# Land Subsidence Susceptibility Mapping Using Bayesian, Functional, and Meta-Ensemble Machine Learning Models

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## Abstract

**:**

## 1. Introduction

## 2. Land Subsidence in the Study Area

## 3. Construction of Spatial Database

^{−2}cm/s), moderately (10

^{−2}–10

^{−3}cm/s), slightly (10

^{−3}–10

^{−5}cm/s), and very slightly (10

^{−5}–10

^{−7}cm/s) permeable and practically impermeable (<10

^{−7}cm/s), respectively. In this study, the permeability grade ranged from 4–4.5 (slightly permeable). The groundwater data were collected from a report published in May 1996 by the Coal Industry Promotion Board. Borehole point data should be converted into raster data for spatial analysis, and the accuracy of a raster map depends on the number of data points. However, the available borehole data were limited in this study. Therefore, raster maps from the limited borehole data were constructed using an inverse distance weighting (IDW) interpolation method, which is useful for predicting values at unmeasured locations where data are insufficient [11].

## 4. Methods

#### 4.1. Models

#### 4.1.1. Bayes Net (BN)

#### 4.1.2. Naïve Bayes (NB)

_{j}/x

_{i}) for all possible output classes as shown in Equation (2). The class with the largest posterior probability is predicted as follows:

_{i}is the input factor, y

_{j}is the output class, P(y

_{j}) is the prior probability, and P(y

_{j}/x

_{i}) is the conditional probability.

_{i}.

#### 4.1.3. Logistic Regression (LR)

_{1}, x

_{2}, …, x

_{n}are the input factors, ${\mathrm{c}}_{0}$ is the model intercept, and ${\mathrm{c}}_{1},\text{}\dots ,{\text{}\mathrm{c}}_{\mathrm{n}}$ are the regression coefficients to be approximated. In this study, P is the probability of subsidence occurrence and 1 − P is probability that subsidence will not occur. The function f(x) is represented as logit (P).

#### 4.1.4. Multilayer Perceptron (MLP)

#### 4.1.5. Logit Boost (LB)

_{i}= x

_{1}, x

_{2}, …, x

_{n}, where n is the number of input factors; y = [1, 0] represents two output classes (subsidence or non-subsidence). The LB algorithm is trained in the following steps [47]:

- Assign weights ${\mathsf{\omega}}_{\mathrm{i}}=\frac{1}{\mathrm{n}},\text{}\mathrm{i}=1,2,\dots ,\mathrm{n},\text{}\mathrm{f}\left(\mathrm{x}\right)\text{}=\text{}0$ and probability estimates ${\mathrm{p}}_{\mathrm{e}}\left({\mathrm{x}}_{\mathrm{i}}\right)=\text{}\xbd\text{}.$
- For m = 1, 2, ..., m, repeat the following steps:
- Compute the working response and weights:$${\mathrm{r}}_{\mathrm{i}}\text{}=\text{}\frac{\left[{\mathrm{y}}_{\mathrm{i}}^{*}-{\mathrm{p}}_{\mathrm{e}}\left({\mathrm{x}}_{\mathrm{i}}\right)\right]}{[{\mathrm{p}}_{\mathrm{e}}\left({\mathrm{x}}_{\mathrm{i}}\right)\left(1-\mathrm{p}\left({\mathrm{x}}_{\mathrm{i}}\right)\right]}$$$${\mathsf{\omega}}_{\mathrm{i}}={\mathrm{p}}_{\mathrm{e}}\left({\mathrm{x}}_{\mathrm{i}}\right)(1-\mathrm{p}\left({\mathrm{x}}_{\mathrm{i}}\right)$$
- Fit the function by weighted least-squares regression of ${\mathrm{r}}_{\mathrm{i}}$ to ${\mathrm{x}}_{\mathrm{i}}$ using weights ${\mathsf{\omega}}_{\mathrm{i}}$.
- Update the function as:$$\mathrm{f}\left(\mathrm{x}\right)\text{}\leftarrow \text{}\mathrm{f}\left(\mathrm{x}\right)\text{}+\frac{1}{2}{\mathrm{f}}_{\mathrm{m}}\left(\mathrm{x}\right)$$$$\mathrm{p}\left(\mathrm{x}\right)\leftarrow \frac{{\mathrm{e}}^{\mathrm{f}\left(\mathrm{x}\right)}}{{\mathrm{e}}^{\mathrm{f}\left(\mathrm{x}\right)}+{\mathrm{e}}^{-\mathrm{f}\left(\mathrm{x}\right)}}$$

- Output the classifier.$$\mathrm{sign}\left[\mathrm{f}\left(\mathrm{x}\right)\right]=\mathrm{sign}\left[{\displaystyle \sum}_{\mathrm{m}=1}^{\mathrm{M}}{\mathrm{f}}_{\mathrm{m}}\left(\mathrm{x}\right)\right]$$$$=\{\begin{array}{c}1\left(\mathrm{subsidence}\right)\mathrm{i}\mathrm{f}\mathrm{f}\left(\mathrm{x}\right)0\\ -1\left(\mathrm{non}\text{}\mathrm{subsidence}\right)\mathrm{i}\mathrm{f}\mathrm{f}\left(\mathrm{x}\right)\ge 0\end{array}$$

#### 4.2. Model Evaluation and Comparison

## 5. Results

#### 5.1. LSS Mapping

#### 5.2. Validation

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Eight factors influencing coal mine subsidence were used as input data in this study: (

**a**) Geology, (

**b**) land use, (

**c**) slope, (

**d**) distance from drift, (

**e**) distance from lineament, (

**f**) groundwater depth, (

**g**) rock mass rating (RMR), and (

**h**) permeability.

**Figure 4.**Flowchart for the generation of land subsidence susceptibility (LSS) maps using various machine learning models including Bayes net, naïve Bayes (NB), logistic, multilayer perceptron, and logit boost models.

**Figure 5.**LSS maps generated using the five algorithms: (

**a**) Bayes net, (

**b**) NB, (

**c**) logistic, (

**d**) multilayer perceptron, and (

**e**) logit boost.

**Figure 6.**Susceptibility index rank (x-axis) and subsidence occurrence (y-axis) of the five algorithms.

**Table 1.**Description of representative land subsidence in the study area [22].

Location | Structure | Elevation (m) | Mining Depth (m) | Thickness (m) and Slope of Coal Seam | Subsidence Depth (mm) | Other |
---|---|---|---|---|---|---|

S1 | Railway | 885 | 20–30 | 1–2 40–50° | 90 | -The coal seam is oblique to the railroad. -Shallow depth of mine -Sinkhole-type subsidence |

S2 | Railway | 885 | 0 | – | 72 | -Progression of cavity by mining -Subsidence by limestone cavity |

S3 | Railway | 885 | 30–50 | 1–2 20° | 329 | -Subsidence along railway |

S4 | Railway | 885 | 40–65 | 2 20° | 223 | -Shallow depth of mine -Coal bonanza |

S5 | Tunnel Railway | 810 | 30–260 | 105 50–70° | 65 | -The tunnel is located above the mine cavity. -Vertical cracks and leakage in tunnel |

S6 | Road | 765 | 60–98 | 3 20° | 508 | -Residential area and elementary school -Differential subsidence |

**Table 2.**Description of geological stratigraphy in Taebaek [30].

Geological Aage | Formation | Thickness (m) | Description |
---|---|---|---|

Quaternary | Alluvium (Qa) | ~20 | - Gravel, sand, and clay |

Permian | ^{⏝}_{⏜}^{⏝}_{⏜}^{⏝}_{⏜}^{⏝}_{⏜}^{⏝}_{⏜}^{⏝} | 250–350 | - Mainly milky white–light green coarse–very coarse sandstone with greenish-gray–gray shale interbeds. Intercalations of pinkish sandstone, purple shale, and grayish-green sandy shale in the upper part. The sandstone is less compact than that of the Hambaegsan Formation. |

Dosagog (Pd) | |||

Hambaegsan (Ph) | 70–250 | - Mainly milky white–light gray coarse sandstone with some interbeds of black shale with thickness of 2–3 m. Some pebbly sandstones occur at the base. | |

Jangseong (Pj) | 80–150 | - Four–five cyclothems consisting of dark-gray sandstone, black shale, and coal seam. Abundant plant fossils occur in the shale above the coal seam, the most valuable anthracite bed, of the 3rd–4th cyclothem from the bottom. | |

^{⏝}_{⏜}^{⏝}_{⏜}^{⏝}_{⏜}^{⏝}_{⏜}^{⏝}_{⏜}^{⏝} | |||

Carboniferous | Geumcheon (Cg) | 50–100 | - Mainly dark-gray–black shale and dark-gray fine sandstone intercalated with dark-gray limestone lenses and two to three thin coal seams |

Manhang (Cm) | 250–300 | - Mainly purple, greenish-gray, or light-green shale and light-green–green or light-gray medium–very coarse sandstone intercalated with three–four limestone lenses. Conglomerates with a thickness of a few meters occur at the base in some places. | |

^{⏝}_{⏜}^{⏝}_{⏜}^{⏝}_{⏜}^{⏝}_{⏜}^{⏝}_{⏜}^{⏝} | |||

Ordovician | Makgol (Om) | - In the upper part, gray–dark gray limestone intercalated with dolomite |

ID | Depth of Borehole | Depth of Groundwater (m) | RMR (grade) | Permeability (grade) | Geology |
---|---|---|---|---|---|

B1 | 50.0 | 32.0 | 3.4 | - | Alluvium-Hambaegsan |

B2 | 50.0 | 27.2 | 3.4 | 4.5 | Alluvium-Hambaegsan |

B3 | 30.0 | - | 3.4 | - | Alluvium-Hambaegsan |

B4 | 60.2 | - | 3.4 | 4 | Alluvium-Hambaegsan |

B5 | 86.3 | - | 2.0 | - | Alluvium-Hambaegsan |

B6 | 80.0 | - | 2.0 | 4 | Alluvium-Hambaegsan |

B7 | 33.0 | 27.5 | - | - | Jangseong |

B8 | 20.5 | 27.7 | - | - | Jangseong |

B9 | 40.0 | 26.1 | - | - | Jangseong |

B10 | 35.5 | - | 4.4 | - | Jangseong |

B11 | 30.0 | 15.7 | - | 4 | Jangseong |

B12 | 40.5 | 21.6 | - | 4 | Jangseong |

B13 | 41.1 | 29.4 | - | - | Jangseong |

B14 | 22.0 | - | 3.2 | - | Jangseong |

B15 | 35.7 | 20.0 | - | - | Jangseong |

B16 | 40.8 | 20.0 | - | - | Jangseong |

B17 | 50.5 | 14.7 | - | - | Jangseong |

B18 | 58.0 | - | 3.2 | - | Jangseong |

B19 | 54.0 | 42.5 | 2.5 | 4 | Hambaegsan-Jangseong |

B20 | 60.0 | - | 3.0 | - | Hambaegsan-Jangseong |

B21 | 115.0 | - | 3.0 | - | Hambaegsan-Jangseong |

B22 | 80.0 | - | 3.0 | - | Hambaegsan-Jangseong |

B23 | 80.0 | - | 4.5 | - | Hambaegsan-Jangseong |

B24 | 84.0 | - | 4.3 | - | Jangseong |

B25 | 80.4 | 18.0 | - | - | Jangseong |

B26 | 19.5 | 5.0 | 3.3 | - | Hambaegsan |

B27 | 200.0 | - | 4.3 | - | Hambaegsan-Jangseong |

B28 | 40.0 | 5.0 | 3.3 | - | Hambaegsan-Jangseong |

B29 | 35.0 | 5.5 | 3.3 | - | Hambaegsan-Jangseong |

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**MDPI and ACS Style**

Oh, H.-J.; Syifa, M.; Lee, C.-W.; Lee, S. Land Subsidence Susceptibility Mapping Using Bayesian, Functional, and Meta-Ensemble Machine Learning Models. *Appl. Sci.* **2019**, *9*, 1248.
https://doi.org/10.3390/app9061248

**AMA Style**

Oh H-J, Syifa M, Lee C-W, Lee S. Land Subsidence Susceptibility Mapping Using Bayesian, Functional, and Meta-Ensemble Machine Learning Models. *Applied Sciences*. 2019; 9(6):1248.
https://doi.org/10.3390/app9061248

**Chicago/Turabian Style**

Oh, Hyun-Joo, Mutiara Syifa, Chang-Wook Lee, and Saro Lee. 2019. "Land Subsidence Susceptibility Mapping Using Bayesian, Functional, and Meta-Ensemble Machine Learning Models" *Applied Sciences* 9, no. 6: 1248.
https://doi.org/10.3390/app9061248