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Estimation of the error of the results of indirect measurements of some quantities
https://doi.org/10.32446/0368-1025it.2020-1-18-24
Abstract
The basic mathematical provisions that determine the necessary and sufficient conditions for the application of the method of linearization of nonlinear functions of random arguments in the evaluation of errors of the results of indirect measurements are considered, and the need to present the assessment of the arising systematic component of the error and the degree of approximate representation of functions is noted. Within the framework of the necessary and sufficient conditions for the expansion of an arbitrary function into a Taylor series, a new analytical formula for the approximation of a nonlinear function in the form of a quotient of independent random arguments is obtained, which allows to exclude the questions of refinement of the results by adding terms to the Taylor series and estimating the degree of approximation of a nonlinear function by the values of the corresponding residual terms when evaluating the errors of indirect measurements. It is shown that the obtained new approximation for the replacement of such a function allows us to determine the practical conditions under which to estimate the errors of the corresponding results it is possible to use known, and quite simple, formulas for estimating the absolute and relative errors without preprocessing the results of direct measurements.
About the Author
E. V. Eremin
All-Russian research Institute of physical-technical and radio engineering measurements
Russian Federation
Russian Federation
Evgenii V. Eremin
Mendeleevo, Moscow region
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Review
For citations:
Eremin E.V. Estimation of the error of the results of indirect measurements of some quantities. Izmeritel`naya Tekhnika. 2020;(1):18-24. (In Russ.) https://doi.org/10.32446/0368-1025it.2020-1-18-24
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