Approaches to system modeling. Basic approaches to modeling systems Approaches to modeling objects of study

Concept of the system

We live in a world that consists of many different objects that have various properties and interact with each other. For example, the objects of the surrounding world are the planets of the Solar System, which have different properties (mass, geometric dimensions, etc.) and interact with the Sun and each other according to the law of universal gravitation.

Each planet is part of a larger object - the Solar System, which in turn is part of the Galaxy. At the same time, each planet consists of atoms of different chemical elements, which consist of elementary particles. Thus, in fact, each object can consist of a collection of other objects, i.e. forms a system.

An important feature of the system is its holistic functioning. A system is not a set of individual elements, but a collection of interconnected elements. For example, a personal computer is a system that consists of various devices that are interconnected both hardware (physically connected to each other) and functionally (exchange information).

Definition 1

A system is a collection of interconnected objects, which are called system elements.

Note 1

Each system has its own structure, which is characterized by the composition and properties of the elements, their relationships and connections with each other. The system is able to maintain its integrity under the influence of various external factors and internal changes as long as its structure remains unchanged. If the structure of the system changes (for example, when one of its elements is removed), it may cease to function as a single whole. For example, if you remove one of the computer devices (for example, the motherboard), the computer will stop working, that is, it will stop functioning as a system.

The basic principles of systems theory appeared in the study of dynamic systems and their functional elements. A system is a group of interconnected elements that act together to accomplish a predetermined task. Using systems analysis, it is possible to determine the most realistic ways to perform a given task, which ensure maximum satisfaction of the stated requirements.

The elements that form the basis of systems theory are not created through hypotheses, but are obtained experimentally. To start building a system, you need to have general characteristics of technological processes, which are also necessary when creating mathematically formulated criteria that the process or its theoretical description must satisfy. The modeling method is one of the most important methods of scientific research and experimentation.

Systems approach

To build models of objects, a systems approach is used, which is a methodology for solving complex problems. This methodology is based on considering an object as a system that operates in a certain environment. A systematic approach allows us to reveal the integrity of an object, identify and study its internal structure, as well as connections with the external environment. In this case, the object is a part of the real world, which is isolated and studied in connection with the problem being solved in constructing a model. In addition, when using a systems approach, a consistent transition from the general to the specific is assumed, which is based on consideration of the design goal, and the object is considered in relation to the environment.

A complex object can be divided into subsystems, which are parts of the object and satisfy the following requirements:

1. subsystem is a functionally independent part of an object that is connected to other subsystems and exchanges information and energy with them;
2. each subsystem may have functions or properties that do not coincide with the properties of the entire system;
3. each of the subsystems can be divided down to the element level.

Here, an element is understood as a lower-level subsystem, which further division does not seem appropriate from the perspective of the problem being solved.

Note 2

Thus, the system is represented as an object consisting of a set of subsystems, elements and connections for its creation, research or improvement. In this case, an enlarged representation of the system, which includes the main subsystems and connections between them, is called macrostructure, and a detailed consideration of the internal structure of the system down to the level of elements is called microstructure.

The concept of a system is usually associated with the concept of a supersystem - a system of a higher level, which includes the object in question, and the function of any system can be defined only through the supersystem. Also important is the concept of the environment - a set of objects in the external world that significantly influence the efficiency of the system, but are not part of the system and its supersystem.

In a systems approach to building models, the concept of infrastructure is used, which describes the relationship of the system with its environment (environment).

Isolating, describing and studying the properties of an object that are essential for a specific task is called object stratification.

With a systems approach to modeling, it is important to determine the structure of the system, which is defined as a set of connections between system elements that reflect their interaction.

There are structural and functional approaches to modeling.

With a structural approach, the composition of the selected elements of the system and the connections between them are determined. The set of elements and connections makes up the structure of the system. Typically, a topological description is used to describe the structure, which makes it possible to identify the component parts of the system and determine their connections using graphs.

Less commonly used is a functional description, which considers individual functions - algorithms for system behavior. In this case, a functional approach is implemented, which defines the functions performed by the system.

With a systems approach, different sequences of model development are possible based on two main design stages: macro-design and micro-design. At the macro-design stage, a model of the external environment is built, resources and limitations are identified, a system model and criteria for assessing adequacy are selected.

The micro-design stage depends on the type of model chosen. This stage involves the creation of information, mathematical, technical or software modeling systems. When microdesigning, the main technical characteristics of the created model are established, the time spent working with it and the cost of resources to obtain the required quality of the model are estimated.

When building a model, regardless of its type, it is necessary to adhere to the principles of a systematic approach:

1. consistently move through the stages of creating a model;
2. coordinate information, resource, reliability and other characteristics;
3. correctly correlate different levels of model construction;
4. adhere to the integrity of the individual stages of model design.

Static information models

Any system continues to exist in space and time. At different points in time, the system is determined by its state, which describes the composition of the elements, the values ​​of their properties, the magnitude and nature of the interaction between the elements, etc.

For example, the state of the Solar system at certain points in time is described by the composition of the objects that are included in it (the Sun, planets, etc.), their properties (size, position in space, etc.), the magnitude and nature of their interaction (gravitational force, electromagnetic waves and etc.).

Models that describe the state of a system at a certain point in time are called static information models.

For example, in physics, static information models are models that describe simple mechanisms, in biology - models of the structure of plants and animals, in chemistry - models of the structure of molecules and crystal lattices, etc.

Dynamic information models

The system can change over time, i.e. there is a process of change and development of the system. For example, when the planets move, their position relative to the Sun and among themselves changes; the chemical composition of the Sun, radiation, etc. changes.

Models that describe the processes of change and development of systems are called dynamic information models.

For example, in physics, dynamic information models describe the movement of bodies, in chemistry - the processes of chemical reactions, in biology - the development of organisms or animal species, etc.

When modeling systems, two approaches are used: classical (inductive), which developed historically first, and systemic, which has been developed recently.

Classic approach. Historically, the classical approach to studying an object and modeling a system was the first to emerge. The classical approach to synthesizing a system model (M) is presented in Fig. 3. The real object to be modeled is divided into subsystems, initial data (D) for modeling are selected and goals (T) are set, reflecting individual aspects of the modeling process. Based on a separate set of initial data, the goal of modeling a separate aspect of the system’s functioning is set; on the basis of this goal, a certain component (K) of the future model is formed. A set of components is combined into a model.

That. the components are summed up, each component solves its own problems and is isolated from other parts of the model. We apply the approach only to simple systems, where the relationships between components can be ignored. Two distinctive aspects of the classical approach can be noted:

1. there is a movement from the particular to the general when creating a model;

2. the created model (system) is formed by summing up its individual components and does not take into account the emergence of a new systemic effect.

Rice. 3. Classical approach to constructing an object and studying the model

Systems approach – a methodological concept based on the desire to build a holistic picture of the object being studied, taking into account the elements of the object that are important for the problem being solved, the connections between them and external connections with other objects and the environment. With the increasing complexity of modeling objects, the need arose to observe them from a higher level. In this case, the developer considers this system as some subsystem of a higher rank. For example, if the task is to design a monitoring system for a separate object, then from the perspective of a systems approach we must not forget that this system is an integral part of a certain complex. The basis of the systems approach is the consideration of the system as an integrated whole, and this consideration during development begins with the main thing - the formulation of the purpose of operation. In Fig. 4. The process of synthesizing a system model based on a systems approach is conventionally presented. It is important for the systems approach to determine the structure of the system - the set of connections between the elements of the system, reflecting their interaction.

Rice. 4. Systematic approach to constructing an object and studying the model

There are structural and functional approaches to studying the structure of a system and its properties. With a structural approach, the composition of the selected elements of the system and the connections between them are revealed. In the functional approach, algorithms for the behavior of the system are considered (functions are properties that lead to the achievement of a goal).

Test questions for section 2

1. What is determined during the system analysis process?

2. What is determined in the process of system synthesis?

3. How is the effectiveness of the system assessed?

4. What is meant by an optimal system?

5. Properties inherent in a complex system and their brief description.

6. What is the problem of choosing the level of detail of models?

7. List the main stages of system modeling.

Topic 5. MODEL APPROACH

Model is an abstract description of a system (object, process, problem, concept) in some form different from the form of their real existence

Modeling begins with the formation of the subject of research - a system of concepts that reflects the characteristics of the object that are essential for modeling. This task is quite complex, which is confirmed by different interpretations in the scientific and technical literature of such fundamental concepts as system, model, modeling. Such ambiguity does not indicate the fallacy of some terms and the correctness of other terms, but reflects the dependence of the subject of research (modeling) both on the object under consideration and on the goals of the researcher. A distinctive feature of modeling complex systems is its versatility and variety of uses; it becomes an integral part of the entire life cycle of the system. This is explained primarily by the manufacturability of models implemented on the basis of computer technology: a fairly high speed of obtaining modeling results and their relatively low cost.

Approaches to system modeling

Currently, in the analysis and synthesis of complex (large) systems, a systems approach has been developed, which differs from the classical (or inductive) approach. The latter considers the system by moving from the particular to the general and synthesizes (constructs) the system by merging its components, developed separately. In contrast, the systems approach involves a consistent transition from the general to the specific, when the basis of consideration is the goal, and the object under study is isolated from the environment.

With a systematic approach to modeling systems, it is necessary, first of all, to clearly define the purpose of the modeling. Since it is impossible to completely simulate a really functioning system (the original system, or the first system), a model (the model system, or the second system) is created for the problem at hand. Thus, in relation to modeling issues, the goal arises from the required modeling tasks, which allows one to approach the selection of criteria and evaluate which elements will be included in the created model M. Therefore, it is necessary to have a criterion for selecting individual elements in the created model.

It is important for the systems approach to determine the structure of the system - the set of connections between the elements of the system, reflecting their interaction. The structure of a system can be studied from the outside from the point of view of the composition of individual subsystems and the relationships between them, as well as from the inside, when individual properties are analyzed that allow the system to achieve a given goal, i.e. when the functions of the system are studied. In accordance with this, a number of approaches have been outlined to study the structure of a system with its properties, which should, first of all, include structural and functional.

With a structural approach, the composition of the selected elements of the system S and the connections between them are revealed. The set of elements and connections between them allows us to judge the structure of the system. The latter, depending on the purpose of the study, can be described at different levels of consideration. The most general description of the structure is a topological description, which allows one to define the constituent parts of the system in the most general terms and is well formalized on the basis of graph theory.

Less general is the functional description, when individual functions are considered, i.e. algorithms for the behavior of the system, and a functional approach is implemented that evaluates the functions that the system performs, and by function is meant a property that leads to the achievement of a goal. Because a function displays a property and a property displays system interaction S with the external environment W, then the properties can be expressed in the form of either some characteristics of the elements s i and subsystems Sj, or systems S generally.

If you have some standard of comparison, you can enter the quantitative and qualitative characteristics of the systems. For a quantitative characteristic, numbers are entered that express the relationship between this characteristic and the standard. The qualitative characteristics of the system are found, for example, using the method of expert assessments.

Manifestation of system functions over time S(t), i.e. the functioning of the system, means the transition of the system from one state to another, i.e. movement in the space of states C. When using the system S The quality of its functioning is very important, determined by the efficiency indicator and being the value of the efficiency evaluation criterion. There are different approaches to choosing performance evaluation criteria. System S can be assessed either by a set of particular criteria or by some general integral criterion.

It should be noted that the created model M from the point of view of the systems approach, it is also a system, i.e. S"= S" (M), and can be considered in relation to the external environment W. The simplest models are those in which a direct analogy of the phenomenon is preserved. Models are also used in which there is no direct analogy, but only laws and general patterns of behavior of system elements are preserved S. Correct understanding of the relationships both within the model itself M, and its interaction with the external environment W is largely determined by what level the observer is at.

Model synthesis process M based on a systems approach is presented in Fig. 5.1.

When modeling, it is necessary to ensure maximum efficiency of the system model. Efficiency is usually defined as a certain difference between some indicators of the value of the results obtained as a result of operating the model and the costs that were invested in its development and creation.

Regardless of the type of model used M when constructing it, it is necessary to be guided by a number of principles of a systematic approach: 1) proportional and consistent progress through the stages and directions of creating the model; 2) coordination of information, resource, reliability and other characteristics; 3) the correct relationship between individual hierarchy levels in the modeling system; 4) the integrity of individual separate stages of model construction.

Model M must meet the specified purpose of its creation, therefore the individual parts must be arranged mutually, based on a single system task. The goal can be formulated qualitatively, then it will have greater content and for a long time can reflect the objective capabilities of a given modeling system. When a goal is formulated quantitatively, a target function arises that accurately reflects the most significant factors influencing the achievement of the goal.

Building a model is one of the system problems in which solutions are synthesized based on a huge number of initial data, based on proposals from large teams of specialists. Using a systems approach in these conditions allows not only to build a model of a real object, but also on the basis of this model to select the required amount of control information in a real system, evaluate its performance indicators and thereby, based on modeling, find the most effective option for constructing and the most profitable mode of operation of a real system S.

Lecture 4.2. Modeling methods and technologies

Modeling Goals

In almost all sciences about nature, living and inanimate, about society, the construction and use of models is a powerful tool of knowledge. Real objects and processes can be so multifaceted and complex that the best way to study them is often to build a model that reflects only some facet of reality and therefore many times simpler than this reality, and to study this model first. Models are used to solve all kinds of problems. From this set, the main purposes of using models can be identified:

1) understand how a specific object works, what is its structure, basic properties, laws of development and interaction with the outside world ( understanding);

2) learn to manage an object (or process) and determine the best methods of management for given goals and criteria ( control);

3) predict direct and indirect consequences of the implementation of specified methods and forms of impact on the object ( forecasting).

Classical(or inductive) an approach modeling considers the system, moving from the particular to the general, and synthesizes it by merging components developed separately. Systems approach involves a consistent transition from the general to the specific, when the basis of consideration is the goal, while the object stands out from the surrounding world.

When creating a new object with useful properties, criteria are set that determine the degree of usefulness of the resulting properties. Since any modeling object is a system of interconnected elements, the concept of a system has been introduced. System S– there is a purposeful set of interconnected elements of any nature. The external environment E is a set of elements of any nature existing outside the system that influence the system or are influenced by it.

In system modeling, first of all, the purpose of the modeling is clearly defined. Creating a model that is a complete analogue of the original is labor-intensive and expensive, so the model is created for a specific purpose.

It is important for the systems approach to determine system structure- a set of connections between elements of the system, reflecting their interaction. There are a number of approaches to studying a system and its properties, which include structural and functional. When structural, the composition of the selected elements of the system S and the connections between them are revealed. The set of elements and connections allows us to judge the properties of the selected part of the system. In the functional approach, functions (algorithms) of system behavior are considered, and each function describes the behavior of one property under external influence E. This approach does not require knowledge of the structure of the system, and its description consists of a set of functions of its response to external influences. The classical method of building a model uses a functional approach. A component that describes the behavior of one property and does not reflect the actual composition of the elements is accepted as a model element. The components are isolated from each other, which does not reflect well the system being modeled. This method of constructing a model is applicable only for simple systems, because requires the inclusion in the functions that describe the properties of the system, relationships between properties that may be poorly defined or unknown.

As the systems being modeled become more complex, when it is impossible to take into account all the mutual influences of properties, a system method based on a structural approach is used. In this case, the system S is divided into a number of subsystems S i with their own properties, which are easier to describe by functional dependencies, and the connections between the subsystems are determined. In this case, the system functions in accordance with the properties of individual subsystems and connections between them. This eliminates the need to describe the functional relationships between the properties of the system S, which makes the model more flexible, because changing the properties of one of the subsystems automatically changes the properties of the system.

Lecture 4.3. Model classification

Depending on the nature of the processes being studied in the system S and the purpose of modeling, there are many types of models and ways of classifying them, for example, by purpose of use, the presence of random influences in relation to time, feasibility of implementation, scope of application, etc.

Currently, in the analysis and synthesis of complex (large) systems, a systems approach has been developed, which differs from the classical (or inductive) approach. Classic approach examines the system by moving from the particular to the general and synthesizes (constructs) the system by merging its components, developed separately. In contrast to this systems approach involves a consistent transition from the general to the specific, when the basis of consideration is the goal, and the object under study is distinguished from the environment.

Simulation object. Specialists in the design and operation of complex systems deal with control systems at various levels that have a common property - the desire to achieve a certain goal. We will take this feature into account in the following definitions of the system.

System or object S- a purposeful set of interconnected elements of any nature.

External environment E- a set of elements of any nature existing outside the system that influence the system or are under its influence.

Depending on the purpose of the study, different relationships between the object S itself and the external environment E can be considered. Thus, depending on the level at which the observer is located, the object of study can be distinguished in different ways and different interactions of this object with the external environment can take place.

With the development of science and technology, the object itself is continuously becoming more complex, and now they are talking about the object of research as some complex system that consists of various components interconnected with each other. Therefore, considering the systems approach as the basis for building large systems and as the basis for creating methods for their analysis and synthesis, it is first of all necessary to define the very concept of a systems approach.

Systems approach- this is an element of the doctrine of the general laws of development of nature and one of the expressions of the dialectical doctrine. With a systematic approach to modeling systems, it is necessary first of all to clearly define the purpose of the modeling. Since it is impossible to completely simulate a really functioning system (the original system, or the first system), a model (the model system, or the second system) is created for the problem at hand.

Thus, in relation to modeling issues, the goal arises from the required modeling tasks, which allows one to approach the selection of a criterion and evaluate which elements will be included in the created model M. Therefore, it is necessary to have a criterion for selecting individual elements into the created model.

Approaches to systems research. It is important for the systems approach to determine system structure- a set of connections between elements of the system, reflecting their interaction. Structure systems can be studied

1. from outside from the point of view of the composition of individual subsystems and the relationships between them,

2. and from the inside, when individual properties are analyzed that allow the system to achieve a given goal, i.e. when the functions of the system are studied.

In accordance with this, a number of approaches have been outlined to the study of the structure of a system with its properties, which should first of all include structural approach And functional approach.

At structural approach the composition of the selected elements of the system S and the connections between them are revealed. The set of elements and connections between them allows us to judge the structure of the system. The latter, depending on the purpose of the study, can be described at different levels of consideration. The most general description of the structure is a topological description, which allows one to define the constituent parts of the system in the most general terms and is well formalized on the basis of graph theory.

Less common is functional description, when individual functions are considered, i.e., system behavior algorithms, and implemented functional approach, which evaluates the functions that the system performs, whereby a function is understood as a property that leads to the achievement of a goal. Since a function displays a property, and a property reflects the interaction of the system S with the external environment E, the properties can be expressed in the form of either some characteristics of the elements and subsystems of the system, or the system S as a whole. If there is some comparison standard, you can enter quantitative and qualitative characteristics of systems. For a quantitative characteristic, numbers are entered that express the relationship between this characteristic and the standard. The qualitative characteristics of the system are found, for example, using the method of expert assessments.

The manifestation of system functions in time S(t), i.e. the functioning of the system, means the transition of the system from one state to another, i.e. movement in the state space Z.

The systems approach was used in systems engineering due to the need to study large real systems, when the insufficiency and sometimes erroneousness of making any particular decisions affected. The emergence of a systems approach was influenced by the increasing amount of initial data during development, the need to take into account complex stochastic relationships in the system and the influences of the external environment E. All this forced researchers to study a complex object not in isolation, but in interaction with the external environment, as well as in conjunction with other systems of some kind. metasystems. The systems approach allows us to solve the problem of building a complex system, taking into account all factors and possibilities, proportional to their significance, at all stages of studying the system S and building the model M.

The systems approach means that each system S is an integrated whole even when it consists of separate disconnected subsystems. Thus, the basis of the systems approach is the consideration of the system as an integrated whole, and this consideration during development begins with the main thing - the formulation of the purpose of operation.

The process of synthesis of the M model based on the systems approach is conventionally presented in Fig. b. Based on the initial data D, which is known from the analysis of the external system, those restrictions that are imposed on the system from above or based on the possibilities of its implementation, and based on the purpose of operation, the initial requirements are formulated T to the system model S. Based on these requirements, approximately some subsystems are formed P, elements E and the most difficult stage of synthesis is carried out - the choice IN components of the system, for which special criteria for selecting HF are used. When modeling, it is necessary to ensure maximum efficiency of the system model.

Efficiency usually defined as a certain difference between some indicators of the value of the results obtained as a result of operating the model and the costs that were invested in its development and creation.