4. Models

The concept of the model. The concept of a model of an object arises in connection with the need to study the possibilities of using this object to solve problems, solve problems, and achieve the goals of an activity. Therefore, such an object is also logical to call the object under study om .

We will proceed from the following definition:

“The model of the object being studied is an auxiliary object that gives answers to questions regarding the object being studied” .

For systems:

“The model of the system under study is an auxiliary system that gives answers to questions regarding the system under study” .

In turn, for technology -

“The model of the technology being studied is an assistive technology that gives answers to questions regarding the technology being studied” .

For the main and additional parts of the technology -

“The model of the studied part of the technology is an auxiliary system that gives answers to questions regarding the studied part of the technology ”.

In turn, for the object being modeled -

“The model of the object under study is an auxiliary system that gives answers to questions regarding the object under study” .

For parts of the simulated object -

“The model of the studied part of the production system is an auxiliary system that gives answers to questions regarding the studied part of the object being modeled”.

At its core, the model provides answers in relation to the object being studied to a certain subject who studies this object with different goals - analysis, research, monitoring, etc. In other words, a model is a source of new knowledge about the object being studied, which is necessary to supplement the student’s knowledge of this object. Then you can determine that

A model is a set of methods and / or means of ensuring interaction between the external environment represented by the object being studied and the internal environment of the student, represented, in this case, as a complex of his knowledge about the external environment.

The model of the object being studied can also be called a modeling object, and the object being studied can be called a simulated object.

Each known model of an object has one or several known main features, which are considered as axioms in the theory of this model. A theory based on a set of axioms using the accepted inference rules of a particular model can answer questions regarding a real object, in the event that a real object satisfies the conditions of the same set of axioms.

In other words, the general principle of modeling is that

the real object being modeled and the model used must satisfy one set of axioms.

Compiling a single model of an object in the form that allows you to get all the answers to questions regarding the object being studied is impossible and for this reason any real objects are represented using a number of well-known models of object systems of a given class . Each such well-known object model allows you to answer some set of questions regarding the construction and operation of a particular object or class of objects.

Depending on the purpose of studying the object - analysis, research, design, etc., various methods of constructing models are used. Consider the most common types of models.

? Conceptual, structural and mathematical models of dynamic systems.

As a rule, all models are conceptual, structural or mathematical. Consider these types of models on the example of dynamic systems modeling [34] .

A dynamic system is an ordered set of mutually related elements existing in reality, i.e. in space and time.

The external environment of a dynamic system is everything that is not an element of this system.

Each element of the system is usually characterized by a set of quantitative and / or qualitative characteristics that change over time.

The state (behavior) of the system at each fixed point in time is described by an unambiguous expression of the characteristics of the system elements.

The classic examples of a dynamic system are the Earth-Moon system; the solar system, whose elements are the sun, planets and comets; A galaxy whose elements are individual stars, constellations and planetary systems (including the Solar System).

At present, there are three levels in the theory of modeling systems: conceptual modeling, structural modeling; math modeling.

Classical examples of conceptual and structural models are:

- Ptolemy's geocentric model, according to which the Earth is the center of the whole Universe; The sun, stars and planets revolve around the earth. This is an example of a model that does not satisfy the general Principle of Modeling, since the real object being modeled (the Universe) and the model used (the Ptol emey model) do not satisfy one set of axioms ;

- Copernican's heliocentric model, according to which the Sun is in the center of the near-Earth Universe, the planets move around the Sun, the stars are moved to great distances from the Sun, the observed movements of the stars in the sky are not true, but appear to be due to the daily rotation of the Earth around its axis;

Classical examples of mathematical models are:

- the laws of planetary motion established by I. Kepler in mathematical form;

- mathematical modeling by I. Newton, L. Euler of the mechanical motion of solids;

- The law of conservation of energy and matter of M.V. Lomonosov.

In general, mathematical models are divided into the following classes according to the degree of generality and detail:

1) mathematical theories of real processes and situations;

2) applied mathematical models;

3) math problems.

The models of the “mathematical problem” class contain a specific mathematical formulation of the problem, where the known and unknown quantities and their connecting mathematical relations, numerical data for known values, and also clearly formulated what is required to find, establish, or define are indicated.

The models of the class “applied mathematical models” also contain a number of input and output values, connecting their mathematical relationships, and it is not specifically stated which values ​​are known and which are unknown. It indicates only in general form the intended list of tasks that can be formulated and solved on the basis of this applied model.

The models of the class “mathematical theories of real processes and situations” contain a fairly complete and common set of mathematical relationships. These ratios express real physical, chemical, biological, sociological, and other laws that allow us to develop an applied mathematical model for their mathematical formulation and solution of the required set of problems.

In contrast to conceptual models, mathematical theory leads to the numerical solution of the problems of a simulated object.

? The process and structure of the simulated object. In simulated objects, process and structure models are studied.

The process of a simulated object is represented as a certain combination of expedient elementary resource transformations - the elementary processes of producing the result of a simulated object. All these transformations are modeled as functions of time. In other words, the process of a simulated object is that with the help of which the simulated object is realized in time. Process models are temporary models.

The structure of a simulated object is modeled as a certain set of elements of production (people, machines, devices, equipment, automated workplaces), within each of which the flow of a certain elementary process of a simulated object is localized. All these elements of the simulated object are “linked” to a specific place in space (water, air, earth, outer space). The structure of the simulated object is that with the help of which the simulated object is realized in space. Structure models are spatial models.

? Consider the most frequently used models of processes and structures .

To model the processes and structures of objects, the principle of the “black box” is often used, according to which to predict the behavior of an object it is not necessary to know exactly how its process and structure are arranged. This principle is widely applied in modeling such large systems as production systems, based on an analysis of the characteristics of information on input and output flows and system resources.

Two types of machine models are used for modeling: analog and discrete.

Analog models are, as a rule, process models in the form of ordinary differential equations and partial differential equations solved on analog and digital computers.

Discrete models, i.e. models with a developed system of logical transitions and conditions described using the apparatus of discrete mathematics (mathematical logic and theory of algorithms, theory of languages ​​and language processors, algebraic systems, etc.) are solved using digital computers.

There are also models of the processes of systems that are focused on the solution using analog-digital complexes, since in many cases the models of the processes of the simulated object are continuously discrete .

To solve the problems of process modeling, imitating models are effective. For these models, the problem of the greatest correspondence of the model structure to the structure of the simulated process is not posed. The main task is the most reliable reproduction of the response of the modeled process to external, including input effects in the form of changes in the characteristics of the converted resource. Selection of a set of operators converting input information into output information is made using statistical mathematical methods.

The process model is structured in the form of blocks in accordance with reliable ideas about the structure of the object being modeled. Each block of the model simulates the behavior of a particular system, which is a subsystem of the object being modeled. Imitating models allow adjusting the set of transformation operators in accordance with the current behavior of the simulated system, creating simulation and business games for making decisions on the design, management, development of production systems.

Processes in production facilities are often modeled using “informal” graphical models. Graphic models make it possible to visually depict in the form of diagrams, graphs, other simple and complex graphic constructions, particular and general qualitative and quantitative characteristics of models of the object being modeled. Informal models are, as a rule, a stage preceding the construction of formal mathematical, economic, and economic-mathematical models of the object being modeled.

Formal mathematical models of production processes can be differential (in the form of differential equations), logical (in the form of equations of mathematical logic), set-theoretic, algebraic (in the form of algebraic equations and systems), graph (in the form of oriented and non-oriented graphs), combinatorial ( in the form of models of placement of objects in accordance with special rules), mixed.

Models of production processes and systems can be stochastic and deterministic, i.e. taking into account (in the first case) and not taking into account (in another case) the random nature of changes in the characteristics of production processes and resources transformed by the system.

To construct stochastic models of the processes of systems, special modeling methods are used [35] .

The processes and structures of the object being modeled can be described using functional, morphological and informational approaches .

The functional approach is used to describe the process of the object being modeled. The process model of a simulated object is represented as a set of functions that transform incoming resources into the final result of the functioning of the simulated object - knowledge, product, service, project, program, policy, etc. The final result and input resources of the object are represented as functions of time. At any given time, the state of the object being modeled is described by a set of information on the characteristics of the input resources and output results. The functional model predicts changes in the process state of the object being modeled over time.

The morphological approach is intended for modeling the structure of the object being modeled, the structures of its parts. At the same time, there are elements of the object and transport and warehouse relations between them, designed to ensure interactions: information, energy, financial, social, material, etc.

The information approach allows you to create a model for transforming an information resource, both for any element and for a part of the object being modeled, as well as for the transformation carried out by the object being modeled as a whole. The information approach allows you to create an information model of the object being modeled, which gives an integral description of the system, regardless of its nature and the nature of the resources being transformed.

? The subject of activity as a simulated object. Throughout the life cycle of a certain object of activity, its development and relations with the external environment are the subject of the activity of the subject of activity . In this case, the subject of the activity must ensure the achievement of the goal of the activity of the given object (both its own and missionary). First, this is the achievement of the missionary goal of production in the interests of the external environment. And, secondly, as is known from the previous presentation, there is also its own goal of survival, preservation and development of the object. To the model of the subject of activity, which is significantly modified during the life cycle of the object of activity, from the standpoint of system technology, certain requirements are imposed.

In the initial phases of the conceptual stage of the object being created, the subject of activity performs analytical and research functions in relation to him. These functions are associated with the analysis of the needs and capabilities of the external environment in the creation of this object. The subject of activity may be an analytical group, a research team. At subsequent phases of the conceptual stage, if a decision is made to create this object, the subject of the activity develops the project of the object being created. The business model is complemented by a project team model and a project management team. The functions of the subject of activity of the object being created at this stage are to coordinate the project with representatives of the external environment on issues of ecology, economics, sociology, etc., and also to draw up plans for the implementation of the project of the object being created.

At the stage of the physical implementation of the project of the object of activity, the tasks of the subject of activity are connected with the implementation of the object being created in space and time (structure and process). Here, the research and project functions of the subject of activity are associated only with the need to adjust the project in the course of the implementation of a functioning facility. At this stage, the object management functions are increasing, including the management of the development of the object. There are new functions of the subject of activity associated with the preparation of the draft of the new object, which will replace the object in question with its obsolescence and withdrawal from circulation.

At the postphysical stage, the functions of the subject of activity in relation to the object are reduced to storing information about him on paper and computer media and in the form of samples; The subject of activity at this stage is an archive, museum or data bank.

It can be said that the model of a subject of activity contains such subsystems as “analyst”, “researcher”, “designer”, “expert”, “licensor”, “production manager”, “development system”, “controller”, “archivist”, who are experiencing different stages of their life cycles in accordance with the tasks that the subject performs in relation to a specific object of activity.

? The project . A project is the most complete model of some simulated object, suitable for the physical implementation of the idea of ​​creating and developing this object, and the designer is an essential part of the model of the subject of activity of the modeled object, which deserves separate consideration. The functions of the designer are closely related to production engineering.

The system design is the most important type of model of the object being modeled, since it is with the help of the project that the object moves from the idea of ​​its creation to the physical implementation, and then to the postphysical stage. When designing systems, there are: macro- design (external design) and micro- design (internal design).

Макропроект можно рассматривать, как совокупность трех комплексов моделей – комплекс моделей внешней среды, комплекс моделей триады «объект-субъект-результат» проектируемого объекта, комплекс моделей его процесса и структуры. Такая совокупность описывает роль проектируемой триады «объект-субъект-результат» для внешней среды и роль внешней среды для проектируемой триады «объект-субъект-результат». Модель внешней среды – важный компонент, оказывающий существенное влияние на формирование макромодели проектируемого объекта. С позиций системной технологии внешняя среда включает все системы, которые не контролируются системой-субъектом данной триады и всеми ее подсистемами («исследователь», «проектировщик» и т.д.).

Микропроект можно рассматривать, как совокупность моделей проектируемой триады «объект-субъект-результат», а также ее подсистем, элементов, элементарных процессов, транспортно-складских взаимодействий между ними, описывающую роль элементов, элементарных процессов и взаимодействий для моделируемого объекта, а также, что не менее важно в смысле целостности объекта деятельности, роль моделируемого объекта для них.

? Принцип целостности моделирования. На основе общего Принципа моделирования можно сформулировать Принцип целостности моделирования в виде:

для формирования и осуществления ц елостной деятельности совокупность «моделируемый объект и моделирующий объект» необходимо представлять одной совокупностью аксиом построения целостного объекта, справедливой также и для обоих объектов совокупности.

Тогда очевидно справедлив следующий Принцип целостности моделирования для системы:

для формирования и осуществления ц елостной системы совокупность «моделируемая система и моделирующая система» необходимо представлять одной совокупностью аксиом построения целостной системы, справедливой также и для каждой из обоих систем совокупности.

Также справедлив и следующий Принцип целостности моделирования для технологии:

для формирования и осуществления ц елостной технологии совокупность «моделируемая технология и моделирующая технология» необходимо представлять одной совокупностью аксиом построения целостной технологии, справедливой также и для каждой из обоих технологий совокупности.

В общем виде Принцип целостности моделирования можно сформулировать в следующем виде:

для формирования и осуществления ц елого совокупность «моделируемое целое и моделирующее целое» необходимо представлять одной совокупностью аксиом построения ц елостного целого, справедливой также и для каждого из обоих целых совокупности.

В заключение можно отметить следующее:

1) как правило, концептуальные, структурные, математические и иные модели и моделируемые ими объекты удовлетворяют одному набору аксиом. Но используемый в конкретных моделях этих трех видов набор аксиом является, как правило, подмножеством аксиом реального объекта. Образно говоря, любая модель описывает только часть реального моделируемого объекта; для достоверной модели, как правило, это ключевая часть объекта, определяющая смену его состояний при определенных начальных условиях с необходимой для практики точностью;

2) система, технология и модель имеют определения, фактически являющиеся частными видами представления целого с позиций целостного метода системной технологии. Другими словами, реальные система, технология и модель являются разновидностями частичной реализации целого. У каждой из этих разновидностей частичной реализации целого мы изучили присущие им особенные правила и условия реализации целого, которые автором были использованы при построении системной технологии;

3) в существующих моделях не ставится задача соответствия постулатам целостного целого; в связи с этим необходимо решение задачи создания целостных и целых моделей объектов моделирования для решения задач создания целостной и целой деятельности. С этой целью в данном разделе предложен Принцип целостности моделирования.

See also

• The concept of modeling. Ways to present models
• Modeling. Introduction