COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan,China
©2006 Tsinghua University Press & Springer-Verlag
Study on Displacement Predication of Landslide Based on Grey System
and Evolutionary Neural Network
W. Gao *
Department of Civil Engineering, Wuhan Polytechnic University, Wuhan, 430023 China
Email: [email protected]
Abstract Displacement predication of landslide is very important in control of landslide disaster. Considering the
monotonously increasing character of time series of the landslide displacement, a new intelligent prediction method
combining Grey System and Evolutionary Neural Network (ENN) is proposed here. In this method, based on the
principles of displacement decomposition, the trend of time series is extracted by Grey System and the deviation of
Grey System is approximated by the new ENN proposed here. In this new ENN, the architecture and algorithm
parameters can evolve simultaneously through combining modified BP algorithm and Immunized Evolutionary
Programming proposed by author. This new method is applied in Xintan landslide, and the results show that the
generalization of the new method is good and it can predict the displacement of landslide very well.
Key words: landslide, predication, intelligent method, ENN, grey system
INTRODUCTION
Landslide is a very serious geological disaster. For there are lot of mountains in the west of china, as the progress of
West Development Project in China, more and more landslide disasters will be encountered. So, how to control the
landslide has become a very important work. To control landslide disaster, the forecasting of landslide is a very
powerful method. But the development of landslide is a very complicated dynamic procedure. To describe this system
very accurately is very hard. But the measured displacement series can describe the general laws of landslide
development. So, some methods [1-5] for displacement predication of landslide are proposed. From analysis of those
methods [1,6] we can find that, the evolutionary neural network can describe displacement series more accurately and
more easily, and is a better method. Generally, the time series of the landslide displacement can be divided into some
sections, such as, even section, periodic section and fluctuant section, et al. For different sections, different methods
should be taken. But in previous studies using neural network, this problem have not been mentioned. To solve this
problem very well, in this paper, an intelligent method combining Grey System and Evolutionary Neural Network is
proposed.
NEW INTELLIGENT METHOD FOR LANDSLIDE PREDICATION
1. Division of time series of the landslide displacement Supposing ui is measured time series of landslide, it can be
divided as follows,
u i = u si − vi
(1)
where usi is the trend section of displacement time series, and vi is the deviation section.
The previous studies show that [4], the trend of landslide displacement time series can be described by grey system
very well. But the deviation section is still a very complicated time series. For describing this time series, the
evolutionary neural network is a very suitable method.
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2. Grey system model for trend section Generally, the trend section of landslide displacement can be concluded into
two types. One type is a kind of monotonously increasing curve that is a concave line. To describe this curve, the
GM(1,1) model in grey system is a very suitable one. Another type is an S shape curve. To describe this curve, the
Verhulst model or DGM(2,1) model in gery system is an very suitable one.
Here, the grey system is only to extract the trend, so its precision is not exigent. And the only objective is that the
deviation is not a monotonously increasing curve. The details of the grey system can be found in reference [7].
3. Evolutionary neural network model for deviation section As in above description, the precision of grey system
is not high, so the deviation section is still a very complicated series. Even if the precision of grey system is high, it is
very hard to guarantee that the deviation section is a simple random series. So, to describe the deviation section very
well, the neural network is very suitable.
So, to construct a neural network model for modeling displacement time series, the construction of neural network is
the main problem to be solved. Because in this problem, the hidden layer construction and input layer construction all
must to be confirmed. This problem can be solved by evolutionary algorithm very well. Here, as a primary study, the
evolutionary neural network which construction is confirmed by evolutionary algorithm and which weight is
confirmed by MBP algorithm is proposed. To make problem simpler and generalization bigger, the three layers neural
network is studied. So, here, only the number of input neuron and number of hidden layer neuron are to be confirmed.
In MBP algorithm, there are two parameters, iterating step η and inertia parameter α , to be confirmed. These two
parameters affected MPB algorithm very seriously. So, these two parameters are all confirmed by evolutionary
algorithm. And then, in evolutionary neural network, there are four parameters to be evolved. In order to get the better
effect, the new evolutionary algorithm- immunized evolutionary programming [8] proposed by author is used in
evolutionary neural network.
Generally, the trend section of landslide displacement can be concluded into two types. One type is a kind of
monotonously increasing curve that is a concave line. To describe this curve, the GM(1,1) model in grey system is a
very suitable one. Another type is an S shape curve. To describe this curve, the Verhulst model or DGM(2,1) model in
gery system is an very suitable one.
The details of this new evolutionary neural network are given as follows.
(1) The search range of input neuron and hidden layer neuron are given firstly. And also the search range of two
parameters in MBP algorithm are given. And some evolutionary parameters, such as evolutionary generation stop
criteria, individual number in one population, the error criteria of evolutionary algorithm, number of output neuron in
neural network, iterating stop criteria and iterating error criteria in MBP algorithm are all given.
It must be pointed out that, to construct the suitable samples, the number of input neuron must be smaller than total
number of time series.
(2) One network construction is generated by two random numbers in search range of input neuron and hidden layer
neuron. And also, one kind of MBP algorithm is created by two random numbers in search range of parameters η and
α . And then, one individual can be generated by the four parameters.
It must be pointed out that, for two numbers of neuron are integer numbers and two MBP parameters are real numbers,
so the expressions of one individual must be structural data.
(3) To one individual, its fitness value can be gotten by follow steps.
a. The whole time series of landslide displacement is divided to construct the training samples based on number of
input neuron and number of hidden layer neuron. And also, the total number of samples is noted.
b. The whole learning samples are to be divided into two parts. One part is the training samples, which is to get the
non-linear mapping network. The other part is the testing samples, which is to test the generalization of network.
c. The initial linking weights of network individual are generated randomly.
d. The iterating step of MBP algorithm is taken as j = 1 .
e. This network individual is trained by testing samples, and the square error E(j) is computed, and this error is taken
as minimum error of the whole training, min E = E ( j ) . If minE is smaller than the error criteria of evolutionary
algorithm, then the fitness value is minE. And the computing process is transferred to step (3).
f. This network individual is trained by training samples. If its training error is smaller than iterating error criteria of
MBP algorithm, then the fitness value is also the minE. And the computing process is transferred to step (3).
g. The whole linking weights are adjusted by MBP algorithm.
h. j = j + 1 , and the computing process is transferred to step e.
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i. If j is lager than iterating stop criteria of MBP algorithm, then the fitness value is also the minE. And the computing
process is transferred to step (3).
(4) If the evolutionary generation reaches its stop criteria or computing error reaches error criteria of evolutionary
algorithm, then the algorithm stop. At this time, the best individual in last generation is the searching result.
(5) Every individuals in population are mutated. For there are different data types in one individual, the different
mutation types are used for each parameter. For numbers of input neuron and hidden layer neuron are integer number,
the uniform mutation is used. For parameters η and α are real numbers, the adaptive Cauchi mutation is used. And
then the offspring population is generated.
(6) The fitness value of each individual in offspring population is calculated by the method in step (3).
(7) The set of offspring population and parent population is selected by selection operation based on thickness, then
the new offspring population is generated.
(8) The number of evolutionary generation increases 1, then the computing process is transferred to step (4).
From the above algorithm, the four parameters, number of input neuron, number of hidden layer neuron, two
parameters η and α in MBP algorithm can be confirmed. So, the optimization neural network for deviation section of
landslide displacement series can be gotten.
APPLICATION OF NEW INTELLIGENT METHOD IN REAL ENGINEERING EXAMPLE
To verify the above algorithm, the displacement time series of Xintan landslide [3] is used.
The displacement time series on key measured point of A3 is showed as in follow Table 1.
Table 1. Measured displacement and calculated displacement of Xintan landslide
Time
step
Measured
ones
Trend of
GM(1,1)
Deviation
section
Training
samples of
ENN
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
0.077
0.092
0.615
0.65
0.69
0.738
0.846
0.962
1.0
1.03
1.061
1.077
1.1
1.23
2.46
2.754
2.83
2.92
3.46
4.00
4.25
4.38
4.615
5.77
0.414
0.468
0.529
0.599
0.677
0.766
0.866
0.979
1.108
1.253
1.417
1.602
1.811
2.048
2.316
2.619
2.962
3.350
3.788
4.284
4.844
5.478
6.195
0.322
-0.146
-0.120
-0.091
-0.091
-0.080
-0.096
-0.020
0.078
0.192
0.34
0.502
0.581
-0.411
-0.437
-0.210
0.042
-0.109
-0.211
0.034
0.464
0.677
1.146
1.120
1.091
1.060
1.080
1.096
1.020
0.922
0.808
0.660
0.498
0.4184
1.411
1.437
1.210
0.957
1.110
1.211
0.966
0.535
Generalize
d results
Calculated
results
0.460
1.382
1.359
1.268
1.087
1.116
1.135
0.826
0.559
0.585
0.804
1.267
2.431
2.675
2.888
3.049
3.467
3.923
4.110
4.403
5.064
5.999
The measured displacements can also be showed in Figure 1. From the Figure, we can see that, the trend of
displacement is a kind of concave exponential curve. To model it, the GM(1,1) model is a suitable one. Also, to test the
forecasting capability of our algorithm, the data at step 23 and 24 cannot be used.
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Figure 1: Measured displacement and computing displacement of Xintan landslide
According to the model process of GM(1,1), we can get the GM(1,1) model of trend section as follows.
xˆ (1) (k + 1) = ( x ( 0 ) (1) −
0.379826 0.122959 k
0.379826
)e
+
− 0.122959
− 0.122959
(2)
From above model, we can get the trend series of landslide displacement. So, we can also get the deviation section
series. The two series are all showed in Table 1. By some pre-disposal to deviation section series, the samples of ENN
can be gotten, which is also showed in Table 1.
After computing, we can get the follow results. The number of input node is 12. The number of hiding node is 14. The
parameters in MBP algorithm are η = 0.226 and α = 0.948 .
By the above results, we can get the computing displacements as in Table 1 and Figure 1.
From the above results, we can get the follow conclusions. The new intelligent algorithm proposed in this paper can
reveal the essential rule of landslide displacements. It has not only the good approximated capability, but also the good
forecasting capability, and is a very good method for modeling the landslide displacement.
CONCLUSIONS
The new intelligent algorithm proposed in this paper can solve the problem of landslide displacement forecasting very
well. In this method, based on the principles of displacement decomposition, the trend of displacement time series is
extracted by Grey System and the deviation of Grey System is approximated by the new ENN. So, the different method
is used to model the different section of displacement. And the whole forecasting capability is very well. At last, one
real engineering example is used to verify this new algorithm, and the results are very well.
REFERENCES
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3. Huang ZQ. Study on non-linear mechanism of slope evolution and forecasting of landslide, Beijing, China,
1999 (in Chinese).
4. Liu HW, Fan J W. Forecasting and analysis of landslide displacement based on Grey System theory. J. Chengdu
Science and Technology Univ., 1992; 2: 57-64 (in Chinese).
5. Shi YS, Xu DJ. Application of time series analysis method in slope displacement forecasting. Rock and Soil
Mechanics, 1995; 16: 1-7.
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6. Gao W. Study on neural network method for displacement forecasting in geo-technical engineering.
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