Model

The term modeling refers to both the construction (creation) of models and their study.

Several models of different types can be mapped to the same systems.

General Model Requirements

Modeling always involves making assumptions of varying degrees of importance. In this case, the following model requirements must be satisfied:

• adequacy , that is, the correspondence of the model to the original real system and taking into account, first of all, the most important qualities, relationships and characteristics. It is very difficult to assess the adequacy of the selected model, especially, for example, at the initial stage of design , when the form of the created system is still unknown. In such a situation, they often rely on the experience of previous developments or apply certain methods, for example, the method of successive approximations ;
• accuracy , that is, the degree of coincidence of the results obtained in the process of modeling with pre-established, desired. An important task here is to assess the required accuracy of the results and the available accuracy of the source data, matching them both with each other and with the accuracy of the model used;
• universality , that is, the applicability of the model to the analysis of a number of similar systems in one or more modes of functioning. This allows you to expand the scope of the model to solve a wider range of tasks;
• appropriate cost-effectiveness , that is, the accuracy of the results obtained and the generality of the solution to the problem should be tied to the cost of modeling. And a good choice of model, as practice shows, is the result of a compromise between the resources allocated and the features of the model used;
• and etc.

Choosing a model and ensuring modeling accuracy is considered one of the most important modeling tasks.

Model accuracy and modeling errors

Modeling errors are caused by both objective reasons related to the simplification of real systems, and subjective ones, caused by a lack of knowledge and skills, character traits of a person. Errors can be prevented, compensated or taken into account. And an assessment of the correctness of the results is always required. In technology, a quick assessment of model accuracy is often carried out in the following ways:

• check the correspondence of the results to the physical (common) sense. It is convenient to do this for the particular case of the model, when the solution is obvious. Sometimes they even say that even before solving the problem, the engineer should already have the character and order of the expected result. But the accuracy of such a representation depends on the development of physical imagination and experience with similar systems;
• check the fulfillment of particular obvious conditions of the problem, which also allows you to cut off unacceptable solutions;
• check compliance with the trend of changes in the values ​​and signs of the results (monotony, cyclicity, smoothness, etc.);
• check the correctness of the dimensionality of the result obtained (if the work is carried out with analytical dependencies).

It is known that through rough measurements , the use of measuring instruments with low accuracy or approximate initial data, it is impossible to obtain accurate results. On the other hand, it is pointless to carry out, for example, a calculation accurate to a gram, if you then need to round the result (say, indicate in the form ) to one hundred grams, or determine the average value more precisely than its constituent values, etc. Therefore, it is important remember the following:

• the accuracy of the results of calculations and experimental studies of the model cannot exceed the accuracy of the source data, the instruments used, measuring instruments , etc .;
• the type of model chosen should be consistent with the accuracy of the source data and the required accuracy of the results;
• the desired accuracy of the results should be consistent with the needs and realities of the practice.

The main types of models

By the way reality is displayed, three main types of models are distinguished - heuristic, natural and mathematical.

Heuristic Models

Heuristic models , as a rule, are images drawn in the human imagination. Their description is carried out in the words of a natural language (for example, a verbal information model) and, usually, is ambiguous and subjective. These models are non-formalizable, that is, they are not described by formal logical and mathematical expressions, although they are born on the basis of the representation of real processes and phenomena.

Heuristic modeling is the main way to break beyond the ordinary and established. But the ability to such modeling depends, first of all, on the wealth of a person’s imagination, his experience and erudition. Heuristic models are used in the initial stages of design or other activities when information about the developed system is still scarce. At subsequent design stages, these models are replaced with more specific and accurate ones.

Field Models

A distinctive feature of these models is their similarity to real systems (they are material), and the difference is in the sizes, number and material of elements, etc. By belonging to the subject area, the models are divided into the following:

• Physical models . They are real products, samples, experimental and full-scale models, when there is an unambiguous correspondence between the parameters of the system and the models of the same physical nature. Sizing of such models is carried out in compliance with the theory of similarity . Physical models are divided into three-dimensional (models and layouts) and flat (tremplets):
  • in this case, a (physical) model is understood to mean a product or device, which is a simplified likeness of an object under study or that allows one to recreate an investigated process or phenomenon. For example, subject models, such as reduced copies of the original (a globe as a model of the Earth, a toy airplane taking into account its aerodynamics);
  • a template ^[4] means a product that is a flat scale display of an object in the form of a simplified orthogonal projection or its outline. Trepletotanotars are cut out of film, cardboard, etc., and used in the study and design of buildings, installations, structures;
  • Under the model understand the product, assembled from models and / or templates.

Physical modeling is the basis of our knowledge and a means of testing our hypotheses and calculation results. The physical model allows you to cover the phenomenon or process in all its diversity, the most adequate and accurate, but quite expensive, time-consuming and less universal. In one form or another, they work with physical models at all stages of design;

• Technical models ;
• Social models ;
• Economic models , for example, a business model ;
• etc.

Mathematical Models

Mathematical models are formalized, that is, they are a set of interconnected mathematical and formal logical expressions, usually reflecting real processes and phenomena (physical, mental, social, etc.). According to the presentation form there are:

• analytical models . Their solutions are sought in a closed form, in the form of functional dependencies. They are convenient when analyzing the essence of the described phenomenon or process and using them in other mathematical models, but finding their solutions can be very difficult;
• numerical models . Their solutions are a discrete series of numbers (tables). The models are universal, convenient for solving complex problems, but not visual and time-consuming when analyzing and establishing relationships between parameters. Currently, such models are implemented in the form of software systems - software packages for calculation on a computer. Software complexes are applied, tied to a subject area and a specific object, phenomenon, process, and general, implementing universal mathematical relations (for example, calculating a system of algebraic equations);
• formal logical information models are models created in a formal language.

For example:

• a model of a formal system in mathematics and logic as any collection of objects whose properties and relations between them satisfy the axioms and rules for deriving a formal system, thereby serving as a joint ( implicit ) definition of such a combination;
• a model in the theory of algebraic systems as a combination of a certain set and properties and relations given on its elements;
• reference model .

The construction of mathematical models is possible in the following ways (for more details, see the Mathematical Model ):

• in an analytical way, that is, a conclusion from physical laws, mathematical axioms or theorems;
• experimentally, that is, by processing the results of the experiment and selecting approximating (approximately coincident) dependencies.

Mathematical models are more universal and cheaper, they allow you to set up a “clean” experiment (that is, within the limits of the accuracy of the model, investigate the influence of a particular parameter with the constancy of others), predict the development of a phenomenon or process, and find ways to control them. Mathematical models are the basis for building computer models and applying computer technology.

The results of mathematical modeling need to be compared with the data of physical modeling in order to verify the data obtained and to refine the model itself. On the other hand, any formula is a kind of model and, therefore, is not an absolute truth , but only a stage on the path to its knowledge.

Intermediate Model Views

The intermediate types of models include:

• graphic models . They occupy an intermediate place between heuristic and mathematical models. Represent various images:
  • graphs ;
  • Schemes
  • sketches . This simplified image of a device is largely characterized by heuristic features;
  • drawings . Here, the internal and external relations of the simulated (designed) device, its dimensions are already specified;
  • schedules ;
  • polygonal model in computer graphics as an image of an object, "stitched" from many polygons.
• analog models . They allow one to study physical phenomena or mathematical expressions by studying other physical phenomena that have similar mathematical models. An example is the dynamic analogy method, which is widely used in acoustics ( electro-acoustic analogies ), as well as in mechanics ;
• and etc.

There are other types of “borderline” models, for example, economic-mathematical , etc.

The choice of model type depends on the volume and nature of the initial information about the device in question and the capabilities of the engineer, researcher. By increasing the degree of conformity with reality, the models can be arranged in the following series: heuristic (figurative) - mathematical - full-scale (experimental).

The number of parameters characterizing the behavior of not only a real system, but also its model, is very large. To simplify the process of studying real systems, four levels of their models are distinguished, differing in the number and degree of importance of the considered properties and parameters. This is a functional, fundamental, structural and parametric model.

Functional Model

The functional model is designed to study the features of the system (its functioning) and its purpose in relation to internal and external elements.

Function - the most essential characteristic of any system, reflects its purpose, what it is needed for. Such models operate primarily with functional parameters . Graphical representations of these models are flowcharts . They reflect the order of actions aimed at achieving specified goals (the so-called 'functional diagram'). The functional model is an abstract model .

Principle of Action Model

The model of the principle of action ( principle model , conceptual model ) characterizes the most essential (principal) connections and properties of a real system. These are the fundamental physical, biological, chemical, social and similar phenomena that ensure the functioning of the system, or any other fundamental provisions on which the planned activity or the process under study is based. They strive to ensure that the number of considered properties and parameters characterizing them is small (the most important ones are left), and the visibility of the model is maximum, so that the complexity of working with the model does not distract attention from the essence of the phenomena being studied. As a rule, the parameters describing such models are functional as well as physical characteristics of processes and phenomena. Fundamental starting points (methods, methods, directions, and so on) underlie any activity or work.

So, the principle of operation of a technical system is the sequence of performing certain actions based on certain physical phenomena (effects) that provide the required functioning of this system.

Examples of models of the principle of action: fundamental and applied sciences (for example, the principle of building a model, initial principles for solving a problem), social life (for example, principles for selecting candidates, providing assistance), economics (for example, principles of taxation, calculating profit), culture (for example artistic principles).

Working with models of the principle of action allows you to identify promising areas of development (for example, mechanics or electrical engineering) and requirements for possible materials (solid or liquid, metallic or non-metallic, magnetic or non-magnetic, and so on).

The correct choice of the fundamental principles of functioning determines the viability and effectiveness of the developed solution. So, no matter how much the design of an airplane with a rotary engine is improved, it will never develop supersonic speed, not to mention flying at high altitudes. Only the use of another physical principle, for example, jet propulsion and a jet engine created on its basis, will allow to overcome the sound barrier.

A graphical representation of the models of the principle of action is a block diagram , a functional diagram , a circuit diagram .

For example, for technical models, these schemes reflect the process of transforming a substance, as the material basis of a device, through certain energy influences in order to implement the required functions ( functional-physical scheme ). In the diagram, the types and directions of influence, for example, are shown by arrows, and the objects of influence - by rectangles.

Structural Model

A clear definition of the structural model does not exist. So, under the structural model of a device, they can mean:

• structural diagram , which is a simplified graphic image of the device, giving a general idea of ​​the shape, location and number of its most important parts and their mutual relations;
• a topological model that reflects the interconnections between objects that are independent of their geometric properties.

The structural model of a process usually means the sequence characterizing it and the composition of the stages and stages of work, a set of procedures and technical means involved, and the interaction of process participants.

For example, this can be a simplified image of the links of the mechanism in the form of rods, flat figures ( mechanics ), rectangles with lines with arrows ( automatic control theory , flowcharts of algorithms), a plan of a literary work or bill, etc. The degree of simplification depends on completeness of the source data about the device under study and the required accuracy of the results. In practice, types of structural schemes can vary from simple small schemes (minimum number of parts, simplicity of their surface shapes) to images close to the drawing (high degree of description detail, complexity of the used surface forms).

Perhaps the image of the structural diagram in scale. This model is referred to as structural-parametric . Her example is the kinematic diagram of the mechanism on which the dimensions of the simplified parts (lengths of rod rods, radii of circle wheels, etc.) are plotted to scale, which allows a numerical estimate of some of the characteristics under study.

To increase the perception of completeness in structural diagrams, in the symbolic (alphabetic, conventional signs) form, parameters characterizing the properties of the displayed systems can be indicated. The study of such schemes allows us to establish the relationship (functional, geometric, etc.) between these parameters, that is, to present their relationship in the form of equalities f (x ₁ , x ₂ , ...) = 0, inequalities f (x ₁ , x ₂ , ...) > 0 and in other expressions.

Parametric Model

A parametric model is a mathematical model that allows you to establish a quantitative relationship between the functional and auxiliary parameters of the system. A graphic interpretation of such a model in technology is a drawing of the device or its parts with the numerical values ​​of the parameters.

Research Objectives

Depending on the objectives of the study, the following models are distinguished:

• functional . Designed to study the features of the system (its functioning), its purpose in conjunction with internal and external elements;
• functional physical . Designed to study the physical (real) phenomena used to implement the functions embedded in the system;
• models of processes and phenomena , such as kinematic, strength, dynamic, and others. Designed to study certain properties and characteristics of the system, ensuring its effective functioning.

By presentation features

In order to emphasize the distinctive feature of the model, they are divided into simple and complex, homogeneous and heterogeneous, open and closed, static and dynamic, probabilistic and deterministic, etc. It is worth noting that when they say, for example, about a technical device as simple or complex, closed or open, etc., in reality they do not mean the device itself, but the possible appearance of its model, thus emphasizing the peculiarity of the composition or working conditions.

• There is no clear rule for separating models into complex and simple . Typically, a sign of complex models is the variety of functions performed, a large number of components, the branched nature of relationships, close relationship with the external environment, the presence of elements of randomness, time variability, and others. The concept of system complexity is subjective and is determined by the time and money required for its study, the required level of qualification, that is, it depends on a particular case and a specific specialist.
• The separation of systems into homogeneous and heterogeneous is carried out in accordance with a pre-selected attribute: the physical phenomena used, materials, shapes, etc. Moreover, the same model with different approaches can be both homogeneous and heterogeneous. So, a bicycle is a homogeneous mechanical device, because it uses mechanical methods of transmitting motion, but heterogeneous in the types of materials from which the individual parts are made (rubber tire, steel frame, plastic saddle).
• All devices interact with the environment, exchange signals, energy, and matter with it. Models are considered open if their influence on the environment or the influence of external conditions on their condition and quality of functioning cannot be neglected. Otherwise, the systems are considered as closed , isolated.
• Dynamic models, in contrast to static ones , are in constant development, their state and characteristics change in the course of work and over time.
• The characteristics of probabilistic (in other words, stochastic ) models are randomly distributed in space or change in time. This is a consequence of both the random distribution of the properties of materials, the geometric dimensions and shapes of the object, and the random nature of the effects of external loads and conditions. The characteristics of deterministic models are known in advance and accurately predictable.

Knowing these features facilitates the modeling process, as it allows you to choose the type of model that best suits the given conditions. This choice is based on the selection of essential and discarding secondary factors in the system and should be confirmed by research or previous experience. Most often in the modeling process they focus on creating a simple model, which saves time and money on its development. However, increasing the accuracy of the model, as a rule, is associated with an increase in its complexity, since it is necessary to take into account a large number of factors and relationships. A reasonable combination of simplicity and required accuracy also indicates the preferred type of model.

In psychology, modeling is the study of mental phenomena and processes using real (physical) or ideal models. In this case, “model” is understood as a system of objects or signs reproducing some essential properties of the original system. The presence of partial similarity relations ( homomorphism ) allows us to use the model as a “substitute” (or “representative”) of the system under study.

Psychological modeling is considered as creating a formal model of a psychic or socio-psychological phenomenon , that is, a formalized abstraction of this phenomenon, reproducing the main, key, according to this researcher , moments. The purpose of such modeling can be both an experimental study of the phenomenon on the model, and the use of the model in vocational education (training, training). In this regard, there are two types of models ^[5] :

• Internal, mental models (as a set of mental images) of a person, which reflects the subjective picture of the world or its fragments (for example, mental models of the profession, professional environment, professional activity, self-concept , etc.). These mental models “provide” a person’s activity, determine his attitude to the world and to himself. The outstanding Russian psychologist V. N. Pushkin ^[6] in 1965 wrote that “there is not a single type of human labor based on which there would be no corresponding form of information modeling of the world” ^[7] , but as a subject of study of psychological science, the scientist proposed to consider the "elucidation of the laws of construction and operation of brain information models of the external world", serving human behavior ^[6] .
• Objectivized (“man-made”) models are systems of objects or signs that reproduce some of the essential properties of the original system ( verbal and symbolic models of the profession, professional environment, professional activity, human self-awareness , etc.). They are created on the basis of preliminary study and understanding of mental processes achieved by the researcher (psychological structure of activity, self-awareness, etc.), as well as fragments of the objective world in which the phenomena under study occur (for example, specific human activity). Such models as original didactic tools are important for providing vocational education and training ^[8] and are associated, inter alia, with pedagogical design ^[5] . Such models may be descriptive.

Models of a specialist (professional)

According to K.K. Platonov (1970), three types of professional models are distinguished:

• The normative model is compiled on the basis of instructions, charters, training programs, etc.
• an exponential (from the English expectation - expectation) model is determined by the opinions of experts who are well versed in this profession
• The empirical model describes a professional who actually exists in certain conditions ^[9]

In modern representations, the specialist model includes the following components ^{[10] [11]} :

• professiogram - a description of the psychological requirements of the profession for the activities and personality of the employee
• professional and job requirements - a description of the specific content of the activity, its professional tasks in a particular position, at a particular workplace
• qualification profile - a combination of the necessary types of professional activity and the degree of their qualification, qualification categories, etc.

When developing a specialist model in this form, it is considered ^[12] that special attention should be paid to the development of qualitative (as opposed to quantitative) and reference requirements for a professional. The specialist’s model appears as the image of a professional, as it should be - expressed verbally (verbally) and recorded in certain regulatory documents.

Profession Model

The psychological model of the profession, according to S. A. Druzhilov, includes three components (submodels) ^[5] :

1. The psychological model of the professional environment (professional environment). The professional environment includes the object and subject of labor, means of labor, professional tasks, working conditions ^[13] , as well as the human (professional) environment. The system of ideas about the components of a professional environment (a system of images) constitutes an internal, psychological model of a professional environment ^[5] . As a necessary component of the component model of a professional environment, a psychological model of the problem situation is included ^[14] .
2. The psychological model of professional activity (as a system of images of human interaction with the professional environment, as well as images of goals, results, methods for their achievement, algorithms, possible consequences of erroneous actions, etc.). This refers to a conceptual model of activity , considered as an internal, psychic, figurative, conceptual and effective model ^[15] , formed in the head of an actor in the process of professional education and gaining work experience.
3. The psychological model of self-consciousness of a professional person (as an individual , person, subject of activity and individuality ), including the system of his properties and relations. As such a model is the internal professional self-concept of a person ^[16] .

Modeling Activities: Specificity

Activity as an object of modeling is specific in that it can be represented both as a structure and as a process ^[17] .

• Model (values)
• Analogy
• Business simulation
• Scientific picture of the world
• Parameter (technique)
• Physical model (simulation)

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• Stoff V. A. On the role of the model in the knowledge of L., 1963
• Khoroshev A.N. Introduction to the management of the design of mechanical systems: Textbook. - Belgorod, 1999 .-- 372 p. - ISBN 5-217-00016-3 . 2011 electronic version
• Yudin A. D. Extreme models in economics. M., 1979.