Том 62, № 2 (2019)

Techniques for verification by the method of rejection with the use of a statistical simulation model are analyzed. Reliability indicators of the results of verification are proposed and their numerical values evaluated. The method used to take into account the uncertainty of measurements in verification is evaluated.

The application of interval analysis in a linear formulation (linear problem of tolerances) to a concrete problem of spectral analysis is considered. The principal procedural objective is to demonstrate the use of a recognizing functional as an investigatory tool. The method of intervalization of the right sides of an interval system of linear algebraic equations without recourse to models of the form of the background under a peak along with the form of united solution sets of an interval system of linear algebraic equations for a particular problem are studied. The solvability of an interval system of linear algebraic equations relative to the sign of the recognizing functional is investigated, and it is shown that in the initial formulation the system is not solvable. Methods of attaining solvability by weakening the tolerances of the right side of the system and through a modification of the matrix are considered and results of the use of both methods are discussed.

We investigate properties of empirical data under random uncertainty. A new approach is proposed to improve the accuracy of constructing a probability density function and estimating its error. The method uses Richardson extrapolation and Runge rules for kernel estimates with various smoothing options. It is shown that the application of the Runge rules enables evaluating the error of kernel estimates for a probability density function and the value of its second derivative.

A procedure for the construction of reference circles of the profile of the axial section of a test shaft or hole, the maximum inscribed circle and minimum circumscribed circle, along with circles that specify the boundaries of a ring of minimal width, is proposed. The radii and coordinates of the centers of the circles are found through minimization or maximization of a corresponding functional constructed on the basis of the coordinates of the points of the profile. The construction procedures presented are implemented in the Mathcad program package. The results obtained may be used to determine deviations from roundness, in particular, in the development of mathematical software of measuring instruments.

We consider measurements of pitch and roll angles using compensation pendulum accelerometers with closed feedback. A three-component mathematical model of a single-axis accelerometer has been developed as a means of measuring pitch and roll angles. The model takes into account the effect of acceleration applied perpendicular to the axis of sensitivity of the accelerometer. The error of the mathematical model is investigated. Methods for accelerometer calibration and a method for taking into account the effect of temperature on its readings using a three-component mathematical model are proposed. The mathematical model is verified using accelerometer calibration results.

We propose a method for determining the instrumental function of the URAGAN muon hodoscope based on the mathematical technique of Monte-Carlo simulation. Various components of the instrumental function simulate operation of the hodoscope and atmospheric reduction of muon flux intensities. We develop a technique for estimating the instrumental function of the hodoscope, and implement a statistical testing algorithm. We discuss applying the estimated instrumental function to various input models for the muon flux density distribution function.

An elementary magnetic emitter is considered as an approximation for the variable magnetic field of an electrically small radiating loop antenna. The frequency limits for applicability of the stationary dipole model are studied. Approximate formulas are obtained for characterizing the difference between the magnetic field of a circular loop antenna and the magnetic field of the equivalent point source.

A special system has been developed for measurement in free space of the following parameters of flat material samples: reflection and transmission coefficients, permittivity and permeability, angular dependence of the transmission coefficient, and temperature dependence of the reflection coefficient of rf absorbing coatings on metal substrates for normal incidence of electromagnetic waves at frequencies of 1–40 GHz. In order to increase the accuracy of the measurements various digital signal processing algorithms are proposed, including a way of suppressing the Gibbs phenomenon at the edges of the frequency band, as well as a method for correcting the results of S-parameter measurements during determinations of the permittivity and permeability of small samples.

We present a method for the evaluation of the charge collection time in an ionization fission chamber with flat electrodes. The mean charge and the time of its collection are determined according to the parameters of electric signals recorded at the output of the measuring system. We use a model of formation of current pulse in the detector and a mathematical model of measuring circuit. The procedure of finding the charge collection time and the mean charge per pulse is approved in experiments with KNT-34-type ionization fission chambers. Various possibilities of practical application of the proposed procedure are considered.

We consider the possibility of application of autogenerating measuring converters as secondary converters allowing one to create electrotechnical monitoring devices (EMD) for the simultaneous or separate measurements of the parameters of multicomponent agricultural products. A procedure of formation of the transfer functions of EMD and creation of idealized models used in measuring the humidity and conductivity of grains is proposed. The results of investigations reveal a principal possibility of development of the EMD with instrumental errors that do not exceed 0.1% within the range of humidity of grains 5–30%.