Computer experiment in the process of modeling. Computer experiment. Control questions and tasks
In conclusion of the chapter, we consider the question: where to attribute a computer experiment and computer simulation ( computer simulations) !
Initially, computer simulation appeared in meteorology and nuclear physics, but today the range of its application in science and technology is extremely wide. In this regard, the example of "global modeling" is very indicative, where the world is viewed as a set of interacting subsystems: population, society, economy, food production, innovation complex, Natural resources, habitat, countries and regions of the world (the first example is the report published in 1972 to the Club of Rome "Limits to Growth"). The development and interaction of these subsystems determine the world dynamics.
Obviously, we are dealing here with a supercomplex system with a lot of nonlinear interactions, for which unable to build a VIO model type. Therefore, here proceed as follows. A multidisciplinary group is assembled, consisting of specialists belonging to various subsystems. This group, based on the knowledge of its members, makes up a block diagram of a large number of elements and relationships. This block diagram is converted into a mathematical computer model representing the system being modeled. After that, numerical experiments are carried out with a computer model, i.e. computer experiments that, from the side of creating models of objects and processes, debugging and execution, resemble a real complex experiment.
There is a certain analogy between thought and computer experiments. In the case of a computer experiment, the computer model worked out in the course of it is an analogue of the FIE model in a mental FIE experiment. In both cases, experimental research is an element of the search for an adequate theoretical model. In the course of this search, in the first case, FECs and interactions between them (and their value) are selected, and in the second case, elements and relationships (and their value). From this comparison it is obvious that in both cases the emergence of new knowledge is possible as a result of such experimental activity. That is, the computer models correspond to the theoretical RES models of the phenomenon, and the computer experiment is a tool for their construction. In this case, experimentation takes place with the model, and not with the phenomenon (according to the work, the same is indicated in the works).
In physics and other natural sciences, in the case of "laboratory" phenomena, a real experiment can change something in the phenomenon itself ("ask it a question"). If this turns out to be enough to create a FIR model, and the only question remains about refining its parameters, then in this case the computer model has a more trivial application than described above, the solution complex equations, describing a physical or technical system, and selection of parameters for systems for which the VIO model is already specified. This case is often referred to as a "numerical experiment".
However, physics also considers phenomena that need to be qualitatively studied before they are placed in the laboratory, for example, the release of nuclear energy or the birth of elementary particles. A similar situation can arise: 1) in the cases of economic or technical complexity of a real experiment listed for a thought experiment, 2) in the absence of a PRI model, i.e. the absence of a theory of the phenomenon (as in the case of turbulent flows). In nuclear physics and particle physics we have the first if not both cases. Here we have a situation similar to "global simulation" and start experimenting with theoretical models through computer simulations. Therefore, it is not surprising that computer simulation appeared very early in nuclear physics.
So, a computer experiment and computer models in a non-trivial case, as in the "global simulation" example, correspond, respectively, to a mental RES experiment and theoretical RES models of the phenomenon.
An experiment is a form of communication between two sides - a phenomenon and a theoretical model. In principle, this implies the possibility of manipulation with two sides. In the case of a real experiment, experimentation occurs with a phenomenon, and in the case of a mental and computer experiment, which can be considered as an analogue of a mental one, with a model. But in both cases, the goal is to obtain new knowledge in the form of an adequate theoretical model.
- This includes E. Winsberg's remark: "It is not true that a real experiment always manipulates only the object of interest. In fact, both in a real experiment and in a simulation, there is a complex relationship between what is manipulated in the study, on the one hand, and world, which are the goal of the study - on the other ... Mendel, for example, manipulated peas, but was interested in studying the phenomenon of general heredity ".
computer experiment with the system model during its research and design is carried out in order to obtain information about the characteristics of the process of functioning of the object under consideration. The main task of planning computer experiments is to obtain the necessary information about the system under study under resource constraints (computer time, memory, etc.). Among the particular tasks solved when planning computer experiments are the tasks of reducing the cost of computer time for modeling, increasing the accuracy and reliability of modeling results, checking the adequacy of the model, etc.
The effectiveness of computer experiments with models significantly depends on the choice of the experimental plan, since it is the plan that determines the volume and procedure for performing calculations on a computer, methods for accumulating and statistical processing of the system simulation results. . Therefore, the main task of planning computer experiments with a model is formulated as follows: it is necessary to obtain information about the object of modeling, given in the form of a modeling algorithm (program), with minimal or limited expenditure of machine resources for the implementation of the modeling process.
The advantage of computer experiments over natural ones is the ability to fully reproduce the conditions of the experiment with the model of the system under study. . A significant advantage over full-scale ones is the ease of interrupting and resuming computer experiments, which allows the use of sequential and heuristic planning techniques that may not be feasible in experiments with real objects. When working with a computer model, it is always possible to interrupt the experiment for the time necessary to analyze the results and make decisions about its further course (for example, on the need to change the values of the model characteristics).
The disadvantage of computer experiments is that the results of some observations depend on the results of one or more previous ones, and therefore they contain less information than independent observations.
In relation to the database, a computer experiment means the manipulation of data in accordance with the set goal using the tools of the DBMS. The purpose of the experiment can be formed based on the general purpose of the simulation and taking into account the requirements of a particular user. For example, there is a database "Dean's office". The overall goal of creating this model is to manage the educational process. If you need to obtain information about the progress of students, you can make a request, i.e. conduct an experiment to select the desired information.
The DBMS environment toolkit allows you to perform the following operations on data:
1) sorting - ordering data according to some attribute;
2) search (filtering) - selection of data that satisfies a certain condition;
3) creation of calculation fields - transformation of data into another form based on formulas.
Information model management is inextricably linked with the development of various criteria for searching and sorting data. Unlike paper file cabinets, where sorting is possible according to one or two criteria, and the search is generally carried out manually - by sorting through cards, computer databases allow you to set any sorting forms for various fields and various search criteria. The computer will sort or select the necessary information without time expenditure according to the given criterion.
For successful work with the information model, database software environments allow you to create calculation fields in which the original information is converted into a different form. For example, based on semester grades, a special built-in function can calculate a student's GPA. Such calculated fields are used either as additional information or as criteria for searching and sorting.
A computer experiment includes two stages: testing (checking the correctness of operations) and conducting an experiment with real data.
After formulating formulas for calculated fields and filters, you need to make sure that they work correctly. To do this, you can enter test records for which the result of the operation is known in advance.
The computer experiment ends with the output of the results in a form convenient for analysis and decision making. One of the advantages of computer information models is the ability to create various forms of presentation of output information, called reports. Each report contains information that meets the purpose of a particular experiment. The convenience of computer reports lies in the fact that they allow you to group information according to given criteria, enter the final fields for counting records by group and in general for the entire database, and then use this information to make a decision.
The environment allows you to create and store several typical, frequently used report forms. Based on the results of some experiments, you can create a temporary report that is deleted after copying it to Text Document or printouts. Some experiments do not require reporting at all. For example, it is required to select the most successful student for awarding an increased scholarship. To do this, it is enough to sort by the average score of grades in the semester. The required information will contain the first entry in the list of students.
| Lesson planning for the school year | Main stages of modeling
Lesson 2
Main stages of modeling
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By studying this topic, you will learn:
What is modeling;
- what can serve as a prototype for modeling;
- what is the place of modeling in human activity;
- what are the main stages of modeling;
- what is a computer model;
What is a computer experiment.
computer experiment
To give life to new design developments, to introduce new technical solutions into production or test new ideas, you need an experiment. An experiment is an experiment that is performed with an object or model. It consists in performing some actions and determining how the experimental sample reacts to these actions.
At school, you conduct experiments in the lessons of biology, chemistry, physics, geography.
Experiments are carried out when testing new product samples at enterprises. Usually, a specially designed setup is used for this purpose, which makes it possible to conduct an experiment in laboratory conditions, or the real product itself is subjected to all kinds of tests (a full-scale experiment). To study, for example, the performance properties of a unit or assembly, it is placed in a thermostat, frozen in special chambers, tested on vibration stands, dropped, etc. It is good if it is a new watch or a vacuum cleaner - the loss during destruction is not great. What if it's a plane or a rocket?
Laboratory and full-scale experiments require large material costs and time, but their significance, nevertheless, is very great.
With the development of computer technology, a new unique method of research has appeared - a computer experiment. In many cases, computer simulation studies have come to help, and sometimes even to replace, experimental samples and test benches. The stage of conducting a computer experiment includes two stages: drawing up an experiment plan and conducting a study.
Experiment plan
The experiment plan should clearly reflect the sequence of work with the model. The first step in such a plan is always to test the model.
Testing is the process of checking the correctness of the constructed model.
Test - a set of initial data that allows you to determine the correctness of the construction of the model.
To be sure of the correctness of the obtained modeling results, it is necessary: ♦ to check the developed algorithm for building the model; ♦ make sure that the constructed model correctly reflects the properties of the original, which were taken into account in the simulation.
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 or predetermined in other ways.
For example, if you use calculation formulas in modeling, then you need to select several options for the initial data and calculate them “manually”. This is test tasks. When the model is built, you test with the same inputs and compare the results of the simulation with the conclusions obtained by calculation. If the results match, then the algorithm is developed correctly, if not, it is necessary to look for and eliminate the cause of their discrepancy. Test data may not reflect the real situation at all and may not carry semantic content. However, the results obtained in the process of testing may prompt you to think about changing the original information or sign model, primarily in that part of it where the semantic content is laid down.
To make sure that the constructed model reflects the properties of the original, which were taken into account in the simulation, it is necessary to select a test example with real source data.
Conducting research
After testing, when you have confidence in the correctness of the constructed model, you can proceed directly to the study.
The plan should include an experiment or series of experiments that meet the objectives of the simulation. Each experiment must be accompanied by an understanding of the results, which serves as the basis for analyzing the results of modeling and making decisions.
The scheme for preparing and conducting a computer experiment is shown in Figure 11.7.
Rice. 11.7. Scheme of a computer experiment
Analysis of simulation results
The ultimate goal of modeling is to make a decision, which should be developed on the basis of a comprehensive analysis of the simulation results. This stage is decisive - either you continue the study, or finish. Figure 11.2 shows that the results analysis phase cannot exist autonomously. The conclusions obtained often contribute to an additional series of experiments, and sometimes to a change in the problem.
The results of testing and experiments serve as the basis for developing a solution. If the results do not correspond to the goals of the task, it means that mistakes were made at the previous stages. This can be either an incorrect statement of the problem, or an overly simplified construction of an information model, or an unsuccessful choice of a modeling method or environment, or a violation of technological methods when building a model. If such errors are identified, then the model needs to be corrected, that is, a return to one of the previous stages. The process is repeated until the results of the experiment meet the objectives of the simulation.
The main thing to remember is that the detected error is also the result. As the proverb says, you learn from your mistakes. The great Russian poet A. S. Pushkin also wrote about this:
Oh, how many wonderful discoveries we have
Prepare enlightenment spirit
And experience, the son of difficult mistakes,
And genius, paradoxes friend,
And chance, god is the inventor...
Control questions and tasks
1. What are the two main types of modeling problem statement.
2. In the well-known "Problem Book" by G. Oster, there is the following problem:
The evil witch, working tirelessly, turns 30 princesses into caterpillars a day. How many days will it take her to turn 810 princesses into caterpillars? How many princesses a day would have to be turned into caterpillars to get the job done in 15 days?
Which question can be attributed to the type of "what will happen if ...", and which - to the type of "how to do so that ..."?
3. List the most well-known goals of modeling.
4. Formalize the playful problem from G. Oster's "Problem Book":
From two booths located at a distance of 27 km from one another, two pugnacious dogs jumped out towards each other at the same time. The first runs at a speed of 4 km / h, and the second - 5 km / h.
How long will the fight start?
5.
Name as many characteristics of the "pair of shoes" object as you can. Compose an information model of an object for different purposes:
■ choice of footwear for hiking;
■ selection of a suitable shoe box;
■ purchase of shoe care cream.
6. What characteristics of a teenager are essential for a recommendation on choosing a profession?
7. Why is the computer widely used in simulation?
8. Name the tools of computer modeling known to you.
9. What is a computer experiment? Give an example.
10. What is model testing?
11. What errors are encountered in the modeling process? What should be done when an error is found?
12. What is the analysis of simulation results? What conclusions are usually drawn?
Home > LectureLECTURE
Topic: Computer experiment. Analysis of simulation results
To give life to new design developments, to introduce new technical solutions into production, or to test new ideas, an experiment is needed. An experiment is an experiment that is performed with an object or model. It consists in performing some actions and determining how the experimental sample reacts to these actions. At school, you conduct experiments in the lessons of biology, chemistry, physics, geography. Experiments are carried out when testing new product samples at enterprises. Usually, a specially designed setup is used for this purpose, which makes it possible to conduct an experiment in laboratory conditions, or the real product itself is subjected to all kinds of tests (a full-scale experiment). To study, for example, the operational properties of a unit or assembly, it is placed in a thermostat, frozen in special chambers, tested on vibration stands, dropped, etc. It’s good if it’s a new watch or a vacuum cleaner - it’s not a big loss upon destruction. And if a plane or a rocket? Laboratory and full-scale experiments require large material costs and time, but their value, nevertheless, is very great. With the development of computer technology, a new unique research method has appeared - computer experiment. In many cases, computer model studies have come to help, and sometimes even to replace, experimental samples and test benches. The stage of conducting a computer experiment includes two stages: drawing up an experiment plan and conducting a study. Experiment plan The experiment plan should clearly reflect the sequence of work with the model. The first point of such a plan is always testing the model. Testing - processcheckscorrectnessbuiltmodels. Test - kitinitialdata, allowingdefinegreat-vilenessbuildingmodels. To be sure of the correctness of the obtained simulation results, it is necessary:
- check the developed algorithm for building the model; make sure that the constructed model correctly reflects the properties of the original, which were taken into account in the simulation.
MODEL TESTING
EXPERIMENT PLAN
CONDUCTING RESEARCH
ANALYSIS OF THE RESULTS
Rice. 11.7. Scheme of a computer experiment
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 of modeling. This stage is decisive - either you continue the study, or finish. Figure 11.2 shows that the results analysis stage cannot exist autonomously. The conclusions obtained often contribute to an additional series of experiments, and sometimes to a change in the task. The results of testing and experiments serve as the basis for developing a solution. If the results do not correspond to the goals of the task, it means that mistakes were made at the previous stages. This may be either an incorrect statement of the problem, or an overly simplified construction of an information model, or an unsuccessful choice of a method or modeling environment, or a violation of technological methods when building a model. If such errors are found, then model adjustment, that is, a return to one of the previous steps. The process is repeated until the results of the experiment meet the objectives of the simulation. The main thing to remember is that the detected error is also the result. As the proverb says, you learn from your mistakes. The great Russian poet A. S. Pushkin also wrote about this: Oh, how many wonderful discoveries are being prepared for us by the spirit of enlightenment And experience, the son of difficult mistakes, And genius, friend of paradoxes, And chance, god the inventor ...
Controlquestionsandtasks
- What are the two main types of problem setting modeling.
- In the well-known "Problem Book" by G. Oster, there is the following problem:
- List the most well-known goals of modeling. Formalize the playful problem from G. Oster's "Problem Book":
The concept of information
DocumentThe world around us is very diverse and consists of a huge number of interconnected objects. To find your place in life, you early childhood together with your parents, and then with your teachers, you will learn all this diversity step by step.
Production editor V. Zemskikh Editor N. Fedorova Art editor R. Yatsko Layout T. Petrova Proofreaders M. Odinokova, M. Schukina bbk 65. 290-214
BookШ39 Organizational culture and leadership / Per. from English. ed. V. A. Spivak. - St. Petersburg: Peter, 2002. - 336 p: ill. - (Series "Theory and practice of management").
Educational and methodological complex in the discipline: "Marketing" specialty: 080116 "Mathematical methods in economics"
Training and metodology complexArea of professional activity: analysis and modeling of economic processes and objects at the micro, macro and global levels; monitoring of economic and mathematical models; forecasting, programming and optimization of economic systems.
