Measurements of physical quantities and their classification. Measurements of physical quantities and their classification Principles and methods of measurement
1. Subject and tasks of metrology
Metrology refers to the science of measurements, the existing means and methods that help to comply with the principle of their unity, as well as ways to achieve the required accuracy.
The origin of the term "metrology" is traced back to two Greek words: metron, which translates as "measure", and logos - "teaching". The rapid development of metrology took place at the end of the 20th century. It is inextricably linked with the development of new technologies. Before that, metrology was only a descriptive scientific subject. Thus, we can say that metrology studies:
1) methods and means for accounting for products according to the following indicators: length, mass, volume, consumption and power;
2) measurements physical quantities and technical parameters, as well as the properties and composition of substances;
3) measurements for control and regulation of technological processes.
There are several main areas of metrology:
1) general theory of measurements;
2) systems of units of physical quantities;
3) methods and means of measurement;
4) methods for determining the accuracy of measurements;
5) the basics for ensuring the uniformity of measurements, as well as the basics for the uniformity of measuring instruments;
6) standards and exemplary measuring instruments;
7) methods for transferring unit sizes from samples of measuring instruments and from standards to working measuring instruments.
Metrology objects should also be distinguished: 1) units of measurement;
2) measuring instruments;
3) the methods used to make the measurements, etc.
Metrology includes: firstly, general rules, norms and requirements, and secondly, issues that need state regulation and control. And here we are talking about:
1) physical quantities, their units, as well as their measurements;
2) principles and methods of measurements and about means of measuring equipment;
3) errors of measuring instruments, methods and means of processing measurement results in order to eliminate errors;
4) ensuring the uniformity of measurements, standards, samples;
5) state metrological service;
6) methodology of verification schemes;
7) working measuring instruments.
In this regard, the tasks of metrology are: improvement of standards, development of new methods of accurate measurements, ensuring the unity and necessary accuracy of measurements.
2 Classification of measurements
Classification of measuring instruments can be carried out according to the following criteria.
1. According to the accuracy characteristic measurements are divided into equal and unequal.
Equivalent measurements a physical quantity is a series of measurements of a certain quantity made using measuring instruments (SI) with the same accuracy, under identical initial conditions.
Unequal measurements a physical quantity is a series of measurements of a certain quantity, made using measuring instruments with different accuracy, and (or) in different initial conditions.
2. By number of measurements measurements are divided into single and multiple.
3. By type of value change measurements are divided into static and dynamic.
Static measurements are measurements of a constant, unchanging physical quantity.
Dynamic measurements are measurements of a changing, non-constant physical quantity.
4. By destination measurements are divided into technical and metrological.
Technical measurements are measurements taken technical means measurements.
Metrological measurements are measurements performed using standards.
5. How the result is presented measurements are divided into absolute and relative.
Absolute measurements are measurements that are performed by means of a direct, immediate measurement of a fundamental quantity and/or the application of a physical constant. Relative measurements- these are measurements in which the ratio of homogeneous quantities is calculated, and the numerator is the compared value, and the denominator is the comparison base (unit).
6. By methods of obtaining results measurements are divided into direct, indirect, cumulative and joint.
Direct measurements- these are measurements performed using measures, i.e. the measured value is compared directly with its measure. An example of direct measurements is the measurement of the angle (a measure is a protractor).
Indirect measurements are measurements in which the value of the measurand is calculated using the values obtained by direct measurements.
Cumulative measurements are measurements, the result of which is the solution of some system of equations. Joint measurements are measurements during which at least two non-homogeneous physical quantities are measured in order to establish the relationship existing between them.
3. Main characteristics of measurements
The following main characteristics of measurements are distinguished:
1) the method by which measurements are taken;
2) the principle of measurements;
3) measurement error;
4) measurement accuracy;
5) correct measurements;
6) reliability of measurements.
Measurement method- this is a method or a set of methods by which a given quantity is measured, that is, a comparison of the measured quantity with its measure according to the accepted principle of measurement.
There are several criteria for classifying measurement methods.
1. According to the methods of obtaining the desired value of the measured value, there are:
1) direct method (carried out using direct, direct measurements);
2) indirect method.
2. According to the methods of measurement, there are:
1) contact measurement method;
2) non-contact measurement method.
Contact measurement method is based on direct contact of any part of the measuring device with the measured object.
At non-contact measurement method the measuring instrument does not come into direct contact with the measured object.
3. According to the methods of comparing a quantity with its measure, they distinguish:
1) direct assessment method;
2) a method of comparison with its unit.
Direct evaluation method is based on the use of a measuring instrument that shows the value of the measured quantity.
Measure comparison method is based on comparing the object of measurement with its measure.
Measuring principle- this is a certain physical phenomenon or their complex, on which the measurement is based.
Measurement error- this is the difference between the result of measuring a quantity and the real (actual) value of this quantity.
Accuracy of measurements- this is a characteristic expressing the degree of compliance of the measurement results with the present value of the measured quantity.
Measurement accuracy- this is a qualitative characteristic of the measurement, which is determined by how close to zero the value of a constant or fixed error that changes during repeated measurements (systematic error).
Measurement reliability is a characteristic that determines the degree of confidence in the obtained measurement results.
4 The concept of a physical quantity The value of systems of physical units
A physical quantity is a concept of at least two sciences: physics and metrology. By definition, a physical quantity is a certain property of an object, a process that is common to a number of objects in terms of quality parameters, but differs quantitatively (individual for each object). There are a number of classifications created on various grounds. The main ones are divided into:
1) active and passive physical quantities - when divided in relation to the signals of measuring information. Moreover, the first (active) in this case are quantities that, without the use of auxiliary energy sources, are likely to be converted into a signal of measuring information. And the second (passive) are such quantities, for the measurement of which it is necessary to use auxiliary energy sources that create a signal of measuring information;
2) additive (or extensive) and non-additive (or intensive) physical quantities - when divided according to the sign of additivity. It is believed that the first (additive) quantities are measured in parts, in addition, they can be accurately reproduced using a multi-valued measure based on the summation of the sizes of individual measures. And the second (non-additive) quantities are not directly measured, since they are converted into a direct measurement of a quantity or a measurement by indirect measurements. In 1791, the National Assembly of France adopted the first ever system of units of physical quantities. It was a metric system of measures. It included: units of lengths, areas, volumes, capacities and weights. And they were based on two now well-known units: the meter and the kilogram.
The scientist based his methodology on three main independent quantities: mass, length, time. And as the main units of measurement of these quantities, the mathematician took milligram, millimeter and second, since all other units of measurement can be easily calculated using the minimum ones. Yes, on present stage development, the following main systems of units of physical quantities are distinguished:
1) cgs system(1881);
2) ICSC system(late 19th century);
3) ISS system(1901)
5. International system of units
The decisions of the General Conference on Weights and Measures adopted the following definitions of the basic units of measurement of physical quantities:
1) a meter is considered to be the length of the path that light travels in a vacuum in 1/299,792,458 of a second;
2) the kilogram is considered equivalent to the existing international prototype of the kilogram;
3) a second is equal to 919 2631 770 periods of radiation corresponding to the transition that occurs between the two so-called hyperfine levels of the ground state of the Cs133 atom;
4) an ampere is considered a measure of that strength of an unchanging current that causes an interaction force on each section of a conductor 1 m long, provided that it passes through two rectilinear parallel conductors, which have such indicators as a negligibly small circular cross-sectional area and infinite length, as well as location at a distance of 1 m apart in a vacuum;
5) kelvin is equal to 1/273.16 of the thermodynamic temperature, the so-called triple point of water;
6) a mole is equal to the amount of substance of the system, which includes the same amount structural elements, as in atoms in C 12 weighing 0.01 2 kg.
In addition, the International System of Units contains two rather important additional units needed to measure flat and solid angles. So, the unit of a plane angle is a radian, or rad for short, which is the angle between two radii of a circle, the length of the arc between which is equal to the radius of the circle. If we are talking about degrees, then the radian is equal to 57 ° 17 "48". And the steradian, or cp, taken as the unit of the solid angle, is, respectively, the solid angle, the location of the vertex of which is fixed at the center of the sphere, and the area cut out by the data angle on the surface of a sphere is equal to the area of a square whose side is equal to the length of the radius of the sphere.Other additional SI units are used to form units of angular velocity, as well as angular acceleration, etc. The radian and steradian are used for theoretical constructions and calculations, since most of the significant for practice, the values of angles in radians are expressed in transcendental numbers.The non-systemic units include the following:
1) a tenth of a bela, decibel (dB), is taken as a logarithmic unit;
2) diopter - light intensity for optical devices;
3) reactive power - Var (VA);
4) astronomical unit (AU) - 149.6 million km;
5) light year, which refers to the distance that a ray of light travels in 1 year;
6) capacity - liter;
7) area - hectare (ha).
There are also units that are not included in the SI at all. These are primarily units such as degrees and minutes. All other units are considered derivatives, which, according to international system units are formed using the simplest equations using quantities whose numerical coefficients are equated to unity. If the numerical coefficient in the equation is equal to one, the derived unit is called coherent.
6. Physical quantities and measurements
The object of measurement for metrology, as a rule, are physical quantities. Physical quantities are used to characterize various objects, phenomena and processes. Separate the basic and derivative from the main values. Seven basic and two additional physical quantities are established in the International System of Units. These are length, mass, time, thermodynamic temperature, amount of matter, luminous intensity and electric current strength, additional units are radians and steradians. Physical quantities have qualitative and quantitative characteristics.
The qualitative difference between physical quantities is reflected in their dimensions. The designation of the dimension is established by the international ISO standard, it is the symbol dim*.
The quantitative characteristic of the object of measurement is its size, obtained as a result of the measurement. The most elementary way to get information about the size of a certain value of a measurement object is to compare it with another object. The result of such a comparison will not be an exact quantitative characteristic, it will only allow you to find out which of the objects is larger (smaller) in size. Not only two, but also a greater number of sizes can be compared. If the dimensions of the measurement objects are arranged in ascending or descending order, then we get order scale. The process of sorting and arranging dimensions in ascending or descending order on an order scale is called ranking. For the convenience of measurements, certain points on the order scale are fixed and are called reference or reference points. The fixed points of the order scale can be assigned numbers, which are often called scores.
Reference scales of order have a significant drawback: the indefinite intervals between fixed reference points.
The best option is the ratio scale. The ratio scale is, for example, the Kelvin temperature scale. On this scale there is a fixed reference point - absolute zero (the temperature at which the thermal movement of molecules stops). The main advantage of the ratio scale is that it can be used to determine how many times one size is larger or smaller than another.
The size of the measurement object can be represented in different types. It depends on what intervals the scale is divided into, with which this size is measured.
For example, the movement time can be represented as follows: T = 1 h = 60 min = 3600 s. These are the values of the measured quantity. 1, 60, 3600 are the numerical values of this value.
7. Standards and exemplary measuring instruments
All issues related to the protection, application and creation of standards, as well as control over their condition, are resolved according to the unified rules established by GOST “GSI. Standards of units of physical quantities. Basic provisions” and GOST “GSI. Standards of units of physical quantities. The order of development and approval, registration, storage and application. Standards are classified according to the principle of subordination. According to this parameter, standards are primary and secondary.
The secondary standard reproduces the unit under special conditions, replacing the primary standard under these conditions. It is created and approved for the purpose of ensuring minimal wear of the state standard. Secondary standards can be divided according to the purpose. So, allocate:
1) copy samples, designed to transfer the sizes of units to working standards;
2) comparison standards, designed to check the integrity of the state standard, as well as for the purposes of replacing it, subject to its damage or loss;
3) witness standards, intended for the division of standards, which, for a number of different reasons, are not subject to direct comparison with each other;
4) working standards, which reproduce the unit from the secondary standards and serve to transfer the size to the standard of a lower rank. Secondary standards are created, approved, stored and used by ministries and departments. \
There is also the concept of "unit standard", which means one means or a set of measuring instruments aimed at reproducing and storing a unit for subsequent transmission of its size to lower measuring instruments, made according to a special specification and officially approved in the prescribed manner as a standard. There are two ways to reproduce units on the basis of dependence on technical and economic requirements:
1) centralized method - with the help of a single state standard for the whole country or a group of countries. All basic units and most of the derivatives are reproduced centrally;
2) decentralized method of reproduction - applicable to derived units, information about the size of which is not transmitted by direct comparison with the standard.
There is also the concept of "exemplary measuring instruments", which are used for the regular translation of unit sizes in the process of checking measuring instruments and are used only in the subdivisions of the metrological service. The category of an exemplary measuring instrument is determined in the course of measurements of metrological certification by one of the bodies of the State Committee for Standards.
Metrology, standardization and certification: lecture notes by Demidov NV
3. Classification of measurements
3. Classification of measurements
Classification of measuring instruments can be carried out according to the following criteria.
1. According to the accuracy characteristic measurements are divided into equal and unequal.
Equivalent measurements a physical quantity is a series of measurements of a certain quantity made using measuring instruments (SI) with the same accuracy, under identical initial conditions.
Unequal measurements a physical quantity is a series of measurements of a certain quantity, made using measuring instruments with different accuracy, and (or) in different initial conditions.
2. By number of measurements measurements are divided into single and multiple.
Single measurement is a measurement of one quantity, made once. Single measurements in practice have a large error, in this regard, it is recommended to perform measurements of this type at least three times to reduce the error, and take their arithmetic mean as a result.
Multiple measurements is a measurement of one or more quantities performed four or more times. A multiple measurement is a series of single measurements. The minimum number of measurements for which a measurement can be considered multiple is four. The result of multiple measurements is the arithmetic mean of the results of all measurements taken. With repeated measurements, the error is reduced.
3. By type of value change measurements are divided into static and dynamic.
Static measurements are measurements of a constant, unchanging physical quantity. An example of such a time-constant physical quantity is the length of a land plot.
Dynamic measurements are measurements of a changing, non-constant physical quantity.
4. By destination measurements are divided into technical and metrological.
Technical measurements- these are measurements performed by technical measuring instruments.
Metrological measurements are measurements performed using standards.
5. How the result is presented measurements are divided into absolute and relative.
Absolute measurements are measurements that are performed by means of a direct, immediate measurement of a fundamental quantity and/or the application of a physical constant.
Relative measurements- these are measurements in which the ratio of homogeneous quantities is calculated, and the numerator is the compared value, and the denominator is the comparison base (unit). The result of the measurement will depend on what value is taken as the basis of comparison.
6. By methods of obtaining results measurements are divided into direct, indirect, cumulative and joint.
Direct measurements- these are measurements performed using measures, i.e. the measured value is compared directly with its measure. An example of direct measurements is the measurement of the angle (a measure is a protractor).
Indirect measurements are measurements in which the value of the measurand is calculated using the values obtained by direct measurements and some known relationship between these values and the measurand.
Cumulative measurements- these are measurements, the result of which is the solution of a certain system of equations, which is composed of equations obtained as a result of measuring possible combinations of measured quantities.
Joint measurements are measurements during which at least two non-homogeneous physical quantities are measured in order to establish the relationship existing between them.
From the book GENERAL REQUIREMENTS FOR THE COMPETENCE OF TESTING AND CALIBRATION LABORATORIES author author unknown5.4.6 Evaluation of measurement uncertainty 5.4.6.1 A calibration laboratory or testing laboratory performing its own calibrations shall have and apply a procedure for evaluating measurement uncertainty for all calibrations and calibration types.5.4.6.2
From the book Metrology, Standardization and Certification: Lecture Notes the author Demidov N V5.6 Traceability of measurements 5.6.1 General All equipment used to carry out tests and/or calibrations, including equipment for additional measurements (e.g. ambient conditions) that have a significant effect on accuracy and validity
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Classification of measurements can be carried out according to the following criteria.
1. According to the accuracy characteristic:
- equal measurements a physical quantity is a series of measurements of a certain quantity made using measuring instruments with the same accuracy, under identical initial conditions.
- unequal measurements a physical quantity is a series of measurements of a certain quantity, made using measuring instruments with different accuracy, and (or) in different initial conditions.
2. By the number of measurements:
- single measurement is a measurement of one quantity, made once. Single measurements in practice have a large error, in this regard, it is recommended to perform measurements of this type at least three times to reduce the error, and take their arithmetic mean as a result.
- multiple measurements is a measurement of one or more quantities performed four or more times. A multiple measurement is a series of single measurements. The minimum number of measurements for which a measurement can be considered multiple is four. The result of multiple measurements is the arithmetic mean of the results of all measurements taken. With repeated measurements, the error is reduced.
3. By type of value change:
- static measurements are measurements of a constant, unchanging physical quantity. An example of such a time-constant physical quantity is the length of a land plot.
- dynamic measurements are measurements of a changing, non-constant physical quantity.
4. According to the purpose of the measurement:
- technical measurements- these are measurements performed by technical measuring instruments.
- metrological measurements are measurements performed using standards.
5. According to the method of presenting the result:
- absolute measurements are measurements that are performed by means of a direct, immediate measurement of a fundamental quantity and/or the application of a physical constant.
- relative measurements- these are measurements in which the ratio of homogeneous quantities is calculated, and the numerator is the compared value, and the denominator is the comparison base (unit). The result of the measurement will depend on what value is taken as the basis of comparison.
6. By methods of obtaining results:
- direct measurements- these are measurements performed using measures, i.e. the measured value is compared directly with its measure. An example of direct measurements is the measurement of the angle (a measure is a protractor).
- indirect measurements are measurements in which the value of the measurand is calculated using the values obtained by direct measurements and some known relationship between these values and the measurand.
y = f(x1, x2, … xn),
where y is the desired physical quantity;
x1,x2,…,xn are quantities subjected to direct measurements.
Example: finding density by volume and mass of a body.
- cumulative measurements- these are measurements, the result of which is the solution of a certain system of equations, which is composed of equations obtained as a result of measuring possible combinations of measured quantities.
For example: finding the mass of an unknown weight based on the ratio of the masses of known weights included in the system of equations.
- joint measurements are measurements during which at least two non-homogeneous physical quantities are measured in order to establish the relationship existing between them.
For example: Finding the resistance of a resistor from temperature.
In aggregate measurements, several quantities of the same name are simultaneously determined, and in joint measurements, opposite ones.
Classification of measuring instruments can be carried out according to the following criteria.
1. According to the characteristic of measurement accuracy, they are divided into equal and unequal.
Equivalent measurements of a physical quantity is a series of measurements of a certain quantity made using measuring instruments (MI) with the same accuracy, under identical initial conditions.
Unequal measurements of a physical quantity is a series of measurements of a certain quantity, made using measuring instruments with different accuracy, and (or) in different initial conditions.
2. According to the number of measurements, measurements are divided into single and multiple.
A single measurement is a measurement of one quantity made once. Single measurements in practice have a large error, in this regard, it is recommended to perform measurements of this type at least three times to reduce the error, and take their arithmetic mean as a result.
Multiple measurements are measurements of one or more quantities performed four or more times. A multiple measurement is a series of single measurements. The minimum number of measurements for which a measurement can be considered multiple is four. The result of multiple measurements is the arithmetic mean of the results of all measurements taken. With repeated measurements, the error is reduced.
3. According to the type of change in the measurement value, they are divided into static and dynamic.
Static measurements are measurements of a constant, unchanging physical quantity. An example of such a time-constant physical quantity is the length of a land plot.
Dynamic measurements are measurements of a changing, non-constant physical quantity.
4. By purpose, measurements are divided into technical and metrological.
Technical measurements are measurements performed by technical measuring instruments.
Metrological measurements are measurements performed using standards.
5. According to the method of presenting the result, measurements are divided into absolute and relative.
Absolute measurements are measurements that are made by direct, direct measurement of a fundamental quantity and/or application of a physical constant.
Relative measurements are measurements in which the ratio of homogeneous quantities is calculated, and the numerator is the compared value, and the denominator is the comparison base (unit). The result of the measurement will depend on what value is taken as the basis of comparison.
6. By methods of obtaining results, measurements are divided into direct, indirect, cumulative and joint.
Direct measurements are measurements performed using measures, i.e. the measurand is compared directly with its measure. An example of direct measurements is the measurement of the angle (a measure is a protractor).
Indirect measurements are measurements in which the value of the measurand is calculated using the values obtained through direct measurements and some known relationship between these values and the measurand.
Cumulative measurements are measurements, the result of which is the solution of a certain system of equations, which is composed of equations obtained as a result of measuring possible combinations of measured quantities.
Joint measurements are measurements during which at least two inhomogeneous physical quantities are measured in order to establish the relationship existing between them.
Measurement error
In the practice of using measurements, their accuracy becomes a very important indicator, which is the degree of closeness of the measurement results to some actual value, which is used for a qualitative comparison of measuring operations. And as a quantitative assessment, as a rule, the measurement error is used. Moreover, the smaller the error, the higher the accuracy is considered.
According to the law of the theory of errors, if it is necessary to increase the accuracy of the result (with the excluded systematic error) by 2 times, then the number of measurements must be increased by 4 times; if it is required to increase the accuracy by 3 times, then the number of measurements is increased by 9 times, etc.
The process of assessing the measurement error is considered one of the most important activities in ensuring the uniformity of measurements. Naturally, there are a huge number of factors that affect the measurement accuracy. Consequently, any classification of measurement errors is rather arbitrary, since often, depending on the conditions of the measurement process, errors can manifest themselves in various groups. In this case, according to the principle of dependence on the form, these expressions of the measurement error can be: absolute, relative and reduced.
In addition, on the basis of dependence on the nature of the manifestation, the causes and possibilities for eliminating measurement errors, they can be components. In this case, the following error components are distinguished: systematic and random.
The systematic component remains constant or changes with subsequent measurements of the same parameter.
The random component changes with repeated changes in the same parameter randomly. Both components of the measurement error (both random and systematic) appear simultaneously. Moreover, the value of the random error is not known in advance, since it can arise due to a number of unspecified factors. This type of error cannot be completely excluded, but their influence can be somewhat reduced by processing the measurement results.
The systematic error, and this is its peculiarity, when compared with a random error, which is detected regardless of its sources, is considered by components in connection with the sources of occurrence.
Components of the error can also be divided into: methodological, instrumental and subjective. Subjective systematic errors are associated with individual features operator. Such an error may occur due to errors in the reading of readings or the inexperience of the operator. Basically, systematic errors arise due to the methodological and instrumental components. The methodological component of the error is determined by the imperfection of the measurement method, the methods of using the SI, the incorrectness of the calculation formulas and the rounding of the results. The instrumental component appears due to the inherent error of the MI, determined by the accuracy class, the influence of the MI on the result, and the resolution of the MI. There is also such a thing as "gross errors or misses", which may appear due to erroneous actions of the operator, malfunction of the measuring instrument, or unforeseen changes in the measurement situation. Such errors, as a rule, are detected in the process of reviewing the measurement results using special criteria. An important element of this classification is the error prevention, understood as the most rational way to reduce the error, is to eliminate the influence of any factor.
Types of errors
There are the following types of errors:
1) absolute error;
2) relative error;
3) reduced error;
4) basic error;
5) additional error;
6) systematic error;
7) random error;
8) instrumental error;
9) methodological error;
10) personal error;
11) static error;
12) dynamic error.
Measurement errors are classified according to the following criteria.
According to the method of mathematical expression, the errors are divided into absolute errors and relative errors.
According to the interaction of changes in time and the input value, the errors are divided into static errors and dynamic errors.
According to the nature of the appearance of errors, they are divided into systematic errors and random errors.
Absolute error is a value calculated as the difference between the value of the quantity obtained during the measurement process and the real (actual) value of the given quantity.
The absolute error of a measure is a value calculated as the difference between the number, which is the nominal value of the measure, and the real (actual) value of the quantity reproduced by the measure.
Relative error is a number that reflects the degree of accuracy of a measurement.
The reduced error is a value calculated as the ratio of the absolute error value to the normalizing value.
The normalizing value is defined as follows:
1) for measuring instruments for which a nominal value is approved, this nominal value is taken as a normalizing value;
2) for measuring instruments, in which the zero value is located on the edge of the measurement scale or outside the scale, the normalizing value is taken equal to the final value from the measurement range. The exception is measuring instruments with a significantly uneven measurement scale;
3) for measuring instruments, in which the zero mark is located within the measurement range, the normalizing value is taken equal to the sum of the final numerical values of the measurement range;
4) for measuring instruments (measuring instruments), in which the scale is uneven, the normalizing value is taken equal to the entire length of the measurement scale or the length of that part of it that corresponds to the measurement range. The absolute error is then expressed in units of length.
Measurement error includes instrumental error, methodological error and reading error. Moreover, the reading error arises due to the inaccuracy in determining the division fractions of the measurement scale.
Instrumental error is an error that occurs due to errors made in the manufacturing process of functional parts of error measuring instruments.
A methodological error is an error that occurs due to the following reasons:
1) inaccuracy in building a model of the physical process on which the measuring instrument is based;
2) incorrect use of measuring instruments.
Subjective error is an error arising due to the low degree of qualification of the operator of the measuring instrument, as well as due to the error of the human visual organs, i.e. the human factor is the cause of the subjective error.
Errors in the interaction of changes in time and the input value are divided into static and dynamic errors.
Static error is an error that occurs in the process of measuring a constant (not changing in time) value.
Dynamic error is an error, the numerical value of which is calculated as the difference between the error that occurs when measuring a non-constant (variable in time) quantity, and a static error (the error in the value of the measured quantity at a certain point in time).
According to the nature of the dependence of the error on the influencing quantities, the errors are divided into basic and additional.
The basic error is the error obtained under normal operating conditions of the measuring instrument (at normal values of the influencing quantities).
Additional error- this is the error that occurs when the values of the influencing quantities do not correspond to their normal values, or if the influencing quantity goes beyond the boundaries of the area of normal values.
Normal conditions are conditions in which all values of the influencing quantities are normal or do not go beyond the boundaries of the range of normal values.
Operating conditions are conditions in which the change in influencing quantities has a wider range (influencing values do not go beyond the limits of the working range of values).
The working range of values of the influencing quantity is the range of values in which the normalization of the values of the additional error is carried out.
According to the nature of the dependence of the error on the input value, the errors are divided into additive and multiplicative.
Additive error is an error that occurs due to the summation of numerical values and does not depend on the value of the measured quantity, taken modulo (absolute).
A multiplicative error is an error that changes with the change in the value of the quantity being measured.
It should be noted that the value of the absolute additive error is not related to the value of the measured quantity and the sensitivity of the measuring instrument. Absolute additive errors are unchanged over the entire measurement range.
The value of the absolute additive error determines the minimum value of the quantity that can be measured by the measuring instrument.
The values of multiplicative errors change in proportion to changes in the values of the measured quantity. The values of multiplicative errors are also proportional to the sensitivity of the measuring instrument. The multiplicative error arises due to the influence of influencing quantities on the parametric characteristics of the instrument elements.
Errors that may occur during the measurement process are classified according to the nature of their occurrence. Allocate:
1) systematic errors;
2) random errors.
Gross errors and misses may also appear in the measurement process.
The systematic error is component the entire error of the measurement result, which does not change or changes naturally with repeated measurements of the same value. Usually, systematic error is tried to be eliminated. possible ways(for example, by using measurement methods that reduce the likelihood of its occurrence), but if a systematic error cannot be excluded, then it is calculated before the start of measurements and appropriate corrections are made to the measurement result. In the process of normalizing the systematic error, the boundaries of its admissible values are determined. The systematic error determines the correctness of measurements of measuring instruments (metrological property).
Systematic errors in some cases can be determined experimentally. The measurement result can then be refined by introducing a correction.
Methods for eliminating systematic errors are divided into four types:
1) elimination of causes and sources of errors before the start of measurements;
2) elimination of errors in the process of already begun measurement by methods of substitution, compensation of errors in sign, oppositions, symmetrical observations;
3) correction of the measurement results by making an amendment (elimination of the error by calculations);
4) determination of the limits of systematic error in case it cannot be eliminated.
Elimination of the causes and sources of errors before the start of measurements. This method is the best option, since its use simplifies the further course of measurements (there is no need to eliminate errors in the process of an already started measurement or make corrections to the result).
To eliminate systematic errors in the process of an already started measurement, apply various ways
The method of introducing corrections is based on the knowledge of the systematic error and the current patterns of its change. When using this method, the measurement result obtained with systematic errors is subject to corrections equal in magnitude to these errors, but opposite in sign.
The method of substitution is that the measured value is replaced by a measure placed in the same conditions in which the object of measurement was located. The substitution method is used when measuring the following electrical parameters: resistance, capacitance and inductance.
The way to compensate for the error in sign is that the measurements are performed twice in such a way that the error, unknown in magnitude, is included in the measurement results with the opposite sign.
The method of opposition is similar to the method of compensation by sign. This method consists in the fact that measurements are performed twice in such a way that the source of error in the first measurement has the opposite effect on the result of the second measurement.
Random error is a component of the error of the measurement result, which changes randomly, irregularly during repeated measurements of the same value. The occurrence of a random error cannot be foreseen and predicted. Random error cannot be completely eliminated; it always distorts the final measurement results to some extent. But you can make the measurement result more accurate by taking repeated measurements. The cause of a random error can be, for example, a random change in external factors affecting the measurement process. A random error during multiple measurements with a sufficiently high degree of accuracy leads to scattering of the results.
Slips and gross errors are errors that are much larger than the systematic and random errors expected under the given measurement conditions. Slips and gross errors may appear due to gross errors in the measurement process, a technical malfunction of the measuring instrument, and unexpected changes in external conditions.
Errors of measuring instruments
The errors of measuring instruments are classified according to the following criteria:
1) according to the way of expression;
2) by the nature of the manifestation;
3) in relation to the conditions of use. According to the method of expression, absolute and relative errors are distinguished.
Relative error is a number that reflects the degree of accuracy of a measuring instrument.
Relative error is expressed as a percentage.
According to the nature of the manifestation of errors, they are divided into random and systematic.
In relation to the conditions of application, the errors are divided into basic and additional.
The basic error of measuring instruments is the error, which is determined if the measuring instruments are used under normal conditions.
The additional error of measuring instruments is an integral part of the error of the measuring instrument, which additionally occurs if any of the influencing quantities goes beyond its normal value.
Dynamic measurement-- a measurement of a quantity whose size changes over time. A rapid change in the size of the measured value requires its measurement with the most accurate determination of the moment in time.
For example, measuring the distance to the ground level with hot air balloon or measuring the DC voltage of an electric current. Essentially, a dynamic measurement is a measurement of the functional dependence of the measurand on time.
The sign according to which the measurement is referred to as static or dynamic is the dynamic error at a given speed or frequency of change of the measured quantity and given dynamic properties of the MI. Assume that it is negligible (for the measurement problem being solved), in which case the measurement can be considered static. If these requirements are not met, it is dynamic.
Dynamic measurement error- error of the measurement result, inherent in the conditions of dynamic measurement. Dynamic error appears when measuring variables and is due to the inertial properties of measuring instruments. The dynamic error of the measuring instrument is the difference between the error of the measuring instrument in dynamic conditions and its static error corresponding to the value of the quantity in this moment time. When developing or designing a measuring instrument, it should be taken into account that an increase in the measurement error and a delay in the appearance of the output signal are associated with changing conditions.
Static and dynamic errors refer to errors in the measurement result. In most devices, static and dynamic errors turn out to be interconnected, since the ratio between these types of errors depends on the characteristics of the device and the characteristic time of change in magnitude.
Static measurements
Static measurement-- measurement of a quantity, which is taken in accordance with the set measurement task as unchanged during the measurement period.
For example: 1) body measurements;
2) measurements of constant pressure;
3) measurements of pulsating pressures, vibrations;
4) measurement of the linear size of the manufactured product at normal temperature can be considered static, since temperature fluctuations in the workshop at the level of tenths of a degree introduce a measurement error of no more than 10 µm/m, which is insignificant compared to the manufacturing error of the part. Therefore, in this measurement task, the measured quantity can be considered unchanged. When calibrating a line measure of length on the state primary standard, thermostating ensures the stability of maintaining the temperature at the level of 0.005 °C. Such fluctuations in temperature cause a thousand times smaller measurement error - no more than 0.01 μm / m. But in this measurement task, it is significant, and taking into account temperature changes in the measurement process becomes a condition for ensuring the required measurement accuracy, so these measurements should be carried out according to the dynamic measurement technique.
Static measurement error- error of the measurement result, inherent in the conditions of static measurement, that is, when measuring constant values after the completion of transient processes in the elements of devices and converters.
