The traditional method for selecting the blur coefficients of kernel functions in nonparametric regression is based on minimizing the root mean square error in the approximation of the desired dependence from the initial statistical data. With an increase in the volume of the training sample of the values of the variables of the restored dependence, the computational costs of optimizing nonparametric regression increase signifi cantly. An unconventional method for selecting the nonparametric regression blurriness coeffi cients optimal for the kernel probability densities of the variables of the recovered dependence is proposed. Statistical estimates of the mean square deviations of the joint probability density of the variables of the restored dependence were used as an optimality criterion for selecting the blur coefficients of kernel probability densities. The proposed technique made it possible to avoid calculating the approximation error of the restored dependence by nonparametric regression, which is confi rmed by the results of computational experiments. The results obtained make it possible to use the method of fast optimization of kernel estimates of probability densities in the synthesis of nonparametric regression.

In this paper describes the current direction in the development of machine tool industry – the introduction of laser technological installations. Methods are given for improving the quality of operations performed on laser machines, for example, operations for cutting sheet materials. The need to improve the method of controlling the adjustable electric drive of laser systems is shown. The features of the construction of information-measuring and control systems of the electric drive are considered. The operation of an adjustable electric drive based on a brushless DC motor with an original arrangement of sensors has been studied. The metrological characteristics of an adjustable electric drive are numerically estimated by the method of circuit simulation. The reliability of the obtained data is experimentally confi rmed by the results of tests of the mock-up sample.

The scientific rationale for the choice of reference circles in the analysis of the roundness of rolling bearing parts is presented. The selection criteria were: physical interpretability, minimum roundness, reliability and performance of the calculation algorithm. The measurement of the inner and outer surfaces of the rings and balls of a single-row radial bearing was carried out on a roundness testers and a coordinate measuring machine. The values of roundness are calculated using four reference circles: least squares, minimum zone, minimum circumscribed, maximum inscribed. It was found that the calculation along the minimum zone circle provides the minimum value of roundness. Statistical Monte-Carlo modeling was carried out to assess the distribution of roundness in a batch of bearings. For this, a technique has been developed that allows, on the basis of harmonic analysis, to identify the distribution parameters of the amplitudes and initial phases of the harmonics of the profi le of parts, and then to simulate the distribution in the batch into account the correlation. The results of statistical modeling have confi rmed that the minimum zone circle has the minimum value of roundness in terms of the arithmetic mean and standard deviation. A numerical algorithm for minimizing the functional in the form of the widt hof the minimum zone was applied to calculate the center of the minimum zone circle. In the area of performance of the objective function, there is one local minimum. The algorithm has proven to be reliable and effi cient. Taking into account all the criteria, it is recommended to use the minimum zone circle for the analysis of the roundness of the rings and balls of rolling bearings.

For the first time, the possibility of measuring the difference in gravitational potentials and orthometric heights using a quantum level based on the gravitational effect of time dilation using ground communication lines is considered. The duplex mode of measurements using two opposite radio channels is theoretically described. The deceleration effect was experimentally measured using a one-way radio link implemented on a fiber-optic link. For measurements, stationary and relocatable quantum hydrogen clocks with relative instability, respectively, (0.5–0.7)∙10^–15 and 1∙10^–15 were used. It was found that in the experiment the gravitational redshift of the frequency between the clocks used has two components: the redshift of the clock master oscillator frequency and the classical redshift in the radio channel. Based on the measurement results, the altitude of the relocated quantum hydrogen clock was calculated, which was (–34.0±0.8) m at the actual altitude –34 m.

 The main systems and elements of the watt balance layout created in D. I. Mendeleyev Institute for Metrology (VNIIM) as part of the research work “Balans” are described. The research results of the characteristics of the systems and elements of the watt-weights layout when working in diff erent modes are shown. The researches were realized using modern high-precision equipment and methods of measurement results processing. The main work directions for upgrading the methods of mass measurement using watt-weights are defi ned.

The problem of non-traceability of the measurement results of relative strain to the state measurement standards of units of magnitudes is considered. The peculiarities of strain measurements are revealed: the dependence of measurement results on measurement conditions. The measurement method and equipment for the implementation of the state primary reference methodology (method) of measurements the surface deformation of an elastically deformed rectangular constant section beam loaded according to the pure bending scheme are described. The procedure for establishing methodological parameters (changes in ambient temperature during measurement, initial flatness of the beam, non-parallelism of the beam faces, etc.) during the development of the state primary reference methodology (method) of measurements is outlined. An algorithm for estimation of measurement uncertainty of strain with indication of the identifi ed sources of uncertainty and their contribution to the total uncertainty of the measurement results is described. The metrological characteristics of the measurement methodology (method) are calculated. This technique will be useful in determining the characteristics of reference and working measurement techniques for the surface strain of an elastically deformed beam of constant rectangular cross-section loaded according to the pure bending scheme.

The systematic errors of the 6GS-40M calibration machine of the Central Aerohydrodynamic Institute are investigated. The machine is designed for calibration of external and internal six-component strain-gauge balances with a maximum normal force of 40 kN. Proceeding from requirements to the aerodynamic characteristic errors of aircraft models during their tests in wind tunnels, the requirements to the calibration errors of strain-gauge balances were obtained: the calibration error related to half of range of the calibration machine components must not exceed 0.05 %. A method is developed for experimental evaluation of systematic errors of calibration machine. Experimental studies were carried out with the help of the developed method to determine the systematic errors of the 6GS-40M calibration machine. Previously obtained analytical expressions for the systematic errors were verifi ed by the results of the experiment. We estimated the corrections to the loads set by the 6GS-40M calibration machine to external and internal six-component strain-gauge balances. The range of corrections was from 0.09 to 0.90 % for the diff erent components of the balances. The developed method of experimental determination of systematic errors may be used for other calibration machines.

The interrelation of metrology and money is investigated. It is shown that the construction of state measuring systems and state monetary systems is based on general metrological principles. To measure the amount of material objects and the amount of money, it is necessary to establish the appropriate units of measurement. To ensure confi dence in these systems and their stability, it is necessary to standardize these units by assigning them a certain number of specifi c material objects (material measures). At the same time, governments are obliged to maintain the constancy of the material measures adopted by the country (national standards).

The standardization of national currency units, by assigning them a specific mass of gold, began to be used in the 18th century and received the name gold standard. In the 70s of the last century the situation changed dramatically: the basic metrological principle – the constancy (invariability) of a single material measure was violated. The gold material measure of monetary units was abandoned.The value of money, instead of a solid material measure, began to be measured by several designated, reserve currencies, the main of which was the dollar. Then these reserve currencies became a commodity that is freely bought and sold in the market. The system has become unstable. The negative consequences were immediate and some of them are summarized in this article. The most crucial consequence was the emergence of a global over-totalitarian, over-monopoly monetary system. In that system the measure of the value of money is the national currency (more than 85 % of trading volumes on currency stock markets), which is regulated by national laws and the national interests of the United States, that are taken into account.

The article examines the return to the metrological principle – reference standardization of monetary units – as the only way out of the scenario in which the international monetary system was trapped. Since the state reserves of gold available today are not enough to restore the gold standard, this article considers the option of resource standardization, in which the standardization of monetary units is provided by a specifi c amount of natural and industrial state resources. As an example, the calculations are made for the Russian ruble. It is shown that resource standardization is available for all countries present on the international market, and is a real way to overcome the problems that have accumulated to date in the international monetary system. The article also notes the possibility of using digital money in the transition and further functioning of state monetary systems organized according to the principle of resource standardization.

The methodology of constructing of temperature scale in the range 692,67–1234,93 K was described. It’s based in the way of the reproduction of a temperature unit by absolutely black body emitters based on the reference points of pure metals of zinc, aluminum, silver and further transferring of the unit of the temperature to a variable temperatures absolutely black body emitter of using a pyrometer-comparator. Both of emitters are absolutely black bodies. Interpolation of values of using pyrometer-comparator performs by Plank law. Sources of uncertainties were analyzed and budget of uncertainties of reproduction of the unit of temperature kelvin by the radiation method was given. Measurement uncertainty of the emitter’s (absolutely black body) temperature connected with pyrometercomparator using is (1.99–2.94)·10^–1 °C, and it allows to use this pyrometer for thermodynamic temperature scale constructing.

The control of unmanned electric cars in the premises has been studied. The problem of ensuring the exact correspondence of control signals to the real movement of vehicles in space is considered. Based on the analysis of the dynamic model of an electric car, it was found that the main causes of errors are the indirect nature of measuring the speed of this vehicle using odometers. To solve this problem, it was proposed to use microwave Doppler sensors of the linear speed of the wheels, the readings of which no longer depend on the slip, mass of the electric car, tire pressure, and other parameters. Formulas have been derived that allow the Doppler frequencies of the sensors to determine the current speed and steering angle of control of an electric car using the Ackermann condition. Based on them, a stable traffi c control system along a given route has been developed, which can be used in robotic transport systems.