continuous and discrete model
TRANSCRIPT
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8/12/2019 Continuous and Discrete Model
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Dr. Pratiksha Saxena
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Numerical simulation approach
Level of Aggregation Policies versus Decisions
Aggregate versus Individuals
Aggregate Dynamics versus Problem solving
Difficulty of the formulation
Nature of the system/problem
Nature of the questionNature of preferred lenses
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Advances in system development ultimately rely on well-constructed predictive models
Applications: traditional fields such as electrical and mechanical engineering
newer domains such as information and bio-technologies
Using appropriate simulation software, we can derivesolutions to difficult problems using such models
Success often depends on having a variety of modelingapproaches available to formulate the right model for theparticular issue at hand
Therefore, a broad familiarity with different types ofmodels is desirable
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1. Static or dynamic models
2. Stochastic, deterministic or chaotic models
3. Discrete or continuous change/models
4. Aggregates or Individuals
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Dynamic: State variables change over time
(System Dynamics, Discrete Event, Agent-
Based, Econometrics?) Static: Snapshot at a single point in time
(Monte Carlo simulation, optimization
models, etc.)
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Deterministic modelis one whose behavior
is entire predictable. The system is
perfectly understood, then it is possible to
predict precisely what will happen.
Stochastic modelis one whose behavior
cannot be entirely predicted.
Chaotic modelis a deterministic model
with a behavior that cannot be entirely
predicted
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Discrete model: the state variables change
only at a countable number of points in time.
These points in time are the ones at which
the event occurs/change in state.Continuous: the state variables change in a
continuous way, and not abruptly from one
state to another (infinite number of states).
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Continuous system models were the firstwidely employed models and aretraditionally described by ordinary andpartial differential equations.
Such models originated in such areas asphysics and chemistry, electrical circuits,mechanics, and aeronautics.
They have been extended to many new areassuch as bio-informatics, homeland security,and social systems.
Continuous differential equation modelsremain an essential component in multi-formalism compositions.
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A host of formalisms have emerged in the lastfew decades that greatly increase our ability toexpress features of the real world and employthem in engineering systems.
Such formalisms include Neural Networks, FuzzyLogic Systems, Cellular Automata, Evolutionaryand Genetic Algorithms, among others.
Hybrid models combine two or more formalisms,e.g., fuzzy logic control of continuousmanufacturing process.
Most often, applications will require such hybridsto address the problem domain of interest.
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Principal
Interest
AverageInterest Rate
Noise
SimulatedPrincipal
Sim Interest
EstimatedInterest Rate
Noise Seed
ObservedInterest Rate
Continuous and Stochastic
Continuous and Deterministic
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Discrete and stochastic
SimulatedPrincipal 1 0
Sim Interest 1 0
AveragePrincipal 0
Averagingtime 0
ObservedInterest Rate 0
SimulatedPrincipal 1
Sim Interest 1
AveragePrincipal
Averagingtime
Observed
Interest Rate
Discrete and Deterministic
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Aggregate model: we look for a more distant
position. Modeler is more distant. Policy
model. This view tends to be more
deterministic. Individual model: modeler is taking a closer
look of the individual decisions. This view
tends to be more stochastic.
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2 approaches:
Time-slicing: move forward in our models in equal
time intervals.
Next-event technique: the model is only examined
and updated when it is known that a state (or
behavior) changes. Time moves from event to event.
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Only from a more distant perspective in which
events and decisions are deliberately blurred
into patterns of behavior and policy structure
will the notion that behavior is a consequence
of feedback structure arise and be perceived
to yield powerful insights.
(Richardson, 1991)
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5. Integration of variables directly evaluated
by analog computers while Dc uses numerical
approximation to solve it.
6. DC can be programmed to any degree ofaccuracy as they use floating point
representation of nubers and can tolerate
extremely wide range of variations.
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1. understand geology of place
2.physical appereance of reservoir and
continuity of flow
3. objective of studyCollect results in concrete terms-material
balance study, water cut, reservoir pressure
4. data is gathered-water spread property
called permeability, map of reservoir nadmeasurement of porosity
5.initial simulation run made to calculate
oroginal water at the site- input
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From the expected growth pattern and
seasonal fluctuations, curve of the projected
demand
Input-river inflow+rainfallNext simulation run to match the historical
data for pressure, water cut, porosity,
permeability
This run takes maximum time(not constant) Seepage and evaporation losses
Output by simulation run