RU2751438C1 - Method for measuring spatial distribution of temperature and device for its implementation - Google Patents

Abstract

FIELD: measuring technology.SUBSTANCE: inventions relate to measuring technology for measuring temperature at various depths of electrically conductive media. The proposed method for measuring the spatial distribution of temperature and a device for its implementation can be used in the production of materials and alloys, in metallurgy, in high-temperature combustion chambers, in the production of temperature sensors, to control the temperature of electrically conductive solids and liquids. A method for measuring the spatial distribution of temperature is claimed, according to which a frequency-modulated electric current with a frequency band of wmin≤w≤wmax(Ohm) is supplied to the investigated electrically conductive object through the surface electrodes, thereby forming a skin layer of variable thickness d, penetrating to a depth of dmin≤d≤dmaxof the object under study. Then in the frequency band wmin≤w≤wmaxthe frequency characteristic of the impedance Z(jw) is measured, which is used to determine the distribution of electrical conductivity over the depth s(d). The distribution s(d) found and the previously experimentally found or theoretically known dependences of the electrical conductivity of the material of the object of study on temperature s=f(T) are used to judge the spatial distribution of temperature over the depth T(d) in the object under study. Also proposed is a device for implementing the proposed method, in which the signal generator is a signal generator with a frequency band wmin≤w≤wmax, the processing unit is a calculator of the frequency response of the impedance Z(jw). The output of the signal generator is the output for connection with the electrically conductive test object using the first electrode, and the second input of the calculator of the frequency response of the impedance Z(jw) is the input for connection with the electrically conductive test object through the second electrode. The output of the calculator of the frequency characteristic of the impedance Z(jw) is connected to the input of the calculator of the distribution of electrical conductivity s(d) and the spatial distribution of temperature T(d).EFFECT: invention ensures the possibility of measuring the temperature distribution along the depth of the electrically conductive object of study.2 cl, 4 dwg

Description

The inventions relate to measuring technology for measuring temperature at various depths of electrically conductive media. The proposed method for measuring the spatial distribution of temperature and a device for its implementation can be used in the production of materials and alloys, in metallurgy, in high-temperature combustion chambers, in the production of temperature sensors, to control the temperature of electrically conductive solids and liquids.

There is a method that implements a device for measuring the spatial distribution of temperature (Patent RU (11) No. 2079822, published 1997, IPC G01K 7/00), based on measuring the saturation current of semiconductor temperature-sensitive elements located at the points of interest for measuring the temperature field.

The closest to the proposed method of spatial distribution of temperature is a method of measuring the spatial distribution of temperature (Patent RU (11) No. 2206878, published 20.06.2003, IPC G01K 7/00) The known method consists in measuring the spatial distribution of temperature by placing thermosensitive sensors at the controlled points N connected in parallel with a two-wire line, supplying an AC voltage signal to one of the inputs of the line and registering the input alternating current I _in ( t ) of a two-wire line, quartz piezoresonance sensors with different resonant frequencies ω _р1 , ω _р2 , ... ω are used as temperature-sensitive sensors _pi , ... ω _pN , a frequency modulated signal in the resonant frequency range of piezoresonance sensors is used as an alternating voltage signal applied to one of the inputs of a two-wire line, after registering the input alternating current I _in ( t ), its amplitude-frequency cn is calculated spectrum S (ω), carry out the first measurement of the resonant frequencies of quartz piezoresonance sensors ω ⁰ _p1 , ω ⁰ _p2 , ... ω ⁰ _pi , ... ω ⁰ _{p N} , according to the position of the maxima of the amplitude-frequency spectrum S (u), generate multifrequency signal, consisting of N signals with frequency deviation, within the range of temperature variation of the resonant frequencies of the sensors ω ⁰ _p1 , ω ⁰ _p2 , ... ω ⁰ _pi , ... ω ⁰ _{p i} , which is fed to one of the inputs of the two-wire line , register the input alternating current I _in ( t ) of the two-wire line, calculate its amplitude-frequency spectrum S (ω), carry out the second measurement of the resonance frequencies of quartz piezoresonance sensors ω ^T _р1 , ω ^T _р2 , ... ω ^T _рi , ... ω ^T _рN according to the position of the maxima of the amplitude-frequency spectrum S (ω), based on which the desired temperature at the controlled points is determined according to the previously experimentally found or theoretically known dependences of the resonance frequency of quartz piezoresonance sensors on the temperature ω _рi ( t ).

Closest to the proposed device for measuring the spatial distribution of temperature and for implementing the proposed method is a device for measuring the spatial distribution of temperature (Patent RU (11) No. 2206878, published 20.06.2003, IPC G01K 7/00 (2000.01)), which contains N temperature-sensitive sensors, connected in parallel by a two-wire line connected to a recorder, which is connected to an alternating voltage source, and, as temperature-sensitive sensors, quartz piezoresonance sensors with different resonant frequencies ω _р1 , ω _р2 , ... ω _рi , ... ω _{рN are used} , as an alternating voltage source, a multifrequency signal generator is used, the recorder contains a series-connected matching circuit, an alternating current amplitude recorder, a spectrum analyzer, a processing and display unit, a processing and display unit is connected to a multifrequency signal generator

The main disadvantage of this method for measuring the spatial temperature distribution and the device for its implementation, selected as prototypes, is the need to place piezoresonance sensors directly into the measurement area, while the thermal distribution inside the research object near the temperature sensors can be distorted and introduce an error in the results of measuring the spatial temperature distribution ... In the proposed method of measurement, this disadvantage is absent, since the temperature-sensitive element is directly the element of the volume of the investigated object. Moreover, its electrophysical and thermosensitive characteristics depend only on the material of the research object and, as a consequence, this measurement method is a non-destructive measurement method.

The technical problem lies in the creation of a method for measuring the spatial distribution of temperature and devices for its implementation, which make it possible to measure the temperature distribution over the depth of the object of study.

The technical result in the proposed method for measuring the spatial distribution of temperature and the device for its implementation is the ability to measure the temperature distribution over the depth of the electrically conductive object of study.

The technical result in a method for measuring the spatial distribution of temperature, including the supply of a frequency-modulated electric current to the object under study in a frequency band, is achieved by the fact that a frequency-modulated electric current with a frequency band of ω _min ≤ ω ≤ ω _{max is supplied to the investigated conductive object through the surface electrodes} , where ω _min is the minimum frequency, ω _max is the maximum frequency, thereby forming a skin layer of variable thickness δ, penetrating to a depth δ _min ≤ δ ≤ δ _{max of} the object under study, where δ _min is the minimum skin layer thickness corresponding to the frequency ω _max , δ _max is the maximum thickness of the skin layer corresponding to the frequency ω _min , the frequency characteristic of the impedance Z ( j ω) is measured in the frequency band ω _min ≤ ω ≤ ω _max , which is used to determine the distribution of electrical conductivity over the depth σ (δ) and according to the found distribution σ (δ) and according to the previously experimentally found or theoretically known dependences of the electric th conductivity of the material of the object of study on the temperature σ = f ( T ) is judged on the spatial distribution of temperature over the depth T (δ) in the object under study.

The technical result in a device for measuring the spatial distribution of temperature (for implementing the proposed method), containing a signal generator connected to the processing unit, is achieved by the fact that the signal generator is a signal generator with a frequency band ω _min ≤ ω ≤ ω _max , where ω _min is the minimum frequency, ω _max is the maximum frequency, the processing unit is the calculator of the frequency response of the impedance Z ( j ω), the output of the signal generator is the output for connection with the electrically conductive object under study using the first electrode, and the second input of the calculator of the frequency response of the impedance Z ( j ω) is an input for connection with an electrically conductive test object through a second electrode, the output of the calculator of the frequency response of the impedance Z ( j ω) is connected to the input of the calculator of the distribution of electrical conductivity σ (δ) and the spatial distribution of temperature T (δ).

Figure 1 shows a block diagram of a device for implementing a method for measuring the spatial distribution of temperature with an electrically conductive object of study.

FIG. 2 shows a functional diagram of the device, explaining the implementation of the method for measuring the spatial distribution of temperature in depth with a connected electrically conductive object of study.

FIG. 3 shows an equivalent electrical diagram of the representation of an electrically conductive research object based on A - matrices.

FIG. 4 shows the algorithm of the calculator of the distribution of electrical conductivity σ (δ) and the spatial distribution of temperature T (δ).

The block diagram of a device for implementing a method for measuring the spatial distribution of temperature with an electrically conductive object of study, shown in Fig. 1, includes: 1 - Signal generator, 2 - Object of study, 3 - First electrode, 4 - Calculator of the frequency response of the impedance Z ( j ω), 5 - Second electrode, 6 - Calculator of the distribution of electrical conductivity in depth σ (δ) and the spatial distribution of temperature T (δ).

The functional diagram of the device, explaining the implementation of the method for measuring the spatial distribution of temperature in depth, shown in Fig. 2, includes: 1 - Signal generator, 2 - Electrically conductive object of study connected to the measurement circuit 2 with a skin layer, 3 - First electrode, 4 - Calculator of the frequency characteristic of the impedance Z ( j ω). 5 - Second electrode, 6 - Calculator of the distribution of electrical conductivity in depth σ (δ) and the spatial distribution of temperature T (δ).

In an example of a specific implementation, the device for measuring the spatial distribution of temperature (for implementing the proposed method), shown in Fig. 1, 2 contains a signal generator 1 with a frequency band ω _min ≤ ω ≤ ω _max , where ω _min is the minimum frequency, ω _max is the maximum frequency, the output of the signal generator 1 is connected to an electrically conductive test object 2 shown in FIG. 3 in the form of an electrical circuit based on A - matrices, using the first electrode 3, and with the calculator of the frequency response of the impedance Z ( j ω) 4, the output of the signal generator 1 is also connected to the input of the calculator of the frequency response of the impedance Z ( j ω) 4, the second the input of which is connected to the electrically conductive test object 2 by means of the second electrode 5, the output of the calculator of the frequency characteristic of the impedance Z ( j ω) 4 is connected to the input of the calculator of the distribution of electrical conductivity σ (δ) and the spatial distribution of temperature T (δ) 6.

In the example of a particular implementation as the signal generator 1 can be used a standard high-frequency generator, e.g., RF generator Russian manufacture AKIP-3417, G4-194, and the like. As calculator frequency characteristic impedance Z (j ω) 4 may be used Illustrations impedance analyzers such as the Keysight E4990A impedance meter. As a calculator of the distribution of electrical conductivity σ (δ) and the spatial distribution of temperature T (δ) 6, a computer or a microcontroller with a program according to the algorithm shown in FIG. 4 can be used. The object of research can be any object or structure made of an electrically conductive material (metals, alloys, carbon fiber composites, etc.), in which it is necessary to measure or control the temperature profile over depth. For example, a structure made of alloy steel for argon welding or forging (forge) pressure welding, during which it is necessary to accurately control the temperature of the weld.

FIG. 3 shows an equivalent electrical diagram of a representation of an electrically conductive research object 2 based on A - matrices. The circuit contains a signal generator 1, which is connected with electrodes 3 and 5 to the object of study 2. When signals with a frequency of ω _min ≤ω≤ω _max in the object of research are sequentially formedN skin layers corresponding to frequencies ω _one, ω _2, ω _{3 ...} ω _N with thickness d _one ,d ₂ ,d ₃ , ...d _{N ...} with step Δδ

, (1)

, (1)

whereN - the required number of points for measuring the temperature profileT(δ). Within Δδ, eachith elementary section can be represented asRL- circuits represented in the diagram by resistorsR _i and inductancesL _i (Fig. 3), forming a resistive-inductiveRL-structure with distributed parameters. Resistanceith elementary section of the chain is equal to:

, (2)

, (2)

– удельная электропроводность материала i-го участка объекта исследования, зависящая от температуры T,

поперечное сечение элементарного участка, l – расстояние между электродами. Импеданс реактивной составляющей i-го участка равен:where

-material conductivityi-th section of the object of study, depending on the temperatureT,

cross-section of an elementary section,l - the distance between the electrodes. Reactive impedancei-th plot is equal to:

, (3)

, (3)

– индуктивность i-го слоя материала объекта,

- реактивное сопротивление индуктивной составляющей. where j is the imaginary unit,

Is the inductance of the i- th layer of the object material,

is the reactance of the inductive component.

The electrical circuit in Fig. 3. is a circuit with distributed parameters, in which for metal conductors [L.A. Weinstein Electromagnetic waves. M .: Radio and communication, 1990. - S. 94]

. (4)

... (4)

правая часть выражения (4) возрастает в

раз.For magnetic conductive materials with magnetic permeability

the right-hand side of expression (4) increases in

once.

схемы можно описать А-матрицей по формуле [Каганов З.Г. Электрические цепи с распределенными параметрами и цепные схемы. М.: Энергоатомиздат, 1990. – С. 25]Each i- th elementary section

schemes can be described by the A-matrix according to the formula [Kaganov Z.G. Distributed electrical circuits and chain diagrams. M .: Energoatomizdat, 1990. - S. 25]

всей цепи описывается как произведение всех матриц А _i Result matrix

the whole chain is described as the product of all matrices А _i

можно определить входной импеданс [Каганов З.Г. Электрические цепи с распределенными параметрами и цепные схемы. М.: Энергоатомиздат, 1990. – С. 24] по формулеFrom the elements of the resulting matrix

you can determine the input impedance [Kaganov ZG. Distributed electrical circuits and chain diagrams. M .: Energoatomizdat, 1990. - P. 24] according to the formula

- волновое сопротивлениеwhere

- wave impedance

индуктивность и сопротивление при однородном распределении температуры

которые находятся из формулы (6) и (7) при предварительном калибровочном измерении.Here

inductance and resistance with uniform temperature distribution

which are found from formulas (6) and (7) during preliminary calibration measurement.

электрическая проводимость меняется в соответствии с профилем температуры

, так как электропроводность металлов и других проводящих материалов всегда зависит от температуры. With an arbitrary distribution of temperature along the depth

electrical conductivity changes according to the temperature profile

, since the electrical conductivity of metals and other conductive materials is always temperature dependent.

, то удельная электропроводность материала объекта постоянна

по глубине. Следовательно, все матрицы одинаковы

и результирующая матрица цепи согласно (6) будет равна: In the case when the temperature in the object of measurement is constant along the depth

, then the specific conductivity of the object material is constant

in depth. Hence all matrices are the same

and the resulting chain matrix according to (6) will be equal to:

. (9)

... (nine)

глубина проникновения будет равна

и результирующая матрица цепи будет равна матрице

(фиг. 3).At maximum measurement frequency

penetration depth will be equal to

and the resulting chain matrix will be equal to the matrix

(Fig. 3).

. (10)

... (10)

результирующая матрица

цепи при глубине проникновения

будет равна произведению двух первых матрицAt a frequency

resulting matrix

chains at penetration depth

will be equal to the product of the first two matrices

(11)

(eleven)

будет равнаThen from this expression the matrix

will be equal

, (12)

, (12)

обратная матрица

.where

inverse matrix

...

и их элементы для частот ω _{N ,} ω _{N -1,} ω _{N -2…} ω ₁ в диапазоне частот от

до

и определить значения

и соответственно

по формуле (2) для различных глубин. Thus, it is possible to sequentially calculate all matrices from

and their elements for frequencies ω _{N ,} ω _{N -one,} ω _{N -2 ...} ω _one in the frequency range from

before

and determine the values

and correspondingly

according to formula (2) for different depths.

The penetration depth δ of an electric current with a frequency ω is proportional to

The lower the frequency u, the deeper the alternating current penetrates. For example, according to [Volin M.L. Parasitic processes in electronic equipment. Ed. 2nd revision, and add. M .: Radio i svyaz, 1981. - P. 65] for frequencies of 100 Hz and 10 MHz, the thickness of the skin layer d for various metals is different and, accordingly, for copper is 6.6 mm and 0.02 mm, for aluminum - 8, 5 mm and 0.025 mm, for various grades of steel - roughly lies in the range from 1 mm to 0.002 mm. If you take a measurement onN frequencies ω _one ,ω ₂ ,ω ₃ ...ω _N , then the depth of penetration into the electrically conductive material of the object will be equal to δ _one ,δ ₂ , δ δ ₃ ...δ _N ... Choosing the required frequency step Δω, it is possible to achieve the required spatial resolution Δδ of temperature profile measurementsT(δ). An estimate of the spatial resolution can be obtained as a total differential from the relation (13):

будет равноThen the required number of measurement points with a given spatial resolution

will be equal

– максимальная толщина скин слоя на минимальной частоте

. Для постоянства разрешающей способности

=const необходимо частоту ω _i и переменный шаг по частоте

выбирать из соотношений:where

- maximum skin layer thickness at minimum frequency

... For consistent resolution

= const necessary frequency ω _i and variable frequency step

choose from the ratios:

FIG. 4 shows the algorithm of the calculator of the electrical conductivity σ (δ) and the spatial distribution of temperatureT(δ) 6. It realizes the calculation of the distribution over the depth δ of the electrical conductivity σ (δ) and temperatureT(δ) according to the measured frequency characteristic of the impedance Z (jω) 4. The first function of this algorithm is to read the impedance Z (jω) from the calculator of the frequency response of impedance 4. Next, the values of frequencies ω _one, ω _2, ω _{3 ...} ω _N in such a way that, according to (15), (16), (17), the thicknesses of the corresponding skin layers are multiples of Δδ_, 2Δδ, 3Δδ, ... NΔδ _... Next, the values of the elements are calculatedBUT _eleven, BUT _21, BUT _12, BUT _22. matricesA _one the first element of the structure at frequencies ω _N ... Then, one calculates sequentially
BUT _one, BUT _2, BUT ₃ … BUT _N - matrix of the structure of the research object 2. In the calculation of eachA _i element, the value of the matrix of the previousA _{i -one} element. Next, the conductivity σ _i skin layer Δδ _i from elementR _i matricesA _i ...Then, using the found values of σ _i and the known dependence σ= f(T). electrical conductivity from temperature the temperature distribution is calculatedT(δ _i ). For a visual display of the dependence of temperature over depth, a graphical representation is offered.

Consider the implementation of the proposed method for measuring the spatial distribution of temperature using a device for its implementation, the block diagram of which is shown in Fig. 1. The calculator of the distribution of electrical conductivity σ (δ) and the spatial distribution of temperature T (δ) 6 operates according to the operation algorithm shown in FIG. 4. A method for measuring the spatial distribution of temperature is that a frequency-modulated electric current with a frequency band ω _min ≤ ω ≤ ω _max , where ω _min is the minimum frequency, ω _max is the maximum frequency, thereby forming a skin layer of variable thickness δ, penetrating to a depth δ _min ≤ δ ≤ δ _{max of} the object under study, where δ _min is the minimum skin layer thickness corresponding to the frequency ω _max , δ _max is the maximum skin layer thickness corresponding to the frequency ω _min . Further, measured by calculating the frequency characteristic of the impedance Z (j ω) 4, in which the input signal from the electrically conductive test object 2 by a second electrode 5 in the frequency band ω _min ≤ ω ≤ ω _max frequency characteristic impedance Z (j ω). Further, using it, using the calculator of the distribution of the specific electrical conductivity σ (δ) and the spatial distribution of temperature T (δ) 6, the distribution of the electrical conductivity over the depth σ (δ) and the distribution of σ (δ) and the previously experimentally found or theoretically the known dependences of the electrical conductivity of the material of the object of study on the temperature σ = f ( T ) are judged on the spatial distribution of the temperature T (δ) in the object under study.

. Суть эффекта заключается в оттеснении протекающего электрического тока проводника и, как следствие, зависимость его импеданса

от частоты

Consider the implementation of the proposed method for measuring the spatial distribution of temperature over depth. The solution to this problem is possible using a well-known physical effect - the appearance of a skin layer in the surface layer of a conductor when passing an alternating current of high frequency

... The essence of the effect is to push back the flowing electric current of the conductor and, as a consequence, the dependence of its impedance

from frequency

(18)

(18)

– комплексное значение напряжения,

– комплексное значение тока. Толщина скин-слоя δ является функцией частоты

и уменьшается с ее повышением по выражению:where

- complex voltage value,

- complex value of the current. Skin thickness δ is a function of frequency

and decreases with its increase in expression:

, (19)

, (nineteen)

– угловая частота. Таким образом, подбирая частоту

переменного тока, можно сформировать практически любую толщину δ скин-слоя, необходимую для зондирования глубинных электрических параметров материала. where y is the specific electrical conductivity of the material, µ is the relative magnetic permeability of the substance, µ ₀ is the magnetic constant,

- angular frequency. Thus, choosing the frequency

alternating current, it is possible to form practically any thickness δ of the skin layer necessary for sounding the deep electrical parameters of the material.

определяют распределение температуры T(д) по глубине д. Для металлов и сплавов зависимость удельного сопротивления от температуры

, как правило, является линейной и выражается формулой:According to the theoretically known dependences of the electrical conductivity of the material of the research object on the temperature σ= f(T) [Handbook of electrical materials / Ed. Yu.V. Koritsky, V.V. Pasynkova, B.M. Tareeva. - M .: Energoizdat, 1988.v.3. - C.239-289.] According to the found distribution of conductivity

determine the temperature distributionT(d) in depth d...For metals and alloys, the dependence of the resistivity on temperature

is usually linear and expressed by the formula:

(20)

(twenty)

– удельное сопротивление материала при температуре

, α - температурный коэффициент сопротивления материала. Следовательно, температуру T _i каждого i-го слоя (i=1,2,3…N) можно определить по электропроводности

из формулыwhere

- material resistivity at temperature

, α is the temperature coefficient of material resistance. Therefore, the temperatureT _i of eachi-thlayer (i = 1,2,3 ... N) can be determined by electrical conductivity

from the formula

(21)

(21)

- известная электропроводность материала объекта при температуре

.where

- known electrical conductivity of the object material at temperature

...

Substituting in (21) the value of electrical conductivity found according to the above algorithm, the temperature at the depth T _{i is} calculated.

The value of the temperature coefficient of resistance α for an unknown material can be determined experimentally using formula (21) or other known methods.

Compared with the prototype in the proposed technical solutions in the method of measuring the spatial distribution of temperature and the device for its implementation, the technical result will be achieved due to the fact that a frequency-modulated electric current with a frequency band of ω _min ≤ω≤ω is supplied to the investigated conductive object through the surface electrodes _max , where ω _min is the minimum frequency, ω _max is the maximum frequency, thus forming a skin layer of variable thickness δ, penetrating to a depth δ _min ≤ _{δ ≤ δ max of} the object under study, where δ _min is the minimum skin layer thickness corresponding to the frequency ω _max , δ _max - the maximum thickness of the skin layer, corresponding to the frequency ω _min , is measured in the frequency band ω _min ≤ _{ω ≤ ω max, the} frequency characteristic of the impedance Z ( j ω), which determines the distribution of electrical conductivity in depth σ (δ) , and according to the found distribution σ (δ) and according to previously experimentally found or theoretically known dependences of the electric the conductivity of the material of the object under study on the temperature σ = f ( T ) is judged on the spatial distribution of temperature over the depth T (δ) in the object under study. And in the device for implementing the proposed method due to the fact that the signal generator is a signal generator with a frequency band ω _min ≤ _{ω ≤ ω max} , where ω _min is the minimum frequency, ω _max is the maximum frequency, the processing unit is the calculator of the frequency response of the impedance Z ( j ω), the output of the signal generator is the output for connection with the electrically conductive test object using the first electrode, and the second input of the calculator of the frequency response of the impedance Z ( j ω) is the input for connection with the electrically conductive test object through the second electrode, the output of the calculator of the frequency response of the impedance Z ( j ω) is connected to the input of the calculator of the distribution of electrical conductivity σ (δ) and the spatial distribution of temperature T (δ).

Claims (2)

1. A method for measuring the spatial distribution of temperature, including supplying a frequency-modulated electric current to the object under study in a frequency band, characterized in that a frequency-modulated electric current with a frequency band ω _min ≤ _{ω ≤ ω max is} supplied to the investigated electrically conductive object through the surface electrodes, where ω _min is the minimum frequency, ω _max is the maximum frequency, thereby forming a skin layer of variable thickness δ, penetrating to a depth δ _min ≤ _{δ ≤ δ max of} the object under study, where δ _min is the minimum skin layer thickness corresponding to the frequency ω _max , δ _max - maximum thickness of the skin layer corresponding to the frequency ω _min, measured in the frequency band ω _min ≤ω≤ω _max frequency characteristic impedance Z (jω), using which the distribution of conductivity in the depth σ (δ), and the found distribution σ (δ) and according to the previously experimentally found or theoretically known dependences of the electrical conductivity of the object material studies on temperature σ = f (T) judge the spatial distribution of temperature over depth T (δ) in the object under study. 2. A device for implementing a method for measuring the spatial distribution of temperature according to claim 1, comprising a signal generator connected to a processing unit, characterized in that the signal generator is a signal generator with a frequency band ω _min ≤ _{ω ≤ ω max} , where ω _min is the minimum frequency , ω _max is the maximum frequency, the processing unit is the calculator of the frequency response of the impedance Z (jω), the output of the signal generator is the output for connection with the electrically conductive object under study using the first electrode, and the second input of the calculator of the frequency response of the impedance Z (jω) is the input for connection with an electrically conductive test object through the second electrode, the output of the calculator of the frequency characteristic of the impedance Z (jω) is connected to the input of the calculator of the distribution of electrical conductivity σ (δ) and the spatial distribution of temperature T (δ).

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