The concept of model and simulation. The concepts of "model", "modeling", various approaches to the classification of models. Modeling steps

The concepts of "model", "modeling", various approaches to the classification of models. Modeling steps

Model (modelium)- about the Latin measure, image, method, etc.

Model- this is a new object, different from the original one, which has properties that are essential for the purposes of modeling and, within the framework of these goals, replace the original object (the object is the original)

Or you can say in other words: a model is a simplified representation of a real object, process or phenomenon.

Conclusion. The model is required in order to:

Understand how a particular object is arranged - what are its structure, basic properties, laws of development and interaction with the outside world;

Learn to manage an object or process and determine best ways management with given goals and criteria (optimization);

Predict the direct and indirect consequences of the implementation of the specified methods and forms of impact on the object;

Classification of models.

Features by which models are classified:

1. Scope of use.

2. Accounting for the time factor and area of ​​use.

3. By way of presentation.

4. Branch of knowledge (biological, historical, sociological, etc.).

5. Scope of use

Educational: visual aids, training programs, various simulators;

Experienced: the model of the ship is tested in the pool to determine the stability of the ship when rolling;

Scientific and technical: an electron accelerator, a device that simulates a lightning discharge, a stand for testing a TV;

Gaming: military, economic, sports, business games;

simulation: the experiment is either repeated many times in order to study and evaluate the consequences of any actions on the real situation, or is carried out simultaneously with many other similar objects, but set in different conditions).

2. Accounting for the factor of time and area of ​​use

Static model - it's like a one-time slice on the object.

Example: You came to the dental clinic for an oral examination. The doctor examined and recorded all the information in the card. Card entries that give a picture of the state oral cavity on the this moment time (the number of milk, permanent, filled, extracted teeth) and will be a statistical model.

Dynamic Model allows you to see changes in an object over time.

An example is the same student's card, which reflects the changes that occur with his teeth at a certain point in time.

3. Classification by way of presentation

First two large groups: material and information. The names of these groups, as it were, show what the models are made of.

material models can otherwise be called subject, physical. They reproduce the geometric and physical properties of the original and always have a real embodiment.

Kids toys. From them, the child receives the first impression of the world around him. A two-year-old child plays with a teddy bear. When, years later, the child sees a real bear in the zoo, he will easily recognize him.

School allowances, physical and chemical experiments. They model processes, such as the reaction between hydrogen and oxygen. Such an experience is accompanied by a deafening bang. The model confirms the consequences of the emergence of an "explosive mixture" of harmless and widespread substances in nature.

Maps when studying history or geography, diagrams of the solar system and the starry sky in astronomy lessons, and much more.

Conclusion. Material models implement a material (touch, smell, see, hear) approach to the study of an object, phenomenon or process.

Information models cannot be touched or seen with one's own eyes, they do not have a material embodiment, because they are built only on information. This modeling method is based on an informational approach to the study of the surrounding reality.

Informational models - a set of information that characterizes the properties and states of an object, process, phenomenon, as well as the relationship with the outside world.

Information characterizing an object or process can have a different volume and form of presentation, be expressed various means. This diversity is as limitless as the possibilities of each person and his imagination are. Information models include sign and verbal.

Iconic model - information model expressed special characters, i.e., by means of any formal language.

Iconic models are all around us. These are drawings, texts, graphs and diagrams.

By the method of implementation, sign models can be divided into computer and non-computer.

Computer model - a model implemented by means of the software environment.

Verbal (from the Latin "verbalis" - oral) model - an information model in a mental or conversational form.

These are models obtained as a result of reflection, conclusions. They may remain mental or be expressed verbally. An example of such a model can be our behavior when crossing the street.

The process of building a model is called modeling, in other words, modeling is the process of studying the structure and properties of the original with the help of a model.

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Ideal modeling fundamentally differs from subject (material) modeling.

Ideal modeling - is based not on the material analogy of the object and the model, but on the analogy of the ideal, conceivable.

iconic modeling is modeling that uses sign transformations of any kind as models: diagrams, graphs, drawings, formulas, symbol sets.

Mathematical modeling is modeling in which the study of an object is carried out by means of a model formulated in the language of mathematics: a description and study of the laws of Newtonian mechanics by means of mathematical formulas.

The modeling process consists of the following steps:

The main task of the modeling process is to choose the model that is most adequate to the original and transfer the results of the study to the original. There are enough common methods and modeling methods.

Before building a model of an object (phenomenon, process), it is necessary to single out its constituent elements and the relationships between them (to conduct a system analysis) and “translate” (display) the resulting structure into some predetermined form - to formalize the information.

Formalization is the process of highlighting and translating internal structure object, phenomenon or process into a certain information structure - form.

Formalization is the reduction of essential properties and features of the modeling object in the chosen form (to the chosen formal language).

Modeling steps

Before undertaking any work, you need to clearly imagine the starting point and each point of the activity, as well as its approximate stages. The same can be said about modeling. The starting point here is the prototype. It can be an existing or projected object or process. The final stage of modeling is making a decision based on knowledge about the object.

The chain looks like this.

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I STAGE. STATEMENT TASKS.

A task is a problem that needs to be solved. At the stage of setting the problem, it is necessary to reflect three main points: the description of the problem, the definition of modeling goals, and the analysis of the object or process.

Task description

The task is formulated in ordinary language, and the description should be understandable. The main thing here is to define the object of modeling and understand what the result should be.

The purpose of the simulation

1) knowledge of the world around

2) creation of objects with specified properties (determined by setting the task "how to do so that ...".

3) determination of the consequences of impact on the object and acceptance right decision. The purpose of modeling problems like “what happens if ...”, (what happens if you increase the fare in transport, or what happens if you bury nuclear waste in such and such an area?)

Object Analysis

At this stage, the modeled object and its main properties are clearly identified, what it consists of, what connections exist between them.

A simple example of subordinate object relationships is sentence parsing. First, the main members (subject, predicate) are distinguished, then the secondary members related to the main ones, then the words related to the secondary ones, etc.

II STAGE. MODEL DEVELOPMENT

1. Information model

At this stage, properties, states, actions and other characteristics of elementary objects are clarified in any form: orally, in the form of diagrams, tables. An idea is formed about the elementary objects that make up the original object, i.e., the information model.

Models should reflect the most significant features, properties, states and relationships of objects of the objective world. It is they who give full information about the object.

2. Iconic model

Before starting the modeling process, a person makes preliminary sketches of drawings or diagrams on paper, derives calculation formulas, i.e., composes an information model in one or another symbolic form, which can be either computer or non-computer.

3. Computer model

A computer model is a model implemented by means of a software environment.

There are many software packages that allow you to study (model) information models. Each software environment has its own tools and allows you to work with certain types information objects.

The person already knows what the model will be and uses the computer to give it an iconic shape. For example, to build geometric models, diagrams, graphical environments are used, for verbal or tabular descriptions - a text editor environment.

STAGE III. COMPUTER EXPERIMENT

With the development of computer technology, a new unique research method has appeared - a computer experiment. computer experiment includes a sequence of work with the model, a set of purposeful user actions on a computer model.

IV STAGE ANALYSIS OF SIMULATION RESULTS

The ultimate goal of modeling is making a decision, which should be developed on the basis of a comprehensive analysis of the results obtained. This stage is decisive - either you continue the study, or finish. Perhaps you know the expected result, then you need to compare the received and expected results. In case of a match, you can make a decision.

According to this feature, models are divided into two broad classes:

• abstract (mental) models;
• material models.

Rice. 1.1.

Often in the practice of modeling there are mixed, abstract-material models.

abstract patterns are certain constructions of generally accepted signs on paper or other material carrier or in the form computer program.

Abstract models, without going into too much detail, can be divided into:

• symbolic;
• mathematical.

Symbolic model- this is a logical object that replaces the real process and expresses the main properties of its relations using a certain system of signs or symbols. It's either the words natural language, or words of the corresponding thesaurus, graphs, diagrams, etc.

The symbolic model may have independent meaning, but, as a rule, its construction is the initial stage of any other simulation.

Mathematical modeling- this is the process of establishing correspondence to the modeled object of some mathematical construction, called a mathematical model, and the study of this model, which allows obtaining the characteristics of the modeled object.

Mathematical modeling - the main objective and the main content of the studied discipline.

Mathematical models can be:

• analytical;
• imitation;
• mixed (analytical and simulation).

Analytical Models- these are functional relationships: systems of algebraic, differential, integro-differential equations, logical conditions. Maxwell's equations - an analytical model of the electromagnetic field. Ohm's law is a model of an electrical circuit.

The transformation of mathematical models according to known laws and rules can be considered as experiments. A solution based on analytical models can be obtained as a result of a single calculation, regardless of the specific values ​​of the characteristics ("in general terms"). This is visual and convenient for identifying patterns. However, for complex systems, it is not always possible to build an analytical model that fully reflects the real process. Nevertheless, there are processes, for example, Markov ones, the relevance of modeling of which by analytical models has been proven by practice.

Simulation. The creation of computers led to the development of a new subclass of mathematical models - simulation.

Simulation modeling involves the representation of the model in the form of some algorithm - a computer program - the execution of which imitates the sequence of changing states in the system and thus represents the behavior of the simulated system.

The process of creating and testing such models is called simulation modeling, and the algorithm itself is called a simulation model.

What is the difference between simulation and analytical models?

In the case of analytical modeling, a computer is a powerful calculator, adding machine. Analytical model solved on a computer.

In the case of simulation modeling, the simulation model - the program - implemented on a computer.

Simulation models quite simply take into account the influence of random factors. For analytical models, this is a serious problem. In the presence of random factors, the necessary characteristics of the simulated processes are obtained by multiple runs (realizations) of the simulation model and further statistical processing of the accumulated information. Therefore, often simulation modeling of processes with random factors called statistical modeling.

If the study of the object is difficult using only analytical or simulation modeling, then mixed (combined), analytical and simulation modeling is used. When constructing such models, the processes of the object functioning are decomposed into constituent subprocesses, and for which, perhaps, analytical models are used, and simulation models are built for the remaining subprocesses.

material modeling based on the use of models representing real technical structures. It can be the object itself or its elements (natural modeling). This may be a special device - a model that has either a physical or geometric similarity to the original. It may be a different device. physical nature than the original, but the processes in which are described by similar mathematical relationships. This is the so-called analog simulation. Such an analogy is observed, for example, between oscillations of a satellite communication antenna under wind load and oscillation electric current in a specially selected electrical circuit.

Often created material abstract models. That part of the operation that cannot be described mathematically is modeled materially, the rest is abstract. Such, for example, are command-and-staff exercises, when the work of headquarters is a full-scale experiment, and the actions of troops are reflected in documents.

Classification according to the criterion considered - the method of implementing the model - is shown in fig. 1.2.

1.3. Modeling steps

Mathematical modeling like any other, it is considered an art and a science. A well-known specialist in the field of simulation modeling Robert Shannon called his book widely known in the scientific and engineering world: " Simulation- art and science". Therefore, in engineering practice there is no formalized instruction on how to create models. And, nevertheless, an analysis of the techniques used by model developers allows us to see a fairly transparent stage of modeling.

First stage: clarification of the goals of modeling. In fact, this is the main stage of any activity. The goal essentially determines the content of the remaining stages of modeling. Note that the difference between a simple system and a complex one is generated not so much by their essence, but also by the goals set by the researcher.

Typically, the goals of modeling are:

• forecast of the object's behavior under new modes, combinations of factors, etc.;
• selection of a combination and values ​​of factors that provide the optimal value of process efficiency indicators;
• analysis of the sensitivity of the system to changes in certain factors;
• verification of various kinds of hypotheses about the characteristics of random parameters of the process under study;
• determination of functional relationships between the behavior ("reaction") of the system and influencing factors, which can contribute to the prediction of behavior or sensitivity analysis;
• clarification of the essence, a better understanding of the object of study, as well as the formation of the first skills for operating a simulated or operating system.

Second phase: building a conceptual model. conceptual model(from lat. conception) - a model at the level of the defining idea, which is formed when studying the modeled object. At this stage, the object is investigated, the necessary simplifications and approximations are established. Significant aspects are identified, secondary ones are excluded. Units of measure and ranges of model variables are set. If possible, then conceptual model is presented in the form of well-known and well-developed systems: queuing, control, auto-regulation, different kind vending machines, etc. conceptual model fully sums up the study of design documentation or experimental examination of the object being modeled.

The result of the second stage is a generalized scheme of the model, fully prepared for a mathematical description - the construction of a mathematical model.

Third stage: choice of a programming or modeling language, development of an algorithm and a model program. The model can be analytical or simulation, or a combination of both. In the case of an analytical model, the researcher must master the solution methods.

In the history of mathematics (and this, by the way, is the history of mathematical modeling) there are many examples of when the need to model various kinds of processes led to new discoveries. For example, the need to simulate motion led to the discovery and development of differential calculus(Leibniz and Newton) and the corresponding solution methods. The problems of analytical modeling of ship stability led Academician A. N. Krylov to create the theory of approximate calculations and an analog computer.

The result of the third stage of modeling is a program compiled in the most convenient language for modeling and research - universal or special.

Fourth stage: planning an experiment. Mathematical model is the object of the experiment. The experiment should be as informative as possible, satisfy the restrictions, provide data with the necessary accuracy and reliability. There is a theory of experiment planning, we will study the elements of this theory that we need in the appropriate place in the discipline. GPSS World, AnyLogic, etc.) and can be applied automatically. It is possible that in the course of the analysis of the obtained results, the model can be refined, supplemented, or even completely revised.

After analyzing the simulation results, they are interpreted, that is, the results are translated into terms subject area. This is necessary because usually subject matter specialist(the one who needs the results of research) does not have the terminology of mathematics and modeling and can perform his tasks, operating only with concepts that are well known to him.

This concludes the consideration of the modeling sequence, having made a very important conclusion about the need to document the results of each stage. This is necessary for the following reasons.

Firstly, modeling is an iterative process, that is, from each stage, a return can be made to any of the previous stages to clarify the information needed at this stage, and the documentation can save the results obtained at the previous iteration.

Secondly, in the case of studying a complex system, large teams of developers participate in it, and different stages are performed by different teams. Therefore, the results obtained at each stage should be transferable to subsequent stages, that is, they should have a unified presentation form and content understandable to other interested specialists.

Thirdly, the result of each of the stages should be a valuable product in itself. For example, conceptual model may not be used for further transformation into a mathematical model, but be a description that stores information about the system, which can be used as an archive, as a learning tool, etc.

Sometimes models are written in programming languages, but this is a long and expensive process. Mathematical packages can be used for modeling, but experience shows that they usually lack many engineering tools. It is optimal to use the simulation environment.

In our course, . Laboratory works and the demos you will encounter in the course should be run as Stratum-2000 environment projects.

The model, made taking into account the possibility of its modernization, of course, has disadvantages, for example, low speed code execution. But there are also undeniable advantages. The structure of the model, connections, elements, subsystems are visible and saved. You can always go back and redo something. A trace in the model design history is preserved (but when the model is debugged, it makes sense to remove service information from the project). In the end, the model that is handed over to the customer can be designed as a specialized automated workstation (AWP), already written in a programming language, in which attention is already mainly paid to the interface, speed parameters and other consumer properties that are important for customer. The workstation is certainly an expensive thing, so it is released only when the customer has fully tested the project in the simulation environment, made all the comments and undertakes not to change his requirements anymore.

Modeling is an engineering science, a technology for solving problems. This remark is very important. Since technology is a way to achieve a result with a known quality in advance and guaranteed costs and deadlines, then modeling, as a discipline:

• studies ways of solving problems, that is, it is an engineering science;
• is a universal tool that guarantees the solution of any problems, regardless of the subject area.

Subjects related to modeling are: programming, mathematics, operations research.

Programming- because the model is often implemented on an artificial medium (plasticine, water, bricks, mathematical expressions ...), and the computer is one of the most versatile carriers of information and, moreover, active (simulates plasticine, water, bricks, counts mathematical expressions, etc.). Programming is a way of presenting an algorithm in a language form. An algorithm is one of the ways of representing (reflecting) a thought, a process, a phenomenon in an artificial computing environment, which is a computer (von Neumann architecture). The specificity of the algorithm is to reflect the sequence of actions. Simulation can use programming if the object being modeled is easy to describe in terms of its behavior. If it is easier to describe the properties of an object, then it is difficult to use programming. If the simulation environment is not built on the basis of the von Neumann architecture, programming is practically useless.

What is the difference between an algorithm and a model?

An algorithm is a process of solving a problem by implementing a sequence of steps, while a model is a set of potential properties of an object. If you put a question to the model and add additional terms in the form of initial data (relationship with other objects, initial conditions, restrictions), then it can be resolved by the researcher with respect to unknowns. The process of solving the problem can be represented by an algorithm (but other methods of solving are also known). In general, examples of algorithms in nature are unknown, they are the product of the human brain, the mind capable of establishing a plan. The algorithm itself is the plan unfolded into a sequence of actions. It is necessary to distinguish between the behavior of objects associated with natural causes, and the craft of the mind, which controls the course of movement, predicts the result on the basis of knowledge and chooses the appropriate behavior.

model + question + additional conditions = task.

Mathematics is a science that provides the ability to calculate models that can be reduced to a standard (canonical) form. The science of finding solutions to analytical models (analysis) by means of formal transformations.

Operations research- a discipline that implements methods for studying models in terms of finding the best control actions on models (synthesis). Mostly deals with analytical models. Helps to make decisions using built models.

Design is the process of creating an object and its model; modeling is a way to evaluate the design result; there is no modeling without design.

Related disciplines for modeling can be recognized as electrical engineering, economics, biology, geography, and others in the sense that they use modeling methods to study their own applied object (for example, a landscape model, an electrical circuit model, a cash flow model, etc.).

As an example, let's see how you can detect and then describe a pattern.

Let's say that we need to solve the “Cutting Problem”, that is, we need to predict how many cuts in the form of straight lines will be required to divide the figure (Fig. 1.16) into a given number of pieces (for example, it is enough that the figure is convex).

Let's try to solve this problem manually.

From fig. 1.16 it can be seen that with 0 cuts, 1 piece is formed, with 1 cut, 2 pieces are formed, with two - 4, with three - 7, with four - 11. Can you now tell in advance how many cuts will be required to form, for example, 821 pieces ? I don't think so! Why are you having a hard time? - You don't know the rule K = f(P) , where K- number of pieces P- the number of cuts. How to detect a pattern?

Let's make a table linking the known numbers of pieces and cuts.

While the pattern is not clear. Therefore, let's consider the differences between individual experiments, let's see how the result of one experiment differs from another. Having understood the difference, we will find a way to move from one result to another, that is, the law connecting K and P .

Already some regularity has appeared, isn't it?

Let's calculate the second differences.

Now everything is simple. Function f called generating function. If it is linear, then the first differences are equal to each other. If it is quadratic, then the second differences are equal to each other. Etc.

Function f There is a special case of Newton's formula:

Odds a , b , c , d , e for our quadratic functions f are in the first cells of the rows of the experimental table 1.5.

So, there is a pattern, and it is as follows:

K = a + b · p + c · p · ( p– 1)/2 = 1 + p + p · ( p– 1)/2 = 0.5 p 2 + 0.5 p + 1 .

Now that the pattern has been determined, we can solve the inverse problem and answer the question: how many cuts do you need to make to get 821 pieces? K = 821 , K= 0.5 p 2 + 0.5 p + 1 , p = ?

We solve a quadratic equation 821 = 0.5 p 2 + 0.5 p + 1 , find the roots: p = 40 .

Let's summarize (pay attention to this!).

We couldn't figure out the solution right away. The experiment proved to be difficult. I had to build a model, that is, to find a pattern between the variables. The model turned out in the form of an equation. By adding a question to the equation and an equation reflecting a known condition, they formed a problem. Since the problem turned out to be of a typical type (canonical), it was possible to solve it using one of the known methods. Therefore, the problem was solved.

And it is also very important to note that the model reflects causal relationships. There is indeed a strong relationship between the variables of the constructed model. A change in one variable entails a change in the other. We have previously said that "the model plays a system-forming and meaning-forming role in scientific knowledge, allows us to understand the phenomenon, the structure of the object under study, to establish the relationship of cause and effect with each other." This means that the model allows you to determine the causes of phenomena, the nature of the interaction of its components. The model links causes and effects through laws, that is, variables are linked together through equations or expressions.

But!!! Mathematics itself does not make it possible to derive any laws or models from the results of experiments., as it may seem after the example just considered. Mathematics is only a way of studying an object, a phenomenon, and, moreover, one of several possible ways of thinking. There is also, for example, a religious method or a method used by artists, emotional-intuitive, with the help of these methods they also learn the world, nature, people, themselves.

So, the hypothesis about the relationship between variables A and B must be introduced to the researcher himself, from the outside, moreover. How does a person do it? It is easy to advise to introduce a hypothesis, but how to teach this, to explain this action, which means, again, how to formalize it? We will show this in detail in the future course “Modeling Artificial Intelligence Systems”.

But why this must be done from the outside, separately, additionally and beyond that, we will explain now. This reasoning bears the name of Gödel, who proved the incompleteness theorem - it is impossible to prove the correctness of a certain theory (model) within the framework of the same theory (model). Look again at fig. 1.12. Model more high level transforms equivalent to lower level model from one view to another. Or generates a model more low level according to its equivalent description. But she cannot transform herself. The model builds the model. And this pyramid of models (theories) is endless.

In the meantime, in order to "not get blown up on nonsense", you need to be on your guard and check everything common sense. Let us give an example, an old well-known joke from the folklore of physicists.

In this paper, we propose to analyze in detail the topic of modeling in computer science. This section is of great importance for the training of future specialists in the field of information technology.

To solve any problem (industrial or scientific), computer science uses the following chain:

It is worth paying special attention to the concept of "model". Without the presence of this link, the solution of the problem will not be possible. Why is the model used and what is meant by this term? We will talk about this in the next section.

Model

Modeling in computer science is the compilation of an image of a real-life object that reflects all the essential features and properties. A model for solving a problem is necessary, since it is, in fact, used in the process of solving.

AT school course Informatics, the topic of modeling begins to be studied as early as the sixth grade. At the very beginning, children need to be introduced to the concept of a model. What it is?

• Simplified similarity of the object;
• Reduced copy of a real object;
• Scheme of a phenomenon or process;
• Image of a phenomenon or process;
• Description of the phenomenon or process;
• Physical analogue of the object;
• Information analogue;
• A placeholder object that reflects the properties of the real object, and so on.

The model is a very broad concept, as it has already become clear from the above. It is important to note that all models are usually divided into groups:

• material;
• ideal.

A material model is understood as an object based on a real-life object. It can be any body or process. This group is further subdivided into two types:

• physical;
• analog.

Such a classification is conditional, because it is very difficult to draw a clear boundary between these two subspecies.

The ideal model is even more difficult to characterize. She is associated with:

• thinking;
• imagination;
• perception.

It includes works of art (theater, painting, literature, and so on).

Modeling Goals

Modeling in computer science is a very important stage, as it has a lot of goals. Now we invite you to get to know them.

First of all, modeling helps to understand the world around us. From time immemorial, people have accumulated the acquired knowledge and passed it on to their descendants. Thus, a model of our planet (globe) appeared.

In past centuries, non-existent objects were modeled, which are now firmly entrenched in our lives (umbrella, mill, and so on). Currently, modeling is aimed at:

• identification of the consequences of any process (increase in the cost of travel or disposal of chemical waste underground);
• ensuring the effectiveness of decisions made.

Simulation tasks

information model

Now let's talk about another type of models studied in the school computer science course. Computer modeling, which every future IT specialist needs to master, includes the process of implementing an information model using computer tools. But what is it, an information model?

It is a list of information about any object. What does this model describe, and what useful information carries:

• properties of the object being modeled;
• his condition;
• connections with the outside world;
• relationships with external entities.

What can serve as an information model:

• verbal description;
• text;
• picture;
• table;
• scheme;
• drawing;
• formula and so on.

A distinctive feature of the information model is that it cannot be touched, tasted, and so on. It does not carry a material embodiment, as it is presented in the form of information.

A systematic approach to creating a model

In what grade of the school curriculum is modeling studied? Informatics grade 9 introduces students to this topic in more detail. It is in this class that the child learns about the systematic approach of modeling. Let's talk about this in a little more detail.

Let's start with the concept of "system". It is a group of interrelated elements that work together to complete a task. Often used to build a model systematic approach, since the object is considered as a system functioning in some environment. If any complex object is modeled, then the system is usually divided into smaller parts - subsystems.

Purpose of use

Now we will consider the goals of modeling (computer science grade 11). Earlier it was said that all models are divided into certain types and classes, but the boundaries between them are conditional. There are several features by which it is customary to classify models: purpose, area of ​​expertise, time factor, presentation method.

As for the goals, it is customary to distinguish the following types:

• educational;
• experienced;
• imitation;
• gaming;
• scientific and technical.

The first type includes educational materials. To the second, reduced or enlarged copies of real objects (a model of a structure, an airplane wing, and so on). allows you to predict the outcome of an event. Simulation modeling is often used in medicine and social sphere. For example, does the model help to understand how people will react to this or that reform? Before you do major surgery human organ transplant, many experiments have been carried out. In other words, the simulation model allows you to solve the problem by trial and error. A game model is a kind of economic, business or war game. With the help of this model, it is possible to predict the behavior of an object in different situations. A scientific and technical model is used to study a process or phenomenon (a device that simulates a lightning discharge, a model of planetary motion solar system etc).

Field of knowledge

In which class do students get more familiar with modeling? Informatics grade 9 focuses on preparing its students for exams for admission to higher educational institutions. Since there are questions on modeling in the USE and GIA tickets, now it is necessary to consider this topic in as much detail as possible. And so, how is the classification by area of ​​knowledge? On this basis, the following types are distinguished:

• biological (for example, artificially induced diseases in animals, genetic disorders, malignant neoplasms);
• firm behavior, market price formation model, and so on);
• historical (family tree, models historical events, model of the Roman army and the like);
• sociological (model of personal interest, the behavior of bankers when adapting to new economic conditions) etc.

Time factor

According to this characteristic, two types of models are distinguished:

• dynamic;
• static.

Already, judging by the name alone, it is not difficult to guess that the first type reflects the functioning, development and change of an object in time. Static, on the contrary, is able to describe an object at a particular moment in time. This view is sometimes called structural, since the model reflects the structure and parameters of the object, that is, it provides a slice of information about it.

Examples are:

• a set of formulas that reflect the movement of the planets of the solar system;
• graph of air temperature change;
• video recording of a volcanic eruption and so on.

Examples of a statistical model are:

• list of planets in the solar system;
• area map and so on.

Presentation method

To begin with, it is very important to say that all models have a shape and form, they are always made of something, somehow presented or described. On this basis, it is accepted as follows:

• material;
• intangible.

The first type includes material copies of existing objects. They can be touched, smelled and so on. They reflect the external or internal properties, actions of an object. What are material models for? They are used for the experimental method of cognition (experimental method).

We also addressed non-material models earlier. They use the theoretical method of knowledge. Such models are called ideal or abstract. This category is divided into several subspecies: imaginary models and informational.

Information models list various information about the object. Tables, figures, verbal descriptions, diagrams, and so on can act as an information model. Why is this model called intangible? The thing is that it cannot be touched, since it does not have a material embodiment. Among information models, there are sign and visual models.

An imaginary model is one of the creative process that takes place in the imagination of a person, which precedes the creation of a material object.

Modeling steps

The 9th grade computer science topic "Modeling and Formalization" has big weight. It is required to be studied. In grades 9-11, the teacher is obliged to introduce students to the stages of creating models. This is what we will do now. So, the following stages of modeling are distinguished:

• meaningful statement of the problem;
• mathematical formulation of the problem;
• developments with the use of computers;
• model operation;
• getting a result.

It is important to note that when studying everything that surrounds us, the processes of modeling and formalization are used. Computer science is a subject dedicated to modern methods studying and solving problems. Therefore, the emphasis is on models that can be implemented using a computer. Special attention in this topic should be given to the point of developing a solution algorithm using electronic computers.

Links between objects

Now let's talk a little about relationships between objects. There are three types in total:

• one to one (such a connection is indicated by a one-way arrow in one or the other direction);
• one-to-many (multiple relationships are indicated by a double arrow);
• many-to-many (such a relationship is indicated by a double arrow).

It is important to note that relationships can be conditional and unconditional. An unconditional relationship involves the use of each instance of an object. And in the conditional, only individual elements are involved.

In order to understand the essence of mathematical modeling, consider the basic definitions, features of the process.

The essence of the term

Modeling is the process of creating and applying a model. It is considered to be any abstract or material object that replaces the real object of modeling in the process of studying. An important point is the preservation of the properties necessary for a full-fledged analysis of the subject.

Computer modeling is a variant of knowledge based on a mathematical model. It implies a system of inequalities, equations, logical sign expressions that fully reflect all the characteristics of a phenomenon or object.

Mathematical modeling involves specific calculations, the use of computer technology. More research is needed to explain the process. This task is successfully solved by computer simulation.

Specificity of computer simulation

This way of studying complex systems is considered effective and efficient. It is more convenient and easier to analyze computer models, since various computational actions can be performed. This is especially true in cases where, for physical or material reasons, real experiments do not allow obtaining the desired result. The logic of such models makes it possible to determine the main factors that determine the parameters of the studied original.

This application of mathematical modeling makes it possible to identify the behavior of an object in various conditions to identify the influence of various factors on his behavior.

Fundamentals of computer modeling

What is the basis for this modeling? What Scientific research based on ICT? Let's start with the fact that any computer simulation is based on certain principles:

• mathematical modeling to describe the process under study;
• application of innovative mathematical models for detailed consideration of the processes under study.

Varieties of modeling

Currently, there are different methods of mathematical modeling: simulation and analytical.

The analytical option is associated with the study of abstract models of a real object in the form of differential, algebraic equations, which provide for the implementation of a clear computer technology that can give an accurate solution.

Simulation modeling involves the study of a mathematical model in the form of a specific algorithm that reproduces the functioning of the analyzed system through the sequential execution of a system of simple calculations and operations.

Features of building a computer model

Let's take a closer look at how this simulation works. What are stages computer research? Let's start with the fact that the process is based on moving away from a clear object or phenomenon being analyzed.

Such modeling consists of two main stages: the creation of a qualitative and quantitative model. Computer study consists in carrying out a system of computational actions on a personal computer aimed at analyzing, systematizing, comparing the results of the study with the real behavior of the analyzed object. If necessary, additional refinement of the model is carried out.

Modeling steps

How is modeling carried out? What are the stages of computer research? So, the following algorithm of actions regarding the construction of a computer model is distinguished:

Stage 1. Setting the goal and objectives of the work, identifying the object of modeling. It is supposed to collect data, formulate a question, identify the goals and forms of research, and describe the results obtained.

Stage 2. Analysis and study of the system. The description of the object, the creation of an information model, the selection of software and technical means, examples of mathematical modeling are selected.

Stage 3. Transition to a mathematical model, development of a design method, selection of an algorithm of actions.

Stage 4. Selection of a programming language or environment for modeling, discussion of analysis options, writing an algorithm in a specific programming language.

Stage 5 It consists in carrying out a complex of computational experiments, debugging calculations, and processing the results obtained. If necessary, the modeling is corrected at this stage.

Stage 6 Interpretation of results.

How is the simulation analyzed? What are research software products? First of all, it implies the use of text, graphic editors, spreadsheets, mathematical packages that allow you to get the maximum result from the research.

Conducting a computational experiment

All methods of mathematical modeling are based on experiments. Under them, it is customary to understand experiments conducted with a model or object. They are in the implementation certain actions, allowing to determine the behavior of the experimental sample in response to the proposed actions.

A computational experiment cannot be imagined without carrying out calculations that are associated with the use of a formalized model.

The basics of mathematical modeling involve research with a real object, but computational actions are carried out with it an exact copy(model). When choosing a specific set of initial indicators of the model, after the completion of computational actions, it is possible to obtain optimal conditions for the full functioning of a real object.

For example, having a mathematical equation that describes the course of the analyzed process, when changing the coefficients, initial and intermediate conditions, we can assume the behavior of the object. In addition, it is possible to create a reliable forecast of the behavior of this object or natural phenomenon under certain conditions. In the case of a new set of initial data, it is important to carry out new computational experiments.

Comparison of received data

In order to carry out an adequate verification of a real object or a created mathematical model, as well as to evaluate the results of research on computer technology with the results of an experiment conducted on a full-scale prototype, comparison of research results is carried out.

The decision to build depends on the discrepancy between the information obtained during the research. finished sample or about adjusting the mathematical model.

Such an experiment makes it possible to replace natural expensive research with calculations on computer technology, for minimal time frames analyze the possibilities of using the object, identify the conditions for its actual operation.

Modeling in environments

For example, in a programming environment, three stages of mathematical modeling are used. At the stage of creating an algorithm and an information model, values ​​are determined that will be input parameters, research results, and their type is revealed.

If necessary, special mathematical algorithms are compiled in the form of block diagrams, written in a specific programming language.

A computer experiment involves the analysis of the results obtained in the calculations, their correction. Among milestones such a study, we note the testing of the algorithm, the analysis of the performance of the program.

Its debugging involves finding and eliminating errors that lead to an undesirable result, the appearance of errors in calculations.

Testing involves checking the correct functioning of the program, as well as assessing the reliability of its individual components. The process consists in checking the operability of the program, its suitability for studying a certain phenomenon or object.

Spreadsheets

Modeling using spreadsheets allows you to cover a large amount of tasks in various subject areas. They are considered a universal tool that allows you to solve the laborious task of calculating the quantitative parameters of an object.

In the case of such a simulation option, some transformation of the algorithm for solving the problem is observed, there is no need to develop a computational interface. At the same time, there is a debugging stage, which includes the removal of data errors, the search for a connection between cells, and the identification of computational formulas.

As the work progresses, additional tasks appear, for example, outputting results to paper, rational presentation of information on a computer monitor.

Sequencing

Modeling is carried out in spreadsheets according to a certain algorithm. First, the objectives of the study are determined, the main parameters and relationships are identified, and a specific mathematical model is compiled based on the information received.

For qualitative consideration of the model, initial, intermediate, as well as final characteristics are used, supplemented with drawings, diagrams. With the help of graphs and charts, they get a visual representation of the results of the work.

Modeling in a DBMS environment

It allows you to solve the following tasks:

• store information, carry out its timely editing;
• organize the available data according to specific characteristics;
• create different criteria for data selection;
• present the information in a convenient way.

As the model is developed on the basis of the initial data, optimal conditions are created for describing the characteristics of the object using special tables.

At the same time, information is sorted, data is searched and filtered, and algorithms for calculations are created. Using the computer information panel, you can create different screen forms, as well as options for obtaining printed paper reports on the progress of the experiment.

If the results obtained do not coincide with the planned options, the parameters are changed, additional studies are carried out.

Application of a computer model

Computational experiment and computer simulation are new scientific research methods. They make it possible to modernize the computing apparatus used to build a mathematical model, to concretize, refine, and complicate experiments.

Among the most promising for practical use, conducting a full-fledged computational experiment, the design of reactors for powerful nuclear power plants is distinguished. In addition, this includes the creation of magnetohydrodynamic transducers electrical energy, as well as a balanced perspective plan for the country, region, industry.

It is with the help of computer and mathematical modeling that it is possible to carry out the design of devices necessary for the study of thermonuclear reactions and chemical processes.

Computer modeling and computational experiments make it possible to reduce far "non-mathematical" objects to the formulation and solution of a mathematical problem.

This opens up great opportunities for the use of the mathematical apparatus in a system with modern computer technology to address issues related to the development outer space, "conquest" of atomic processes.

It is modeling that has become one of the most important options for understanding various surrounding processes and natural phenomena. This knowledge is a complex and time-consuming process, involves the use of a system various kinds modeling, starting with the development of reduced models of real objects, ending with the selection of special algorithms for complex mathematical calculations.

Depending on what processes or phenomena will be analyzed, certain algorithms of actions are selected, mathematical formulas for computing. Computer modeling allows you to get the desired result at minimal cost, important information about the properties and parameters of an object or phenomenon.