A New Approach of Probabilistic Cellular Automata Using Vector Quantization Learning for Predicting Hot Mudflow Spreading Area

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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 2, February 2011

A New Approach of Probabilistic Cellular Automata
Using Vector Quantization Learning for Predicting
Hot Mudflow Spreading Area
Kohei Arai Achmad Basuki
Department of Information Science 1) Department of Information Science, Saga University
Saga University 2) Electronic Engineering Polytechnic Institute of
Saga, Japan Surabaya (EEPIS), Indonesia
Email: arai@is.saga-u.ac.jp Email: basuki@eepis-its.edu

Abstract— In this letter, we propose a Cellular Automata using The previous approach assumes that hot mudflow has similar
Vector Quantization Learning for predicting hot mudflow characteristics to lava flow such as thermal changing, fluid
spreading area. The purpoe of this study is to determine mass transport rules and material mixing.
inundated area in the future. Cellular Automata is an easy It is difficult to describe some physical phenomena caused by
approach to describe the complex states of hot mudflow disaster complex human made landscape objects such as levees,
that have some characteristics such as occurring on the urban
area, levees and surface thermal changing. Furthermore, the
buildings, and other environmental properties. Avolio et al. [4]
Vector Quantization learning determines mass transport in the have proposed an alternative Cellular using minimization
surrounding area in accordance with equilibrium state using differences to simulate lava flow. This approach has
clustering of landslide. Evaluating of prediction result uses stochastically state changing. The key-point of this approach is
ASTER/DEM and SPOT/HRV imaging. Comparison study shows easy to develop. Recently, D’Ambrossio et al. [5] and Del
that this approach obtains better results to show inundated area Negro et al. [6] have applied the stochastic approach to
in this disaster. simulate soil erosion. This approach also uses minimization
differences based on Cellular Automata for other fluid flow
Keywords: Probabilistic cellular automata, vector quantization, phenomena. The idea of the use of the stochastic approach
hot mudflow spreading, prediction, mass transport Introduction makes the alternative approach describe complex landscape
object problems on the hot mudflow disaster [7]. The problem
I. INTRODUCTION of this idea is how to fix probability value of mass transport on
Simulating hot mudflow in the plane and urban area requires each neighbor-cell.
understanding how the surface changing properties vary with The aim of this letter is a new approach of cellular automata
time and space. In order to generate complex flow about model for predicting hazardous area in the hot mudflow
interactions between natural and human made topography, we disaster. This approach uses some ideas such as minimization
need the model of the main mechanical features of hot mud difference model and vector quantization to make cluster of
depending on landscape data. Another difficulty is to compute mass transport possibility depend on altitude, height of mud
the simulation of hot mudflow at acceptable rates. However, and plant [8]. Because of cluster continuity by vector
they are difficult to apply in general conditions. quantization, it looks like the statistical behavior of landscape
Argentini [1] introduced a CA approach to simulate fluid object in the urban area. Vector Quantization determines
dynamic with some obstacles and fluid flow parameters. This cluster of inundated area [9] that makes flow difference in
approach used basic rules in the two-dimensional spaces. neighborhood area easy to define in probability values. A
Vicari [2] introduce CA approach to simulate lava flow. This similar approach has not yet been undertaken for mudflow and
approach used Newtonian fluid dynamic concept. lava flow in any other place, which appeared in the landslide
Combination of both approach obtained a discrete approach area. However, a simple cellular automata approach is
for predicting hot mudflow [3]. This approach yielded correct considered there.
location and direction of hazardous area, but the intersection Simulation results use the landscape map using ASTER DEM,
area between prediction area and real area of hazardous area is and initial parameters of hot mudflow. This paper shows some
around 36.44%. This approach is a deterministic approach simulation result on map view in the varying time and
based on Cellular Automata to estimate the areas potentially percentage of predicting performances. We also show the
exposed to hot mudflow inundation, concentrate mudflow comparison of predicting on inundated area and direction with
characteristics, combine fluid flow and lava flow properties, the other previous approach.
and neglect difficulty to describe a model of complex human
made landscape data and random behavior of state changing.

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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 2, February 2011
II. OVERVIEW OF FLUID DYNAMIC CELLULAR AUTOMATA parameters such as viscosity and surface thermal changing.
Most numerical approaches to modeling landscape This approach is powerful to simulate fluid flow and easy to
evolution simulate the physical flow such as mass transport of develop.
fluid particles, erosive effects of water discharge, infiltration
and absorption by solving complex differential equations. CA III. PROPOSED APPROACH
is an alternative approach to simulate fluid flow using a simple
approach. The current implementation is primarily based on A. General Characteristic of Hot Mudflow Disaster
D’Ambrossio et al. [5] because it uses "very simple On 29 May 2006, the gas exploration operation had caused
approximations intended to describe complex geographical cauldron of hot mud in 6.3 km depth spray out hot mud to
effect" and it able to offer "insight into how thermal and surrounding areas on Sidoarjo, East Java, Indonesia
viscous fluid parameter affects the evolution of landscapes" (7.530553°S; 112.709684° E) [13][14]. This disaster located at
despite its simplicity. the urban area near Sidoarjo (Figure 2-top). Hot mud had
The CA algorithm simulates first-order processes spilled over 5000 m3 per-day. It increased over 170,000 m3
associated with fluvial erosion by iteratively applying a set of per-day as reported by Cyranoski [15] and over 150,000 m3 as
simplified rules to individual cells of a digital topographic grid reported by Harsaputra [16].
[10]. The state represents a number of fluid particles in the
topographic grid, and the subsequent movement and behavior
(diffusion, and erosion) of the cell is controlled by the rules and
a few parameters of the current cell and its surrounding
neighbors [11]. The same rules are applied to all grid cells, i.e.,
there is no outside-imposed distinction between slope and
channel; the model forms its own channels [11].
Figure 1 illustrates how the algorithm works. For example,
fluid particles move to lower elevations, simulating fluid flow
in the landslide grid. There are two varying flows; erosion and
diffusion. The amount of erosion and diffusion each produces
is proportional to the local slope, simulating speedier erosion of
steeper slopes and lesser erosion of hard rock surfaces.

Figure 1. Schematic diagram showing how CA model works

Xiaoming Wei [12] introduced the simple CA approach for
highly viscous fluid. Its movement is mainly a result of gravity,
viscosity damping and friction. This approach uses four
variables to indicate the expanding potential of a liquid cell;
there is solid, liquid, amount of material and energy. Setting a Figure 2. The location of hot mudflow disaster
certain threshold for this variable enables to control the
expanding behavior of the liquid. For each liquid cell, if its Hot mudflow had an immense impact on environment,
energy is higher than a certain threshold, it has the potential to economic and human resource in the future if no
spread along its horizontal neighboring cells [17]. This countermeasure is conducted (Figure 2-bottom) [17]. Within
approach uses four nearest neighbors and four second nearest the first two years, the mud flow disaster destroy some villages,
neighbors. farm lands, factories and public facilities such as schools,
markets, roads, water pipes and gas pipes. Over 17,000 people
Another CA approach to simulate fluid flow uses the
had lost their houses and jobs. If facts, approximately mud
minimization difference approach that was introduced by
blows out 150,000 m3 per-day with the assumption that
Avolio [4] and D’Ambrossio [5]. This approach is one
contains 70% by water. This implies that water come out by
alternative approach to solve fluid dynamic without
687,000 barrel a day. This situation is different from some
sophisticated mathematical formulation. It obtains a
disaster areas where the previously occurred other locations
satisfactory model to simulate the lava flow with various
because it has overmuch mud [18].

33 http://sites.google.com/site/ijcsis/
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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 2, February 2011
Although one possible solution is spillway to Porong River, approach. The algorithm of Minimizatin Differences is as
it does cost and takes a long time and vast human resource. follow:
Therefore, strong demands on prediction of mudflow spreading
volume and mudflow disaster area as well as on how to (a) A is the set of cell not eliminated. Its initial value is set to
evacuate from the area of which the levee that was constructed the number of its neighbors. Each cell on position (i,j)
to prevent mudflow spillover are there for people who are has two components such as soil and mud. The height of
living in the disaster areas. If inundated area are predicted them are gij and sij. Total height of this cell is: hij = gij +
before the mud comes, the Indonesia government makes sij. There is dynamic soil uij, but it is the small portion of
countermeasures to reducing the impact. soil and we adjust on normal distribution of pm.
(b) The average height is found for the set of A of non-
This simulation uses map on February 2008 (Figure 3a) as eliminated cells:
initial map and map on August 2008 as target map (Figure 3b).
This map is landscape approximation using ASTER/DEM and hc + ∑ ci .hi
i∈ A
the height data on the some observation points. The map size is m= (1)
approximate 3.705km×4.036km. The red area is mud inundated nA + 1
area. In this simulation, mud blows from the main crater (big Where:
hole) that has a diameter around 20m [8], and mud moves to hc is height of the center cell.
other locations depend on slope difference and mudflow hi is height of the non-eliminated neighbor cells.
parameters. The key process is mass transport that defines the nA is number of non-eliminated neighbor cells.
amount of mud moving. c is current mass-transport weighting from the learning
process.
(c) The cells with height larger than average height are
eliminated from A.
(d) Go to step (b) until no cell is to be eliminated.
(e) The flows, which minimize the height differences locally,
are such that the new height of the non-eliminated cell is
the value of the average weighting height.
∑ ci .hi
hi = A (2)
nA
When we used probability adjustment depend on height
(a) (b) differences in the previous research, we use Vector
Quantization learning to make cluster space of mass transport
Figure 3. (a) Initial map on February 2008, (b) target map on August 2008
as a probability adjustment in the neighborhood area. We select
some points in the previous map and the nearest points in the
B. Model Definition current map as paired point. We use standard competitive
This model is 2D CA model. It uses two-dimensional grids learning to determine height of points around the surrounding
to describe set of cells. The state of cell S is floating point value area.
that shows the amount of mud and soil particles. In this
research, we define two-type variables of state; the amount of
(
c new = c old + τ c pair + c old ) (3)
mud st(x,y) and the amount of soil ht(x,y). Mud is moving Where:
material. It moves from one cell to its neighbors using
probability of move pmov. The other hand, the small part of mud c new is a new inundated point in the surrounding area.
also changes into the soil using probability of deposition pvis. c old is an inundated point in the previous map.
The model state is as shown in Figure 4. c pair is an inundated point in the current map.
τ is a learning rate.
pmov
st(x,y) In each point, there are some parameters that influence of
pvis mass transport on simulation process such as altitude (ground
ht(x,y)
height), mud height and landslide [8]. Because of the
discontinuous distribution of abrupt mass movement hazards
Figure 4. Mud and soil states. [19], VQ obtains an alternative method to quickly assess the
degree of hazard for each unit. It creates groups without
considering whether or not the units in the same group are
C. Model Definition
continuously distributed. Figure 5 shows the processing
In this research, we use probability Cellular Automata schema of hot mudflow spreading simulation. The learning
based on Minimization Differences [5][7] as the main process using vector quantization determines a cluster space
that describes the probability of mass transport. The probability

34 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 2, February 2011
values add some weighting under flow process in minimization resolution; minimization differences algorithm (48.15%-
differences approach. 65.67%) in our previous research, Avolio’s approach (45.75%-
63.34%) and Vicari’s approach (43.25%-60.25%). Comparison
of these methods is shown in figure 8.

Figure 5. The schematic of hot mudflow spreading simulation

IV. SIMULATION RESULTS (a) (b)
In this simulation, we use the current resolution of
ASTER/DEM (30m×30m). The mud blow volume is around
150.000 m3 per day using Gaussian random number around this
volume. The mixing particle is 70% water and 30% solid
material.

A. Simulation Results
The simulation result is shown as Figure 6. In this figure,
we show the total inundated area (Figure 6a) and the new
inundated area (Figure 6b). The red area is the real inundated
area, the blue area is the predicted area, and the pink area is
intersection between real area and predicted area. In Figure 7a,
the intersection area is above 95% that show this approach (c) (d)
yield a good result of prediction. It is not fair because the Figure 7. Comparison of (a) Vicari’s approach, (b) Avolio’s approach, (c)
prediction accuracy is only for new inundated area. Therefore, CA using Minimum Difference approach, (d) CA using VQ approach
we compare the predicted area and the real area in new
inundated area only. Figure 7b shows that the intersection area
in new inundated area is 71.85%. This result is better that the
previous result that uses minimization difference approach
(56.44%) [7]. Figure 7 shows the comparison between this
approach and other approach.

Figure 8. Comparison with the other approaches

B. Resolution Influences
This simulation runs in some resolution. In normal size, we
use ASTER/DEM map that has resolution 30m and image size
300x300 pixels. The minimum resolution is 200 pixels (map
(a) (b) resolution is 45m). The maximum resolution is 700 pixels (map
Figure 6. The simulation result: (a) total inundated area, (b) new inundated resolution is 12.9m). The prediction performance increases by
area using this approach increasing resolution and become stable on higher resolution as
shown in Fig. 9. This figure shows there are two peak points of
Figure 8 shows combination of CA approach and online intersection area; in resolution 30m and in resolution 20m.
clustering using vector quantization obtain better performance They occur because the resolution of our ASTER/DEM data is
to predict new inundated area (54.13-69.13%) than previous 30m, and we use another data (height data on critical points)
methods in 3x3 Von-Newmann neighborhood system in all that have resolution 20m.

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(IJCSIS) International Journal of Computer Science and Information Security,
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[1] Argentini G, 2003, A first approach for a possible cellular automaton
model of fluids dynamic. Computer Science - Computational AUTHORS PROFILE
Complexity, arXiv:cs/0303003v1.
[2] Vicari A, Alexis H, Del Negro C, Coltelli M, Marsella M, and Proietti C, Kohei Arai
2007, “Modeling of the 2001 Lava Flow at Etna Volcano by a Cellular He received BS, MS and PhD degrees in 1972,74 and 82, respectively.
Automata Approach”, Environmental Modelling & Software 22, He was with The Institute for Industrial Science and Technology of the
pp.1465-1471. University of Tokyo from April 1974 to December 1978 and also was with
National Space Development Agency of Japan from January 1979 to March
[3] Kohei Arai, and Achmad Basuki, 2010, A Cellular Automata Based
1990.During from 1985 to 1987, he was with Canada Centre for Remote
Approach for Prediction of Hot Mudflow Disaster Area, Computational
Sensing as a Post Doctral Fellow of National Science and Engineering
Science and Its Applications – ICCSA 2010, Part II, Lecture Notes in
Research Council of Canada.He moved to Saga University as a professor in
Computer Science 6017, Springer-Verlag Berlin Heidelberg, pp. 119-
Department of Information Science in April 1990.He was councilar for the
129.
Aeronoutics and space related technology committee of the Ministry of
[4] Avolio MV, Di Gregorio S., Mantovani F., Pasuto A., Rongo R., Silvano Science and Technology during from 1998 to 2000. He was councilar of the
S., and Spataro W. (2000), Simulation of the 1992 Tessina Landslide by Saga University for 2002 and 2003. Also he was executive councilar for the
a Cellular Automata Model and Future Hazard Scenarios, International Remote Sensing Sciety of Japan for 2003 to 2005. He is now Adjunct Prof. of
Journal of Applied Earth Observation and Geoinformation, Volume 2, the University of Arizona, USA since 1998. He also is Vice Chiarman of the
Issue 1, pp.41-50. Commission A of ICSU/COSPAR sice 2008. He wrote 26 books and
[5] D’Ambrosio D., Di Gregorio S., Gabriele S. and Claudio R. (2001), A published 227 journal papers.
Cellular Automata Model for Soil Erosion by Water, Physic and
Chemistry of The Earth, EGS, B 26 1 2001, pp.33-39.
Achmad Basuki
[6] Ciro Del Negro, Luigi Fortuna, Alexis Herault, Annamaria Vicari He received BS and MS degrees in 1992 and 2002 respectively.
(2008), Simulations of the 2004 lava flow at Etna volcano using the He was with Electronic Engineering Polytechnic Institute of Surabaya from
magflow cellular automata model, Bulletin of Volcanology, Volume 70, April 1994. Now he studies at Department of Information Science, Saga
Number 7/May, 2008, pp. 805-812, Springer Berlin/Heidelberg, 2008 University for PhD Degree from April 2009. His field is Disaster Spreading
[7] Kohei Arai, Achmad Basuki, Simulation Of Hot Mudflow Disaster With Modeling. He wrote 6 books in Indonesian language and published 20
Cell Automaton And Verification With Satellite Imagery Data, publication papers for conferences and journals.
International Archives of the Photogrammetry, Remote Sensing and

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