Predictions of Weekly Soil Movements Using Moving-Average and Support-Vector Methods: A Case-Study in Chamoli, India

Abstract

Landslides plague the Himalayan region, and landslide occurrence is widespread in hilly areas. Thus, it is important to predict soil movements and associated landslide events in advance of their occurrence. A recent approach to predicting soil movements is to use machine-learning techniques. In machine-learning literature, both moving-average-based methods (Seasonal Autoregressive Integrated Moving Average (SARIMA) model and Autoregressive (AR) model) and support-vector-based methods (Sequential Minimal Optimization; SMO) have been proposed. However, an evaluation of these methods on real-world landslide prediction has been little explored. The primary objective of this paper is to compare SARIMA, AR, and SMO methods in their ability to predict soil movements recorded at a real-world landslide site. A SARIMA model, an AR model, and a SMO model were compared in their ability to predict soil movements (in degrees) at the Tangni landslide in Chamoli, India. Time-series data about soil movements from five-sensors placed on the Tangni landslide hill were collected daily over a 78-week period from July 2012 to July 2014. Different model parameters were calibrated to the training data (first 62-weeks) and then made to predict the test data (the last 16-weeks). Results revealed that the moving-average models (SARIMA and AR) performed better compared to the support-vector models (SMO) during both training and test. Specifically, the SARIMA model possessed the smallest error compared to the AR and SMO models during test. We discuss the implications of using moving-average methods in predicting soil movements and associated landslides at real-world landslide locations.

Full text

Predictions of weekly soil movements using moving-
average and support-vector methods: A case-study in
Chamoli, India
Praveen Kumar1, Priyanka1, Ankush Pathania1, Shubham Agarwal1, Naresh Mali3,
Ravinder Singh4, Pratik Chaturvedi2, K. V. Uday3, Varun Dutt1
1 Applied Cognitive Science Lab, Indian Institute of Technology Mandi, Himachal Pradesh,
India
2 Defence Terrain Research Laboratory, Deference Research and Development Organization
(DRDO), New Delhi, India
3 Geohazard Studies Laboratory, Indian Institute of Technology Mandi, Himachal Pradesh,
India
4 National Disaster Management Authority (NDMA), New Delhi, India
Abstract. Landslides plague the Himalayan region, and landslide occurrence is
widespread in hilly areas. Thus, it is important to predict soil movements and
associated landslide events in advance of their occurrence. A recent approach to
predicting soil movements is to use machine-learning techniques. In machine-
learning literature, both moving-average-based methods (Seasonal
Autoregressive Integrated Moving Average (SARIMA) model and
Autoregressive (AR) model) and support-vector-based methods (Sequential
Minimal Optimization; SMO) have been proposed. However, an evaluation of
these methods on real-world landslide prediction has been little explored. The
primary objective of this paper is to compare SARIMA, AR, and SMO methods
in their ability to predict soil movements recorded at a real-world landslide site.
A SARIMA model, an AR model, and a SMO model were compared in their
ability to predict soil movements (in degrees) at the Tangni landslide in Chamoli,
India. Time-series data about soil movements from five-sensors placed on the
Tangni landslide hill were collected daily over a 78-week period from July 2012
to July 2014. Different model parameters were calibrated to the training data (first
62-weeks) and then made to predict the test data (the last 16-weeks). Results
revealed that the moving-average models (SARIMA and AR) performed better
compared to the support-vector models (SMO) during both training and test.
Specifically, the SARIMA model possessed the smallest error compared to the
AR and SMO models during test. We discuss the implications of using moving-
average methods in predicting soil movements and associated landslides at real-
world landslide locations.
Keywords: Landslides, SARIMA, SMO, Autoregression, Soil movements,
Tangni Landslide.
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1 Introduction
Landslides plague the Himalayan region, and landslide occurrence is widespread in
hilly areas of India in states of Himachal Pradesh and Uttarakhand [1]. These landslides
cause a massive damage to life and property [2]. Thus, we need to monitor, predict, and
warn people about soil movements on hills prone to landslides [3]. One way of
predicting soil movements is via machine-learning (ML) algorithms [4]. Such ML
algorithms take certain data attributes as input and predict the value of other attributes
of interest [5].
Several ML algorithms have been proposed in literature [6-17]. Two of the most
popular ones are either based upon moving average or based upon support vectors [10-
14, 16, 17]. For example, the Seasonal Autoregressive Integrated Moving Average
(SARIMA) algorithm and the Autoregressive (AR) algorithm are popular moving-
average-based methods, where the prior values in a time-series are using to predict
future values [16,17]. Similarly, support-vector algorithms like the Sequential Minimal
Optimization (SMO) have also been proposed in literature, where a set of support
vectors closer to the decision boundary are used to develop a prediction [10-14].
Prior research in the ML algorithms for soil-movement prediction has used neural-
network-based methods [6-9], support-vector-based methods [10-14], and moving-
average-based methods [10-17]. For example, reference [10-14] used the support vector
machine algorithm to predict soil movements in landslide-prone locations. Similarly,
reference [16, 17] have used certain moving-average algorithms to predict to predict
soil movements.
Although several ML algorithms have been used in literature to predict soil
movements in the recent past [6-17], the application and comparison of moving-
average-based methods and support-vector-based methods has been less explored. The
primary objective of this paper is to compare certain moving-average-based methods
(SARIMA and AR) with certain support-vector-based methods (SMO) in their ability
to predict soil movements in an active landslide site in the Himalayan mountains.
Specifically, we use a 2-year data about weekly soil-movements from the Tangni
landslide in Chamoli, India, for our investigation.
In what follows, first, we detail the background literature on the use of different
algorithms for predicting soil movements. Next, we detail the working of the SARIMA,
AR, and SMO algorithms and the method of calibrating these algorithms to data from
the Tangni landslide. Finally, we present our results from different algorithms and
discuss the implication of using moving-average-based and support-vector-based
methods for soil movement predictions.
2 Background
Several prior research studies have used neural network models [6-9] for predicting soil
movements as well as finding different triggering factors for such movements. For
example, reference [6, 7] proposed a novel neural network technique called ensemble
of extreme learning machine (E-ELM) and investigated the interactions of different
inducing factors affecting soil movements. Next, reference [8] improved the ELM
model by proposing a M–EEMD–ELM model. Results revealed that the M–EEMD–
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ELM model was consistently better than the basic artificial neural networks (ANNs)
and the unmodified EEMD–ELM model in terms of the same measurements.
Furthermore, reference [9] used a multiple-ANNs switched prediction method on three
typical landslides in Three Gorges Reservoir, namely Baishuihe landslide, Bazimen
landslide, and Shiliushubao landslide. These authors found that the proposed switched
prediction method could significantly improve model generalization compared to the
best individual ANN predictor.
Some researchers have used support-vector-based models for soil movement
predictions [10-14]. For example, reference [10] predicted the landslide displacement
in the Three Gorges Reservoir, China, using a Particle Swarm Optimization and
Support Vector Machine (PSO–SVM) coupling model. The PSO–SVM model was
based on the factors of the precipitation, the variation range of the reservoir and the
displacements of the prior-periods. Results revealed that the proposed PSO–SVM
model could better represent the response relationship between the factors and the
periodic landslide displacement. Similarly, reference [11] presented a comparative
study on landslide nonlinear displacement analysis and prediction using a support
vector machine (SVM), the relevance vector machine (RVM), and the Gaussian process
(GP). Results revealed that the Gaussian process performed better than the support
vector machine, relevance vector machine, and simple artificial neural network (ANN)
models. Furthermore, reference [12] used a case study of landslides in the Ecuadorian
Andes and compared the predictive power of logistic regression, support vector
machines and bootstrap-aggregated classification trees (bagging, double-bagging).
Results revealed that logistic regression with stepwise backward variable selection
yielded the lowest error rates and demonstrates the best generalization capabilities.
Next, reference [13] compared a Least Square Support Vector Machines (LSSVM)
model optimized with Genetic Algorithm, namely GA-LSSVM with a Double
Exponential Smoothing (DES) and LSSVM to empirically forecast landslide
displacement. Results indicated that both GA-LSSVM and DES-LSSVM models were
suitable for accurately predicting the landslide displacement based on precipitation and
displacement observations. Some researchers have also found that a Support Vector
Machine (SVM) regression predicts soil movements in Baishuihe landslide in Three
Gorges Reservoir Area, China, with a small error [14].
Some researchers have also used tree-based models for predicting soil movements
[15]. For example, reference [15] presented a methodology for prediction of landslide
movements using random forests, a machine learning algorithm based on regression
trees. The random forest method was established based on a time series consisting of 2
years of data on landslide movement, groundwater level, and precipitation gathered
from the Kostanjek landslide monitoring system and nearby meteorological stations in
Zagreb (Croatia). The validation results showed the capability of the random forest
model to predict the evolution of daily displacements for the period up to 30 days.
Furthermore, some researchers have found the moving-average models to perform
accurately in predicting soil movements [16, 17]. For example, reference [16] used the
Autoregressive Integrated Moving Average (ARIMA) model was employed to forecast
the accumulative displacement of the Bazimen landslide. Results indicated that the
ARIMA method improved the mining result of traditional static data. Reference [17]
have compared the ARIMA model and the considerable auto regressive (CAR) model
and found both these methods to yield good results.
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Across all the above investigations, either researchers have compared different
support-vector models or different moving-average models. However, research has yet
to compare support-vector models with the moving-average models. In this paper, we
address this literature gap by comparing moving-average models (SARIMA and AR)
with support-vector models (SMO). We perform this investigation by considering the
prediction of soil movements on the Tangni landslide in Chamoli, India. To best of
authors’ knowledge, this study is the first of its kind to compare moving-average-based
methods with support-vector-based models on the Tangni landslide.
3 Study Area
The study was performed in on the Tangni landslide in Chamoli district of Uttarakhand,
India. The study area covers an area of 0.72 km2. It is located on the northern Himalayan
region at latitudes 30° 27’ 54.3” N and longitudes 79° 27’ 26.3” E, at an altitude of
1450 meter (Figure 1A and 1B). As seen in Figure 1B, the landslide is located on
National Highway 58, which connects Ghaziabad in Uttar Pradesh near New Delhi with
Badrinath and Mana Pass in Uttarakhand. The geology of this area consists of slate and
dolomite rocks [3]. The landslide slope is 30º above the road level and 42º below the
road level. The nearby area is a forest of oak and pinewood trees. There have been
several prior landslides in this area causing road blocks and economic losses to tourism
[18].
Fig. 1. (A) Location of the study area. (B) The Tangni landslide on Google Maps.
Data was collected from the Tangni landslide at a daily scale between 1st July 2012
and 1st July 2014 across five different boreholes. These five boreholes are represented
by different colours in Figure 1B (red – borehole 1, green – borehole 2, yellow –
borehole 3, blue – borehole 4, and pink – borehole 5). Each borehole contained five
sensors at different depths (3m, 6m, 9m, 12m, and 15m). Data from some of these five
boreholes was used for evaluating different moving-average and support-vector
methods.
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4 Methodology
4.1 Data Pre-Processing
Data from Tangni landslide in Chamoli, India was obtained from the Defense Terrain
Research Laboratory, Defense Research and Development Organization. The
monitoring system in each of the five boreholes at the Tangni landslide contains
inclinometer sensors at different depths (3m, 6m, 9m, 12m, and 15m). These sensors
measure tilt in mm per m units (essentially the angle the inclinometer tilts). Each
inclinometer sensor is a 0.5-meter long sensor that is installed vertically at different
depths in a borehole. The monitoring system at Tangni landslide has five sensors per
borehole across five boreholes. Thus, in total there are 25 sensors across 5 boreholes.
Figure 2 shows the inclinometer sensor installed in its casing at a certain depth. As
shown in Figure 2, if there is a tilting movement () of the inclinometer of length L,
then the horizontal displacement in the tilting direction is  . For better
understanding, we converted the displacement in mm per m units into a  angle
(degrees), where 1mm/m displacement equalled 0.05729º.
Fig. 2. Inclinometer sensor installed in its casing at a certain depth
First, we calculated the relative tilt angle of each sensor from its initial reading at the
time of installation. Second, we chose only those sensors from each borehole that gave
the maximum average tilt angle over a two-year period. Thus, the data was reduced to
five time-series, where each time-series represented the relative tilt per borehole from
the sensor that moved the most in the borehole across the two-year period. As the daily
data was sparse, we averaged the tilt over weeks to yield 78 weeks of average tilt data
per time-series. Figure 3A-3E represent the average relative tilt per week from five
sensors across five boreholes (one sensor per borehole) that caused the maximum
average tilt across 78 weeks. These five time-series were used to compare the moving-
average-based methods with the support-vector-based methods.
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Fig. 3. Average tilt angle in degrees across five sensors (one per borehole). (A) Borehole 1 and
3m sensor. (B) Borehole 2 and 12m sensor. (C) Borehole 3 and 6m sensor. (D) Borehole 4 and
15m sensor. (E) Borehole 5 and 15m sensor.
By convention, a negative tilt angle was downhill motion and a positive tilt angle was
an uphill motion. As seen in Figure 3C, a downhill motion starts from -0.11º in the 73rd
week and suddenly becomes larger (-4.4º) in the last four weeks. The data was split in
an 80:20 ratio (sixty-two weeks for training and the last sixteen weeks for testing)
across different machine learning algorithms.
4.2 Seasonal Auto-Regressive Integrated Moving-Average
Seasonal Auto-Regressive Integrated Moving-Average (SARIMA) is a statistical
forecasting method popular for univariate time-series data that may contain trend and
seasonal components. It predicts the time-series by describing the auto-correlations in
data [19].
Stationarity of Time-Series: A time-series with constant values over time for mean,
variance, and auto-correlation is stationary. Most statistical forecasting methods
assume that a time-series can be made approximately stationary using mathematical
transformations such as differencing [20]. The first step of building a SARIMA model
is stationarizing the data.
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Auto-Regressive (AR): An auto-regressive component in the SARIMA model
predicts a variable at current state by passing the past values of the same variable to the
model. Thus, an auto-regressive model is defined as:
       
(8)
where p is the auto-regressive trend parameter,  is white noise and   …
denote the movement data of the previous weeks [19].
Moving-Average (MA): A moving-average component in the SARIMA model uses
past prediction errors in a regression model, which is given in equation (9). A moving-
average model is defined as:
    
(9)
where q is the moving-average trend parameter,  is white noise and   
 are the error terms at previous weeks.
If we combine auto-regression (AR) in equation (8) and a moving-average (MA) in
equation (9) model on stationary data, we obtain a non-seasonal ARIMA model, which
is defined as:
       
(10)
SARIMA builds upon an ARIMA model by adding seasonal parts to the ARIMA
model. The seasonal parts of an ARIMA model can have an AR factor, a MA factor,
and an order of difference term. All these factors in seasonal data operate across
multiples of the number of lagged periods in a season. In SARIMA, the three trend
elements that require calibration are the trend AR order ‘p’, the trend difference order
‘d’ and trend MA order ‘q’. Additional four seasonal elements, that require calibration
are the seasonal AR order ‘P’, the seasonal difference order ‘D’, the seasonal MA order
‘Q’ and the number of time steps ‘m’ for a single seasonal period. A SARIMA model
performs differencing of order D at a lag equal to the number of seasons ‘m’ to remove
additive seasonal effects. As with lag 1 differencing to remove the trend, the lag ‘m’
differencing introduces a moving- average term.
4.3 Sequential Minimal Optimization:
John Platt invented sequential minimal optimization (SMO) in 1998 [21]. It is a widely-
used algorithm for solving the quadratic programming (QP) problem that arises during
the training of support vector machines. The goal of the SMO algorithm is to return
alpha parameters (Lagrange multipliers) that satisfy the following constraint
optimization problem:
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

  
(11)
For a Kernel function:
  
(12)
and

  
(13)
4.4 Auto Regression
Auto regression (AR) is a time series model that uses observations from previous time
steps as input to a regression equation to predict the value at the next time step. This
technique can be used on a time-series where input variables are taken as observations
at previous time steps, called lag variables. For example, we can predict the value for
the next time step (t+1) given the observations at the last two time-steps (st-1 and t-2).
As a regression model, this would look as follows:
     
(14)
4.5 Optimization of Model Parameters
Sequential Minimal Optimization (SMO). SMO algorithm has two parameters first
one is complexity parameter (C) that is used to build a 'hyperplane' between two classes
which are used for classification, regression, or other tasks. The C parameter controls
how many instances are used as 'support vectors' to draw the linear separation boundary
in the transformed Euclidean feature space. The second parameter of the SMO
algorithm is an exponent (E) of the kernel function. The kernel function means
transforming data into another dimension that has a clear dividing margin between
classes of data [21]. We varied the C and E parameters in SMO as per the following:
C=0, 1 and E=1, 2, 3, 4 for polynomial kernel; C=0, 1 and E=1, 2 for normalized
polynomial kernel; and, C=0 and E = 1 for RBF kernel.
SARIMA. This model has eight parameters p, d, q, P, D, Q, m, and Trend. Here, p is
the number of autoregressive (AR) terms, d is the order of differencing (I), and q is the
size of the moving average (MA) window. Table 1 shows the range of variations for
different parameters in the SARIMA model. The trend parameter has four different
values, where absent means no trend, constant means constant (horizontal) trend, linear
means linear trend, and finally, the constant with linear trend means there is both a
constant and linear trend. The m parameter means the number of time steps for a single
seasonal period. A parameter value of zero means we do not include that parameter in
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the model. A reason for using the SARIMA model was that it allows one to account for
a seasonal trend present in the time-series.
Table 1. Parameters for SARIMA.
Parameters
Range of Values
Trend Auto Regressive (p)
[0, 1, 2]
Trend Differencing (d)
[0, 1]
Trend Moving-Average (q)
[0, 1, 2]
Trend
[Absent, Constant, Linear, Constant with Linear Trend]
Seasonal Auto-Regressive (P)
[0, 1, 2]
Seasonal Differencing (D)
[0, 1]
Seasonal Moving-Average (Q)
[0, 1, 2]
Seasonal Periods (m)
[0, 1]
Autoregression. This algorithm has parameters corresponding to the beta coefficients
(, and the last n lag terms (t-1, …, t-n).
5 Results
Each algorithm was calibrated to each time-series independently. Table 2 shows the
root-mean squared error (RMSE) results of applying three different algorithms, AR,
SMO, and SARIMA, on the training data across the five boreholes. As can be seen in
the Table, the AR and SARIMA algorithms performed the best and second best and
better compared to the SMO algorithm.
Table 2. The RMSE of different algorithms in the training dataset.
Algorithm
Root-Mean Squared Error (RMSE) in degree of angle
Borehole 1
3m
Borehole 2
12m
Borehole 3
6m
Borehole 4
15m
Borehole 5
15m
AVERAGE
AR
0.844
0.000
0.002
0.015
0.708
0.314
SMO
0.951
0.000
0.002
0.017
0.797
0.353
SARIMA
1.047
0.421
0.016
0.502
0.830
0.563
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Table 3, 4, and 5 show the optimized values of different parameters of in the SMO,
SARIMA, and AR algorithms. For example, in Table 3, the best values of the C and E
parameters were 1.0 for a polynomial kernel function across all boreholes. Similarly,
most the SARIMA models showed non-zero seasonal Q parameter and non-seasonal q
parameter. In certain cases, the seasonal P, the non-seasonal p, and the non-seasonal d
parameters possessed non-zero values. In the AR model, the lag terms varied between
0 and 7 across different boreholes.
Table 3. Optimized hyper-parameters for SMO.
Parameters
Values
E
1
C
1
Kernel function
Polynomial
Table 4. Optimized parameters for SARIMA.
Sensor Location
Borehole Depth
Best Set of Parameters
[(p, d, q), (P, D, Q, m), ‘Trend’]
1
03-meter
[(0, 1, 0), (0, 0, 1, 0), 'Absent']
2
12-meter
[(0, 0, 1), (1, 0, 1, 1), 'Constant’]
3
06-meter
[(0, 1, 1), (0, 0, 0, 0), 'Absent’]
4
15-meter
[(2, 0, 1), (0, 0, 1, 0), 'Absent']
5
15-meter
[(1, 0, 0), (0, 0, 0, 0), 'Absent’]
Table 5. Optimized parameters for Autoregression.
Sensor Location
Borehole Depth
Function
    
1
03-meter
    
2
12-meter
  
3
06-meter
     
4
15-meter
     
5
15-meter
    
   
Table 6 shows the RMSEs from different models across different boreholes in the last
16-weeks of test data. As can be seen in the table, the SARIMA algorithm performed
best compared to the SMO and AR algorithms.
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Table 6. The RMSE of different algorithms in the test dataset.
Algorithm
Root-Mean Squared Error (RMSE) in degree of angle
Borehole 1
3m
Borehole 2
12m
Borehole 3
6m
Borehole 4
15m
Borehole 5
15m
AVERAGE
SARIMA
0.000
0.006
0.525
0.068
1.118
0.343
SMO
0.021
0.000
0.610
0.065
1.158
0.371
AR
0.632
0.000
0.572
0.067
1.419
0.538
Figure 4 shows the fits of the SARIMA algorithm to the time-series data across the
five boreholes in the training and test datasets. Overall, these results are reasonably
good with very small RMSE values.
Training data
Test data
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Fig. 4. Relative angle (in degree) over training data (62 weeks) and test data (16 weeks) from
the best performing SARIMA algorithm. (A) and (B): borehole 1, 3m depth. (C) and (D):
borehole 2, 12m depth. (E) and (F): borehole 3, 6m depth. (G) and (H): borehole 4, 15m depth.
(I) and (J): borehole 5, 15m depth.
6 Discussion and Conclusions
One focus of machine-learning algorithms could be the prediction of soil movements
in advance to timely warn people about impending landslides. In this work, we applied
both moving-average-based models (SARIMA and AR) and support-vector-based
models (SMO) on weekly soil-movement data from the Tangni landslides in Chamoli,
India. All models were calibrated on the first 80% of data and tested on the last 20% of
data. All models could generate the soil-movements in the following week given the
history of movements in prior weeks. Our results revealed that the moving-average-
based models (SARIMA and AR) outperformed the support-vector-based models
(SMO) both during model training and testing. During model testing, among the
moving-average-based models, the SARIMA model outperformed the AR as well.
One likely reason for the SARIMA model to perform better compared to the SMO
and AR models could be because this model has seasonal, auto-regressive, integrated,
and moving-average components built into its working. In contrast, the SMO attempts
to linearize the prediction problem using a kernel function, where the optimized kernel
function may not always be able to do so consistently across all boreholes. Similarly,
the AR model may only contain the AR component and it does not possess other
seasonal, integrated, and moving-average components to perform as well as the
SARIMA model.
In this paper, we were able to show that moving-average-based methods outperform
support-vector-based methods for real-world soil-movement predictions. However, as
part of our future research, we plan to extend these analyses to neural-network-based
methods including the use of both artificial neural networks as well as recurrent neural
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networks (e.g., long short-term memory models). Some of these ideas form the
immediate next steps in our program on soil-movement predictions using machine-
learning techniques.
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