Methods and approaches to modeling distributed systems. Approaches to building a system model. Static information models

Classical(or inductive) approach modeling considers the system, moving from the particular to the general, and synthesizes it by merging components developed separately. Systematic 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 beneficial properties(for example, control systems) are specified criteria, determining the degree of usefulness of the resulting properties. Since any modeling object is a system of interconnected elements, let us introduce the concept of a system. System S there is a purposeful set of interconnected elements of any nature. External environment. E represents a set of elements of any nature existing outside the system that influence the system or are under its influence.

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

The classical method of building a model uses a functional approach, in which the element of the model is taken component describing the behavior of one property and not reflecting the actual composition of the elements. In addition, the system components are isolated from each other, which poorly reflects the modeled system. This method of constructing a model is applicable only for simple systems, since it requires the inclusion in the functions that describe the properties of the system, relationships between properties that may be poorly defined or unknown.

With the complication of modeled systems, when it is impossible to take into account all the mutual influences of properties, it is used system method, based on a structural approach. At the same time, the system S is divided into a number of subsystems S l with their own properties, which, naturally, are easier to describe by functional dependencies, and connections between 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 functional relationships between system properties S, makes the model more flexible, since changing the properties of one of the subsystems automatically changes the properties of the system.

Classification of types of modeling

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 to classify them, for example, by purpose of use, the presence of random influences, relation to time, feasibility of implementation, scope, etc. (Table 14).

Table 14. Model types

By purpose of use models are classified into scientific experiment, in which the model is studied using various means of obtaining data about the object, the possibility of influencing the course of the process, in order to obtain new data about the object or phenomenon; comprehensive testing and production experiment, using full-scale testing of a physical object to obtain high reliability about its characteristics; optimization, related to finding optimal system indicators (for example, finding minimum costs or determination of maximum profit).

According to the presence of impacts per system models are divided into deterministic(there are no random influences in the systems) and stochastic(systems contain probabilistic influences). Some authors classify these same models by the method of estimating parameters systems: in deterministic systems, model parameters are assessed by one indicator for specific values of their initial data; V stochastic systems, the presence of probabilistic characteristics of the initial data allows one to evaluate the system parameters using several indicators.

In relation to time models are divided into static, describing the system at a certain point in time, and dynamic, considering the behavior of a system over time. In turn, dynamic models are divided into discrete, in which all events occur at time intervals, and continuous, where all events occur continuously in time.

If possible, implementation models are classified as mental, describing a system that is difficult or impossible to model realistically, real, in which the system model is represented either by a real object or a part of it, and informational, implementing information processes (occurrence, transmission, processing and use of information) on a computer. In turn, mental models are divided into visual(in which the simulated processes and phenomena occur clearly); symbolic(the system model represents a logical object in which the main properties and relationships of the real object are expressed by a system of signs or symbols) and mathematical(represent systems of mathematical objects that allow one to obtain the studied characteristics of a real object). Real models are divided into full-scale(conducting research on a real object and subsequent processing of experimental results using similarity theory) and physical(conducting research on installations that preserve the nature of the phenomenon and have a physical similarity).

By area of application models are divided into universal, intended for use by many systems, and specialized, created to study a specific system.

Mathematical models

The most important stage in building a model is the transition from a meaningful description to a formal one, which is explained by the participation at this stage of specialists in the subject area where the modeled system exists, and specialists in the field of system modeling. The most convenient language for their communication, the purpose of which is to build an adequate model of the system, is usually the language of mathematical descriptions. Mathematical description the system is compact and convenient for further implementation on a computer for the purpose of statistical testing,

Examples of building dynamic models

When modeling continuous dynamic objects, the models are usually differential equations, linking the behavior of an object with time. A positive property of differential equations is that the same equation models systems of different physical natures.

The independent variable in dynamic systems is usually time, on which the unknown values of the desired function that determine the behavior of the object depend. Mathematical description of the model in general form:

where are n-dimensional vectors and are continuous.

For example, the process of small oscillations of a pendulum is described by the ordinary differential equation

Process in an electrical oscillatory circuit .

Obviously, if we put

We obtain an equation that describes the time state of both systems

A general mathematical model allows one to study one system while simulating the operation of another.

Models of dynamic systems based on differential equations have found wide application in the theory of control of various technical objects. Under the influence of disturbances unknown in advance, the actual behavior of the system deviates from the desired one, specified by the algorithm, and to bring its behavior closer to the required value, automatic control of the system is introduced into the system. It can be built into the system itself, but during simulation the control unit is separated from the system itself. In general, the structure of a multidimensional automatic control system (ACS) is presented in Fig. 3.

Figure 3. Structure of a multidimensional automatic control system.

Information models

Information models in many cases rely on mathematical models, since when solving problems, the mathematical model of the object, process or phenomenon under study is inevitably transformed into an information model for its implementation on a computer. Let's define the basic concepts of the information model.

Information object is a description of a real object, process or phenomenon in the form of a set of its characteristics (information elements), called details. An information object of a certain structure (requisite composition) forms type (class), which is assigned a unique Name. An information object with specific characteristics is called copy. Each instance is identified by a job key details (key). The same details in different information objects can be both key and descriptive. An information object can have multiple keys.

Example. The STUDENT information object has the following requisites: number(grade book number is a key detail), last name, first name, patronymic, date of birth, code of place of study. Information object PERSONAL PROFILE: student number, home address, secondary education certificate number, marital status, children. The STUDY PLACE information object includes the following details: code(key props), name of the university, faculty, group. Information object TEACHER: code(key props), department, last name, first name, patronymic, academic degree, academic title, position.

Relationship, existing between real objects are defined in information models as communications. There are three types of connections: one to one (1:1), one to many(1:∞) and many to many(∞: ∞).

Connection one to one determines that one instance of information object X corresponds to no more than one instance of information object Y, and vice versa.

Example. The information objects STUDENT and PERSONAL PROFILE will be connected by the relation one to one. Each student has certain unique data in his personal file.

When contacting one to many One instance of information object X can correspond to any number of instances of information object Y, but each instance of object Y is associated with at most one instance of object X.

Example. A connection must be established between the information objects PLACE OF STUDY and STUDENT one to many. The same place of study may be repeated many times for different students.

Connection many to many assumes that one instance of information object X corresponds to any number of instances of object Y, and vice versa.

Example. Information objects STUDENT and TEACHER have a connection many to many. Each student learns from many teachers, and each teacher teaches many students.

Examples of information models

Let us define an information model as a connected set of information objects that describe information processes in the subject area under study. We divide existing information models into universal and specialized. Universal models are intended for use in various subject areas, these include: databases And database management systems, automated systems management, knowledge bases, expert systems. Specialized models are designed to describe specific systems, are unique in their capabilities, and are more expensive.

Universal models.

Databases

Databases represent a related set of structured data related to a specific process or phenomenon in a specific subject area.

Database Management System is a software package for creating, organizing the necessary processing, storing and transmitting databases.

The core of any database is data representation model. A data model represents many data structures and the relationships between them.

Distinguish hierarchical, network And relational data models. The hierarchical model represents the relationships between objects (data) in the form of a tree.

The main concepts of the hierarchical model include:

node- a set of data attributes describing the object;

connection- a line connecting the nodes of the lower level with one node of the upper level. In this case, the node at the higher level is called ancestor for the nodes of the lower level corresponding to it, in turn, the nodes of the lower level are called descendants the overlying node associated with them (for example, in Fig. 4. node B1 is the ancestor for nodes CI, C2, and nodes C1, C2 are descendants of node B1);

level- number of the node layer, counted from the root.

Figure 4. Hierarchical data model

Quantity trees in the database is determined by the number root records. Each node has a single path from the root.

Network structure has the same components as the hierarchical one, but each node can be connected to any other node (Fig. 5). The network approach to data organization is an extension of the hierarchical one. In hierarchical models, a child record must have only one ancestor; in network - a descendant can have any number of ancestors.

Figure 5. Network data model

Both of these models are not widely used due to the complexity of implementing graphs in the form of machine data structures, in addition, it is difficult to carry out information search operations in them.

The most widespread is the third data model - relational, it can also describe a hierarchical and network model. The relational model focuses on organizing data in the form of two-dimensional tables.

Artificial intelligence

The ideas of modeling the human mind have been known since ancient times. This was first mentioned in the work of the philosopher and theologian Raymunda Lullia(c.1235 - c.1315) “Great Art”, who not only expressed the idea of a logical machine for solving various problems, based on the universal classification of concepts (XIV century), but also tried to implement it. Rene Descartes(1596-1650) and Gottfried Wilhelm Leibniz(1646-1716) independently developed the doctrine of the innate ability of the mind to know and the universal and necessary truths of logic and mathematics, and worked to create a universal language for the classification of all knowledge. It is on these ideas that the theoretical foundations of creating artificial intelligence are based. Push to further development models of human thinking began to appear in the 40s. XX century COMPUTER. In 1948, an American scientist Norbert Wiener(1894-1964) formulated the main provisions of a new science - cybernetics. In 1956, at Stanford University (USA), at a seminar called “Artificial intelligence* (artificial intelligence), dedicated to solving logical problems, a new scientific direction related to machine modeling of human intellectual functions and called artificial intelligence. The field soon split into two main areas: neurocybernetics and black box cybernetics.

Neurocybernetics turned to the structure of the human brain as the only thinking object and began its hardware modeling. Physiologists have long identified neurons - nerve cells connected to each other - as the basis of the brain. Neurocybernetics deals with the creation of elements similar to neurons and their integration into functioning systems, these systems are called neural networks. In the mid-80s. In the 20th century, the first neurocomputer was created in Japan, simulating the structure of the human brain. Its main area of application is pattern recognition.

Black box cybernetics uses different principles, the structure of the model is not the main thing, what is important is its reaction to the given input data, at the output the model should react like the human brain. Scientists in this area are developing algorithms for solving intellectual problems for existing computing systems. The most significant results:

Maze Search Model(late 50s), which considers the state graph of an object and searches for the optimal path from input data to output data. In practice, this model has not been widely used.

Heuristic programming(early 60s) developed action strategies based on pre-known preset rules (heuristics). Heuristics - a theoretically unfounded rule that allows you to reduce the number of searches in finding the optimal path.

Methods of mathematical logic. The resolution method allows you to automatically prove theorems based on certain axioms. In 1973, a logic programming language was created Prologue, allowing the processing of symbolic information.

Since the mid-70s. The idea of modeling the specific knowledge of expert specialists is being implemented. The first expert systems appear in the USA. Arises new technology artificial intelligence, based on the representation and use of knowledge. Since the mid-80s. artificial intelligence is being commercialized. Investments in this industry are growing, industrial expert systems are appearing, and interest in self-learning systems is increasing.

Knowledge bases

When studying intelligent systems It is necessary to find out what knowledge is and how it differs from data. Concept knowledge are defined in different ways, but there is no comprehensive definition.

Here are some of the definitions:

Knowledge- identified patterns of the subject area (principles, connections, laws) that allow solving problems in this area.

Knowledge- well-structured data, or data about data, or metadata.

Knowledge- a set of information that forms a holistic description corresponding to a certain level of awareness about the issue, object, etc. being described.

From the point of view of artificial intelligence, knowledge is defined as formalized information that is referred to in the process of logical inference. Knowledge bases are used to store knowledge. Knowledge Base- the basis of any intelligent system.

From the point of view of solving problems in a certain subject area, knowledge is conveniently divided into two categories - facts And heuristics. The first category describes circumstances known in the field; knowledge in this category is sometimes called textual, emphasizing its sufficient description in the literature. The second category of knowledge is based on the practical experience of a specialist expert in a given subject area.

In addition, knowledge is divided into procedural And declarative. Historically, procedural knowledge was the first to appear, “scattered” in algorithms. They managed the data. To change them, it was necessary to make changes to the programs. With the development of artificial intelligence, an increasing part of knowledge was formed in data structures: tables, lists, abstract data types, knowledge increasingly became declarative.

Declarative knowledge is a set of information about the characteristics of the properties of specific objects, phenomena or processes, presented in the form of facts and heuristics. Historically, such knowledge was accumulated in the form of various reference books; with the advent of computers, it took the form of databases. Declarative knowledge is often simply called data; it is stored in the memory of an information system (IS) so that it has immediate access for use.

Procedural knowledge stored in the IC memory in the form of descriptions of procedures by which they can be obtained. In the form of procedural knowledge, they usually describe methods for solving problems in the subject area, various instructions, techniques, etc. Procedural knowledge is methods, algorithms, programs for solving various problems in a selected subject area; they form the core of the knowledge base. Procedural knowledge is formed as a result of performing procedures on facts as initial data.

One of the most important problems specific to artificial intelligence systems is knowledge representation. The form of knowledge representation significantly influences the characteristics and properties of the system. To manipulate various knowledge real world it is necessary to simulate them on a computer. There are many knowledge representation models for various subject areas, but most of them belong to the following classes: logical models", production models; semantic networks; frame models.

Traditionally, in the representation of knowledge there are formal logical models, based on classical first-order predicate calculus, when the subject area is described as a set of axioms. All information needed to solve problems is considered as a set of rules and statements, which are represented as formulas in some predicate logic. Knowledge reflects the totality of such formulas, and obtaining new knowledge comes down to the implementation of logical inference procedures. This logical model is applicable mainly in research “ideal” systems, as it imposes high requirements and limitations on the subject area. Industrial expert systems use its various modifications and extensions.

Studies of human decision-making processes have shown that when reasoning and making a decision, a person uses production rules(from English production- inference rule, generating rule). Product model based on rules, allows you to present knowledge in the form of sentences: IF (list of conditions), THEN (list of actions should be performed). Condition - this is the sentence that is searched in the knowledge base, and action There is some operation that is performed when the search is successful. Actions can be like intermediate, appearing further as conditions and targeted, completing the work of the IS. In the production model, the knowledge base consists of a set of rules. The program that controls the enumeration of rules is called output machine. The inference mechanism connects knowledge and creates a conclusion from its sequence. The conclusion happens direct(matching method, from data to target search) or back(a method of generating a hypothesis and testing it, from the goal to the data).

Example. There is a knowledge base fragment consisting of two rules:

Ave. 1: IF “doing business” and “getting to know the Internet”,

TO "electronic commerce".

Ave. 2: IF "owns a computer"

THAT is “getting to know the Internet.”

The system received data: "doing business" And “owns a computer.”

DIRECT OUTPUT: Based on the available data, obtain a conclusion.

1st pass:

Step 1. Check Ex. 1, does not work - there is not enough data “acquaintance with the Internet”.

Step 2. Check Ex. 2, it works, the base is supplemented by the fact “familiarity with the Internet”.

2nd pass

Step 3. Check Ex. 1, works, the system gives the conclusion “electronic commerce”.

REVERSE OUTPUT: Validate the selected goal using existing rules and data.

1st pass:

Step 1. Goal - “electronic commerce”:

Checking Ave. 1, there is no “acquaintance with the Internet” data, they become a new goal, and there is a rule where it is on the right side.

Step 2. Goal - “get to know the Internet”:

Ave. 2 confirms the target and activates it.

2nd pass: Step 3. Ex. 1 confirms the desired target.

The product model attracts developers with its clarity, modularity, ease of making additions and changes, simplicity of the logical inference mechanism, and is most often used in industrial expert systems.

Semantics is a science that studies the properties of signs and sign systems, their semantic connection with real objects. Semantic Web - this is a directed graph, the vertices of which are concepts, and the arcs are relationships between them (Fig. 6). This is the most general model of knowledge, since it contains the means of all properties characteristic of knowledge: internal interpretation, structure, semantic metrics and activity.

Figure 6. Semantic Web

The advantages of network models are: greater expressive capabilities; visibility of the knowledge system, presented graphically; the proximity of the network structure representing the knowledge system to the semantic structure of phrases in natural language; compliance with modern ideas about the organization of human long-term memory. The disadvantages include the fact that the network model does not contain a clear idea of the structure of the subject area that corresponds to it, so its formation and modification is difficult; network models are passive structures; a special apparatus is used to process them formal conclusion. The problem of finding a solution in a knowledge base such as a semantic network comes down to the problem of searching for a fragment of the network corresponding to a certain subnet of the task, which, in turn, indicates another drawback of the model - the difficulty of searching for output on semantic networks.

Network models are a visual and fairly universal means of representing knowledge. However, their formalization in specific models of representation, use and modification of knowledge is a rather labor-intensive process, especially in the presence of multiple relationships between concepts.

Term frame(from the English frame - framework, frame) is proposed to denote the structure of a unit of knowledge, which can be described by a certain set of concepts for its spatial perception. The frame has a certain internal structure, consisting of a set of elements called slots. Each slot, in turn, is represented by a specific data structure, procedure, or may be associated with another frame. The frame model is a technological model of human memory and consciousness, systematized in the form of a unified theory. Unlike other models, a rigid structure is fixed in frames. In general, a frame is defined as follows:

(FRAME NAME: (1st slot name: 1st slot value);

(2nd slot name: 2nd slot value);

(N-ro slot name: N-ro slot value)).

An important property of frames is inheritance of properties, borrowed from semantic network theory. Inheritance occurs through AKO connections (from A Kind Of, which means “this.”). The ACO slot points to a frame over high level hierarchy, from which it is implicitly inherited, i.e. the values of similar slots are transferred. For example, in the network of frames in Fig. 7 “constructor” inherits the properties of the “engineer” and “person” frames, which are at a higher level of the hierarchy.

Figure 7. Frame network

The frame model is quite universal; it allows you to display the entire diversity of knowledge about the world through:

frame-structures, to designate objects and concepts (lecture, notes, department);

frame-roles(student, teacher, dean);

script frames(passing an exam, celebrating a name day, receiving a scholarship);

situation frames(alarm, work mode school day) etc. The main advantage of frames as a model for representing knowledge is their ability to reflect the conceptual basis of the organization of human memory, as well as flexibility and visibility.

Summarizing the analysis of knowledge representation models, we can draw the following conclusions:

The most powerful are mixed models of knowledge representation.

Expert systems

Designed to analyze data contained in knowledge bases and issue recommendations upon user request. They are used in cases where the source data is well formalized, but decision-making requires extensive special knowledge. Expert systems- these are complex software systems that accumulate the knowledge of specialists in specific subject areas and replicate this empirical experience to provide advice to less qualified users.

Subject areas: medicine, pharmacology, chemistry, geology, economics, law, etc., in which most of the knowledge is personal experience high-level specialists (experts) need expert systems. Those areas where most knowledge is represented in the form of collective experience (for example, higher mathematics) do not need them.

An expert system is defined by a set of logically interconnected rules that form the knowledge and experience of a specialist in a given subject area, and a decision mechanism that allows one to recognize a situation, give recommendations for action, and make a diagnosis.

Modern expert systems are capable of:

Based on the totality of signs of the disease, establish a diagnosis, prescribe treatment, dose medications, develop a treatment program;

Perform the tasks of diagnostic systems in the study of phenomena and processes (for example, for blood analysis; production management; studying the state of the bowels of the earth, oil fields, coal deposits, etc.);

Speech recognition, at this stage in a limited area of application;

Recognize human faces, fingerprints, etc.

In Fig. Figure 8 shows the main components of the expert system model: user(specialist in the subject area for whom this system is intended), knowledge engineer(artificial intelligence specialist is an intermediate link between an expert and a knowledge base), user interface(an application that implements a dialogue between the user and the system), knowledge base - expert system core, solver(an application that simulates expert reasoning based on knowledge available in the knowledge base), clarification subsystem ( an application that allows you to explain on the basis of what the expert system makes recommendations, draws conclusions, and what knowledge is used ), intelligent knowledge base editor(an application that gives a knowledge engineer the ability to create a knowledge base interactively ).

Figure 8. Structure of the expert system model.

Characteristic feature Any expert system is capable of self-development. The source data is stored in the knowledge base in the form of facts, between which certain logical connections are established. If testing reveals incorrect recommendations or conclusions on specific issues, or a conclusion cannot be formulated, this means either the absence important facts in its base, or violations in the logical system of connections. In any case, the system itself can generate a sufficient set of questions for the expert and automatically improve its quality.

Control system

Represents a set of interconnected structural models of subsystems that perform the following functions:

planning(strategic, tactical, operational);

accounting- displays the state of the control object as a result of the execution of production processes;

control- determines the deviation of accounting data from planned goals and standards;

operational management- regulates all processes in order to eliminate any deviations from planned and accounting data;

analysis- determines the trend in the operation of the system and reserves, which are taken into account when planning for the next time period.

Using models in composition information systems began with the application of statistical methods and methods financial analysis, which were implemented by commands of conventional algorithmic languages. Later, special languages were created that made it possible to simulate various situations. Such languages make it possible to build models of a certain type that provide solutions when variables change flexibly.

SOFTWARE. BASIC PROGRAMMING CONCEPTS

BASIC CONCEPTS AND DEFINITIONS

The considered PC hardware together is a universal tool for solving a wide range of problems. However, these problems can be solved only if the PC “knows” the algorithm for solving them.

Algorithm(algorithm) - an exact prescription that determines the process of converting source data into the final result.

General properties of any algorithm are:

– discreteness – the ability to split the algorithm into separate elementary actions;

– certainty (determinism) of the algorithm ensures the unambiguity of the result (repeatability of the result obtained during repeated calculations with the same initial data) and eliminates the possibility of distortion or ambiguous interpretation of the prescription;

– effectiveness – obligatory obtaining of a certain result in a finite number of steps, and if it is impossible to obtain a result, a signal that this algorithm is not applicable to solve the problem;

– mass character – the ability to obtain results with different initial data for a certain class of similar problems.

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 planets 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 different atoms 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, personal computer is a system that consists of various devices, which 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, when you remove one of the computer devices (for example, 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. Simulation method is one of the most important methods scientific research and experimentation.

Systematic 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:

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

Here, an element is understood as a lower-level subsystem, which does not seem appropriate to further divide 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 internal structure systems down to the level of elements - 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 basic technical specifications created model, estimate the time of working with it and the cost of resources to obtain the required quality of the model.

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

consistently move through the stages of creating a model;
coordinate information, resource, reliability and other characteristics;
correctly correlate different levels of model construction;
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 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; changes chemical composition Sun, radiation, etc.

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.

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 everything life cycle systems. 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 distinguished 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, that is, when the functions of the system are studied. In accordance with this, a number of approaches to studying the structure of a system with its properties have emerged, 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. Most general description structure is a topological description that allows you to determine in the most general concepts components of the system and 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 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 systematic approach in these conditions allows not only to build a model of a real object, but also to choose based on this model required quantity control information in a real system, evaluate its performance indicators and thereby, based on modeling, find the most effective option for constructing and 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 its structure is, basic properties, laws of development and interaction with the outside world ( understanding);

2) learn to manage an object (or process) and determine the best ways management with 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) approach modeling considers the system, moving from the particular to the general, and synthesizes it by merging components developed separately. Systematic 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 the behavior of the system 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 the 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.

Classic approach- study of the relationships between in separate parts, and the development of a system model is seen as the summation of individual components into an overall model. Suitable for implementation relatively simple models with the separation of individual functions of a real object and making a decision about the independence of these functions.

The process of synthesis of model M based on the classical (inductive) approach is presented in Fig. 1.1, a. The real object to be modeled is divided into separate subsystems, i.e., the initial data D for modeling is selected and goals C are set that reflect individual aspects of the modeling process. Based on a separate set of initial data D, the goal of modeling a separate aspect of the system’s functioning is set; on the basis of this goal, a certain component K is formed future model. The set of components is combined into a model M. Thus, developing a model M based on the classical approach means summing up the individual components into a single model, with each component solving its own problems and isolated from other parts of the model.

Systematic 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. We can give different definitions of the systems approach, but the most correct is the one that allows us to evaluate the cognitive essence of this approach using such a method of studying systems as modeling. Therefore, it is very important to isolate the system S itself and the external environment E from objective existing reality and a description of the system based on system-wide positions.

A systematic approach allows us to solve the problem of building complex system taking into account all factors and possibilities, proportional to their significance, at all stages of system research and model construction.

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. 1.1, 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 on the basis of the purpose of operation, the initial requirements T for the system model are formulated. On the basis of these requirements, approximately some subsystems P and E elements are formed, and the most complex stage of synthesis is carried out - the selection of B components of the system, for which special criteria for selecting CVs are used.