MODELS AND MEASURESIN THEORY AND PRACTICE OF MEASUREMENTS
Authors: Babak V.P. , Zaporozhets A.A. , Kuts Y.V. , Scherbak L.M. 
Published: January 2021

It is known that deterministic and probabilistic models of measured quantities, processes and fields, as well as physical and probabilistic measures, make it possible to form a measurement result, to provide it with the properties of objectivity and reliability. On their basis, the measuring instruments necessary for obtaining new knowledge and maintaining the process of technological development of production are being developed and improved. Therefore, the issues of improving and developing models and measures in measurement methodology play an increasingly important role in achieving high measurement accuracy and expanding the areas of their application. The article is devoted to the features and results of the study of the application of models and measures in measurements.

It is shown that the physical correctness and the need for setting up measuring experiments, performing tasks and conditions for their implementation, substantiating adequate models and measures significantly affect the obtained measurement result. The features of the modern methodology of using models of signals and fields and measures for evaluating the results of measuring physical quantities, including thermophysical ones, which are represented by random quantities and angles are presented. In the general case, a measure is a countably additive set function that acquires only negative values ​​in any way, including infinity. The use of charge as a mathematical model significantly expands the boundaries of the practical application of the methods of measure theory in metrology. Examples of probabilistic measures on a straight line, on a circle and a charge, as well as physical measures are considered. The concept of coordination of physical and probabilistic measures has been substantiated with the aim of a unified approach to assessing the measurement result. The joint use of physical and probabilistic measures for the formation of a measurement result allows to a certain extent overcome the problem of measurement homomorphism. An example of using a set of physical and probabilistic measures in the hardware and software modules of information and measuring systems is given. The probabilistic normalized measure is a non-physical degree, but a measure of the totality of the action of various random factors on the value and characteristics of data and the result of measurements when they are carried out. The use of a probabilistic measure in the statistical processing of measurement data makes it possible to increase the accuracy of the measurement result compared to the accuracy of the measurement data.

The degree of information protection during measurements is complex. The measure is formed by many factors, the action of most of which is of a random nature. This makes it possible to determine such a measure as probabilistic, which can be applied both for individual operations, for example, transmission of measurement data via communication channels, registration of the measurement result, and for the entire measurement process as a whole.

The stochastic approach in the theory of measurements is of particular importance in the case of measurements of physical quantities that have a pronounced probabilistic nature, for example, in the case of nano-measurements, the study of quantum effects, and the like.

Currently, the use of the SI international system of units at the quantum level and the concept of uncertainty for evaluating measurement results, which are the foundation of measurement practice, requires a wide range of theoretical and simulation studies of measurement processes in various subject areas to form a unified measurement methodology.