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Safety Science
journal homepage: www.elsevier.com/locate/safety
Slope stability prediction for circular mode failure using gradient boosting
machine approach based on an updated database of case histories
Jian Zhoua,d, Enming Lia, Shan Yanga,⁎, Mingzheng Wangb, Xiuzhi Shia, Shu Yaod, Hani S. Mitric
a School of Resources and Safety Engineering, Central South University, Changsha 410083, China
bMIRARCO – Mining Innovation, Laurentian University, Sudbury P3E 2C6, Canada
c Department of Mining and Materials Engineering, McGill University, Montreal, QC H3A 0E8, Canada
d Shenzhen Zhongjin Lingnan Nonfemet Company Limited, Shenzhen 518042, China
A R T I C L E I N F O
Keywords:
Slope stability
Circular failure
Gradient boosting machine (GBM)
Predictive modeling
Mine safety
A B S T R A C T
Prediction of slope stability is one of the most crucial tasks in mining and geotechnical engineering projects. The
accuracy of the prediction is very important for mitigating the risk of slope instability and enhancing mine safety
in preliminary design. However, existing methods such as traditional statistical learning models are unable to
provide accurate results for slope instability due to the complexity and uncertainties of multiple related factors
with small unbalanced data samples thus requiring complex data processing algorithms. To address this lim-
itation, this paper presents a novel prediction method that utilizes the gradient boosting machine (GBM) method
to analyze slope stability. The GBM-based model is developed by the freely available R Environment software,
trained and tested with the parameters obtained from the detailed investigation of 221 different actual slope
cases between 1994 and 2011 with circular mode failure available in the literature. The stability of the circular
slope accounts for the unit weight (γ), cohesion (c), angle of internal friction (φ), slope angle (β), slope height
(H) and pore water pressure coefficient (ru). A fivefold cross-validation procedure is implemented to determine
the optimal parameter values during the GBM modeling and an external testing set is employed to validate the
prediction performance of models. Area under the curve (AUC), classification accuracy rate and Cohen’s Kappa
coefficient have been employed for measuring the performance of the proposed model. The analysis of AUC,
accuracy together with kappa for the dataset demonstrate that the GBM model has high credibility as it achieves
a comparable AUC, classification accuracy rate and Cohen’s kappa values of 0.900, 0.8654 and 0.7324, re-
spectively for the prediction of slope stability. Also, variable importance and partial dependence plots are used to
interpret the complex relationships between the GBM predictive results and predictor variables.
1. Introduction
Slope stability analysis is one of the most important and critical
problems in mining and geotechnical engineering projects such as open-
pit mining operations, dams, embankments, earth dams, landfills and
highways. Disastrous consequences of slope collapse necessitate better
tools for predicting their occurrences. Such hazards are responsible for
heavy destructions of public/private property, disruptions of traffic,
and loss of human lives every year (Sah et al., 1994; Shi et al., 2010;
Hoang and Pham, 2016; Basahel and Mitri, 2018).
Perhaps starting with Terzaghi’s 1950 work entitled “Mechanism of
Landslides” (Terzaghi, 1950), more scholars began to pay attention to
analyzing the stability of a slope in terms of theoretical, analytical,
experimental, numerical (i.e., finite difference, finite element and
discrete element) and statistical approaches which have been used
worldwide. For example, literature studies on limit equilibrium method
(LEM) and finite element method (FEM) slope stability analyses are
extensively available (Xu and Low, 2006; Cheng et al., 2007). However,
when a slope fails with a complex mechanism such as internal de-
formation and brittle fracture, progressive creep, liquefaction of weaker
soil layers (Chen and Chameau, 1983; Duncan, 1996; Yu et al., 1998;
Eberhardt, 2003), LEM simulations may become inadequate. Moreover,
FEM is computationally more time consuming as compared to LEM. On
the other hand, numerous studies have been undertaken in recent years
to develop several computational intelligence approaches for slope
stability analysis (i.e. Sah et al., 1994; Sakellariou and Ferentinou,
2005; Samui, 2008; Das et al., 2011; Manouchehrian et al., 2014; Liu
et al., 2014; Gao, 2015; Suman et al., 2016; Hoang and Pham, 2016).
https://doi.org/10.1016/j.ssci.2019.05.046
Received 17 October 2018; Received in revised form 24 February 2019; Accepted 28 May 2019
⁎ Corresponding author.
E-mail addresses: csujzhou@hotmail.com (J. Zhou), lem123456@csu.edu.cn (E. Li), yangshan@csu.edu.cn (S. Yang), mz_wang_rock@outlook.com (M. Wang),
shixiuzhi@263.net (X. Shi), miningyaoshu@126.com (S. Yao), hani.mitri@mcgill.ca (H.S. Mitri).
Safety Science 118 (2019) 505–518
Available online 05 June 2019
0925-7535/ © 2019 Elsevier Ltd. All rights reserved.
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For example, Lu and Rosenbaum (2003) combined the artificial neural
network (ANN) and the gray system method to evaluate slope stability
based on geotechnical properties and historical behaviors of the col-
lected slope cases. Accordingly, Wang et al. (2005) and Das et al. (2011)
applied the ANN to predict the slope stability. Zhao et al. (2012) em-
ployed the relevance vector machine to explore the nonlinear re-
lationship between slope stability and its influence factors. Liu et al.
(2014) used extreme learning machine technique for the evaluation and
prediction of stability of slopes with 97 cases. Hoang and Pham (2016)
introduced metaheuristic-optimized least squares support vector clas-
sification for slope assessment with 168 cases. However, few research
works have been systematically performed to precisely predict and
evaluate a level of safety of the structures. For example, empirical or
semi-empirical approaches have been employed with local monitoring
data and are open to improvement because they are based on limited
collected data (Basahel and Mitri, 2017). Furthermore, the estimation
of reliable values of model input parameters is found to be an in-
creasingly difficult task before applying sophisticated numerical
methods. Artificial intelligence studies provide new alternatives to
empirical methods and some other conventional statistical techniques.
However, these methods usually require a large amount of data and
they are mostly computationally expensive. Determining suitable
tuning parameters and architecture of ANN models remains a difficult
task; the optimal choice of kernel and regularization parameters of
relevance vector machine and support vector machine models often
need expert knowledge for different data characteristics. Additionally,
these methods seldom provide information about the relative sig-
nificance of various parameters. Moreover, it can be shown that part of
the data set is duplicated in the aforementioned studies after carefully
examining their dataset. Hence, predicting slope stability and inter-
preting the contribution of influencing parameters still pose a con-
siderable challenge for mining and geotechnical engineers.
Contrastingly, Friedman (2001) proposed a simple and highly
adaptive method for many kinds of applications, which is called gra-
dient boosting machine (GBM). As a relatively new algorithm, the GBMhttp://refhub.elsevier.com/S0925-7535(18)31651-5/h0305
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	Slope stability prediction for circular mode failure using gradient boosting machine approach based on an updated database of case histories
	Introduction
	Materials and methods
	Data set and predictor variables
	Gradient boosting machine algorithm
	Evaluation of classifier’s performance
	Hyper-parameters tuning of GBM classifier
	Results and discussions
	Descriptive analysis
	GBM model development and validation
	Variable importance and partial dependence plots
	Limitations
	Conclusions
	Acknowledgments
	Supplementary material
	Referencesis a family of powerful supervised machine learning techniques that
have shown promising results in terms of prediction performance, ro-
bustness and speed in a wide range of practical applications (Friedman,
2001, 2002; Kuhn and Johnson, 2013; Lu et al., 2016; Zhou et al.,
2016a, 2016b, 2019b). This benefits from two main features: (a) It
optimizes hyper-parameters in function space which ensures the custom
loss functions much easier to implement; and (b) Boosting focuses
progressively on complicated cases that gives an optimal technique to
handle unbalanced datasets by enhancing the impact of the positive
label. It is therefore motivating to investigate the capability of GBM in
slope stability prediction. To construct and confirm the GBM model, a
dataset including real cases of slope evaluation has been collected from
the literature. In addition, the training process of the GBM is enhanced
by the fivefold CV used for the model evaluation.
2. Materials and methods
2.1. Data set and predictor variables
In this work, the database consists of 221 cases (the numbers of
stable and failure slope cases are 115 and 106, respectively), which are
taken from information published by Sah et al. (1994), Xu and Shao
(1998), Feng and Hudson (2004), He et al. (2004), Jin et al. (2004),
Wang et al. (2005), Li et al. (2006), Chen et al. (2009), Su (2009), Wang
(2009), Xu et al. (2009), Chen et al. (2011), Xiao et al. (2011) and Zhu
et al. (2011) over sixty sites which can be found in Table 1. Height (H),
overall slope angle (β), and unit weight (γ) are the basic geometrical
slope design parameters; they often dictate the conditions for the soil
slope failure (Michalowski, 1995). Slope stability decreases sharply if
the height of slope increases. The cohesion (C) and the internal friction
angle (φ) are two key mechanical parameters associated with slope
stability according to the well-known Mohr-Coulomb failure criterion in
geomaterials. The shear-strength reduction technique (Dawson et al.,
1999) is implemented by a series of trial factors of safety with C and φ
being adjusted with each iteration. The technique is extensively em-
ployed in engineering practice for geotechnical stability problems.
When the angle φ becomes equal to that between the resultant force
and the normal force, the limit equilibrium state is reached and failure
occurs due to shearing (Duncan et al., 2014). The external triggering
factor considered in this study is the pore water ratio (ru) which is
defined as the ratio of the pore water pressure to the overburden
pressure (Michalowski, 1995; Kim et al., 1999; Liu et al., 2014). The
parameters that have been selected are related to the geometry and the
geotechnical properties of each slope. More specifically, the parameters
used for circular failure are the slope height (H), cohesion (C), slope
angle (β), unit weight (γ), pore water pressure ratio (ru), and angle of
internal friction (φ). This makes a total of 6 parameters, which is in line
with what is usually adopted for circular failure analysis in the litera-
ture (Sah et al., 1994; Lu and Rosenbaum, 2003; Sakellariou and
Ferentinou, 2005; Samui, 2008; Shi et al., 2010; Das et al., 2011;
Manouchehrian et al., 2014; Liu et al., 2014; Gao, 2015; Suman et al.,
2016; Hoang and Pham, 2016).
2.2. Gradient boosting machine algorithm
Gradient boosting machine (GBM), as one of the most popular su-
pervised machine learning technique, was proposed by Friedman (2001
and 2002), and then GBM was proved to be an effective tool to solve
regression and classification problems by many scholars (Friedman,
2001; Lu et al., 2016; Touzani et al., 2018; Zhou et al., 2016a, 2016b,
2019b). In this study, the slope stability database was categorized into
either “stable” or “failure” case. This is a typical binary classification
problem. Therefore, GBM is considered to use for distinguishing slope
stability and slope failure in this paper. On this point, the basic concept
Nomenclature
LEM limit equilibrium method
FEM finite element method
AUC area under the ROC curve
CV cross validation
ROC receiver operating characteristic curve
H height, m
β overall slope angle, °
γ unit weight, kN/m3
Φ angle of internal friction, °
ru pore water ratio
C cohesion, kPa
F failure
S stable
PCA principal component analysis
MLP Multi-Layer Perceptron
ANN Artificial Neural Network
RF Random Forest
SVM Support Vector Machine
GBM Gradient Boosting Machine
FPR False Positive Rate
TPR True Positive Rate
CAR Classification Accuracy Rate
SSC Slope Stability Classification
PA Producer's Accuracy
UA User's Accuracy
PDP Partial Dependence Plots
J. Zhou, et al. Safety Science 118 (2019) 505–518
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Table 1
Slope stability database used for modeling GBM classifier.
No. Location H β γ C Φ ru Stability
1 Congress street, open cut slope, Chicago, USA 8.23 35 18.68 26.34 15 0 Failure
2 Brightlingsea slide, UK 3.66 30 16.5 11.49 0 0 Failure
3 Unknown 30.5 20 18.84 14.36 25 0 Stable
4 Unknown 30.5 20 18.84 57.46 20 0 Stable
5# Case 1: open pit iron ore mine, India 100 35 28.44 29.42 35 0 Stable
6# Case 2: open pit iron ore mine, India 100 35 28.44 39.23 38 0 Stable
7 Open pit chromite mine, Orissa, India 40 30 20.6 16.28 26.5 0 Failure
8# Sarukuygi landslide, Japan 50 20 14.8 0 17 0 Failure
9 Case 1: open pit iron ore mine, Goa, India 88 30 14 11.97 26 0 Failure
10 Mercoirol open pit coal mine, France 120 53 25 120 45 0 Stable
11 Marquesade open pit iron ore mine, Spain 200 50 26 150.05 45 0 Stable
12 Unknown 6 30 18.5 25 0 0 Failure
13 Unknown 6 30 18.5 12 0 0 Failure
14 Case 1: Highvale coal mine, Alberta, Canada 10 30 22.4 10 35 0 Stable
15 Case 2: Highvale coal mine, Alberta, Canada 20 30 21.1 10 30.34 0 Stable
16# Case 1: open pit coal mine, Newcastle coalfield, Australia 50 45 22 20 36 0 Failure
17# Case 2: open pit coal mine, Newcastle coalfield, Australia 50 45 22 0 36 0 Failure
18 Unknown 4 35 12 0 30 0 Stable
19 Unknown 8 45 12 0 30 0 Failure
20 Unknown 4 35 12 0 30 0 Stable
21 Unknown 8 45 12 0 30 0 Failure
22 Pima open pit mine, Arizona, USA 214 37 23.47 0 32 0 Failure
23# Case 1: Wyoming, USA 115 40 16 70 20 0 Failure
24 Seven Sisters Landslide, UK 10.67 22 20.41 24.9 13 0.35 Stable
25 Case 1: The Northolt slide, UK 12.19 22 19.63 11.97 20 0.405 Failure
26 Selset Landslide, Yorkshire, UK 12.8 28 21.82 8.62 32 0.49 Failure
27 Saskatchewan dam, Canada 45.72 16 20.41 33.52 11 0.2 Failure
28 Case 2: The Northolt slide, UK 10.67 25 18.84 15.32 30 0.38 Stable
29# Sudbury slide, UK 7.62 20 18.84 0 20 0.45 Failure
30 Folkstone Warren slide, Kent, UK 61 20 21.43 0 20 0.5 Failure
31 River bank side, Alberta, Canada 21 35 19.06 11.71 28 0.11 Failure
32 Unknown 30.5 20 18.84 14.36 25 0.45 Failure
33# Unknown 76.81 31 21.51 6.94 30 0.38 Failure
34# Case 2: open pit iron ore mine, Goa, India 88 30 14 11.97 26 0.45 Failure
35 Athens slope, Greece 20 45 18 24 30.15 0.12 Failure
36 Open pit coal mine Allori coalfield, Italy 100 20 23 0 20 0.3 Failure
37# Case 1: open pit coal mine, Alberta, Canada 15 45 22.4 100 45 0.25 Stable
38 Case 2: open pit coal mine, Alberta, Canada 10 45 22.4 10 35 0.4 Failure
39 Case 3: open pit coal mine, Newcastle coalfield, Australia 50 45 20 20 36 0.25 Failure
40 Case 4: open pit coal mine, Newcastle coalfield, Australia 50 45 20 20 36 0.5 Failure
41# Case 5: open pit coal mine, Newcastle coalfield, Australia 50 45 20 0 36 0.25 Failure
42 Case 6: open pit coal mine, Newcastle coalfield, Australia 50 45 20 0 36 0.5 Failure
43 Case 1: Harbour slope, Newcastle, Australia 8 33 22 0 40 0.35 Stable
44 Case 2: Harbour slope, Newcastle, Australia 8 33 24 0 40 0.3 Stable
45# Case 3: Harbour slope, Newcastle, Australia 8 20 20 0 24.5 0.35 Stable
46 Case 4: Harbour slope, Newcastle, Australia 8 20 18 5 30 0.3 Stable
47# Unknown 50 45 20 20 36 0.25 Failure
48 Unknown292 47.1 27 40 35 0 Failure
49 Unknown 284 50 25 46 35 0 Stable
50# Unknown 366 46 31.3 68 37 0 Failure
51 Unknown 299 44.5 25 46 36 0 Stable
52 Unknown 480 40 27.3 10 39 0 Stable
53 Unknown 393 46 25 46 35 0 Stable
54# Unknown 330 49 25 48 40 0 Stable
55 Unknown 305 47 31.3 68.6 37 0 Failure
56# Unknown 299 45.5 25 55 36 0 Stable
57 Unknown 213 47 31.3 68 37 0 Failure
58# Three Gorges hydropower project, China 73 45 26.49 150 33 0.15 Stable
59 Three Gorges hydropower project, China 130 50 26.7 150 33 0.25 Stable
60 Three Gorges hydropower project, China 120 52 26.89 150 33 0.25 Stable
61 Three Gorges hydropower project, China 80 45.3 26.57 300 38.7 0.15 Failure
62# Three Gorges hydropower project, China 155 54 26.78 300 38.7 0.25 Failure
63 Three Gorges hydropower project, China 138 58 26.81 200 35 0.25 Stable
64 Three Gorges hydropower project, China 92.2 40 26.43 50 26.6 0.15 Stable
65# Three Gorges hydropower project, China 170 50 26.69 50 26.6 0.25 Stable
66 Three Gorges hydropower project, China 108 59 26.81 60 28.8 0.25 Stable
67 Dingjiahe phosphorus mine, China 236 41 27.8 27.8 27 0.1 Stable
68 Guilin-Liuzhou highway, China 100 25.6 27.1 22 18.6 0.19 Failure
69 Xiaolangdi reservoir, China 150 23.75 21.2 0 35 0.25 Failure
70 Xiaolangdi reservoir, China 150 23.75 21.2 0 35 0.25 Failure
71 Xiaolangdi reservoir, China 150 23.75 21.2 0 35 0.25 Stable
(continued on next page)
J. Zhou, et al. Safety Science 118 (2019) 505–518
507
Table 1 (continued)
No. Location H β γ C Φ ru Stability
72 Xiaolangdi reservoir, China 150 23.75 21.2 0 35 0.25 Stable
73 Xiabandi reservoir, China 78 26.5 22.3 0 40 0.25 Stable
74 Jingzhumiao reservoir, China 46 26.5 18.6 0 32 0.25 Stable
75 Jingzhumiao reservoir, China 46 21.8 18.6 0 32 0.25 Stable
76 Yuecheng reservoir, China 39 19.29 18.8 9.8 21 0.25 Failure
77 Yuecheng reservoir, China 73 18.43 21.2 0 35 0.25 Stable
78# Gushan reservoir, China 38 17.07 17.2 10 24.25 0.4 Stable
79 Laobu reservoir, China 54 21.04 19 11.9 20.4 0.75 Stable
80 Wenyuhe reservoir, China 53 15.52 18 5 26.5 0.4 Failure
81 Wenyuhe reservoir, China 53 15.52 18 5 22 0.4 Failure
82 Hongwuyi reservoir, China 51 18.43 17.4 20 24 0.4 Failure
83 Hongwuyi reservoir, China 51 18.43 17.8 21.2 13.92 0.4 Stable
84 Lingli reservoir, China 40 21.8 18.8 8 26 0.4 Failure
85 Lingli reservoir, China 40 21.8 18.8 8 26 0.4 Failure
86# Lingli reservoir, China 40 21.8 18 21 21.33 0.4 Failure
87# Zhejiang sea wall, China 9 21.8 17.6 10 16 0.4 Stable
88 Zhejiang sea wall, China 9 21.8 17.6 10 8 0.4 Stable
89 Hunan anxiang reservoir, China 15 45 17.4 14.95 21.2 0.4 Failure
90 Qing River area landslide, China 400 18 22 29 15 0 Failure
91# Qing River area landslide, China 380 23 23 24 19.8 0 Failure
92 Qing River area landslide, China 196 30 22 40 30 0 Stable
93 Qing River area landslide, China 210 24 22.54 29.4 20 0 Stable
94 Qing River area landslide, China 257 30 22 21 23 0 Failure
95 Qing River area landslide, China 190 26 23.5 10 27 0 Failure
96 Qing River area landslide, China 290 20 22.5 18 20 0 Stable
97 Qing River area landslide, China 220 25 22.5 20 16 0 Stable
98 Qing River area landslide, China 8.23 35 18.68 26.34 15 0 Failure
99 Qing River area landslide, China 3.66 30 16.05 11.49 0 0 Failure
100 Qing River area landslide, China 30.5 20 18.84 14.36 25 0 Stable
101 Qing River area landslide, China 100 35 28.44 29.42 35 0 Stable
102 Qing River area landslide, China 100 35 28.44 39.23 38 0 Stable
103# Qing River area landslide, China 40 30 20.6 16.28 26.5 0 Failure
104# Qing River area landslide, China 50 20 14.8 0 17 0 Failure
105 Qing River area landslide, China 88 30 14 11.97 26 0 Failure
106 Qing River area landslide, China 120 53 25 12 45 0 Stable
107# Qing River area landslide, China 200 50 26 15 45 0 Stable
108 Qing River area landslide, China 115 40 16 7 20 0 Failure
109 Qing River area landslide, China 10.67 22 20.41 24.9 13 0 Stable
110 Qing River area landslide, China 12.19 22 19.63 11.98 20 0 Failure
111 Qing River area landslide, China 12.8 28 21.83 8.62 32 0 Failure
112 Qing River area landslide, China 45.72 16 20.41 33.52 11 0 Failure
113 Qing River area landslide, China 10.67 25 18.84 15.32 30 0 Stable
114 Qing River area landslide, China 7.62 20 18.84 0 20 0 Failure
115# Qing River area landslide, China 61 20 21.43 0 20 0 Failure
116# Yudonghe landslide, China 565 21 21 20 24 0 Stable
117# Guzhang gaofeng slope, China 150 35 27 27.3 29.1 0.26 Failure
118 Guzhang gaofeng slope, China 184 37 27 27.3 29.1 0.22 Failure
119# Guzhang gaofeng slope, China 126.5 34 27 27.3 29.1 0.3 Failure
120 Chengmenshan open pit copper mine, China 285 50 25 46 35 0.25 Stable
121 Baijiagou earth slope, China 36 30 20.45 16 15 0.25 Stable
122 Jingping first stage hydropower station, China 60 45 27 70 22.8 0.32 Stable
123# Left bank accumulation body of Xiaodongjiang hydropower station, China 10 45 22 10 35 0.403 Failure
124# Longxi landslide of Longyangxia hydropower Station, China 30 45 20 20 36 0.503 Failure
125 Chana landslide of Longyangxia hydropower Station, China 50 45 20 0.1 36 0.29 Failure
126 Canal slope of Baoji gorge with Wei River diversion project, China 50 45 20 0.1 36 0.503 Failure
127 Yellowstone landslide in the Three Gorges of the Yangtze River, China 8 33 22 0 40 0.393 Stable
128 Baiyian landslide in the Three Gorges reservoir area, China 8 33 24 0 40 0.303 Stable
129 Baihuanping landslide in the Three Gorges reservoir area, China 8 20 20 0 24.5 0.35 Stable
130 Gaojiazui landslide in the Three Gorges reservoir area, China 8 33 18 0 30 0.303 Stable
131 Songshan ancient landslide at Lechangxia hydropower station, China 420 43 27 43 35 0.29 Failure
132# Back channel landslide in the Three Gorges reservoir area, China 407 42 27 50 40 0.29 Stable
133 Jipazi landslide in the Three Gorges reservoir area, China 359 42 27 35 35 0.29 Stable
134# Jiuxianping Landslide in the Three Gorges reservoir area, China 320 37.8 27 37.5 35 0.29 Stable
135 Heishe landslide, China 301 42.6 27 32 33 0.29 Failure
136 Liujiawuchang landslide in the Three Gorges reservoir area, China 239 42.2 27 32 33 0.29 Stable
137 Majiaba landslide in the Three Gorges Reservoir Area, China 110 41 27.3 14 31 0.29 Stable
138# Sandengzi landslide in the Three Gorges Reservoir Area, China 135 41 27.3 31.5 29.703 0.293 Stable
139 Yaqianwan landslide in the Three Gorges Reservoir Area, China 90.5 50 27.3 16.2 28 0.29 Stable
140 No.3 landslide of Sanbanxi hydropower station, China 92 50 27.3 36 1 0.29 Stable
141 Shijiapo landslide, China 511 41 27.3 10 39 0.29 Stable
142 Tanggudong landslide, China 470 40 27.3 10 39 0.29 Stable
143 Tianbao landslide, China 443 47 25 46 35 0.29 Stable
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J. Zhou, et al. Safety Science 118 (2019) 505–518
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Table 1 (continued)
No. Location H β γ C Φ ru Stability
144 Shipingtai landslide of Xiaoxi hydropower station, China 435 44 25 46 35 0.29 Stable
145 Dongyemiao landslide, China 432 46 25 46 35 0.29 Stable
146 Hongtupo landslide, China 230 30 26 150 45 0.29 Stable
147 Lianziya landslide in the Three Gorges reservoir area, China 6.003 30 18.5 25 0 0.29 Failure
148 No. 6 landslide of Jishixia hydropower station, China 6.003 30 18.5 12 0 0.29 Failure
149 No.7 landslide of Tianshengqiao second cascade hydropower station, China 10 30 22 10 35 0.29 Stable
150 Kualiangzi landslide, China 30 30 21 10 30.343 0.29 Stable
151 No.1 landslide of Jishixia hydropower station, China 50 45 22 10 36 0.29 Failure
152 Daxi landslide, China 30 45 22 20 36 0.29 Failure
153# Right Bank landslide of Zihong reservoir, China 4 35 12 0.03 30 0.29 Failure
154 Zhongyangcun landslide, China 8 45 12 0 30 0.29 Failure
155 Zhaojiatang landslide, China 4 35 12 0 30 0.29 Stable
156 Yangdagou landslide of Xunyang hydropower station, China 200.5 49 31.3 68 37 0.29 Failure
157# Sujiaping Landslide, China 50 45 20 30 36 0.29 Failure
158 Maidipo Landslide, China 40.3 37.8 19.6 21.8 29.5 0.25 Stable
159 Maoping Landslide, China 61.9 36.5 23.1 25.2 29.2 0.4 Stable
160 Shaling Landslide, China 23.5 47.5 23.8 3138.7 0.31 Stable
161# Niugunhan Landslide, China 88 40.2 22.3 20.1 31 0.19 Stable
162# Xieliupo Landslide, China 115 49.1 23.5 25 20 0.41 Stable
163 Zhaojiatang Landslide, China 40.3 46.2 23 20 20.3 0.25 Stable
164 Touzhaigou Landslide, China 123.6 41.5 21.5 15 29 0.36 Stable
165 Shenzhen reservoir diversion tunnel landslide, China 45.2 30.3 23.4 15 38.5 0.28 Failure
166 Taipingyi hydropower station diversion tunnel landslide, China 201.2 46.8 19.6 17.8 29.2 0.37 Stable
167 Bawangshan Landslide, China 49.5 45.8 22.1 45.8 49.5 0.21 Stable
168# Jiangxi Qiyi Reservoir, China 50 20.32 18.82 25 14.6 0.4 Failure
169 KSH slope in Tailie elementary school, China 10 10 20 8 20 0 Failure
170 KSH slope on the right of Circle E of Tailie Overpass, China 30 30 27.3 37.3 31 0 Stable
171# KSH landslide on the left of K71+625∼K71+700, China 35 25 20.6 26.31 22 0 Failure
172 KSH slope of Pingxite Bridge, China 50 40 21.6 6.5 19 0 Failure
173 KSH slope on the right of K76+085∼K76+200, China 35 28 22.4 28.9 24 0 Failure
174# KSH slope on the left of K77+920∼K78+100, China 33 30 23.2 31.2 23 0 Failure
175 KSH slope on the left of K79+165∼K79+300, China 26 30 26.8 37.5 32 0 Stable
176 KSH slope on the right of K79+920∼K80+035, China 42 25 27.4 38.1 31 0 Stable
177 Landslide on the right of ZAK0+315∼ZAK0+407, China 50 50 21.8 32.7 27 0 Failure
178 KSH slope on the left of K83+260∼K83+360, China 60 35 21.8 27.6 25 0 Failure
179 KSH slope on the right of K88+300∼K88+420, China 21 30 26.5 35.4 32 0 Stable
180 KSH slope on the right of K88+700∼K88+876, China 39 35 26.5 36.1 31 0 Stable
181# KSH slope on the right of K89+730∼K89+841, China 69 30 27 35.8 32 0 Stable
182 KSH slope on the right of K90+225∼K90+345, China 22 25 27 38.4 33 0 Stable
183# KSH slope on the left of K98+520∼K98+710, China 52 50 21.4 28.8 20 0 Failure
184 KSH slope on the left of K99+120∼K99+260, China 55 38 26 42.4 37 0 Stable
185 KSH slope on the left of K100+280∼K100+410, China 30 25 26 39.4 36 0 Stable
186# KSH slope on the left of K100+615∼K100+915, China 26 25 25.6 38.8 36 0 Stable
187 Landslide on the left of K103+330∼K103+450, China 53 45 20 30.3 25 0 Failure
188 KSH slope on the left of K104+610∼K104+805, China 50 30 25.8 34.7 33 0 Stable
189 KSH sandslide on the left of K104+892∼K105+052, China 99 35 21.8 28.8 26 0 Failure
190 KSH sandslide on the left of K105+260∼K105+330, China 60 30 21.8 31.2 25 0 Failure
191 KSH slope on the left of K106+268～K106+577, China 51 30 24 41.5 36 0 Stable
192 KSH slope on the left of K106+992∼K107+085, China 50 35 24 40.8 35 0 Stable
193# KSH landslide on the left of K107+856∼K107+968, China 70 35 20.6 27.8 27 0 Failure
194 KSH landslide on the left of K108+960∼K109+010, China 55 35 20.6 32.4 26 0 Failure
195 KSH slope on the left of K109+841∼K109+900, China 40 27 25.8 38.2 33 0 Stable
196 KSH slope on the left of K110+200∼K110+274, China 45 25 25.8 39.4 33 0 Stable
197 KSH landslide on the left of K110+421∼K110+500, China 31 40 21.1 33.5 28 0 Failure
198 KSH landslide on the left of K110+980∼K110+240, China 75 30 21.1 34.2 26 0 Failure
199 KSH slope on the right of K112+720∼K112+815, China 52 25 26.6 42.4 37 0 Stable
200 KSH slope on the left of K113+500∼K113+580, China 42 35 26.6 44.1 38 0 Stable
201# KSH slope on the left of K114+060∼K114+167, China 60 35 26.6 40.7 35 0 Stable
202 KSH slope on the left of K114+224∼K114+258, China 40 30 25.8 41.2 35 0 Stable
203 KSH slope on the left of K117+200∼K117+412, China 33 30 25.8 43.3 37 0 Stable
204# KSH front slope of tunnel in SongjieyaK122+310, China 60 45 21.7 32 27 0 Failure
205 KSH landslide on the right of K122+350∼K122+455, China 65 40 20.6 28.5 27 0 Failure
206# KSH landslide on the left of K127+440∼K127+590, China 70 40 21.5 29.8 26 0 Failure
207 KSH slope on the left of K127+761∼K127+882, China 36 34 26.5 42.9 38 0 Stable
208 KSH landslide on the left of K137+650∼K137+730, China 45 30 20.8 15.6 20 0 Failure
209 KSH landslide on the left of K138+624∼K138+797, China 40 30 20.8 14.8 21 0 Failure
210 KSH landslide on the right of K75+760∼K76+000, China 58 40 19.6 29.6 23 0 Failure
211# KSH slope on the right of ZBK0+000∼ZBK0+185, China 35 20 25.4 33 33 0 Failure
212 KSH landslide on the left of K84+602∼K85+185, China 50 50 22.4 29.3 26 0 Failure
213# KSH slope on the right of K91+614∼K91+660, China 30 35 26.2 41.5 36 0 Stable
214 KSH slope on the right of K91+720∼K91+771, China 36 23 26.2 42.3 36 0 Stable
215# KSH slope on the left of K100+950∼K101+300, China 32 30 25.6 39.8 36 0 Stable
(continued on next page)
J. Zhou, et al. Safety Science 118 (2019) 505–518
509
of GBM classification technique is concisely generalized. During the
process of GBM model training, a specific function is formed to make a
distinction between slope stability and slope failure. Assume that there
are M samples in the training set, and the number of features of samples
is K, thus the training set can be mathematically represented as
= =X x{ }i i
M
1, and x Ri
K . As for corresponding labels, because slope
stability classification belongs to binary classification category, they
can be defined as = =Y y{ }i i
M
1 and y {0, 1}i , in which 0 represents failure
(F) slope and 1 represents stable (S) slope. In GBM, the aggregation of
loss function needs to be minimized by means of a binary function es-
timation xP( ), in which the argument of the minimum of aggregation
y x( , P( ))i i can be shown as follows (Hastie et al., 2001):
= =
= =
=
=
y x i M
x x n L
P arg min ( , P( )), 1, 2, ,
P( ) ( ), 1, 2, ,
i
M
i i
n
L
n
P
1
1 (1)
where L represents the number of iterations. The aggregation x{ ( )}n
devised in an incremental pattern; at the n-th iteration, a new random
classification function n is added to optimize the aggregation of the loss
function while ={ }g g
n
1
1 keeps fixed.
The main idea of GBM is that by assembling a series of weak pre-
diction function n (also called parameterized base-learners), under the
continued process of model training, the misjudgement ratio is de-
creased and the ultimate prediction model is generated (Friedman,
2001). In GBM, these parameterized base-learners contain some para-
meters need to be tuned. The decision trees are considered as the base-
learners in GBM, for this reason, the optimized parameters include the
threshold for splitting each node, the feature to split in each internal
node.
To simplify calculation, the loss can be termed in an approximate
recursion at the n-th iteration as follows:
+ + +y x x y x x h x( , P ( ) ( )) ( , P ( )) 1
2
( ) ( )i n i n i i n i n i i m i1 1
2
(2)
where = =x xP ( ) ( )n i g
n
g i1 1
1 and =
=
hi
y x
x x x
( , P( ))
P( ) P( ) P ( )
i i
i i n i1
The estimate function n obtained by minimizing the right hand side
of recursion (2) which can be transformed into the following mini-
mization form:
=
x hargmin 1
2
( ( ) )
i
M
n i i
1
2
n (3)
As a rule of thumb, a suitable step size (shrinkage parameter) is
applied to n before it is added to Pn 1, then update n and output xP( ).
To establish the relationship between slope stability and influence
variables, the slope data processing was performed using the gbm R-
package (Ridgeway, 2007) within R Environment software
(Development Core Team, 2017). Further detailed mathematical de-
scription over GBM can be referred from references (Friedman, 2001;
Hastie et al., 2001; Kuhn and Johnson, 2013) and more details about
implementation can be in the help of R package documentation man-
uals.
2.3. Evaluation of classifier’s performance
In this work, the predictive performance of GBM algorithm on slope
stability data was evaluated by the area under the curve (AUC) from the
receiver operating characteristic (ROC) curve (Bradley, 1997). The ROC
curve plots the relationship between sensitivity and specificity is em-
ployed to evaluate the performance of different classifiers. The ROC
(Zhou et al., 2019b) is a 2D plot of false positive rate (FPR) (1-speci-
ficity) versus true positive rate (TPR or sensitivity) in horizontal and
verticalaxes, respectively. Relationship between AUC and discrimina-
tion accuracy can be interpreted using five degrees of rating (Bradley,
1997): not discrimination (0.5–0.6), poor discrimination (0.6–0.7), fair
discrimination (0.7–0.8), good discrimination (0.8–0.9) and excellent
discrimination (0.9–1). Additionally, the prediction models of GBM was
also evaluated using other popular criteria such as classification accu-
racy rate (CAR) and the Cohen’s Kappa coefficient, Sensitivity and
Specificity that are often computed from a confusion matrix (Hastie
et al., 2001; Kuhn and Johnson, 2013). The definitions of these metrics
are as follows:
= +CAR (TP TN)/N (4)
=Kappa (CAR Pe)/(1 Pe) (5)
= = + =TPR Recall TP/(TP FN) Sensitivity (6)
= + =FPR FP/(TN FP) (1 Specificity) (7)
= +Precision TP/(TP FP) (8)
Table 1 (continued)
No. Location H β γ C Φ ru Stability
216 KSH slope on the left of K102+691∼K102+880, China 60 35 25.6 36.8 34 0 Stable
217 KSH slope on the right of K118+360∼K118+549, China 37 30 26.2 42.8 37 0 Stable
218 KSH slope on the right of K119+823∼K119+951, China 68 35 26.2 43.8 38 0 Stable
219 KSH sandslide on the right of K124+340∼K124+562, China 42 30 20.6 32.4 26 0 Failure
220 KSH slope on the right of K131+280∼K131+380, China 54 42 26.5 41.8 36 0 Stable
221 KSH landslide on the left of K138+840∼K138+930, China 53 30 20.8 15.4 21 0 Failure
Case 1–46 reported by Sah et al. (1994).
Case 47–57 reported by Feng and Hudson (2004).
Case 58–66 reported by Xu and Shao (1998).
Case 67 reported by Li et al.(2006).
Case 68 reported by He et al. (2004).
Case 69–89 reported by Chen et al. (2009); Xiao et al. (2011).
Case 90–116 reported by Wang et al. (2005).
Case 117–119 reported by Jin et al., (2004).
Case 120 reported by Zhu et al. (2011).
Case 121 reported by Su (2009).
Case 122 reported by Xu et al. (2009).
Case 123–168 reported by Wang (2009).
Case 169–221 reported by Chen et al. (2011).
KSH-Kaili-Sansui highway.
# Testing Sample by Selecting Stochastically.
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= × × +F1 2 (Recall Precision)/(Recall Precision) (9)
where Pe= [(TN+FN)×(TN+FP)+(TP+ FP)×(TP+FN)]/N2 re-
presents an expected accuracy based on confusion matrix (Zhou et al.,
2019b); TN, FN, TP and FP denotes the numbers of true negatives, false
negatives, true positives and false positives, respectively; N denotes the
number of samples.
2.4. Hyper-parameters tuning of GBM classifier
The use of the GBM algorithm for estimation SSC involves careful
tuning of hyper-parameters to achieve expert-level performances. The
grid search method (Zhou et al., 2012) is a suitable tuning method for
determining reasonable optimized hyper-parameters of models when
the number of tuned hyper-parameters is relatively small. It involves a
pre-determined tuning range of each hyper-parameter and exhaustively
compares combinations of all hyper-parameters. The k-fold cross vali-
dation (CV) is quite typical and popular in practice as validation
methods in the field of supervised machine learning (Hoang and Pham,
2016; Zhou et al., 2015, 2016a, 2016b), and the k was herein set to be
five for considering the computation time and bias. In contrast to the
index of CAR and Kappa, ROC metrics are only suitable for binary
classification problems and can be broken down into sensitivity and
specificity, whilst the AUC represents a models ability to discriminate
between positive (stable) and negative (failure) classes. Moreover, the
slope stability as a binary classification problem is really a trade-off
between sensitivity and specificity. In this regard, the optimum hyper-
parameters were selected to be hyper-parameters with which the GBM
classifier could achieve the maximum AUC. After the optimum hyper-
parameters were obtained through fine grid search and five-fold CV
with the whole training set, the optimum GBM classifier was used to
predict the independent slope test set.
3. Results and discussions
3.1. Descriptive analysis
The violin plots of each property which combine density estimates
and box plots in displaying data structure are shown in Fig. 1 for all
slope cases histories. Fig. 1 provides the relevant input parameters used
to develop the slope stability prediction models range with their max-
imum values, median values and minimum values, also the third and
first quartile is represented as the bottom and the top of the thickline in
the center of the violin plots, respectively. The main advantage of violin
plots, compared to a box plot is the fact that VIP presents the density.
Furthermore, the wider violin plots corresponds to the higher density.
The distributions of these variables and the relationship between SSC
and other input variables are demonstrated in the correlation matrix
plot in Fig. 2, which can be seen the pairwise relationship between
parameters with corresponding correlation coefficients and the mar-
ginal frequency distribution for each parameter. It can be also con-
cluded that all parameters have no relatively good/meaningful corre-
lation with each other. Moreover, principal component analysis (PCA)
(Jolliffe, 2011) is also utilized to explain the variance-covariance
structure of a set of variables through linear combinations of those
variables and enhance the visualization of the collected updated slope
dataset, as shown in Fig. 3. It is comprehensible that there are over-
lapping domains between the two classes of SSC from a two-dimen-
sional space. Additionally, there are some indicators with significant
skewness which can have an impact on GBM prediction models, as
demonstrated in Fig. 1. Thus all variables were transformed by the
approach of the Box-Cox in this study (Kuhn and Johnson, 2013). After
the transformations, the original data is conformed to a normal dis-
tribution, and the indicators have been centered and scaled before
conducting the GBM classifier model.
3.2. GBM model development and validation
To estimate slope stability classification (SSC), height (H), cohesion
(c), slope angle (β), unit weight (γ), pore water pressure (ru), and angle
of internal friction (φ) were defined as input parameters into the GBM
model and the slope stability state (Failed/Stable) as output, as shown
in Fig. 4. Thus the relationship between the state of SSC and these
parameters can be described as SSC= f(γ, H, c, φ, β, ru). In order to
determine reasonable and efficient optimized hyper-parameters of
GBM, a five-fold CV procedure (Kuhn and Johnson, 2013; Zhou et al.,
2015, 2016a, 2016b, 2016c) was implemented to determine the op-
timal parameter values based on the original training data set, with the
original test removed completely from the CV process. GBM algorithm
generally has four tweaking parameters which can be fine-tuned
Fig. 1. Violin plots showing the distribution of observed slope cases.
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(Ridgeway, 2007; Kuhn and Johnson, 2013): n.trees (number of trees
which is the number of gradient boosting iteration), interaction.depth
(the complexity of the tree), shrinkage (learning rate) and n.min-
obsinnode (the minimum number of observations in trees' terminal
nodes). If these parameters are not tuned correctly it may result in over-
fitting. Thus it should be tuned aforementioned parameters for a good
fit.
To conduct the experiment, the dataset comprising of 221 cases is
Fig. 2. Correlation matrix of variables for all slope cases.
Fig. 3. PCA model for illustration of the slope data: (a) Scree plot; (b) a biplot of the first two components; and (c) component matrix and scores.
J. Zhou, et al. Safety Science 118 (2019) 505–518
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Fig. 4. Diagnostic model of prediction of the circular slope stability state using GBM method.
Fig. 5. Plots of resampling profiles to examine the relationship between estimates of performance and tuning parameters for the GBM model with AUC.
(a) RF (b) SVM (c) ANN
Fig. 6. Plots of resampling profiles to examine the relationshipbetween estimates of performance and tuning parameters for the RF, SVM and ANN models with AUC.
J. Zhou, et al. Safety Science 118 (2019) 505–518
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randomly split into two subsets. Thus, the dataset is randomly split 80:
20 into training and test datasets, in which the training data sets are
used to train the GBM model, and the testing data sets are used to ex-
amine the classification and prediction accuracy of the proposed model.
We used the gbm (Ridgeway, 2007), and caret (Kuhn, 2008) packages
from the R statistical environment (R Development Core Team, 2017)
for fit models, assessing relative contributions and making predictions.
To prevent overfitting and determining user-defined parameters used in
GBM classifier (Fig. 4), given the fact that a GBM classifier is based on
several parameters such as the maximum depth (interaction.depth or J)
of a tree, maximum number of trees or number of iterations (T or
n.trees), sample rate (shrinkage or r), and the regularization parameter
(n.minobsinnode or η), we performed a hyperparameter optimization
by varying these parameters creating a grid of T× J× r× η=720
combinations, in particular T ∈{100, 200, 300, …, 900, 1000}, J ∈ {1,
3, 5, 7, 9, 11, 13, 15}, r ∈ {0.001,0.01,0.05,0.1}, and η ∈{1, 2, 5}. We
then performed five-fold CV for each of the combinations. Finally, we
selected the optimal GBM classifier based on five-fold CV results with
the maximal five-fold CV AUC, in particular having the parameters
T= 300, J= 13, r= 0.1, and η=1 (see Fig. 5). Additionally, the final
GBM classifier for slope stability had a maximum training accuracy of
0.8166 for 169 sets of training data using the fivefold CV procedure.
In order to compare the performance of the GBM classifier, the
methods of artificial neural network (ANN), random forest (RF) and
support vector machines (SVM) (Hastie et al., 2001; Wang et al., 2005;
Samui, 2008; Zhou et al., 2012, 2015, 2016a, 2017, 2019a) are corre-
spondingly applied comparatively to generate results on these slope
cases. The same data samples are normalized before modeling in order
to reduce the effect of units and range difference. The Multi-Layer
Perceptron (MLP) neural network is applied in the ANN investigation
and done in the nnet package (Venables and Ripley, 2002) with a single
hidden layer. ROC was also used to select the optimal model using the
Table 2
Tuning parameters for each model associated with their results.
Model Tuning parameters Value Optimal value AUC Sensitivity Specificity
ANN Size (hidden neurons) {1, 2, …, 10} 7 0.8881 0.8150 0.8608
Decay {0.01, 0.03, 0.05, 0.07} 0.07
SVM Cost {1, 2, 4, 8, 16, 32} 1 0.8740 0.6958 0.8824
Sigma {0.0025, 0.005, 0.01, 0.015, 0.02, 0.025, 0.25, 1} 1
RF mtry {1, 2, 3, …, 6} 6 0.8815 0.7758 0.8287
min.node.size {2, 4, 6} 2
GBM n.trees {100, 200, …, 1000} 300 0.8976 0.7891 0.8380
Interaction.depth {1, 3, 5, …, 15} 13
Shrinkage {0.001, 0.01, 0.05, 0.1} 0.1
n.minobsinnode {1, 2, 5} 1
Fig. 7. Boxplot distributions of training set with metric of ROC for four methods – resulting from five-fold CV procedure by the algorithms.
Table 3
Confusion matrices and their performance for GBM prediction model based on 221 slope cases.
Note: The diagonal elements (correct decisions) are marked in bold with grey.
J. Zhou, et al. Safety Science 118 (2019) 505–518
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largest value. Fig. 6 demonstrates tuning parameters of the ANN, SVM
and RF models by fivefold CV processes. The optimal values of weight
penalty parameter (delay) and size of the network (size) used for the
ANN model was=0.07 and= 7, respectively. Thus the optimal ar-
chitecture of 6×7×1 was obtained for the ANN model. The RBF
kernel function (Zhou et al., 2012) with two parameters (Cost and
Sigma) for fine tuning is applied in the SVM investigation and im-
plemented from the e1071 (Karatzoglou et al., 2006) package. The cost
parameter of the SVM model is optimized as Cost= 1, and the gamma
parameter of the kernel function is Sigma=1. Random forest classifier
is implemented by ranger package (Wright and Ziegler, 2017). Three
parameters of the random forest model are optimized by the CV method
as mtry=6, splitrule= gini, and min.node.size= 2. The hyperpara-
meter settings for ANN, SVM, and RF as well as their prediction results
are shown in Table 2. It can be easily observed that the GBM classifier
yields slightly better performance for training set than ANN, SVM, and
RF classifiers. The boxplot in Fig. 7 reports the performance of afore-
mentioned classifiers using the same slope data on fivefold CV phrase
with training set average AUC, sensitivity and specificity with their
variances. The difference between lower and upper quartiles in GBM
classifier is comparatively smaller than the other classifiers that show
relatively low variance of accuracies. From Fig. 7, SVM has the tightest
interquartile range for ROC and GBM has the tightest interquartile
range for Sensitivity. Additionally, the training accuracy of final ANN,
SVM and RF classifiers for slope stability is 0.8402, 0.7988 and 0.8047,
respectively, for 169 sets of training data using fivefold CV procedure.
To validate the predictive models based on the predicted and
measured (real) values, fifty two testing samples were validated by the
optimized GBM classifier. The results are presented in Table 3. The CAR
and Cohen’s Kappa coefficient for test data was determined to be
0.8654 and 0.7324 (reflecting substantial agreement), respectively.
Producer's accuracy (PA) and user's accuracy (UA) (Congalton and
Green, 2009) for each class using the GBM model are also presented in
Table 3 based on the confusion matrices. Obviously, the results are
identical with field observations and the accuracy of this GBM classi-
fication model for test set is more appropriate in contrast to other three
methods.
An ROC curve was also implemented to evaluate the performance of
GBM classifier in slope stability. The results of the prediction rate
curves are represented in Fig. 8. According to the results, the area under
the curve (AUC) of ROC was calculated as 0.900, 0.889, 0.888 and
0.897 for GBM, SVM, ANN and RF approaches, respectively. The AUC
determines the goodness of the performance of the GBM classifier in
large extent where the value of 1.0 represents the ideal performance.
The kappa and F1 scores (See Fig. 9) together also show GBM is clear
Fig. 8. ROC curve of the GBM classifier with the optimal hyper-parameters on slope test set.
Fig. 9. Kappa vs F1 on the Test Set.
J. Zhou, et al. Safety Science 118 (2019) 505–518
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winners. Thus, it can be seen that the capability of the GBM was ex-
cellent for slope stability prediction.
3.3. Variable importance and partial dependence plots
While assessing predictive performance for predictor variables,
contribution to the model is also calculated over the GBM classification
model. In this study, the relative importance of six variables for the
GBM model can be estimated by the function of varImp() in caret
package (Kuhn, 2008), and variables are sorted by average importance
across the classes, as shown in Fig. 10. The ROC statistic is calculated as
a relative measure of the variable importance, and the result is depicted
in Fig. 8. Among all the variables, it can be easily observed that, for the
circular failure mechanism, relative variable importance analysis de-
monstrated that the geometrical slope design parameters (γ, C and H)
are the most influential on the stability of slope, followed by the in-
dicator φ, β and ru. It is obvious, though, that the other input para-
meters are also important according to the GBM classifier. This result
was predictable because the slope state parameters were chosen in
accordance with standard engineering models. These results are con-
sistent with the correlation matrix (Fig. 2) of the variables that have the
highest coefficients for these variables. Wen et al. (2013) reported that
γ, C and φ are the main factors affecting slope stability. Manouchehrian
et al. (2014) also foundthat γ is more sensitive than other parameters,
and higher values of γ, C and φ can enhance the stability of the slope in
engineering practice. In this regard, the grouting reinforcement tech-
nique provides an effective way for improving slope performance (i.e.,
increasing bulk density and shear strength of slope) and thus mitigating
the occurrence of slope failure in engineering practice.
Partial dependence plots (PDP) proposed by Friedman (2001) can be
visualized the learned relationship between features and predictions. To
better understand the misclassifications of the GBM model for the slope
independent test set and further explore the relevance of features on clas-
sification results, PDP for the six relevant features are generated with the
pdp package (Greenwell, 2017) in the optimum GBM model, as shown in
Fig. 11. Obviously, PDP gives a visual picture about the marginal effect of a
feature on the class prediction. Particularly, there are more variation for
given predictor variables (γ, C and H) that indicates the value of that
variable affects the GBM classifier quite a few from single variable plot.
3.4. Limitations
The GBM approach for slope stability against circular failure has
Fig. 11. Partial dependence plots of the influencing variables in the optimum GBM model for predicting slope stability. Color represent the intensity of affect on GBM
model. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 10. Variable importance plot generated by the GBM classifier.
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proven better than supervised machine learning classifiers, however, has
some limitations that need to be addressed in future research. Firstly, the
present study is limited to circular failure analysis. Other types of failure
mechanisms such as plane, toppling, wedge and buckling failure, require
different causative factors incorporating a number of case histories.
Secondly, other external or triggering factors such as rainfalls, earth-
quakes and man-made activities can significantly affect slope stability,
but these are ignored in this study because relevant data acquisition is a
difficult task. Thirdly, the limitation of GBM classifier is that the datasets
are relatively small; only 221 cases are involved in GBM modeling. A
larger dataset should be analyzed to improve the model’s precision and
reliability. Also, sampling bias and class imbalance are important parts
of model uncertainty that have a significant impact on the predictive
slope stability classification models and should be addressed in future.
Moreover, the performance of ANN, SVM, RF and GBM classifiers can be
improved by tuning hyper-parameters via optimization strategies such
as heuristic algorithms (Zhou et al., 2012, 2019c) and Bayesian opti-
mization (Snoek et al., 2012). Additionally, even though binary classi-
fication problem for slope stability was performed with high accuracy,
regression problems for the factor of safety and multi-output classifi-
cation problems for slope stability analysis have not been investigated in
this study. Lastly, other advanced supervised machine learning techni-
ques that show good performance on the nonlinear relationship mod-
elling such as extreme gradient boosting (Chen and Guestrin, 2016) has
not been investigated and compared on SSC prediction. These limita-
tions should be carefully considered in future.
4. Conclusions
In this work, the GBM method has been successfully employed to
investigate the state of slope stability using 221 historical cases of slope
conditions recorded. The state of slope stability is formulated as a
classification problem in which prediction outputs are either “stable” or
“failed” using the GBM model. Six different predictive variables that
characterize the material behavior and the slope geometrical features as
well as the influence of external triggering parameters are considered as
input variables to identify if a circular slope failure could occur. To
examine the goodness of fit of the GBM model, tuning parameters are
considered optimized based on the classification model that achieved
the highest AUC during the fivefold CV process. Relative variable im-
portance and PDP analysis demonstrated that the geometrical slope
design parameters (γ, C and H) are the most influential on the stability
of slope. Findings reveal that the GBM classifier can explore the non-
linear relationship between slope stability and its influence factors.
However, even though the results of the analysis are remarkable and
encouraging there are still certain questions that remain open. The ef-
fect of data imbalance on the prediction of slope stability will be dis-
cussed in future. The developed model may be improved by analyzing a
larger dataset and also can be recommended its applicability to other
mining and geotechnical engineering failure issues when data is avail-
able.
Acknowledgments
This work is supported by the National Natural Science Foundation
Project of China (Grant No. 41807259), the Natural Science Foundation
of Hunan Province (Grant No. 2018JJ3693), the China Postdoctoral
Science Foundation funded project (Grant No. 2017M622610) and the
Sheng Hua Lie Ying Program of Central South University.
Appendix A. Supplementary material
Supplementary data to this article can be found online at https://
doi.org/10.1016/j.ssci.2019.05.046.
References
Basahel, H., Mitri, H.S., 2017. Application of rock mass classification systems to rock
slope stability assessment: a case study. J. Rock Mech. Geotech. Eng. 9, 993–1009.
Basahel, H., Mitri, H.S., 2018. Probabilistic assessment of rock slopes stability using the
response surface approach – a case study. Int. J. Min. Sci. Technol. https://doi.org/
10.1016/j.ijmst.2018.11.002.
Bradley, A.P., 1997. The use of the area under the ROC curve in the evaluation of machine
learning algorithms. Pattern Recogn. 30 (7), 1145–1159.
Chen, C., Xiao, Z., Zhang, G., 2011. Stability assessment model for epimetamorphic rock
slopes based on adaptive neuro-fuzzy inference system. Electron. J. Geotech. Eng. 16
(A), 93–107.
Chen, L.Q., Peng, Z.B., Chen, W., Peng, W.X., Wu, Q.H., 2009. Artificial neural network
simulation on prediction of clay slope stability based on fuzzy controller. J. Central
South Univ. (Sci. Technol.) 40 (5), 1381–1387.
Chen, R.H., Chameau, J.L., 1983. Three-dimensional limit equilibrium analysis of slopes.
Geotechnique 33 (1), 31–40.
Chen, T., Guestrin, C., 2016. Xgboost: a scalable tree boosting system. In: Proceedings of
the 22nd ACM sigkdd International Conference on Knowledge Discovery and Data
Mining. ACM, pp. 785–794.
Cheng, Y.M., Lansivaara, T., Wei, W.B., 2007. Two-dimensional slope stability analysis by
limit equilibrium and strength reduction method. Comput. Geotech. 34 (3), 137–150.
Congalton, R.G., Green, K., 2009. Assessing the Accuracy of Remotely Sensed Data:
Principles and Practices, second ed. Taylor and Francis, Boca Raton, FL, USA, pp.
183p.
Das, S.K., Biswal, R.K., Sivakugan, N., Das, B., 2011. Classification of slopes and pre-
diction of factor of safety using differential evolution neural networks. Environ. Earth
Sci. 64 (1), 201–210.
Dawson, E.M., Roth, W.H., Drescher, A., 1999. Slope stability analysis by strength re-
duction. Geotechnique 49 (6), 835–840.
Duncan, J.M., Wright, S.G., Brandon, T.L., 2014. Soil Strength and Slope Stability. John
Wiley & Sons.
Duncan, J.M., 1996. State of the art: limit equilibrium and finite-element analysis of
slopes. J. Geotech. Eng. 122 (7), 577–596.
Eberhardt, E., 2003. Rock slope stability analysis—utilization of advanced numerical
techniques. Earth and Ocean Sciences at UBC Report. University of British Columbia
(UBC), Vancouver, Canada.
Feng, X.T., Hudson, J.A., 2004. The ways ahead for rock engineering design methodol-
ogies. Int. J. Rock Mech. Min. Sci. 41 (2), 255–273.
Friedman, J.H., 2001. Greedy functionapproximation: a gradient boosting machine. Ann.
Stat. 1189–1232.
Friedman, J.H., 2002. Stochastic gradient boosting. Comput. Stat. Data Anal. 38 (4),
367–378.
Gao, W., 2015. Stability analysis of rock slope based on an abstraction ant colony clus-
tering algorithm. Environ. Earth Sci. 73 (12), 7969–7982.
Greenwell, B.M., 2017. pdp: an R package for constructing partial dependence plots. R J.
9 (1), 421–436.
Hastie, T., Robert, T., Friedman, J.H., 2001. The Elements of Statistical Learning.
Springer, New York, pp. 339p.
He, F., Wu, S.R., Zhang, Y.Q., Bao, H.M., 2004. A neural network method for analyzing
compass slope stability of the highway. Acta Geosci. Sin. 25 (1), 95–98.
Hoang, N.D., Pham, A.D., 2016. Hybrid artificial intelligence approach based on meta-
heuristic and machine learning for slope stability assessment: a multinational data
analysis. Expert Syst. Appl. 46, 60–68.
Jin, L.X., Feng, W.J., Zhang, J.S., 2004. Maximum likelihood estimation on safety coef-
ficients of rocky slope near dam of Fengtan project. Chin. J. Rock Mech. Eng. 23 (11),
1891–1894.
Jolliffe, I., 2011. Principal component analysis. In: International Encyclopedia of
Statistical Science. Springer, Berlin, Heidelberg, pp. 1094–1096.
Karatzoglou, A., Meyer, D., Hornik, K., 2006. Support vector machines in R. J. Stat. Softw.
15, 28.
Kim, J., Salgado, R., Yu, H.S., 1999. Limit Analysis of soil slopes subjected to pore-water
pressures. J. Geotech. Geoenviron. Eng., ASCE 125 (1), 49–58.
Kuhn, M., 2008. Building predictive models in R using the caret package. J. Stat. Softw.
28 (5), 1–26.
Kuhn, M., Johnson, K., 2013. Applied predictive modeling. Springer, New York.
Li, W.X., Yang, S.C., Chen, E.Z., 2006. Neural network method of analysis of natural slope
failure due to underground mining in mountainous areas. Rock Soil Mech. 27 (9),
1563–1566.
Liu, Z., Shao, J., Xu, W., Chen, H., Zhang, Y., 2014. An extreme learning machine ap-
proach for slope stability evaluation and prediction. Nat. Hazards 73 (2), 787–804.
Lu, J., Lu, D., Zhang, X., Bi, Y., Cheng, K., Zheng, M., Luo, X., 2016. Estimation of
elimination half-lives of organic chemicals in humans using gradient boosting ma-
chine. Biochim. Biophys. Acta (BBA)-General Subjects 1860 (11), 2664–2671.
Lu, P., Rosenbaum, M.S., 2003. Artificial neural networks and grey systems for the pre-
diction of slope stability. Nat. Hazards 30 (3), 383–398.
Manouchehrian, A., Gholamnejad, J., Sharifzadeh, M., 2014. Development of a model for
analysis of slope stability for circular mode failure using genetic algorithm. Environ.
Earth Sci. 71 (3), 1267–1277.
Michalowski, R.L., 1995. Slope stability analysis: a kinematic approach. Géotechnique,
London 45 (2), 283–293.
R Core Team, 2017. R: A language and environment for statistical computing. R
Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, https://
www.R-project.org/. Accessed March 20, 2018.
Ridgeway, G., 2007. Generalized boosted models: a guide to the GBM package. Available
J. Zhou, et al. Safety Science 118 (2019) 505–518
517
https://doi.org/10.1016/j.ssci.2019.05.046
https://doi.org/10.1016/j.ssci.2019.05.046
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0005
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0005
https://doi.org/10.1016/j.ijmst.2018.11.002
https://doi.org/10.1016/j.ijmst.2018.11.002
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0015
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0015
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0020
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0020
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0020
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0025
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0025
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0025
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0030
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0030
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0035
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0035
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0035
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0045
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0045
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0050
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0050
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0050
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0055
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0055
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0055
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0060
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0060
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0065
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0065
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0070
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0070
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0075
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0075
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0075
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0085
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0085
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0090
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0090
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0095
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0095
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0100
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0100
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0105
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0105
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0110
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0110
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0115
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0115
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0120
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0120
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0120
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0130
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0130
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0130
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0135
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0135
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0140
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0140
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0145
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0145
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0150
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0150
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0155
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0165
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0165
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0165
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0170
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0170
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0175
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0175
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0175
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0180
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0180
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0185
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0185
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0185
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0190
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0190
https://www.R-project.org/
https://www.R-project.org/
francisco.wong
Resaltado
francisco.wong
Resaltado
francisco.wong
Resaltado
francisco.wong
Resaltado
francisco.wong
Resaltado
francisco.wong
Resaltado
at: http://cran.r-project.org/web/packages/gbm/index.html. Accessed March 20,
2018.
Sah, N.K., Sheorey, P.R., Upadhyama, L.W., 1994. Maximum likelihood estimation of
slope stability. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 31, 47–53.
Sakellariou, M.G., Ferentinou, M.D., 2005. A study of slope stability prediction using
neural networks. Geotech. Geol. Eng. 23 (4), 419.
Samui, P.,2008. Slope stability analysis: a support vector machine approach. Environ.
Geol. 56 (2), 255–267.
Shi, X.Z., Zhou, J., Zheng, W., Hu, H.Y., Wang, H.Y., 2010. Bayes discriminant analysis
method and its application for prediction of slope stability. J. Sichuan Univ.: Eng. Sci.
Ed. 42 (3), 63–68.
Snoek, J., Larochelle, H., Adams, R.P., 2012. Practical bayesian optimization of machine
learning algorithms. Adv. Neural Inf. Process. Syst. 2951–2959.
Su, Y., 2009. Safety Risk Assessment on Mountain Road High Slope. Master thesis.
Jiaotong University, Chongqing.
Suman, S., Khan, S.Z., Das, S.K., Chand, S.K., 2016. Slope stability analysis using artificial
intelligence techniques. Nat. Hazards 84 (2), 727–748.
Terzaghi, K., 1950. Mechanisms of landslides. Geological Society of America, Engineering
Geology (Berkey), New York, USA, pp. 83–123.
Touzani, S., Granderson, J., Fernandes, S., 2018. Gradient boosting machine for modeling
the energy consumption of commercial buildings. Energy Build. 158, 1533–1543.
Venables, W.N., Ripley, B.D., 2002. Modern Applied Statistics with S, fourth edn.
Springer, New York, USA, pp. 495.
Wang, C., 2009. Study on Prediction Methods for High Engineering Slope. Master thesis.
Beijing Jiaotong University.
Wang, H.B., Xu, W.Y., Xu, R.C., 2005. Slope stability evaluation using back propagation
neural networks. Eng. Geol. 80 (3–4), 302–315.
Wen, S.L., La, H.B., Wang, C.Z., 2013;al.,. Analysis of influence factors of slope stability.
In: Applied Mechanics and Materials. Trans Tech Publications, pp. 34–38.
Wright, M.N., Ziegler, A., 2017. ranger: a fast implementation of random forests for high
dimensional data in C++ and R. J. Stat. Softw. 77 (1), 1–17.
Xiao, Z.Y., Chen, C.F., Ji, Y.X., 2011. Applying adaptive neuro-fuzzy inference system to
stability assessment of reservoir slope. Bull. Soil Water Conserv. 31 (5), 186–190.
Xu, B., Low, B.K., 2006. Probabilistic stability analyses of embankments based on finite
element method. J. Geotech. Geoenviron. Eng. 132 (11), 1444–1454.
Xu, F., Xu, W.Y., Wang, K., 2009. Slope stability analysis using least square support vector
machine optimized with ant colony algorithm. J. Eng. Geol. 17 (2), 253–257.
Xu, W., Shao, J.F., 1998. Artificial neural network analysis for the evaluation of slope
stability. In: Application of Numerical Methods to Geotechnical Problems. Springer,
Vienna, pp. 665–672.
Yu, H.S., Salgado, R., Sloan, S.W., Kim, J.M., 1998. Limit analysis versus limit equilibrium
for slope stability. J. Geotech. Geoenviron. Eng. 124 (1), 1–11.
Zhao, H., Yin, S., Ru, Z., 2012. Relevance vector machine applied to slope stability
analysis. Int. J. Numer. Anal. Methods Geomech. 36 (5), 643–652.
Zhou, J., Li, E., Wei, H., Li, C., Qiao, Q., Armaghani, D.J., 2019a. Random forests and
cubist algorithms for predicting shear strengths of rockfill materials. Appl. Sci. 9 (8),
1621.
Zhou, J., Li, E.M., Wang, M.Z., Chen, X., Shi, X.Z., Jiang, L.S., 2019b. Feasibility of sto-
chastic gradient boosting approach for evaluating seismic liquefaction potential
based on SPT and CPT case histories. J. Perform. Constr. Facil 30 (3), 04019024.
Zhou, J., Nekouie, A., Arslan, C.A., Pham, B.T., Hasanipanah, M., 2019c. Novel approach
for forecasting the blast-induced AOp using a hybrid fuzzy system and firefly algo-
rithm. Eng. Comp. 1–10. https://doi.org/10.1007/s00366-019-00725-0.
Zhou, J., Li, X.B., Mitri, H.S., 2015. Comparative performance of six supervised learning
methods for the development of models of pillar stability. Nat. Hazards 79 (1),
291–316.
Zhou, J., Li, X.B., Mitri, H.S., 2016a. Classification of rockburst in underground projects:
comparison of ten supervised learning methods. J. Comput. Civil Eng. 30 (5),
04016003.
Zhou, J., Shi, X.Z., Du, K., Qiu, X.Y., Li, X.B., Mitri, H.S., 2017. Feasibility of random-
forest approach for prediction of ground settlements induced by the construction of a
shield-driven tunnel. Int. J. Geomech. 17 (6), 04016129.
Zhou, J., Shi, X.Z., Huang, R.D., Qiu, X.Y., Chen, C., 2016b. Feasibility of stochastic
gradient boosting approach for predicting rockburst damage in burst-prone mines.
Trans. Nonferrous Metals Soc. China 26 (7), 1938–1945.
Zhou, J., Shi, X.Z., Li, X.B., 2012. Long-term prediction model of rockburst in under-
ground openings using heuristic algorithms and support vector machines. Saf. Sci. 50
(4), 629–644.
Zhou, J., Shi, X.Z., Li, X.B., 2016c. Utilizing gradient boosted machine for the prediction
of damage to residential structures owing to blasting vibrations of open pit mining. J.
Vib. Control 22 (19), 3986–3997.
Zhu, B.H., Zhou, D., Chen, S.X., Wang, L., 2011. Evaluation of slope stability by improved
BP neural network with L-M method. West-China Explor. Eng. 10, 21–24.
J. Zhou, et al. Safety Science 118 (2019) 505–518
518
http://cran.r-project.org/web/packages/gbm/index.html
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0205
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0205
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0210
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0210
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0215
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0215
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0220
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0220
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0220
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0225
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0225
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0230
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0230
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0235
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0235
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0240
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0240
http://refhub.elsevier.com/S0925-7535(18)31651-5/h9015
http://refhub.elsevier.com/S0925-7535(18)31651-5/h9015
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0245
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0245
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0250
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0250
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0255
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0255
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0260
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0260
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0265
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0265
http://refhub.elsevier.com/S0925-7535(18)31651-5/h9035
http://refhub.elsevier.com/S0925-7535(18)31651-5/h9035
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0270
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0270
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0275
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0275
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0280
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0280
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0280
http://refhub.elsevier.com/S0925-7535(18)31651-5/h9005
http://refhub.elsevier.com/S0925-7535(18)31651-5/h9005
http://refhub.elsevier.com/S0925-7535(18)31651-5/h9010
http://refhub.elsevier.com/S0925-7535(18)31651-5/h9010
http://refhub.elsevier.com/S0925-7535(18)31651-5/h9020
http://refhub.elsevier.com/S0925-7535(18)31651-5/h9020
http://refhub.elsevier.com/S0925-7535(18)31651-5/h9020
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0285
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0285
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0285
https://doi.org/10.1007/s00366-019-00725-0
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0290
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0290
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0290
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0295
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0295
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0295
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0300
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0300
http://refhub.elsevier.com/S0925-7535(18)31651-5/h0300