• V. I. Levin Penza State Technological University, Penza, Russian Federation



Measuring instrument, calibration characteristic, measured value, measurement result, interval mathematics


Context. When designing various measuring instruments, the problem arises of constructing the so-called calibration characteristic
of a measuring device, i.e. the quantitative dependence of the measurement result on the measured value. This characteristic is
inverse to the direct characteristic – the dependence of the measured value on the measurement result. This problem is solved on the
basis of approximate data obtained during the experiment with the measuring instrument. A new method for solving this problem is
proposed, based on the apparatus of interval mathematics.
Objective. The aim of the work is to develop a completely formalized method for constructing the calibration characteristic
of a measuring instrument from approximate data obtained in the experiment with this instrument.
Method. The method proposed in this article consists in presenting the function of direct con-version of a measuring device in the
form of a linear interval function, determining its interval parameters (coefficients) from experimental data and solving the resulting
interval dependence between the measurement result and the measured quantity with respect to the measured value. The method of
solving interval equations is used.
Result. General formulas are obtained that determine interval calibration characteristic of the measuring instrument on the basis of
data obtained in the experiment with the instrument. A detailed analysis of formulas is performed. General laws are established that
obey direct and inverse (calibration) characteristics of measuring instrument, as well as the relationship between direct and inverse
characteristics (if the instrument is linear transformer).
Conclusions. The article proposes a new approach to the construction of calibration characteristics of measuring instruments,
based on use of interval mathematics, for processing data from experiments with instruments. This approach, unlike existing ones,
makes it possible to build calibration characteristics of measuring devices and analyze them purely analytically.

Author Biography

V. I. Levin, Penza State Technological University, Penza

Doctor of Science, Professor of Mathematical Department


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Mathematical and computer modelling