CN100549684C - Image rebuilding method based on Square double mode self-calibration sensor - Google Patents

Abstract

The invention provides a kind of square double mode self-calibration sensor, the xsect of this sensor includes three layers, layer structure has been the metal tube layer of the fixing and shielding action of structure, and interlayer structure is an insulating material layer, and the endothecium structure layer is attached to a plurality of electrodes on the insulation course; Described electrode is distributed on the same cross section according to certain rules, and described electrode is distributed on the same cross section according to certain rules, and the interval of adjacent electrode is not equidistant.Two kinds of image rebuilding methods based on this sensor are provided simultaneously.Beneficial effect is at square measured zone, and this double mode electric imaging system sensor has been expanded measurement range, can measure cross section difference/encourage nonsynchronous object, has from the character of demarcating.Adopt multiple incentive mode, realize synchronous co-located measurement, the real part and the imaginary part information of the electrical impedance distribution of measuring the cross section are merged mutually, simplified the design and the realization of bimodal measuring system software and hardware.

Description

Image rebuilding method based on square double mode self-calibration sensor

Technical field

The present invention relates to a kind of detection means and application thereof, particularly is that a kind of square double mode self-calibration sensor reaches the image rebuilding method based on this sensor.

Background technology

Electrical impedance tomography technology (Electrical Impedance Tomography--EIT) is the visualisation parameters detection technique of a kind of polyphasic flow of getting up of development in recent years.For realizing visualization measurement, the core component of total system is an impedance transducer, obtains the impedance information of medium on the tube section by it, and then realizes parameter detecting with forms such as tomographies.

At present, be the EIT system sensor that commercial Application designs, mostly be the metering system of single mode.According to the difference of obtaining measurement parameter character, can be divided into Electrical Resistance Tomography (Electrical Resistance Tomography-ERT) and capacitance chromatography imaging (Electrical Capacitance Tomography-ECT).

The ERT system, be mainly used in measured resistivity/distribution of conductivity, its electrode generally contacts with measured matter, non-conductive material composition more for a long time in being studied object, potential electrode contacts with electron opaque material, cause potential electrode floating empty, thereby cause the resistance/conductance metering circuit saturated easily, limited measurement range and the precision of ERT.For this reason, adopt inwall to increase the way of conducting ring in the patent (US2004130338-A1), make potential electrode by conducting ring and measured matter indirect contact, thereby solved the floating empty problem of potential electrode, sensitive the uniformity coefficient and the signal to noise ratio (S/N ratio) of measurement are made moderate progress, but make the same section gauge of imaginary part difficult more, be unfavorable for the synchro measure of impedance information actual situation portion.

The ECT system, be mainly used in and measure permittivity (specific inductive capacity) distribution, its electrode generally is disposed on the Insulating frame (as patent: US5130661-A, US5291791-A, patent: CN01229907, " a kind of square capacitance chromatographic imaging sensor ", application number is that 01112515.2 denomination of invention is " a capacitance chromatography imaging measuring system "), do not contact with measured matter, sensitivity profile is under some influence, and when being studied in the object conductive materials composition more for a long time, measured signal is very big, thereby cause anti-stray capacitance metering circuit saturated easily, limited measurement range and the precision of ECT.

At present EIT sensor (as patent: ERT/ECT bimodal imaging system composite array sensor, application number: 200510122587.4), impedance real part and imaginary part information are detected respectively by electric resistance sensor and capacitive transducer and obtain, to realize the information extraction of impedance actual situation portion.But,, need take the timesharing incentive measure to avoid two kinds of coupling effects between the exciting field owing to there are two kinds of sensors, it or not synchronous co-located measurement truly, and make hardware circuit complicated, and introduce unnecessary error, also be unfavorable for the fusion of impedance actual situation portion information.Measure for realizing impedance actual situation portion information synchronous co-located truly, (the double mode electric imaging system sensor reaches the image rebuilding method based on this sensor to patent, application number: 200610013339.0) provided on the same electrode of round section sensor the sensor design scheme that co-located synchronously records impedance information, but also only at the sensor of round section.

EIT sensor in the industry at present is mostly at circular pipe, and cross sectional shape is designed to circle mostly.But, can often run into square measured zone, as recirculating fluidized bed in practical application.Before the present invention, the ECT sensor that square measured zone adopts can't realize that still the synchro measure of actual situation portion information is (as patent CN01229907, denomination of invention be " a kind of square capacitance chromatographic imaging sensor), limited the application in the Dual-Phrase Distribution of Gas olid with certain humidity is measured of EIT technology.And the sensor before the present invention does not all have the computable even corresponding measured value that distributes, thereby does not have from the function of demarcating.

Summary of the invention

The objective of the invention is at the square-section pipeline, provide a kind of square double mode self-calibration sensor and based on the image rebuilding method of this sensor, be beneficial to realize obtaining of impedance information, the real part of medium distribution of impedance and imaginary part information on the same tube section of synchronization gain, and then simplify the design of hardware and software of electric impedance imaging system, expansion measurement range greatly; And based on the analytic model of this sensor, provide it and can provide a kind of pattern of voltage drive flexibly and corresponding sensitive field distribution expression formula simultaneously for from the calculated value of demarcating, provide two kinds of quick image reconstruction methods at last.

For achieving the above object, the technical solution used in the present invention provides two kinds of image rebuilding methods based on square double mode self-calibration sensor:

A kind of image rebuilding method based on square double mode self-calibration sensor,

This method realizes by square double mode self-calibration sensor, the xsect of described sensor includes three-decker, layer structure has been the metal tube layer 1 of the fixing and shielding action of structure, and interlayer structure is an insulating material layer 2, and endothecium structure layer 3 is attached to a plurality of electrodes on the insulation course 2; Described insulating material layer 2 thickness are less than 3% of described thickness of electrode, and electric field intensity is less than the disruptive strength of insulating material layer 2 between assurance electrode and the metal tube layer 1, described electrode is distributed on the same cross section according to certain rules, the position of electrode and size are by calculating, and the interval of adjacent electrode is not equidistant;

The step of this method is as follows:

A. be the square impedance transducer of N for the potential electrode number, the pass that driving voltage distributes on voltage distribution and the sensor electrode array in the corresponding circular tube section is:

In the formula: Re[] represent to get real, i is an imaginary unit, V _kThe amplitude of representing k the voltage on the electrode, S _kRepresent the arc length that k electrode pair answered,

Be a holomorphic function, the real part of f (z)

The voltage of expression tube section distributes, the electric force lines distribution of imaginary part ψ (z) expression tube section;

Change the driving voltage on each electrode, can access multiple incentive mode, the voltage in the corresponding multiple tube section distributes; (scan round constitutes the j-by-j incentive mode for 1≤j≤N/2) apply ac-excited voltage synchronously on the individual adjacent electrode, the equal ground connection of remaining electrode at j;

B. for k electrode, two angles of circumference establishing the corresponding circular tube section in its border are respectively α and β, then basis:

Wherein, R is corresponding circular tube section radius, and v is corresponding circular tube section medium when evenly distributing, corresponding conductivity or electric permittivity epsilon or complex impedance rate; S _kRepresent the arc length that k electrode pair answered, M _kIt is the measured value that obtains on k the electrode;

According to M _kExpression formula, calculate rectangular tube cross section medium when evenly distributing, capacitance and electric conductivity value on k electrode;

C. based on the j-by-j incentive mode, calculate responsive, promptly the sensitivity coefficient of any point real part of impedance and imaginary part is in the round tube cross section:

M _mWhen being n electrode excitation, the capacitance or the electric conductivity value that record on m electrode, M _nWhen being m electrode excitation, the capacitance or the electric conductivity value that record on n electrode are convenience of calculation, S _{M, n}Be reduced to:

In the formula, c is a real constant, makes c=1 in the calculating;

D. based on the j-by-j incentive mode, the S that calculates _{M, n}, pass through expression formula

Δv＝(S ^TS+μI) ^-1S ^TΔM

Calculate responsive, i.e. the electrical impedance change value of any point in the tube section, wherein, Δ v is the variable quantity of permittivity or conductivity; S=[S _{M, n}], promptly the element of the capable n row of the m of matrix S is S _{M, n}, matrix S ^TBe the transposition of matrix S, μ is a regularization parameter undetermined, and I is and matrix S ^TThe unit matrix of S same order, Δ M represent the capacitance of surveying or electric conductivity value and the tube section medium calculated value when evenly distributing poor;

E. with above-mentioned responsive, promptly the electrical impedance change value of any point is represented with the form of gray scale in the tube section, and arrives square region through conformal transformation, obtains the reconstructed image of the corresponding distribution of impedance that distributes of square-section measured value.

Another kind is realized by square double mode self-calibration sensor based on the image rebuilding method of square double mode self-calibration sensor, the xsect of described sensor includes three-decker, layer structure has been the metal tube layer 1 of the fixing and shielding action of structure, interlayer structure is an insulating material layer 2, and endothecium structure layer 3 is attached to a plurality of electrodes on the insulation course 2; Described insulating material layer 2 thickness are less than 3% of described thickness of electrode, and electric field intensity is less than the disruptive strength of insulating material layer 2 between assurance electrode and the metal tube layer 1, described electrode is distributed on the same cross section according to certain rules, the position of electrode and size are by calculating, and the interval of adjacent electrode is not equidistant;

The step of this method is as follows:

A. by conformal transformation, square or rectangle being transformed to border circular areas, is the square impedance transducer of N for the potential electrode number, and the pass that driving voltage distributes on voltage distribution and the sensor electrode array in the corresponding circular tube section is:

In the formula: Re[] represent to get real, i is an imaginary unit, V _kThe amplitude of representing k the voltage on the electrode, S _kRepresent the arc length that k electrode pair answered,

Be a holomorphic function, the real part of f (z) The voltage of expression tube section distributes, the electric force lines distribution of imaginary part ψ (z) expression tube section;

Change the driving voltage on each electrode, can access multiple incentive mode, the voltage in the corresponding multiple tube section distributes; (scan round constitutes the j-by-j incentive mode for 1≤j≤N/2) apply ac-excited voltage synchronously on the individual adjacent electrode, the equal ground connection of remaining electrode at j;

B. be the square impedance transducer of N for the potential electrode number, behind conformal transformation in the corresponding circle tube section voltage distribute with the sensor electrode array on the pass that distributes of driving voltage be

In the formula: Re[ ] represent to get real, i is an imaginary unit, V _kThe amplitude of representing k the voltage on the electrode, S _kRepresent the arc length that k electrode pair answered,

Be a holomorphic function, the real part of f (z)

The voltage of expression tube section distributes, the electric force lines distribution of imaginary part ψ (z) expression tube section;

Change the driving voltage on each electrode, can obtain multiple incentive mode, the multiple voltage in the respective tube cross section distributes;

C. for k electrode, by conformal transformation theoretical and

Wherein, R is corresponding circular tube section radius, and v is corresponding circular tube section medium when evenly distributing, corresponding conductivity or electric permittivity epsilon or complex impedance rate; s _kRepresent the arc length that k electrode pair answered, M _kIt is the measured value that obtains on k the electrode;

D. according to the expression formula of conformal transformation theory and line of electric force:

$z=\frac{R(e^{i{\mathrm{\θ}}_0}-e^{c+\mathrm{id}+i{\mathrm{\θ}}_1})}{e^{c+\mathrm{id}}-1}$

Wherein, R is corresponding circular tube section radius, and R is the tube section radius, and i is an imaginary unit, θ ₀And θ ₁Be the central angle that electrode both sides bound pair is answered, c is for waiting constant of line of electric force correspondence, and d is an adjustable parameter, calculates the projection domain that waits the line of electric force correspondence of square sensor;

E. the measured value that each electrode pair is answered is divided by with the corresponding calculated value that evenly distributes, and obtains corresponding ratio, according to corresponding ratio, changes the resistance value in the projection domain, obtains the reconstructed image of the corresponding distribution of impedance that distributes of measured value.

The invention has the beneficial effects as follows at square measured zone, this double mode electric imaging system sensor overcome traditional single Electrical Resistance Tomography narrow with the capacitance chromatography imaging range ratio, measure the cross section different/encourage nonsynchronous shortcoming, have from the character of demarcating.Adopt multiple incentive mode, realize synchronous co-located measurement, the real part and the imaginary part information of the electrical impedance distribution of measuring the cross section are merged mutually, make the design and the realization of bimodal measuring system software and hardware more succinct, thereby expanded measurement range and the measuring accuracy and the response speed of existing ERT and ECT system greatly.Therefore,, make up,, have following advantage as a kind of fluidized bed on-line measurement device than the ERT system of single mode or the multisensor of ECT system or two kinds of mode based on the electricity imaging of bimodal sensor:

1. combine the measurement advantage of resistance mode and two kinds of mode of electric capacity mode, measurement range is widened, belong to non-intrusion type measurement and cheap fast, be used in the Dual-Phrase Distribution of Gas olid measurement with certain humidity.

2. the excitation and the measurement synchronization of resistance mode and two kinds of mode of electric capacity mode are carried out, and the excitation electrical field boundary condition of the xsect of two kinds of mode correspondences is identical, satisfy identical measuring principle, Hardware Design that is adopted and software design are also basic identical, thereby make the bimodal Design of Measurement System and realize more succinct.

3. based on the analytic model of this sensor, can provide a kind of pattern of voltage drive flexibly and corresponding sensitive field, be the impedance real part of any point correspondence on the tube section and the uniform expression of imaginary part sensitivity profile, and the sensitive field distribution of traditional E RT and ECT system is inconsistent, sensitive uniform expression based on this sensor more helps the fusion of impedance real part and imaginary part information.Provide two kinds of fast imaging methods of realizing measuring the cross section species distribution at last, realize electrical impedance tomography.

Description of drawings

Fig. 1 is a sensor construction sectional view of the present invention;

Fig. 2 is a sensor construction sectional view of the present invention;

Fig. 3 is the design sketch that concerns of sensor construction of the present invention cross section and round section;

Fig. 4 is based on the lucky big vast promise husband regularized image method for reconstructing of sensor of the present invention image reconstruction design sketch to circulation;

Fig. 5 is based on back projection's image rebuilding method of sensor of the present invention image reconstruction design sketch to semicanal stream.

Among the figure:

1, metal tube layer 2, insulating material layer

3, electrode 4, realization impedance measurement electrode array

5, the guard electrode array that has measurement of correlation data acquisition effect

Embodiment

Reaching embodiment in conjunction with the accompanying drawings is illustrated the image rebuilding method that double mode electric imaging system sensor of the present invention reaches based on this sensor.

As Fig. 1, shown in 2, xsect at this double mode electric imaging system sensor, its structure is formed by three layers, the exterior layer structure is a metal tube layer 1, playing structure fixes and shielding action, interlayer structure is thin insulating material layer 2, its thickness is less than 3% of electrode size, and electric field intensity is less than the disruptive strength of insulating material layer 2 between assurance electrode and the metal tube layer 1, inner layer structure layer 3 is attached to a plurality of electrodes on the insulation course 2, electrode is distributed on the same cross section according to certain rules, and the position of electrode and size are by calculating, and the interval of adjacent electrode is also inequality.Described have two at least attached to the number of electrodes on the insulation course 2, when number of electrodes is two, can realize the measurement of square shaped tube section one dimension impedance information.

In longitudinal cross-section that should the double mode electric imaging system sensor; its structure is to arrange three less row electrod-arrays of separation; interval between electrod-array is less than 5% of the electrode longitudinal length; the electrod-array 4 in centre position is realized the impedance measurement in rectangular tube cross section; the two arrays of electrodes array 5 of two side positions is for having the guard electrode array of measurement of correlation data acquisition effect.In the longitudinal cross-section, its structure also can realize the function of impedance measurement if only arrange one group of electrod-array, can simplify hardware circuit design like this, but can reduce measuring accuracy, weakens measurement function.

This double mode electric imaging system sensor adopts the alternating voltage excitation, and measuring object is the electrical impedance distribution of tube section, comprises the electric permittivity distribution of tube section and the distribution of conductivity of tube section.Described electrode can be realized the synchro measure of electrical impedance real part and imaginary part, and provides responsive based on sensor model, i.e. the impedance image method for reconstructing of the sensitivity formula of tube section and tube section.

Two kinds of image rebuilding methods based on square double mode self-calibration sensor of the present invention are described as follows:

1, lucky big vast promise husband regularization method

The S that obtains based on the Model Calculation of sensor of the present invention _{M, n}, can provide lucky big vast promise husband regularization (Tikhonov regularization) method of image reconstruction, the formula of embodying is

Δv＝(S ^TS+μI) ^-1S ^TΔM

In the formula, Δ v is the variable quantity of permittivity or conductivity, S=[S _{M, n}], promptly the element of the capable n row of the m of matrix S is S _{M, n}, matrix S ^TBe the transposition of matrix S, μ is a regularization parameter undetermined, and I is and matrix S ^TThe unit matrix of S same order, Δ M represent the capacitance of surveying or electric conductivity value and the tube section medium calculated value when evenly distributing poor.

Concrete implementation procedure is:

A. be the square impedance transducer of N for the potential electrode number, the pass that driving voltage distributes on voltage distribution and the sensor electrode array in the corresponding circular tube section is

In the formula: Re[ ] represent to get real, i is an imaginary unit, V _kThe amplitude of representing k the voltage on the electrode, S _kRepresent the arc length that k electrode pair answered, Be a holomorphic function (holomorphic function), the real part of f (z)

The voltage of expression tube section distributes, the electric force lines distribution of imaginary part ψ (z) expression tube section.

Change the driving voltage on each electrode, can obtain multiple incentive mode, the voltage in the corresponding multiple tube section distributes; (scan round constitutes the j-by-j incentive mode for 1≤j≤N/2) apply ac-excited voltage synchronously on the individual adjacent electrode, the equal ground connection of remaining electrode at j.

B. for k electrode, establish the corresponding circular tube section in its border two angles of circumference be respectively α and β, then basis

In the formula, R is corresponding circular tube section radius, and v is corresponding circular tube section medium when evenly distributing, corresponding conductivity or electric permittivity epsilon or complex impedance rate, S _kRepresent the arc length that k electrode pair answered.

According to M _kExpression formula, calculate rectangular tube cross section medium when evenly distributing, capacitance and electric conductivity value on k electrode.

When c. the electrical impedance bimodal image rebuild to adopt 1-by-1 incentive mode (but or when exciting electrode and potential electrode reciprocity, can also be combination of electrodes), the general expression formula of sensitivity profile can be determined by following content.

For square sensor, during as if m electrode excitation, the voltage that generates on tube section is distributed as During n electrode excitation, the voltage that generates on tube section is distributed as

Then sensitive field distribution is satisfied in the rectangular tube cross section

Two formulas are subtracted each other

Because the voltage of exciting electrode is V, potential electrode ground connection, so

In the formula, v _mWhen being m electrode excitation, conductivity of any or permittivity in the rectangular tube cross section, v _nWhen being n electrode excitation, the conductivity or the permittivity of rectangular tube cross section same point; M _mWhen being n electrode excitation, the capacitance or the electric conductivity value that on m electrode, record, M _nWhen being m electrode excitation, the capacitance or the electric conductivity value that on n electrode, record.Thereby the real part of a certain point impedance and the sensitivity coefficient of imaginary part can be unified to be expressed as in responsive (rectangular tube cross section)

Be convenience of calculation, S _{M, n}Can be reduced to

In the formula, c is a constant, and can think does not influence calculating by c=1.S _{M, n}Can obtain by conformal transformation by the Potential Distributing expression formula that reaches in the circle territory.

To instead in the result that border circular areas obtains shift square region onto, thereby obtain corresponding electric capacity/electric conductivity value on the size of electrode of square-section sensor correspondence and the potential electrode, and corresponding sensitivity profile.

The analytic model of sensor according to the present invention, for initial distribution based on even permittivity/distribution of conductivity field, m electrode and n electrode excitation, one as exciting electrode, and one as potential electrode, and pairing sensitivity coefficient can be described as

In the formula, θ _0mAnd θ _1mBe the central angle starting point and the terminal point of m the electrode pair border circular areas of answering, θ _0nAnd θ _1nBe central angle starting point and the terminal point that n electrode pair answered border circular areas, the following formula computing is an inner product operation.

According to electric capacity/electric conductivity value corresponding on the potential electrode that calculates, can demarcate sensor, can realize image reconstruction by obtaining corresponding sensitivity profile.

D. based on the j-by-j incentive mode, the S that calculates _{M, n}, pass through expression formula

Δv＝(S ^TS+μI) ^-1S ^TΔM

Calculate responsive, i.e. the electrical impedance change value of any point in the tube section, in the formula, Δ v is the variable quantity of permittivity or conductivity; S=[S _{M, n}], promptly the element of the capable n row of the m of matrix S is S _{M, n}, matrix S ^TBe the transposition of matrix S, μ is a regularization parameter undetermined, and I is and matrix S ^TThe unit matrix of S same order, Δ M represent the capacitance of surveying or electric conductivity value and the tube section medium calculated value when evenly distributing poor.

E. with above-mentioned responsive, promptly the electrical impedance change value of any point is represented with the form of gray scale in the tube section, and arrives square region through conformal transformation, obtains the reconstructed image of the corresponding distribution of impedance that distributes of square-section measured value.

2. wait the line of electric force back projection method

At first, by conformal transformation, square or rectangle are transformed to border circular areas, then basis

For the arbitrary excitation pattern.Can calculate the electric force lines distribution in sensor respective tube cross section, and then can obtain the respective projection territory, obtaining can be by the back projection method such as line of electric force such as grade of elementary function analytic expression calculating.Than the projecting method that adopts numerical solution to realize traditionally, the projection domain of using in this method is obtained by the elementary function analytical expression.As to the j-by-j incentive mode, be studied the corresponding expression formula shape of waiting line of electric force in zone as

$z=\frac{R(e^{i{\mathrm{\θ}}_0}-e^{c+\mathrm{id}+i{\mathrm{\θ}}_1})}{e^{c+\mathrm{id}}-1},$

In the formula, R is corresponding circular tube section radius, and i is an imaginary unit, θ ₀And θ ₁Be the central angle that electrode both sides bound pair is answered, c is for waiting constant of line of electric force correspondence, and d is an adjustable parameter.

Then, by conformal transformation obtain corresponding square region etc. electric force lines distribution.

Based on back projection's image rebuilding method of this sensor, the step of this method is:

A. by conformal transformation, square or rectangle are transformed to border circular areas.

B. be the square impedance transducer of N for the potential electrode number, behind conformal transformation in the corresponding circle tube section voltage distribute with the sensor electrode array on the pass that distributes of driving voltage be

In the formula: Re[] represent to get real, i is an imaginary unit, V _kThe amplitude of representing k the voltage on the electrode, S _kRepresent the arc length that k electrode pair answered,

Be a holomorphic function, the real part of f (z)

The voltage of expression tube section distributes, the electric force lines distribution of imaginary part ψ (z) expression tube section.

Change the driving voltage on each electrode, can obtain multiple incentive mode, the multiple voltage in the respective tube cross section distributes.

C. for k electrode, by conformal transformation theoretical and

In the formula: R is the tube section radius, when v is evenly distribution for the tube section medium, and corresponding conductivity or electric permittivity epsilon.Calculate the tube section medium when evenly distributing, capacitance and electric conductivity value on k electrode.

D. according to conformal transformation theoretical and

$z=\frac{R(e^{i{\mathrm{\θ}}_0}-e^{c+\mathrm{id}+i{\mathrm{\θ}}_1})}{e^{c+\mathrm{id}}-1}$

In the formula: R is the tube section radius, and i is an imaginary unit, θ ₀And θ ₁Be the central angle that electrode both sides bound pair is answered, c is for waiting constant of line of electric force correspondence, and d is an adjustable parameter.

Calculate the projection domain that waits the line of electric force correspondence of square sensor.

E. the measured value that each electrode pair is answered is divided by with the corresponding calculated value that evenly distributes, and obtains corresponding ratio, according to corresponding ratio, changes the resistance value in the projection domain; Obtain the reconstructed image of the corresponding distribution of impedance that distributes of measured value.

The theoretical foundation of calculating in the above-mentioned image rebuilding method is

(1) Laplace's equation (Laplace equation)

In the formula: the conductivity (conductivity) or the permittivity (permittivity) of the position correspondence of the plural z=x+yi representative of v (z) representative.

(2) conformal transformation (conformal transformation) theory.

At first, by conformal transformation with the square or rectangular domain transformation to border circular areas, as Fig. 3.The conformal transformation of corresponding square area, expression-form is

$w=\frac{\mathrm{sn}(\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="C20071005716600201.png"\; state="\{\{state\}\}">z</figure-callout>}\sqrt{2},k)}{\sqrt{2}\mathrm{dn}(\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="C20071005716600201.png"\; state="\{\{state\}\}">z</figure-callout>}\sqrt{2},k)}$

In the formula: w is the coordinate of border circular areas correspondence, and z is the coordinate of square area correspondence, $k=\frac{1}{\sqrt{2}}.$ Sn () and dn () are elliptic function.

The conformal transformation of corresponding rectangular region, expression-form is

$w=\frac{a-\mathrm{sn}(z,k)}{\stackrel{\&OverBar;}{a}-\mathrm{sn}(z,k)}$

In the formula: w is the coordinate of border circular areas correspondence, and z is the coordinate of rectangular region correspondence, and k is determined that by rectangular size sn () is an elliptic function, and a and a be conjugation each other.

Consider the border circular areas that square region obtains behind conformal transformation, setting v (z) is a constant at whole tube section, according to the Poisson formula of Laplace's equation at border circular areas:

The size of design electrode, and the Electric Field Distribution of correspondence when calculating even thing field distribution.Wherein f (z) is a holomorphic function (holomorphic function), its real part

The voltage in expression round tube cross section distributes, the electric force lines distribution in imaginary part ψ (z) expression round tube cross section.

For the square impedance transducer that constitutes by N electrode, be example with N=16, the amplitude of the voltage on k electrode is V _k(k=1,2,3 ..., 16), its voltage on corresponding circular tube section behind the conformal transformation then

Distribution can be expressed as

In the formula: Re[ ] expression gets real, S _kThe arc length of expression electrode k correspondence, according to

For k electrode, establish its border correspondence two angles of circumference be respectively α and β, then corresponding measured value is on this electrode

$=v\left|\mathrm{Im}\right[\frac{\log \left(\frac{{\mathrm{Re}}^{\mathrm{i\&beta;}}-{\mathrm{Re}}^{i{\mathrm{\&theta;}}_1}}{{\mathrm{Re}}^{\mathrm{i\&beta;}}-{\mathrm{Re}}^{i{\mathrm{\&theta;}}_0}}\right)-\log \left(\frac{{\mathrm{Re}}^{\mathrm{i\&alpha;}}-{\mathrm{Re}}^{i{\mathrm{\&theta;}}_1}}{{\mathrm{Re}}^{\mathrm{i\&alpha;}}-{\mathrm{Re}}^{i{\mathrm{\&theta;}}_0}}\right)}{\mathrm{\&pi;i}}\left]\right|$

$=\frac{v}{\mathrm{\&pi;}}\left|\mathrm{Re}\right[\log \left(\frac{e^{\mathrm{i\&beta;}}-e^{i{\mathrm{\&theta;}}_1}}{e^{\mathrm{i\&beta;}}-e^{i{\mathrm{\&theta;}}_0}}\right)-\log \left(\frac{e^{\mathrm{i\&alpha;}}-e^{i{\mathrm{\&theta;}}_1}}{e^{\mathrm{i\&alpha;}}-e^{i{\mathrm{\&theta;}}_0}}\right)\left]\right|$

For equally distributed thing field, M _kCan directly be calculated by following formula, according to conformal transformation character, corresponding square sensor has computable standard value, and because square sensor is more easily processed, guarantees machining precision easily, thereby sensor has from the function of demarcating.

For arbitrary potential electrode, the arc length of establishing its border circular areas correspondence behind conformal transformation is s, the capacitance that obtains, and promptly the expression formula of the imaginary part eigenwert of electrical impedance is

For arbitrary potential electrode, the arc length of establishing its border circular areas correspondence behind conformal transformation is s, the electric conductivity value that obtains, and promptly the expression formula of the real part eigenwert of electrical impedance is

Thereby for arbitrary potential electrode, the arc length of establishing its border circular areas correspondence behind conformal transformation is s, and the real part and the imaginary part of corresponding electrical impedance can be provided by unified measured value expression formula M

In the formula: V is measured interelectrode electric potential difference.When v (z)=ε (z), measured value M=C; When v (z)=σ (z), measured value M=G; Can also make v (z)=σ (z)+j ω ε (z), unify to handle as the complex impedance rate, processing mode belongs in the protection domain of the present invention.So by the analysis to measured value expression formula M, this sensor has two kinds of anti-mode of synchronous co-located measuring resistance, the i.e. function of resistance mode and electric capacity mode.

With 16 electrode sensors is example, owing to the voltage on 16 electrodes is respectively V _k(k=1,2,3 ..., 16) and value arbitrarily, therefore,, can provide N/2 kind typical case incentive mode at least for sensor with N electrode structure.

One 16 electrode sensor has 8 kinds of typical incentive modes, i.e. 1-by-1 pattern, 2-by-2 pattern, 3-by-3 pattern, 4-by-4 pattern, 5-by-5 pattern, 6-by-6 pattern, 7-by-7 pattern, 8-by-8 pattern.

The specific implementation method of j-by-j (1≤j≤8) incentive mode is:

Single pass comprises 16 actions.In the 1st step, electrode 1 to j applies the alternating voltage that amplitude is V, the equal ground connection of all the other 16-j electrode on j electrode altogether synchronously; The 2nd step, the first step, electrode 2 to j+1 applies the alternating voltage that amplitude is V, the equal ground connection of all the other 16-j electrode on j electrode altogether synchronously; In the 3rd step, electrode 3 to j+2 applies the alternating voltage that amplitude is V, the equal ground connection of all the other 16-j electrode on j electrode altogether synchronously; By that analogy, in the 16th step, electrode 16 and electrode 1 to j-1 apply the alternating voltage that amplitude is V, the equal ground connection of all the other 16-j electrode on j electrode altogether synchronously.The independent measurement number of every kind of incentive mode correspondence is as following table

Incentive mode	The independent measurement number	Incentive mode	The independent measurement number
				1-by-1	16(16-1)/2＝120	5-by-5	16(16-5)/2＝88
2-by-2	16(16-2)/2＝112	6-by-6	16(16-6)/2＝80
				3-by-3	16(16-3)/2＝104	7-by-7	16(16-7)/2＝72
4-by-4	16(16-4)/2＝96	8-by-8	16(16-8)/2＝64

Consider the reciprocity effect, adopt above-mentioned incentive mode, the sensor that 16 electrodes constitute has 120 independent measurement numbers.Usually, for the sensor that N electrode constitutes, total N* (N-1)/2 an independent measurement number by voltage drive pattern flexibly, can be adjusted to satisfy the requirement of measuring accuracy or speed, adapts to the specific requirement of different application occasion.

Fig. 4 is based on the lucky big vast promise husband regularized image method for reconstructing of this sensor image reconstruction design sketch to circulation.Fig. 5 is based on back projection's image rebuilding method of this sensor image reconstruction design sketch to semicanal stream.As the result who schemes to rebuild shows, based on the image reconstruction algorithm of this sensor, can identify flow pattern preferably.

Circulation and semicanal stream are two kinds of typical two phase flow patterns, to having relatively high expectations of visualization measurement, so generally can be used as the tested object of image rebuilding method.Sensor-based back projection image rebuilding method, the visualization measurement of suitable circulation flow pattern; The big vast promise husband of sensor-based Ji regularization method is fit to the visualization measurement that semicanal flows flow pattern; Two kinds of image rebuilding methods, the visualization measurement of suitable different flow patterns can replenish mutually, learn from other's strong points to offset one's weaknesses respectively; And above two kinds of image rebuilding methods, it is sensor-based Ji big vast promise husband regularization method and based on sensor back projection image rebuilding method, all have advantages such as succinct, that calculated amount is little, robustness good, required storage space is little, being suitable for real-time online image reconstruction and hardware realizes, therefore, the ONLINE RECOGNITION and the visualization measurement that help high speed two-phase flow pattern.

More than to the description of the present invention and embodiment thereof, be not limited thereto, only be one of embodiments of the present invention shown in the accompanying drawing.Under the situation that does not break away from the invention aim,, all belong to protection domain of the present invention without creatively designing and similar structure of this technical scheme or embodiment.

Claims (2)

1, a kind of image rebuilding method based on square double mode self-calibration sensor, this method realizes by square double mode self-calibration sensor, the xsect of described sensor includes three-decker, layer structure has been the metal tube layer (1) of the fixing and shielding action of structure, interlayer structure is insulating material layer (2), and endothecium structure layer (3) is attached to a plurality of electrodes on the insulation course (2); Described insulating material layer (2) thickness is less than 3% of described thickness of electrode, and electric field intensity is less than the disruptive strength of insulating material layer (2) between assurance electrode and the metal tube layer (1), described electrode is distributed on the same cross section according to certain rules, the position of electrode and size are by calculating, and the interval of adjacent electrode is not equidistant;

The step of this method is as follows:

A. be the square impedance transducer of N for the potential electrode number, the pass that driving voltage distributes on voltage distribution and the sensor electrode array in the corresponding circular tube section is:

In the formula: Re[] represent to get real, i is an imaginary unit, V _kThe amplitude of representing k the voltage on the electrode, S _kRepresent the arc length that k electrode pair answered, Be a holomorphic function, the real part of f (z)

The voltage of expression tube section distributes, the electric force lines distribution of imaginary part ψ (z) expression tube section;

Change the driving voltage on each electrode, can access multiple incentive mode, the voltage in the corresponding multiple tube section distributes; (scan round constitutes the j-by-j incentive mode for 1≤j≤N/2) apply ac-excited voltage synchronously on the individual adjacent electrode, the equal ground connection of remaining electrode at j;

B. for k electrode, two angles of circumference establishing the corresponding circular tube section in its border are respectively α and β, then basis:

Wherein, R is corresponding circular tube section radius, and v is corresponding circular tube section medium when evenly distributing, corresponding conductivity or electric permittivity epsilon or complex impedance rate; S _kRepresent the arc length that k electrode pair answered, M _kIt is the measured value that obtains on k the electrode;

According to M _kExpression formula, calculate rectangular tube cross section medium when evenly distributing, capacitance and electric conductivity value on k electrode;

C. based on the j-by-j incentive mode, calculate responsive, promptly the sensitivity coefficient of any point real part of impedance and imaginary part is in the round tube cross section:

M _mWhen being n electrode excitation, the capacitance or the electric conductivity value that record on m electrode, M _nWhen being m electrode excitation, the capacitance or the electric conductivity value that record on n electrode are convenience of calculation, S _{M, n}Be reduced to:

In the formula, c is a real constant, makes c=1 in the calculating;

D. based on the j-by-j incentive mode, the S that calculates _{M, n}, pass through expression formula

Δv＝(S ^TS+μI) ^-1S ^TΔM

Calculate responsive, i.e. the electrical impedance change value of any point in the tube section, wherein, Δ v is the variable quantity of permittivity or conductivity; S=[S _{M, n}], promptly the element of the capable n row of the m of matrix S is S _{M, n}, matrix S ^TBe the transposition of matrix S, μ is a regularization parameter undetermined, and I is and matrix S ^TThe unit matrix of S same order, Δ M represent the capacitance of surveying or electric conductivity value and the tube section medium calculated value when evenly distributing poor;

E. with above-mentioned responsive, promptly the electrical impedance change value of any point is represented with the form of gray scale in the tube section, and arrives square region through conformal transformation, obtains the reconstructed image of the corresponding distribution of impedance that distributes of square-section measured value.

2, a kind of image rebuilding method based on square double mode self-calibration sensor, this method realizes by square double mode self-calibration sensor, the xsect of described sensor includes three-decker, layer structure has been the metal tube layer (1) of the fixing and shielding action of structure, interlayer structure is insulating material layer (2), and endothecium structure layer (3) is attached to a plurality of electrodes on the insulation course (2); Described insulating material layer (2) thickness is less than 3% of described thickness of electrode, and electric field intensity is less than the disruptive strength of insulating material layer (2) between assurance electrode and the metal tube layer (1), described electrode is distributed on the same cross section according to certain rules, the position of electrode and size are by calculating, and the interval of adjacent electrode is not equidistant;

The step of this method is as follows:

A. by conformal transformation, square or rectangle being transformed to border circular areas, is the square impedance transducer of N for the potential electrode number, and the pass that driving voltage distributes on voltage distribution and the sensor electrode array in the corresponding circular tube section is:

In the formula: Re[] represent to get real, i is an imaginary unit, V _kThe amplitude of representing k the voltage on the electrode, S _kRepresent the arc length that k electrode pair answered,

Be a holomorphic function, the real part of f (z)

The voltage of expression tube section distributes, the electric force lines distribution of imaginary part ψ (z) expression tube section;

Change the driving voltage on each electrode, can access multiple incentive mode, the voltage in the corresponding multiple tube section distributes; (scan round constitutes the j-by-j incentive mode for 1≤j≤N/2) apply ac-excited voltage synchronously on the individual adjacent electrode, the equal ground connection of remaining electrode at j;

B. be the square impedance transducer of N for the potential electrode number, behind conformal transformation in the corresponding circle tube section voltage distribute with the sensor electrode array on the pass that distributes of driving voltage be

In the formula: Re[ ] represent to get real, i is an imaginary unit, V _kThe amplitude of representing k the voltage on the electrode, S _kRepresent the arc length that k electrode pair answered,

Be a holomorphic function, the real part of f (z)

The voltage of expression tube section distributes, the electric force lines distribution of imaginary part ψ (z) expression tube section;

Change the driving voltage on each electrode, can obtain multiple incentive mode, the multiple voltage in the respective tube cross section distributes;

C. for k electrode, by conformal transformation theoretical and

Wherein, R is corresponding circular tube section radius, and v is corresponding circular tube section medium when evenly distributing, corresponding conductivity or electric permittivity epsilon or complex impedance rate; s _kRepresent the arc length that k electrode pair answered, M _kIt is the measured value that obtains on k the electrode;

D. according to the expression formula of conformal transformation theory and line of electric force:

$z=\frac{R(e^{{\mathrm{i\&theta;}}_0}-e^{c+\mathrm{id}+i{\mathrm{\&theta;}}_1})}{e^{c+\mathrm{id}}-1}$

Wherein, R is corresponding circular tube section radius, and R is the tube section radius, and i is an imaginary unit, θ ₀And θ ₁Be the central angle that electrode both sides bound pair is answered, c is for waiting constant of line of electric force correspondence, and d is an adjustable parameter, calculates the projection domain that waits the line of electric force correspondence of square sensor;

E. the measured value that each electrode pair is answered is divided by with the corresponding calculated value that evenly distributes, and obtains corresponding ratio, according to corresponding ratio, changes the resistance value in the projection domain, obtains the reconstructed image of the corresponding distribution of impedance that distributes of measured value.

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