ASSESSING THE INFORMATIVENESS OF THE CONTROLLED PARAMETERS IN THE TASK OF IDENTIFYING THE STATE OF THE SYSTEM
Abstract
The effectiveness of solving the problem of identifying the system state significantly depends on the number of controlled parameters and the degree of their informativeness. The traditional method for assessing the informativeness of these parameters is based on the measure of distance between the probability distributions of the values of the controlled parameter for different states of the system proposed by Kullback. The shortcomings of Kullback measure have been revealed. Firstly, the value of this measure is not normalised and is not limited from above. Secondly, this measure is asymmetric, i.e. its numerical value depends on the way its components enter the calculation ratio. The method for calculating the informativeness criterion proposed in this paper takes into account the uncertainty that arises due to the fuzzy description of the boundaries of the areas of possible values of the controlled parameters for each of the possible states of the system. An important enhancement of the known methods for assessing the informativeness of the controlled parameters is to take into account the real existing inaccuracy in estimating the values of the results of measuring these parameters themselves. These circumstances determine the subject and purpose of the study that is the development of a method for calculating the distance between the distributions of fuzzy values of the controlled parameter, free from the shortcomings of the Kullback measure. To calculate the measure of the distance between the distributions of the values of the controlled parameter under conditions of uncertainty of the initial data, described in terms of fuzzy mathematics, a symmetric criterion is proposed, which is easily calculated. Examples of the criterion calculation are given. The possibilities of increasing the level of informativeness of the criterion using analytical descriptions of membership functions of fuzzy values of the controlled parameter for different states of the system are considered.
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