CN104090164B - The measuring method of a kind of one-dimensional distribution of conductor conductivity based on compressed sensing principle and device - Google Patents
The measuring method of a kind of one-dimensional distribution of conductor conductivity based on compressed sensing principle and device Download PDFInfo
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Abstract
The present invention relates to measuring method and the device of a kind of one-dimensional distribution of conductor conductivity based on compressed sensing principle, the method includes: the surface of the programmable switch electrode band containing tens of to hundreds of programmable switch electrodes with conductor to be measured is fitted tightly by step one；Generate bernoulli stochastical sampling matrix by computer, from this matrix, take out row vector successively；Step 2 records the resistance value that in sampling matrix, different rows vector is corresponding, draws resistance sampling vector；Step 3 selects corresponding sparse transformation according to difference detection conductor, constitutes super complete dictionary；Step 4 utilizes recovery algorithms distribution one-dimensional to conductor resistance to be measured to rebuild, and utilizes resistivity computing formula to try to achieve the one-dimensional distribution of conductor resistance rate, more inverted obtains the one-dimensional distribution results of conductor conductivity.The present invention has measurement process simplicity, certainty of measurement is high and measures the advantages such as quick, it is adaptable to the upgrading to existing conductivity measuring apparatus.
Description
Technical field
The present invention relates to the measuring method of a kind of conductor conductivity, particularly relate to a kind of based on compressed sensing principle
The measuring method of the one-dimensional distribution of conductor conductivity and device.
Background technology
The measuring method of conductor conductivity has a wide range of applications, such as in each field of every profession and trade: water sample monitoring,
Soil analysis, the examination of materials etc..Along with the progress of science and technology, production to various products in modern industrial and agricultural production
Process has had higher performance and technology requirement, and this is accomplished by each factor of production link is carried out strict control
System.The measuring method of conductor conductivity is applicable to the inspection of conductive paper thickness evenness and measures, and pedotheque vertically divides
Cloth inspection is measured, and the inspection of wire resistance silk electrical conductivity is measured, and the inspection of insulating materials electrical conductivity is measured, electroconductive nylon
The fields such as electrical conductivity inspection measurement, but the measurement to conductor conductivity spatial distribution, yet there are no clearly, become
Ripe and concrete implementation method.
Chinese patent application 201010188421.3 proposes " a kind of conductivity of graphite measuring method and measurement dress
Put ", although the program have simple to operate, cost is relatively low and be applicable to various anisotropic material electrical conductivity survey
The advantage of amount, but there is also following obvious deficiency: one is that the electrical conductivity measuring N number of point must carry out n times measurement,
Its pendulous frequency is many, and the systematic measurement error brought is big；Two is to measure to be both needed to mobile micrometric displacement mobile device every time,
Not only waste the plenty of time, and conductor conductivity is closely related with the environmental factor such as temperature, humidity, because measuring
Environmental factor interference between time length meaning and repetitive measurement is big, will substantially increase single measurement error.
Chinese patent application 201210305745.X proposes one " triangular wave excitation the solution of Integral Processing
Conductivity measuring method and Key Circuit ", although the program has the elimination impact of distribution of electrodes electric capacity, elimination
The impact of certainty of measurement is improved the advantage measuring stability by randomness interference, but there is also following obvious deficiency:
One is to be only capable of measuring the electrical conductivity situation that solution is overall, it is impossible to the concrete distribution of conductivity situation measuring solution；Two
It it is the concrete spread condition that cannot measure solution concentration.
Known compressed sensing (compressed sensing is called for short CS) theory makes signals collecting breach Nai Kui
The restriction of this special sampling thheorem, it is proposed that as long as signal is compressible or is sparse at certain transform domain, that
Just can with one with conversion base incoherent observing matrix conversion gained height dimensional signal projected to one low
On dimension space, then by solve an optimization problem just can from the projection that these are a small amount of with high probability reconstruct
Go out original signal realizes principle.The survey of the one-dimensional distribution of conductor conductivity is carried out if, with compressed sensing principle
Amount, can be only by an electrical conductivity testing circuit, through repeatedly utilizing programmable switch group random combine to sample
Product are sampled, then are recovered by certain algorithm, quickly obtain conductor conductivity distribution results the most accurately.
But there is presently no to see utilizes compressed sensing principle to the method measuring the one-dimensional distribution of conductor conductivity.
In sum, the deficiencies in the prior art how are overcome to become in current conductor conductivity field of measuring technique
One of great difficult problem urgently to be resolved hurrily.
Summary of the invention
It is an object of the invention to the deficiency for overcoming prior art to exist and provide a kind of based on compressed sensing principle
The measuring method of the one-dimensional distribution of conductor conductivity and device, the present invention has that measurement process is easy, certainty of measurement
The advantages such as high and measurement is quick, it is adaptable to the upgrading to existing conductivity measuring apparatus.
Measurement side according to the one-dimensional distribution of a kind of based on compressed sensing principle conductor conductivity that the present invention proposes
Method, it is characterised in that comprise the following specific steps that:
Step one, leads the programmable switch electrode band containing tens of to hundreds of programmable switch electrodes with to be measured
The surface of body fits tightly；Generate bernoulli stochastical sampling matrix by computer, take out successively from this matrix
Row vector, then the control end by computer export row vector signal to programmable switch electrode band, control tens of extremely
The on off operating mode of hundreds of programmable switch electrodes, 0 pair of inductive switch Guan Bi, 1 correspondence switches off；
Step 2, accesses conductor two ends to be measured by the measurement electrode of electrical impedance tester, records in sampling matrix
The resistance value that different rows vector is corresponding, draws resistance sampling vector；
Step 3, selects corresponding sparse transformation according to difference detection conductor, constitutes super complete dictionary；
Step 4, utilizes recovery algorithms distribution one-dimensional to conductor resistance to be measured to rebuild, utilizes resistivity to calculate
Formula: ρ=RS/L, wherein: ρ be resistivity, R be resistance value, L be that the length of conductor to be measured, S are
Cross-sectional area, tries to achieve the one-dimensional distribution of conductor resistance rate, more inverted obtains the one-dimensional distribution results of conductor conductivity.
The further preferred version of measuring method of the present invention is:
By the programmable switch electrode containing tens of to hundreds of programmable switch electrodes described in step one of the present invention
Carry the surface with conductor to be measured to fit tightly, refer to that each programmable switch electrode is the most mutually gone here and there at one-dimensional square
Connection, and fit tightly with conductive surface to be measured, form Observable mask.
The structural formula generating bernoulli stochastical sampling matrix described in step one of the present invention is: matrix Φ ∈ RM×NShould
Each element of matrix obeys the bernoulli distribution of symmetry independently, it may be assumed that
Owing to only existing break-make two states in circuit, therefore above formula matrix can be reduced to:
Above formula ΦsIn every a line be considered as one group of dominant vector, computer is successively according to the row vector of this matrixOutput low and high level controls switch, 0 pair of inductive switch Guan Bi, the part measured conductor that i.e. this switch is corresponding
Being switched on and off short circuit, this part is not counted in the resistance of now gained；1 correspondence switches off, i.e. this part counts this
Time gained resistance.
Described in step 2 of the present invention, resistance sampling vector, refers to be obtained many by different rows vector correspondence in sampling matrix
Individual resistance sampling valueAgain by all ofIt is multiplied byIt is normalized, finally gives by M
The resistance sampling vector Y=[y that linear projection observed samples value is constituted1, y2..., yM]T∈RM；Wherein: when leading
The distribution of resistance of body is N-dimensional real signal X=[x1, x2..., xN]T∈RN, resistance sampling vector Y the most now
It is Y=Φ X for signal X being performed the result of a compression observation.
Sparse transformation described in step 3 of the present invention, refers to recover one-dimensional point of conductor resistance from resistance sampling vector Y
Cloth signal X, it is desirable to X is sparse vector or X is sparse in a transform domain.
Recovery algorithms described in step 4 of the present invention, refers to that recovering one-dimensional conductor resistance from resistance sampling vector Y divides
Cloth signal X is one and solves system of linear equations, sparse or compressible at conductor resistance one-dimensional distribution signal X
The underdetermined system of equations is solved under premise:
s.t.ACSΘ=Φ X=Y
Recovery algorithms described in step 4 of the present invention is base back tracking method, matching pursuit algorithm, orthogonal matching pursuit method or is total to
Yoke gradient method.
The one-dimensional distribution measurement method of a kind of based on compressed sensing principle conductor conductivity proposed according to the present invention
Device, it includes electrical impedance tester, it is characterised in that also include that electrical impedance tester is powered-down with programmable switch
Pole band and computer are sequentially connected with；Wherein: programmable switch electrode band includes tens of to hundreds of programmable switches
Electrode, control unit containing single-chip microcomputer and communication interface, and each programmable switch of programmable switch electrode band
Close electrode be upwards serially connected at one-dimensional square and fit tightly as Observable mask with conductive surface to be measured；Able to programme
Switch electrode band, control unit and communication interface are sequentially connected with；Described single-chip microcomputer is 51 single-chip microcomputers, msp430
Single-chip microcomputer or atmega single-chip microcomputer；Described computer is containing matlab software, C Plus Plus software or java
The computer of software.
The present invention compared with prior art its remarkable advantage is: one be the present invention be based on compressed sensing principle
The one-dimensional distribution measurement method of conductor conductivity created and device, it is only necessary to the measurement electrode of electrical impedance tester is connect
Enter conductor two ends to be measured, easy measurement reliably can be carried out, substantially reduce pendulous frequency, be less than or equal to
The 35% of existing pendulous frequency, i.e. 0.35 × n times can rebuild the one-dimensional distribution situation of electrical conductivity in high precision, reduce
The systematic error introduced during measuring, improves certainty of measurement；Two is that the present invention is based on compressed sensing principle
The measurement carried out not only number of times is few, and without mobile any device, measuring speed is fast, hence it is evident that reduces single and surveys
Amount error, provides guarantee for improving the measuring precision；Three is that the present invention can measure the whole of conductor conductivity
Body situation, can measure again the one-dimensional distribution spread condition of conductor conductivity, widen range of application.The present invention with
The comparing result of prior art measuring method and device refers to table 1.The present invention is widely used in existing electrical conductivity
The upgrading of measurement apparatus, is particularly well-suited to the measurement of the one-dimensional distribution situation of electrical conductivity of slender conductor.
Table 1: the present invention and prior art measuring method and the comparing result of device
Accompanying drawing explanation
Fig. 1 is the structural representation of the measurement apparatus that the present invention proposes.
Fig. 2 is the schematic diagram of bernoulli random matrix and the removing method of row vector.
Detailed description of the invention
With embodiment, the detailed description of the invention of the present invention is described in further detail below in conjunction with the accompanying drawings.
The measuring method of the one-dimensional distribution of a kind of based on compressed sensing principle conductor conductivity that the present invention proposes, main
Comprise the following specific steps that:
Step one, in conjunction with Fig. 1, by the programmable switch electrode containing tens of to hundreds of programmable switch electrodes
The surface with conductor to be measured is carried to fit tightly；In conjunction with Fig. 2, generate bernoulli stochastical sampling matrix by computer,
Row vector is taken out successively from this matrix, then by computer export row vector signal to programmable switch electrode band
Controlling end, control the on off operating mode of tens of to hundreds of programmable switch electrodes, 0 pair of inductive switch Guan Bi, 1 is right
Inductive switch disconnects；
Step 2, accesses conductor two ends to be measured by the measurement electrode of electrical impedance tester, records in sampling matrix
The resistance value that different rows vector is corresponding, draws resistance sampling vector；
Step 3, selects corresponding sparse transformation according to difference detection conductor, constitutes super complete dictionary；
Step 4, utilizes recovery algorithms distribution one-dimensional to conductor resistance to be measured to rebuild, utilizes resistivity to calculate
Formula: ρ=RS/L, wherein: ρ be resistivity, R be resistance, L be the length of conductor to be measured, S be horizontal stroke
Sectional area, tries to achieve the one-dimensional distribution of conductor resistance rate, more inverted obtains the one-dimensional distribution results of conductor conductivity.
In conjunction with Fig. 1, the one-dimensional distribution measuring of a kind of based on compressed sensing principle conductor conductivity that the present invention proposes
The device of method, it includes being sequentially connected with by electrical impedance tester, programmable switch electrode band and computer；Its
In: programmable switch electrode band includes tens of to hundreds of programmable switch electrodes, control list containing single-chip microcomputer
Unit and communication interface, and each programmable switch electrode of programmable switch electrode band the most mutually goes here and there at one-dimensional square
Connection also fits tightly as Observable mask with conductive surface to be measured；Programmable switch electrode band, control unit and logical
Letter interface is sequentially connected with；Described single-chip microcomputer is 51 single-chip microcomputers, msp430 single-chip microcomputer or atmega single-chip microcomputer；
Described computer is containing matlab software, C Plus Plus software or the computer of java software.
The specific embodiment of the present invention further explained below.
Embodiment 1, is applied to as a example by the one-dimensional distribution of electrical conductivity of measurement conductive paper by the present invention:
Measure purpose: measure the one-dimensional distribution situation of electrical conductivity of conductive paper, the uniform feelings of thickness of conductive paper can be reflected
Condition, with or without the production technology problem such as crack and impurity.
Measurement apparatus: the measurement apparatus of the present embodiment 1 include electrical impedance tester, programmable switch electrode band and
Computer is sequentially connected with, and wherein, electrical impedance tester uses Beijing perseverance Order instrument and meter Co., Ltd to produce
Permanent Order/HHY8-TA-901；Programmable switch electrode band includes 80 programmable switch electrodes, control units
And communication interface.Concrete assembling is upwards to be serially connected at one-dimensional square by 80 PLC technology switch electrodes,
It is spaced apart 1cm, controls switch by the control unit containing 51 single-chip microcomputers and open and close, and by communication
Interface with containmatlabThe computer of software carries out data communication, and this communication interface uses serial line interface.Survey
Amount sample: conductive paper, the eternally happy Electronics Factory in Guangdong produces, and composition is carbon black and paper pulp, and a size of 100cm (grows)
× 1cm (wide) × 0.2cm (thick).
Measuring method: the present invention is applied to measure the concrete steps of the one-dimensional distribution situation of electrical conductivity of conductive paper and includes
As follows:
Step one, fits tightly each electrode in programmable switch electrode band with conductive paper sample surfaces；Pass through
Computer generates bernoulli stochastical sampling matrix, takes out row vector from this matrix successively, then by computer export
Row vector signal, to the control end of programmable switch electrode band, controls the on off operating mode of programmable switch electrode, and 0
Closing inductive switch, 1 correspondence switches off, and forms Observable mask；Wherein:
The structural formula generating bernoulli stochastical sampling matrix is: matrix Φ ∈ RM×N, each element of this matrix is only
On the spot obey the bernoulli distribution of symmetry, it may be assumed that
Owing to only existing break-make two states in circuit, therefore above formula matrix can be reduced to:
Above formula ΦsIn every a line be considered as one group of dominant vector, computer is successively according to the row vector of this matrixSwitch to 51 Single-chip Controlling by serial line interface output low and high levelElectrode, 0 pair of inductive switch Guan Bi,
The part measured conductor that i.e. this switch is corresponding is switched on and off short circuit, and this part is not counted in the resistance of now gained；1 pair
Inductive switch disconnects, i.e. this part counts the resistance of now gained；
Need to further illustrate: wherein PLC technology number of switches N is the distribution of conductivity that can record
Highest resolution；Controlling switch on and off by M × N rank random matrix, M is the number of times (M of random measurement
< < N), the accuracy recovering signal increases with M and increases, and the N of the present embodiment 1 is 80, M selects 25.
Step 2, utilizes the electrical impedance tester accessing conductive paper sample two ends, records different rows in sampling matrix
The resistance value that vector is corresponding, draws resistance sampling vector；Wherein: described resistance sampling vector, refer to by sampling
In matrix, different rows vector correspondence obtains multiple resistance sampling valueAgain by all ofIt is multiplied by
It is normalized, finally gives the resistance sampling vector being made up of M linear projection observed samples value
Y=[y1, y2..., yM]T∈RM；Wherein: when the distribution of resistance of conductor is N-dimensional real signal
X=[x1, x2..., xN]T∈RN, resistance sampling vector Y the most now is signal X to perform a compression see
The result surveyed is Y=Φ X.
Step 3, selects wavelet transformation as the sparse transformation of distribution of resistance signal, constitutes super complete dictionary；Its
In: sparse transformation, refer to recover conductor resistance one-dimensional distribution signal X from resistance sampling vector Y, it is desirable to
X is sparse vector or X is sparse in a transform domain, it may be assumed that X available orthogonal base vector's
Linear combination formula represents:
Write as matrix form, can be obtained:
X=Ψ Θ
Wherein: Ψ=[ψ1, ψ2..., ψN]∈RN×N(Ψ Ψ is met for orthogonal basis dictionary matrixT=ΨTΨ=I), Θ
Θ is X projection coefficient in a sparse transform-domain, launches sparse coefficient vector Θ=[θ1, θ2..., θN]T；
In conjunction with the compression observation to signal X, note CS information operaor is ACS=Φ Ψ, can obtain:
Y=Φ X=Φ Ψ Θ=ACSΘ
Although recovering Θ from Y is also an ill-conditioning problem, but it is sparse for being because coefficient Θ, so unknown several
Number greatly reduces so that signal reconstruction is possibly realized；
Conventional rarefaction method also includes discrete cosine transform, DFT etc., due to Θ coefficient
Degree of rarefication is largely affected by final recovery effects.Therefore, in order to obtain best recovery effects, can root
Suitable sparse transformation is selected according to different conductors to be measured.
Step 4, is containingmatlabOn the computer of software, utilize recovery algorithms (specifically orthogonal matching pursuit
Method, i.e. OMP) distribution one-dimensional to conductive paper sample resistance rebuild, and utilizes resistivity computing formula to try to achieve
The one-dimensional distribution of conductor resistance rate, more inverted obtain the one-dimensional distribution results of conductivity；Wherein, at conductor electricity
Hinder one-dimensional distribution signal X sparse or compressible on the premise of, orthogonal matching pursuit method (OMP) is used for solving owes fixed
Equation group:
s.t.ACSΘ=Φ X=Y
From resistance sampling vector Y, i.e. recover distribution of resistance signal X；This resistivity computing formula: ρ=RS/L, its
In: ρ be resistivity, R be resistance, L be the length of conductor to be measured, S be cross-sectional area.
Conventional recovery algorithms, in addition to orthogonal matching pursuit method, also can use base back tracking method, matching pursuit algorithm or be total to
Yoke gradient method etc..
Finally calculating the one-dimensional distribution results of electrical conductivity of this sample, its average conductivity is 8.3349 × 10-4s
/m。
Embodiment 2, as a example by the present invention is applied to measure the distribution of electrical conductance of cable rate:
Measure purpose: measure resistance wire distribution of conductivity situation, can reflected resistance silk even thickness situation,
Oxidization condition, each point electrical conductivity the most all can be up to standard etc. problem.
Measurement apparatus: the measurement apparatus of the present embodiment 2 include electrical impedance tester, programmable switch electrode band and
Computer is sequentially connected with, and wherein, electrical impedance tester uses five and half desk-top universal meters of Fluke company
8840A；Programmable switch electrode band includes 240 programmable switch electrodes, control unit and communication interface.
Concrete assembling is upwards to be serially connected at one-dimensional square by 240 PLC technology switch electrodes, be spaced apart 1cm,
Control switch by the control unit containing msp430 single-chip microcomputer to open and close, communication interface can be passed through and contain
The computer of C Plus Plus software carries out data communication, and this communication interface is serial line interface.
Measure sample: nichrome wire (Cr20Ni80), line footpath 0.15mm, long 300 meters, measure wherein 240
Rice.
Measuring method: the present invention be applied to measure the concrete steps of distribution of conductivity situation of resistance wire include as
Under:
Step one, testing resistance silk is drawn every 1 meter and is measured point, by each electrode in programmable switch electrode band
Measure point with sample to be sequentially connected with；Generate bernoulli stochastical sampling matrix, by computer from this matrix successively
Taking out row vector, then the control end by computer export row vector signal to programmable switch electrode band, control can
The on off operating mode of program switch electrode, 0 pair of inductive switch Guan Bi, 1 correspondence switches off, and forms Observable mask；
Wherein:
The structural formula generating bernoulli stochastical sampling matrix is: matrix Φ ∈ RM×N, each element of this matrix is only
On the spot obey the bernoulli distribution of symmetry, it may be assumed that
Owing to only existing break-make two states in circuit, therefore above formula matrix can be reduced to:
Above formula ΦsIn every a line be considered as one group of dominant vector, computer is successively according to the row vector of this matrixSwitched to the control of msp430 single-chip microcomputer by serial line interface output low and high levelElectrode, 0 correspondence is opened
Closing Guan Bi, the part measured conductor that i.e. this switch is corresponding is switched on and off short circuit, and this part is not counted in the electricity of now gained
Resistance；1 correspondence switches off, i.e. this part counts the resistance of now gained；
Need to further illustrate: wherein PLC technology number of switches N is the distribution of conductivity that can record
Highest resolution；Controlling switch on and off by M × N rank random matrix, M is the number of times (M of random measurement
< < N), the accuracy recovering signal increases with M and increases, and the N of the present embodiment 2 is 240, M selects 70.
Step 2, utilizes the electrical impedance tester accessing resistance wire sample two ends, records different rows in sampling matrix
The resistance wire resistance value that vector sampling is corresponding, obtains resistance sampling vector；Wherein: described resistance sampling vector,
Refer to be obtained multiple resistance sampling value by different rows vector correspondence in sampling matrixAgain by all ofIt is multiplied byIt is normalized, finally gives the resistance being made up of M linear projection observed samples value
Vector of samples Y=[y1, y2..., yM]T∈RM；Wherein: when the distribution of resistance of conductor is N-dimensional real signal
X=[x1, x2..., xN]T∈RN, resistance sampling vector Y the most now is signal X to perform a compression see
The result surveyed is Y=Φ X.
Step 3, selects discrete cosine transform as the sparse transformation of the distribution of resistance signal of resistance wire, constitutes super complete
Standby dictionary；Wherein: sparse transformation, refer to recover the one-dimensional distribution signal of conductor resistance from resistance sampling vector Y
X, it is desirable to X is sparse vector or X is sparse in a transform domain, it may be assumed that X available orthogonal base vectorLinear combination formula represent
Write as matrix form, can be obtained:
X=Ψ Θ
Wherein: Ψ=[ψ1, ψ2... ψN]∈RN×N(Ψ Ψ is met for orthogonal basis dictionary matrixT=ΨTΨ=I), Θ
Θ is X projection coefficient in a sparse transform-domain, launches sparse coefficient vector Θ=[θ1, θ2..., θN]T；
In conjunction with the compression observation to signal X, note CS information operaor is ACS=Φ Ψ, can obtain:
Y=Φ X=Φ Ψ Θ=ACSΘ
Although recovering Θ from Y is also an ill-conditioning problem, but it is sparse for being because coefficient Θ, so unknown several
Number greatly reduces so that signal reconstruction is possibly realized；
Conventional rarefaction method, in addition to discrete cosine transform, also includes wavelet transformation, DFT etc.,
Owing to the degree of rarefication of Θ coefficient is largely affected by final recovery effects.Therefore, best extensive in order to obtain
Multiple effect, can select suitable sparse transformation according to different conductors to be measured.
Step 4, on the computer containing C Plus Plus software, (concrete employing base chases after to utilize recovery algorithms
Track method, i.e. BP) distribution one-dimensional to conductive paper sample resistance rebuild, and utilizes resistivity computing formula to try to achieve
The one-dimensional distribution of conductor resistance rate, more inverted obtain the one-dimensional distribution results of conductivity；Wherein, at conductor electricity
Hinder one-dimensional distribution signal X sparse or compressible on the premise of, base back tracking method (BP) is used for solving the underdetermined system of equations:
s.t.ACSΘ=Φ X=Y
From resistance wire resistance sampling vector Y, i.e. recover distribution of resistance signal X；This resistivity computing formula: ρ=RS
/ L, wherein: ρ be resistivity, R be resistance, L be the length of conductor to be measured, S be cross-sectional area.
Conventional recovery algorithms, in addition to base back tracking method (BP), also can be adopted matching pursuit algorithm, orthogonal matching pursuit or be total to
Yoke gradient method etc..
Owing to bernoulli random matrix is higher with connecting and disconnecting of the circuit correlation, so observing matrix usually uses bernoulli
Matrix, but the inventive method is not only limited to bernoulli random matrix, uses other any kind of observing matrixes,
As long as can be the most corresponding with connecting and disconnecting of the circuit relation, it is possible to use the inventive method to show that one-dimensional conductor conductivity divides
Cloth.
Finally calculating the one-dimensional distribution results of electrical conductivity of this sample, its average conductivity is 9.1729 × 105s
/m。
In the detailed description of the invention of the present invention, all explanations not related to belong to techniques known, refer to public affairs
Know that technology is carried out.
Above detailed description of the invention and embodiment are a kind of based on compressed sensing principle the leading to present invention proposition
The measuring method of the one-dimensional distribution of bulk conductivity and the concrete support of device technique thought, it is impossible to limit the present invention with this
Protection domain, every according to the present invention propose technological thought, that is done on the basis of the technical program is any
Equivalent variations or the change of equivalence, all still fall within the scope of technical solution of the present invention protection.
Claims (10)
1. the method for the one-dimensional distribution measuring of conductor conductivity based on compressed sensing principle, it is characterised in that
Comprise the following specific steps that:
Step one, leads the programmable switch electrode band containing tens of to hundreds of programmable switch electrodes with to be measured
The surface of body fits tightly；Generate bernoulli stochastical sampling matrix by computer, take out successively from this matrix
Row vector, then the control end by computer export row vector signal to programmable switch electrode band, control tens of extremely
The on off operating mode of hundreds of programmable switch electrodes, 0 pair of inductive switch Guan Bi, 1 correspondence switches off；
Step 2, accesses conductor two ends to be measured by the measurement electrode of electrical impedance tester, records in sampling matrix
The resistance value that different rows vector is corresponding, draws resistance sampling vector；
Step 3, selects corresponding sparse transformation according to difference detection conductor, constitutes super complete dictionary；
Step 4, utilizes recovery algorithms distribution one-dimensional to conductor resistance to be measured to rebuild, utilizes resistivity to calculate
Formula: ρ=RS/L, wherein: ρ be resistivity, R be resistance, L be the length of conductor to be measured, S be horizontal stroke
Sectional area, tries to achieve the one-dimensional distribution of conductor resistance rate, more inverted obtains the one-dimensional distribution results of conductor conductivity.
The one-dimensional distribution measuring side of conductor conductivity based on compressed sensing principle the most according to claim 1
Method, it is characterised in that by powered-down for the programmable switch containing tens of to hundreds of programmable switch electrodes described in step one
Pole band fits tightly with the surface of conductor to be measured, refers to that each programmable switch electrode is the most mutually gone here and there at one-dimensional square
Connection, and fit tightly with conductive surface to be measured, form Observable mask.
The one-dimensional distribution measuring side of conductor conductivity based on compressed sensing principle the most according to claim 1
Method, it is characterised in that the structural formula generating bernoulli stochastical sampling matrix described in step one is: matrix
Φ∈RM×N, each element of this matrix obeys the bernoulli distribution of symmetry independently, it may be assumed that
Owing to only existing break-make two states in circuit, therefore above formula matrix can be reduced to:
Above formula ΦsIn every a line be considered as one group of dominant vector, computer is successively according to the row vector of this matrix
Output low and high level controls switch, 0 pair of inductive switch Guan Bi, and the part measured conductor that i.e. this switch is corresponding is switched on and off
Short circuit, this part is not counted in the resistance of now gained；1 correspondence switches off, i.e. this part counts now gained
Resistance.
The one-dimensional distribution measuring side of conductor conductivity based on compressed sensing principle the most according to claim 1
Method, it is characterised in that resistance sampling vector described in step 2, refers to be obtained by different rows vector in sampling matrix is corresponding
To multiple resistance sampling valuesAgain by all ofIt is multiplied byBe normalized, finally give by
The resistance sampling vector Y=[y that M linear projection observed samples value is constituted1,y2,...,yM]T∈RM；Wherein: when
The distribution of resistance of conductor is N-dimensional real signal X=[x1,x2,...,xN]T∈RN, resistance sampling vector Y the most now
Being Y=Φ X for signal X performs the result of a compression observation, wherein Φ is bernoulli stochastical sampling square
Battle array.
The measuring method of one-dimensional distribution of conductivity based on compressed sensing principle the most according to claim 1,
It is characterized in that sparse transformation described in step 3, refer to recover one-dimensional point of conductor resistance from resistance sampling vector Y
Cloth signal X, it is desirable to X is sparse vector or X is sparse in a transform domain.
The measuring method of one-dimensional distribution of conductivity based on compressed sensing principle the most according to claim 1,
It is characterized in that recovery algorithms described in step 4, refer to that recovering one-dimensional conductor resistance from resistance sampling vector Y divides
Cloth signal X is one and solves system of linear equations, sparse or compressible at conductor resistance one-dimensional distribution signal X
The underdetermined system of equations is solved under premise:
s.t.ACSΘ=Φ X=Y
Wherein: Ψ be orthogonal basis dictionary matrix, Θ be X projection coefficient in sparse transformation, ACSFor compressed sensing
Information operaor, Φ are bernoulli stochastical sampling matrix.
7. according to the measurement of based on compressed sensing principle the one-dimensional distribution of conductivity described in claim 1 or 6
Method, it is characterised in that recovery algorithms described in step 4 is base back tracking method, matching pursuit algorithm, orthogonal matching pursuit
Method or conjugate gradient method.
8. the one-dimensional distribution measuring side of conductor conductivity based on the compressed sensing principle described in claim 1
The device of method, it includes electrical impedance tester, it is characterised in that also include electrical impedance tester and programmable switch
Electrode band and computer are sequentially connected with；Wherein: programmable switch electrode band includes tens of to hundreds of programmable switch
Close electrode, control unit containing single-chip microcomputer and communication interface, and programmable switch electrode band is each able to programme
Switch electrode is upwards serially connected at one-dimensional square and fits tightly as Observable mask with conductive surface to be measured；Described
Programmable switch electrode, control unit and communication interface are sequentially connected with.
One-dimensional distribution of conductivity measuring method based on compressed sensing principle the most according to claim 8
Device, it is characterised in that computer is for containingmatlabSoftware, C Plus Plus software or the calculating of java software
Machine.
Based on compressed sensing principle one-dimensional distribution of conductivity measurement side the most according to claim 8 or claim 9
The device of method, it is characterised in that described single-chip microcomputer is 51 single-chip microcomputers, msp430 single-chip microcomputer or atmega monolithic
Machine.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410164002.4A CN104090164B (en) | 2014-04-22 | 2014-04-22 | The measuring method of a kind of one-dimensional distribution of conductor conductivity based on compressed sensing principle and device |
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| CN104678181B (en) * | 2015-03-23 | 2017-09-29 | 攀钢集团研究院有限公司 | Rail resistance rate measuring method |
| CN110133056A (en) * | 2019-05-30 | 2019-08-16 | 浙江大学 | A kind of conductivity measurement system of highly conductive liquid |
| CN113252984B (en) * | 2021-07-06 | 2021-11-09 | 国网湖北省电力有限公司检修公司 | Measurement data processing method and system based on Bluetooth insulator measuring instrument |
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