Modelling Wildfire Dynamics via Interacting Automata

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Modelling Wildfire Dynamics via Interacting
Automata
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• Original title
• Modelling Wildfire Dynamics via Interacting
  Automata
• Authors
• Adam Dunn, George Milne
• Autorhs of this presentation
• Slawomir Chylek (S.Chylek_at_stud.elka.pw.edu.pl)
• Mariusz Kostrzewa (M.T.Kostrzewa_at_stud.elka.pw.edu.
  pl)

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• Table of contents
• Abstract
• Related research
• Modelling fire spread
• Modelling wildfire via interactive automata
• Cellular automata
• Circal formalism
• Encoding spatial information
• The discretisation of the landscape
• Neighbourhood
• Next state transition function
• Application

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• Abstract
• This document is describing basic concept of
  students project which goal is to build computer
  program simulating spreading of wildfire. The
  idea of algorithm for prediction was created by
  Adam Dunn and George Milne in their article
  Modelling Wildfire Dynamic via Interactive
  Automata

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• Modelling wildfire spreading
• Fire spread is socially and economically
  important, also it is complex problem, difficult
  to to model ant it is computationally expensive
  to simulate.
• A specific problem is the heterogeneity of
  landscape.

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• Related research
• Previous approaches to modeling the fire spread
  were
• empirically-based
• physically-based,
• a combination of both of these.

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• The landspace comprises variables like
• Fuel load
• Slope gradient
• Slope orientation
• Wind
• Our model of landscape uses only the for variable
  mentaned above.

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• Modelling wildfire via interactive automata
• We use cellular automata principles to discretise
  the time and space of the model, the interactions
  between the cells are defined explicitly as a set
  of actions.
• The spatial information are encoded into cellurar
  state.

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• Cellular automata
• A cellular automaton (plural cellular automata)
  is a discrete model studied in computability
  theory, mathematics, and theoretical biology. It
  consists of an infinite, regular grid of cells,
  each in one of a finite number of states. The
  grid can be in any finite number of dimensions.
  Time is also discrete, and the state of a cell at
  time t is a function of the states of a finite
  number of cells (called its neighborhood) at time
  t-1. These neighbors are a selection of cells
  relative to the specified cell, and do not
  change. (Though the cell itself may be in its
  neighborhood, it is not usually considered a
  neighbor.) Every cell has the same rule for
  updating, based on the values in this
  neighbourhood. Each time the rules are applied to
  the whole grid a new generation is created. (from
  www.wikipedia.org)

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• Circal formalism
• CIRcuit CALculus is a process algebra whose basic
  features permit a natural representation of time
  without any extension to the process algebra
  framework together with a constraint-based
  modelling mechanism, in which the behaviour of a
  process may be contrained simply by composing it
  with another process which represents the
  constraint. Timing events can be represented as
  ordinary actions, which follow the same rules as
  any other action. The use of this representation,
  on top of constraint-based modelling, results in
  a methodology for describing timing constraints
  within variuos time models.

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• Circal terms
• Process - a process is simply a state of the
  system, that evolves from one process to another.
  A process also
• designs the possible future behaviour of a system
  that is in this state.
• Event - an event is a signal that is shared by
  some of the processes, and the set of asserted
  events determines
• the new state of the system (like transitions in
  finite state machines).
• Sort - the sort of a process is the set of
  events it can respond to.
• Environment - all the events that are in the sort
  of the implemented processes form the
  environment, that
• is in fact the interface between a Circal system
  and the real hardware system that it controls.

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• Circal operators
• Termination - ? is a deadlocked process, that
  cannot evolve.
• Guarding - Given a process P and a non-empty set
  of events S, S P is a process that synchronises
  to perform all the events of S and then behaves
  as P
• Choice - Given two processes P and Q, PQ is a
  process that can behave either as P or as Q,
  depending on the environment (i.e. of the
  asserted events).
• Non-determinism - Given two processes P and Q,
  PQ is a process that can behave either as P or
  as Q, with the choice depending only on the
  process itself, and being independent of the
  environment.
• Composition - Given two processes P and Q, PQ is
  a process that runs P and Q in parallel, with
  synchronisation occurring for shared events.
• Abstraction - Given a process P and event set S,
  P-S is a process that behaves as P and that
  encapsulates the events of S, which are then
  hidden externally.
• Relabelling - Given a process P and two events a
  and b, Pa/b behaves as P, except that all
  occurences of event b are replaced by event a.
• Definition - Given a process Q and an identifier
  P, P?Q defines P to have the behaviour of Q, thus
  allowing recursive definitions.
• Others

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• Encoding spatial information
• To encode the state in the automation we use the
  state defined as follows
• sS F ? S ? O ? W,
• F (fuel), S (slope gradient), O (slope
  orientation), W (wind),
• F unburnt, burning, burnt
• S flat, slight, mid, steep,
• O n, s, e, w,
• W f, n, nw, w, sw, s, se, e, ne,

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• The discretisation of the landscape
• divided into equally sized cells,
• specified map of neighborhood
• each cell's state determined by a next-state
  transition function.

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• Neighbourhood

Center cell
Neighbourhood of center cell
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• Next state transition function
• Example function for cell slopes upwards towards
  the north and has midranged gradient and an
  eastearly wind direction.

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• Application (1)
• Input data
• Landscape
• Start points of fire spread
• Input data are read from a file or randomly
  generated.

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• Application (2)
• The fire spread is visualized dynamically
• Results are written to a file in a gnuplot format
• State of every cell
• Sum of unburned/burning/burned cells

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• Application (3)
• Testing criteria
• Fire spread goes in every direction on flat land
  without wind
• Fire spread makes ellipse on slope terrain
• Fire spread goes in the same direction as wind

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• Thank for your attention.