# OBTAINING AND INTERPRETATION OF THE RESULTS OF SYSTEM MODELING, Features of obtaining simulation results. - Modeling of systems

## OBTAINING AND INTERPRETATION OF THE RESULTS OF SYSTEM MODELING

At the third stage of modeling - the stage of obtaining and interpreting the results of modeling - the computer is used to make working calculations for a compiled and well-established program. The results of these calculations allow us to analyze and formulate conclusions about the characteristics of the process of functioning of the modeled system. 5

## Features of obtaining simulation results.

When implementing modeling algorithms on a computer, information is produced on the states of the process of functioning of the systems under study r (/) e . This information is the starting material for determining approximate estimates of the desired characteristics, that is, the evaluation criteria. An evaluation criterion will be called any quantitative indicator by which you can judge the results of modeling the system. Criteria for evaluation are indicators obtained on the basis of processes actually occurring in the system or obtained on the basis of specially formed functions of these processes [4, 29, 35].

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In the course of the computer experiment, the behavior of the model M of the process of functioning of the system ^ is studied on a given time interval [0, 7]. Therefore, the evaluation criterion is in general a vector random function defined on the same interval:

Often, simpler evaluation criteria are used, for example, the probability of a certain state of the system at a given time t * e [0, 7], the absence of failures and failures in the system on the interval [0, 7], etc. When interpreting simulation results different statistical characteristics of the law of distribution of the evaluation criterion are calculated.

Consider the general scheme for fixing and processing the results of modeling the system, which is shown in Fig. 3.4. We will consider a hypothetical model A /, designed to study the behavior of the system S on the time interval [0, 7 *]. In the general case, the criterion for interpreting the simulation results is the nonstationary random n - dimensional process d (/). For definiteness, we assume that the state of the simulated system K is checked every A/time units, i.e., the & quot; A & quot; principle is used. In this case, the values ​​ d (/ A /), y = b ~ k, of the criterion d (/) are calculated. Thus, the properties of the random process q (t) are judged from the properties of the random sequence d (/ A /), y = 6, k, or, in other words, by properties m-dimensional vector of the form

The process of functioning of the system A on the interval (0, 7] is modeled ^ -fold with obtaining independent realizations i = 1, N. of the vector q. The model works on the interval [ 0, 7] is called the model run.

On the diagram shown in Fig. 3.4, it is indicated:/= *;/= /; K = k M = M; T = /; & gt; & gt; D = D /;

& lt; 2 ^ I

In general, the algorithms for fixing and statistical processing of simulation data contain three cycles. We believe that there is a computer model M m of the system 5.

The inner loop (blocks 5 - 8) allows you to get the sequence?, (/) =? (/ A /), I = OG & quot; at times t = 0, A /, 2A *, - & quot;/cA/= 7 '. The main block 7 realizes the procedure for calculating the sequence y/(/): EXIT [U1 (T)]. It is in this block that the process of functioning of the simulated system 5 is simulated on the time interval [0, 7].

Intermediate cycle (blocks 3 - 10), in which the repeated running of the model is organized, allowing after the appropriate statistical processing of results to judge the estimates of the characteristics of the modeled version of the system. The end of the modeling of the variant of the system A can be determined not only by a given number of realizations (block 10), as it is shown in the diagram, but also by the specified accuracy of simulation results. This loop contains a block 9, which implements the commit procedure

Fig. 3.4. Algorithm for fixing and processing system simulation results

modeling results for the 1st model run

The outer loop (blocks 1 - 12) covers both preceding cycles and additionally includes blocks 7, 2, 77, 12, control sequences modeling of variants of system S. Here the search of optimal structures, algorithms and parameters of the system S, is organized, i.e., the block 11 processes the simulation results of the investigated to block 12 checks the satisfaction of the received estimates of the characteristics of the process of functioning of the system q /(0 by the required one (searches for the optimal version of the system [S (AO)), the block 1 changes the structure, algorithms and parameters of the system S at the level of input of the initial data for the next [S (K)]. Block 13 implements the function of issuing simulation results for each to variant of the model of the system S k , i.e., the BPM IQK.

This scheme allows statistical processing of simulation results in the most general case for a non-stationary criterion q (/). In special cases, we can confine ourselves to simpler schemes [22, 29, 37].

If the properties of the modeled system S are determined by the value of the criterion q (/) at some given time, for example, at the end of the period of the model functioning t = kAt = T , the processing reduces to an estimate of the distribution of the n-dimensional vector q (/) in the independent realizations 5. (0 & quot;/= 1, N, N model runs.

If in the simulated system S after a certain time has elapsed from the beginning of the work/ 0 = & pound; 0 A/stationary mode is set, then o It can be judged from one, rather long, implementation of the q x criterion (i), stationary and ergodic on the interval [f 0 , T]. For the above circuit, this means that the middle loop (n = 1) is excluded and an operator is added to start processing the values ​​ q t (/ Ar ) for j ^ k 0 .

Another feature of the methods of statistical processing of simulation results applied in practice is connected with the study of the process of functioning of systems with the help of models of block construction. In this case, it is often necessary to apply separate modeling of individual model blocks when imitation of input actions for one block is carried out based on estimates of the criteria obtained previously on another block of the model. In case of separate modeling, either the direct recording in the storage of the realizations of the criteria, or their approximation, obtained on the basis of statistical processing, can take place

simulation results with the subsequent use of random number generators to simulate these effects.

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