An emergence of intelligent devices, a large number of sensors, the issue of their identification and interaction becomes relevant in the era of information technologies development. A control object, a structural diagram of an identification system, an algorithm for the correlation method of identification have been considered in the article, and a general idea of managing the process of recognizing an information network object has been given.
Consider a control object described by the equations = = + + , +
; ∞ 0 ∞ 0 ∞ 0 ∞ 0 ( ) = ∫ ℎ( )
( − ) .
( ) = (
where r1ff is a known number characterizing the intensity of the “white noise.” where the matrix A and the n-dimensional vectors , , ′ are unknown; f(t) and x(t) are the external disturbance and noise, which are immeasurable random functions with zero mathematical expectation.
Depending on the identification method, additional restrictions will be imposed on external disturbances and interferences (their white noise, limited dispersion, etc.).
Since the object (
The purpose of object identification (
+ .
= +
;
where ℎ( − ) is an impulse transient function, which is determined by the correlation method.
Equation (
We multiply (
Assuming further { ( )} = { ( )} = 0 and applying the mathematical expectation operation, { ( ) ( − )} = ∫ ℎ( ) { ( − ) ( − )} + { ( ) ( − )}.
(
If external influence ( ) and hindrance ( ) are independent, then { ( ) ( − )} = 0. In
addition, denoting the correlation function { ( − ) ( − )} = ( − ), and the
crosscorrelation function { ( ) ( − )} = ( ), we write (
( ) = (
Thus, if the external influence is a random process of the white noise type, uncorrelated with the measurement noise, then the cross-correlation function of the input and output signals is directly proportional to the impulse transient function. The block diagram of the identification system is shown in Ошибка! Источник ссылки не найден..
( )= ( ) ℎ( )=ℎ( ) }
≤ ≤ ( + 1) ( = ̅0̅,̅̅̅). ( ) = ∑ =0 [( − ) ℎ( ) ( = ̅0̅,̅̅̅).
(0) = [ (0)ℎ(0) + (− )ℎ( ) + ⋯ + (− )ℎ( )] ; ( ) = [ ( )ℎ(0) + (0)ℎ( ) + ⋯ + (−( − 1) )ℎ( )] ;
For = 0, equation (12) is written as
For = 1 random process with the ergodic property, is defined as ( ) = lim
1→∞ 11 ∫0 1 ( − ) ( ) .
Returning to the general case, we note that equation (7) is an integral equation for the unknown function ℎ( ). The numerical solution of this equation forms the basis of the correlation identification method.
Passing to the solution of equation (7), we replace the upper limit in the integral by a finite number 1. This means that the impulse transient function will be determined on the interval [0, 1], and for > 1ℎ( ) = 0. This assumption is quite acceptable for asymptotically stable objects. In addition, we will determine the value of the function ( ) for discrete instants of time that differ from one another by the value T, therefore, we divide the interval [0, 1) into = 1/ intervals.
(9) (10) (11) (12) etc.
Let us introduce vectors and matrix (2 ) = [ (2 )ℎ(0) + ( )ℎ( ) + ⋯ + (−( − 2) )ℎ( )] ′ = ‖ (0) ( ) … ( )‖; ℎ′ = ‖ℎ(0), ℎ( ) … ℎ( )‖ = ‖‖ ( ) (0) ⋮ (− ), … , (−
) (0), … , [−( − 1) ] ⋮
‖‖. ( )
[( − 1) ], … , (0) ( ) = (− ) ( = ̅0̅,̅̅̅).
Note that the matrix R is symmetric, since the correlation function is even, therefore
ℎ.
Whence the required vector is ℎ = −1 . ( ) = 1 =−01 ( ) [( + ) ] ( = ̅0̅,̅̅̅), ∑ ( ) = 1 =−01 ( ) [( + ) ] ( = ̅0̅,̅̅̅). ∑
and the matrix from the experimental data. In this connection, we write on the basis of (10) an approximate expression
Thus, the algorithm for identifying the impulse transient function is reduced to calculating the correlation and cross-correlation functions by formulas (16), (15), and then solving equation (14).
The considered concepts and definitions make it possible to construct an algorithm for the recognition process in the form of a rule of the sequential search for solutions, which ensures the development of an optimal plan for conducting experiments. The meaning of such an algorithm is that, based on the prehistory of experimentation, as well as on the basis of information obtained as a result of previous experiments, it determines the optimal plan for further experiments, all subsequent stages of the object with the help of these means should be identified.
The general record of the algorithm providing sequential planning of experiments can be represented as algorithm 2, … , ; 0, 2, . . ,
absent. = { 0; 1, 1( 1); 2( 1 ), 2( 1 , 2); … ; ( 1, … , −1), ( 1, … , ), … }, (7.10) In the algorithm 0 means that the final decision that an object belongs to the class is made without experiments. In this case, all operations indicated in the algorithm 1, … , ; 1, . . , are absent. If the algorithm 0 is absent, then the first stage experiments are assigned 1. If, on the basis of the characteristics of the object, determined from the information of the experiments of the first stage, a final decision is made about its belonging to any class 1( 1), then all operations indicated in the
The presence of a member in the algorithm ( 1, … , −1) means that, based on the study of the features of the recognized object, obtained as a result outcome experiments 1, … , −1 .
( 1, … , ), then this means that after receiving the outcomes 1, … , experiments 1, … , , conducted according to the rule , the final decision is made about the belonging of the recognized object to the class and no further experiments are carried out. The procedure for planning experiments in accordance with the algorithm (17) is schematically shown in Ошибка! Источник ссылки не найден..
It follows from the consideration of the scheme that the algorithm works as follows. Let the object enter the recognition system. It was found that making a final decision without conducting experiments 0 inappropriate and to determine its sign it was decided to conduct the experiment 1. Let us assume that the possible outcomes of the experiment are 1 − ′ 1 and ′′1. These outcomes are experiment 2( ′ 1) will be ′ 2 or ′′2′, then the final decisions should be made 2( ′ 1, ′ 2) or 2( ′ 1, ′′2), , , = 1, … , , and if the outcome is ′′2, then it is necessary to conduct an experiment 3( ′ 1, ′′2). Outcomes of this experiment ′ 3 and ′′3 are analyzed again, and a plan for the further development of experiments is developed.
The algorithm works like a feedback system. Indeed, every time. the experimental results are used to adjust the plan for subsequent experiments.