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Using neural networks to predict slope movements

F. Mayoraz, T. Cornu, L. VullietSwiss Federal Institute of Technology, Lausanne, Switzerland

ABSTRACT : The prediction of slope movements with time is of great importance as it may affect thesafety of constructions, infrastructures and human life. In this paper, a new approach of prediction is pro-posed, making use of neural networks. The type of network is presented first, and the technique is then

applied to two landslides in Switzerland (La Chenaula) and in France (Salldes). Input parameters are dis-cussed in detail (velocity, pore pressure and rainfalls) as well as training and testing procedures. It is shownthat neural networks are easier to implement and more general than statistical regressive models, and givereliable results.

1. INTRODUCTION

1.1 Predicting landslide movements

The necessity of predicting the occurrence and thekinematics of landslide is quite obvious and tendsto increase with increasing urbanism needs(buildings and infrastructures constructed on land-slide prone area). As part of a maintenance pro-gram, prediction models can be used to plan reha-bilitation works; included in an alarm system, theymay even save human lives.

However, the task is anything but simple. Tostart with, boundary conditions are not easilyknown: geometry of the free surface and the slidingbase - if any -, groundwater seepage conditions,time evolution of rainfalls, etc. Then the material

behavior depends on complex features, on whichvery limited information exists : soil/rock type,heterogeneities, macro-structure, stress-strain-timematerial behavior, hydromechanical coupling, etc.Finally, financial resources are always limited andprevent from undertaking in-depth hydro-geotech-nical investigations.

Two very different but complementary ap-proaches are possible: the mechanical approach,using continuum theory of varying complexity, andthe statistical approach including regression analy-sis, time series analysis or hydrology-derived res-

ervoir models.Neural networks belong to the second(statistical) category but are believed to be evenmore efficient if implemented in the heart of me-chanical models from the first category (for exam-

ple by using neural networks for the boundary con-ditions or even in place of a constitutive model - seeGhaboussi et al. 1994).

This paper is a first attempt to predict slope mo-vements by neural networks based on parameters

such as rainfalls, pore pressure and displacements.

1.2 Neural networks in civil engineering

Well known in electrical science, operational orregulation research, artificial neural networks(ANN) are starting to be very popular in civil engi-neering. In fact, very recent publications show afast growth of interest in all fields including thegeotechnical domain: constitutive modeling, piledynamic testing, soil compaction, soil classifica-tion, finite element analysis coupled with neural

networks, expert systems, etc. (see for example theproceedings edited by Pande & Petruszczak 1995,or Siriwardane & Zaman 1994).

It is the belief of the authors that neural networksconstitute a promising tool for the engineeringworld, and strengthen what is now called softcomputing, a mimic of biological processes(including fuzzy logic, etc.).

2. FUNCTION APPROXIMATION WITH ANN

2.1Multilayered neural net structure

Multilayered perceptrons (MLPs) are the mostcommon type of artificial neural networks (ANN)used for both classification and function approxi-

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mation (Lippmann 1987) . In this section, a quickoverview of the use of MLPs is presented for func-tion approximation and the corresponding learningtechniques are discussed.

The structure of MLPs is based on the widelyknown basic neuron shown on Figure 1. A basicneuron withNinputs containsNadjustable weightsw

1, w

2, ..., w

Nand performs a weighted sum of its

inputs, threshold by a non-linear function. In MLPalgorithms, the threshold function is usually asigmod function of the form (see Figure 1):

fe

( )( )

=+

1

1(1)

2.1 Transfer function of an MLP

It has been shown that a network composed of oneintermediate layer of basic neurons and of one out-

put neuron without threshold function (Figure 2) isa universal approximator. Such a network can ap-proximate any given function with sufficient preci-sion, provided that enough neurons are given onthe intermediate layer (Leshno et al. 1993).

Given a set of points in the N-dimensional in-puts space, {(x1

k,x 2k,... ,xN

k)}, k={1,2,...,P} andthe set of corresponding outputs, {ok}, the learningprocess is then reduced to a multidimensional nonconstrained optimization process in the space de-fined by every weight of the system. A learningalgorithm tries to fit the transfer function T to thedata. This transfer function may be expressed asfollows:

T x x x v f w xN ii

N

ij

j

M

j j( , ,..., ) ( )1 21 1

= = =

(2)

where xj are the input values, N and M are thenumber of inputs and the number of neurons in theintermediate layer respectively, and P is the numberof inputs vectors in the training set; wij are theweights of the connections between the inputs andthe neurons of the intermediate layer, vi the weights

of the connections between the neurons of the in-termediate layer and the output neuron; j are thebiases of the neurons of the intermediate layer, isthe bias of the output neuron and f the sigmodfunction defined above.

2.2 Supervised learning methods for MLPs

The purpose of supervised learning algorithms forMLPs is to find the proper weight configuration soas to approximate a given function. These algo-

rithms are usually based on iterative gradient de-scent methods or on Gauss-Newton methods.

1()

Figure 1. Basic neuron and sigmod function.

The so called backpropagation principle (LeCun1985) makes it possible to compute the gradient ofthe output error E of the multilayered neural net,usually defined as:

E T x x x ok k

N

k k

k

P

= =

( ( , ,..., ) )1 22

1

(3)

with respect to each of the connection weights. Thepartial derivative with respect to weights of nonterminal layers are computed recurrently as a func-tion of the one of the next layer.

The first attempts to run backpropagation basedlearning on MLPs used simple gradient methodswith either constant gradient step or steps varyingaccording to predetermined laws. These first meth-

ods where somewhat hampered by the need ofguessing a good parameterization of the gradientstep. From these first attempts, backpropagationbased learning gained the reputation of being aslow, unreliable mechanism, very sensitive to pa-rameter tuning.

Sophisticated optimization algorithms from op-erational research have been adapted to learningwith MLPs, improving convergence speed andquality of the method, and providing automatictuning of the gradient step at each iteration. Conju-gate gradient methods and quasi-Newtonian meth-

ods have been successfully applied to this field (fora survey see Battiti 1992). Among these methods,the most reliable are the well known Polack-Ribiereconjugate gradient method and the so calledmemoryless BFGS method (Shanno 1978).

The Marquardt-Levenberg algorithm, often usedin non linear least squares problems, has beenadapted to learning in MLPs (Hagan and Menhaj1994). It is an approximation to Newton's methodinstead of a pure gradient descent. Though itsmemory requirements make it impractical for largeneural networks, it compares favorably againstconjugate gradient techniques for learning in neural

networks of reasonable size. This is the algorithmused in this study.

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2.3 On the optimal number of hidden neurons

The above mentioned learning methods for MLPsassume a predetermined number of neurons and afixed connectivity pattern. The hidden neurons of aneural network are the neurons in the intermediatelayers. While the number of input and output neu-rons are determined by the respective number of

input and output parameters of the current applica-tion, the choice of the number of hidden neurons isusually not as easy.

When there are too few hidden neurons, the neu-ral network will not be able to solve the learningproblem. If there are too many, the convergence ofthe learning algorithm will be slowed down, mighteven be compromised due to local minima; in addi-tion, there is a risk of overfitting in this case, i.e. ofbad classification performance on new situationsthat are not part of the learning set.

Though a few constructive learning algorithmsare currently under investigation to solve this prob-lem, the number of intermediate neurons is usuallydecided in a heuristic way. In our work, the optimalnumber of hidden neurons is determined empiri-cally as the minimal number of neurons for whichprediction performance is satisfying, without lead-ing to overfitting or exaggerately long learningtimes.

3. NETWORK CONFIGURATION

The network chosen in our case is characterized by

one hidden layer and one output layer with only oneneuron. Every input neurons are connected to everyneurons of the hidden layer (see Figure 2). Thethreshold function is a sigmod function for thehidden layer and is linear for the output layer.

3.1 Choice of input parameters

Three types of input parameters are used in thisanalysis: the rainfalls, the pore pressure and thevelocity. From the raw meteorological data on rain-

falls different operations are needed: First, evapo-transpiration is substracted to obtain the net rain-falls. Then, to eliminate noise a moving average ona three days period is used and negative values areset to zero. In order to test the time response of thelandslide to rainfalls four net rainfalls values areconsidered, i.e. one, two, three, resp. four weeksbefore the considered time. To take into account thevolume of rain over some period three values areconsidered, i.e. the sums of the last one, two, resp.three weeks. This gives a total of seven input pa-rameters for the rain (the Pl3 in Figure 2).

Secondly, for the pore-water pressures, the pre-

sent value as well as the value one resp. two daysbefore present are used, thus a total of three inputparameters for the pore-pressure (P(t) to P(t-2) inFigure 2).

V5 (t)

Pl

Pl

Pl

7

14

28Pl3 (t-7)

Pl3 (t-14)

P (t)

P (t-1)

P (t-2)

V5(t-1)

V5(t-2)

Pl3 (t-21)

Pl3 (t-28)

inputshiddenlayer

outputlayer

Figure 2. Network geometry and inputs (V5 = ve-locity average on a 5 days period, P = pore pres-sure, Pl3 = rainfalls average on a 3 days period, Pl= rainfalls).

Finally, the last two input parameters (V5 in Fig-ure 2) are the sliding velocity one day, resp. two

days before the present time.

3.2 Output parameter

Instead of predicting a future displacement, thatwould be an explicit function of time, it has beenchosen to predict the future velocity, thus respect-ing material objectivity.

Therefore, the output of the model is the velocityat present time and the plotted results are smoothedout by calculating five days moving averages.

4. SITES CONSIDERED

4.1 La Chenaula landslide

4.1.1 General context

The landslide of La Chenaula is the first of the twolandslides considered in this paper. It is situatedEast of the city of Lausanne in Switzerland and

covers an area of 2.5 ha. The thickness of the slid-ing mass is about 12 m; the material is a soft highlyplastic silty clay overlaying a molassic substratum.The average slope angle is 10 and the sliding sur-

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face is more or less parallel to the terrain. The riverChandelar flows at the foot of the landslide.

The sliding mass can be divided into two zonesof different sliding velocities (DUTI 1986): fast andslow. We only treat here the zone of fast move-ments where, in April 1983, a catastrophic accel-eration moved the mass 15 m in three days (Vavg= 5m/day).

4.1.2 Field instrumentation

In December 1980, the Chenaula landslide wasinstrumented with a series of inclinometric tubes inwhich readings were taken about every month.Although most inclinometers functioned until thecatastrophic movement, the tubes installed in thezone of rapid sliding were soon sheared. One ofthem was then transformed into an open-pipepiezometer equipped with an automatic limnigraph;water levels were recorded continuously until April

1983.An important geodetic mesh was put in place inWinter 1981 to record surface displacements. Thelarge number of measuring points cover a widezone and have been surveyed regularly.

4.1.3 Input data

Input data are given as daily averages. As no incli-nometric measurements are available in the fastmoving zone since the time the tubes were cut, acorrelation between geodetic and inclinometric

measurements in the slow moving zone is used tofind the displacements at the sliding surface in thefast zone based on surface measurement. Consid-ering movement at the sliding surface permits toneglect effects like error cone of the inclinometerreading, surface creep, etc. Daily values are ob-tained by extrapolating between discrete readingswith a differentiable interpolation function.

Piezometric data are given by the limnigraph.Rainfall intensity is obtained from a Federal me-

teo station based in Pully, only a few kilometersaway.

4.2 Salldes landslide

4.2.1 General context

The second landslide analyzed here is at Salldesnear Clermont-Ferrand (France); it has been thour-ouly studied by the Laboratoire des Ponts etChausses (LPC). The sliding mass concerns anarea of 250 m in length and is composed of clayeycolluvium of about 6 m in thickness overlying a

marl and marly limestones substratum. The slidingsurface is inclined by only 7 with respect to hori-zontal.

As a difference with the La Chenaula landslide,Salldes is not characterized by a catastrophicmovement but by a slow and varying velocity.

4.2.2 Field instrumentation

As the site of Salldes was used in a research proj-ect on the behavior of a road fill built on a creepingslope the instrumentation is very complete and con-

nected to an automatic data acquisition system(Cartier & Pouget, 1988). Thus continuous read-ings of rainfalls, pore-water pressures and dis-placements are available between 1988 and 1992.They are quite homogeneous in space and thus asingle set of data can be used for the entire site.

Piezometric readings are taken close to the slid-ing surface with an electric pressure transducer.Displacements are derived from angular measure-ments done with a servo-accelerometer installed inthe zone of maximum shear strains.

4.2.3 Input data

In the present analysis of Salldes landslide, thedata from mainly 1992 are used. It corresponds tothe period of larger variations in displacements.Here again, daily average values are considered.These values are not interpolated from discretereadings as in La Chenaula but are taken directlyfrom the acquisition system.

The displacements as a function of time are char-acterized by rapid accelerations (velocity peaks)followed by periods of rest.

5. SIMULATIONS RESULTS

5.1 Procedure

For both cases (La Chenaula and Salldes land-slides), the number of input vectors is given in Ta-ble 1. For the landslide of La Chenaula, the totalanalyzed period is 550 days, beginning September2nd 1981. In the case of Salldes, the total analyzed

period is 365 days, starting February 25th 1992.The input vectors are divided into three sets.The first one is the training set, used by the algo-

rithm to find the weights configuration. The secondone is the validation set. It is used to avoid overfit-ting : periodically, the network applies the

Table 1.Dimension of the input vectors

Case Number and position of vectors per settotal[d]

training[d]

valid.[d]

test[d]

Chenaula 1-550 1-415 416-435 416-550

Salldes 1-365 1-216 217-236 237-365

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weights resulting of the training on this set; as soonas the global error on this set reaches a minimum,iterations are stopped.

The third set is the test set, which uses the pre-viously determined weights on data that the net-work never saw. In order for this special algorithmto work properly the size of the training and valida-tion sets is such that they both contained at least one

velocity peak.It is shown that convergence of the training algo-rithm is very dependent on the random initializationof weights. In some cases, the algorithm gets stuckin local minima, but this can be easily detectedautomatically; in these cases, the global output erroron the training set doesn't decrease satisfactorily.Training has to be launched again with new randomvalues. Only a few trials are needed to find out agood initial weights configuration.

For the Salldes case only, a first simulation isalso tried out to predict the pore pressure based onthe rainfalls and on previous piezometric measure-ments.

5.2 Predicting pore-water pressure

Since it is well known that velocity is mainly influ-enced by the effective stress state, pore-pressure isan important controlling parameter. It is interestingto find out if the pore pressure could be predicteddirectly from the rainfalls (this could save somecostly instrumentation).

The test has been performed on Salldes only

and the results of the prediction is shown on Figure3. They are quite encouraging. However commentsmust be added : First, the previous pore pressurevalues P(t-1 day) and P(t-2 days) are used and theirweights turn out to be very large, i.e. they mainlygovern the prediction. Other simulation taking onlythe rainfalls into account give poor results. Similarconclusions were drawn by Pouget when using aregressive statistical model (Pouget & Livet 1994).

This can be an indication of the complexity ofthe groundwater seepage behavior.

5.3 Predicting velocity (La Chenaula)

In the case of La Chenaula landslide, the predictionof the sliding velocity is presented in Figure 4.Again, the result is quite good.

Here, the comments are different that previously:the rainfalls turn out to be very important in thequality of the prediction. It is illustrated in Figure 5,where a network only fed with the values of veloci-ties V5(t-1) and V5(t-2) exhibits bad results on thetest set, though the convergence of training is good.The neural network is able to find out by itself the

relative influence of the input parameters. A statisti-cal model for the pore pressure in Salldes wouldnot apply to the sliding velocity in La Chenaula.

220 240 260 280 300 320 340 360 3800

5

10

15

20

25

30

35

40

inputs vectors [days]

pore

pressure[kPa]

_._._ measured

____ calculated

Figure 3. Prediction of the pore pressure (Salldes);8 neurons in the hidden layer; mean error = 0.87kPa ( 4.7 % of mean pressure).

420 440 460 480 500 520 540 5600.1

0.2

0.3

0.4

0.5

0.6

0.7

inputs vectors [days]

velocity[cm/d]

_._._ measured

____ calculated

Figure 4. Prediction of the velocity (La Chenaula);8 neurons in the hidden layer; mean error = 0.02cm/d (4.6 % of mean velocity).

420 440 460 480 500 520 540 5600.4

0.2

0

0.2

0.4

0.6

0.8

inputs vectors [days]

velocity[cm/d]

_._._ measured

____ calculated

Figure 5. Prediction of the velocity (La Chenaula);8 neurons in the hidden layer; mean error = 0.29cm/d (68 % of mean velocity).

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220 240 260 280 300 320 340 360 3800.5

0

0.5

1

1.5

2

2.5

inputs vectors [days]

veloc

ity

[10

4

rad/d]

____ calculated

_._._ measured

Figure 6. Prediction of the velocity (Salldes); 10neurons in the hidden layer; mean error = 0.13*10-4

rad/d (28 % of mean velocity).

5.4 Predicting velocity (Salldes)

In the case of Salldes landslide, the prediction ofthe sliding velocity is presented in Figure 6, show-ing very good results.

Similarly to the pore pressure prediction, themain weights are put on the previous values of ve-locity instead of simply using the pore-pressure andthe rainfalls.

It is shown that results of simulations without

validation set tend to give generally very good con-vergences on the training set but less precise pre-dictions on the test set.

6. CONCLUSION

It as been shown that a neural network can be ofgreat value in predicting the movements of land-slides. The main advantages are related to the factthat almost the same network architecture can beused for different sites and different output pa-rameter. A careful check of weight values will giveclues about the controlling inputs parameters.

The presented results are short term predictions.In order to predict on a longer period an adaptiverecurrent approach is now under study.

Another important conclusion is that the qualityof input data is essential; in most studied case,readings are done manually at various intervals intime. The use of neural network in this field wouldrequire automatic data acquisition systems.

ACKNOWLEDGEMENT

This work was supported in part by the Swiss Fed-eral Highway Administration, grant no 54/95,4217.01; this contribution is gratefully acknowl-edged. We would like to thank Mr. P. Pouget of

the LPC in Clermont-Ferrand for giving us the datafor the Salldes case, and to Mrs. A. Osa-Wyserfor the initial pre-processing of the La Chenaulalandslide data set.

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