# Forecasting of Landslide Displacement Using a Probability-Scheme Combination Ensemble Prediction Technique

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Description of Uncertainty Sources

#### 2.2. Ensemble Prediction

#### 2.3. Quantile Regression Neural Network

#### 2.3.1. Quantile Regression

#### 2.3.2. Quantile Regression Neural Network

#### 2.4. Kernel Density Estimation (KDE)

#### 2.5. Ensemble Prediction Employing QRNNs and KDE

#### 2.6. Evaluation Metrics and Uncertainty Quantification

^{2}) MSE, RMSE, NRMSE, and MAPE—were applied to assess the performance of point prediction. R

^{2}, MSE, RMSE, NRMSE, and MAPE are defined as

## 3. Case Study: Fanjiaping Landslide

#### 3.1. Features of the Fanjiaping Landslide

^{3}.

^{3}. The Tanjiahe landslide extends from an elevation of 135 m at the toe to 420 m at the crown (Figure 4c,d). The slope surface consists of alternating gentle and comparatively steep landforms. The sliding direction of the landslide is 345°.

^{3}.

#### 3.2. Input Data

#### 3.3. Triggering Factors of the Landslide Movements

#### 3.4. QRNNs-KDE-Based Method for Ensemble Prediction

#### 3.4.1. Data Splitting and Normalization

#### 3.4.2. QRNN Modelling

#### 3.4.3. PDF Estimation by KDE

#### 3.4.4. Final Ensemble Prediction

## 4. Results

^{2}. Moreover, compared with predictions at monitoring point ZG289 using the Copula-KSVMQR approach in [3], the QRNNs-KDE approach provided more accurate prediction with smaller MAPE and RMSE.

## 5. Discussion

^{*}in Figure 11). Constructing an ensemble model (h

^{’}in Figure 11) might not be better than the single best prediction model h

^{*}, but it does reduce the risk of choosing a bad learner with poor generalizability (schematic in Figure 11a). From a computational perspective, in a single model the training algorithms might get stuck in lock optima by only performing a local search. Constructing an ensemble model by searching from different starting positions might be a better alternative (schematic in Figure 11b). From a representational perspective, it is possible that the searched hypothesis space might not contain the true model h

^{*}. Constructing an ensemble model might expand the representable space (schematic in Figure 11c).

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**General framework for ensemble prediction models. (

**a**) Homogeneous ensemble model and (

**b**) heterogeneous ensemble model.

**Figure 2.**The overall flowchart of ensemble prediction based on the quantile regression neural networks and kernel density estimation (QRNNs-KDE) approach.

**Figure 4.**Topographic map and geological profile of the Fanjiaping landslide. (

**a**) Topographic map of the Muyubao landslide. (

**b**) Geological profile of the Muyubao landslide along sections A-A′, as recorded with monitoring instruments. (

**c**) Topographic map of the Tanjiahe landslide. (

**d**) Geological profile of the Tanjiahe landslide along sections B-B′, as recorded with monitoring instruments.

**Figure 5.**Reservoir water level, monthly rainfall intensity, and cumulative displacement from the Fanjiaping landslide area.

**Figure 6.**(

**a**–

**d**) Cumulative displacement at monitoring point ZG295, monthly rainfall intensity, and reservoir water level spanning the period of 2009, 2011, 2012, and 2015. (

**e**) Cumulative displacement at monitoring points ZG296 and ZG297, daily rainfall intensity, and reservoir water level spanning the period of June 2016 to October 2017. (

**f**) Annual displacement at monitoring point ZG291, ZG294, ZG288, and ZG289, and reservoir water level spanning the period of 2007 to 2017.

**Figure 7.**Probability density functions (PDFs) for the Fanjiaping landslide at ZG289 from February 2015 to June 2015.

**Figure 9.**Comparisons of the final ensemble predictions and observations for the Fanjiaping landslide at ZG289 and ZG291.

**Figure 10.**Comparisons of the observations and the constructed PIs at a 90% confidence level for the Fanjiaping landslide at ZG289 and ZG291 using QRNNs-KDE and bootstrap-ELM-ANN. (

**a**) 90% PIs at ZG291 using QRNNs-KDE; (

**b**) 90% PIs at ZG291 using bootstrap-ELM-ANN; (

**c**) 90% PIs at ZG289 using QRNNs-KDE, (

**d**) 90% PIs at ZG289 using bootstrap-ELM-ANN.

**Figure 11.**Schematic that shows the fundamental benefits of the ensemble prediction model from statistical (

**a**), computational (

**b**), and representational (

**c**) perspectives. h

^{*}is the true prediction model; h

_{1}, h

_{2}, and h

_{3}are single prediction models; and h

^{’}is the ensemble prediction model obtained by combining the single prediction models h

_{1}, h

_{2}, and h

_{3}. The outer black curve is the hypothesis space of all possible models. The inner blue curve denotes the subset of hypotheses that give reasonable accuracy with the available training data (modified from [47]).

Parameter | Value | Parameter | Value |
---|---|---|---|

Maximum number of iterations | 5000 | Penalty for weight decay regularization | 1 |

Number of quantiles | 99 | Number of input nodes | 7 |

Number of repeated trials | 5 | Number of hidden nodes | 5 |

**Table 2.**Comparisons of predictions obtained from QRNNs-KDE, BP, RBF, ELM, and SVM for the Fanjiaping landslide.

Monitoring Point | Model | BP | RBF | ELM | SVM | QRNNs-KDE | |
---|---|---|---|---|---|---|---|

Index | |||||||

ZG289 | R^{2} | 0.99730 | 0.99992 | 0.99785 | 0.99993 | 0.99997 | |

MSE | 3192.07 | 99.54 | 2538.74 | 78.12 | 30.69 | ||

RMSE | 56.50 | 9.98 | 50.39 | 8.84 | 5.54 | ||

NRMSE | 0.032263 | 0.005697 | 0.028772 | 0.005047 | 0.003163 | ||

MAPE | 2.74 | 2.00 | 1.57 | 1.27 | 1.17 | ||

ZG291 | R^{2} | 0.99991 | 0.99759 | 0.99991 | 0.99995 | 0.99997 | |

MSE | 206.32 | 5684.98 | 215.41 | 119.75 | 70.15 | ||

RMSE | 14.36 | 75.40 | 14.68 | 10.94 | 8.38 | ||

NRMSE | 0.005953 | 0.031251 | 0.006083 | 0.004536 | 0.003471 | ||

MAPE | 3.97 | 1.96 | 2.59 | 2.33 | 0.41 |

**Table 3.**Comparisons of 90% PIs obtained from Bootstrap-ELM-ANN and QRNNs-KDE for the Fanjiaping landslide.

Monitoring Point | Index | PICP | NPIW | CWC | |
---|---|---|---|---|---|

Model | |||||

ZG289 | Bootstrap-ELM-ANN | 100% | 0.27 | 0.2071 | |

QRNNs-KDE | 100% | 0.0215 | 0.1661 | ||

ZG291 | Bootstrap-ELM-ANN | 99% | 0.024 | 0.143 | |

QRNNs-KDE | 99% | 0.018 | 0.085 |

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**MDPI and ACS Style**

Ma, J.; Liu, X.; Niu, X.; Wang, Y.; Wen, T.; Zhang, J.; Zou, Z. Forecasting of Landslide Displacement Using a Probability-Scheme Combination Ensemble Prediction Technique. *Int. J. Environ. Res. Public Health* **2020**, *17*, 4788.
https://doi.org/10.3390/ijerph17134788

**AMA Style**

Ma J, Liu X, Niu X, Wang Y, Wen T, Zhang J, Zou Z. Forecasting of Landslide Displacement Using a Probability-Scheme Combination Ensemble Prediction Technique. *International Journal of Environmental Research and Public Health*. 2020; 17(13):4788.
https://doi.org/10.3390/ijerph17134788

**Chicago/Turabian Style**

Ma, Junwei, Xiao Liu, Xiaoxu Niu, Yankun Wang, Tao Wen, Junrong Zhang, and Zongxing Zou. 2020. "Forecasting of Landslide Displacement Using a Probability-Scheme Combination Ensemble Prediction Technique" *International Journal of Environmental Research and Public Health* 17, no. 13: 4788.
https://doi.org/10.3390/ijerph17134788