Main types of measurements in metrology. Main types and methods of measurements, their classification
According to the method of obtaining the measurement result
According to the method of presenting measurement results
According to the nature of the change in time of the measured EF
Accuracy characteristics
By number of measurements
- one-time(measurements are performed once);
- multiple(a series of multiple measurements of EF of the same size)
-equally accurate(a series of measurements of any quantity, carried out by measuring instruments of equal accuracy under the same conditions and with the same care);
- unequal(a series of measurements of any quantity, carried out with measuring instruments differing in accuracy and under different conditions).
- static;
- dynamic.
- absolute(measurement of a quantity in its units);
- relative(measurements of changes in a quantity in relation to the same quantity taken as the original). Relative measurements, all other things being equal, can be performed more accurately than absolute ones, since the total error does not include the error of the measure of quantity.
- straight(the desired PV value is obtained directly from experimental data).
- indirect– determination of the desired value of a physical quantity based on the results of direct measurements of other physical quantities that are functionally related to the desired quantity. In this case, the numerical value of the desired quantity is found by calculation. Indirect measurements, in turn, are divided into cumulative and joint.
Aggregate Measurements– measurements of several quantities of the same name carried out simultaneously, in which the required measurements of quantities are determined by solving a system of equations obtained by measuring these quantities in various combinations.
Joint measurements– simultaneous measurements of two or more different quantities to determine the relationship between them. The numerical values of the required quantities, as in the case of cumulative measurements, are found from a system of equations connecting the values of the sought quantities with the value of the quantities measured directly (or indirectly). The number of equations must be no less than the number of required quantities.
Measurement is a complex process and the following characteristics are important for it: the principle and method of measurement, result, error, accuracy, convergence, reproducibility, correctness and reliability.
Measuring principle– a physical phenomenon or effect underlying measurements.
Method of measurement– a technique or a set of techniques for comparing a measured physical quantity with its unit in accordance with the implemented measurement principle.
Measurement result– the value of a quantity obtained by measuring it.
Measurement result error– deviation of the measurement result from the true (actual) value of the measured quantity.
Accuracy of measurement result– one of the characteristics of measurement quality, reflecting the closeness to zero error of the measurement result. High measurement accuracy corresponds to small errors. Accuracy is quantified by the reciprocal value of the relative error module, for example, if the relative error is 0.01, then the accuracy is 100.
Convergence of measurement results– closeness to each other of the results of measurements of the same quantity, performed repeatedly using the same means, the same method under the same conditions and with the same care. The accuracy of measurements reflects the influence of random errors on the measurement result.
Reproducibility– closeness of measurement results of the same quantity, obtained in different places, by different methods and means, by different operators, at different times, but reduced to the same conditions (temperature, pressure, humidity, etc.).
Right– characteristic of the quality of measurements, reflecting the closeness to zero of systematic errors in their results.
Credibility– a characteristic of the quality of measurements, reflecting confidence in their results, which is determined by the probability (confidence) that the true value of the measured quantity is within the specified limits (confidence). Measurements are divided into reliable and unreliable depending on how much the probabilistic characteristics of their deviation from the actual value of the measured values are known.
Question #5
The importance of metrology for scientific and technological progress and in the development of the country's economy. Main tasks and problems of metrology.
As already noted, in practical life a person deals with measurements everywhere. At every step, measurements of such quantities as length, volume, weight, time, etc. are encountered and have been known since time immemorial.
The importance of measurements in modern society is great. They serve not only as the basis of scientific and technical knowledge, but are of paramount importance for accounting of material resources and planning, for domestic and foreign trade, for ensuring product quality, interchangeability of components and parts and improving technology, for ensuring labor safety and other types of human activity.
Metrology is of great importance for the progress of natural and technical sciences, since increasing the accuracy of measurements is one of the means of improving the ways of human knowledge of nature, discoveries and practical application of precise knowledge.
To ensure scientific and technological progress, metrology must be ahead of its development in other areas of science and technology, because for each of them, accurate measurements are one of the main ways to improve them.
The acceleration of scientific and technological progress is in direct connection with the intensive development of metrology and precision measurement technology, necessary both for the development of natural and exact sciences, and for the creation of new technology and improvement of technical control and management tools. All this poses a number of important challenges for metrology.
In the field of units of measurement, one of the main tasks is their unification on the basis of the widespread implementation of a unified International System of Units (SI). This system ensures uniformity of units used for all fields of science and technology. The requirements for the highest level in measuring instruments - for standards - are significantly increasing. The accuracy of measurements in industry in many cases approaches the maximum possible given the state of technology and, therefore, the accuracy of the standards themselves. The next step is the increasingly widespread use of fundamental physical constants and atomic constants, characterized by high stability, as the basis for new, more advanced standards.
To maintain the uniformity of measurements carried out in different places and at different times, it is necessary to ensure the transfer of the size of units from standards to working measuring instruments with the least loss of accuracy. The design of modern standards and methods of transmitting the size of units must ensure the fulfillment of this requirement.
An urgent task is to extend precise measurements to areas of very small and large values of measured quantities (small and large masses, deep vacuum and ultra-high pressures, ultra-low and ultra-high temperatures, ultra-high frequencies, etc.). The need to transfer the size of units of measurement to instruments that measure vanishingly small or extremely large values of quantities often does not allow one to limit oneself to one standard and requires the creation of several independent special standards for the same quantity.
The issues of carrying out extremely accurate measurements under special non-stationary conditions, under dynamic conditions, at high accelerations, high or very low temperatures, pressures, and frequencies also become of great importance.
The development of measuring and measuring-control systems has led to qualitative changes in the measurement process itself. In addition to quantities, processes that have numerous parameters and characteristics are compared. Metrological support should also be extended to measurement and control systems.
There are also important problems in the field of measurement theory. The development of mathematical statistics and the theory of random functions influences the issues of metrological processing of measurement results.
The widespread use of automatic control and regulation methods requires additions to existing metrological concepts and ideas. Methods and measuring instruments used in medicine, construction, the chemical industry and other branches of science and technology must be improved.
Serving as the scientific basis of measuring technology, metrology must ensure the necessary reliability and accuracy of the resulting measurement information, as well as legally determine the uniformity of measurements in the country, the uniformity of methods for monitoring technological processes and testing products. Metrology generalizes practical experience in this area and accordingly directs the development of measuring technology.
Metrology is organically connected with standardization, and this connection is expressed primarily in the standardization of units of measurement, the system of state standards, measuring instruments and verification methods, in the creation of standard samples of the properties and composition of a substance. In turn, standardization is based on metrology, which ensures the correctness and comparability of test results for materials and products, and also borrows from metrology methods for determining and monitoring quality indicators
In close interaction, metrology and standardization are important levers of technical progress in all areas of science and the country's economy.
9. Measuring instruments and their characteristics
In the scientific literature, technical measuring instruments are divided into three large groups. These are: measures, calibers and universal measuring instruments, which include measuring instruments, control and measuring instruments (instruments), and systems.
1. A measure is a means of measurement that is intended to reproduce a physical quantity of the required size. The measures include plane-parallel length measures (tiles) and angular measures.
2. Gauges are certain devices, the purpose of which is to control and search within the required boundaries of dimensions, relative positions of surfaces and shapes of parts. As a rule, they are divided into: smooth limit gauges (staples and plugs), as well as threaded gauges, which include threaded rings or staples, threaded plugs, etc.
3. A measuring instrument, presented in the form of a device that produces a signal of measuring information in a form understandable to observers.
4. A measuring system, understood as a certain set of measuring instruments and certain auxiliary devices that are connected to each other by communication channels. It is designed to produce measurement information signals in some form that is suitable for automatic processing, as well as for translation and use in automatic control systems.
5. Universal measuring instruments, the purpose of which is to use to determine actual dimensions. Any universal measuring instrument is characterized by its purpose, operating principle, that is, the physical principle underlying its construction, design features and metrological characteristics.
When monitoring angular and linear indicators, direct measurements are used; relative, indirect or cumulative measurements are less common. In the scientific literature, among direct measurement methods, the following are usually distinguished:
1) direct assessment method, which is a method in which the value of a quantity is determined by the reading device of the measuring device;
2) the method of comparison with a measure, which is understood as a method in which a given value can be compared with a value reproduced by a measure;
3) the addition method, which usually means a method when the value of a obtained quantity is supplemented with a measure of the same quantity so that the device used for comparison is affected by their sum equal to a predetermined value;
4) differential method, which is characterized by measuring the difference between a given value and a known value reproducible by a measure. The method gives results with a fairly high level of accuracy when using rough measuring instruments;
5) the zero method, which is essentially similar to the differential method, but the difference between a given quantity and a measure is reduced to zero. Moreover, the zero method has a certain advantage, since the measure can be many times smaller than the measured value;
6) the substitution method, which is a comparative method with a measure in which the measured quantity is replaced by a known quantity that is reproduced by the measure. Let us remember that there are also non-standardized methods. This group typically includes the following:
1) the method of opposition, which implies a method in which a given value, as well as the value reproduced by the measure, act on the comparison device at the same time;
2) the coincidence method, characterized as a method in which the difference between the compared quantities is measured using the coincidence of marks on scales or periodic signals.
10. Classification of measuring instruments
Measuring instrument (MI)– this is a technical means or a set of means used to carry out measurements and having standardized metrological characteristics. With the help of measuring instruments, a physical quantity can not only be detected, but also measured.
Measuring instruments are classified according to the following criteria:
1) by methods of constructive implementation;
2) for metrological purposes.
According to the methods of constructive implementation, measuring instruments are divided into:
1) measures of magnitude;
2) measuring transducers;
3) measuring instruments;
4) measuring installations;
5) measuring systems.
Measures of quantity- These are measuring instruments of a certain fixed size, repeatedly used for measurement. Highlight:
1) unambiguous measures;
2) multivalued measures;
3) sets of measures.
A certain number of measures, which technically represents a single device within which it is possible to combine existing measures in different ways, is called a store of measures.
The object of measurement is compared with the measure using comparators (technical devices). For example, a comparator is a lever scale.
Standard samples (RM) belong to unambiguous measures. There are two types of standard samples:
1) standard composition samples;
2) standard samples of properties.
Standard sample of composition or material- this is a sample with fixed values of quantities that quantitatively reflect the content of all its constituent parts in a substance or material.
A standard sample of the properties of a substance or material is a sample with fixed values of quantities that reflect the properties of a substance or material (physical, biological, etc.).
Each standard sample must undergo metrological certification by the metrological service authorities before it begins to be used.
Standard samples can be used at different levels and in different areas. Highlight:
1) interstate CO;
2) state COs;
3) industry-specific SBs;
4) CO of the organization (enterprise).
Measuring transducers (MT)– these are measuring instruments that express the measured quantity through another quantity or convert it into a measurement information signal, which can subsequently be processed, converted and stored. Measuring transducers can transform the measured quantity in different ways. Highlight:
1) analog converters (AC);
2) digital-to-analog converters (DACs);
3) analog-to-digital converters (ADCs). Measuring transducers can occupy different positions in the measurement chain. Highlight:
1) primary measuring transducers that are in direct contact with the measurement object;
2) intermediate measuring transducers, which are located after the primary transducers. The primary measuring transducer is technically isolated; signals containing measurement information are sent from it to the measuring circuit. The primary measuring transducer is a sensor. Structurally, the sensor can be located quite far from the next intermediate measuring device, which should receive its signals.
Mandatory properties of the measuring transducer are standardized metrological properties and inclusion in the measurement chain.
Measuring device is a means of measurement by which a value of a physical quantity belonging to a fixed range is obtained. The design of the device usually contains a device that converts the measured quantity with its indications into a form that is optimally convenient for understanding. To display measurement information, the design of the device uses, for example, a scale with an arrow or a digital indicator, through which the value of the measured quantity is recorded. In some cases, the measuring device is synchronized with a computer, and then the measurement information is displayed on the display.
In accordance with the method of determining the value of the measured quantity, the following are distinguished:
1) direct measuring instruments;
2) measuring instruments for comparison.
Direct measuring instruments- these are devices through which you can obtain the value of the measured quantity directly on the reading device.
Comparison measuring device is a device by means of which the value of a measured quantity is obtained by comparison with a known quantity corresponding to its measure.
Measuring instruments can display the measured value in different ways. Highlight:
1) indicating measuring instruments;
2) recording measuring instruments.
The difference between them is that with the help of an indicating measuring device you can only read the values of the measured quantity, and the design of a recording measuring device also allows you to record the measurement results, for example, by means of a diagram or drawing on some information carrier.
Reading device– a structurally isolated part of a measuring instrument, which is intended for reading readings. The reading device can be represented by a scale, pointer, display, etc. Reading devices are divided into:
1) scale reading devices;
2) digital reading devices;
3) recording reading devices. Scale reading devices include a scale and a pointer.
Scale is a system of marks and corresponding sequential numerical values of the measured quantity. Main characteristics of the scale:
1) the number of divisions on the scale;
2) division length;
3) division price;
4) range of indications;
5) measurement range;
6) measurement limits.
Scale division– this is the distance from one scale mark to the next mark.
Division length- this is the distance from one axial line to the next along an imaginary line that passes through the centers of the smallest marks on a given scale.
Scale division price is the difference between the values of two adjacent values on a given scale.
Scale range– this is the range of scale values, the lower limit of which is the initial value of this scale, and the upper limit is the final value of this scale.
Measuring range– this is the range of values within which the normalized maximum permissible error is established.
Measurement limits– this is the minimum and maximum value of the measurement range.
Almost uniform scale- this is a scale in which the division prices differ by no more than 13% and which has a fixed division price.
Significantly uneven scale- this is a scale in which the divisions become narrower and for the divisions of which the value of the output signal is half the sum of the limits of the measurement range.
The following types of measuring instrument scales are distinguished:
1) one-sided scale;
2) two-sided scale;
3) symmetrical scale;
4) zero-free scale.
Single sided scale- This is a scale with zero at the beginning.
Double sided scale- This is a scale in which the zero is not located at the beginning of the scale.
Symmetrical scale- This is a scale in which the zero is located in the center.
Measuring setup– this is a measuring instrument, which is a set of measures, PIs, measuring instruments, etc., performing similar functions, used to measure a fixed number of physical quantities and collected in one place. If the measuring installation is used for testing products, it is a test bench.
Measuring system– this is a measuring instrument, which is a combination of measures, PIs, measuring instruments, etc., performing similar functions, located in different parts of a certain space and intended to measure a certain number of physical quantities in a given space.
According to metrological purpose, measuring instruments are divided into:
1) working measuring instruments;
2) standards.
Working measuring instruments (RMI)– these are measuring instruments used to carry out technical measurements. Working measuring instruments can be used in different conditions. Highlight:
1) laboratory measuring instruments that are used in scientific research;
2) production measuring instruments that are used to monitor the progress of various technological processes and product quality;
3) field measuring instruments that are used during the operation of aircraft, cars and other technical devices.
Each individual type of working measuring instrument has certain requirements. The requirements for laboratory working measuring instruments are a high degree of accuracy and sensitivity, for production measuring instruments - a high degree of resistance to vibrations, shocks, temperature changes, for field measuring instruments - stability and proper operation in various temperature conditions, resistance to high levels of humidity.
Standards- These are measuring instruments with a high degree of accuracy, used in metrological studies to convey information about the size of a unit. More accurate measuring instruments convey information about the size of the unit and so on, thus forming a kind of chain, in each subsequent link of which the accuracy of this information is slightly less than in the previous one.
Information about the size of the unit is provided during the verification of measuring instruments. Testing of measuring instruments is carried out to confirm their suitability.
11. Metrological characteristics of measuring instruments and their standardization
Metrological properties of measuring instruments– these are properties that have a direct impact on the results of measurements carried out by these means and on the error of these measurements.
Quantitative and metrological properties are characterized by indicators of metrological properties, which are their metrological characteristics.
Metrological characteristics approved by ND are standardized metrological characteristics. Metrological properties of measuring instruments are divided into:
1) properties that determine the scope of application of measuring instruments:
2) properties that determine the precision and correctness of the obtained measurement results.
The properties that determine the scope of application of measuring instruments are determined by the following metrological characteristics:
1) measurement range;
2) sensitivity threshold.
Measuring range– this is the range of value values in which the maximum error values are normalized. The lower and upper (right and left) limits of measurements are called the lower and upper limits of measurements.
Sensitivity threshold– this is the minimum value of the measured quantity that can cause noticeable distortion of the received signal.
The properties that determine the precision and correctness of the obtained measurement results are determined by the following metrological characteristics:
1) correctness of the results;
2) precision of results.
The accuracy of the results obtained by certain measuring instruments is determined by their error.
Error of measuring instruments is the difference between the result of measuring a quantity and the real (actual) value of this quantity. For a working measuring instrument, the real (actual) value of the measured quantity is considered to be the reading of the working standard of a lower rank. Thus, the basis of comparison is the value shown by a measuring instrument that is higher in the verification scheme than the measuring instrument being tested.
Q n =Q n ?Q 0 ,
where AQ n is the error of the measuring instrument being tested;
Q n – the value of a certain quantity obtained using the measuring instrument being tested;
Standardization of metrological characteristics– this is the regulation of the limits of deviations of the values of real metrological characteristics of measuring instruments from their nominal values. The main goal of standardizing metrological characteristics is to ensure their interchangeability and uniformity of measurements. The values of real metrological characteristics are established during the production of measuring instruments; later, during the operation of the measuring instruments, these values must be checked. If one or more standardized metrological characteristics fall outside the regulated limits, the measuring instrument must either be immediately adjusted or removed from service.
The values of metrological characteristics are regulated by the relevant standards of measuring instruments. Moreover, metrological characteristics are standardized separately for normal and operating conditions of use of measuring instruments. Normal conditions of use are conditions in which changes in metrological characteristics caused by external factors (external magnetic fields, humidity, temperature) can be neglected. Operating conditions are conditions in which the variation of influencing quantities has a wider range.
12. Metrological support, its fundamentals
Metrological support, or MO for short, is the establishment and use of scientific and organizational foundations, as well as a number of technical means, norms and rules necessary to comply with the principle of unity and the required accuracy of measurements. Today, the development of ME is moving towards a transition from the existing narrow task of ensuring the unity and required accuracy of measurements to the new task of ensuring the quality of measurements. The meaning of the concept of “metrological support” is deciphered in relation to measurements (testing, control) as a whole. However, this term is also applicable in the form of the concept “metrological support of a technological process (production, organization),” which implies MO measurements (testing or control) in a given process, production, organization. The object of MO can be considered all stages of the life cycle (LC) of a product (product) or service, where the life cycle is perceived as a certain set of sequential interconnected processes of creating and changing the state of a product from the formulation of initial requirements for it to the end of operation or consumption. Often, at the stage of product development, in order to achieve high quality of the product, a selection of controlled parameters, accuracy standards, tolerances, measuring instruments, control and testing is made. And in the process of developing MO, it is desirable to use a systematic approach, in which the specified software is considered as a certain set of interrelated processes united by one goal. This goal is to achieve the required measurement quality. In the scientific literature, as a rule, a number of similar processes are identified:
1) establishing a range of measured parameters, as well as the most appropriate accuracy standards for product quality control and process control;
2) feasibility study and selection of measuring instruments, testing and control and establishment of their rational nomenclature;
3) standardization, unification and aggregation of the control and measuring equipment used;
4) development, implementation and certification of modern methods of measurement, testing and control (MTI);
5) verification, metrological certification and calibration of instrumentation and control equipment or control and measuring equipment, as well as testing equipment used at the enterprise;
6) control over the production, condition, use and repair of CIO, as well as over strict adherence to metrology rules and standards at the enterprise;
7) participation in the process of creating and implementing enterprise standards;
8) implementation of international, state, industry standards, as well as other regulatory documents of Gosstandart;
9) carrying out metrological examination of projects of design, technological and regulatory documentation;
10) carrying out an analysis of the state of measurements, developing on its basis and carrying out various activities to improve MO;
11) training of employees of relevant services and departments of the enterprise to perform control and measurement operations.
The organization and conduct of all MO activities is the prerogative of metrological services. Metrological support is based on four layers. In fact, they have a similar name in the scientific literature – fundamentals. So, these are the scientific, organizational, regulatory and technical foundations. I would like to pay special attention to the organizational foundations of metrological support. Organizational services for metrological support include the State Metrological Service and the Departmental Metrological Service.
The State Metrological Service, or GMS for short, is responsible for ensuring metrological measurements in Russia at the intersectoral level, and also carries out control and supervisory activities in the field of metrology. The GMS includes:
1) state scientific metrological centers (SSMC), metrological research institutes responsible, according to the legislative framework, for the issues of application, storage and creation of state standards and the development of regulations on the issues of maintaining the uniformity of measurements in a fixed form of measurements;
2) bodies of the State Migration Service on the territory of the republics that are part of the Russian Federation, bodies of autonomous regions, bodies of autonomous districts, regions, territories, the cities of Moscow and St. Petersburg.
The main activities of the State Migration Service bodies are aimed at ensuring the uniformity of measurements in the country. It includes the creation of state and secondary standards, the development of systems for transferring the sizes of PV units to working SIs, state supervision over the condition, use, production, and repair of SIs, metrological examination of documentation and the most important types of products, and methodological guidance for MS of legal entities. The management of the State Migration Service is carried out by Gosstandart.
Departmental metrological service, which, in accordance with the provisions of the Law “On Ensuring the Uniformity of Measurements”, can be created at the enterprise to ensure MO. It should be headed by a representative of the administration with the appropriate knowledge and authority. When carrying out activities in the areas provided for in Article 13 of this Law, the creation of a metrological service is mandatory. Such areas of activity include:
1) healthcare, veterinary medicine, environmental protection, maintaining labor safety;
2) trade transactions and mutual settlements between sellers and buyers, which usually include transactions using slot machines and other devices;
3) government accounting operations;
4) state defense;
5) geodetic and hydrometeorological works;
6) banking, customs, tax and postal operations;
7) production of products supplied under contracts for the needs of the state in accordance with the legislative framework of the Russian Federation;
8) monitoring and testing product quality to ensure compliance with the mandatory requirements of state standards of the Russian Federation;
9) mandatory certification of goods and services;
10) measurements carried out on behalf of a number of government agencies: courts, arbitration, prosecutors, government bodies of the Russian Federation;
11) registration activities related to national or international records in the field of sports. The metrological service of a state governing body includes the following components:
1) structural units of the chief metrologist as part of the central apparatus of the government agency;
2) head and base organizations of metrological services in industries and sub-sectors, appointed by the governing body;
3) metrological service of enterprises, associations, organizations and institutions.
Another important section of IR is its scientific and methodological foundations. Thus, the main component of these fundamentals are the State Scientific Metrological Centers (SSMC), which are created from enterprises and organizations under the jurisdiction of Gosstandart or their structural divisions that perform various operations on the creation, storage, improvement, application and storage of state standards of units of quantities, and , in addition, developing regulatory rules for the purpose of ensuring the uniformity of measurements, employing highly qualified personnel. Assigning the status of SSMC to an enterprise, as a rule, does not affect its form of ownership and organizational and legal forms, but only means classifying them as a group of objects that have special forms of state support. The main functions of the SSMC are the following:
1) creation, improvement, application and storage of state standards of units of quantities;
2) carrying out applied and fundamental research and development in the field of metrology, which may include the creation of various experimental installations, initial measures and scales to ensure the uniformity of measurements;
3) transfer from state standards of initial data on the sizes of units of quantities;
4) conducting state tests of measuring instruments;
5) development of equipment required for HMS;
6) development and improvement of regulatory, organizational, economic and scientific foundations for activities aimed at ensuring the uniformity of measurements depending on specialization;
7) interaction with the metrological service of federal executive authorities, organizations and enterprises with the status of a legal entity;
8) providing information regarding the uniformity of measurements of enterprises and organizations
9) organization of various events related to the activities of the GSHF, GSSSD and GSSO;
10) conducting an examination of sections of the Ministry of Defense of federal and other programs;
11) organization of metrological examination and measurements at the request of a number of government bodies: court, arbitration, prosecutor’s office or federal executive authorities;
12) training and retraining of highly qualified personnel;
13) participation in the comparison of state standards with national standards available in a number of foreign countries, as well as participation in the development of international norms and rules.
The activities of the SSMC are regulated by Decree of the Government of the Russian Federation dated February 12, 1994 No. 100.
An important component of the basis of MO are, as mentioned above, methodological instructions and guidance documents, which mean normative documents of methodological content, developed by organizations subordinate to the State Standard of the Russian Federation. Thus, in the field of scientific and methodological foundations of metrological support, the State Standard of Russia organizes:
1) carrying out research activities and development work in assigned areas of activity, and also establishes rules for carrying out work on metrology, standardization, accreditation and certification, as well as on state control and supervision in subordinate areas, and provides methodological management of these works;
2) provides methodological guidance for training in the areas of metrology, certification and standardization, establishes requirements for the degree of qualifications and competence of personnel. Organizes training, retraining and advanced training of specialists.
13. Measurement error
In the practice of using measurements, their accuracy becomes a very important indicator, which represents the degree of closeness of the measurement results to some actual value, which is used for qualitative comparison of measurement operations. And as a quantitative assessment, as a rule, measurement error is used. Moreover, the smaller the error, the higher the accuracy is considered.
According to the law of error theory, if it is necessary to increase the accuracy of the result (with systematic error excluded) by 2 times, then the number of measurements must be increased by 4 times; if it is necessary to increase the accuracy by 3 times, then the number of measurements is increased by 9 times, etc.
The process of assessing 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 influence the accuracy of measurement. Consequently, any classification of measurement errors is rather arbitrary, since often, depending on the conditions of the measurement process, errors can appear in different groups. Moreover, according to the principle of dependence on the form, these expressions of measurement error can be: absolute, relative and reduced.
In addition, depending on the nature of the manifestation, the causes of occurrence and the possibility of elimination, measurement errors can be components. In this case, the following components of error are distinguished: systematic and random.
The systematic component remains constant or changes with subsequent measurements of the same parameter.
The random component changes when the same parameter is changed randomly again. Both components of the measurement error (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.
Systematic error, and this is its peculiarity, when compared with random error, which is detected regardless of its sources, is considered according to its components in connection with the sources of occurrence.
The components of error can also be divided into: methodological, instrumental and subjective. Subjective systematic errors are associated with the individual characteristics of the operator. Such an error may occur due to errors in readings or operator inexperience. Basically, systematic errors arise due to methodological and instrumental components. The methodological component of the error is determined by the imperfection of the measurement method, methods of using SI, incorrectness of calculation formulas and rounding of results. The instrumental component appears due to the intrinsic error of the SI, determined by the accuracy class, the influence of the SI on the result, and the resolution of the SI. There is also such a thing as “gross errors or misses”, which can appear due to erroneous operator actions, malfunction of measuring instrument or unforeseen changes in the measurement situation. Such errors are usually discovered in the process of reviewing measurement results using special criteria. An important element of this classification is error prevention, understood as the most rational way to reduce error, which is to eliminate the influence of any factor.
14. Types of errors
The following types of errors are distinguished:
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, errors are divided into absolute errors and relative errors.
Based on the interaction of changes in time and the input value, errors are divided into static errors and dynamic errors.
Based on the nature of their occurrence, errors are divided into systematic errors and random errors.
Absolute error– this is a value calculated as the difference between the value of a quantity obtained during the measurement process and the real (actual) value of this quantity.
The absolute error is calculated using the following formula:
Q n =Q n ?Q 0 ,
where AQ n – absolute error;
Q n– the value of a certain quantity obtained during the measurement process;
Q 0 – the value of the same quantity taken as the basis of comparison (real value).
Absolute error of the measure– this is a value calculated as the difference between the number, which is the nominal value of the measure, and the real (real) value of the quantity reproduced by the measure.
Relative error is a number that reflects the degree of measurement accuracy.
The relative error is calculated using the following formula:
where?Q – absolute error;
Q 0 – real (real) value of the measured quantity.
Reduced error is a value calculated as the ratio of the absolute error value to the normalizing value.
The standard value is determined as follows:
1) for measuring instruments for which a nominal value is approved, this nominal value is taken as the standard value;
2) for measuring instruments in which the zero value is located at 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 whose zero mark is located inside 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 whole 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, method error, and counting error. Moreover, the counting error arises due to the inaccuracy in determining the division fractions of the measurement scale.
Instrumental error– this is an error that arises due to errors made during the manufacturing process of functional parts of measuring instruments.
Methodological error is an error that occurs for the following reasons:
1) inaccuracy in constructing a model of the physical process on which the measuring instrument is based;
2) incorrect use of measuring instruments.
Subjective error– this 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 cause of the subjective error is the human factor.
Errors in the interaction of changes over time and the input quantity are divided into static and dynamic errors.
Static error– this is an error that arises in the process of measuring a constant (not changing over time) quantity.
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 (time-variable) quantity and the 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, errors are divided into basic and additional.
Basic error– this is the error obtained under normal operating conditions of the measuring instrument (at normal values of the influencing quantities).
Additional error– this is an error that occurs when the values of influencing quantities do not correspond to their normal values, or if the influencing quantity exceeds the boundaries of the region of normal values.
Normal conditions– these are conditions in which all values of influencing quantities are normal or do not go beyond the boundaries of the normal range.
Working conditions– these are conditions in which the change in influencing quantities has a wider range (the influencing values do not go beyond the boundaries of the working range of values).
Working range of influencing quantities– this is the range of values in which the values of the additional error are normalized.
Based on the nature of the error’s dependence on the input value, errors are divided into additive and multiplicative.
Additive error– this is an error that arises due to the summation of numerical values and does not depend on the value of the measured quantity taken modulo (absolute).
Multiplicative bias is an error that changes with changes in the values 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 constant 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 elements of the device.
Errors that may arise during the measurement process are classified according to the nature of their occurrence. Highlight:
1) systematic errors;
2) random errors.
Gross errors and errors may also occur during the measurement process.
Systematic error- this is a component of the entire error of the measurement result, which does not change or changes naturally with repeated measurements of the same quantity. Usually, a systematic error is tried to be eliminated in possible ways (for example, by using measurement methods that reduce the likelihood of its occurrence), but if the systematic error cannot be eliminated, 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 permissible values are determined. Systematic error determines the accuracy of measurements of measuring instruments (metrological property).
Systematic errors in some cases can be determined experimentally. The measurement result can then be clarified by introducing a correction.
Methods for eliminating systematic errors are divided into four types:
1) elimination of the 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 by sign, opposition, symmetrical observations;
3) correction of measurement results by making an amendment (elimination of errors by calculations);
4) determination of the limits of systematic error in case it cannot be eliminated.
Elimination of causes and sources of errors before starting 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 already started measurement or make corrections to the result obtained).
To eliminate systematic errors in the process of already started measurement, various methods are used
Method of introducing amendments is based on knowledge of the systematic error and the current patterns of its change. When using this method, corrections are made to the measurement result obtained with systematic errors, equal in magnitude to these errors, but opposite in sign.
Substitution method consists in the fact that the measured quantity is replaced by a measure placed in the same conditions in which the object of measurement was located. The replacement method is used when measuring the following electrical parameters: resistance, capacitance and inductance.
Sign error compensation method consists in the fact that measurements are performed twice in such a way that an error of unknown magnitude is included in the measurement results with the opposite sign.
Method of opposition similar to the sign compensation method. This method consists of taking measurements twice so that the source of error in the first measurement has an opposite effect on the result of the second measurement.
Random error- this is a component of the error of the measurement result, changing randomly, irregularly when performing repeated measurements of the same quantity. The occurrence of a random error cannot be foreseen or 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 when carrying out repeated measurements with a sufficiently high degree of accuracy leads to scattering of the results.
Mistakes and gross errors– these are errors that far exceed the systematic and random errors expected under the given measurement conditions. Errors and gross errors can appear due to gross errors during the measurement process, technical malfunction of the measuring instrument, or unexpected changes in external conditions.
15. Quality of measuring instruments
Measuring instrument quality– this is the level of conformity of the device to its intended purpose. Therefore, the quality of a measuring instrument is determined by the extent to which the purpose of measurement is achieved when using the measuring instrument.
Main purpose of measurement– this is obtaining reliable and accurate information about the measurement object.
In order to determine the quality of the device, it is necessary to consider the following characteristics:
1) device constant;
2) sensitivity of the device;
3) sensitivity threshold of the measuring device;
4) accuracy of the measuring device.
Device constant- this is a certain number multiplied by a reading in order to obtain the desired value of the measured quantity, i.e., the reading of the device. In some cases, the constant of the device is set as the value of the scale division, which represents the value of the measured quantity corresponding to one division.
Device sensitivity– this is a number in the numerator of which is the amount of linear or angular movement of the pointer (if we are talking about a digital measuring device, then the numerator will be a change in the numerical value, and the denominator will be the change in the measured value that caused this movement (or change in the numerical value)) .
Sensitivity threshold of the measuring device– a number that is the minimum value of the measured quantity that the device can record.
Meter Accuracy– this is a characteristic that expresses the degree of correspondence of the measurement results to the real value of the measured quantity. The accuracy of a measuring instrument is determined by establishing the lower and upper limits of the maximum possible error.
It is practiced to divide instruments into accuracy classes based on the permissible error.
Accuracy class of measuring instruments– this is a general characteristic of measuring instruments, which is determined by the boundaries of the main and additional permissible errors and other characteristics that determine accuracy. Accuracy classes of a certain type of measuring instruments are approved in regulatory documentation. Moreover, for each individual accuracy class, certain requirements for metrological characteristics are approved. The combination of established metrological characteristics determines the degree of accuracy of a measuring instrument belonging to a given accuracy class.
The accuracy class of a measuring instrument is determined during its development. Since metrological characteristics usually deteriorate during operation, it is possible to lower its accuracy class based on the results of the calibration (verification) of the measuring instrument.
16. Errors of measuring instruments
The errors of measuring instruments are classified according to the following criteria:
1) by 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.
The absolute error is calculated using the formula:
?Q n =Q n ?Q 0 ,
Where ? Q n – absolute error of the measuring instrument being tested;
Q n– the value of a certain quantity obtained using the measuring instrument being tested;
Q 0 – the value of the same quantity taken as the basis of comparison (real value).
Relative error is a number that reflects the degree of accuracy of a measuring instrument. The relative error is calculated using the following formula:
Where ? Q – absolute error;
Q 0 – real (real) value of the measured quantity.
The relative error is expressed as a percentage.
Based on the nature of their manifestation, errors are divided into random and systematic.
In relation to the conditions of application, errors are divided into basic and additional.
Basic error of measuring instruments– this is the error, which is determined if the measuring instruments are used under normal conditions.
Additional error of measuring instruments- this is a component of the error of the measuring instrument, which arises additionally if any of the influencing quantities goes beyond the limits of its normal value.
17. Metrological support of measuring systems
Metrological support– this is the approval and use of scientific, technical and organizational foundations, technical instruments, norms and standards in order to ensure the unity and established accuracy of measurements. Metrological support in its scientific aspect is based on metrology.
The following goals of metrological support can be distinguished:
1) achieving higher quality products;
2) ensuring the greatest efficiency of the accounting system;
3) provision of preventive measures, diagnosis and treatment;
4) ensuring effective production management;
5) ensuring a high level of efficiency of scientific work and experiments;
6) ensuring a higher degree of automation in the field of transport management;
7) ensuring the effective functioning of the system of regulation and control of working and living conditions;
8) improving the quality of environmental supervision;
9) improving the quality and increasing the reliability of communication;
10) providing an effective system for assessing various natural resources.
Metrological support of technical devices- This
a set of scientific and technical means, organizational measures and activities carried out by relevant institutions in order to achieve the unity and required accuracy of measurements, as well as the established characteristics of technical instruments.
Measuring system– a measuring instrument, which is a combination of measures, measuring instruments, measuring instruments, etc., performing similar functions, located in different parts of a certain space and intended to measure a certain number of physical quantities in a given space.
Measuring systems are used for:
1) technical characteristics of the measurement object, obtained by carrying out measurement transformations of a certain number of quantities dynamically changing in time and distributed in space;
2) automated processing of the obtained measurement results;
3) recording the obtained measurement results and the results of their automated processing;
4) converting data into system output signals. Metrological support of measuring systems implies:
1) determination and standardization of metrological characteristics for measuring channels;
2) checking technical documentation for compliance with metrological characteristics;
3) testing measuring systems to establish the type to which they belong;
4) carrying out tests to determine compliance of the measuring system with the established type;
5) carrying out certification of measuring systems;
6) carrying out calibration (checking) of measuring systems;
7) ensuring metrological control over the production and use of measuring systems.
Measuring channel of the measuring system- this is a part of a measuring system, technically or functionally separate, designed to perform a specific completed function (for example, to perceive a measured quantity or to obtain a number or code that is the result of measurements of this quantity). Divided:
1) simple measuring channels;
2) complex measuring channels.
Simple measuring channel is a channel that uses a direct measurement method, implemented through ordered measurement transformations.
In a complex measuring channel, a primary part and a secondary part are distinguished. In the primary part, a complex measuring channel is a combination of a certain number of simple measuring channels. Signals from the output of simple measuring channels of the primary part are used for indirect, cumulative or joint measurements or to obtain a signal proportional to the measurement result in the secondary part.
Measuring component of a measuring system is a measuring instrument that has separately standardized metrological characteristics. An example of a measuring component of a measuring system is a measuring instrument. The measuring components of a measuring system also include analog computing devices (devices that perform measurement conversions). Analog computing devices belong to the group of devices with one or more inputs.
The measuring components of measuring systems are of the following types.
Binding component is a technical device or element of the environment used for the exchange of signals containing information about the measured quantity between the components of the measuring system with the minimum possible distortion. An example of a connecting component would be a telephone line, a high-voltage power line, or transition devices.
Computing component is a digital device (part of a digital device) designed to perform calculations, with installed software. The computing component is used to calculate
merging measurement results (direct, indirect, joint, cumulative), which represent a number or corresponding code, calculations are made based on the results of primary transformations in the measuring system. The computing component also performs logical operations and coordinates the operation of the measuring system.
Complex Component- this is an integral part of the measurement system, which is a technically or territorially integrated set of components. The complex component completes measurement transformations, as well as computational and logical operations that are approved in the adopted algorithm for processing measurement results for other purposes.
Auxiliary Component is a technical device designed to ensure the normal functioning of the measuring system, but does not take part in the process of measurement transformations.
According to the relevant GOSTs, the metrological characteristics of a measuring system must be standardized for each measuring channel included in the measuring system, as well as for complex and measuring components of the measuring system.
As a rule, the manufacturer of the measuring system determines the general standards for the metrological characteristics of the measuring channels of the measuring system.
The normalized metrological characteristics of the measuring channels of the measuring system are designed to:
1) ensure determination of measurement error using measuring channels under operating conditions;
2) ensure effective control over the compliance of the measuring channel of the measuring system with standardized metrological characteristics during testing of the measuring system. If determination or control over the metrological characteristics of the measuring channel of the measuring system cannot be carried out experimentally for the entire measuring channel, the standardization of metrological characteristics is carried out for the component parts of the measuring channel. Moreover, the combination of these parts should represent an entire measuring channel
It is possible to normalize error characteristics as metrological characteristics of the measuring channel of a measuring system both under normal conditions of use of measuring components, and under operating conditions that are characterized by such a combination of influencing factors in which the module of the numerical value of the error characteristics of the measuring channel has the maximum possible value. For greater efficiency, the error characteristics of the measuring channel are also normalized for intermediate combinations of influencing factors. These error characteristics of the measuring channels of the measuring system must be checked by calculating them according to the metrological characteristics of the components of the measuring system, which represent the measuring channel as a whole. Moreover, the calculated values of the error characteristics of the measuring channels may not be verified experimentally. But nevertheless, it is mandatory to monitor metrological characteristics for all components (components) of the measuring system, the norms of which are the initial data in the calculation.
The standardized metrological characteristics of complex components and measuring components must:
1) ensure the determination of the error characteristics of the measuring channels of the measuring system under operating conditions of use using the standardized metrological characteristics of the components;
2) ensure effective control over these components during testing carried out to establish the type and verify compliance with standardized metrological characteristics. For the computing components of the measuring system, if their software was not taken into account in the process of normalizing metrological characteristics, calculation errors, the source of which is the functioning of the software (calculation algorithm, its software implementation), are normalized. For the computing components of the measuring system, other characteristics may also be normalized, subject to taking into account the specifics of the computing component, which may affect the characteristics of the component parts of the measurement channel error (characteristics of the error component), if the component error arises due to the use of a given program for processing measurement results.
Technical documentation for the operation of the measuring system must include a description of the algorithm and the program operating in accordance with the described algorithm. This description should allow the calculation of the error characteristics of the measurement results using the error characteristics of the component part of the measuring channel of the measuring system located in front of the computing component.
For connecting components of a measuring system, two types of characteristics are standardized:
1) characteristics that ensure such a value of the component of the error of the measuring channel caused by the connecting component, which can be neglected;
2) characteristics that make it possible to determine the value of the component of the error of the measuring channel caused by the connecting component.
18. Selection of measuring instruments
When choosing measuring instruments, first of all, the permissible error value for a given measurement, established in the relevant regulatory documents, must be taken into account.
If the permissible error is not provided for in the relevant regulatory documents, the maximum permissible measurement error must be regulated in the technical documentation for the product.
When choosing measuring instruments, the following should also be taken into account:
1) permissible deviations;
2) measurement methods and control methods. The main criterion for choosing measuring instruments is the compliance of the measuring instruments with the requirements of measurement reliability, obtaining real (actual) values of the measured quantities with a given accuracy with minimal time and material costs.
To optimally select measuring instruments, you must have the following initial data:
1) the nominal value of the measured quantity;
2) the magnitude of the difference between the maximum and minimum value of the measured quantity, regulated in regulatory documentation;
3) information about the conditions for carrying out measurements.
If it is necessary to select a measuring system based on the criterion of accuracy, then its error must be calculated as the sum of the errors of all elements of the system (measures, measuring instruments, measuring transducers), in accordance with the law established for each system.
The preliminary selection of measuring instruments is made in accordance with the accuracy criterion, and the final selection of measuring instruments must take into account the following requirements:
1) to the working range of values of quantities that influence the measurement process;
2) to the dimensions of the measuring instrument;
3) to the mass of the measuring instrument;
4) to the design of the measuring instrument.
When choosing measuring instruments, it is necessary to take into account the preference of standardized measuring instruments.
19. Methods for determining and accounting for errors
Methods for determining and accounting for measurement errors are used to:
1) based on the measurement results, obtain the real (actual) value of the measured quantity;
2) determine the accuracy of the results obtained, i.e. the degree of their correspondence to the real (actual) value.
In the process of determining and accounting for errors, the following are assessed:
1) mathematical expectation;
2) standard deviation.
Point parameter estimate(mathematical expectation or standard deviation) is an estimate of a parameter that can be expressed in a single number. A point estimate is a function of experimental data and, therefore, must itself be a random variable distributed according to a law depending on the distribution law for the values of the original random variable. The distribution law of point estimate values will also depend on the parameter being estimated and on the number of tests (experiments).
Point estimates are of the following types:
1) unbiased point estimate;
2) effective point estimate;
3) consistent point estimate.
Unbiased point estimate is an estimate of the error parameter, the mathematical expectation of which is equal to this parameter.
Efficient point estimate is a point estimate. whose variance is less than the variance of any other estimate of this parameter.
Consistent point estimate is an estimate that, as the number of tests increases, tends to the value of the parameter being assessed.
Basic methods for determining grades:
1) maximum likelihood method (Fisher method);
2) least squares method.
1. Maximum likelihood method is based on the idea that information about the actual value of the measured quantity and the dispersion of measurement results, obtained through repeated observations, is contained in a number of observations.
The maximum likelihood method consists of finding estimates at which the likelihood function passes through its maximum.
Maximum likelihood estimates are estimates of the standard deviation and estimates of the true value.
If random errors are distributed according to the normal distribution law, then the maximum likelihood estimate for the true value is the arithmetic mean of the observation results, and the dispersion estimate is the arithmetic mean of the squared deviations of the values from the mathematical expectation.
The advantages of maximum likelihood estimators are that these estimators:
1) unbiased asymptotically;
2) asymptotically efficient;
3) asymptotically distributed according to the normal law.
2. Least square method consists in taking from a certain class of estimates the estimate with the minimum variance (the most effective). Of all linear estimates of the real value, where some constants are present, only the arithmetic mean reduces to the smallest value of variance. In this regard, provided that the values of random errors are distributed according to the normal distribution law, the estimates obtained using the least squares method are identical to the maximum likelihood estimates. Estimation of parameters using intervals is carried out by finding confidence intervals within which the actual values of the estimated parameters are located with given probabilities.
Confidence limit of random deviation is a number that represents the length of the confidence interval divided in half.
With a sufficiently large number of tests, the confidence interval decreases significantly. If the number of tests increases, then it is permissible to increase the number of confidence intervals.
Detection of gross errors
Gross errors– these are errors that far exceed the systematic and random errors expected under the given measurement conditions. Errors and gross errors can appear due to gross errors during the measurement process, technical malfunction of the measuring instrument, or unexpected changes in external conditions. In order to eliminate gross errors, it is recommended to approximately determine the value of the measured quantity before starting measurements.
If, during measurements, it turns out that the result of an individual observation is very different from other results obtained, it is necessary to establish the reasons for such a difference. Results obtained with a sharp difference can be discarded and the value re-measured. However, in some cases, discarding such results can cause a noticeable distortion in the dispersion of a number of measurements. In this regard, it is recommended not to rashly discard differing results, but to supplement them with the results of repeated measurements.
If it is necessary to eliminate gross errors in the process of processing the results obtained, when it is no longer possible to adjust the measurement conditions and carry out repeated measurements, then statistical methods are used.
The general method of testing statistical hypotheses allows you to find out whether there is a gross error in a given measurement result.
20. Processing and presentation of measurement results
Usually measurements are one-time. Under normal conditions, their accuracy is quite sufficient.
The result of a single measurement is presented as follows:
Where Y i– value of the i – th reading;
I – amendment.
The error of the result of a single measurement is determined when the measurement method is approved.
In the process of processing measurement results, various types of distribution laws are used (normal distribution law, uniform distribution law, correlation distribution law) of the measured quantity (in this case it is considered random).
Processing the results of direct equal-precision measurements Direct measurements- these are measurements through which the value of the measured quantity is directly obtained. Direct, mutually independent measurements of a certain quantity are called equal-precise or equally scattered, and the results of these measurements can be considered as random and distributed according to the same distribution law.
Usually, when processing the results of direct equal-precision measurements, it is assumed that the results and measurement errors are distributed according to the normal distribution law.
After removing the calculations, the value of the mathematical expectation is calculated using the formula:
Where x i– value of the measured quantity;
n– number of measurements taken.
Then, if the systematic error is determined, its value is subtracted from the calculated value of the mathematical expectation.
Then the value of the standard deviation of the values of the measured value from the mathematical expectation is calculated.
Algorithm for processing the results of multiple equal-precision measurements
If a systematic error is known, it must be excluded from the measurement results.
Calculate the mathematical expectation of the measurement results. The arithmetic mean of the values is usually taken as the mathematical expectation.
Set the value of the random error (deviation from the arithmetic mean) of the result of a single measurement.
Calculate the variance of the random error. Calculate the standard deviation of the measurement result.
Check the assumption that the measurement results are normally distributed.
Find the value of the confidence interval and confidence error.
Determine the value of the entropy error and the entropy coefficient.
21. Verification and calibration of measuring instruments
Calibration of measuring instruments– this is a set of actions and operations that determine and confirm the real (actual) values of metrological characteristics and (or) the suitability of measuring instruments that are not subject to state metrological control.
The suitability of a measuring instrument is a characteristic determined by the compliance of the metrological characteristics of the measuring instrument with the technical requirements approved (in regulatory documents or by the customer). The calibration laboratory determines the suitability of the measuring instrument.
Calibration replaced the verification and metrological certification of measuring instruments, which were carried out only by the state metrological service. Calibration, in contrast to verification and metrological certification of measuring instruments, can be carried out by any metrological service, provided that it has the ability to provide appropriate conditions for calibration. Calibration is carried out on a voluntary basis and can even be carried out by the metrological service of the enterprise.
But nevertheless, the metrological service of the enterprise is obliged to fulfill certain requirements. The main requirement for the metrological service is to ensure compliance of the working measuring instrument with the state standard, i.e. calibration is part of the national system for ensuring the uniformity of measurements.
There are four methods of verification (calibration) of measuring instruments:
1) method of direct comparison with the standard;
2) comparison method using a computer;
3) method of direct measurements of quantities;
4) method of indirect measurements of quantity.
Method of direct comparison with the standard facilities
measurements subjected to calibration, with a corresponding standard of a certain category, is practiced for various measuring instruments in such areas as electrical measurements, magnetic measurements, determination of voltage, frequency and current. This method is based on measurements of the same physical quantity by a calibrated (verified) device and a reference device simultaneously. The error of the calibrated (verified) device is calculated as the difference between the readings of the calibrated device and the reference device (i.e., the readings of the reference device are taken as the real value of the physical quantity being measured).
Advantages of the method of direct comparison with the standard:
1) simplicity;
2) visibility;
3) the possibility of automatic calibration (verification);
4) the possibility of calibration using a limited number of instruments and equipment.
Comparison method using a computer is carried out using a comparator - a special device through which the readings of the calibrated (verified) measuring instrument are compared with the readings of the reference measuring instrument. The need to use a comparator is determined by the impossibility of directly comparing the readings of measuring instruments measuring the same physical quantity. A comparator can be a measuring instrument that equally perceives the signals of the reference measuring instrument and the device being calibrated (verified). The advantage of this method is the consistency in time of comparison of values.
Direct measurement method used in cases where it is possible to compare the measuring instrument being calibrated with the standard one within the established measurement limits. The direct measurement method is based on the same principle as the direct comparison method. The difference between these methods is that using the direct measurement method, a comparison is made at all numerical marks of each range (subrange).
Indirect measurement method used in cases where the real (actual) values of the measured physical quantities cannot be obtained through direct measurements or when indirect measurements are higher in accuracy than direct measurements. When using this method, to obtain the desired value, first look for the values of quantities associated with the desired value by a known functional relationship. And then, based on this dependence, the desired value is found by calculation. The indirect measurement method is usually used in automated calibration (verification) installations.
In order for the transfer of the dimensions of units of measurement to working instruments from the standards of measurement units to be carried out without large errors, verification schemes are drawn up and used.
Verification diagrams is a normative document that approves the subordination of measuring instruments that take part in the process of transferring the size of a unit of measurement of a physical quantity from a standard to working measuring instruments using certain methods and indicating the error. Verification schemes confirm the metrological subordination of the state standard, discharge standards and measuring instruments.
Verification schemes are divided into:
1) state verification schemes;
2) departmental verification schemes;
3) local verification schemes.
State verification schemes are established and valid for all measuring instruments of a certain type used within the country.
Departmental verification schemes are installed and act on measuring instruments of a given physical quantity, subject to departmental verification. Departmental verification schemes should not conflict with state verification schemes if they are established for measuring instruments of the same physical quantities. Departmental verification schemes can be established in the absence of a state verification scheme. In departmental verification schemes it is possible to directly indicate certain types of measuring instruments.
Local verification schemes are used by metrological services of ministries and also apply to measuring instruments of enterprises subordinate to them. A local verification scheme may apply to measuring instruments used at a particular enterprise. Local verification schemes must necessarily meet the requirements of subordination approved by the state verification scheme. The preparation of state verification schemes is carried out by the research institutes of the Gosstandart of the Russian Federation. The research institutes of the Gosstandart are the owners of state standards.
Departmental verification schemes and local verification schemes are presented in the form of drawings.
State verification schemes are established by the State Standard of the Russian Federation, and local verification schemes are established by metrological services or enterprise managers.
The verification scheme approves the procedure for transferring the size of units of measurement of one or more physical quantities from state standards to working measuring instruments. The verification scheme must contain at least two stages of transferring the size of units of measurement.
The drawings representing the verification diagram must include:
1) names of measuring instruments;
2) names of verification methods;
3) nominal values of physical quantities;
4) ranges of nominal values of physical quantities;
5) permissible values of errors of measuring instruments;
6) permissible error values of verification methods.
22. Legal basis of metrological support. Basic provisions of the Law of the Russian Federation “On Ensuring the Uniformity of Measurements”
Unity of measurements– this is a characteristic of the measurement process, meaning that the measurement results are expressed in units of measurement established and adopted by law and the assessment of measurement accuracy has an appropriate confidence level.
Main principles of uniformity of measurements:
1) determination of physical quantities with the mandatory use of state standards;
2) the use of legislatively approved measuring instruments, subject to state control and with unit sizes transferred directly from state standards;
3) use only legally approved units of measurement of physical quantities;
4) ensuring mandatory systematic control over the characteristics of operating measuring instruments at certain periods of time;
5) ensuring the necessary guaranteed measurement accuracy when using calibrated (verified) measuring instruments and established measurement techniques;
6) use of the obtained measurement results under the obligatory condition of assessing the error of these results with an established probability;
7) ensuring control over the compliance of measuring instruments with metrological rules and characteristics;
8) ensuring state and departmental supervision of measuring instruments.
The Law of the Russian Federation “On Ensuring the Uniformity of Measurements” was adopted in 1993. Before the adoption of this Law, standards in the field of metrology were not regulated by law. At the time of its adoption, the Law contained many innovations, ranging from approved terminology to licensing of metrological activities in the country. The Law was clearly delineated responsibilities of state metrological control and state metrological supervision, new calibration rules were established, and the concept of voluntary certification of measuring instruments was introduced.
Basic provisions.
First of all, the objectives of the law are as follows:
1) protection of the legal rights and interests of citizens of the Russian Federation, law and order and the economy of the Russian Federation from possible negative consequences caused by unreliable and inaccurate measurement results;
2) assistance in the development of science, technology and economics by regulating the use of state standards of units of quantities and the use of measurement results with guaranteed accuracy. Measurement results must be expressed in the units of measurement established in the country;
3) promoting the development and strengthening of international and inter-company relations and connections;
4) regulation of requirements for the manufacture, release, use, repair, sale and import of measuring instruments produced by legal entities and individuals;
5) integration of the measurement system of the Russian Federation into world practice.
Areas of application of the Law: trade; healthcare; environment protection; economic and foreign economic activity; some areas of production related to the calibration (verification) of measuring instruments by metrological services owned by legal entities, carried out using standards subordinate to state standards of units of quantities.
The Law legislates the following basic concepts:
1) uniformity of measurements;
2) measuring instrument;
3) standard unit of value;
4) state standard of unit of value;
5) regulatory documents to ensure the uniformity of measurements;
6) metrological service;
7) metrological control;
8) metrological supervision;
9) calibration of measuring instruments;
10) calibration certificate.
All definitions approved in the Law are based on the official terminology of the International Organization of Legal Metrology (OIML).
The main articles of the law regulate:
1) the structure of the organization of state bodies for ensuring the uniformity of measurements;
2) regulatory documents ensuring the uniformity of measurements;
3) established units of measurement of physical quantities and state standards of units of quantities;
4) measuring instruments;
5) measurement methods.
The law approves the State Metrological Service and other services involved in ensuring the uniformity of measurements, metrological services of state governing bodies and forms of implementation of state metrological control and supervision.
The Law defines the types of liability for violations of the Law.
The Law approves the composition and powers of the State Metrological Service.
In accordance with the Law, an institute for licensing metrological activities was created in order to protect the legal rights of consumers. Only the bodies of the State Metrological Service have the right to issue a license.
New types of state metrological supervision have been established:
1) the quantity of goods being alienated;
2) the number of goods in the package during the process of packaging and selling.
In accordance with the provisions of the Law, the scope of state metrological control is increasing. It added banking operations, postal operations, tax operations, customs operations, and mandatory product certification.
In accordance with the Law, a system of certification of measuring instruments, based on a voluntary principle, is being introduced, which verifies measuring instruments for compliance with metrological rules and the requirements of the Russian calibration system for measuring instruments.
23. Metrological service in Russia
The State Metrological Service of the Russian Federation (SMS) is an association of state metrological bodies and is engaged in coordinating activities to ensure the uniformity of measurements. The following metrological services exist:
1) State Metrological Service;
2) State Service for Time and Frequency and Determination of Earth Rotation Parameters;
3) State Service for Standard Samples of the Composition and Properties of Substances and Materials;
4) State service of standard reference data on physical constants and properties of substances and materials;
5) metrological services of state governing bodies of the Russian Federation;
6) metrological services of legal entities. All of the above services are managed by the State Committee of the Russian Federation for Standardization and Metrology (Gosstandart of Russia).
State Metrological Service contains:
1) state scientific metrology centers (SSMC);
2) State Migration Service bodies on the territory of the constituent entities of the Russian Federation. The State Metrological Service also includes centers of state standards, specializing in various units of measurement of physical quantities.
The State Service for Time and Frequency and Determination of Earth Rotation Parameters (GSVP) is engaged in ensuring the uniformity of measurements of time, frequency and determination of Earth rotation parameters at the interregional and intersectoral levels. The measurement information of the State Microwave Radio is used by the navigation and control services of aircraft, ships and satellites, the Unified Energy System, etc.
The State Service for Standard Samples of the Composition and Properties of Substances and Materials (SSSO) is engaged in the creation and implementation of a system of standard samples for the composition and properties of substances and materials. The concept of materials includes:
1) metals and alloys;
2) petroleum products;
3) medications, etc.
GSSO is also developing instruments designed to compare the characteristics of standard samples and the characteristics of substances and materials produced by different types of enterprises (agricultural, industrial, etc.) in order to ensure control.
The State Service for Standard Reference Data on Physical Constants and Properties of Substances and Materials (GSSSD) is engaged in the development of accurate and reliable data on physical constants, properties of substances and materials (minerals, oil, gas, etc.). GSSSD measurement information is used by various organizations involved in the design of technical products with increased accuracy requirements. SSSSD publishes reference data agreed with international metrological organizations.
Metrological services of state governing bodies of the Russian Federation and metrological services of legal entities can be created in ministries, enterprises, institutions registered as a legal entity, in order to carry out various types of work to ensure the unity and proper accuracy of measurements, to ensure metrological control and supervision.
24. State system for ensuring the uniformity of measurements
The state system for ensuring the uniformity of measurements was created to ensure the uniformity of measurements within the country. The state system for ensuring the uniformity of measurements is implemented, coordinated and managed by the State Standard of the Russian Federation. Gosstandart of the Russian Federation is a state executive body in the field of metrology.
The system for ensuring the uniformity of measurements performs the following tasks:
1) ensures the protection of the rights and legally established interests of citizens;
2) ensures the protection of the established law and order;
3) ensures the protection of the economy.
The system for ensuring the uniformity of measurements carries out these tasks by eliminating the negative consequences of unreliable and inaccurate measurements in all spheres of human life and society using constitutional norms, regulations and decrees of the government of the Russian Federation.
The system for ensuring the uniformity of measurements operates according to:
1) the Constitution of the Russian Federation;
2) Law of the Russian Federation “On ensuring the uniformity of measurements”;
3) Decree of the Government of the Russian Federation “On the organization of work on standardization, ensuring uniformity of measurements, certification of products and services”;
4) GOST R 8.000–2000 “State system for ensuring the uniformity of measurements.”
The state system for ensuring the uniformity of measurements includes:
1) legal subsystem;
2) technical subsystem;
3) organizational subsystem.
The main objectives of the State System for Ensuring the Uniformity of Measurements are:
1) approval of effective ways to coordinate activities in the field of ensuring the uniformity of measurements;
2) ensuring research activities aimed at developing more accurate and advanced methods and methods for reproducing units of measurement of physical quantities and transferring their sizes from state standards to working measuring instruments;
3) approval of the system of units of measurement of physical quantities allowed for use;
4) establishment of measurement scales allowed for use;
5) approval of the fundamental concepts of metrology, regulation of the terms used;
6) approval of the system of state standards;
7) production and improvement of state standards;
8) approval of methods and rules for transferring the sizes of units of measurement of physical quantities from state standards to working measuring instruments;
9) carrying out calibration (verification) and certification of measuring instruments that are not covered by the scope of state metrological control and supervision;
10) implementation of information coverage of the system for ensuring the uniformity of measurements;
11) improvement of the state system for ensuring the uniformity of measurements.
Legal subsystem- this is a set of interrelated acts (approved by legislation and regulations) that have the same goals and approve mutually agreed upon requirements for certain interconnected objects of the system for ensuring the uniformity of measurements.
Technical subsystem is a collection of:
1) international standards;
2) state standards;
3) standards of units of measurement of physical quantities;
4) standards of measurement scales;
5) standard samples of the composition and properties of substances and materials;
6) standard reference data on physical constants and properties of substances and materials;
7) measuring instruments and other instruments used for metrological control;
8) buildings and premises designed specifically for high-precision measurements;
9) research laboratories;
10) calibration laboratories.
The organizational subsystem includes metrological services.
25. State metrological control and supervision
State metrological control and supervision (GMKiN) is provided by the State Metrological Service to verify compliance with the norms of legal metrology approved by the Law of the Russian Federation “On Ensuring the Uniformity of Measurements”, state standards and other regulatory documents.
State metrological control and supervision applies to:
1) measuring instruments;
2) standards of quantities;
3) measurement methods;
4) quality of goods and other objects approved by legal metrology.
The scope of application of State metrological control and supervision extends to:
1) healthcare;
2) veterinary practice;
3) environmental protection;
4) trade;
5) settlements between economic agents;
6) accounting operations carried out by the state;
7) defense capability of the state;
8) geodetic work;
9) hydrometeorological work;
10) banking operations;
11) tax transactions;
12) customs operations;
13) postal operations;
14) products supplied under government contracts;
15) checking and monitoring product quality to ensure compliance with the mandatory requirements of state standards of the Russian Federation;
16) measurements that are carried out at the request of judicial authorities, the prosecutor's office and other government bodies;
17) registration of sports records on a national and international scale.
It should be noted that inaccuracy and unreliability of measurements in non-manufacturing areas such as healthcare can lead to serious consequences and safety risks. Inaccuracy and unreliability of measurements in the field of trade and banking operations, for example, can cause huge financial losses for both individual citizens and the state.
The objects of State metrological control and supervision may be, for example, the following measuring instruments:
1) devices for measuring blood pressure;
2) medical thermometers;
3) instruments for determining the level of radiation;
4) devices for determining the concentration of carbon monoxide in vehicle exhaust gases;
5) measuring instruments intended to control the quality of goods.
The Law of the Russian Federation establishes three types of state metrological control and three types of state metrological supervision.
Types of state metrological control:
1) determination of the type of measuring instruments;
2) verification of measuring instruments;
3) licensing of legal entities and individuals engaged in the production and repair of measuring instruments. Types of state metrological supervision:
1) over the manufacture, condition and operation of measuring instruments, certified methods of performing measurements, standards of units of physical quantities, compliance with metrological rules and regulations;
2) the number of goods that are alienated in the process of trade operations;
3) the quantity of goods packaged in packaging of any type during the process of packaging and sale.
According to the method of obtaining the values of a physical quantity measurements can be direct, indirect, cumulative and joint, each of which is carried out using absolute and relative methods (see clause 3.2.).
Rice. 3. Classification of types of measurements
Direct measurement– a measurement in which the desired value of a quantity is found directly from experimental data. Examples of direct measurements are determining length using linear measures or determining temperature with a thermometer. Direct measurements form the basis of more complex indirect measurements.
Indirect measurement – measurement in which the desired value of a quantity is found on the basis of a known relationship between this quantity and quantities obtained by direct measurements, for example, trigonometric methods of measuring angles, in which the acute angle of a right triangle is determined from the measured lengths of the legs and hypotenuse, or measuring the average diameter of a thread using the three-wire method or, the power of an electrical circuit based on the voltage measured by a voltmeter and current measured by an ammeter, using a known dependence. In some cases, indirect measurements provide more accurate results than direct measurements. For example, the errors in direct measurements of angles using goniometers are an order of magnitude higher than the errors in indirect measurements of angles using sine rulers.
Joint are measurements made simultaneously of two or more opposite quantities. The purpose of these measurements is to find a functional relationship between quantities.
Example 1. Construction of a calibration characteristic y = f(x) measuring transducer, when sets of values are simultaneously measured:
X 1, X 2, X 3, …, X i, …, X n
Y 1, Y 2, Y 3, …, Y i, …, Y n
Example 2. Determination of the temperature coefficient of resistance by simultaneous resistance measurements R and temperature t and then defining the dependency a(t) = DR/Dt:
R 1 , R 2 , …, R i , …, R n
t 1 , t 2 , …, t i , …, t n
Aggregate Measurements are carried out by simultaneous measurement of several quantities of the same name, at which the desired value is found by solving a system of equations obtained as a result of direct measurements of various combinations of these quantities.
Example: the mass value of the individual weights of the set is determined from the known value of the mass of one of the weights and from the results of measurements (comparisons) of the masses of various combinations of weights.
There are weights with masses m 1, m 2, m 3.
The mass of the first weight is determined as follows:
The mass of the second weight will be determined as the difference between the masses of the first and second weights M 1.2 and the measured mass of the first weight:
The mass of the third weight will be determined as the difference in the mass of the first, second and third weights ( M 1,2,3) and measured masses of the first and second weights ():
Often this is the way to improve the accuracy of measurement results.
Cumulative measurements differ from joint ones only in that with cumulative measurements several quantities of the same name are measured simultaneously, and with joint measurements they measure different quantities.
Cumulative and joint measurements are often used when measuring various parameters and characteristics in the field of electrical engineering.
By the nature of the change in the measured value There are static, dynamic and statistical measurements.
Static– measurements of PVs that do not change over time, for example, measuring the length of a part at normal temperature.
Dynamic– measurements of time-varying PV, for example measuring distance to ground level from a descending aircraft, or voltage in an alternating current network.
Statistical measurements are associated with determining the characteristics of random processes, sound signals, noise levels, etc.
By accuracy There are measurements with the highest possible accuracy, control and verification and technical.
Measurements with the highest possible accuracy– these are reference measurements related to the accuracy of reproducing units of physical quantities, measurements of physical constants. These measurements are determined by the current state of the art.
Control and verification– measurements, the error of which should not exceed a certain specified value. These include measurements performed by laboratories of state supervision over the implementation and compliance with standards and the state of measuring equipment, measurements by factory measurement laboratories and others, carried out using means and techniques that guarantee an error not exceeding a predetermined value.
Technical measurements– measurements in which the error of the result is determined by the characteristics of measuring instruments (MI). This is the most widespread type of measurement, carried out using working measuring instruments, the error of which is known in advance and is considered sufficient to perform this practical task.
Measurements by way of expressing measurement results can also be absolute and relative.
Absolute measurement– a measurement based on direct measurements of one or more basic quantities, as well as on the use of values of physical constants. In linear and angular absolute measurements, as a rule, one physical quantity is found, for example, the diameter of a shaft using a caliper. In some cases, the values of the measured quantity are determined by direct reading on the scale of the device, calibrated in units of measurement.
Relative dimension– measurement of the ratio of a quantity to a quantity of the same name, which plays the role of a unit. At relative method measurements, the value of the deviation of the measured value relative to the size of the installation standard or sample is assessed. An example is measurement on an optimometer or minimeter.
By number of measurements a distinction is made between single and multiple measurements.
Single measurements– this is one measurement of one quantity, i.e. the number of measurements is equal to the number of measured quantities. The practical application of this type of measurement is always associated with large errors, so at least three single measurements should be carried out and the final result should be found as the arithmetic mean value.
Multiple measurements characterized by an excess of the number of measurements of the number of measured quantities. Usually the minimum number of measurements in this case is more than three. The advantage of multiple measurements is a significant reduction in the influence of random factors on the measurement error.
The types of measurements given include various methods, i.e. methods for solving the measurement problem with theoretical justification according to the accepted methodology.
There are several types of measurements. When classifying them, they usually proceed from the nature of the dependence of the measured quantity on time, the type of measurement equation, the conditions that determine the accuracy of the measurement result and the methods of expressing these results.
1) According to the nature of the dependence of the measured quantity on time:
a) static- occur when the measured value is practically constant (measurements of body size, constant pressure);
b) dynamic, associated with quantities that undergo certain changes during the measurement process (measurements of pulsating pressures, vibrations).
2) By way of obtaining results:
a) Direct measurements- measurements in which the desired value of a physical quantity is found directly from experimental data by directly comparing it with the measure. (measurement of pressure, temperature, etc.).
b) Indirect measurements- measurements in which the desired quantity is determined on the basis of a known relationship between this quantity and quantities subjected to direct measurements, i.e. They measure not the actual quantity being determined, but others that are functionally related to it. The value of the measured quantity is found through a transformation or through an established formula (determining the volume of a body by direct measurements of its geometric dimensions, finding the electrical resistivity of a conductor by its resistance, length and cross-sectional area).
c) Aggregate measurements- these are simultaneously measurements of several quantities of the same name that characterize a given object or product, in which the required one is determined by solving a system of equations obtained by direct measurements of various combinations of these quantities (determining the mass of individual weights of a set (or weather forecasting based on measurements of wind force, air humidity, fronts, etc.).
d) Joint measurements- these are simultaneously measurements of two or several inhomogeneous physical quantities to find the dependencies between them (measurement of electrical resistance at certain temperature parameters and temperature coefficients of the measuring resistor based on direct measurements of its resistance at different temperatures).
3) According to the conditions that determine the accuracy of the result:
a) Measurements of the highest possible accuracy, achievable with the existing level of technology.
These include, first of all, standard measurements related to the highest possible accuracy of reproduction of established units of physical quantities, and, in addition, measurements of physical constants, primarily universal ones (for example, the absolute value of the acceleration of gravity, etc.). This class also includes some special measurements that require high accuracy.
b) Control and verification measurements, the error of which, with a certain probability, should not exceed a certain specified value.
These include measurements performed by laboratories for state supervision of the implementation and compliance with standards and the state of measuring equipment and factory measurement laboratories, which guarantee the error of the result with a certain probability not exceeding a certain predetermined value.
c) Technical measurements, in which the error of the result is determined by the characteristics of the measuring instruments.
Examples of technical measurements are measurements performed during the production process at machine-building enterprises, on switchboards of power plants, etc.
4 ) According to the method of expressing measurement results:
a) Absolute are measurements that are based on direct measurements of one or more basic quantities or on the use of values of physical constants (determining length in meters, electric current in amperes, acceleration of gravity in meters per second squared).
b) Relative are called measurements of the ratio of a quantity to a quantity of the same name, which plays the role of a unit, or measurements of a quantity in relation to the quantity of the same name, taken as the initial one (measurement of relative air humidity, defined as the ratio of the amount of water vapor in 1 m3 of air to the amount of water vapor that saturates 1 m j air at a given temperature).
5) According to the nature of the change in the measured quantity:
a) Static- used to measure random processes, and then to determine the average statistical value;
b) Constant— used to control continuous processes.
6) According to the amount of measurement information:
a) Single measurements is one measurement of one quantity, i.e. the number of measurements is equal to the number of measured quantities. The practical application of this type of measurement is always associated with large errors.
b) Multiple measurements- characterized by an excess of the number of measurements of the number of measured quantities. The advantage of multiple measurements is a significant reduction in the influence of random factors on measurement error.
The main characteristics of the measurements are:
Measurement principle;
Measurement method;
Error;
Accuracy;
Right;
Credibility.
Measuring principle- a physical phenomenon or a set of physical phenomena underlying measurements (measurement of body weight using weighing using gravity proportional to mass, temperature measurement using the thermoelectric effect).
Measurement method— a set of techniques for using principles and measuring instruments. Measuring instruments are the technical means used that have standardized metrological properties.
Distinguish direct assessment methods And comparison methods.
When measuring direct assessment method the desired value of the quantity is determined directly from the reading device of the measuring instrument, which is calibrated in the appropriate units.
Comparison method with measure - a method of measurement in which the quantity being measured is compared with the quantity reproduced by the measure (for example, comparing mass on a lever scale). A distinctive feature of comparison methods is the direct participation of the measure in the measurement procedure, while in the direct assessment method the measure is not explicitly present during the measurement, and its dimensions are transferred to the reading device (scale) of the measuring instrument in advance, during its calibration. The presence of a comparing device is mandatory in the comparison method.
The method of comparison with a measure has several varieties: the zero method, the differential method, the substitution method and the coincidence method.
Null method(or the method of complete balancing) is a method of comparison with a measure in which the resulting effect of the influence of the measured quantity and the counter-effect of the measure on the comparing device is reduced to zero.
For example. Measuring mass on equal-arm scales, when the effect on the scales of mass m x is completely balanced by the mass of weights m 0 (Figure 2).
Figure 2 - Full balancing method
At differential method complete balancing is not carried out, and the difference between the measured value and the value reproduced by the measure is counted on the scale of the device.
For example. Measuring mass on equal-armed scales, when the effect of mass m x on the scales is partially balanced by the mass of weights m 0 , and the mass difference is counted on a scale, graduated in mass units (Figure 3).
Figure 3 - Differential method
In this case, the value of the measured quantity m x = m 0 + m, where m — scale readings
Substitution method - a method of comparison with a measure, in which the measured quantity is replaced by a known quantity that is reproduced by the measure.
For example: Weighing on a spring scale. The measurement is carried out in two steps. First, the mass to be weighed is placed on the scale pan and the position of the scale pointer is noted; then the mass m x is replaced by the mass of weights m 0, selecting it so that the scale indicator is set in exactly the same position as in the first case. It is clear that m x = m 0 (Figure 4).
Figure 4 - Substitution method
IN coincidence method the difference between the measured value and the reproducible value is measured using the coincidence of scale marks or periodic signals.
For example . Measuring shaft speed using a strobe light - the shaft is periodically illuminated by flashes of light, and the frequency of the flashes is selected so that the mark applied to the shaft appears stationary to the observer. The coincidence method, which uses the coincidence of the main and vernier scale marks, is implemented in caliper instruments used to measure linear dimensions.
Measurement error— deviation of the measurement result from the true value of the measured value. The error is caused by the influence of many factors, such as: the nature of the measured value, the quality of the measuring instruments used, the measurement method, measurement conditions (temperature, humidity, pressure, etc.), individual characteristics of the person performing the measurements, etc. Under the influence of these factors the measurement result will differ from the true value of the measured value.
Accuracy of measurements- a qualitative characteristic of measurements, reflecting the closeness of their results to the true value of the measured value.
Quantitatively, accuracy can be expressed by the value “accuracy class”. This is a characteristic that depends on the method of expressing the limits of permissible errors of measuring instruments. The introduction of an accuracy class pursued the goal of classifying measuring instruments by accuracy. Nowadays, when the circuits and designs of measuring instruments have become more complex, and the areas of application of measuring instruments have expanded greatly, other factors have begun to significantly influence the measurement error: changes in external conditions and the nature of changes in the measured quantities over time.
The error of measuring instruments has ceased to be the main component of the measurement error, and the accuracy class does not allow us to fully solve the practical problems listed above. The scope of practical application of the “accuracy class” characteristic is limited only to such measuring instruments that are intended for measuring static quantities. In international practice, the “accuracy class” is established only for a small part of devices.
Correct measurements— the quality of measurements, reflecting the closeness to zero of systematic errors in their results (i.e., such errors that remain constant or naturally change with repeated measurements of the same quantity). The accuracy of measurements depends, in particular, on how much the actual size of the unit in which the measurement is made differs from its true size (by definition), i.e. on the extent to which the measuring instruments used for a given type of measurement were correct (correct).
Credibility characterizes confidence in measurement results and divides them into two categories: reliable and unreliable, depending on whether the probabilistic characteristics of their deviations from the true values of the corresponding quantities are known or unknown. Therefore, such probabilities should be considered as criteria for the reliability of control in order to correctly characterize the quality and safety parameters within the tolerance limits.
The presence of error limits the reliability of measurements, i.e. introduces a limitation on the number of reliable significant digits of the numerical value of the measured value and determines the accuracy of measurements. The measurement error characteristics must be selected when testing product samples in accordance with the requirements for control reliability.
Measurements as the main object of metrology are mainly related to physical quantities:
Physical quantity- one of the properties of a physical object, phenomenon, process, which is qualitatively common to many physical objects, while differing in quantitative value.
A physical quantity that, by definition, is assigned a numerical value equal to one is called unit of physical quantity.
There are basic and derived units.
Basic units of physical quantity are chosen arbitrarily, regardless of other units (unit of length - meter, unit of mass - kilogram, unit of temperature - degree, etc.)
Units formed using formulas expressing the relationship between physical quantities are called derived units. In this case, units of quantities will be expressed through units of other quantities. For example, the unit of speed is meter per second (m/s), the unit of density is kilogram per meter squared (kg/m2).
Different units of the same size differ from each other in their size. Such units are called multiples(for example, a kilometer is 10 3 m, a kilowatt is 10 3 W) or practical (for example, a millimeter is 10 -3 m, a millisecond is 10 -3 s). Such units are obtained by multiplying or dividing the independent or derived unit by a whole number, usually 10.
Units of physical quantities are combined according to a certain principle into systems of units. These principles are as follows: they arbitrarily establish units for certain quantities, called basic units and using formulas through the basic ones, all derived units for a given measurement area are obtained. The set of basic and derived units related to a certain system of quantities and formed in accordance with accepted principles is system of units of physical magnitude.
The variety of unit systems for various areas of measurement created difficulties in scientific and economic activity both in individual countries and on an international scale. Therefore, the need arose to create a unified system of units that would include units of quantities for all branches of physics.
The International System of Units consists of seven basic units, two supplementary units and the required number of derived units.
The main ones include:
The unit of length is the meter - the length of the path that light travels in a vacuum in 1/299792458 of a second;
The unit of mass is the kilogram - a mass equal to the mass of the international prototype of the kilogram;
Unit of time - second - duration of 9192631770 periods of radiation corresponding to the transition between two levels of the hyperfine structure of the ground state of the cesium-133 atom in the absence of disturbance from external fields;
The unit of electric current strength is ampere - the strength of a constant current, which, when passing through two parallel conductors of infinite length and negligibly small circular cross-section, located at a distance of 1 m from each other in a vacuum, would create a force between these conductors equal to 2. 10~7 N per meter of length;
The unit of thermodynamic temperature, the kelvin, is part of the thermodynamic temperature of the triple point of water. The use of the Celsius scale is also permitted;
The unit of quantity of a substance - mole - is the amount of substance of a system containing the same number of structural elements as there are atoms contained in a carbon-12 nuclide weighing 0.012 kg;
The unit of luminous intensity is the candela - the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540-10 12 Hz, the energy intensity of which in this direction is 1/683 W/sr.
The first three units (meter, kilogram, second) allow the formation of derived units for measuring mechanical and acoustic quantities. By adding a fourth unit, the kelvin, to these, derivative units can be formed for measuring thermal quantities.
Units (meter, kilogram, second, ampere) serve as the basis for the formation of derived units in the field of electrical, magnetic and ionizing radiation measurements. The unit mole is used to form units in the field of physicochemical measurements.
Additional units are:
Flat Angle Unit- radian and solid angle unit- steradians are used to form derivative units associated with angular quantities (for example, angular velocity, luminous flux, etc.).
MEASUREMENT SCALES
Name scale- this is a qualitative, not a quantitative scale; it does not contain zero or units of measurement (for example, a color scale).
Such scales are used to classify objects whose properties appear only in relation to equivalence (match or mismatch). These properties cannot be considered physical quantities, therefore scales of this type are not PV scales. In naming scales, assessment is carried out using human senses; the most adequate result is the one chosen by the majority of experts. Since these scales are characterized only by equivalence relations, they do not contain the concepts of zero, “more or less” and units of measurement.
Order scale - characterizes the value of the measured quantity in points (for example, earthquake scale; wind force, etc.).
It is monotonically changing and allows us to establish “more - less” relationships between quantities characterizing this property. Zero exists or does not exist, but it is fundamentally impossible to introduce units of measurement, since a proportionality relation has not been established for them and, accordingly, it is impossible to judge how many times more or less specific manifestations of a property are.
Interval scale- has a conditional zero value, and the intervals are set by agreement (for example, time scale, length scale).
These scales are a further development of order scales. The scale consists of equal intervals, has a unit of measurement and an arbitrarily chosen beginning - a zero point. Such scales include chronology and temperature scales.
Ratio scale - has a natural zero value, and the unit of measurement is established by agreement, depending on the requirement for measurement accuracy (for example, weight scale).
From a formal point of view, this scale is an interval scale with a natural origin. All arithmetic operations are applicable to the values obtained on the ratio scale, which is of great importance when measuring EF.
Currently, there are many types of measurements, distinguished by the physical nature of the measured quantity and the factors that determine various conditions and measurement modes. The main types of measurements of physical quantities, including linear-angular ones (GOST 16263–70), are straight, indirect, cumulative, joint, absolute And relative.
Most widely used direct measurements , consisting in the fact that the desired value of the measured quantity is found from experimental data using measuring instruments. The linear dimension can be set directly using the scales of a ruler, tape measure, caliper, micrometer, the acting force - with a dynamometer, temperature - with a thermometer, etc.
The direct measurement equation has the form:
where Q is the desired value of the measured quantity; X is the value of the measured quantity obtained directly from the readings of the measuring instruments.
Indirect– such measurements in which the desired quantity is determined by the known relationship between this quantity and other quantities obtained by direct measurements.
The indirect measurement equation has the form:
Q = f (x 1, x 2, x 3, ...),
where Q is the desired value of the indirectly measured quantity; x 1, x 2, x 3, ... – values of quantities measured by direct measurement.
Indirect measurements are used in cases where the desired value is impossible or very difficult to measure directly, i.e. direct type of measurement, or when the direct type of measurement gives a less accurate result.
Examples of an indirect type of measurement are establishing the volume of a parallelepiped by multiplying three linear quantities (length, height and width) determined using the direct type of measurement, calculating engine power, determining the electrical resistivity of a conductor by its resistance, length and cross-sectional area, etc.
An example of an indirect measurement is also the measurement of the average diameter of an external fastening thread using the “three wires” method. This method is based on the most accurate determination of the average thread diameter d2 as the diameter of a conventional cylinder, the generatrix of which divides the thread profile into equal parts P/2 (Fig. 2.1):
where Dmeas – distance, including wire diameters, obtained by direct measurements;
d 2 – diameter of the wire, ensuring contact with the thread profile at points lying on the generatrice d 2;
α – thread profile angle;
P – thread pitch.
Aggregate Measurements carried out by simultaneous measurement of several quantities of the same name, at which the desired value is found by solving a system of equations obtained by direct measurements of various combinations of these quantities. An example of cumulative measurements is the calibration of the weights of a set using the known mass of one of them and the results of direct comparisons of the masses of various combinations of weights.
For example, it is necessary to calibrate a burnt mass of 1; 2; 5; 10 and 20 kg. An exemplary weight is 1 kg, marked 1 volume.
Let's take measurements, changing the combination of weights each time:
1 = 1 06 + A; 1 + l rev = 2 + b; 2 = 2 + With; 1+2 + 2 = 5 + d etc.
Letters A, b, With, d– unknown values of weights that have to be added or subtracted from the mass of the weight. By solving the system of equations, you can determine the value of each weight.
Joint measurements– simultaneous measurements of two or more different quantities to find the relationship between them, for example, measurements of the volume of a body made with measurements of various temperatures that determine the change in the volume of this body.
The main types of measurements, based on the nature of the measurement results for various physical quantities, include absolute and relative measurements.
Absolute measurements are based on direct measurements of one or more physical quantities. An example of an absolute measurement would be measuring the diameter or length of a roller with a caliper or micrometer, or measuring temperature with a thermometer.
Absolute measurements are accompanied by an assessment of the entire measured value.
Relative measurements are based on measuring the ratio of the measured quantity, which plays the role of a unit, or measuring a quantity in relation to the quantity of the same name, taken as the initial one. As samples, standard measures in the form of plane-parallel end length measures are often used.
An example of relative measurements can be measurements of the calibers of plugs and staples on horizontal and vertical optimeters with the setting of measuring instruments according to standard measures. When using reference standards or reference parts, relative measurements can improve the accuracy of measurement results compared to absolute measurements.
In addition to the types of measurements considered, according to the main characteristic - the method of obtaining the measurement result, types of measurements are also classified according to the accuracy of the measurement results - into equally accurate And unequal, according to the number of measurements – per multiple And one-time, in relation to the change in the measured value over time – by static And dynamic, by the presence of contact of the measuring surface of the measuring instrument with the surface of the product - on contact And contactless and etc.
Depending on the metrological purpose, measurements are divided into technical– production measurements, control and verification And metrological– measurements with the highest possible accuracy using standards in order to reproduce units of physical quantities to transfer their size to working measuring instruments.
Measurement methods
In accordance with RMG 29–99, the main measurement methods include the direct assessment method and comparison methods: differential, zero, substitution and coincidence.
Direct method– a measurement method in which the value of a quantity is determined directly from the reading device of a direct-acting measuring device, for example, measuring a shaft with a micrometer and force with a mechanical dynamometer.
Methods for comparison with a measure– methods in which the measured value is compared with the value reproduced by the measure:
differential method characterized by measuring the difference between the measured quantity and a known quantity reproduced by the measure. An example of a differential method is the measurement with a voltmeter of the difference between two voltages, one of which is known with great accuracy, and the other is the desired value;
null method– in which the difference between the measured quantity and the measure is reduced to zero. In this case, the zero method has the advantage that the measure can be many times smaller than the measured value, for example, weighing on scales, when the load being weighed is on one shoulder, and a set of reference weights is on the other;
substitution method– a method of comparison with a measure, in which the measured value is replaced by a known value reproduced by the measure. The substitution method is used when weighing with alternately placing the measured mass and weights on the same scale;
coincidence method– a method of comparison with a measure, in which the difference between the measured quantity and the value reproduced by the measure is measured using the coincidence of scale marks or periodic signals. An example of using this method is measuring length using a vernier caliper.
Depending on the type of measuring instruments used, instrumental, expert, heuristic and organoleptic measurement methods are distinguished.
Instrumental method is based on the use of special technical means, including automated and automated ones.
Expert method The assessment is based on the judgment of a group of specialists.
Heuristic methods estimates are based on intuition.
Organoleptic methods assessments are based on the use of human senses. Assessment of the condition of an object can be carried out by element-by-element and complex measurements. The element-by-element method is characterized by measuring each product parameter separately. For example, eccentricity, ovality, cut of a cylindrical shaft. The complex method is characterized by measuring the total quality indicator, which is influenced by its individual components. For example, measuring the radial runout of a cylindrical part, which is affected by eccentricity, ovality, etc.; control of profile position along limit contours, etc.
