) were taken as input variables, and unfrozen water content (W

_{u}) was taken as the output variables. The range of their change is shown in Table 3.

#### 3.1. Numerical Simulation Based on a BP Neural Network

#### 3.1.1. Determining the Network Structure

#### 3.1.2. Input Layer and Output Layer

#### 3.1.3. Number of Hidden Layer Nodes

^{2}). The MSE is expressed by Equation (6), and R

^{2}is expressed by Equation (7).

^{2}. This was used as the standard for choosing the hidden layer number. Figure 6 shows that when the R

^{2}value is maximal, the number of neurons is 9. Figure 7 shows that when the MSE is minimal, the number of neurons is 9, too. Therefore, the number of hidden neurons selected for the predictive model was 9.

#### 3.1.4. Implementation Process

- Sample data were normalized, as shown in Equation (2);
- Sample data were classified;
- The BP neural network was established;
- Training was performed;
- After the training was completed, testing was carried out;
- Error analysis and result prediction were performed.

#### 3.2. Numerical Simulation Based on an Adaptive Fuzzy Neural Inference System (FIS)

#### 3.2.1. The Fuzzy Inference System

#### 3.2.2. The Adaptive Network-Based Fuzzy Inference System (ANFIS)

_{i}represents the number of fuzzy divisions of x

_{i}and A

_{i}represents a fuzzy set. The fuzzy set [39] is defined as: For a given universe X, a mapping O

_{A}:X → [0, 1] is able to determine a fuzzy set A in X. O

_{A}is called the membership function of the fuzzy set A.

_{ij}represents the center of the membership function and ∅

_{i}represents the width of the membership function.

_{ij}represents the central value of the membership function.

## 4. Results and Discussion

^{2}). The calculation formulae are given by Equations (6) and (7).

^{−4}and 1.36 × 10

^{−2}, respectively, and the correlation coefficients are 0.9965 and 0.9444, respectively. Likewise, in the training and testing stage, the mean square errors of the ANFIS model are 1.704 × 10

^{−4}and 4.833 × 10

^{−3}, respectively, and the correlation coefficients are 0.9988 and 0.9897 respectively (Table 6). It can be seen that the MSE and the MAPE of the ANFIS are smaller than those of the BPNN, and the R

^{2}of the ANFIS is larger than that of the BPNN.

^{−4}and 8.30 × 10

^{−4}, respectively, the average value ($\overline{\mathrm{MAPE}}$) of the mean absolute percentage errors were 7.21 and 7.15, respectively, and the average value of the correlation coefficients were 0.9940 and 0.9940, respectively. The p-values of both models in the 5-fold cross-validation are smaller than 0.05. Therefore, according to the four evaluation indicators of cross-validation, both models performed well during the training phase, but ANFIS was slightly better.

^{−2}and 2.40 × 10

^{−2}, respectively, the average value ($\overline{\mathrm{MAPE}}$) of the mean absolute percentage errors were 35.73 and 26.13, respectively, and the average value of the correlation coefficients were 0.7643 and 0.8339, respectively. In the two models, the $\overline{\mathrm{MSE}}$ and $\overline{\mathrm{MAPE}}$ of ANFIS are the smallest, and the average value of the correlation coefficient is the largest. When k is 2, the p-value of BPNN is 0.0972, and when k is 4, the p-value of ANFIS is 0.1457. The p-values were slightly greater than 0.05, only 0.0472 and 0.0957 higher, respectively, in addition, the p-values of both models in the 5-fold cross-validation are smaller than 0.05. Therefore, during the testing phase, the predictive performance of ANFIS is better than that of BPNN.

## 5. Conclusions

- During the freezing process, the saline soil mainly experienced three stages: High temperature, mutation, and stability. When the content of salt was fixed, the greater the initial water content, the greater the content of unfrozen water. The content of unfrozen water decreased with decreasing temperature and eventually tended to stabilize.
- During the freezing process, the salt content was inversely proportional to the freezing point, and the ice point was reduced with increasing of salt content. As the temperature decreased, the content of unfrozen water was high in the samples with high salt content.
- In the process of freezing and melting, the content of unfrozen water decreased with decreasing temperature and increased with increasing temperature. At temperatures below freezing point, the unfrozen water content during the freezing process was always greater than that during the melting process, and the unfrozen water content showed as hysteresis phenomenon.
- The comparison shows that both BPNN and ANFIS prediction models can predict the unfrozen water content well. However, the accuracy of the two models was evaluated by way of their mean square error, mean absolute percentage error, and correlation coefficient. The ANFIS model had greater accuracy than did the BPNN. The ANFIS prediction model is more suitable for predicting the unfrozen water content in saline soil areas of Western Jilin.
- The research shows that the ANFIS can be utilized for predicting unfrozen water content, and the model will be further applied to studying water and salt migration in frozen soil. The research results will contribute to soil and water conservation, soil improvement, and engineering construction in the saline soil area of Western Jilin, which is conducive to the restoration of the ecological environment and the sustainable development of economy and construction.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Effect of freezing and melting processes on unfrozen water content: (

**a**) Unfrozen water content curve of sample 2; (

**b**) unfrozen water content curve of sample 3; (

**b**) unfrozen water content curve of sample 4.

**Figure 7.**Mean squared error (MSE) value of the training data when the number of hidden layer units changes.

**Figure 10.**Comparison between experimental and predicted Wu values for the backpropagation neural network (BPNN) and adaptive network-based fuzzy inference system (ANFIS) models.

**Figure 11.**Forecasting curves of test samples: (

**a**) The prediction results of the BPNN model are fitted to the experimental results; (

**b**) the prediction results of the ANFIS model are fitted to the experimental results.

Sample | Initial Water Content (%) | Salt Content (%) | Mass Percentage Concentration (%) |
---|---|---|---|

1 | 24 | 0 | 0 |

2 | 24 | 1.5 | 5.9 |

3 | 24 | 3 | 11.1 |

4 | 19 | 1.5 | 7.3 |

Samples | 1 | 2 | 3 | 4 | ||
---|---|---|---|---|---|---|

Wu (%) | ||||||

T (°C) | ||||||

−0.2 | 23.65 | 22.86 | 23.15 | 17.20 | ||

−0.5 | 23.38 | 23.13 | 23.45 | 17.18 | ||

−1 | 23.12 | 22.56 | 22.73 | 17.11 | ||

−3 | 5.73 | 22.27 | 22.65 | 16.87 | ||

−5 | 4.59 | 22.09 | 21.86 | 16.76 | ||

−10 | 2.94 | 6.38 | 15.08 | 6.39 | ||

−15 | 2.22 | 3.92 | 9.37 | 4.05 | ||

−20 | 1.60 | 2.66 | 9.08 | 2.90 |

Water Content (%) | Salt Content (%) | Temperature (°C) | Unfrozen Water Content (%) | |
---|---|---|---|---|

Maximum | 24 | 1.5 | −0.2 | 23.65 |

Minimum | 19 | 0 | −20 | 1.6 |

Range | 5 | 1.5 | 19.8 | 22.05 |

Variable properties | Input | Input | Input | Output |

Measured Value (%) | BPNN | ANFIS | ||
---|---|---|---|---|

Predictive Value (%) | Relative Error (%) | Predictive Value (%) | Relative Error (%) | |

23.65 | 23.56 | 0.36 | 23.93 | 1.21 |

23.15 | 22.83 | 1.42 | 23.31 | 0.66 |

17.20 | 17.28 | 0.48 | 17.29 | 0.55 |

23.38 | 23.41 | 0.13 | 24.05 | 2.88 |

23.45 | 22.81 | 2.72 | 23.13 | 1.35 |

17.18 | 17.03 | 0.87 | 17.05 | 0.79 |

23.12 | 22.44 | 2.95 | 22.02 | 4.75 |

22.73 | 22.78 | 0.19 | 22.92 | 0.83 |

17.11 | 16.75 | 2.07 | 17.15 | 0.27 |

5.73 | 6.71 | 17.11 | 6.05 | 5.55 |

22.27 | 23.01 | 3.34 | 22.27 | 0.00 |

22.65 | 22.57 | 0.34 | 22.62 | 0.12 |

4.59 | 3.83 | 16.50 | 4.34 | 5.52 |

22.09 | 21.23 | 3.89 | 22.09 | 0.00 |

21.86 | 22.12 | 1.18 | 21.87 | 0.03 |

16.76 | 16.77 | 0.05 | 16.75 | 0.06 |

2.94 | 3.18 | 8.50 | 3.06 | 4.37 |

6.38 | 7.34 | 14.96 | 6.38 | 0.01 |

15.08 | 15.04 | 0.32 | 15.08 | 0.01 |

6.39 | 7.04 | 10.14 | 6.40 | 0.09 |

2.22 | 2.79 | 26.01 | 2.04 | 7.84 |

4.05 | 3.77 | 6.88 | 4.04 | 0.21 |

1.60 | 1.66 | 3.64 | 1.71 | 7.33 |

2.66 | 2.06 | 22.31 | 2.66 | 0.00 |

9.08 | 8.33 | 8.32 | 9.08 | 0.00 |

2.90 | 2.82 | 2.67 | 2.91 | 0.20 |

Mean absolute percentage error | - | 6.05 | - | 1.72 |

Maximum relative error | - | 26.01 | - | 7.84 |

Measured Value (%) | BPNN | ANFIS | ||
---|---|---|---|---|

Predictive Value (%) | Relative Error (%) | Predictive Value (%) | Relative Error (%) | |

22.86 | 23.30 | 1.95 | 25.07 | 9.69 |

23.13 | 23.32 | 0.81 | 24.03 | 3.91 |

22.56 | 23.32 | 3.36 | 22.91 | 1.54 |

16.87 | 17.07 | 1.18 | 19.36 | 14.79 |

3.92 | 3.73 | 4.87 | 5.04 | 28.51 |

9.37 | 3.14 | 66.43 | 10.25 | 9.44 |

Mean absolute percentage error | - | 13.10 | - | 11.31 |

Maximum relative error | - | 66.43 | - | 28.51 |

Statistics Parameters | BPNN | ANFIS | ||
---|---|---|---|---|

Training Set | Testing Set | Training Set | Testing Set | |

R^{2} | 0.9965 | 0.9444 | 0.9988 | 0.9897 |

MSE | 5.366 × 10^{−4} | 1.360 × 10^{−2} | 1.704 × 10^{−4} | 4.833 × 10^{−3} |

**Table 7.**Evaluation index of cross-validation of unfrozen water content prediction models (training phase).

Statistics Parameters | R^{2} | p-Value | MSE | MAPE | ||||
---|---|---|---|---|---|---|---|---|

Model | BPNN | ANFIS | BPNN | ANFIS | BPNN | ANFIS | BPNN | ANFIS |

k = 1 | 0.9939 | 0.9933 | 6.06 × 10^{−27} | 1.61 × 10^{−26} | 9.32 × 10^{−4} | 9.78 × 10^{−4} | 6.29 | 7.52 |

k = 2 | 0.9938 | 0.9965 | 4.98 × 10^{−28} | 5.76 × 10^{−31} | 9.26 × 10^{−4} | 5.11 × 10^{−4} | 7.22 | 5.63 |

k = 3 | 0.9944 | 0.9857 | 1.42 × 10^{−28} | 1.20 × 10^{−23} | 9.11 × 10^{−4} | 1.87 × 10^{−3} | 7.49 | 9.68 |

k = 4 | 0.994 | 0.9978 | 4.73 × 10^{−27} | 3.70 × 10^{−32} | 9.48 × 10^{−4} | 3.25 × 10^{−4} | 7.75 | 7.25 |

k = 5 | 0.9938 | 0.9968 | 4.90 × 10^{−28} | 1.68 × 10^{−31} | 9.11 × 10^{−4} | 4.61 × 10^{−4} | 7.31 | 5.65 |

average value | 0.9940 | 0.9940 | - | - | 9.26 × 10^{−4} | 8.30 × 10^{−4} | 7.21 | 7.15 |

**Table 8.**Evaluation index of cross-validation of unfrozen water content prediction models (testing phase).

Statistics Parameters | R^{2} | p-Value | MSE | MAPE | ||||
---|---|---|---|---|---|---|---|---|

Model | BPNN | ANFIS | BPNN | ANFIS | BPNN | ANFIS | BPNN | ANFIS |

k = 1 | 0.6309 | 0.8728 | 0.0329 | 0.0021 | 7.86 × 10^{−2} | 1.92 × 10^{−2} | 54.55 | 41.98 |

k = 2 | 0.5378 | 0.9667 | 0.0972 | 0.0004 | 9.61 × 10^{−2} | 8.44 × 10^{−3} | 59.28 | 15.56 |

k = 3 | 0.9809 | 0.9763 | 0.0001 | 0.0002 | 7.20 × 10^{−3} | 4.62 × 10^{−3} | 22.84 | 25.30 |

k = 4 | 0.7302 | 0.3723 | 0.0143 | 0.1457 | 3.17 × 10^{−2} | 8.37 × 10^{−2} | 27.15 | 38.65 |

k = 5 | 0.942 | 0.9816 | 0.0013 | 0.0001 | 1.19 × 10^{−3} | 3.86 × 10^{−3} | 14.84 | 9.16 |

average value | 0.7643 | 0.8339 | - | - | 4.51 × 10^{−2} | 2.40 × 10^{−2} | 35.73 | 26.13 |

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**MDPI and ACS Style**

Liu, Y.; Wang, Q.; Zhang, X.; Song, S.; Niu, C.; Shangguan, Y.
Using ANFIS and BPNN Methods to Predict the Unfrozen Water Content of Saline Soil in Western Jilin, China. *Symmetry* **2019**, *11*, 16.
https://doi.org/10.3390/sym11010016

**AMA Style**

Liu Y, Wang Q, Zhang X, Song S, Niu C, Shangguan Y.
Using ANFIS and BPNN Methods to Predict the Unfrozen Water Content of Saline Soil in Western Jilin, China. *Symmetry*. 2019; 11(1):16.
https://doi.org/10.3390/sym11010016

**Chicago/Turabian Style**

Liu, Yufeng, Qing Wang, Xudong Zhang, Shengyuan Song, Cencen Niu, and Yunlong Shangguan.
2019. "Using ANFIS and BPNN Methods to Predict the Unfrozen Water Content of Saline Soil in Western Jilin, China" *Symmetry* 11, no. 1: 16.
https://doi.org/10.3390/sym11010016