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3. Stages of constructing mathematical models

Construction of mathematical models of objects and systems is carried out in stages in series, each of which carried out the appropriate checks and produced documenting the actions.
There are 3 stages of constructing mathematical models (Figure 2):
1. Statement of intent model.
2. The implementation model.
3. Preparation and analysis of results.

Figure 2. Block diagram of the steps of constructing a mathematical model
 
At the first stage the estimated model in abstract terms.
1. Statement of the Problem.
2. Determination of the information requirements.
3. Gather information.
4. The hypotheses and assumptions (for lack of information).
5. Analysis of the problems (tasks).
6. Determination of parameters and variables (according to the notation according to GOST).
7. Selection of performance criteria (e.g., reliability, performance, while the probabilities of different events, the operation time characteristics, the characteristics of the measurement errors, and so on). For each of the criteria established wording, then mathematical description.
8. Preparation, validation of the model.
9. Determination of approximate expressions (mathematical model of the system must be deterministic, stochastic, averaged).
10. Description of the design model.
11. Check the model (carried out by competent persons).
12. Documentation of the first stage.
 
The second step is to check compliance with the dimensions of the terms in the equations.
1. Conclusion of detailed mathematical equations model.
2. Preparation flowchart model.
3. Check the flowchart (includes analysis of values ​​of the characteristics in order to determine the system of reserves and the permissible range of the parameter).
4. Preparation of flow diagrams.
5. Verification of the circuit program.
6. Preparation of the program of the mathematical model.
7. Checking the mathematical model.
8. Selection of computational tools.
9. Preparation of specifications for the programs (each option must be described, and describes the scope of application).
10. The Plan of workers settlements.
11. Planning for the experiment with the model.
12. Documentation of the second stage.
 
In the third stage, the thorough inspection of the model created and carried out special tests.
1. Perform calculations workers.
2. Analysis of the results (theoretical and experimental analysis).
3. Preparation of response surfaces.
4. Conclusion of the regression equation.
5. Evaluation of generalized results.
6. Preparation of the conclusions.
7. Issue of recommendations on the use of the model.
8. Documentation of the third stage.
 
In constructing the model, perhaps returning to the previous steps in connection with unsatisfactory results or errors. Designing performed until until all the defects are eliminated. The resulting model should satisfy all major selected criteria of adequacy.

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