ORIGINAL ARTICLE

A hybrid machine learning and computing model for forecastingdisplacement of multifactor-induced landslides

Xing Zhu1 & Qiang Xu1 & Minggao Tang1 & Huajin Li1 & Fangzhou Liu2

Received: 14 September 2016 /Accepted: 24 March 2017# The Natural Computing Applications Forum 2017

Abstract A novel hybrid model composed of least squaressupport vector machines (LSSVM) and double exponentialsmoothing (DES) was proposed and applied to calculateone-step ahead displacement of multifactor-induced land-slides. The wavelet de-noising and Hodrick-Prescott filtermethods were used to decompose the original displacementtime series into three components: periodic term, trend termand random noise, which respectively represent periodic dy-namic behaviour of landslides controlled by the seasonal trig-gers, the geological conditions and the random measuringnoise. LSSVM and DES models were constructed and trainedto forecast the periodic component and the trend component,respectively. Models’ inputs include the seasonal triggers (e.g.reservoir level and rainfall data) and displacement valueswhich are measurable variables in a specific prior time. Theperformance of the hybridmodel was evaluated quantitatively.Calculated displacement from the hybrid model is excellentlyconsistent with actual monitored value. Results of this workindicate that the hybrid model is a powerful tool for predictingone-step ahead displacement of landslide triggered by multi-ple factors.

Keywords Landslidedisplacement computing .Least squaressupport vector machine . Double exponential smoothing .

Three Gorges Reservoir

1 Introduction

Contributing factors to the occurrence of landslides includegeological conditions, morphological, hydrogeology andphysical factors as well as human activities [19]. In theThree Gorges Reservoir area of China, as seasonal intenserainfall and significant fluctuation of the reservoir water level,landslides have become the most serious issue that pose agreat threat to of the local residents, properties and infrastruc-tures along the Yangtze River [10, 16, 20, 30]. Considerableresearches on landslide monitoring and early warning havebeen carried out recently [3, 11, 19, 23]. The evaluation andforecasting of potential landslide is very important foravoiding and/or reducing its induced damages. To date, defor-mation of slope is regarded as the reliable indicator of thelandslide activities. The research on monitoring and forecast-ing of landslide deformation has become an essential task andhot topic for landslide early warning [12, 30]. It is hard toaccurately evaluate the slope stability in advance by usingconventional analysis methods (e.g. limit equilibrium, a math-ematical model) because the evolution process of landslide ischaracterized as non-linear dynamic behaviour which relatingto uncertainties of geological conditions and diverse externalfactors, such as intense rainfall and fluctuation of reservoirwater level in the Three Gorges area [15, 16]. Many artificialintelligence-based methods [5–7, 14, 17, 18, 29] with strongcapability on handling non-linear problems have been widelyadapted for the forecasting of landslide displacement, such astime series regression, functional network, artificial neuralnetwork (ANN) and support vector machines (SVM). Thetime series regression method normally determines the evolu-tion trend of displacement, in which it fails to take the externalaffecting factors into account for forecasting of landslide de-formation and its accuracy is not very high. In most cases, thepractical application performance of ANN is limited by the

* Qiang Xuxq@cdut.edu.cn

1 State Key Laboratory of Geohazard Prevention and GeoenvironmentProtection (Chengdu University of Technology), Chengdu 610059,China

2 School of Civil and Environmental Engineering, Georgia Institute ofTechnology, Atlanta, GA, USA

DOI 10.1007/s00521-017-2968-x(2018) 30:38 –38Neural Comput & Applic

/Published online: 25 May 2017

25 35

http://crossmark.crossref.org/dialog/?doi=10.1007/s00521-017-2968-x&domain=pdf

following drawbacks: slow convergence speed, over-fittingand poor generalization capability with limited training sam-ples [10, 13]. In order to overcome the above mentioned draw-backs of the traditional methods, a novel machine learningmethod based on the principle of structural risk minimization,SVM, has been proposed. Furthermore, an improved versionof SVM, least squares support vector machines (LSSVM), isproposed to improve the computational efficiency and accu-racy. To date, LSSVM has been successfully applied to land-slide deformation prediction [2, 7, 12, 14, 15]. However, theprediction accuracy of directly applying LSSVM to forecaststepwise displacement of landslides triggered by seasonal in-tense rainfall and changes of reservoir water level in the ThreeGorges Reservoir still needs to be improved.

We propose a hybrid model composed of double exponen-tial smoothing and least squares support vector machines forlandslide displacement forecasting in this paper. Two typicalmultiple factors influenced landslide cases (i.e. the Baishuihelandslide and Shuping landslide) in the Three GorgesReservoir were chosen to demonstrate the proposed model.A comparative study to Genetic Optimized LSSVM is alsocarried out to highlight the advantages of this proposedmodel.

2 A novel hybrid machine learning and computingmodel

2.1 Description of the proposed hybrid model

By analysing the characteristics of landslide deformationbased on the field observations (cumulative displacement,monthly rainfall intensity and monthly reservoir water level),the cumulative displacement time series shows a stepwisecharacter with a steady monotonic increasing trend in the longterm. Hence, the cumulative displacement can be decomposedinto periodic and trend components that determined by sea-sonal triggers and geological conditions [20], respectively. Inaddition, random noise part in the cumulative displacementtime series introduced by field observation or other reasonsshould be extracted and de-noised for high predictive accura-cy. Figure 1 shows the flow chart of the novel hybrid model.Firstly, the measuring error/noise of total observed displace-ment utilizing GPS is extracted by the wavelet de-noisingmethod, and then the filtered time series is divided into peri-odic and trend parts by using the Hodrick-Prescott filter.Secondly, The LSSVM model is proposed and adapted to betrained and tested based on the periodic part sample and ex-ternal influence factors (i.e. rainfall and reservoir water level),whilst exponential smoothing method is employed to calcu-late the trend component just based on observed trend partsample. The total displacement is obtained by adding suchtwo components and then compared to the observed displace-ment to validate this proposed model.

2.1.1 Time series decomposition using Hodrick-Prescott filterand wavelet de-noising method

The original observed displacement time series are dividedinto three parts:

d ¼ dp þ dt þ dr ð1Þ

where d is the total displacement, dp is the periodic part, dt isthe trend part and dris the random noise term.

Wavelet is widely applied in signal de-noising. Inthis study, wavelet-based de-noising method wasadapted to remove random noise from original displace-ment. The MATLAB built-in function wden() can beeasily used to perform an automatic de-noising processof a one-dimensional time series. The soft heuristicSURE threshold and ‘sym8’ wavelet are selected in thisstudy. The random noise item can be obtained bysubtracting the output of this filter from the origin data,then the filtered displacement time series are dividedinto the periodic and trend components by theHodrick-Prescott filter.

Hodrick-Prescott filter was firstly proposed byWhittaker in 1923 [27] and then was popularized inthe field of economics in the 1990s by economistsRobert J. Hodrick and Nobel Memorial Prize winnerEdward C. Prescott [9]. It is widely used in macroeco-nomics to remove the periodic component of a timeseries from raw data. It is applied to obtain asmoothed-curve representation of a time series, one thatis more sensitive to the long-term trend changes than tothe short-term fluctuations. The sensitivity of the trendto short-term fluctuation can be adjusted by modifying aparameter λ. A trend component of a time series can besolved using the Hodrick-Prescott filter as follows:

minτ ∑

Ni¼1 yi−τ ið Þ2 þ λ∑N−1i¼2 τ iþ1−τ ið Þ− τ i−τ i−1ð Þ½ �2

� �ð2Þ

where yi for I = 1, 2,…,N denotes the logarithms of a timeseries variable. τ is the trend component, and λ is the smooth-ing parameter for sensitivity of trend to a cyclical/periodiccomponent. The first term of Eq. (2) is the sum of the squareddeviations which penalizes the periodic component, whilst thesecond term is a multiple λ of the sum of the squares of thetrend component’s second differences that penalizes varia-tions in the growth rate of the trend component. As λ increasesin value, the smoothed series becomes more linear.Appropriate value of λ should be selected depending on theperiodicity of the data. Normally, it is suggested that 100 as avalue of λ for yearly data, 1600 for quarterly data and 14,400for monthly data. In this study, the sharp increase of displace-ment occurred one time in every year. Hence, the value of thesmoothing parameter λ is determined to be 100.

38 6 (2018) 30:38 –38Neural Comput & Applic 25 352

2.1.2 Periodic displacement forecasting using LSSVM modelwith multiple factors

SVM has a strong capability for dealing with complex non-linear problems, for example solving pattern recognition andclassification [24, 25]. In this study, the relationship betweenthe environmental influencing factors (rainfall and reservoirwater level) and the deformation of landslide is complicatednon-linear and cannot be learned using conventional method.Few researches are proposed for forecasting of landslide dis-placement with SVM and optimized SVM model [20, 30].However, their accuracy is still room for improving.Therefore, LSSVM is used to predict the periodic displace-ment based on the multiple factors. LSSVM is an extendedversion of SVM which uses the linear least squares criteria tothe loss function instead of inequality constraints [22].

In LSSVM, given a training data set of N samplesxi; yif gNi¼1 with input data xi ∈ Rn and yi ∈ R being the corre-sponding target values, where Rn is the n-dimensional vectorspace and R is the one-dimensional vector space. The LSSVMcarries out mapping of the samples with a linear regressionfunction in a high-dimensional feature space:

f xð Þ ¼ wTϕ xð Þ þ b ð3Þ

wherew ∈ Rn denotes the adjustable weight vector, b ∈ R is thebias and ø(.) is the non-linear kernel mapping function, whichmaps the input vector x to the high-dimensional space. Basedon the structural risk minimization principle, the objectivefunction of the LSSVM can be written as follows [21]:

minw;b;σ J w;σð Þ ¼ 12 wTwþ γ

2∑Ni¼1e

2i ð4Þ

Fig. 1 Flow chart of proposedhybrid model. (1) Totaldisplacement decomposed intoperiodic and trend components.(2) Trained Pmodel for predictingthe periodic component ofdisplacement. (3) Trained DESmodel for estimating the trendcomponent of displacement

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where γ ≥ 0 is a regularization parameter, ei is slack variable,which is subject to the equality constraints:

yi ¼ wTϕ xið Þ þ bþ ei; i ¼ 1; 2;…;N ð5Þ

Lagrangian form of Eq. (4) is defined as follows:

L w; b;σ;αð Þ ¼ 12wTw

þ 12γ∑Ni¼1e

2i −∑

Ni¼1αi w

Tϕ xið Þ þ bþ ei−yi� �

ð6Þ

where αi is the Lagrange multiplier. Then, the KKT (Karush-Kuhn-Tucker) conditions for optimality are

∂L∂w

¼ 0 ; ∂L∂b

¼ 0 ; ∂L∂ei

¼ 0 ; ∂L∂αi

¼ 0 ð7Þ

Elimination of w and eiwill yield a linear system instead ofa quadratic programming problem:

0 1TN1N K þ γ−1IN

� �bα

� �¼ 0

Y

� �ð8Þ

with Y = [y1, y2, … , yN]T, 1N = [1, … , 1]

T and α = [α1,… , αN]

T. Finally, the output of the LSSVM model can beexpressed as follows [8]:

f xð Þ ¼ ∑Ni¼1αiK x; xið Þ þ b ð9Þ

K is a kernel function matrix, and Kij = ø(xi)Tø(xj) =K(xi,

xj). In this study, RBF kernel function is chosen due to itsfewer parameters and excellent non-linear mapping perfor-mance. RBF kernel function is given by

K x; xið Þ ¼ exp − 12σ2 x−xik k2

� ð10Þ

where σ2 is the parameter related to the bandwidth of thekernel in statistics, which is an important parameter for thegeneralization behaviour of a kernel method.

Compared to the classical SVM model, the solution ofLSSVM is easier and faster [4, 26]. As mentioned above,the two parameters (regularization parameter γ and kernelparameter σ2) have obvious influences on the efficiency andgeneralization performance of the LSSVM model. In thisstudy, the two optimized parameters are selected as the pairswhich result in the lowest validation root mean square error(RMSE) using grid search method that can be easily and ef-fectively implemented with LSSVM toolbox in MATLAB[22].

In the Three Gorges Reservoir area, the deformation oflandslides along the Yangtze River is characterized by increas-ing suddenly during the period of intense rainfall and declineof reservoir water level. And then, displacement rate of

landslides becomes slow when the influencing factors disap-pear. Therefore, the fluctuation of the reservoir water level ofcurrent month to the prior month was considered as a curialinput factor. And rainfall in the current month and prior monthare considered as the other input factors due to lagging effectof landslide deformation responding to rainfall. In addition,the inherent state vector is also considered as the inputs of thismodel because it represents the dynamic state of landslide inthe short term. Figure 2 shows the topography of the LSSVMmodel for landslide periodic displacement forecasting. Theoutput of this model is the predictive periodic displacementin one-step ahead.

2.1.3 Trend displacement calculation using doubleexponential smoothing

The exponential smoothing (ES) method is a forecastingmethod based on the weighted combinations of past observa-tions, where recent observations are given relatively moreweight than older ones [28]. The double exponential smooth-ing (DES) is an extension of exponential smoothing. The basicidea behind DES is to introduce a term to take into account thepossibility of a series exhibiting some form of trend. It isuseful for time series that exhibits a certain trend, and its slopecomponent is itself updated through exponential smoothing.Therefore, DES is employed in this study to predict the trendcomponent of displacement based on the observed value.

In DES, given an observed time series {xi}, we use {Si} torepresent the smoothed value of the DES for time i, and {bi} isour best estimate of the trend at time i. The output of the DESalgorithm is described as Fi + 1, a predictive value of x at timei + 1. The formulas of the double exponential smoothing algo-rithm are shown as follows:

Si ¼ α*xi þ 1−αð Þ* Si−1 þ bi−1ð Þ ð11Þbi ¼ γ* Si−Si−1ð Þ þ 1−γð Þ*bi−1 ð12ÞFiþ1 ¼ Si þ bi ð13Þ

where i = 1 , 2 , 3… , α is the data smoothing factor that rangefrom 0 to 1 and γ is the trend soothing factor, 0 < γ < 1 . In this

Fig. 2 Construction of the LSSVMmodel with multiple factors as inputs

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study, Fi + 1 is the calculated one-step ahead trend displace-ment of landslide, and Si is the measured trend displacementvalue of landslide at present; α and γ are respectively deter-mined to be 0.99 and 0.98 by trial and error approach.

Finally, the predictive total displacement can be obtainedby adding the periodic predictive value estimated by LSSVMmodel and the trend predictive value estimated by DES.

2.2 Criteria of forecasting performance evaluation

To justify the performance of this model, it is very importantto choose appropriate performance evaluation indicators. Inthis study, the following four quantitative evaluations areused, namely root mean squares error (RMSE), mean absolutepercentage error (MAPE), correlation coefficients (R2) andpredictive accuracy (PA). The above indicators can be definedas follows:

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N∑Ni¼1 Oi−Pið Þ2

rð14Þ

MAPE ¼ 1N∑Ni¼1

Oi−PiOi

��������� 100% ð15Þ

R2 ¼∑OP−N ⋅OP

� �2

∑O2−N ⋅O2

� ∑P2−N ⋅P

2� ð16Þ

PA ¼ 100−MAPEð Þ% ð17Þ

where i = 1 , 2 , … ,N. O and P are the actual observedvalue and calculated value, respectively. And O and P arethe mean values corresponding to the observation andcalculation.

Another evaluation metric utilized is accuracy factor (Af), asimple multiplicative factor denoting the spread of resultsabout the forecasting, which is calculated as follows [1]:

Af ¼ 10

∑ log Pi

.Oi

� ���� ���N

0@

1A

ð18Þ

Here, Af = 1 indicates a perfect agreement between all thecalculated displacement and the observed displacement.

3 Case studies

With the aim to illustrate the effectiveness of the hybrid DES-LSSVM model proposed, two landslide cases in the ThreeGorges Reservoir area are presented and studied in the follow-ing section.

3.1 Case I: the Baishuihe landslide

3.1.1 Dataset

The Baishuihe landslide is located in the town of Zigui onwhich the south bank of the Yangtze River, and its 56 kmaway from the west of the Three Gorges Dam of China [16].Figure 3 shows the photography of the Baishuihe landslide.Totally, 11 professional GPS stations for monitoring cumula-tive displacement of the landslide were deployed on site. Theobserved displacement time series at ZG118 monitoring sta-tion are selected as the study sample for our proposed modelbecause it locates in the trailing edge of the slope so as toreflect the dynamic behaviour of this landslide. Figure 4ashows the cumulative displacement at ZG118 monitoringpoint corresponding the synchronized observations for month-ly rainfall and reservoir water level. Figure 4b shows the localcorrelation between the periodic component of total displace-ment and monthly external influencing factors. It indicatesthat the remarkable increase of landslide periodic displace-ment is led by the intense rainfall and the significant declineof reservoir water level. In contrast to this, the periodic dis-placement decreases in the non-rainfall season and the risestage of reservoir water level.

3.1.2 Results

In this case, 55 groups of monitoring data between June 2003and December 2007 are chosen as training set to construct thedisplacement forecasting model, and 40 observations fromJanuary 2008 to May 2011 are selected as testing/forecastingset to validate the effectiveness of the proposed model. It isnoting that only one-step-ahead forecasting is performed inthis study. Actually, multistep-ahead forecasting can also becarried out, but the performance of forecasting for periodicdisplacement in such a case is not very good because the sharpincrease of displacement is the timely response of landslide toexternal influencing factors. However, the trend of the totaldisplacement can be calculated with DES method perfectlybecause it represents the inherent physical evolution processof landslide in the long term.

Fig. 3 Photography of the Baishuihe landslide

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Figure 5 shows the training and forecasting results of theperiodic and trend components of total displacement at theBaishuihe landslide. As shown in Fig. 5a, b, the macroevolu-tion trend of this landslide can be perfectly calculated using

the proposed DES model with the observed trend values inprior 2 months. The correlation coefficient between the pre-dictions and the observations is 0.99989. Figure 5b illustratesthat the proposed DES method has a good extrapolated ability

Fig. 4 Displacement of the Baishuihe landslide. aMonitoring time series of cumulative displacement, monthly rainfall and reservoir water level at theBaishuihe landslide. b Cross relationship between periodic displacement and seasonal factors

Fig. 5 Trained and testing results of periodic and trend displacement ofBaishuihe landslide. a Training and prediction using DESmodel for trenddisplacement. b Linear regression analysis between observed trend value

and calculated trend value. c Training and prediction using the LSSVMmodel for the periodic displacement. d Linear regression analysisbetween observed periodic value and predicted periodic value

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for macroevolution process of landslide. The prediction resultand performance of the LSSVM model for the periodic dis-placement of the landslide are shown in Fig. 5c, d. The con-structed LSSVM model with consideration of changes of theinfluencing factors shows a good predictive performance inlocal periodic displacement forecasting of the Baishuihelandslide.

Accordingly, as was explained in Eq. (1), the total predic-tive displacement can be obtained from the summation of thecalculated trend displacement using the DES method and theperiodic component displacement using the LSSVM model.Figure 6 shows the calculated result and the performance ofthe proposed hybrid model for total displacement prediction.The correlation coefficient of 0.99945 shows that the greatconsistency between the values predicted and the displace-ment observed.

3.2 Case II: Shuping landslide

3.2.1 Dataset

The Shuping landslide is also one of the most activeones in the Three Gorges Reservoir area. It is locatedin the Shuping village of Zigui County on the rightbank of the Yangtze River. Figure 7 shows the photog-raphy of this landslide. Actually, it was divided into twoparts by a valley: sliding areas I and II. It totally coversan area of around 0.55 km2 and has approximately vol-ume of 2.750 × 107 m3 with width of about 700 malong the Yangtze River. The deformation of Shupinglandslide has been monitored continuously using sixGPS monitoring stations since June 2003. The GPS ob-served data at monitoring station namely ZG85, locatingat the lower part of the sliding area I, is selected as ourstudy sample.

Figure 8a shows the measured timer series of cumulativedisplacement of the Shuping landslide and the observed res-ervoir water level, rainfall from 2005 to 2012 with time step of1 month. There is no significant rapid deformation before thereservoir water level rose to 145 m in 2006. Generally, thedisplacement data indicates a continuous increase with step-wise evolution from 2007. It is derived that the sharp increasein the displacement may be directly influenced by the fluctu-ation of the reservoir water level and the intense rainfall inevery year. Figure 8b shows the local cross correlationbetween the periodic component of total displacementand monthly environmental factors. It indicates that theremarkable increase of landslide periodic displacementis led by the intense rainfall and the significant declineof reservoir water level. In contrast to this, the periodicdisplacement is decreasing in the non-flood season andthe rise stage of reservoir water level. The total dis-placement of landslide remains nearly stable after a sig-nificant rise of reservoir water level. The deformationcharacteristic of the Shuping landslide is same as thatof the Baishuihe landslide.

Fig. 6 a Forecasting results of total cumulative displacement at Baishuihe landslide. b Linear regression analysis between the observations (O) and thepredictions (P) for testing sample

Fig. 7 Photography of the Shuping landslide

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3.2.2 Results

In this case, 55 groups of monitoring data between April 2005and October 2009 are chosen as training set to construct the

displacement forecasting model for the Shuping landslide, and40 observations fromNovember 2009 to June 2012 are selectedas forecasting set to validate the effectiveness of the proposedmodels. As mentioned above, one-step ahead forecasting just is

Fig. 8 Deformation characteristic of the Baishuihe landslide. a Monitoring time series of landslide cumulative displacement, monthly rainfall andreservoir water level at the Baishuihe landslide. b Cross-relationship between periodic displacement and seasonal factors

Fig. 9 Trained and testing results of periodic and trend displacement ofthe Shuping landslide. a Training and prediction using the DESmodel fortrend displacement. b Linear regression analysis between observed trend

value and predicted trend value. c Training and prediction using theLSSVM model for the periodic displacement. d Linear regressionanalysis between observed periodic value and predicted periodic value

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carried out in this study, which means that the displacement ofthe landslide in 1 month ahead would be calculated.

Figure 9 shows the training and prediction results of theperiodic and trend components of total displacement atShuping landslide. As shown in Fig. 9a, b, the macroscopicevolution trend of this landslide can be perfectly predictedusing the proposed DES method with the observed trendvalues in prior 2 months. The correlation coefficient betweenthe predictions and the observations is 0.99999. Once again,Fig. 9b proves that the proposed DES method has a goodpredictive capability for macro evolution process of landslide.The prediction result and performance of the LSSVM modelfor the periodic displacement of the landslide are shown inFig. 9c, d. The proposed LSSVM model with considerationof changes of the influencing factors shows a good predictiveperformance in local periodic displacement prediction of theShuping landslide.

Finally, the summation of the predicted trend displacementand the periodic component displacement is regarded as thecumulative displacement of the landslide. Figure 10 shows thepredicted result and the performance of the proposed hybridmodel at Shuping landslide case. The correlation coefficient of0.9993 also shows that the great consistency between the pre-dicted displacement and the measured total displacement.

In addition, the LSSVM model with genetic algorithm(GA) optimization is applied to the same data samples to showthe advantage of the proposed hybrid model. The vector withrainfall in the current and prior months, the fluctuation ofreservoir water level in the current month to the prior monthand observed total displacement values in the prior 2 monthsis used to as the input of the GA-LSSVM model, and theoutput of the LSSVM is the predicted total displacement.Figure 11 shows the comparison results of GA-LSSVM andthe proposed hybrid model for the same prediction sets at the

Fig. 10 Predicted cumulative displacement using the proposedmodel forthe Shuping landslide. a Training set during from April 2005 to October2009 and testing set during November 2009 to June 2012. b Linear

regression analysis between the observed cumulative displacement (O)and the predicted cumulative displacement (P) for testing set

Fig. 11 Comparison of the values calculated and observed for thecumulative displacement. a Calculated values of the GA-LSSVMmodel and the proposed hybrid model for the Baishuihe landslide. b

Calculated values of the GA-LSSVM model and the proposed hybridmodel for the Shuping landslide

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two study cases, respectively. The comparative results of twodifferent models’ performance for same samples is given byRMSE, MAPE, R2, PA and Af (Table 1).

Obviously, the results obtained from Table 1 indicate thatthe forecasting performance of the proposed hybrid modelconstructed with Hodrick-Prescott filter, LSSVM and doubleexponential smoothing methods is better than the GA-LSSVM. Therefore, the decomposition for time series influ-enced by external seasonal factors is very important in theproposed hybrid model. The periodic component of total dis-placement is the timely of landslide mass responding to thechanges of external influencing factors. And the trend term oftotal displacement is the long-term evolution process of thelandslide. So, the LSSVM-based model is more suitable forthe non-linear, complicated periodic displacement forecastingthan for total displacement forecasting, whilst the DES meth-od would be preferable for forecasting of the inherent evolu-tion behaviour of landslide. It is clear that the proposed modelcan effectively improve the accuracy of landslide displace-ment forecasting.

4 Conclusion

A hybrid machine learning and computing model was pro-posed for calculating one-step ahead displacement of land-slides triggered by multiple factors. Wavelet de-noising algo-rithm was used to reduce the random noise of measured dis-placement time series. The Hodrick-Prescott filter was appliedto divide the de-noised time series into trend component con-trolled by geological conditions in long-term and periodiccomponent influenced by the seasonal triggering factors. Byanalysing the basic characteristics of landslides, the fluctua-tion of the reservoir level and the seasonal rainfall are crucialinfluencing factors in the periodic stepwise deformation oflandslides. The LSSVM and DES models were constructedand trained to predict the periodic component and the trendcomponent, respectively. Models’ inputs include the seasonaltriggers (e.g. reservoir level and rainfall data) and displace-ment values which are measurable variables in a specific priortime. Subsequently, the total displacement predicted was ob-tained by adding the output values of the LSSVM and DESmodels. The performance of the hybrid model was evaluatedquantitatively. Calculated displacement from the hybrid

model is excellently consistent with actual monitored value.Correlation coefficients and predictive accuracy of the hybridmodel are more than 0.9993 and 99.19%, respectively.Moreover, comparison between the proposed hybrid modeland GA-LSSVM model shows accuracy and superiority ofthe model. Results of this work indicate the hybrid model isa powerful tool for predicting one-step ahead displacement oflandslide influenced by multiple influence factors.

Acknowledgements This study was supported by the National BasicResearch Program (973 Program) (grant numbers: 2013CB733200,2014CB744703), the Funds for Creative Research Groups of China(grant number: 41521002) and the National Natural Science Foundationof China (grant number: 41502293).

Compliance with ethical standards

Conflict of interest The authors declare that they have no conflicts ofinterest.

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Table 1 Comparison between performances of the proposed model and that of GA-LSSVM model

Model cases The proposed model (DES-LSSVM) GA-LSSVM

RMSE (mm) MAPE (%) R2 PA (%) Af RMSE (mm) MAPE (%) R2 PA (%) Af

Baishuihe 25.2291 0.81 0.99945 99.19 1.0048 84.8616 3.60 0.99488 96.40 1.0800

Shuping 27.8819 0.73 0.99928 99.27 0.9973 64.1504 2.14 0.99622 97.86 1.0398

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A hybrid machine learning and computing model for forecasting displacement of multifactor-induced landslidesAbstractIntroductionA novel hybrid machine learning and computing modelDescription of the proposed hybrid modelTime series decomposition using Hodrick-Prescott filter and wavelet de-noising methodPeriodic displacement forecasting using LSSVM model with multiple factorsTrend displacement calculation using double exponential smoothing

Criteria of forecasting performance evaluation

Case studiesCase I: the Baishuihe landslideDatasetResults

Case II: Shuping landslideDatasetResults

ConclusionReferences