The issues of calibration of sound pressure measuring instruments in the air (measuring microphones, sound level meters, etc.) are considered. At free-field calibration of measuring devices by a secondary method (by comparison with a reference measuring microphone), one of the sources of error is the determination of the free-field sensitivity of a reference microphone, defi ned as the sum of its pressure sensitivity and the typical diffraction correction. This approach to determining the free field sensitivity of a reference microphone was used due to the absence in the Russian Federation of a standard that implements the free-field calibration of measuring microphones by primary method and due to dependence on foreign acoustic laboratories, which are the source of data on typical diffraction corrections for measuring microphones. As part of the course to ensure the technological sovereignty of the Russian Federation in key areas of measurement and to ensure the transfer of the unit of sound pressure in air with high accuracy to measuring instruments intended for use in free-field conditions, the State Primary Standard of the unit of sound pressure in air and audiometric scales GET 19-2018 was improved with the aim of implementing the free-field calibration of measuring microphones using the primary method. The free-field calibration of measuring microphones is implemented using the reference anechoic chamber built at VNIIFTRI and Russian-made measuring equipment, which together form the reference complex EK-SP, included in the State Primary Standard of the unit of sound pressure in air and audiometric scales GET 19-2025. GET 19-2025 provides a free-fi eld calibration frequency range of 1–25 kHz with an unexcluded systematic error within 0.07–0.15 dB depending on the frequency, and the standard deviation of the result of 10 measurements is 0.02–0.1 dB depending on the frequency. Improving the accuracy of measurements in a free sound field is important for the aviation and engine industries, the rocket and space industry, transport, communications, ecology and healthcare.

The issues of calibration of underwater noise measurement instruments, which in modern hydroacoustics are represented by hydroacoustic measurement instruments – primary transducers and underwater measuring systems based on primary transducers, are considered. Much attention is paid to laboratory calibrations in water tank conditions of underwater measuring systems, the dimensions of which are several times larger than the dimensions of the primary transducers used in them. Such underwater measuring systems have signifi cant sensitivity nonuniformity, therefore their amplitude and phase frequency characteristics must be measured in a free fi eld with high frequency resolution and underwater measuring systems must be calibrated in frequency bands. The geographic range of application for hydroacoustic measurement instruments, from southern latitudes to northern ones (in the Northern Sea Route), requires studying the dependence of their metrological characteristics on changes in water temperature and excess hydrostatic pressure across the entire operating frequency range from a few hertz to hundreds of kilohertz. Modern underwater sonar and communication technologies require methods and instruments for measuring the phase sensitivity characteristics of primary transducers. To solve the above-mentioned issues, the State primary standard of units of sound pressure and vibrational velocity in aquatic environments GET 55-2017 was improved, which allowed the transfer of units only to primary transducers at one-third-octave frequencies and the calibration of primary transducer under excess pressure only in a limited frequency range of 5–500 Hz at water temperature of 15–25 °C. As a result of the conducted research, the metrological characteristics of the standard GET 55-2017 were improved and its functional capabilities were expanded, and the State primary standard of units of sound pressure and vibrational velocity in aquatic environments GET 55-2025 was approved. The stated goals were achieved through the inclusion in GET 55-2025 of new-generation measuring facilities and a unique hydroacoustic equipment complex developed at VNIIFTRI. The metrological characteristics of GET 55-2025 are presented. The reference facilities and hydroacoustic equipment included in GET 55-2025 are described. As a result, GET 55-2025 implements and ensures the reproduction and transfer of the unit of sound pressure in the aquatic environment with a minimum frequency step of 1 Hz in the range of 500–1·10⁶ Hz, studies of the characteristics of hydroacoustic measuring instruments in a free fi eld in the range of 2–500 kHz at an excess pressure of up to 15 MPa and an aquatic temperature of 4–35 °C, measurement of the phase-frequency characteristics of the sensitivity of primary transducers in the frequency range of 50–200 kHz, measurement of the frequency characteristics of the sensitivity of underwater measuring systems, the length of which does not exceed 3 m and weighing no more than 50 kg, in the frequency range of 1–250 kHz with a frequency resolution of 1 Hz, and also reproduction and transfer of the unit of the phase angle of sensitivity of primary transducers. GET 55-2025 ensured the principle of advanced development of metrology in hydroacoustics.

The problems of structural analysis of statistical data and construction of linear models of stochastic dependencies under a priori uncertainty are considered. A modified estimate of the correlation coefficient is proposed and investigated, which forms the basis for the structural analysis of statistical data. Unlike the traditional Pearson correlation coefficient, the modified estimator is based on normalizing random variables by the modes of their probability densities. To find modes of distribution laws, kernel estimates of probability densities of the random variables being analyzed are used. The choice of the blurriness coefficients for the kernel functions of nonparametric probability density estimates is based on the condition of maximizing the likelihood function. An alternative approach to choosing blurriness coefficients is to minimize the standard deviations of nonparametric probability density estimates. Estimates of traditional and modified correlation coefficients are examined. Their application in constructing linear approximations of statistical relationships is discussed. For this purpose, remote sensing data from a test forest area damaged by the Siberian silk moth was used. Two sets of spectral feature pairs were identified, differing in the large and small values of the correlation coefficient estimates under consideration. The correlation coefficient estimates were compared, and the corresponding nonparametric probability density estimates for the spectral features were analyzed. In the analysis of errors in linear approximations of dependencies between spectral features, the conditions for the advantage of traditional and modified estimates of correlation coefficients were determined. The obtained results can be used in the synthesis of algorithms for structural analysis of remote sensing data of natural objects.

In state verification schemes, the errors of primary standards of units are replaced by estimates of measurement uncertainty. This is due to the lack of an explicit verbal and mathematical definition of the term “error of a primary standard”. However, the disadvantage of measurement uncertainty estimates is the risk of their failure due to the lack of a verification of the applicability condition. This condition is practically formulated in the “Guide for Expressing Measurement Uncertainty”, but it does not have a quantitative criterion. The reason for this deficiency is the incomplete description of the measured quantity in the indirect measurement method, as well as the inadequacy of the corresponding equation or mathematical model of the measurement object. In this article, the error of the primary unit standard is determined based on the conversion formula. The formula is considered as a probability distribution of deviations from the nominal (nominative) value of a reproducible quantity using data obtained according to verification schemes. The formula is considered as a probability distribution of deviations from the nominal (nominative) value of a reproducible quantity using data obtained according to verification schemes. The use of this distribution as a reproducibility characteristic makes it possible to control the convergence conditions. This removes the problem of the true value as an unknown quantity, which served as the basis for replacing the concept of error with measurement uncertainty.

The paper describes the problems that arise during the calibration of measuring instruments and are related to the mathematical processing of the measurement protocol, in particular, the use of a compositional approach to evaluating the accuracy of calibration results. The paper presents methodological features and an effective technology for the mathematical processing of the calibration protocol in accordance with the current regulatory documents R 50.2.004-2000 “GSI. Determination of the characteristics of mathematical models of dependencies between physical quantities in solving measurement problems. Basic principles”, MI 1317-2004 “GSI. Results and characteristics of measurement errors. Forms of presentation. Methods of use in testing product samples and monitoring their parameters” and MI 2916-2005 “GSI. Identifi cation of probability distributions in solving measurement problems” using specialized and diverse non- specialized software. In order to improve the compositional approach, the MMI-Calibration 3.0 software has been developed. The MMI-Calibration 3.0 software takes into account the errors that arise due to the inadequacy of the calibration function, and it also generates a calibration chart that takes into account the tolerance intervals for a given confidence level for the most time-consuming part of calibration, which is the statistical processing of the measurement protocol. Within the framework of the MMI-calibration 3.0 program, it is possible to apply a generalized solution to the calibration problem, based on a compositional approach, which allows to speed up and simplify the computational part of the problem. The results obtained will be useful, for example, for specialists of calibration (verification) laboratories.

The problem of increasing the accuracy of grain moisture measurements while minimizing the hardware of a dielectric moisture meter is considered. To solve it, an algorithmic compensation of the analog path errors, implemented on an 8-bit microcontroller, is proposed. The developed algorithm for converting the capacitance of the sensing element (sensor) into a digital code provides high slew rates of the test voltage and ensures direct interfacing of the sensor with the microcontroller. The software and hardware for a capacitance measuring transducer have been developed, its main characteristics have been determined, and the possibility of its use as part of dielectric grain moisture meters has been assessed. A unipolar meander generated by the microcontroller's built-in timer/counter is used as a test signal applied through a reference resistor to the capacitive sensor. The maximum and minimum voltages on the sensor are converted into digital codes, which are used to calculate the actual capacitance value. The capacitance is also calculated using a parameter that depends on the resistance of the reference resistor and the square wave frequency. The sensor voltages are converted into digital codes by comparing them with a reference voltage generated by a pulse-width modulator integrated into the microcontroller and an external RC filter. Voltage comparison is performed by an analog comparator built into the microcontroller. Using simulation modeling, the dependence of the parameters of the converted test signal on the sensor capacitance was investigated. The model was developed in the SimInTech environment, which is designed for solving problems of mathematical modeling, synthesizing control algorithms, and programming computing devices. The experimental capacitance measurement converter is built using the Arduino Nano development board (Arduino, Italy), which contains the ATmega328PB microcontroller (Microchip Technology Inc, USA). The square wave frequency in the experiment was 500 kHz. Over a capacitance range of 25–45 pF, the resolution of the capacitance measuring converter was 0.1 pF. The deviation of the measurement results from the set capacitance value measured by the LCR-819 precision device (GW Instek, Taiwan) did not exceed ±0.2 pF. The capacitance measuring converter was tested as part of experimental moisture meters manufactured at Stavropol State Agrarian University for a range of 9–19 % wheat grain moisture at a grain temperature of 23–25 °C. The deviation of the results of wheat grain moisture measurements by experimental moisture meters did not exceed ±0.6 % of the moisture content determined according to GOST 13586.5-2015 “Grain. Method of moisture content determination”. The optimal fi eld of application for the converter is information-measuring and control systems based on capacitive sensors. systems based on capacitive sensors.

The article describes the developed system of calibration of measures of regular surface roughness using a stylus profilometer based on Form Talysurf PGI and a laser displacement interferometer XL-80. Based on the analysis of foreign developments and experimental studies of the metrological characteristics of unit length measures in the lateral (1D and 2D reference gratings) and vertical directions, the requirements for a reference installation based on the Form Talysurf PGI profilometer and for calibration parameters of trapezoidal roughness samples are formulated. For traceability to the definition of the unit of length-meter in the SI stylus profilometer system in the vertical direction along the OZ axis, a phase grating interferometer was used in the reference instrument Form Talysurf PGI as part of the GET 113-2014. For traceability to the definition of the length unit-meter in the SI probe profilometer Form Talysurf PGI system in the lateral direction along the OX axis, a measuring system has been developed in which reflector of XL-80 laser displacement interferometer is installed on the traverse unit of the profilometer. To test the developed calibration system for regular surface roughness measures, grids with step values of 20 μm, 50 μm, and 100 μm were calibrated. Experimental studies were conducted for a set of developed standards for transferring the unit of length in the fi eld of measuring surface roughness parameters in the lateral and vertical directions. The calibration uncertainty (±2σ) was estimated according to the measurement uncertainty budget analysis. The expended uncertainty of the calibration (±2σ) of Ra standards (nominal value 0.03–0.04 μm) are in range 0.06–0.18 μm and in the range of 0.06–0.18 μm for pitch parameter (nominal value of Sm 100, 50, 20 μm). A set of height and pitch roughness parameters calibrated using the developed measurement system with calculated extended calibration uncertainties is designed to transfer units of length to measuring instruments in the fi eld of measuring surface roughness parameters in the lateral and vertical directions.

Various linear acceleration transducers are reviewed, and their advantages and disadvantages are noted. Classical microelectromechanical accelerometers are miniature but susceptible to electromagnetic interference, and their metrological characteristics are insufficiently stable. Traditional fiber-optic sensors based on fiber Bragg gratings or Fabry-Perot interferometers provide high sensitivity but are characterized by complex optical schemes, large dimensions, and high sensitivity to temperature drifts, which hinders their integration into navigation, avionics, and space technology systems. An optical linear acceleration transducer based on controlled coupled optical waveguides has been developed. The functional scheme of the transducer includes a sensing element, an optical radiation source, photodetectors, current-to-voltage converters, and a differential signal processing circuit. A mathematical model is proposed describing the dependence of the coupling coefficient of optical waveguides on mechanical stresses induced by acceleration. The model takes into account the influence of the photoelastic effect. Mathematical modeling of the transducer operation was performed for various geometric parameters of the sensing element design. Experimental studies of the optical linear acceleration transducer were conducted, which confirmed the validity of the proposed model: a sensitivity of 10.5 mV·s²·m^–1 was achieved with nonlinearity not exceeding 0.68 % in an acceleration range of ±200 m/s². The operability of the transducer based on an optical splitter with fused waveguides has been demonstrated. Such a transducer can also be implemented using planar coupled waveguides.

This article examines the problem of reducing interferometer measurement errors for optical surface flatness deviations (measurement errors), a topical issue in the optical industry. It is shown that in order to reduce the error of measurement data, it is necessary to eliminate the component caused by deviations in the shape of the reference surfaces of the optical elements of Fizeau or Twyman-Green interferometers. Two main groups of methods for reducing the measurement error of deviations from flatness are briefly described: methods using a liquid standard and three-plane methods. A method has been developed for mathematical compensation of deviations from flatness of reference optical elements (attachments) in Fizeau-type interference installations. This method is based on the three-plane method with wavefront expansion in Zernike polynomials up to the fifth order and allows you to determine the topography of the reference surfaces of the nozzles. To implement the three- plane method, mathematical expressions are derived, by which the main parameters of the deviation of the shape of the reference surfaces are determined. The results of the practical implementation of the three-plane method using a measure of deviation from flatness with a diameter of 300 mm are presented. Experimental studies were carried out at the Research Institute of Optical and Electronic Instrumentation. The components of the instrumental measurement error are estimated. It was revealed that the greatest contribution to the measurement error is made by the random measurement error and the component caused by the deformation of the fl at plates used during their rotation. Application of the proposed mathematical compensation method made it possible to reduce the measurement error of parameters of deviation from flatness of optical surfaces at the enterprise by more than 30 %, its implementation and use can be useful at optical-mechanical enterprises for quality control of deviation of the shape of large-sized optical parts.

Contact-type vibration sensors (accelerometers) are primarily used to assess the condition of moving machines. Their susceptibility to electromagnetic interference, the need to attach them to each monitored element, and the impossibility of mounting them on rotating machine parts limit the capabilities and portability of vibration analysis. To improve the portability of defect detection and protect the sensor signal from pulsed electromagnetic interference present in production environments that mask signals indicating defects, a method for contactless diagnostics of moving machines has been proposed. The method is modeled using a dual-channel microwave interferometric displacement sensor designed to assess the technical condition of gears based on their vibration. Direct conversion of vibration into displacement is achieved through quadrature processing of the sensor's output signal. Diagnostics involves searching for signs of defects in the received signal in the form of specific frequencies inherent to a particular defect. These frequencies are characteristic of damaged gear teeth, shaft misalignment, and damage to associated bearings. Synchronous time averaging, signal envelope calculation, spectral analysis, and digital filtering were used to identify defect frequencies. To improve the signal-to-noise ratio, preprocessing of the signal was performed, highlighting the spectral excess, and the bandpass filter parameters required for re-filtering were determined. The onset and localization of degradation of a specific gear component at an early stage were determined by identifying characteristic signal harmonics associated with the corresponding defect. The obtained results are relevant for mobile, contactless monitoring of defects based on vibration of machines with moving and rotating parts. In an industrial environment, the proposed method is less expensive and more reliable than the laser method and is insensitive to sound interference, which is typical for the acoustic method.

Within the framework of a current area of research in the fi eld of speech acoustics – non-invasive analysis of speech production processes – the acute problem of insuffi cient accuracy of parametric methods for coding a turbulent (noise) type voice source is considered. In order to overcome this problem, a method for coding a sound source with increased accuracy has been developed, based on a hybrid model of linear speech prediction, which combines the advantages of parametric and nonparametric approaches to speech signal modeling. In this case, the parametric approach is implemented in the form of a vector of linear prediction coeffi cients, and the nonparametric approach is implemented in the form of a clipped sequence of linear prediction error samples. Using the author's software, a full-scale experiment on a set of the whispered speech sounds of the control speaker has been set up and carried out. Compared to a known method for encoding a turbulent sound source based on a noise-excited linear prediction model, the developed method is characterized by an accuracy gain of 2.5 dB or more in the mean square error of linear prediction metric, while guaranteeing speaker voice recognition from the decoded (reconstructed) speech signal. The obtained results will be useful in developing low-cost systems and technologies for digital processing, synthesis, and transmission of speech with multiple data compression. Promising applications of the developed method include digital voice biometrics systems, in which speaker voice recognition is a key requirement for the speech signal encoding method.