The Landslide Risk Evaluation

Published Date: 02 Nov 2017

INTRODUCTION

Landslide risk/hazard analysis can be defined as the probability of occurrence within a specific period of time and within a given area of a potentially damaging phenomenon [1]. Landslide risk evaluation is carried out here to identify and predict the number of potentially harmful occurrences of landslides for a given time period. The approach employed here is more of quantitative assessment rather than a qualitative one.

Rainfall is one of the main causes of all landslides that occur in Ooty, Nilgiris. Landslides due to excessive rainfall are not an uncommon phenomenon in the considered study area. Ooty receives an average yearly rainfall in excess of 1200mm coupled with the fact that the soil in Ooty is laterite and the presence of a large number of cut slopes makes the region a landslide prone area. Landslides pose a great threat both to life and property. Researchers nowadays usually employ remote sensing techniques and sub surface analysis but this can be quite cost intensive. Researchers employing artificial neural networks in their analysis have previously used a single step process of directly predicting landslide risk with variables such as rainfall intensity, pore pressure, topographic map, drainage map, soil map, geology map, land cover and Normalized Difference Vegetation Index. Due to the lack of availability of these data a two step methodology has been proposed which involves the prediction of rainfall first followed by rainfall thresholding in order to categorize the landslide risks.

In this chapter we first identify the different variables affecting rainfall. Once identified, these are pre-processed using a suitable technique and fed into an error back propagation network in order to forecast rainfall. Different combinations of weight updation techniques and architecture are used to identify the best case scenario. Genetic algorithm is then used to optimise starting weights in the back propagation network to remove randomness in the starting weights. Radial basis function network is another neural network approach which has been implemented. The forecasted rainfall is then used with a rainfall thresholding equation which is used to classify landslide risk for a given time period.

METHODOLGY

The proposed two stage methodology involves firstly forecasting rainfall followed by rainfall thresholding in order to classify rainfall induced landslide risks. In order to forecast rainfall firstly we must identify variables that are to be taken as inputs to the artificial neural network in order to forecast rainfall. These include the past 4 days values of rainfall(mm), humidity, temperature(0C) and the month. This data is then pre-processed using suitable techniques and then fed into an artificial neural network which forecasts rainfall. The forecasted rainfall data is then compared to the threshold rainfall value which is computed using the rainfall thresholding equation in order to classify different landslide risks.

The above mentioned methodology is implemented in matlab R2012b.

DESIGNING ANN MODELS

The design of an ANN model includes a number of systematic processes. These

include:-

Collecting data

Pre-processing data

Building the network

Training the network

Testing the network

4.3.1 Data Collection

The first step in designing the ANN models is to first identify the required variables followed by finding a source to acquire the sample training and testing data. The identified input variables include the past four days of rainfall data(mm), humidity, temperature(0C) and which month that day fall on. These input variables are collected for Ooty, Nilgiris from 2009 to 2012 through the online worldwide database of www.worldweatheronline.com.

Inputs may be given as a four input model where only the past 4 days of rainfall are given as input to the ANN or as a seven input model which includes past four days of rainfall data, humidity, temperature and which moth that day falls on. The month related to the day of forecast has been used as a differentiator in order to identify the monsoon seasons in Nilgiris. Due to the presence of similar input conditions of temperature and humidity during summer and winter the presence of month as input becomes an important differentiator.

4.3.2 Pre-processing data

After the process of data collection is over the acquired data has to be checked for missing values. Missing values are replaced by averaging the neighbouring values. Normalizing the input values before presenting them to the ANN is important, since mixing with large magnitudes and small magnitudes will confuse the learning algorithm on the importance of each variable and may force it to reject input data with smaller magnitude[2].

We use min-max normalization in order to map the actual input values to values between [0,1]. The lowest value(min) is set to 0.0 and the highest value(max) is set to 1.0. Using this technique inputs that are measured using different scales or different units of measure can be compared easily.

The normalized value is given by:

(Input-minimum observed value)/(maximum observed value-minimum observed value)

This way rainfall data(mm), humidity, temperature(0C) and month value are all scaled down to values between [0,1].

4.3.3 Building the network At this stage we specify the number of hidden layers(in case of BPN), number of nodes/neurons in each layer, activation function used, weight updation technique and the performance function.

BPN can have more than one hidden layer while RBFN can have only a single hidden layer. A comparative study was conducted on one hidden layer and two hidden layer architecture with varying number of nodes/neurons in each case for BPN. The nodes in the single hidden layer were varied to have twice as many neurons as that of the input, more than twice the number of nodes compared to that of the input, equal number of neurons and less than the number of neurons in the input layer. In case of the two hidden layer architecture similar variations in the number of hidden nodes was implemented in order to find the most optimum case.

The learning rates also were decided at this stage. The system takes the learning rates by default to be 0.01. Variations in this value between [0,1] proved that the default value itself gave the best results.

There are three activation functions that can be used in the hidden layer or the output layer of an error back propagation network. These include hyperbolic tangential sigmoid(tansig), logarithmic sigmoid(logsig) and linear(purelin). The activation function being used in the Radial basis function network is a Gaussian function.

The mathematical notations for these functions can be represented as follows:-

Linear:- f(x)=x

Hyperbolic tangential sigmoid:- f(x)=(ex-e-x)/ (ex+e-x)

Logarithmic sigmoid:- f(x)=1/(1+ex)

Gaussian RBF:- φj(x)=exp((-1/2σj2||x-xj||2))

There were a total of six different training algorithms that were used in this project in BPN.

These include:-

Gradient Descent

Gradient descent with momentum

Gradient descent with adaptive learning

Gradient descent with momentum and adaptive learning

Resilient Backpropagation

Levenberg marquardt

Further starting weights were predefined using genetic algorithm. Genetic algorithm was used as an optimising tool in order to give specific starting weights rather than randomly generating them for each run.

The performance function specified for each case is the mean squared error(MSE).

In RBFN the parameters that can be altered include inputs, outputs, goal MSE and spread factor. The goal MSE was set as 0.004. The spread factor was varied using values ranging from [0,1].

4.3.4 Training the network

During the training process for each input set, the weights are adjusted such that the actual output is more closer to the target output. In this project a period of 3 years is used as training data (2010-2012).

As mentioned in the previous section, in BPN there are six different training algorithm used namely gradient descent, gradient descent with adaptive learning, gradient descent with momentum, gradient decent with momentum and adaptive learning, resilient back propagation and Levenberg marquardt technique.

Gradient descent backpropagation

dX=lr*dperf/dX

The change in gradient is computed as the product of the learning rate and partial derivative of the performance function w.r.t weights and biases.

The performance function used is the error function which is the mean square error which can be mathematically represented as:-

where E=error function

tk=Desired output

σ(zk)=Actual output

The learning rates is set to 0.01 and the maximum number of epochs are fixed to 1000.

Gradient descent backpropagation with adaptive learning

dX=lr*dperf/dX

Just like the previous case the change in gradient is computed as the product of the learning rate and partial derivative of the performance function w.r.t weights and biases. Initially the learning rates are specified to be 0.01. If the new error computed exceed the previous error by 1.04 the learning rate is multiplied by a factor equalling 0.7 in order to slow down the learning process but instead if the new error is less than the previous error then the learning rate is multiplied by 1.05 in order to speed up the learning process.

Gradient descent backpropagation with momentum

dX=mc*dXprev+lr*(1-mc)*dperf/dX

It is a form of the gradient descent with the presence of an additional momentum factor term. The momentum factor was set to 0.9 which is the default value in matlab. The term dXprev represents the previous change in weight. Similar to the previous cases the learning rate was set to default values of 0.01.

Gradient descent backpropagation with momentum and adaptive learning

dX=mc*dXprev+lr*(1-mc)*dperf/dX

The change in gradient formula is same as that in the previous case and it too is a the gradient descent with the presence of an additional momentum factor term. The momentum factor was set to 0.9 which is the default value in matlab. The term dXprev represents the previous change in weight. Initially the learning rates are specified to be 0.01. If the new error computed exceed the previous error by 1.04 the learning rate is multiplied by a factor equalling 0.7 in order to slow down the learning process but instead if the new error is less than the previous error then the learning rate is multiplied by 1.05 in order to speed up the learning process.

Resilient Backpropagation

dX=deltaX.*sign(gX)

In previous cases the magnitude of the partial derivative was used to determine the change in gradient value but in case of resilient backpropagation technique we use the sign of the partial derivative. Multi layer networks usually use sigmoid transfer function in the hidden layers. These function maps large variations in inputs to values between [0,1] in logarithmic sigmoid and [-1,1] in hyperbolic tangential sigmoid. Sigmoid functions are characterised by the fact that their slopes must approach zero as their inputs get larger. However using the gradient descent technique to train the network may cause problems because the gradient can have very small magnitude and therefore cause small change in the weights and biases, even though the weights and biases may be far away from their optimal values. The purpose of the resilient backpropagation (Rprop) training algorithm is to eliminate the harmful effects of the magnitudes of the partial derivatives. In this case only the sign of the derivative was used to determine the direction of the weight update, the magnitude of the derivative has no effect on the weight update. The size of the weight change is determined by a separate update value. The update value for each weight and bias is increased by a factor delt_inc whenever the derivative of the performance function with respect to that weight has the same sign for two successive iterations. The update value is decreased by a factor delt_dec whenever the derivative with respect to that weight changes sign from the previous iteration. If the derivative is zero, the update value remains the same.

Levenberg marquardt

Instead of using the partial derivative, it computes the jacobian of the error function.

H=JTJ

g=JTe

xk+1=xk-dX

dX=[JTJ+µI]-1JTe

e is all the errors, I is the identity matrix µis the iterative incremental step

Firstly the hessian matrix is computed by finding out the jacobian of the error function w.r.t the weights and the bias and then multiplying it with the transpose of that jacobian. Then the gradient g is computed by multiplying the transpose of the jacobian computed with the errors. dX is the change in value of x and it is subtracted from the current value to get the value for the next iteration.

These six algorithms are used as training algorithms during the training part of the process.

4.3.5 Testing the network

In order to test the performance of the trained network unseen data is introduced to the network. For the case study of Ooty, Nilgiris, weather data for the year 2009 was used to test the trained network model. The predicted rainfall was then compared to the desired results in the test year. In order to evaluate the performance of the developed ANN models the mean square error(MSE) was computed for the test year case. Lower the MSE better was the network trained.

The MSE can be mathematically represented as:-

MSE=(1/n)Σi=1(di-oi)2

n represents the total number of input sets

d represents the desired output

o represents the predicted value

PROGRAMMING ANN MODELS

MATLAB is a numerical computing environment and also a programming language. It allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creating user interfaces and interfacing with programs in other languages. Neural Network Toolbox provides functions and apps for modelling complex nonlinear systems that are not easily modelled with a closed-form equation. Neural Network Toolbox supports supervised learning with feedforward, radial basis, and dynamic networks. It also supports unsupervised learning with self-organizing maps and competitive layers. With the toolbox you can design, train, visualize, and simulate neural networks. You can use Neural Network Toolbox for applications such as data fitting, pattern recognition, clustering, time-series prediction, and dynamic system modelling and control.

In this paper MATLAB (R2012b) is used to generate command line functions for developing BPN and RBF ANN models and performance functions for calculating the model performance error which is the MSE.

The program first starts reading data from certain .mat files which contain the training and testing data set and were created from multiple .txt files which contained rainfall, humidity and temperature values before they were processed(normalized). These combined .txt files are then pre-processed using min max normalization and stored onto to a single .mat input file and a single .mat output file. The input and output variables are stored in separate .mat files. The input variables(past four days rainfall, humidity, temperature and the month) are represented in a 7X1457 matrix which essentially relates to 1457 samples of 7 input elements. The first four rows represent past four days of rainfall followed by temperature, humidity and finally the month. The output variable(next day rainfall predicted) is represented in a 1X1457 matrix which contains desired value of rainfall to be predicted. The training set and the testing set were in the same file and were differentiated by specifying range of column values for training and testing.

training_inputs=t5(:,362:1457);

training_targets=t_tar1(1,362:1457);

The training period was taken to be for three years (2010-2012) and the testing period was taken to be as 2009.

testing_inputs=t5(:,1:361);

testing_targets=t_tar1(1,1:361);

MATLAB creates a feed forward network using the built in function "feedforward" which creates a feed forward network back propagation network. The number of hidden layers are specified at this stage.

net=feedforward(hiddenlayersize);

Once the network is created different network parameters like transfer function, performance functions, maximum no. of epochs, weight updation function can be changed easily.

The network is configured as follows:

net.trainFnc='trainlm';

net.trainparam.min_grad=0.00000001;

net.trainParam.epochs=1000;

net.trainParam.lr=0.01;

net.layers{1}.transferFcn = 'tansig';

net.layers{2}.transferFcn = 'purelin';

net.performFcn = 'mse';

where

trainFnc :- defines the function used tot train the network

trainparam.min_grad:- denotes the minimum performance gradient

trainParam.epochs:- denotes the maximum number of epochs to train

trainParam.lr:-denotes the learning rate

transferFnc:- denotes the activation function used at different layers

performFnc:-denotes the performance function

Once the network is created and configured it is then trained by using the following function.

net=train(net,inputs,targets);

Once the training is completed testing is done by simulating the network with test input data.

op=sim(net, testing_inputs);

Performance function i.e. the MSE calculated will be used to determine which architecture, training function etc give the most optimum results. Lower the MSE value better the results.

Genetic algorithm is used to predefine the weights in order to obtain global minimum point.

In order to do this we first use the gaoptimset function in matlab which returns a listing of the fields in the options structure as well as valid parameters and the default parameter. Options such as the tolerance function, the maximum number of generations etc are decided using this function.

ga_opts = gaoptimset('TolFun', 1e-8,'display','iter');

After defining the options in gaoptimset we use the ga function to find a local unconstrained minimum x to the objective function(MSE).

[x_ga_opt, err_ga] = ga(h, Nw, ga_opts);

x_ga_opt represents the optimised starting weights and biasesh represents the fitness function value

Nw represents the total number of weights and biases

These computed weights and biases are then used as predefined staring weights in network.

The function newrb is used to create a RBF network by including one neuron at a time.The number of neurons are incremented for each iteration until the desired MSE value is achieved.

The call for this function is:-

net=newrb(inputs,targets,0.004,1.0);

The first two terms represent the input and the output terms. The third term represents the goal MSE value and the last term represents the spread factor term. The spread factor term here is varied between values 0 to 1.

RAINFALL THRESHOLDING

Once the rainfall for the next day has been predicted, the next step is to evaluate and categorize landslides based on a rainfall thresholding equation.

The rainfall thresholding equation for Nilgiris is

RT=220-0.61*R5ad

where R5ad is the sum of the past 5 days rainfall, RT is the threshold value.

In order to do evaluate and categorize landslides based on a rainfall thresholding equation we first must calculate the rainfall thresholds for each day in the test year. In order to do this we first compute the sum of the past 5 days of rainfall for each day in the test year. These computed values are stored in a matrix and then substituted in the above equation in order to calculate rainfall thresholds for each day in the testing year.

Once the rainfall thresholds have been calculated the next step is to use the neural network to predict the rainfall expected for each day of the test year.

If the value of the predicted rainfall for a particular day exceeds the rainfall thresholds for the same day then the risk of landslide occurrence is high. If the value of predicted rainfall falls between RT and (RT-20) then risk of landslide occurrence is moderate. If the value of predicted rainfall is less than (RT-20) then the risk of landslide occurrence is low.

From observing tables 5.1, 5.2, 5.3 and 5.4 we see that a seven input two hidden layer architecture with Levenberg Marquardt weight updation technique had the lowest MSE(0.0079) and predicted four high risk landslides in the test year. In table 5.6 we observe that the use of genetic algorithm in order to predefine starting weights and biases gave a slightly better result with MSE value equal to 0.0078. Table 5.5 shows us that the use of the use of radial basis function showed a reduction in computational time with similar MSE results with the lowest MSE result achieved for a spread factor 0.7.