Place the stages of computer modeling in the correct order. Structure and main stages of the modeling process

Modeling is a creative process. It is very difficult to put it into a formal framework. In the most general form, it can be presented step by step in the following form.

Stage I. Formulation of the problem

Each time when solving a specific problem, such a scheme may undergo some changes: some block may be removed or improved. All stages are determined by the task and modeling goals.

In the most general sense, a task is a problem that needs to be solved. The main thing is to define the modeling object and understand what the result should be.

Based on the nature of the formulation, all problems can be divided into two main groups. The first group includes tasks in which it is necessary to study how the characteristics of an object change under some influence on it. This formulation of the problem is usually called “what will happen if...”. The second group of tasks has the following generalized formulation: what impact should be made on the object. so that its parameters satisfy some given condition? This formulation of the problem is often called “how to do so that...”.

The goals of the simulation are determined by the design parameters of the model. Most often, this is a search for an answer to the question posed in the formulation of the problem. Next they move on to a description of the object or process. At this stage, the factors on which the behavior of the model depends are identified. When modeling in spreadsheets, only those parameters that have quantitative characteristics can be taken into account. Sometimes the problem can already be formulated in a simplified form, and it clearly sets goals and defines the model parameters that need to be taken into account.

When analyzing an object, it is necessary to answer the following question: can the object or process under study be considered as a single whole, or is it a system consisting of simpler objects? If it is a single whole, then you can move on to building an information model. If it is a system, you need to move on to analyzing the objects that make it up and determining the connections between them.

Main goals of modeling:

Understand how a specific object works, its structure, properties, laws of development.

Learn to control an object under given conditions.

Predict the consequences of a certain impact on an object.

Stage II. Model development

Based on the results of the object analysis, an information model is compiled. It describes in detail all the properties of an object, their parameters, actions and relationships.

Next, the information model must be expressed in one of the symbolic forms. Considering that we will work in a spreadsheet environment, the information model must be converted into a mathematical one. Based on information and mathematical models, a computer model is compiled in the form of tables, in which three areas of data are distinguished: initial data, intermediate calculations, results. The source data is entered manually. Calculations, both intermediate and final, are carried out using formulas written according to the rules of spreadsheets.

Stage III. Computer experiment

To give life to new design developments, introduce new technical solutions into production, or test new ideas, an experiment is needed. In the recent past, such an experiment could be carried out either in laboratory conditions on installations specially created for it, or in situ, i.e. on a real sample of the product, subjecting it to all kinds of tests. This requires large material costs and time. Computer studies of models came to the rescue. When conducting a computer experiment, the correctness of the models is checked. The behavior of the model is studied under various object parameters. Each experiment is accompanied by an understanding of the results. If the results of a computer experiment contradict the meaning of the problem being solved, then the error must be looked for in an incorrectly chosen model or in the algorithm and method for solving it. After identifying and eliminating errors, the computer experiment is repeated.

Stage IV. Analysis of simulation results.

The final stage of modeling is model analysis. Based on the obtained calculation data, we check how well the calculations correspond to our understanding and modeling goals. At this stage, recommendations for improving the adopted model and, if possible, the object or process are determined.

System (simulation) modeling owes its birth to prof. Massachusetts Institute of Technology (USA) to J. Forrester, who first used this method to model the production and economic activities of an enterprise. The system dynamics method gained the greatest popularity in the early 70s after the appearance of the works of J. Forrester and D. Meadows on global modeling in the global development projects “World-2” and “World-3”. The availability of an approach to constructing mathematical models and the applicability of system dynamics ideas for solving a wide range of problems in ecology, economics, and demography have contributed to the widespread introduction of simulation modeling in various fields of knowledge.

Simulation system is a set of models that simulate the phenomenon under study, combined with databases, the ability to visualize and analyze the results obtained for decision making.

One of the domestic founders of system modeling, academician N.N. Moiseev noted that simulation has become one of the most important means of system analysis. Imitation is a successful example of a combination of mathematics and the knowledge of a specialist (expert) in a specific subject area. One of the main areas in system modeling is the ability to plan machine experiments to solve assigned problems. For this purpose, models are created that imitate reality.

Simulation modeling of system dynamics consists of a number of stages:

Formulation of the goals and objectives of modeling;

Building a conceptual diagram of the model;

Formalization of the model;

Software implementation;

Identification of model parameters;

Model verification;

Forecast and decision making.

Model building, as a rule, has an iterative nature, involving active interaction between subject specialists (biologists, ecologists, geographers, etc.) and mathematicians (“modellers”) at various stages of model construction. Let's look at the stages of creating a model in more detail.

Formulation of the goals and objectives of modeling

Any modeling begins with the formulation of the problem, defining the general goal of the study. Then, from the general goal of the study, they move on to the list of questions that need to be answered during the modeling process. To describe a natural phenomenon (object), various models can be used (multiple modeling options). It should be remembered that each model is only an approximation, with varying degrees of accuracy or detail, of the natural object in question, and in this respect the modeling capabilities are limited. The researcher's task is to select the best model in each specific case and be able to interpret the results obtained.

One of the important points of this stage is a meaningful analysis of theoretical ideas about the modeled object, existing experience (including negative) in constructing analogous or similar models.

The success of modeling, in addition to theoretical studies, is largely determined by the capabilities of information support for simulation models, since the lack of necessary data to build a model can negate all efforts to create it. Geographic modeling requires detailed information that takes into account, where possible, the diversity of the landscape structure of the territory.

Building a Conceptual Model Diagram

Building a conceptual model diagram includes:

a) description of the structure of the model;

b) identifying the main variables of the model;

c) determining the boundaries of the modeled system;

d) determination of the prediction interval and modeling step;

e) determining the accuracy of the simulation.

The description of the model structure consists of listing all elements (blocks) of the modeled system and the connections between them. Graphically, the model is presented as graph or flowchart.

The identification of the main variables of the model is directly related to the determination of the boundaries of the modeled system. Thus, the model distinguishes internal (endogenous) and external (ecogenic) variables depending on the selected boundaries of the system. Within the boundaries, the system is considered closed. Closedness of a system is a relative concept, which is determined by the specific formulation of the problem being solved. Connections (material, energy and information) are established between the variables of the model.

This stage of modeling is perhaps the most popular among geographers and ecologists. Sometimes this type of modeling is called constructing a conceptual balance model.

The structuring of graphical models should provide the ability to construct a sign (algorithmic) model. It is at this stage that the interaction between the “subject specialist” and the “model designer” becomes especially important.

The simulation step is determined by the simulation interval. If the modeling interval is tens of years, then the step is set to 1 year; if a seasonal forecast is being built, then the modeling step is set to 1 day. It is believed that within the step the modeled parameter remains constant.

Formalization of the model

Formalization of the model consists in determining the analytical dependencies between the model variables. Any model, as a rule, is based on the law of conservation of matter and energy, which is written in the form of balance equations, and balance equations can be presented both in algebraic form and in the form of differential equations, including partial differential equations. The system of balance equations is supplemented by a number of empirical dependencies, usually in algebraic form. The system of equations is solved by known mathematical methods.

Lesson objectives:

• Educational:
  • updating knowledge on the main types of models;
  • study the stages of modeling;
  • develop the ability to transfer knowledge to a new situation.
  • consolidate the acquired knowledge in practice.
• Developmental:
  • development of logical thinking, as well as the ability to highlight the main thing, compare, analyze, generalize.
• Educational:
  • cultivate the will and perseverance to achieve final results.

Lesson type: learning new material.

Teaching methods: lecture, explanatory and illustrative (presentation), frontal survey, practical work, test

Forms of work: group work, individual work.

Means of education: didactic material, demonstration screen, handouts.

DURING THE CLASSES

I. Organizational moment

Preparation for the lesson: greeting, checking students' readiness for work.

II. Preparation for active activities at the main stage of the lesson

Announcement of the work plan for the lesson.

Updating of reference knowledge

Students answer test questions on the topic “Types of models”

1. Determine which of the listed models are material and which are informational. Please indicate material model numbers only.

A) Model of the decoration of a theatrical production.
B) Costume sketches for a theatrical performance.
B) Geographical atlas.
D) Volumetric model of a water molecule.
E) The equation of a chemical reaction, for example: CO 2 + 2NaOH = Na 2 CO 2 3 + H 2 O.
E) Model of a human skeleton.
G) Formula for determining the area of ​​a square with side h: S = h 2 .
H) Train schedule.
I) Toy steam locomotive.
K) Subway map.
K) Table of contents of the book.

2. For each model in the first column, determine what type it is (second column):

3. Determine which aspect of the original object is being modeled in the examples given.

4. Which of the following models are dynamic?

A) Map of the area.
B) Friendly cartoon.
C) A program that simulates the movement of dial hands on the display screen.
D) Essay plan.
D) Graph of air temperature changes during the day.

5. Which of the following models are formalized?

A) Algorithm flowchart.
B) Cooking recipe.
C) Description of the appearance of a literary character.
D) Assembly drawing of the product.
D) Book form in the library.

6. Which of the following models are probabilistic?

A) Weather forecast.
B) Report on the activities of the enterprise.
B) Device operation diagram.
D) Scientific hypothesis.
D) Table of contents of the book.
E) Plan of events dedicated to Victory Day.

7. Is the type of the following model correctly defined: “The graph of the expected change in daily air temperature is a dynamic formalized model of the behavior of this weather indicator, intended for short-term forecasting”?

A) Yes.
B) No.

8. Which of the statements are true?

A) The formula of a chemical reaction is an information model.
B) The table of contents of the book is a recording probabilistic unformalized model of its content.
C) An ideal gas in physics is an imaginary model that simulates the behavior of a real gas.
D) House design - a graphical reference probabilistic model that describes the appearance of the object.

9. For each model, determine its type according to its role in managing the modeling object.

Student answer sheet for the “Types of Models” test

Last name, first name, class__________________________________________

Source:Beshenkov S.A., Rakitina E.A. Solving typical modeling problems. //Informatics at school: Supplement to the journal “Informatics and Education”, No. 1–2005. M.: Education and Informatics, 2005. – 96 p.: ill.

IV. Learning new material

Teacher's opening speech: “We continue to work on the topic “Models and Simulation.” Today we will look at the main stages of modeling.”
Studying new material on the topic: “Main stages of modeling”, using a presentation ( Annex 1 ).

Stage I. Formulation of the problem

The problem formulation stage is characterized by three main points: description of the problem, determination of modeling goals.

Description of the task

When describing a problem, a descriptive model is created using natural languages ​​and pictures. Using a descriptive model, you can formulate basic assumptions using the problem conditions.
Based on the nature of the formulation, all problems can be divided into two main groups.
TO first group we can include tasks in which it is necessary to study how the characteristics of an object will change under some influence on it: “what will happen if?..”. . For example, will it be sweet if you put two teaspoons of sugar in tea?
Second group The problem has the following formulation: what impact must be made on the object in order for its parameters to satisfy some given condition? This formulation of the problem is often called “how to do it so that...”. For example, what volume must a balloon filled with helium be in order for it to rise upward with a load of 100 kg?
Third group These are complex tasks. An example of such an integrated approach is solving the problem of obtaining a chemical solution of a given concentration:

A well-posed problem is one in which:

• all connections between the initial data and the result are described;
• all initial data are known;
• a solution exists;
• the problem has only one solution.

Purpose of modeling

Defining the purpose of modeling allows you to clearly establish which input data are important, which are unimportant, and what is required to be obtained as an output.

Formalization of the task

To solve any problem using a computer, it is necessary to present it in a strict, formalized language, for example, using the mathematical language of algebraic formulas, equations or inequalities. In addition, in accordance with the goal, it is necessary to select parameters that are known (initial data) and that need to be found (results), taking into account restrictions on the permissible values ​​of these properties.
However, it is not always possible to find formulas that express the result through the initial data. In such cases, approximate mathematical methods are used to obtain the result with a given accuracy.

Stage II. Model development

The information model of the problem allows you to make a decision on choosing a software environment and clearly present the algorithm for constructing a computer model.

Information model

1. Select the type of information model;
2. Determine the essential properties of the original that need to be included in the model, discard
   unimportant (for this task);
3. To build a formalized model is a model written in a formal language (mathematics, logic, etc.) and reflecting only the essential properties of the original;
4. Develop an algorithm for the model. An algorithm is a clearly defined order of actions that need to be performed to solve a problem.

Computer model

A computer model is a model implemented using a software environment.
The next step is to transform the information model into a computer model, i.e. express it in a computer-readable language. There are various ways to build computer models, including:
– creation of a computer model in the form of a project in one of the programming languages;
– building a computer model using spreadsheets, computer-aided drafting systems, or other applications. The choice of software environment determines the algorithm for constructing a computer model, as well as the form of its presentation.

Stage III. Computer experiment

Experiment is a study of the model in the conditions of interest to us.
The first point of a computer experiment is testing the computer model.
Testing is a test of a model on simple initial data with a known result.
To check the correctness of the model construction algorithm, a test set of initial data is used, for which the final result is known in advance.
For example, if you use calculation formulas in modeling, then you need to select several options for the initial data and calculate them “manually”. Once the model is built, you test with the same input data and compare the simulation results with the calculated data. If the results coincide, then the algorithm is correct; if not, errors must be eliminated.
If the algorithm of the constructed model is correct, then you can move on to the second point of the computer experiment - conducting a study of the computer model.
When conducting research, if a computer model exists in the form of a project in one of the programming languages, it needs to be launched, input the initial data and obtain the results.
If a computer model is examined, for example in a spreadsheet, a chart or graph can be constructed.

Stage IV. Analysis of simulation results

The ultimate goal of modeling is to analyze the results obtained. This stage is decisive - either continue the research or finish it.
The basis for developing a solution is the results of testing and experiments. If the results do not correspond to the goals of the task, it means that errors or inaccuracies were made at the previous stages. This could be either an incorrect formulation of the problem, or errors in the formulas, or an unsuccessful choice of the modeling environment, etc. If errors are identified, then the model needs to be adjusted, that is, a return to one of the previous stages. The process is repeated until the experimental results meet the modeling goals.

V. Consolidation of the studied material

1). Questions for discussion in class:

– Name the two main types of modeling problems.
– List the most well-known purposes of modeling.
– What characteristics of a teenager are important for recommendations on choosing a profession?
– For what reasons is the computer widely used in modeling?
– Name the computer modeling tools you know.
– What is a computer experiment? Give an example.
– What is model testing?
– What errors occur during the modeling process? What should you do when an error is discovered?
– What is the analysis of modeling results? What conclusions are usually drawn?

2) Task. Make the largest box from a square piece of cardboard.

VI. Summing up the lesson

Analyze student work and announce grades for work in class.

VII. Self-study assignment

Write a short summary of the lesson and study it.

Modeling process steps

In general, the modeling process consists of several stages:

1. Description modeling object. To do this, the structure of the phenomena that make up the real process is studied. As a result of this study, a meaningful description of the process appears, in which it is necessary to present, as clearly as possible, all the necessary patterns. From this description it follows staging applied problem. The problem statement determines the modeling goals, the list of required quantities, and the required accuracy. Moreover, the formulation may not have a strict mathematical formulation.

A meaningful description serves as the basis for constructing formalized scheme– an intermediate link between a meaningful description and a mathematical model. It is not always developed, but when, due to the complexity of the process under study, a direct transition from a meaningful description to a mathematical model turns out to be impossible. The form of presentation of the material should also be verbal, but there must be a precise mathematical formulation of the research problem, process characteristics, system of parameters, dependencies between characteristics and parameters.

2. Model selection, which well captures the essential properties of the original and is easy to research. The transformation of a formalized scheme into a mathematical model is carried out using mathematical methods without the influx of additional information. At this stage, all relationships are written in analytical form, logical conditions are written in the form of inequalities, and analytical form is given to all information if possible. When constructing a mathematical description, equations of various types are used: algebraic (stationary modes), ordinary differential equations (non-stationary objects), partial differential equations are used to mathematically describe the dynamics of objects with distributed parameters. If the process has both deterministic and stochastic properties, integro-differential equations are used).

3. Model study. In this case, all actions are performed on the model and are aimed directly at obtaining knowledge about this object, at establishing the laws of its development. An important advantage of model research is the ability to repeat many phenomena for different initial conditions and with different patterns of their changes over time.

4. Interpretation of results. At this stage, the issue of transferring the values ​​obtained from the mathematical model to the real object of study is considered. The researcher is interested in the properties of the object which is replaced by the model. The possibility of such knowledge translation exists due to the presence of a certain correspondence between the elements and relations of the model and the elements and relations of the original. These connections are established during the modeling process. When using a mathematical model, one should keep in mind the question of the accuracy of the results - the degree of adequacy of the description of the object.

The success of using mathematical modeling depends on how well the model was built, the adequacy, the degree of knowledge of the model, and the ease of operating with it. The use of computers in mathematical modeling makes it possible to study, under any conditions, the variation of parameters and indicators of external factors to obtain any conditions, incl. and not implemented in full-scale experiments. This implies the possibility of obtaining answers to many questions that arise at the stage of development and design of objects without the use of other, more complex methods.

Stages of the modeling process - concept and types. Classification and features of the category "Stages of the modeling process" 2017, 2018.

Topic 2. Main stages of modeling

Plan:

1. Formalization
2. Modeling stages
3. Modeling goals.

1. Formalization

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

Formalization - is the process of identifying the internal structure of an object, phenomenon or process and translating it into a specific information structure- form.

Modeling of any system is impossible without preliminary formalization. In fact, formalization is the first and very important stage of the modeling process. Models reflect the most essential things in the objects, processes and phenomena being studied, based on the stated purpose of the modeling. This is the main feature and main purpose of the models.

Example. It is known that the strength of tremors is usually measured on a ten-point scale. In fact, we are dealing with the simplest model for assessing the strength of this natural phenomenon. Indeed, the “stronger” relation, which operates in the real world, is here formally replaced by the “more” relation, which has meaning in the set of natural numbers: the weakest earthquake corresponds to the number 1, the strongest - 10. The resulting ordered set of 10 numbers is a model that gives idea of ​​the strength of tremors.

2. Modeling stages

Before taking on 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 a prototype. It can be an existing or designed object or process. The final stage of modeling is making a decision based on knowledge about the object.

The chain looks like this:

Examples.

Modeling when creating new technical means can be considered using the example of the history of the development of space technology.

To realize space flight, two problems had to be solved: to overcome gravity and to ensure advancement in airless space. Isaac Newton spoke about the possibility of overcoming the Earth's gravity in the 17th century. K. E. Tsiolkovsky proposed to create a jet engine for movement in space, which uses fuel from a mixture of liquid oxygen and hydrogen, which release significant energy during combustion. He compiled a fairly accurate descriptive model of the future interplanetary spacecraft with drawings, calculations and justifications. Less than half a century passed before the descriptive model of K. E. Tsiolkovsky became the basis for real modeling in the design bureau under the leadership of S. P. Korolev. In full-scale experiments, various types of liquid fuel, the shape of a rocket, a flight control system and life support for astronauts, instruments for scientific research, etc. were tested. The result of versatile modeling was powerful rockets that launched artificial Earth satellites, ships with astronauts on board, and space stations.

Let's look at another example. Famous chemist of the 18th century. Antoine Lavoisier, studying the combustion process, carried out numerous experiments. He simulated combustion processes with various substances, which he heated and weighed before and after the experiment. It turned out that some substances become heavier after heating. Lavoisier suggested that something was added to these substances during the heating process. Thus, modeling and subsequent analysis of the results led to the definition of a new substance - oxygen, to the generalization of the concept of “combustion”, provided an explanation for many known phenomena and opened new horizons for research in other fields of science, in particular in biology, since oxygen turned out to be one of the main components respiration and energy exchange of animals and plants.

Modeling is a creative process. It is very difficult to put it into a formal framework. In its most general form, it can be presented in stages, as shown in the diagram:

Modeling stages

When solving a specific problem, this scheme may undergo some changes: some block will be removed or improved, some will be added. The content of the stages is determined by the task and modeling goals.

Let's consider the main stages of modeling in more detail.

StageI. Statement of the problem

A task is a problem that needs to be solved. At the stage of setting the task it is necessary:

1) describe the task,

2) determine the goals of the modeling,

3) analyze an object or process.

Description of the task.

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