Errors Of Indirect Measurements Research Articles

Evaluation of the error of indirect measurements of physical-mechanical characteristics of materials by dynamic indentation method

The metrological problems of measuring the physic and mechanical characteristics of materials by dynamic indentation are considered. It is shown that the estimation of measurement error demanding the creation of the reference blocks is ineffective due to the wide variety of controlled materials and a wide range of changes in their properties. A technique has been developed for evaluating the accuracy of measurements based on the errors of individual parameters included in the calculation equation, i.e. by determining the error of indirect measurements. The technique is based on the estimation of the boundaries of the random error of the measured characteristics of the material and the non-excluded systematic errors of the parameters that are used for the calculations of needed characteristics. The results of experimental studies are presented, indicating that due to the different character of the dependencies of hardness and elastic modulus, the error in measuring the elastic modulus exceeds the error in measuring hardness. In addition, it was found that the error in measuring the characteristics of materials by the dynamic indentation method exceeds the measurement error by the static indentation method and can be reduced by increasing the accuracy of the equipment used for the registration of impact process. The obtained values of the physic and mechanical characteristics of the materials and the values of the measurement error show that the dynamic indentation method can effectively solve the problem of non-destructive testing of hardness, elastic modulus, and strain hardening exponent of metals and products with an appropriate error.

Comment on ‘How long is my toilet roll-a simple exercise in mathematical modelling’

In the article ‘How long is my toilet roll-a simple exercise in mathematical modelling’ several models of increasing complexity are introduced and solved to calculate indirectly the length of paper on a toilet-roll. All these results are presented without errors. The authors of this comment believe the error analysis of measurements made in a laboratory is an important part of the experiment. The calculation of the absolute errors in indirect measurements provides us with information about the confidence that we must have in our experimental results. For that reason, the error calculation for all approximations has been made.

Estimation of the error of the results of indirect measurements of some quantities

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.

ОСЦИЛОГРАФІЧНИЙ МЕТОД ВИМІРЮВАННЯ ФАЗОВОГО ЗСУВУ НА БАЗІ ДВОНАПІВПЕРІОДНОГО ПЕРЕТВОРЕННЯ

The subject matter of the article is the oscilloscope methods of measuring the phase shift of two harmonic signals, after carrying out their two-half-period transformation and summing. The goal is to develop ways to implement an oscilloscope method of measuring the phase shift of two harmonic signals, which will significantly reduce the component of measurement error caused by phase non-symmetry of the transmission channels, by reducing their length. Analyze the measurement error for each of the methods for determining the phase shift of two harmonic signals using their two-half-periodic transformation. The tasks: statement of measurement problem of determination of phase shift of two harmonic signals; analysis of known oscilloscope methods of phase shift measurement, development of methods for implementing the oscilloscope method based on the analysis of the characteristics of the total signal obtained during the two-half-period transformation; estimation of measurement errors for each method. The methods used are the methodology for estimating measurement errors in indirect measurements. The following results were obtained. Methods for implementing an oscilloscope measurement method using the total signal after a two-half-period transformation based on the analysis of temporal characteristics and local extrema of this signal are proposed. The list of measuring operations that implement each method is defined. The analysis of the components of measurement errors was performed and the degree of correlation was determined. Synthesized ratios for the calculation of measurement error. Conclusions. The scientific novelty of the obtained results is the following: an oscilloscopic method has been developed that will allow reducing substantially the component of the error caused by phase non-symmetry of the signal transmission channels; obtained ratios for the implementation of the oscilloscope measurement method using two-half-period conversion; obtained ratios to calculate the standard deviation of the total measurement error in each of the proposed methods.

Error estimation of the physical and mechanical characteristics measurements by indentation

The active application in the practice of testing the indentation methods, in particular to measure the physical and mechanical properties of metals, polymers, biological technologies demands to development techniques for the measurement error estimation. At the same time existing traditional measurement error evaluation system, based on the using of the reference blocks, is not always suitable for use in testing and research laboratories. The aim of this work was development the technique for estimating the indirect measurements error of materials physical and mechanical characteristics that can be applied in practice and based on the existing standards. Checking of the proposed approach using the experimental values of the hardness and elastic modulus obtained during static indentation for various metals.It is shown that since the initial information about the material is an indentation curve representing the dependence of the load versus penetration depth of the indenter into the material tested, then it is better to confirm the metrological characteristics of the indentation measuring devices using the applied force and achieved displacement, but to estimate the accuracy of determining the properties through the error of indirect measurements. The equations for calculating the hardness and modulus of elasticity are derived. It allows to determine the component value most influencing the error magnitude. The calculation of error on the base of the value of boundary of a random and non-exclusive systematic error was carrying out.The advantage of the developed technique is the fact that the measurement of the physical and mechanical characteristics is based on the experimental data and does not require the creation of the additional metrological assurance. The proposed approach seems appropriate to extend for the determination of the measurement error of other characteristics: the yield point, the strain hardening exponent, creep, relaxation, determined by the indentation methods.

Nondestructive testing of the quality of winding impregnation in electric machines

The topicality of this work is accounted for by a need to upgrade the evaluation of the quality of winding impregnation in electric machines and to raise their safety margin and reliability. Our goal is to substantiate the possibility of using the measured capacitance of the winding of an electric machine (with respect to its magnetic core) for testing the impregnation of cavities in the major insulation and assessing metrological characteristics of the proposed testing technique. Methods of electric measurements for studying the capacitance characteristics of electric-machine windings, formulae for calculating the dielectric constant of binary mixtures, and techniques for assessing the errors of indirect measurements have been used.

Determination of the Error of Measurements of the Impedance of Electronic Components Using a Vector Circuit Analyzer

Methods of calculating the error of indirect measurements of the impedance of electronic components from the results of measurements of the S-parameters, carried out using a vector circuit analyzer are considered. Expressions are obtained relating the error in determining the impedance and the effective parameters of the measuring instrument. A typical calculation of the error using the example of the S5048 precision vector circuit analyzer is presented.

A general framework for error analysis in measurement-based GIS Part 1: The basic measurement-error model and related concepts

This is the first of a four-part series of papers which proposes a general framework for error analysis in measurement-based geographical information systems (MBGIS). The purpose of the series is to investigate the fundamental issues involved in measurement error (ME) analysis in MBGIS, and to provide a unified and effective treatment of errors and their propagation in various interrelated GIS and spatial operations. Part 1 deals with the formulation of the basic ME model together with the law of error propagation. Part 2 investigates the classic point-in-polygon problem under ME. Continuing to Part 3 is the analysis of ME in intersections and polygon overlays. In Part 4, error analyses in length and area measurements are made. In this present part, a simple but general model for ME in MBGIS is introduced. An approximate law of error propagation is then formulated. A simple, unified, and effective treatment of error bands for a line segment is made under the name of “covariance-based error band”. A new concept, called “maximal allowable limit”, which guarantees invariance in topology or geometric-property of a polygon under ME is also advanced. To handle errors in indirect measurements, a geodetic model for MBGIS is proposed and its error propagation problem is studied on the basis of the basic ME model as well as the approximate law of error propagation. Simulation experiments all substantiate the effectiveness of the proposed theoretical construct.

The Systematic Error of Measurements of the Local Pressure of an Acoustic Field by a Laser Doppler Anemometer

A method and the errors of indirect measurements of the values of the local pressure of an acoustic field in liquids and gases from the results of an estimate of the oscillatory velocity of microparticles are discussed. It is shown that when a laser Doppler method of measuring velocity is used, a systematic component of the error occurs due to the acoustooptical effect. The ranges of the parameters of the medium, of the acoustic wave and of the measuring equipment in which the systematic error can be reduced to the required value are determined.

Standardizing the Errors of Indirect Measurements with Constriction-Type Variable-Pressure Flowmeters

The relative and absolute measurement errors are examined for devices using constrictions operated under various conditions. The practical metrology of indirect measurements can be based on a principle of equal absolute errors at the boundaries of the measurement range.

Error Estimation for Indirect Measurements: Interval Computation Problem Is (Slightly) Harder Than a Similar Probabilistic Computational Problem

One of main applications of interval computations is estimating errors of indirect measurements. A quantity y is measured indirectly if we measure some quantities xi related to y and then estimate y from the results x, of these measurements as f(x1,..., xn) by using a known relation f. Interval computations are used “to find the range of f(x1,...,xn) when xi are known to belong to intervals xi = [xi — Δi,xi + Δi],” where Δi are guaranteed accuracies of direct measurements. It is known that the corresponding problem is intractable (NP-hard) even for polynomial functions f.

Analytic construction of the elements of indirect measurement systems

The problem of minimizing the error of indirect measurements on the basis of directly measurable parameters is considered. The solution of the problem may be reduced to analytic construction of the characteristics of the elements of the measurement system.

Methods of reducing the errors of indirect measurements under dynamic conditions

Methods of reducing the errors of indirect measurements under dynamic conditions

Systematic Errors in Indirect Measurements of the Velocity of Sound

An analysis is made of certain methods of measuring the velocity of sound. Specifically, attention is centered on those methods based upon measurements of the electrical driving-point impedance of the transducer and the observation of some phenomenon of that impedance which is recurrent as the position of the reflector in the acoustic chamber is changed. Consideration is given to the influences of small losses in the propagation of sound in the chamber and of the existence of nonplane wave fronts. It is shown that such measurements can be subject to significant systematic errors arising from the method itself. The nature and magnitude of such errors are discussed.