CN107607999A - A kind of measuring method to ferromagnetic target far field magnetic moment vector - Google Patents

A kind of measuring method to ferromagnetic target far field magnetic moment vector Download PDF

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CN107607999A
CN107607999A CN201710724583.6A CN201710724583A CN107607999A CN 107607999 A CN107607999 A CN 107607999A CN 201710724583 A CN201710724583 A CN 201710724583A CN 107607999 A CN107607999 A CN 107607999A
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magnetic moment
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CN107607999B (en
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康崇
郑权
樊黎明
康曦元
张晓峻
耿卓杉
陈鑫
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Harbin Engineering University
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Harbin Engineering University
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Abstract

The present invention is to provide a kind of measuring method to ferromagnetic target far field magnetic moment vector.With scalar Magnetic Sensor forming array, based on far field dipole model of magnetic, the measuring method to target magnetic moment vector with geomagnetic total field is devised.Eliminate geomagnetic total field and change over time the influence uneven with spatial distribution, it is proposed that determine the criterion function of magnetic moment size and Orientation.Based on this criterion function and measured data, target magnetic moment size and Orientation is solved.Measuring method to ferromagnetic target far field magnetic moment proposed by the invention, only need target once to be moved along known paths near array and measurement can be achieved.The simple efficiently and accurately of measuring method.

Description

A kind of measuring method to ferromagnetic target far field magnetic moment vector
Technical field
The present invention relates to a kind of measuring method in earth's magnetic field, specifically a kind of target magnetic dipole magnetic moment vector Measuring method.
Background technology
Earth's magnetic field is the important physical amount for reflecting the processes such as Earth evolution, geological structure differentiation.Dipole model of magnetic is very It is multi-field to be applied, because the magnetic phenomenon of nature can be equivalent to the superposition in several magnetic dipole magnetic fields, specific In the case of can also be equivalent to a magnetic dipole.Earth's magnetic field can magnetize ferromagnetic material, due to the presence of magnetic target, Its caused induced field can cause the change of spatially Distribution of Magnetic Field, so as to produce magnetic anomaly within this space.Utilize magnetic anomaly Often detection far field objects, can be approximately the magnetic field of a magnetic dipole by magnetic field of the goal.Therefore measurement target magnetic dipole magnetic Moment vector is the premise for realizing target magnetic detection and target demagnetization, is all had great importance to magnetic detection and anti-magnetic detection.
Earth's magnetic field is formed by stacking by the magnetic field components of different changing rules.Change with time feature in consideration earth's magnetic field, Faster earth's magnetic field, which will be changed over time, turns into the variation magnetic field of the earth, changes over time earth's magnetic field that is relatively slow or being basically unchanged As the stabilizing magnetic field of the earth.Therefore in magnetic survey it is necessary to trying every possible means to be reduced or eliminated the influence of this variation magnetic field.
Earth's magnetic field is vector field, and the magnetic survey Technical comparing based on vector sensor is ripe, also popular, is had very More advantages.The vector Magnetic Sensor mainly used in magnetic survey at present includes fluxgate magnetic sensor and MEMS Magnetic Sensors Deng but three axles need critical alignment when vector sensor is installed, and also need to real-time measurement sensor attitude information during use, sense Device temperature drift is big.Because when these complicated use conditions can not meet its measurement accuracy will decline.And resultant field Magnetic Sensor High resolution, detection range is remote, in the absence of temperature drift problem, it is not necessary to strict attitude information, without three axle Correction Problemss.Therefore profit There is the advantages of precision is high, simple and reliable with the measurement of geomagnetic total field sensor, this measures target magnetic moment also with geomagnetic total field The advantages of.But target magnetic moment is vector, except with size, also direction, plus ambient field, there is multiple unknown numbers, from algorithm Upper theory, solved based on geomagnetic total field, it is necessary to which building multidimensional independent equation group could calculate, it is therefore desirable to build geomagnetic total field measurement Array could be realized.
The content of the invention
It is an object of the invention to provide a kind of measurement result is accurate, simply efficiently to ferromagnetic target far field magnetic moment vector Measuring method.
The object of the present invention is achieved like this：
Step 1：Array of magnetic sensors is built, obtains geomagnetic field measuring value
Array of magnetic sensors forms square, the distance of four scalar sensors to array center by four scalar sensors All it is D, D is referred to as array aperture, and target is moved along known path, and the movement locus of target and array are in same level Interior, scalar sensors i positions are (xi,yi,zi), i=1,2,3,4, target position is (x, y, z), then scalar senses Device i measured value is：
Wherein, T0Earth's magnetic field is worth during for without target, μ0It is space permeability, PmIt is the magnetic moment vector of magnetic dipole target, Pm Size be | Pm|, PmDirection inclination angle and drift angle be respectively α, β, earth magnetism field direction inclination angle and drift angle are respectively θ,
Step 2：Eliminate the influence of variation magnetic field
In array of magnetic sensors, positioned at (xi,yi,zi) scalar sensors i in t measured value Ti(t,xi,yi, zi), positioned at (xj,yj,zj) scalar sensors j in t measured value be Tj(t,xj,yj,zj)；In t0Moment scalar sensors i Measured value with j is respectively Ti(t0,xi,yi,zi),Tj(t0,xj,yj,zj)
Make Δ Tij=Ti(t,xi,yi,zi)-Tj(t,xj,yj,zj)-[Ti(t0,xi,yi,zi)-Tj(t0,xj,yj,zj)] (2)
Wushu (1) substitutes into formula (2) and obtains Δ TijTheoretical value Δ Tij|Theory, Δ TijExperiment value Δ Tij|ExperimentRoot According to (2) formula by scalar sensors i, j in t, t0Moment measured value draws, Δ TijIt is array of magnetic sensors measured value in time and sky Between on double gradient,
ΔTij|Theory=Δ Tij|Experiment(3)；
Step 3：Separate target magnetic moment size and Orientation
It is defined as follows function：
a|TheoryAnd b |TheoryEliminated in expression formula | Pm|, a |TheoryAnd b |TheoryOnly it is α, β function, and a |ExperimentAnd b |ExperimentIt is known quantity as experimental measurements, first solves magnetic moment direction, then solves magnetic moment size；
Step 4：The solution of target magnetic moment direction
The motion path of known target, each measurement point coordinates is (x on pathn,yn,zn), (n=0,1,2......m), Order
L (α, β) represents a in all n measurement points, the absolute error sum between the theory and measured data of b functions Inverse, L (α, β) numerical value is bigger, and error is smaller；Find suitable α, β so that L (α, β) reaches maximum, determines α, β；L(α, The criterion function of magnetic moment direction β) is just to determine, thus solves the direction of target magnetic moment；
Step 5：The solution of target magnetic moment size
By fixed α, β value is updated to formula (2), definition
Ls(|Pm|) represent absolute value error in all measurement points between each sensor measured data and theoretical value it The inverse of sum, Ls (| Pm|) numerical value is bigger, error is smaller, and it is suitable to find | Pm| so that Ls (| Pm|) reach maximum, it is determined that | Pm|, Ls (| Pm|) just it is to determine the criterion function of magnetic moment size.
The invention provides a kind of measuring method to ferromagnetic target far field magnetic moment vector.Formed ground with scalar Magnetic Sensor The total field measurement array of magnetic, using far field dipole model of magnetic, devise and calculated based on measurement of the geomagnetic total field to target magnetic moment vector Method.Because earth's magnetic field changes over time, abnormity point in spatial distribution also be present, by designing the double gradient in earth's magnetic field Algorithm, the influence and the influence of free air anomaly field that elimination earth's magnetic field changes over time.Propose and determine magnetic moment size and Orientation Criterion function, and the solution to magnetic target magnetic moment direction and size is realized based on this criterion function.
The main feature of the measuring method to ferromagnetic target far field magnetic moment vector of the present invention is embodied in：
1st, array of magnetic sensors as shown in Figure 1 is built, the array forms square-shaped planar by four scalar Magnetic Sensors Array, the movement locus with ferromagnetic target is in same level.Target is moved along known trajectory, and ferromagnetism target moves to During each known location point, scalar Magnetic Sensor records the geomagnetic total field intensity level at each sensing station in real time.The survey is described The principle expression formula of value is shown in formula (1), after the influence for excluding various change magnetic field, is solved for formula (1) algorithm for design, The size and Orientation of target magnetic moment vector can be determined.
2nd, the double gradient function of geomagnetic total field intensity measurements over time and space is proposed, sees formula (2), introduces two Weight gradient function can eliminate earth's magnetic field with the influence of time and spatial variations to measurement result.Ferromagnetic target is along known trajectory Motion, array measures the geomagnetic total field intensity level of each sensing station, not total for earth magnetism when solving target magnetic moment vector Field intensity function is formula (1) direct solution, but is that formula (3) solves for double gradient function, in such solving result Eliminate earth's magnetic field and change over time the influence uneven with spatial distribution.
3rd, propose the criterion function for determining magnetic moment direction and size, using criterion function obtain target magnetic moment direction and Size.The criterion function of magnetic moment direction is proposed, sees formula (4), target magnetic moment is obtained by the extreme-value problem of solution formula (4) Direction.(direct solution formula (3) difficulty is too big, and the pole of solution formula (4) is converted into for the problem of this solution formula (3) Value problem.) on the basis of target magnetic moment direction is obtained, it is proposed that the criterion function of target magnetic moment size is shown in formula (5), passes through The extreme-value problem of solution formula (5) obtains target magnetic moment size.The algorithm makes all measurement points on track be involved in calculating, phase When in motion process of target complete repeatedly measurement, ensure that measurement accuracy, simplify solution difficulty, ensure that measurement Real-time.
The method of measurement target magnetic moment vector provided by the invention, target only need to once be moved along known paths, you can The multiple measurement of target magnetic moment is realized, thus measurement result is accurate, method is simply efficient, hidden for the detection of target magnetic method and target magnetic Body provides Technical Reference.
Brief description of the drawings
Fig. 1 oriented arrays and target motion mode embodiment schematic diagram.
Fig. 2 targets magnetic moment vector calculates process flow diagram flow chart.
Fig. 3 functions a and position y measured data of experiment and theory curve.
Fig. 4 functions b and position y measured data of experiment and theory curve.
Fig. 5 L (α, β) and α, β diagram of block.
Fig. 6 Ls (| Pm|) with | Pm| curve map.
Embodiment
Illustrate below for a more detailed description to the present invention.
Step 1：Array is built, obtains geomagnetic field measuring value
Array of magnetic sensors as shown in Figure 1 is built, array forms square by four scalar sensors, and sensor arrives The distance of array center is all D, referred to as array aperture.Target is moved along known path, and the movement locus and battle array of target It is listed in same level.Sensor i positions are (xi,yi,zi) (i=1,2,3,4), target position for (x, y, Z), then sensor i measured value is：
Wherein, T0Earth's magnetic field is worth during for without target, μ0It is space permeability, PmIt is the magnetic moment vector of magnetic dipole target, its Middle PmSize be | Pm|, PmDirection inclination angle and drift angle be respectively α, β, earth magnetism field direction inclination angle and drift angle are respectively θ,
Step 2：Eliminate the influence of variation magnetic field
In sensor array, positioned at (xi,yi,zi) sensor i in t measured value Ti(t,xi,yi,zi), it is located at (xj,yj,zj) sensor j in t measured value be Tj(t,xj,yj,zj)；In t0Moment sensor i and j measured value difference For Ti(t0,xi,yi,zi),Tj(t0,xj,yj,zj)
Make Δ Tij=Ti(t,xi,yi,zi)-Tj(t,xj,yj,zj)-[Ti(t0,xi,yi,zi)-Tj(t0,xj,yj,zj)] (2)
Wushu (1) substitutes into formula (2) and can obtain Δ TijTheoretical value Δ Tij|Theory, Δ TijExperiment value Δ Tij|Experiment Can be by sensor i, j in t, t according to (2) formula0Moment measured value is drawn.ΔTijIt is two of array measurement over time and space Weight gradient.
ΔTij|Theory=Δ Tij|Experiment (3)
In the equation group of formula (3), the earth's magnetic field amount of changing with time and the uneven influence of spatial distribution are eliminated.Therefore Target magnetic moment vector P is calculated using formula (3)m, changed over time with earth's magnetic field it is unrelated, it is also whether uniform with earth's magnetic field spatial distribution It is unrelated.
Step 3：Separate target magnetic moment size and Orientation
In order to solution formula (3) obtains [| Pm|, α, β], it is defined as follows function：
a|TheoryAnd b |TheoryEliminated in expression formula | Pm|, a |TheoryAnd b |TheoryOnly it is α, β function.And a |ExperimentAnd b |ExperimentIt is known quantity as experimental measurements.Thus can first solve magnetic moment direction, after solve magnetic moment again Size.
Step 4：The solution of target magnetic moment direction
The motion path of known target, each measurement point coordinates is (x on pathn,yn,zn), (n=0,1,2......m). Order
L (α, β) represents a in all n measurement points, the absolute error sum between the theory and measured data of b functions Inverse, L (α, β) numerical value is bigger, and error is smaller.Find suitable α, β so that L (α, β) reaches maximum, it is possible to α is determined, β.L (α, β) is just to determine the criterion function of magnetic moment direction.Thus can solves the direction of target magnetic moment.
Step 5：The solution of target magnetic moment size
By fixed α, β value is updated to formula (2), definition
Ls(|Pm|) represent absolute value error in all measurement points between each sensor measured data and theoretical value it The inverse of sum, it is clear that Ls (| Pm|) numerical value is bigger, error is smaller.Therefore it is suitable to find | Pm| so that Ls (| Pm|) reach maximum Value, it is possible to it is determined that | Pm|。Ls(|Pm|) just it is to determine the criterion function of magnetic moment size.
So far, magnetic moment vector PmDirection determined by the maximum problem for solving (4) formula, and the size of magnetic moment | Pm| Solution is provided by the maximum problem for solving (5) formula.
The practicality of institute's extracting method is verified using experiment.Such as Fig. 1, array has 4 resultant field Magnetic Sensors, aperture D =4m, the parallel y-axis reverse driving of measured target automobile, away from y-axis 32.02m, from y=32.8m linear uniform motion to y=-41m. Scalar Magnetic Sensor is laid on the tripod of aluminum, and sensor is away from ground 1.43m.Local geomagnetic inclination θ=63.3 °, partially AngleIt is transformed into measuring coordinate system, θ=63.3 °, drift anglet0Choose target be in y=32.8m when Carve.The size of target magnetic moment is calculated by algorithm and experimental data | Pm|=476Am2, direction inclination angle size α=0.85rad, side To drift angle β=4.21rad.
Fig. 2 is target magnetic moment vector measuring and calculating process flow diagram flow chart.
In Fig. 3, transverse axis represents y position, longitudinal axis representative function a value.Curve represents a theoretical value a in figure |TheoryWith Y relation curve, the soft dot in figure represent a experiment value a |ExperimentWith y relation, a |ExperimentWith a |TheoryCompared with Good coincide.
In Fig. 4, transverse axis represents y position, longitudinal axis representative function b value.Curve represents b theoretical value b in figure |TheoryWith Y relation curve, the soft dot in figure represent b experiment value b |ExperimentWith y relation, b |TheoryWith b |ExperimentCompared with Good coincide.
Fig. 5 represents L (α, β) and α, β diagram of block,In the range of β ∈ (0,2 π), L (α, β) There is maximum L (α, β)MAX.Formula (4) is calculated, as α=0.8500, during β=4.2122, and L (α, β)MAX=1.81.
Fig. 6 represents target magnetic moment size | Pm| and function Ls (| Pm|) relation curve, as | Pm|=476Am2When, Ls (| Pm |)=4.4685, reach maximum.

Claims (1)

  1. A kind of 1. measuring method to ferromagnetic target far field magnetic moment vector, it is characterized in that comprising the following steps：
    Step 1：Array of magnetic sensors is built, obtains geomagnetic field measuring value
    Array of magnetic sensors forms square by four scalar sensors, and the distance of four scalar sensors to array center is all D, D are referred to as array aperture, and target is moved along known path, and the movement locus of target and array be in same level, Scalar sensors i positions are (xi,yi,zi), i=1,2,3,4, target position is (x, y, z), then scalar sensors i Measured value be：
    Wherein, T0Earth's magnetic field is worth during for without target, μ0It is space permeability, PmIt is the magnetic moment vector of magnetic dipole target, PmIt is big It is small to be | Pm|, PmDirection inclination angle and drift angle be respectively α, β, earth magnetism field direction inclination angle and drift angle are respectively θ,
    Step 2：Eliminate the influence of variation magnetic field
    In array of magnetic sensors, positioned at (xi,yi,zi) scalar sensors i in t measured value Ti(t,xi,yi,zi), it is located at (xj,yj,zj) scalar sensors j in t measured value be Tj(t,xj,yj,zj)；In t0Moment scalar sensors i and j survey Value is respectively Ti(t0,xi,yi,zi),Tj(t0,xj,yj,zj)
    Make Δ Tij=Ti(t,xi,yi,zi)-Tj(t,xj,yj,zj)-[Ti(t0,xi,yi,zi)-Tj(t0,xj,yj,zj)] (2)
    Wushu (1) substitutes into formula (2) and obtains Δ TijTheoretical value Δ Tij|Theory, Δ TijExperiment value Δ Tij|ExperimentAccording to (2) formula by scalar sensors i, j in t, t0Moment measured value draws, Δ TijIt is array of magnetic sensors measured value in time and space On double gradient,
    ΔTij|Theory=Δ Tij|Experiment(3)；
    Step 3：Separate target magnetic moment size and Orientation
    It is defined as follows function：
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    Step 4：The solution of target magnetic moment direction
    The motion path of known target, each measurement point coordinates is (x on pathn,yn,zn), (n=0,1,2......m), order
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    A in all n measurement points of L (α, β) expressions, the inverse of the absolute error sum between the theory and measured data of b functions, L (α, β) numerical value is bigger, and error is smaller；Find suitable α, β so that L (α, β) reaches maximum, determines α, β；L (α, β) is exactly The criterion function of magnetic moment direction is determined, thus solves the direction of target magnetic moment；
    Step 5：The solution of target magnetic moment size
    By fixed α, β value is updated to formula (2), definition
    <mrow> <mi>L</mi> <mi>s</mi> <mrow> <mo>(</mo> <mo>|</mo> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>|</mo> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>m</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>3</mn> </munderover> <mo>|</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <mi>i</mi> <mn>4</mn> </mrow> </msub> <mo>(</mo> <mrow> <mo>|</mo> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>|</mo> <mo>,</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>n</mi> </msub> </mrow> <mo>)</mo> <msub> <mo>|</mo> <mrow> <mi>T</mi> <mi>h</mi> <mi>e</mi> <mi>o</mi> <mi>r</mi> <mi>y</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <mi>i</mi> <mn>4</mn> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <msub> <mo>|</mo> <mrow> <mi>E</mi> <mi>x</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mi>i</mi> <mi>m</mi> <mi>e</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> <mo>|</mo> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    Ls(|Pm|) represent falling for absolute value error sum in all measurement points between each sensor measured data and theoretical value Number, Ls (| Pm|) numerical value is bigger, error is smaller, and it is suitable to find | Pm| so that Ls (| Pm|) reach maximum, it is determined that | Pm|, Ls (|Pm|) just it is to determine the criterion function of magnetic moment size.
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