# Prediction of the Structural Yield Strength of Saline Soil in Western Jilin Province, China: A Comparison of the Back-Propagation Neural Network and Support Vector Machine Models

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{+}. The cementation strength of bound water film between soil particles is thus easily affected by water content and salt content, and compaction is also an important factor affecting the strength of soil. Therefore, in this study, the back-propagation neural network (BPNN) model and a support vector machine (SVM) are used to explore the relationship of saline soil’s SYS with its compactness, water content, and salt content. In total, 120 data points collected by a high-pressure consolidation experiment are applied to building BPNN and SVM model. For eliminate redundant features, Pearson correlation coefficient (r

_{PCC}) is used as an evaluation standard of feature selection. The K-fold cross-validation method was used to avoid over fitting. To compare the performance of the BPNN and SVM models, three statistical parameters were used: the determination coefficient (R

^{2}), root mean square error (RMSE), and mean absolute percentage deviation (MAPD). The result shows that the average values of R

^{2}, RMSE, and MAPD of the BPNN model are superior to the values of the SVM. We conclude that the BPNN model is slightly better than the SVM for predicting the SYS of saline soil. Thus, the BPNN model is used to analyze the factor sensitivity of SYS. The results indicate that the influence degrees of the three parameters are as follows: water content > compactness > salt content. This study can provide a basis for estimating the structural yield pressure of soil from its basic properties, and can provide a new way to obtain parameters for geotechnical engineering, ensuring safety while maintaining symmetry in engineering costs.

## 1. Introduction

_{PCC}) is an evaluation standard for feature selection. The K-fold cross-validation method was used to avoid overfitting. The BPNN and SVM were used to determining the relationship of SYS with the water content, salt content, and compactness of saline remolded soil in the west of Jilin Province, and the prediction model for SYS was established. Finally, the influence of water content, salt content and compactness on the SYS was studied.

## 2. Materials and Methods

#### 2.1. Study Area

^{3}, and the natural moisture content was 3.20%~17.40%. Due to strong evaporation, the surface layer had the lowest moisture content at 3.20%. The organic content was 0.168%~0.488%. The grain size composition of the soil samples was obtained by particle size analysis, which showed that the sand content of the samples is 5.66%~15.99%, the silt content is 46.92%~57.81%, and the clay content is 26.21%~45.07%. Thus, the saline soil is mainly composed of silt particles, followed by clay particles and sand particles.

^{+}and K

^{+}was determined by a flame photometer.

_{3}

^{−}, and the primary cation is Na

^{+}. The high clay and silt content in the saline soil increases the specific surface area and surface energy, and also makes the adsorption capacity of the soil surface stronger [9]. Combined with the high content of Na

^{+}, a thick diffusion layer forms on the surface of soil particles, which will weaken the bound water connection between particles until it disappears [19].

_{3}

^{−}content, and SO

_{4}

^{2−}content. Therefore, the 40 cm soil layer was selected as the experimental soil for studying the compression characteristics of saline soil in Zhenlai, and the results from the physical and chemical tests are shown in Table 1 and Table 2.

#### 2.2. Data Preparation

#### 2.2.1. Specimen Design

^{+}in the soil, the thicker the bound water film on the outer surface of the soil particles [20]. When the water content is very low, salt crystallizes and forms a bond between soil particles. With an increase of the water content, the strength and the stability of the soil decreases because the salt dissolves in water, which thickens the bound water film and weakens the connection between soil particles. Because the salt content and water content are the factors that affect the thickness and cementation strength of the bound water film between soil particles, they have a great influence on the structural strength of saline soil. The natural salt content of the 40 cm soil layer in western Jilin Province is 0.408%, and the highest was 1.7%, so the salt content was set to 0.0%, 0.4%, 1.0%, and 2.0%. Combined with the natural water content and the optimal water content, the water content was set to 13%, 14%, 15%, 16%, 17%, 18%, 19%, 20%, 21%, and 23%.

#### 2.2.2. High Pressure Consolidation Test

#### 2.2.3. Feature Selection

_{PCC}) is an evaluation standard of feature selection. Its values range from −1 to 1. The closer the value is to −1 or 1, the stronger the correlation between features. The formula of the Pearson correlation coefficient is as follows [22]:

_{i}is water content, salt content or compactness, and y

_{i}is the structural yield strength. $\overline{x}$ and $\overline{y}$ are the average values of the corresponding variables, and n is the number of samples. Generally speaking, r

_{PCC}< 0.40 indicates weak correlation among variables, 0.40 ≤ r

_{PCC}< 0.70 indicates moderate correlation, 0.70 ≤ r

_{PCC}< 0.9 indicates strong or high correlation, and extremely strong correlation is indicated when 0.90 ≤ r

_{PCC}≤ 1.

#### 2.2.4. K-Fold Cross-Validation

#### 2.3. Methodology

#### 2.3.1. Back Propagation Neural Network (BPNN)

#### 2.3.2. Support Vector Machine (SVM)

_{i},x

_{j}) is called the kernel function, which is equal to the inner product of two vectors, x

_{i}and x

_{j}, in their characteristic spaces, φ(x

_{i}) and φ(x

_{j}). The kernel function must satisfy the Mercer theorem. The common kernel functions include the linear function, radial basis function, and multi-layer perception function.

_{i}in the formula can be obtained by solving the following quadratic programming problems:

_{i}-α

_{i}*) is non-zero in the formula, and the corresponding data points are support vectors. C is a normal number that determines the balance between empirical risk and regularization [44,45].

#### 2.3.3. Model Evaluation

^{2}, RMSE and average relative deviation (MRD) to evaluate the predictive effect of the support vector regression (SVR) and BPNN models for the energy loss of a stepped spillway [46]. Zhang (2017) used the R

^{2}, RMSE and MAPD to evaluate the predictive effect of the general regression neural network (GRNN) and BPNN models for frost heave behavior [34]. According to the significance of the above statistical parameters, this study compares the performance of BPNN and SVM models by using three parameters: the R

^{2}, RMSE, and MAPD methods.

- (1)
- Coefficient of determination (R
^{2}), also named the decision coefficient (R^{2}): In a regression analysis, R^{2}is an index that reflects the approximation between the regression predictions and real data. More specifically, R^{2}indicates the proportion of the variance in the dependent variable that is predicted or explained by the predictor variable, also known as the independent variable. When the range of values is 0–1, the closer the values are to 1, the closer the regression predicted values are to the experimental data:$${R}^{2}=1-\frac{{{\displaystyle \sum}}_{i=1}^{N}{\left(P\_SY{S}_{i}-E\_SY{S}_{i}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{N}{\left(P\_SY{S}_{i}\right)}^{2}}$$_{i}is the predicted SYS, E_SYSi is measured SYS, and N is the total amount of data. - (2)
- Root mean square error (RMSE): the RMSE is used to accurately measure the prediction errors of the different models of a particular dataset. The smaller the RMSE, the higher the matching degree between the predicted value and the experimental value:$$RMSE=\sqrt{\frac{1}{N}{\displaystyle \sum}_{i=1}^{N}{\left(P\_SY{S}_{i}-E\_SY{S}_{i}\right)}^{2}}$$
- (3)
- Mean absolute percentage deviation (MAPD): Because the explanation of the relative error by MAPD is very intuitive, it is often used for model evaluation. The smaller the MAPD, the better the prediction effect of the model:$$MAPD=\frac{100\%}{N}{{\displaystyle \sum}}_{i=1}^{N}|\frac{P\_SY{S}_{i}-E\_SY{S}_{i}}{P\_SY{S}_{i}}|.$$

## 3. Results

#### 3.1. Determination of BPNN Parameters

_{in}is the number of neurons in the input layer, n

_{out}is the number of neurons in the output layer, and a

_{0}is the revised value, ranging from 0 to 10.

^{2}is the closest to 1, and the RMSE and MAPD values are the smallest. Therefore, the optimal number of hidden neurons of the BPNN model is 8.

#### 3.2. SVM Parameter Determination

## 4. Discussions

#### 4.1. Model Performance Comparison

^{2}ranges of the five BPNN models during the training and testing stage were 0.974~0.986 and 0.943~0.986, respectively. The R

^{2}ranges of the five SVM models during the training and testing stage were 0.961~0.976 and 0.931~0.983, respectively. The R

^{2}

_{min}and R

^{2}

_{max}values of the BPNN models during the training and testing stage were greater than those of the SVM models, and the R

^{2}ranges of BPNN models were smaller than those of the SVM models. The difference between the R

^{2}

_{max}and R

^{2}

_{min}of the BPNN and SVM models during the training stage was 0.012 and 0.015 respectively. The difference between the R

^{2}

_{max}and R

^{2}

_{min}of the BPNN and SVM models during the testing stage was 0.043 and 0.052, respectively. This shows that the R

^{2}fluctuation of the BPNN model is smaller than that of the SVM model under different dataset grouping conditions. The explanation degree of independent variable to dependent variable is less affected by dataset grouping.

_{max}and RMSE

_{min}of the BPNN models during the training and testing stage were less than those of the SVM models. The difference between the RMSE

_{max}and RMSE

_{min}of the BPNN and SVM models during the training stage was 16.137 and 16.284, respectively. The difference between the RMSE

_{max}and RMSE

_{min}of the BPNN and SVM models during the testing stage was 49.413 and 57.068, respectively. The RMSE range of BPNN models is smaller than that of SVM models. The RMSE of the SVM models for the K-2 group of testing dataset was 99.438, which indicates that the prediction error of the SVM models for K-2 group of the testing dataset was greater than other dataset group. Under different dataset grouping conditions, the RMSE fluctuation of the BPNN models was smaller, and the prediction errors of the BPNN models ware less affected by grouping.

_{max}and MAPD

_{min}of the BPNN models during the training and testing stage were less than or that of SVM models. The MAPDs of the five SVM models during the training stage and the testing stage were all bigger than that of BPNN models. which indicates that the prediction errors of the SVM models were all greater than BPNN models.

^{2}and RMSE ranges of the five BPNN models during the training and testing stage were more concentrated than that of the SVM models, which shows that the statistical parameters of the SVM models fluctuate greatly with different dataset groupings. The performance of the SVM models is greatly affected by different dataset groupings. This illustrates that the stability of the BPNN model is better than that of the SVM model.

^{2}of the BPNN models during the training and testing stages was closer to 1 than that of SVM models. The average RMSE of the BPNN during the training and testing stage were 11.805 and 7.035 smaller than that of SVM, respectively. This showed that the prediction error of the BPNN models was smaller than that of SVM models. This indicates that the predicted data for the BPNN models match the experimental data well. The average MAPDs of the BPNN during training and testing stages were 0.022% and 0.024% smaller than that of SVM, respectively. This shows that the relative error of the BPNN model is less than that of the SVM model, so the prediction effects of the BPNN models are better.

^{2}of K-2, K-3, and K-5 datasets in the testing stage are only slightly lower than those in the training stage, and even the R

^{2}of K-1 and K-4 datasets in the testing stage are higher than those in the training stage. The results of RMSE and MAPD showed opposite regularity. And the results of the SVM model parameters showed the similar regularity. Moreover, the model parameters of BPNN and SVM models are very stable, neither excellent nor poor. Thus, the performance of BPNN and SVM models is stable, the generalization ability of the model is good for the data of this study, and the generalization ability for external data needs to be explored and improved in future research.

^{2}values were all less than 0.80. The model performance was poor and the generalization ability was weak. Karim (2016) proposed a two-fold simple empirical model with R

^{2}= 83%, which greatly improved the performance of the model [55]. In this study, the R

^{2}results of the pre-consolidation pressure prediction models are all above 90%. Therefore, compared with the existing empirical formula model, the performance of the BPNN and SVM models established in this study are much better.

#### 4.2. Sensitivity Analysis

^{2}of the BPNN-3 during the training and testing stages were greater than 0.969 and were closer to 1 than the average R

^{2}of the other two models. This shows that the proportion of variance in the dependent variable that is explained by the independent variable is high in BPNN-3. The R

^{2}of BPNN-1 was the smallest, and the average R

^{2}value during the training and testing stages was about 0.9. This shows that the proportion of variance in the dependent variable which is explained by the independent variable decreases obviously when the water content of the input variable is removed.

^{2}average value of the BPNN-1 model is the smallest when removing the water content of the input variable, and the RMSE and MAPD average values are also larger than BPNN-2 and BPNN-3, the proportion of variance in the dependent variable that is predicted or explained by the independent variable of the model is reduced significantly, and the prediction error and relative error increase significantly when removing the water content of the input variable. Therefore, it can be concluded that the influence degree of each variable is as follows: water content > compaction degree > salt content.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Change of ion concentration with depth: (

**a**) distribution of anions; (

**b**) distribution of cations.

**Figure 4.**The structural yield strength (SYS) of the saline soil in Zhenlai is obtained by the high pressure consolidation test: (

**a**) Triple high pressure consolidation apparatus produced by Nanjing Soil Instrument Factory; (

**b**) soil sample: ω = 15%, S = 0.4%, C = 90%; (

**c**) soil sample: ω = 17%, S = 0.4%, C = 90%; (

**d**) soil sample: ω = 19%, S = 0.4%, C = 90%; (

**e**) soil sample: ω = 23%, S = 0.4%, C = 90%; (

**f**) Compression curve of saline soil in double logarithmic coordinates.

**Figure 6.**Average values of model evaluation parameters when the hidden neurons of the back propagation neural network (BPNN) varied: (

**a**) coefficient of determination (R

^{2}); (

**b**) root mean square error (RMSE); (

**c**) mean absolute percentage deviation (MAPD).

**Figure 7.**Relationship between the estimated structural yield strength (SYS) of the BPNN models based on K-1 dataset and measured SYS: (

**a**) training stage; (

**b**) testing stage.

**Figure 8.**Relationship between the estimated SYS (structural yield strength) of the SVM models and measured SYS: (

**a**) training stage; (

**b**) testing stage.

**Figure 9.**Relationship the estimated SYS (structural yield strength) of the BPNN-1 models (dewatering) and measured SYS: (

**a**) BPNN-1 in training stage; (

**b**) BPNN-1 in testing stage.

**Figure 10.**Relationship the estimated SYS (structural yield strength) of the BPNN-2 models (de-compaction degree) and measured SYS: (

**a**) BPNN-2 in training stage; (

**b**) BPNN-2 in testing stage.

**Figure 11.**Relationship the estimated SYS (structural yield strength) of the BPNN-3 models (desalination content) and measured SYS: (

**a**) BPNN-3 in training stage; (

**b**) BPNN-3 in testing stage.

Property | Grain Size Composition | Water Content ω (%) | Optimum Water Content ω_{0} (%) | Atterberg Limits | |||
---|---|---|---|---|---|---|---|

Sand (%) | Silt (%) | Clay (%) | Liquid Limit (%) | Plastic Limit (%) | |||

Value | 8.0 | 53.5 | 38.5 | 14.46 | 20.5 | 35 | 17 |

Soluble Content (%) | Main Ions Concentration(mmol/kg) | Organic Content (%) | |||||
---|---|---|---|---|---|---|---|

Na^{+} | K^{+} | Mg^{2+} + Ca^{2+} | SO_{4}^{2−} | HCO_{3}^{−} | Cl^{−} | ||

0.408 | 9.88 | 0.19 | 2.99 | 8.82 | 12.54 | 2.40 | 0.189 |

Number | ω (%) | C (%) | S (%) | SYS (kPa) | Number | ω (%) | C (%) | S (%) | SYS (kPa) | Number | ω (%) | C (%) | S (%) | SYS (kPa) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 13 | 85 | 0.0 | 320 | 41 | 16 | 90 | 0.0 | 331 | 81 | 19 | 95 | 0.0 | 335 |

2 | 13 | 85 | 0.4 | 383 | 42 | 16 | 90 | 0.4 | 427 | 82 | 19 | 95 | 0.4 | 363 |

3 | 13 | 85 | 1.0 | 464 | 43 | 16 | 90 | 1.0 | 412 | 83 | 19 | 95 | 1.0 | 285 |

4 | 13 | 85 | 2.0 | 464 | 44 | 16 | 90 | 2.0 | 325 | 84 | 19 | 95 | 2.0 | 285 |

5 | 13 | 90 | 0.0 | 403 | 45 | 16 | 95 | 0.0 | 394 | 85 | 20 | 85 | 0.0 | 245 |

6 | 13 | 90 | 0.4 | 391 | 46 | 16 | 95 | 0.4 | 479 | 86 | 20 | 85 | 0.4 | 316 |

7 | 13 | 90 | 1.0 | 497 | 47 | 16 | 95 | 1.0 | 469 | 87 | 20 | 85 | 1.0 | 279 |

8 | 13 | 90 | 2.0 | 509 | 48 | 16 | 95 | 2.0 | 393 | 88 | 20 | 85 | 2.0 | 254 |

9 | 13 | 95 | 0.0 | 457 | 49 | 17 | 85 | 0.0 | 191 | 89 | 20 | 90 | 0.0 | 367 |

10 | 13 | 95 | 0.4 | 400 | 50 | 17 | 85 | 0.4 | 209 | 90 | 20 | 90 | 0.4 | 407 |

11 | 13 | 95 | 1.0 | 521 | 51 | 17 | 85 | 1.0 | 292 | 91 | 20 | 90 | 1.0 | 299 |

12 | 13 | 95 | 2.0 | 598 | 52 | 17 | 85 | 2.0 | 260 | 92 | 20 | 90 | 2.0 | 279 |

13 | 14 | 85 | 0.0 | 462 | 53 | 17 | 90 | 0.0 | 237 | 93 | 20 | 95 | 0.0 | 422 |

14 | 14 | 85 | 0.4 | 447 | 54 | 17 | 90 | 0.4 | 288 | 94 | 20 | 95 | 0.4 | 457 |

15 | 14 | 85 | 1.0 | 483 | 55 | 17 | 90 | 1.0 | 343 | 95 | 20 | 95 | 1.0 | 335 |

16 | 14 | 85 | 2.0 | 475 | 56 | 17 | 90 | 2.0 | 272 | 96 | 20 | 95 | 2.0 | 343 |

17 | 14 | 90 | 0.0 | 631 | 57 | 17 | 95 | 0.0 | 260 | 97 | 21 | 85 | 0.0 | 209 |

18 | 14 | 90 | 0.4 | 457 | 58 | 17 | 95 | 0.4 | 355 | 98 | 21 | 85 | 0.4 | 251 |

19 | 14 | 90 | 1.0 | 545 | 59 | 17 | 95 | 1.0 | 443 | 99 | 21 | 85 | 1.0 | 248 |

20 | 14 | 90 | 2.0 | 578 | 60 | 17 | 95 | 2.0 | 306 | 100 | 21 | 85 | 2.0 | 152 |

21 | 14 | 95 | 0.0 | 813 | 61 | 18 | 85 | 0.0 | 208 | 101 | 21 | 90 | 0.0 | 292 |

22 | 14 | 95 | 0.4 | 468 | 62 | 18 | 85 | 0.4 | 240 | 102 | 21 | 90 | 0.4 | 316 |

23 | 14 | 95 | 1.0 | 558 | 63 | 18 | 85 | 1.0 | 275 | 103 | 21 | 90 | 1.0 | 266 |

24 | 14 | 95 | 2.0 | 627 | 64 | 18 | 85 | 2.0 | 232 | 104 | 21 | 90 | 2.0 | 266 |

25 | 15 | 85 | 0.0 | 327 | 65 | 18 | 90 | 0.0 | 249 | 105 | 21 | 95 | 0.0 | 351 |

26 | 15 | 85 | 0.4 | 408 | 66 | 18 | 90 | 0.4 | 316 | 106 | 21 | 95 | 0.4 | 389 |

27 | 15 | 85 | 1.0 | 404 | 67 | 18 | 90 | 1.0 | 318 | 107 | 21 | 95 | 1.0 | 299 |

28 | 15 | 85 | 2.0 | 306 | 68 | 18 | 90 | 2.0 | 249 | 108 | 21 | 95 | 2.0 | 299 |

29 | 15 | 90 | 0.0 | 363 | 69 | 18 | 95 | 0.0 | 286 | 109 | 23 | 85 | 0.0 | 226 |

30 | 15 | 90 | 0.4 | 448 | 70 | 18 | 95 | 0.4 | 347 | 110 | 23 | 85 | 0.4 | 229 |

31 | 15 | 90 | 1.0 | 464 | 71 | 18 | 95 | 1.0 | 346 | 111 | 23 | 85 | 1.0 | 201 |

32 | 15 | 90 | 2.0 | 376 | 72 | 18 | 95 | 2.0 | 261 | 112 | 23 | 85 | 2.0 | 139 |

33 | 15 | 95 | 0.0 | 537 | 73 | 19 | 85 | 0.0 | 197 | 113 | 23 | 90 | 0.0 | 266 |

34 | 15 | 95 | 0.4 | 473 | 74 | 19 | 85 | 0.4 | 219 | 114 | 23 | 90 | 0.4 | 272 |

35 | 15 | 95 | 1.0 | 497 | 75 | 19 | 85 | 1.0 | 248 | 115 | 23 | 90 | 1.0 | 226 |

36 | 15 | 95 | 2.0 | 433 | 76 | 19 | 85 | 2.0 | 226 | 116 | 23 | 90 | 2.0 | 254 |

37 | 16 | 85 | 0.0 | 313 | 77 | 19 | 90 | 0.0 | 269 | 117 | 23 | 95 | 0.0 | 343 |

38 | 16 | 85 | 0.4 | 355 | 78 | 19 | 90 | 0.4 | 331 | 118 | 23 | 95 | 0.4 | 355 |

39 | 16 | 85 | 1.0 | 385 | 79 | 19 | 90 | 1.0 | 272 | 119 | 23 | 95 | 1.0 | 285 |

40 | 16 | 85 | 2.0 | 298 | 80 | 19 | 90 | 2.0 | 237 | 120 | 23 | 95 | 2.0 | 285 |

K-Fold Cross-Validation | Evaluation Parameters | Number of the Hidden Neurons | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||

K-1 | R^{2} | 0.97 | 0.97 | 0.97 | 0.97 | 0.97 | 0.97 | 0.98 | 0.98 | 0.97 | 0.97 | 0.97 |

RMSE | 66 | 62 | 67 | 66 | 66 | 60 | 56 | 56 | 70 | 62 | 62 | |

MAPD | 0.14 | 0.12 | 0.14 | 0.13 | 0.13 | 0.12 | 0.11 | 0.11 | 0.14 | 0.12 | 0.12 | |

K-2 | R^{2} | 0.98 | 0.98 | 0.97 | 0.98 | 0.98 | 0.98 | 0.99 | 0.99 | 0.98 | 0.98 | 0.98 |

RMSE | 53 | 52 | 56 | 52 | 50 | 48 | 42 | 42 | 51 | 44 | 45 | |

MAPD | 0.12 | 0.12 | 0.13 | 0.12 | 0.11 | 0.11 | 0.09 | 0.09 | 0.12 | 0.10 | 0.10 | |

K-3 | R^{2} | 0.97 | 0.98 | 0.97 | 0.97 | 0.97 | 0.98 | 0.98 | 0.98 | 0.97 | 0.97 | 0.97 |

RMSE | 60 | 57 | 62 | 60 | 59 | 56 | 47 | 47 | 66 | 59 | 59 | |

MAPD | 0.12 | 0.11 | 0.13 | 0.12 | 0.12 | 0.11 | 0.09 | 0.09 | 0.15 | 0.12 | 0.12 | |

K-4 | R^{2} | 0.97 | 0.97 | 0.96 | 0.96 | 0.97 | 0.97 | 0.97 | 0.97 | 0.96 | 0.97 | 0.98 |

RMSE | 65 | 65 | 68 | 69 | 64 | 62 | 58 | 58 | 72 | 64 | 56 | |

MAPD | 0.14 | 0.14 | 0.15 | 0.15 | 0.13 | 0.13 | 0.12 | 0.12 | 0.15 | 0.13 | 0.11 | |

K-5 | R^{2} | 0.97 | 0.97 | 0.97 | 0.97 | 0.97 | 0.97 | 0.98 | 0.98 | 0.96 | 0.97 | 0.98 |

RMSE | 65 | 65 | 66 | 65 | 64 | 59 | 57 | 57 | 69 | 64 | 58 | |

MAPD | 0.13 | 0.13 | 0.13 | 0.13 | 0.13 | 0.12 | 0.11 | 0.11 | 0.14 | 0.14 | 0.11 |

**Note:**(1) K-1, K-2, K-3, K-4, and K-5 represent the five datasets divided by five-fold cross-validation method; (2) R

^{2}: coefficient of determination; (3) RMSE: root mean square error; (4) MAPD: mean absolute percentage deviation.

Projects | Parameters | K-1 | K-2 | K-3 | K-4 | K-5 |
---|---|---|---|---|---|---|

Rough selection results | C | 1.7411 | 16 | 256 | 16 | 256 |

g | 5.27803 | 0.108819 | 0.0625 | 0.0625 | 0.0625 | |

MSE | 0.0137 | 0.0159 | 0.0095 | 0.1258 | 0.0112 | |

Fine selection results | C | 1.4142 | 16 | 5.65685 | 16 | 0.5 |

g | 0.5 | 0.176777 | 0.0625 | 0.125 | 0.353553 | |

MSE | 0.0154 | 0.0155 | 0.0114 | 0.0117 | 0.0122 |

**Note:**(1) C: the penalty factor of the model; (2) g: a parameter of the kernel function; (3) MSE: mean square error.

K-Fold Cross-Validation | BPNN | SVM | ||||
---|---|---|---|---|---|---|

R^{2} | RMSE | MAPD | R^{2} | RMSE | MAPD | |

K-1 | 0.978 | 55.523 | 0.106 | 0.967 | 66.791 | 0.120 |

K-2 | 0.986 | 41.809 | 0.091 | 0.976 | 52.294 | 0.116 |

K-3 | 0.984 | 47.061 | 0.087 | 0.967 | 65.182 | 0.131 |

K-4 | 0.974 | 57.946 | 0.120 | 0.961 | 68.578 | 0.133 |

K-5 | 0.976 | 57.270 | 0.112 | 0.967 | 65.788 | 0.127 |

Average | 0.980 | 51.922 | 0.103 | 0.967 | 63.727 | 0.125 |

**Note:**(1) BPNN: back propagation neural network; (2) SVM: support vector model; (3) R

^{2}: coefficient of determination; (4) RMSE: root mean square error; (5) MAPD: mean absolute percentage deviation; (5) K-1, K-2, K-3, K-4, and K-5 represent the five datasets divided by five-fold cross-validation method.

K-Fold Cross-Validation | BPNN | SVM | ||||
---|---|---|---|---|---|---|

R^{2} | RMSE | MAPD | R^{2} | RMSE | MAPD | |

K-1 | 0.985 | 41.554 | 0.105 | 0.983 | 42.370 | 0.130 |

K-2 | 0.943 | 90.967 | 0.150 | 0.931 | 99.438 | 0.171 |

K-3 | 0.960 | 69.996 | 0.168 | 0.955 | 72.646 | 0.177 |

K-4 | 0.986 | 45.334 | 0.093 | 0.982 | 48.486 | 0.109 |

K-5 | 0.982 | 47.399 | 0.102 | 0.966 | 67.484 | 0.155 |

Average | 0.971 | 59.050 | 0.124 | 0.963 | 66.085 | 0.148 |

**Note:**(1) BPNN: back propagation neural network; (2) SVM: support vector model; (3) R

^{2}: coefficient of determination; (4) RMSE: root mean square error; (5) MAPD: mean absolute percentage deviation; (5) K-1, K-2, K-3, K-4, and K-5 represent the five dataset divided by five-fold cross-validation method.

Evaluation Parameters | Training Stage | Testing Stage | ||||
---|---|---|---|---|---|---|

R^{2} | RMSE | MAPD | R^{2} | RMSE | MAPD | |

BPNN-1 | 0.919 | 101.005 | 0.236 | 0.892 | 114.365 | 0.271 |

BPNN-2 | 0.966 | 66.420 | 0.140 | 0.949 | 81.488 | 0.174 |

BPNN-3 | 0.976 | 56.128 | 0.118 | 0.970 | 62.900 | 0.142 |

**Note:**(1) R

^{2}: coefficient of determination; (2) RMSE: root mean square error; (3) MAPD: mean absolute percentage deviation; (4) BPNN-1: dewatering; (5) BPNN-2: de-compaction degree; (6) BPNN-3: desalination content.

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## Share and Cite

**MDPI and ACS Style**

Peng, W.; Wang, Q.; Zhang, X.; Sun, X.; Li, Y.; Liu, Y.; Kong, Y.
Prediction of the Structural Yield Strength of Saline Soil in Western Jilin Province, China: A Comparison of the Back-Propagation Neural Network and Support Vector Machine Models. *Symmetry* **2020**, *12*, 1163.
https://doi.org/10.3390/sym12071163

**AMA Style**

Peng W, Wang Q, Zhang X, Sun X, Li Y, Liu Y, Kong Y.
Prediction of the Structural Yield Strength of Saline Soil in Western Jilin Province, China: A Comparison of the Back-Propagation Neural Network and Support Vector Machine Models. *Symmetry*. 2020; 12(7):1163.
https://doi.org/10.3390/sym12071163

**Chicago/Turabian Style**

Peng, Wei, Qing Wang, Xudong Zhang, Xiaohui Sun, Yongchao Li, Yufeng Liu, and Yuanyuan Kong.
2020. "Prediction of the Structural Yield Strength of Saline Soil in Western Jilin Province, China: A Comparison of the Back-Propagation Neural Network and Support Vector Machine Models" *Symmetry* 12, no. 7: 1163.
https://doi.org/10.3390/sym12071163