What is the point of models

1.1. Models and modeling

This section is intended to provide an insight into the modeling method. According to the common usage, the word has model at least seven distinguishable from each other Meanings. One of these is selected and used in the following:

Under a model An object or system (of the original) is understood to be a similar object or system with the help of which one can solve tasks that are not possible or not expedient to solve on the original.

The general properties of models form the basis of various Classifications.

Well you can aims and reasons for and against the use of the model are discussed. Applications of models are with Conclusions by analogy connected so that the general structure of a conclusion by analogy is to be considered.

Finally, the field of view is narrowed further, and Simulation models occur as a special class of models. They are dynamic models in which processes or time sequences are simulated.

History of modeling

The Greeks and Romans used models made of wood, wax, clay or plaster as a prototype or copy (simulacrum).

Real objectModel usage
ArtworkClear presentation before execution
cityPresentation of conquests on the occasion of triumphal parades

This stone cube was found on the beach of the Black Sea and probably dates from the first century BC. Its sides are marked with letters from the Greek alphabet. You can find it in the Odessa Archaeological Museum. What purpose may this cube have served?

cube are still important props for many today Games. Games are often models of real or fantastic, imagined parts of the world. The effects of chance are reproduced with the dice.

The surface of a Icosahedron or regular twenty flax is made up of twenty equilateral triangles. If you distribute the digits from 0 to nine in such a way that each stands on exactly two triangles, the icosahedron is the ideal decimal cube.

Models and Systems

Two reference works are cited on the current meaning of the word model:

Large foreign dictionary (Bibliography Institute Leipzig 1980)

model

  1. Sample / prototype / type / design
  2. scaled down replica
  3. Wooden or metal model for mold
  4. A piece of clothing that is only available once and made according to a special design
  5. figurative or living object of study by the artist
  6. Visual spatial image (stereometry)
  7. Simplifying replication of essential structures and functions of complicated and complex formations of reality in order to solve a certain task, which the mastering of the original is impossible or inexpedient

American Heritage Dictionary

model n.

  1. A small object, usually built to scale, that represents in detail another, often larger object.
  2. a. A preliminary work or construction that serves as a plan from which a final product is to be made. b Such a work or construction used in testing or perfecting a final product ..
  3. A schematic description of a system, theory, or phenomenon that accounts for its known or inferred properties and may be used for further study of its characteristics.
  4. A style or design of an item.
  5. One serving as an example to be imitated or compared.
  6. One that serves as the subject for an artist, especially a person employed to pose for a painter, sculptor, or photographer.
  7. A person employed to display merchandise, such as clothing or cosmetics.
  8. Zoology. An animal whose appearance is copied by a mimic.

The model term used in this course corresponds to the seventh word meaning in the German version and comes close to the third in the English version:

model
of an object (of the original) is a similar object, with the help of which a task can be solved, the solution of which is not possible or not expedient on the original.
Similar must be those properties that are essential to the task.

The classic model is the solution one Task or class similar Tasks. Today, models that provide a solution are used to an increasing extent more diverse Serve tasks or different classes of tasks.

A flight simulator is a device that is used for
  • retraining on a new type of aircraft,
  • the training of emergency situations and
  • reviewing pilots' responses and skills
is being used.

A more general formulation can be found in (Klaus / Liebscher 1976):

The concept of the model
is a three-digit relation R.(M, S, O).
In it is M. the model, S. a cybernetic system for which M. the model represents and O the object from which M. is a model.
When between an object M. and an object O There are analogies M. for a cybernetic system S. (Subject) model, provided that informational relationships can contribute to the behavior of S. across from M. to influence.

The word is often found in practical usage and also in the following text system. Its meaning is explained here pragmatically:

system
is the general name for the object to be examined, for the original, for the area of ​​reality for which a model is being built or used. A dynamic system that changes over time is often called process. The sequence of changes that occur in a system is also referred to as a process.

The attached collection of quotations on modeling and simulation gives a more precise idea of ​​the use of these terms, especially in textbooks.

Modeling as a Scientific Method

The concept of a model that has just been introduced leaves open the classes of tasks for which models are used. To put it simply, one can say: a model of an original is a somehow useful object that is similar to the original. A model of this type is also referred to below as Model in the broader sense are designated.

In the natural and technical sciences, the concept of a model is often more narrowly defined:

model
is the name of a similar object that can be investigated and experimented with in order to transfer the knowledge gained on the model to the original. Such a model is intended here as Model in the strict sense are designated.

Modeling in the strict sense comprises the following stages or stages of work:

  • the determination of a task for the use of the model,
  • the creation or selection of a model for an original system,
  • checking and ensuring the conformity of the model with the task that verification is called,
  • the observation of the original system with the aim of obtaining observation values ​​that are to be included in the model as input data or parameter values,
  • checking the correspondence of the model and the original with regard to the task at hand, too Validation called,
  • Investigations, calculations and experiments on the model with the aim of gaining knowledge,
  • the transfer of the knowledge to the original and
  • checking the validity of the model-related findings for the original.

The modeling understood in this way is a fundamental method of scientific work. Other basic methods of scientific work are observation and measurement, abstraction, classification and theorizing. Theories often have classes of models for real classes of objects as their content.

Classification of models

Models can be classified according to the similarity of properties. How to label a model as

attributedescription
geometric,if it is geometrically similar to the original,
physically,if it uses physical effects that also occur in the original,
biological,if it is biologically related or similar to the original,
material,if substances are used in it that also appear in the original,
structurally,if there is a structural similarity to the original, d. H. has the same named components and the same relations between them,
functional,if its function, d. H. its input-output behavior is similar to the original,
stochastic,if random influences and components occur in it, if random generators are used to simulate the random influences occurring in the original,
deterministic,if there are no random influences,
static,if there are no time-dependent changes in it,
dynamic,if it is subject to time-dependent changes,
continuous or continuous,if all quantities occurring in it are continuous functions of time and no sudden changes in value or status occur,
discreet,if there are sudden changes in value or status,
combined,if there are sudden changes in value or status and, in addition, non-linear, time-dependent processes that can be represented by differential equations,
physically,when it exists in material, physical form
abstract or mathematical,if it is not physical, but is suitable as an abstract image of the original for the solution of tasks (identifications, deductions and calculations are possible as tasks),
Computer model,if the computer is used as a model of the original object with a suitable program. Those to be introduced later Simulation models are predominantly computer models: the computer and program together form the model that is being experimented with.

This classification is not disjoint: Belonging to a class excludes belonging to another class Not out. A model can e.g. B. be geometrical, physical and functional at the same time.

Operations research, a branch of applied mathematics, deals with mathematical models of systems and processes in the areas of logistics, manufacturing, transport and other fields of application. Please have a look at http://opsresearch.com/cgi-bin/mainIndex.cgi for an interesting, java-based collection of such models!

Examples

classCity-
lock
Berlin
Ver
search-
animal
Promotional
system
Flight-
simu-
lator
Barber
Shop
University-
place
Day
construction
geometric+-++-+-
physically--++---
biological-+-----
structurally+++++++
functional-++++++
stochastic (s)
determined (d)
dsdssss
static (s)
dynamic (d)
sdddddd
physically++++---
abstract---++++
Computer model---++++

Picture: Model of the Berlin City Palace
Built in 1994 on a 1: 1 scale


Picture: Model of a conveyor system
at the Institute for Materials Handling, ..., Logistics at the University of Magdeburg
built from components of a model kit system


Each model attribute is the basis of a possible classification.

This is the simulation model of a hairdressing salon
  • not geometrical, if it does not take into account the geometrical positions of the acting objects (hairdresser, customers).
  • not physical, because its physical properties do not match the original,
  • not biological because it has no biological properties,
  • not material because it has no relation to the material composition of the original,
  • abstract, because many properties of the original (e.g. material, physical, noises and smells) are abstracted,
  • structural, because you can find components of the original in the model,
  • functional, because the input-output behavior of the model comes close to or should come close to the original,
  • stochastic, because the times between the arrival of two customers and the length of time the hairdresser was served are modeled as random variables,
  • not determined or deterministic, because random influences are modeled,
  • not static, but
  • dynamic, because changes over time are simulated,
  • discreet, because sudden changes in value and status occur, and
  • Computer model, because the computer acts as a model when it is processed.

Objectives of using the model

The use of models instead of originals has four classic goals:

aimcommentModel category
entertainment Almost all games create artificial reality Models
in the further
sense
replacementA computer can serve as a replacement for a computer that is no longer or not yet available. A prosthesis is a replacement for a missing or defective organ.
trainingSimulators enable safe and inexpensive training for pilots, system operators and dispatchers. Training the reaction in emergency situations is not possible on the original
Knowledge gainFindings from model experiments are transferred to the original by analogy conclusions Model in the strict sense

For simulation and animation models, further goals have been added in recent years, which will be discussed at the appropriate point.

Reasons for and against using a model

Models as artificial reality are used instead of originals because they

  • cheaper or more accessible,
  • available sooner or later,
  • safe to use and
  • usable with a different time scale

are.

hazards the use of models

in the uncritical transfer of results to realityResults of model experiments can only be transferred to the original by analogy conclusions. You don't always need to be true.
in the manipulability of the resultsBecause models and results can be manipulated, the simulation is already available as a High tech justification tool to justify arbitrary decisions.

Two clear examples of situations where experiments on the original are not possible are cited here:

Conclusions by analogy

Findings from the use of a model M. will be through Conclusion by analogy on the original O transfer. An inference by analogy has the following format:
O has the properties 1, 2,. . , n
M. has the properties 1, 2,. . , n+1
______________________________________
Also O has the property n+1

Inferences by analogy are not logical, but inductive. They are based on the hope that the similarity between the original and the model is greater than is known with certainty.

Example of a conclusion by analogy

Humans have a known anatomical structure and physiological functionality.
The experimental animal pig is anatomically and physiologically similar to humans.
The new drug X stimulates the pig's circulation.
___________________________________________________________
X also stimulates the human cycle.
In order to reduce the uncertainty of conclusions by analogy, models validated. This is understood to mean the determination of the degree of conformity with the original with regard to the intended use goal (s).
Improving the match between the model and the original is called calibration designated.

Simulation and animation models

Simulation models or Simulators
are dynamic models that are usually implemented by programs. The simulation clock or simulation time runs while they are being processed, and status changes are simulated in a chronological sequence that corresponds to the time and process sequence in the original.
simulation
is the development and use of simulation models.
Features or properties of the original are represented in the model by model parameters or model variables. Processes running in the original are represented by algorithms.
Simulation run
is the one-time execution of the simulation model for the set total simulation time or Simulation duration.

The simulation models to be considered in the following are not geometrical, physical, biological or material.

  • They are abstract.
  • They are structural: they contain components of the original and their relationships.
  • They are functional because they reflect the reaction of the original system to external influences.
  • They are continuous, discreet or combined. The following text focuses on discrete models.
  • After all, they are almost always computer models.

Only introductory examples are carried out by hand, with a sheet of paper, a pencil and a random number tablet. Simulation and simulation models are subjects of the next section.

Animation models
are called models that make temporal processes visually accessible, preferably in a pictorial, non-textual form. They create sequences of images which, when changed quickly, give the impression of movement.
The generated images are geometrically similar to the original. An animation model is either a component of a simulation model or it is supplied with data from the simulation model. Data that describe a chronologically ordered stream of events are called Trace data.

Animation models are models in the broader sense. The aim of their use is often the validation of the underlying simulation models. In addition, they serve less to gain knowledge than to present or explain processes and models.

Animation and animation models are subject of Section 1.3.

Control questions

Basic concepts of modeling and simulation

  1. What are some of the current meanings of the word model?
  2. Which model term is used in this course?
  3. What is a simulation model?
  4. What does simulation mean?

Classes of models

  1. How can you classify models?
  2. How do you distinguish between discrete and continuous models?
  3. When are models called stochastically?
  4. What do you understand by a geometric model?
  5. What are dynamic models and what are the names of non-dynamic models?
  6. What are the characteristics of stochastic models and what are the names of non-stochastic models?
  7. How do discrete and continuous models differ?
  8. Name some classes of models and corresponding examples.
  9. What are verification and validation of a model?

Model usage

  1. Explain some of the goals of using models.
  2. What are the reasons for using models instead of real objects?
  3. Give some reasons that speak against the use of models!
  4. What advantages do experiments on the original have over model experiments?
  5. Why do you simulate computers by computers?

Gaining knowledge with models

  1. How do you use models to gain knowledge?
  2. Explain the structure of a conclusion by analogy!
  3. Compare the conclusion by analogy with deductive inferences!
  4. Give an example of a conclusion by analogy!

literature

Buslenko, N.P. and J.A. Schreider. The Monte Carlo method and its implementation with electronic digital computers. Leipzig, B.G. Teubner Verlagsgesellschaft 1964
Klaus, G. and K. Liebscher, Eds. Dictionary of Cybernetics. Berlin 1976
Law, A.M. and W.D. Kelton. Simulation Modeling and Analysis. Second Edition McGraw-Hill New York 1991
Sobol, I. M. The Monte Carlo Method. Chicago, The University of Chicago Press 1974