1. Classification of measurements.
2. Types and methods of measurements.
3. Types of measuring instruments and their main metrological characteristics.
4. Accuracy classes of measuring instruments.
5. Metrological characteristics of digital devices.
1. Classification of measurements
Classification of measuring instruments can be carried out according to the following criteria.
1. Accuracy characteristics measurements are divided into equal and unequal.
Equally accurate measurements of a physical quantity are a series of measurements of a certain quantity made using measuring instruments (MI) of equal accuracy under identical initial conditions.
Unequally accurate measurements of a physical quantity are a series of measurements of a certain quantity made using measuring instruments with different accuracy and (or) under different initial conditions.
2. By quantity measurements measurements are divided into single and multiple.
Single measurement - measurement taken once.
Multiple measurement - one size measurement quantities, the result of this measurement is obtained from several subsequent single measurements (counts).
How many measurements do we need to make to consider that we have made multiple measurements? No one can answer this for sure. But we know that with the help of tables of statistical distributions, a number of measurements can be studied according to the rules of mathematical statistics with the number of measurements n ≥ 4. Therefore, it is believed that a measurement can be considered multiple if the number of measurements is at least 4.
3. By type changes in the measurement value are divided into static and dynamic.
Static measurements- These are measurements of a constant, unchanging physical quantity.
For example, measuring the linear size of a manufactured product at normal temperature can be considered static, since temperature fluctuations in the workshop at the level of tenths of a degree introduce a measurement error of no more than 10 μm/m, which is insignificant compared to the manufacturing error of the part.
Dynamic measurements are measurements of a changing, non-constant physical quantity. For example, measuring the distance to the Earth's surface from a balloon or measuring the constant voltage of an electric current. Essentially, a dynamic measurement is a measurement of the functional dependence of the measured quantity on time.
4. By purpose measurements are divided into technical and metrological.
Technical measurements are measurements performed by technical measuring instruments.
Example: for monitoring and managing experimental developments, monitoring technological parameters of products or all kinds of production processes, managing traffic flows, in medicine when making a diagnosis and treatment, monitoring the state of the environment, etc.
Metrological measurements - measurements to implement the unity and required accuracy of technical measurements (measurements performed using standards).
These include:
Reproduction of units and scales of physical quantities by primary standards and transfer of their sizes to less accurate standards;
Calibration of measuring instruments;
Measurements made during calibration or verification of measuring instruments;
Other measurements performed for this purpose (for example, measurements during mutual comparisons of standards of the same level of accuracy) or to satisfy other internal needs of metrology (for example, measurements to clarify fundamental physical constants and reference standard information about the properties of materials and substances, measurements to confirm declared measurement laboratory capabilities).
Metrological measurements are carried out using standards.
5. By way of presenting the result measurements are divided into absolute and relative.
Absolute measurements are measurements that are made by directly measuring a fundamental quantity and/or applying a physical constant. As an example, measuring force using a dynamometer would be a relative measurement, while measuring it by using a physical constant g (acceleration of universal gravitation) and measures of mass (basic quantity SI) - absolute.
Relativemeasurements- these are measurements in which the ratio of homogeneous quantities is calculated, with the numerator being the quantity being compared, and the denominator being the basis of comparison (unit). For example, a relative measurement is the determination of the activity of a radionuclide in a source by measuring its ratio to the activity of a radionuclide in another source certified as a reference measure of quantity.
6. By methods of obtaining resultsmeasurements are divided into direct, indirect, cumulative and joint.
Direct measurement is a measurement carried out using a measuring instrument that stores the unit or scale of the quantity being measured. As an example, measuring the length of a product with a caliper, electrical voltage with a voltmeter, etc.
Indirectmeasurements are measurements in which the value of the measurand is calculated using values obtained through direct measurements. For example, finding the density of a homogeneous body based on its mass.
Aggregate measurements - measurements of several homogeneous quantities simultaneously, when the values of these quantities are found by solving a system of equations obtained by measuring various combinations of these quantities. Example, measuring the resistance of resistors connected by a triangle by measuring the resistance between different vertices of the triangle; Based on the results of three measurements, the resistance of the resistors is determined.
Joint - these are measurements made simultaneously by two or more different names quantities to find the functional relationship between them. Examples of joint measurements are determining the length of a rod as a function of its temperature or the dependence of the electrical resistance of a conductor on pressure and temperature.
Physical quantity- a property of physical objects that is qualitatively common to many objects, but quantitatively individual for each of us. The qualitative side of the concept of “physical quantity” determines its type (for example, electrical resistance as a general property of electrical conductors), and the quantitative side determines its “size” (the value of the electrical resistance of a specific conductor, for example R = 100 Ohm).
Size of physical quantity– quantitative determination of a value inherent in a specific object, system, phenomenon or process.
Physical quantity value– an estimate of the size of a physical quantity in the form of a certain number of units of measurement accepted for it. Numerical value of a physical quantity– an abstract number expressing the ratio of the value of a physical quantity to the corresponding unit of a given physical quantity (for example, 10V is the value of the voltage amplitude, and the number 10 itself is a numerical value).
The true value of a physical quantity They call the value of a physical quantity that would ideally reflect the corresponding property of an object in qualitative and quantitative terms. It is impossible to determine it experimentally due to inevitable measurement errors.
Measurement error– deviation of the measurement result from the true value of the measured physical quantity. There are two main postulates in metrology: 1) the true value of the quantity being determined exists and is constant; 2) the true value of the measured quantity cannot be found.
The actual value of a physical quantity they call it a value found experimentally and so close to the true value that for a certain purpose it can be used instead. The actual value of a physical quantity is determined using standard measures and instruments, the errors of which can be neglected in comparison with the errors of the working measuring instruments used.
International system of units of physical quantities. Units of physical quantities are divided into basic and derivative and combined into systems of units of physical quantities.
The SI system is based on seven basic and two additional physical quantities. Basic units: meter, kilogram, second, ampere, kelvin, mole and candela.
Unit of length - meter– the path length that light travels in a vacuum in 1/299792458 of a second;
unit of mass – kilogram– mass equal to the mass of the international prototype kilogram, representing a cylinder made of an alloy of platinum and iridium;
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;
unit of electric current–ampere- the strength of an unchanging 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 one another, would create a force between these conductors equal to each meter of length;
thermodynamic temperature unit– kelvin-1/273.16 part of the thermodynamic temperature of the triple point of water, i.e. the temperature at which the three phases of water - vapor, liquid and solid - are in dynamic equilibrium;
unit of amount of substance– mole – the amount of a substance containing as many structural elements as are contained in carbon -12 weighing 0.012 kg;
unit of luminous intensity– candela – the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency (wavelength of about 0.555 µm), whose radiant energy in this direction is 1/683 W/sr (sr - steradian).
Additional units SI systems are intended only to form units of angular velocity and angular acceleration. Additional physical quantities of the SI system include plane and solid angles.
Radian (rad) – the angle between two radii of a circle whose arc length is equal to that radius.
Steradian (avg) – a solid angle with its vertex at the center of the sphere, cutting out on its surface an area equal to the area of a square with a side equal to the radius of the sphere.
Derived SI units are formed from basic and supplementary units.
Units of physical quantities are divided into systemic and non-systemic.
System unit– a unit of physical quantity included in one of the accepted systems. All basic and derivatives, as well as multiples and submultiples units are systemic.
Non-systemic unit– a unit of physical quantity that is not included in the accepted systems of units. Non-systemic units are divided into: permitted on a par with SI units; approved for use in special areas; temporarily permitted and obsolete. For example, plane angles are most often measured in angular degrees, minutes, and seconds. These non-systemic units are approved for use on a par with SI units. Among the widely used non-system units, one should note the kilowatt-hour, degree Celsius, etc.
In practice, the use of whole units is not always convenient, since very large or very small values are obtained as a result of measurements. Therefore, the SI system has its decimal multiples and submultiples, which are formed using multipliers. A multiple unit of a physical quantity is a unit that is an integer number of times larger than the system quantity, for example kilohertz (10 3 Hz). A fractional unit of a physical quantity is a unit that is an integer number of times smaller than the system one, for example a microhenry (10 -6 Hn). The names of multiple and submultiple units of the SI system contain a number of prefixes corresponding to the factors.
Basic characteristics of measurements. The main characteristics of measurements are: result and error.
Result measurements of a physical quantity – the value of a physical quantity obtained by measuring it. Corrections are often made to the results obtained.
– the difference between the readings of the measuring instrument and the true value of the measured physical quantity.
Measurement quality characterized by accuracy, correctness, convergence and reproducibility, reliability, as well as the size of permissible errors.
Credibility– characteristic of the quality of measurements, reflecting confidence in their results, which is determined by the confidence probability that the true value of the measured quantity is in some given interval. Such an interval is called a confidence interval and between its boundaries with a given confidence probability
the true value of the estimated parameter is found. In (1.1), the parameter q is the error significance level, and are the lower and upper limits of the confidence interval.
Physical quantity scale– an ordered sequence of values of a physical quantity, adopted based on the results of precise measurements. Among the scales, three main types should be distinguished: scales of names, intervals and absolute scales.
Name scale (classification scale) is based on attributing numbers to an object, playing the role of simple names.
Interval scale (difference scale) reflects the difference in values of a physical quantity. These scales include the Celsius, Fahrenheit and Reaumur temperature scales. In the Celsius temperature scale, the temperature at which the ice melts is taken as the starting point for the temperature difference.
Absolute scales have a natural unambiguous definition of the unit of measurement. These scales correspond to relative values: gain, attenuation, etc.
Types of measurements. The types of measurements are determined by the physical nature of the measured quantity, the required accuracy and the required speed of measurements, the conditions and mode of measurements, etc. The most widely used classification is based on general methods for obtaining measurement results, according to which measurements are divided into direct, indirect, joint and cumulative.
Direct are called measurements in which the desired value of a quantity is found directly from the readings of the measuring instrument. Analytically direct measurements are written in the form
where X is the value of a quantity found by measuring it and called the measurement result.
Indirect measurements– these are measurements in which the value of the measured quantity is found on the basis of a known relationship between it and quantities determined by direct measurements that were carried out under the same conditions. Indirect measurements can be characterized by the following formula:
where are the results of direct measurements of quantities associated by a functional dependence with the desired value of the measured quantity A.
Cumulative are called simultaneous measurements of several quantities of the same name, in which their values are found by solving a system of equations obtained by direct or indirect measurements of various combinations of these quantities.
Joint are called simultaneous measurements of two or more different quantities to establish the relationship between them.
Therefore, joint measures can be interpreted as a generalization of indirect measures, and cumulative measures as a generalization of direct measures.
Standards, their classification.Reference– a measuring instrument (or a set of measuring instruments) that ensures the reproduction and (or) storage of a unit of physical quantity with the highest accuracy for a given level of development of measuring equipment in order to transfer its size to subordinate measuring instruments in the verification scheme.
Each standard must have three interrelated properties: immutability, reproducibility and comparability.
Immutability- the property of a standard to keep the size of a unit of physical quantity reproduced by it unchanged over a long period of time.
Reproducibility– the ability to reproduce a unit of physical quantity with the smallest error for the existing level of development of measuring technology.
Comparability– the possibility of comparison with the standard of other measuring instruments that are lower in the verification scheme, primarily secondary standards, with the highest accuracy for the corresponding level of development of measurement technology.
Standards are usually classified depending on their purpose, in accordance with which it is planned to equip the relevant metrological services with primary, special, national, international and secondary standards.
Primary standard ensures the reproduction of a unit of physical quantity with the highest accuracy in the country. Primary standards are unique measuring instruments, often representing very complex measuring systems. These standards form the basis of the state system for ensuring the uniformity of measurements and are divided into special, national, state and international.
Special standard reproduces a physical quantity under special conditions and replaces the primary standard for them. Primary and special standards are the original standards for the country; they are approved as national.
National – a primary (or special) standard recognized as a source standard on the territory of the state. National standards are created, stored and used by the country's central metrological scientific institutes.
International - a standard adopted by international agreement as an international basis for harmonizing the sizes of units reproduced and stored by national standards.
Secondary standard– standard, the value of which is established according to the primary standard. Secondary standards are part of the subordinate means of storing units and transferring their sizes; they are created in cases where it is necessary to organize verification work, as well as to ensure the safety and least wear of the state standard. According to their purpose, secondary standards are divided into witness standards, copy standards, comparison standards and working standards.
Standard witness serves to check the safety and immutability of the state standard and replace it in case of damage or loss. Currently, the international standard of the kilogram has a witness standard.
Reference copy designed to convey unit size to working standards. It is created when it is necessary to carry out a large number of verification works in order to protect the primary or special standard from premature wear. A copy standard is a copy of a state standard for metrological purposes.
Standard of comparison used for mutual comparison of standards, which for one reason or another cannot be directly compared with each other.
Working standard- a measure, measuring device or transducer approved as exemplary and used for verification of other measuring instruments against them. Working standards are intended for verification of the most accurate measuring instruments. Working standards, if necessary, are divided into 1st, 2nd and subsequent categories, which determine the order of their subordination in accordance with the verification scheme.
Basic literature:
Further reading:
Security questions:
1. What is a physical quantity and the dimension of a physical quantity?
2. Give basic, additional and derived physical quantities?
3. What is a physical quantity scale?
4. What is a standard of physical quantity?
Lecture topic 2. Measurements. Measurement errors. Purpose of measurements. Quality, accuracy and errors of measurements. Systematic errors. Methods for eliminating systematic errors.
Purpose of measurements- obtaining a result, i.e. an assessment of the true value of a physical quantity. To do this, measurements must be carried out with the greatest possible reliability and accuracy. But no matter how accurate and perfect the measurement tools and methods are, and no matter how carefully the measurements are carried out, their result always differs from the true value of the measured value, i.e. determined with some error.
If a direct measurement of a physical quantity is carried out once (the so-called single direct measurement), then the result of the measurement is the direct reading of the measuring instrument. At the same time, for the error measurement result the error of the measuring instrument is often taken into account.
In the case of multiple observations, the measurement result and its error are found by various methods of statistical processing of all observations performed.
Quality, accuracy and measurement errors. The quality of measurements is understood as a set of properties that determine the receipt of the results of these measurements with the required accuracy characteristics in the required form and within the established time frame. The quality of measurements is characterized, first of all, by such indicators as accuracy (error), correctness and reliability. The accuracy of a measurement result is the main characteristic of the quality of measurements, reflecting the closeness to zero error of this result.
The error of the measurement result The deviation of the found value from the true value of the measured physical quantity is called. Since the true value of the measured quantity is not known, when quantifying the error, they use actual value of a physical quantity.
Measuring instrument error represents the difference between the readings of the measuring instrument and the true (actual) value of the measured physical quantity. This error characterizes the accuracy of the measurement results carried out by the measuring instrument used.
Absolute error, expressed in units of the measured value, is the deviation of the measurement result x from the true value x and
The absolute error characterizes the value and sign of the resulting error, but does not determine the quality of the measurement itself. A characteristic of measurement quality is measurement accuracy, reflecting the measure of proximity of the measurement result to the true value of the measured quantity. High measurement accuracy corresponds to a small error.
Relative error is the ratio of the absolute measurement error to the true value of the measured quantity:
A measure of measurement accuracy is the accuracy indicator, the inverse of the relative error module: . Often the relative error is expressed as a percentage: . Because usually<< то относительная погрешность может быть определена как или
Given error expressing the potential accuracy of measurements, the ratio of the absolute error to some standard value (for example, to the final scale value) is called:
Systematic errors- components of measurement error that remain constant or change naturally during repeated measurements of a quantity under the same conditions. Their distinguishing feature is that they can be predicted and detected. Systematic errors are identified by a detailed analysis of their possible sources and reduced by introducing appropriate corrections, using more accurate instruments, calibrating instruments using working measures, etc.
Random errors components of measurement error that change randomly in value and sign during repeated measurements of the same physical quantity under the same conditions. Random components of the measurement error lead to ambiguity in the readings and appear during repeated measurements of the same physical quantity in the form of some scatter in the results obtained. They can be caused, for example, by incorrect functioning of the electronic components of the measuring device.
Gross errors (misses)- errors significantly exceeding those expected under given measurement conditions. They arise due to unaccounted external influences. Thus, gross errors can be caused by short-term surges in the supply voltage when powerful energy consumers are connected to the network. Errors can also be caused by incorrect actions of the operator, in particular, errors that arise when he writes off the readings of the measuring device.
So, if gross errors are not taken into account, the absolute measurement error, determined by expression (2.1), can be represented as the sum of the systematic and random components:
From relation (2.4) it follows that the absolute error, like the measurement result, is random size.
Methodological errors arise due to the imperfection of the measurement method, incorrectness of the algorithms or formulas used to calculate the measurement results, due to the influence of the chosen measuring instrument on the measured signal parameters, etc. If, for example, a voltmeter has an insufficiently high input resistance, then connecting it to the circuit can change the distribution of currents and voltages in it. In this case, the measurement result will differ from the actual one.
Example 2.1. Let us show how a methodological error appears when measuring the resistance of the resistor R x using the ammeter = voltmeter method (Fig. 2.1).
Solution. To determine the value of resistance R x, it is necessary to measure the current I R flowing through the resistor and the voltage drop across it U R .
In the figure shown. 2.1 circuit implementing this measurement method, the voltage drop across the resistor R x measured by voltmeter V directly, while the ammeter A measures the total current, one part of which flows through a resistor, and the other part through a voltmeter. As a result, the measured resistance value will not be R x=U R / I R , A R" =U R /(I R +I V), and a methodological error will appear. The methodological error decreases and tends to zero with current, that is, with the internal resistance of the voltmeter.
Instrumental (hardware) errors arise due to the imperfection of measuring instruments, i.e. from their own errors. Instrumental errors can be reduced by using a more accurate instrument.
External errors associated with the deviation of one or more influencing quantities from normal values or their exit beyond the normal region.
Subjective errors caused by errors of the experimenter when taking readings (errors from the negligence and inattention of the experimenter).
Static errors arise when measuring a time-stable value of the measured quantity.
Dynamic errors occur during dynamic measurements, when the measured physical quantity changes over time. The reason for the appearance of dynamic errors is the discrepancy between the speed (time) characteristics of the device and the rate of change of the measured value.
Basic error measuring instruments takes place under normal operating conditions specified in regulatory documents.
Additional error measuring instruments occurs due to the exit of any of the influencing quantities beyond the normal range of values.
Systematic errors. The sources of systematic components of measurement error can be the object and method of measurement, measuring instruments, measurement conditions and the experimenter. At the same time, estimating systematic components is a rather difficult metrological task. Its importance is determined by the fact that knowledge of the systematic error makes it possible to introduce an appropriate correction into the measurement result and thereby increase its accuracy. The difficulty lies in the difficulty of detecting systematic error, since it cannot be detected through repeated measurements (observations).
Permanent are such systematic measurement errors that remain unchanged (maintain magnitude and sign) throughout the entire series of measurements.
Variables are called errors that change during the measurement process. The presence of a significant systematic error variable distorts estimates of the characteristics of the random error. Therefore, it must be identified and excluded from the measurement results.
Methods for eliminating systematic errors. In real conditions, it is impossible to completely eliminate the systematic component of the error. There are always some unaccounted factors that need to be taken into account and which will cause systematic measurement error. This means that the systematic error is also random and its determination is determined only by established traditions of processing and presenting measurement results.
Permanent systematic errors can only be detected by comparing measurement results with others obtained using more accurate measurement methods and instruments. In some cases, systematic error can be eliminated by eliminating sources of error before starting measurements (error prevention), and during the measurement process by introducing known corrections to the measurement results.
Substitution method provides the most complete compensation for constant systematic error. The essence of this method is to replace the measured value with a known value A, obtained using an adjustable measure, so that the reading of the measuring device remains unchanged. The value of the measured quantity is read in this case using the measure indicator. When using this method, the error of an inaccurate measuring device is eliminated, and the measurement error is determined only by the error of the measure itself and the error of reading the measured value according to the measure indicator.
Sign error compensation method used to eliminate a constant systematic error, in which only the sign changes depending on the measurement conditions. With this method, two measurements are performed, the results of which are respectively , where x and is the measured value. The average value of the results obtained is (x 1 + x 2)/2 = x and represents the final measurement result, which does not contain error.
Amendment method allows you to quite simply calculate and eliminate systematic errors from the measurement result. Correction C is a quantity of the same name as the measured x and is introduced into the measurement result in order to eliminate systematic error. If accepted and systematic error is completely excluded from the measurement result.
The corrections are determined experimentally or through special theoretical studies and are given in the form of formulas, graphs or tables.
Contrasting method used in radio measurements to reduce constant systematic errors when comparing a measured quantity with a known quantity of approximately equal value, reproduced by a corresponding reference measure.
Randomization method is based on the principle of formally converting systematic errors into random ones. This method allows you to effectively reduce the constant systematic error (methodological and instrumental) by measuring a certain value with a number of similar instruments and then assessing the measurement result in the form of the mathematical expectation (arithmetic mean value) of a series of observations performed. In this method, when processing measurement results, random changes in error from device to device are used.
Basic literature:
Further reading:
Classification of measurements can be carried out according to the following criteria.
1. According to the accuracy characteristics:
- equal-precision measurements A physical quantity is a series of measurements of a certain quantity made using measuring instruments of equal accuracy under identical initial conditions.
- unequal measurements a physical quantity is a series of measurements of a certain quantity made using measuring instruments with different accuracy and (or) under different initial conditions.
2. By number of measurements:
- single measurement is a measurement of one quantity made once. In practice, single measurements have a large error; therefore, to reduce the error, it is recommended to perform measurements of this type at least three times, and take their arithmetic average as the result.
- multiple measurements is a measurement of one or more quantities performed four or more times. A multiple measurement is a series of single measurements. The minimum number of measurements at which a measurement can be considered multiple is four. The result of multiple measurements is the arithmetic average of the results of all measurements taken. With repeated measurements, the error is reduced.
3. By type of change in value:
- static measurements- These are measurements of a constant, unchanging physical quantity. An example of such a time-constant physical quantity is the length of a land plot.
- dynamic measurements– these are measurements of a changing, non-constant physical quantity.
4. According to the purpose of measurement:
- technical measurements– these are measurements performed by technical measuring instruments.
- metrological measurements are measurements made using standards.
5. By way of presenting the result:
- absolute measurements– these are measurements that are performed through direct, direct measurement of a fundamental quantity and (or) the application of a physical constant.
- relative measurements- these are measurements in which the ratio of homogeneous quantities is calculated, with the numerator being the quantity being compared, and the denominator being the basis of comparison (unit). The measurement result will depend on what value is taken as the basis of comparison.
6. By methods of obtaining results:
- direct measurements– these are measurements performed using measures, i.e. the measured quantity is compared directly with its measure. An example of direct measurements is the measurement of an angle (measure - protractor).
- indirect measurements are measurements in which the value of the measurand is calculated using values obtained through direct measurements and some known relationship between these values and the measurand.
y = f (x1, x2, … xn),
where y is the desired physical quantity;
x1,x2,…,xn – quantities subject to direct measurements.
Example: finding density from the volume and mass of a body.
- cumulative measurements– these are measurements, the result of which is the solution of a certain system of equations, which is composed of equations obtained as a result of measuring possible combinations of measured quantities.
For example: finding the mass of an unknown weight based on the ratio of the masses of known weights included in the system of equations.
- joint measurements– these are measurements during which at least two inhomogeneous physical quantities are measured in order to establish the relationship that exists between them.
For example: Finding the resistance of a resistor versus temperature.
In cumulative measurements, several quantities of the same name are simultaneously determined, and in joint measurements, different quantities are determined.
Dynamic measurement-- measurement of a quantity whose size changes over time. A rapid change in the size of the measured quantity requires its measurement with the most accurate determination of the moment in time.
For example, measuring the distance to the Earth's surface from a balloon or measuring the constant voltage of an electric current. Essentially, a dynamic measurement is a measurement of the functional dependence of the measured quantity on time.
The sign by which a measurement is classified as static or dynamic is the dynamic error at a given speed or frequency of change of the measured quantity and the specified dynamic properties of the SI. Let us assume that it is negligible (for the measurement problem being solved), in this case the measurement can be considered static. If these requirements are not met, it is dynamic.
Dynamic measurement error- error of the measurement result inherent to the conditions of dynamic measurement. Dynamic error appears when measuring variable quantities and is caused by the inertial properties of measuring instruments. The dynamic error of a measuring instrument is the difference between the error of the measuring instrument under dynamic conditions and its static error corresponding to the value of the quantity at a given time. When developing or designing a measuring instrument, it should be taken into account that an increase in measurement error and a delay in the appearance of the output signal are associated with changing conditions.
Static and dynamic errors refer to the errors in the measurement result. In most instruments, static and dynamic errors are interconnected, since the relationship between these types of errors depends on the characteristics of the instrument and the characteristic time of change in the value.
Static measurements
Static measurement-- measurement of a quantity that is accepted, in accordance with the assigned measurement task, as unchanged throughout the measurement period.
For example: 1) body size measurements;
2) constant pressure measurements;
3) measurements of pulsating pressures, vibrations;
4) measurement of the linear size of a manufactured product at normal temperature can be considered static, since temperature fluctuations in the workshop at the level of tenths of a degree introduce a measurement error of no more than 10 μm/m, which is insignificant compared to the manufacturing error of the part. Therefore, in this measurement task, the measured quantity can be considered unchanged. When calibrating a line length measure against the state primary standard, thermostatting ensures the stability of maintaining the temperature at the level of 0.005 °C. Such temperature fluctuations cause a thousand times smaller measurement error - no more than 0.01 μm/m. But in this measurement task it is essential, and taking into account temperature changes during the measurement process becomes a condition for ensuring the required measurement accuracy, therefore these measurements should be carried out using the dynamic measurement technique.
Static measurement error- the error of the measurement result inherent in the conditions of static measurement, that is, when measuring constant quantities after the completion of transient processes in the elements of devices and converters.
Classification of measuring instruments can be carried out according to the following criteria.
1. Accuracy characteristics measurements are divided into equal and unequal.
Equal-precision measurements a physical quantity is a series of measurements of a certain quantity made using measuring instruments (MI) with the same accuracy under identical initial conditions.
Unequally accurate measurements a physical quantity is a series of measurements of a certain quantity made using measuring instruments with different accuracy and (or) under different initial conditions.
2. By number of measurements measurements are divided into single and multiple.
Single measurement is a measurement of one quantity made once. In practice, single measurements have a large error; therefore, to reduce the error, it is recommended to perform measurements of this type at least three times, and take their arithmetic average as the result.
Multiple measurements is a measurement of one or more quantities performed four or more times. A multiple measurement is a series of single measurements. The minimum number of measurements at which a measurement can be considered multiple is four. The result of multiple measurements is the arithmetic average of the results of all measurements taken. With repeated measurements, the error is reduced.
3. By type of change in value measurements are divided into static and dynamic.
Static measurements- These are measurements of a constant, unchanging physical quantity. An example of such a time-constant physical quantity is the length of a land plot.
Dynamic measurements– these are measurements of a changing, non-constant physical quantity.
4. By purpose measurements are divided into technical and metrological.
Technical measurements – These are measurements performed by technical measuring instruments.
Metrological measurements are measurements made using standards.
5. By way of presenting the result measurements are divided into absolute and relative.
Absolute measurements– these are measurements that are performed through direct, direct measurement of a fundamental quantity and (or) the application of a physical constant.
Relative measurements- these are measurements in which the ratio of homogeneous quantities is calculated, with the numerator being the quantity being compared, and the denominator being the basis of comparison (unit). The measurement result will depend on what value is taken as the basis of comparison.
6. By methods of obtaining results measurements are divided into direct, indirect, cumulative and joint.
Direct measurements– these are measurements performed using measures, i.e. the measured quantity is compared directly with its measure. An example of direct measurements is the measurement of an angle (measure - protractor).
Indirect measurements are measurements in which the value of the measurand is calculated using values obtained through direct measurements and some known relationship between these values and the measurand.
Aggregate Measurements– these are measurements, the result of which is the solution of a certain system of equations, which is composed of equations obtained as a result of measuring possible combinations of measured quantities.
Joint measurements – These are measurements during which at least two inhomogeneous physical quantities are measured in order to establish the relationship that exists between them.
4. Units of measurement
In 1960, at the XI General Conference on Weights and Measures, the International System of Units (SI) was approved.
The International System of Units is based on seven units covering the following fields of science: mechanics, electricity, heat, optics, molecular physics, thermodynamics and chemistry:
1) unit of length (mechanics) – meter;
2) unit of mass (mechanics) – kilogram;
3) unit of time (mechanics) – second;
4) unit of electric current (electricity) – ampere;
5) unit of thermodynamic temperature (heat) – kelvin;
6) unit of luminous intensity (optics) – candela;
7) unit of quantity of a substance (molecular physics, thermodynamics and chemistry) – mole.
There are additional units in the International System of Units:
1) unit of measurement of a plane angle – radian;
2) unit of measurement of solid angle – steradian Thus, through the adoption of the International System of Units, units of measurement of physical quantities in all fields of science and technology were streamlined and brought to one type, since all other units are expressed through seven basic and two additional SI units. For example, the amount of electricity is expressed in terms of seconds and amperes.
Main measurement characteristics
The following main measurement characteristics are distinguished:
1) the method by which measurements are taken;
2) measurement principle;
3) measurement error;
4) measurement accuracy;
5) correctness of measurements;
6) reliability of measurements.
Measurement method- this is a method or a set of methods by which a given quantity is measured, i.e., a comparison of the measured quantity with its measure according to the accepted principle of measurement.
There are several criteria for classifying measurement methods.
1. According to the methods of obtaining the desired value of the measured quantity, the following are distinguished:
1) direct method (carried out using direct, direct measurements);
2) indirect method.
2. According to measurement techniques, there are:
1) contact measurement method;
2) non-contact measurement method. Contact measurement method based on direct contact of any part of the measuring device with the measured object.
At non-contact measurement method the measuring device does not come into direct contact with the object being measured.
3. According to the methods of comparing a quantity with its measure, the following are distinguished:
1) direct assessment method;
2) method of comparison with its unit.
Direct assessment method is based on the use of a measuring device that shows the value of the measured quantity.
Comparison method with measure based on comparing the object of measurement with its measure.
Measuring principle– this is a certain physical phenomenon or their complex on which the measurement is based. For example, temperature measurement is based on the phenomenon of expansion of a liquid when it is heated (mercury in a thermometer).
Measurement error is the difference between the result of measuring a quantity and the real (actual) value of this quantity. Error, as a rule, arises due to insufficient accuracy of measurement tools and methods or due to the inability to provide identical conditions for repeated observations.
Measurement accuracy– this is a characteristic that expresses the degree of correspondence of the measurement results to the real value of the measured quantity.
Quantitatively, the measurement accuracy is equal to the relative error minus the first power, taken modulo.
Correct measurement– this is a qualitative characteristic of a measurement, which is determined by how close to zero the value of a constant or fixed error that changes during repeated measurements (systematic error). This characteristic usually depends on the accuracy of the measuring instruments.
The main characteristic of measurements is the reliability of the measurements.
Reliability of measurements is a characteristic that determines the degree of confidence in the obtained measurement results. According to this characteristic, measurements are divided into reliable and unreliable. The reliability of measurements depends on whether the probability of deviation of the measurement results from the real value of the measured value is known. If the reliability of the measurements is not determined, then the results of such measurements, as a rule, are not used. The reliability of measurements is limited above by the error