System properties of the model. Basics of systems modeling. General characteristics of the processes of collection, transmission and processing of information
Model (lat. modulus - measure) is a substitute object for the original object, which provides the study of some of the properties of the original.
Model - a specific object created for the purpose of obtaining and (or) storing information (in the form of a mental image, description by symbolic means or a material system), reflecting the properties, characteristics and connections of an object - an original of arbitrary nature, essential for the task solved by the subject.
Modeling - the process of creating and using the model.
Modeling goals
- Knowledge of reality
- Experimenting
- Design and management
- Predicting object behavior
- Training and education of specialists
- Data processing
Classification by presentation
- Material - reproduce the geometric and physical properties of the original and always have a real embodiment (children's toys, visual teaching aids, models, models of cars and airplanes, etc.).
- a) geometrically similar large-scale, reproducing the spatial and geometric characteristics of the original, regardless of its substrate (models of buildings and structures, educational dummies, etc.);
- b) based on the theory of similarity, substrate-like, reproducing with scaling in space and time the properties and characteristics of the original of the same nature as the model (hydrodynamic models of ships, blowing models of aircraft);
- c) analog instrumental, reproducing the investigated properties and characteristics of the original object in a modeling object of another nature on the basis of some system of direct analogies (a variety of electronic analog modeling).
- Information - a set of information characterizing the properties and states of an object, process, phenomenon, as well as their relationship with the outside world).
- 2.1. Verbal - verbal description in natural language).
- 2.2. Iconic - information model, expressed by special signs (by means of any formal language).
- 2.2.1. Mathematical - a mathematical description of the relationship between the quantitative characteristics of the modeling object.
- 2.2.2. Graphic - maps, drawings, diagrams, graphs, diagrams, graphs of systems.
- 2.2.3. Tabular - tables: property object, object object, binary matrices, and so on.
- Ideal - material point, absolutely rigid body, mathematical pendulum, ideal gas, infinity, geometric point, and so on ...
- 3.1. Unformalized models - systems of ideas about the original object, formed in the human brain.
- 3.2. Partially formalized.
- 3.2.1. Verbal - a description of the properties and characteristics of the original in some natural language (text materials of project documentation, a verbal description of the results of a technical experiment).
- 3.2.2. Graphic iconic - features, properties and characteristics of the original, really or at least theoretically available directly to visual perception (artistic graphics, technological maps).
- 3.2.3. Graphic conditional - data of observations and experimental studies in the form of graphs, diagrams, schemes.
- 3.3. Quite formalized (mathematical) models.
Model properties
- Limb: the model reflects the original only in a finite number of its relations and, in addition, the modeling resources are finite;
- Simplification: the model displays only the essential aspects of the object;
- Approximation: reality is shown by the model roughly or roughly;
- Adequacy: how well the model describes the system being modeled;
- Informativeness: the model must contain sufficient information about the system - within the framework of the hypotheses adopted when building the model;
- Potentiality: predictability of the model and its properties;
- Complexity: ease of use;
- Completeness: all necessary properties are taken into account;
- Adaptability.
- The model is a "four-place construction", the components of which are the subject; the task solved by the subject; the original object and the description language or the way the model is reproduced. The task solved by the subject plays a special role in the structure of the generalized model. Outside the context of a problem or class of problems, the concept of a model has no meaning.
- Generally speaking, each material object corresponds to an infinite set of equally adequate, but essentially different models associated with different problems.
- A task-object pair also corresponds to a set of models containing, in principle, the same information, but differing in the forms of its presentation or reproduction.
- The model, by definition, is always only a relative, approximate similarity of the original object and, in terms of information, is fundamentally poorer than the latter. This is its fundamental property.
- The arbitrary nature of the original object, which appears in the adopted definition, means that this object can be material and material, can be of a purely informational nature and, finally, can be a complex of heterogeneous material and information components. However, regardless of the nature of the object, the nature of the problem being solved and the method of implementation, the model is an information education.
- Particular, but very important for theoretically developed scientific and technical disciplines is the case when the role of the object-modeling in a research or applied problem is played not by a fragment of the real world, considered directly, but by some ideal construct, i.e. in fact, another model, created earlier and practically reliable. Such a secondary, and in the general case, n-fold modeling can be carried out by theoretical methods, followed by verification of the results obtained using experimental data, which is typical for fundamental natural sciences. In less theoretically developed fields of knowledge (biology, some technical disciplines), the secondary model usually includes empirical information that existing theories do not cover.
2. General features and properties of models.
Common features of models
1. The model is a "four-place construction", the components of which are the subject; the task solved by the subject; the original object and the description language or the way the model is reproduced. The task solved by the subject plays a special role in the structure of the generalized model. Outside the context of a problem or class of problems, the concept of a model has no meaning.
2. Each material object corresponds to an innumerable set of equally adequate, but essentially different models associated with different tasks.
3. A task-object pair corresponds to a set of models containing, in principle, the same information, but differing in the forms of its presentation or reproduction.
4. The model is always only a relative, approximate semblance of the original object and in terms of information is fundamentally poorer than the latter.
5. The arbitrary nature of the original object, which appears in the adopted definition, means that this object can be material and material, can be of a purely informational nature and, finally, can be a complex of heterogeneous material and information components. However, regardless of the nature of the object, the nature of the problem being solved and the method of implementation, the model is an information education.
6. In a particular case, the role of the object of modeling in a research or applied problem is played not by a fragment of the real world, considered directly, but by some ideal structure, ie. in fact, another model, created earlier and practically reliable.
PROPERTIES OF MODELS
1) limb: the model reflects the original only in a finite number of its relations and, in addition, the modeling resources are finite;
2) simplification: the model displays only the essential aspects of the object;
3) approximation: the reality is displayed by the model approximately;
4)· adequacy: the degree of success of the model's description of the modeling object;
5) informativeness: the model must contain sufficient information about the system - within the framework of the hypotheses adopted when building the model.
- purposefulness - the model always reflects a certain system, i.e. has a purpose;
- finiteness - the model displays the original only in a finite number of its relations and, in addition, the modeling resources are finite;
- Simplicity - the model displays only the essential aspects of the object and, in addition, should be easy to study or reproduce;
approximation - the reality is shown by the model roughly or approximately;
- adequacy - the model should successfully describe the modeled system;
- clarity, visibility of its main properties and relationships;
- availability and manufacturability for research or reproduction;
- informativeness - the model should contain sufficient information about the system (within the framework of the hypotheses adopted in the construction of the model) and should make it possible to obtain new information;
preservation of the information contained in the original (with the accuracy of the hypotheses considered when constructing the model);
- completeness - the model should take into account all the basic connections and relationships necessary to ensure the goal of modeling;
- stability - the model should describe and ensure the stable behavior of the system, even if it is initially unstable;
- integrity - the model implements some system (i.e. the whole);
- isolation - the model takes into account and displays a closed system of necessary basic hypotheses, connections and relationships;
- adaptability - the model can be adapted to various input parameters, environmental influences;
- controllability (imitation) - the model must have at least one parameter, the changes of which can imitate the behavior of the modeled system under various conditions;
- evolving - the possibility of developing models (previous level).
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The main properties models... - purposefulness - model always displays some system, i.e. has a purpose; - limb ... -
The main properties models... - purposefulness - model -
The main properties models... - purposefulness - model always displays some system, i.e. has a purpose; - limb - m. -
The main properties arithmetic mean. To reduce the complexity of calculations used the main properties Wed arithm -
The main properties living organisms. A) The unity of the chemical composition.
It is associated with the acquisition of new characteristics by organisms and properties. -
Two properties total benefits: 1) non-competitiveness, i.e. an increase in the number of consumers of the good does not entail a decrease in the utility provided to each of them. -
Model sliding threads Huxley and her the main provisions.
Water is a medium with a large number of hydrogen bonds, it is they who determine the special properties water
A type model depends on the informational essence of the modeled system, on the connections and relations of its subsystems and elements, and not on its physical nature.
For example, mathematical descriptions ( model) the dynamics of the epidemic of an infectious disease, radioactive decay, the acquisition of a second foreign language, the release of products of a manufacturing enterprise, etc. can be considered the same in terms of their description, although the processes themselves are different.
The boundaries between models of various types are rather arbitrary. We can talk about different modes of use models - imitation, stochastic, etc.
Typically the model includes: object O, subject (optional) A, task Z, resources B, environment modeling FROM.
The model can be formally represented as: M \u003d< O, Z, A, B, C >.
The main properties any model:
- purposefulness - the model always reflects a certain system, i.e. has a purpose;
- finiteness - the model reflects the original only in a finite number of its relations and, in addition, the modeling resources are finite;
- simplicity - the model displays only the essential aspects of the object and, in addition, should be easy to study or reproduce;
- approximation - the reality is shown by the model roughly or approximately;
- adequacy - the model must successfully describe the modeled system;
- visibility, visibility of its main properties and relationships;
- availability and manufacturability for research or reproduction;
- informativeness - the model should contain sufficient information about the system (within the framework of the hypotheses adopted when building the model) and should make it possible to obtain new information;
- preservation of the information contained in the original (with the accuracy of the hypotheses considered when constructing the model);
- completeness - the model must take into account all the basic connections and relationships necessary to ensure the goal of modeling;
- stability - the model should describe and ensure the stable behavior of the system, even if it is initially unstable;
- integrity - the model implements a certain system, i.e. whole;
- isolation - the model takes into account and displays a closed system of necessary basic hypotheses, connections and relationships;
- adaptability - the model can be adapted to various input parameters, environmental influences;
- controllability - the model must have at least one parameter, the changes of which can imitate the behavior of the modeled system under various conditions;
- the possibility of developing models (previous level).
Life cycle of the simulated system:
- collection of information about the object, hypothesis, preliminary model analysis;
- design of the structure and composition of models (submodels);
- construction of model specifications, development and debugging of individual sub-models, assembly of the model as a whole, identification (if necessary) of model parameters;
- model research - the choice of a research method and the development of a modeling algorithm (program);
- study of the adequacy, stability, sensitivity of the model;
- assessment of modeling tools (spent resources);
- interpretation, analysis of modeling results and establishment of some cause-and-effect relationships in the system under study;
- generation of reports and design (national economic) solutions;
- refinement, modification of the model, if necessary, and return to the system under investigation with new knowledge obtained through the model and modeling.
Modeling is a method of systems analysis.
Often in system analysis with a model approach to research, one methodical mistake can be made, namely, the construction of correct and adequate models (submodels) of the subsystems of the system and their logically correct linkage does not guarantee the correctness of the model of the entire system constructed in this way.
A model built without taking into account the relationships of the system with the environment and its behavior in relation to this environment can often only serve as another confirmation of Gödel's theorem, or rather, its corollary, which states that in a complex isolated system there can be truths and conclusions that are correct in this system and incorrect outside it.
The science of modeling consists in dividing the modeling process (systems, models) into stages (subsystems, submodels), a detailed study of each stage, relationships, connections, relationships between them and then effectively describing them with the maximum possible degree of formalization and adequacy.
In case of violation of these rules, we get not a model of the system, but a model of "own and incomplete knowledge".
Modeling is viewed as a special form of experiment, an experiment not on the original itself, i.e. simple or ordinary experiment, but over a copy of the original. The isomorphism of the original and model systems is important here. Isomorphism - equality, sameness, similarity.
Models and modeling applied in the main areas:
- in teaching (both models, modeling, and the models themselves);
- in the knowledge and development of the theory of the systems under study;
- in forecasting (output data, situations, system states);
- in management (the system as a whole, its individual subsystems), in the development of management decisions and strategies;
- in automation (system or its individual subsystems).
