Method for rapidly acquiring magnetic field sensitivity matrix based on magnetic sensor array

Abstract

The invention relates to a magnetic field sensitivity matrix rapid acquisition method based on a magnetic sensor array, and the method comprises the steps: introducing a virtual coil to replace a magnetic sensor in simulation, carrying out the calculation to obtain a virtual coil voltage sensitivity matrix, and rapidly obtaining a magnetic field sensitivity matrix through the relation between the voltage of the virtual coil and the magnetic flux density. And the magnetic field sensitivity matrix is used for imaging the defect position and size of the non-ferromagnetic metal plate by the magnetic sensor.

Description

Technical Field

[0001] The invention belongs to the technical field of industrial non-destructive testing imaging and relates to a method for quickly acquiring a magnetic field sensitivity matrix in eddy current tomography based on a magnetic sensor array. Technical Background

[0002] Non-ferromagnetic metal sheets are widely used in the automotive, energy, aerospace and other fields. Materials are often damaged or defective during manufacturing and use, threatening industrial processes and even personal safety. Traditional eddy current testing obtains defect images by performing C-scans using a single probe or an array probe. However, the mechanical scanning equipment used in C-scans makes eddy current testing equipment less portable and may have scanning errors. Eddy Current Tomography (ECT) is a non-destructive testing method based on the principle of electromagnetic induction. By passing an alternating excitation signal into the excitation coil, eddy currents are induced on the surface of the specimen. When the eddy current encounters a defect, the eddy current distribution changes, thereby changing the induced signal on the sensor. This technology has the advantages of non-contact, high efficiency, defect visualization, and avoidance of scanning errors. It is widely used in surface defect detection of non-ferromagnetic metal sheets.

[0003] The coil sensors used in traditional eddy current tomography detect changes in the magnetic field and have high sensitivity at high frequencies. Highly conductive non-ferromagnetic metal sheets have a severe skin effect at high frequencies, which limits the detection depth of coil sensor-based eddy current tomography (CSECT). Magnetic sensors directly detect the magnitude of the magnetic field and are not affected by frequency. They can achieve a higher penetration depth at low frequencies. Therefore, magnetic sensor-based eddy current tomography (MSECT) can achieve deep detection of metal defects at low frequencies. However, magnetic sensor-based eddy current tomography lacks an effective method to obtain the magnetic field sensitivity matrix during image reconstruction. Currently, the magnetic field sensitivity matrix is ​​obtained through the perturbation method, which requires repeated solution of the positive problem. In particular, when the sensor structure changes, the sensitivity matrix needs to be recalculated. The low computational efficiency seriously restricts the real-time and adaptability of the detection technology.

[0004] In order to improve the detection efficiency of eddy current tomography technology based on magnetic sensors, there is an urgent need for a more efficient, accurate and effective acquisition method of the magnetic field sensitivity matrix that can adapt to changes in sensor structure, so as to achieve fast and efficient defect detection of non-ferromagnetic metal sheets. Summary of the Invention

[0005] The present invention relates to a method for rapidly acquiring a magnetic field sensitivity matrix based on eddy current tomography using a magnetic sensor array. By introducing a virtual coil in place of a magnetic sensor in a simulation, its voltage sensitivity matrix is ​​calculated. The relationship between the voltage and magnetic flux density of the virtual coil is then used to rapidly acquire the magnetic field sensitivity matrix. This magnetic field sensitivity matrix is ​​then used in subsequent experiments to accurately image the location and size of defects in non-ferromagnetic metal sheets using the magnetic sensor. The technical solution of the present invention is as follows:

[0006] A method for rapidly acquiring a magnetic field sensitivity matrix based on a magnetic sensor array is proposed. By introducing virtual coils in place of magnetic sensors in simulation, the virtual coil voltage sensitivity matrix is ​​calculated. The relationship between the virtual coil voltage and magnetic flux density is used to rapidly acquire the magnetic field sensitivity matrix. The magnetic field sensitivity matrix is ​​then used to image the location and size of defects in non-ferromagnetic metal sheets using magnetic sensors. The method includes the following steps:

[0007] Step 1: Based on the defect detection device for non-ferromagnetic metal sheets using an excitation coil array and a magnetic sensor array, an eddy current sensor array for obtaining a magnetic field sensitivity matrix is ​​established in the simulation. The array includes a regular coil array and a virtual coil array for replacing the magnetic sensors at corresponding positions. The virtual coil is used to replace the magnetic sensor based on eddy current tomography of the magnetic sensor array. The outer diameter of the virtual coil is less than 25% of the outer diameter of the regular coil.

[0008] Step 2: In the simulation, the eddy current sensor array established for obtaining the magnetic field sensitivity matrix is ​​placed on the non-ferromagnetic metal plate to be tested. A sinusoidal excitation signal is sequentially applied to the common coil Ca. The changing electric field generates a changing magnetic field around the coil, inducing eddy currents in the non-ferromagnetic metal plate to be tested, thereby generating a changing electric field. The first electric field intensity value distribution data set is obtained at the inverse problem meshing node of the non-ferromagnetic metal plate to be tested. Sinusoidal excitation signals of the same amplitude and frequency are sequentially fed into the virtual coils, and the second electric field intensity distribution data set is obtained at the inverse problem mesh node.

[0009] Step 3: According to the electromagnetic tomography sensitivity matrix calculation method based on the reciprocity theorem, the voltage sensitivity matrix S of the virtual coil is obtained. V(k,i) ;

[0010] Step 4: According to Faraday's law of electromagnetic induction, establish the induced voltage peak U2 of the virtual coil and the magnetic flux density passing through the cross section of the virtual coil The relationship between the virtual coil cross section and the magnetic flux density in the simulation is approximately uniformly distributed, and the magnetic flux passing through the virtual coil cross section is expressed as the product of the z-axis component of the magnetic flux density and the cross-sectional area of ​​the virtual coil, thereby obtaining the expression of the induced voltage peak value U2 of the virtual coil;

[0011] Step 5: Based on the expression of the induced voltage peak value U2 of the virtual coil obtained in step 4, the magnetic field sensitivity matrix is ​​expressed by the voltage sensitivity matrix as follows:

[0012]

[0013] Where A2 is the cross-sectional area of ​​the virtual coil; ω is the angular frequency of the sinusoidal excitation.

[0014] Furthermore, in step 3, the voltage sensitivity matrix S of the virtual coil V(k,i) for:

[0015]

[0016] Where k represents the excitation-detection pair when the common coil Ca is used as the excitation coil and the virtual coil cb is used as the detection coil; I is the amplitude of the sinusoidal excitation current passed into the common coil; is the electric field intensity at node i of the inverse problem mesh when the ordinary coil Ca is excited; is the electric field intensity at node i of the inverse problem mesh when the virtual coil cb is excited; △v is the mesh volume of the inverse problem

[0017] Furthermore, in step 3, the voltage sensitivity matrix of the virtual coil is expressed as:

[0018]

[0019] Where m is the number of excitation-detection pairs, and n is the number of grids used to divide the inverse problem.

[0020] Furthermore, in step 4, the induced voltage peak value U2 of the virtual coil established is related to the magnetic flux density passing through the cross section of the virtual coil. The relationship between them is:

[0021]

[0022] Where N2 is the number of turns of the virtual coil; is the surface element of the virtual coil cross section;

[0023] The expression of the induced voltage peak U2 of the virtual coil is:

[0024] U2=-jN2A2ωB Z (4)

[0025] Where j is the imaginary unit; B Z is the z-axis component of the magnetic flux density of the virtual coil.

[0026] Furthermore, in step 1, a sinusoidal excitation signal with a frequency of 10 kHz is sequentially supplied to the common coils Ca.

[0027] The beneficial effects of the present invention are: providing a fast method for obtaining a magnetic field sensitivity matrix, setting an excitation coil array in the simulation, and introducing a virtual coil detection array under the excitation coil array instead of a magnetic sensor array, sequentially passing sinusoidal excitation signals into the excitation coil and the virtual coil, obtaining the electric field intensity distribution at the inverse problem mesh subdivision nodes in the measured area, thereby calculating the voltage sensitivity matrix, and quickly obtaining the magnetic field sensitivity matrix based on the relationship between voltage and magnetic flux density, and then reconstructing images of defects on non-ferromagnetic metal sheets based on the magnetic field sensitivity matrix and the regularization method. The magnetic field sensitivity matrix obtained by the present invention is also suitable for defect detection of non-ferromagnetic metal sheets by magnetic sensors in experiments. The present invention makes the acquisition of the magnetic field sensitivity matrix faster, the detection implementation more efficient, and has better detection effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The following drawings illustrate selected embodiments of the present invention, which are illustrative and non-exhaustive and non-limiting, wherein:

[0029] Figure 1 A schematic diagram of a detection device provided in an embodiment of the present invention;

[0030] Figure 2 Schematic diagram of the arrangement and coil parameters of the 16 excitation coil array and the 16 virtual coil detection array introduced in the embodiment of the present invention;

[0031] Figure 3 A schematic diagram of a titanium alloy flat plate with defects under test provided by an embodiment of the present invention;

[0032] Figure 4 A schematic diagram of a voltage and magnetic field sensitivity matrix provided by an embodiment of the present invention;

[0033] Figure 5 A schematic diagram comparing real defects and reconstructed defects provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0034] In magnetic sensor-based eddy current tomography, establishing a magnetic field sensitivity matrix is ​​crucial for image reconstruction. While perturbation-based methods are computationally intensive and slow, this new method uses virtual coils instead of magnetic sensors to rapidly acquire the magnetic field sensitivity matrix, saving computational power. Furthermore, the magnetic field sensitivity matrix and L1 regularization are used to reconstruct defects on non-ferromagnetic plates.

[0035] To make the objectives, technical solutions, and advantages of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, other embodiments obtained by those skilled in the art without creative work are all within the scope of protection of the present invention.

[0036] like Figure 2 Figure 1 shows the eddy current sensor array layout used to obtain the magnetic field sensitivity matrix. It consists of 16 identical regular coils and 16 identical virtual coils, with coil parameters shown. C1-C16 are the 16 regular coils; C17-C32 are the 16 virtual coils introduced in the simulation. These virtual coils replace the magnetic sensors used in eddy current tomography based on magnetic sensor arrays. In the experiment, the centers of the magnetic sensors coincide with the centers of the virtual coils, and the direction of the magnetic field detected by the magnetic sensors coincides with the central axis of the virtual coils.

[0037] The specific implementation steps of the present invention are as follows:

[0038] Step 1: In simulation, Figure 2 The sensor array shown is placed on a 100mm×100mm×2mm lossless titanium alloy flat plate. Sinusoidal excitation signals with an amplitude of 0.8A and a frequency of 10kHz are sequentially applied to ordinary coils C1-C16. The changing electric field generates a changing magnetic field around the coils, inducing eddy currents in the titanium alloy plate under test, which in turn generates a changing electric field. A 16×40,000 electric field intensity value distribution data set is obtained at the inverse problem mesh node (the center point of a 1mm×1mm×1mm cube) of the titanium alloy plate under test.

[0039] Then, a sinusoidal excitation signal with an amplitude of 0.8A and a frequency of 10kHz is applied to the virtual coils c17-c32 in sequence, and a 16×40000 electric field intensity distribution data set is obtained at the inverse problem mesh node (the center point of a 1mm×1mm×1mm cube).

[0040] Step 2: According to the electromagnetic tomography sensitivity matrix calculation method based on the reciprocity theorem, the voltage sensitivity matrix is ​​obtained as follows:

[0041]

[0042] Where k represents the excitation-detection pair when the common coil Ca is used as the excitation coil and the virtual coil cb is used as the detection coil. There are 256 (16 × 16) pairs in total. I is the amplitude of the sinusoidal excitation current flowing into the coil. is the electric field intensity at node i of the inverse problem mesh when the ordinary coil Ca is excited; is the electric field intensity at node i of the inverse problem mesh when the virtual coil cb is excited; △v is the volume of the inverse problem mesh.

[0043] The voltage sensitivity matrix can be expressed as m=256,n=40000. All rows of the voltage sensitivity matrix are superimposed and the data of each column is averaged to obtain the voltage sensitivity map, such as Figure 4 (a) In the figure, red represents the sensitive area detected by the sensor array, and blue represents the insensitive area.

[0044] Step 3: According to Faraday's law of electromagnetic induction, the induced voltage peak U2 of the virtual coil is related to the magnetic flux density passing through the cross section of the virtual coil. The relationship between them is:

[0045]

[0046] Where N2 is the number of turns of the virtual coil; is the surface element of the virtual coil cross section.

[0047] In the simulation, when the outer diameter of the virtual coil is less than 25% of the outer diameter of the ordinary coil, the magnetic flux density in the cross section of the virtual coil is approximately uniformly distributed. The magnetic flux passing through the cross section of the virtual coil can be expressed as the product of the z-axis component of the magnetic flux density and the cross-sectional area of ​​the virtual coil. Therefore, the induced voltage peak value U2 of the virtual coil can be expressed as:

[0048] U2=-jN2A2ωB Z (3)

[0049] Where j is the imaginary unit; A2 is the cross-sectional area of ​​the virtual coil; ω is the angular frequency of the sinusoidal excitation; B Z is the z-axis component of the magnetic flux density of the virtual coil.

[0050] According to formula (3), the magnetic field sensitivity matrix can be expressed by the voltage sensitivity matrix as:

[0051]

[0052] All rows of the magnetic field sensitivity matrix are superimposed and the data of each column are averaged to obtain the magnetic field sensitivity map, such as Figure 4 (b) In the figure, red represents the sensitive area detected by the sensor array, and blue represents the insensitive area.

[0053] Step 4: In the simulation Figure 2 The sensor array shown is placed on a lossless titanium alloy flat plate, and a sinusoidal excitation signal with an amplitude of 0.8A and a frequency of 10kHz is applied to the common coils C1-C16 in turn to extract the virtual

[0054] The z-axis magnetic flux density at the center of coils c17-c32 is used as the detection signal based on eddy current tomography of the magnetic sensor array to obtain a 1×256 row vector

[0055] In the simulation, Figure 2 The sensor array shown is placed in Figure 3 On the damaged titanium alloy flat plate shown in the figure, the sensor array and the defect position are as follows Figure 3 As shown, the defect size is 1mm×6mm×1mm; a sinusoidal excitation signal with an amplitude of 0.8A and a frequency of 10kHz is sequentially applied to the ordinary coils C1-C16, and the z-axis magnetic flux density at the center of the virtual coils c17-c32 is extracted as the detection signal based on the eddy current tomography of the magnetic sensor array, and a 1×256 row vector B is obtained. z .

[0056] The z-axis magnetic flux density change of the virtual coil detected on the lossy and lossless titanium alloy plane plates is △B z for:

[0057]

[0058] Step 5: Based on the sensitivity matrix, solve the forward problem of eddy current tomography by L1 regularization method:

[0059] △B z =S B △σ (6)

[0060] Where △σ is the change in electrical conductivity of the titanium alloy flat plate with or without defects.

[0061] The conductivity distribution △σ is obtained Figure 5 The reconstructed defect image shown, Figure 5 (a) is the actual defect distribution, Figure 5 (b) is the image reconstruction result of the voltage sensitivity matrix in eddy current tomography based on a common coil array. Figure 5 (c) shows the image reconstruction result of the magnetic field sensitivity matrix in eddy current tomography based on the magnetic sensor array. It can be seen that the defect image reconstructed based on the magnetic field sensitivity matrix can clearly reflect the location and size of the defect.

[0062] The method for rapidly acquiring a magnetic field sensitivity matrix of the present invention introduces virtual coils in the simulation to replace magnetic sensors, calculates the voltage sensitivity matrix, and can rapidly acquire the magnetic field sensitivity matrix based on the relationship between voltage and magnetic flux density, thereby reconstructing an image of the defect using the magnetic field sensitivity matrix and the L1 regularization method. In experiments using a magnetic sensor array to detect defects in non-ferromagnetic metal sheets, the magnetic field sensitivity matrix obtained by simulation can also be used to reconstruct an image of the defect. Compared to the perturbation method, the method for rapidly acquiring a magnetic field sensitivity matrix of the present invention is more efficient, improves the implementation speed of eddy current tomography based on magnetic sensors, and has better detection results.

Claims

1. A method for rapidly acquiring a magnetic field sensitivity matrix based on a magnetic sensor array. This method introduces virtual coils in place of magnetic sensors in simulation, calculates the virtual coil voltage sensitivity matrix, and uses the relationship between the virtual coil voltage and magnetic flux density to rapidly acquire the magnetic field sensitivity matrix. This magnetic field sensitivity matrix is ​​then used by the magnetic sensor to image the location and size of defects in non-ferromagnetic metal sheets. The method includes the following steps: Step 1: Based on the defect detection device for non-ferromagnetic metal sheets using an excitation coil array and a magnetic sensor array, an eddy current sensor array for obtaining a magnetic field sensitivity matrix is ​​established in the simulation. The array includes a regular coil array and a virtual coil array for replacing the magnetic sensors at corresponding positions. The virtual coil is used to replace the magnetic sensor based on eddy current tomography of the magnetic sensor array. The outer diameter of the virtual coil is less than 25% of the outer diameter of the regular coil. Step 2: In the simulation, the eddy current sensor array established for obtaining the magnetic field sensitivity matrix is ​​placed on the non-ferromagnetic metal plate to be tested. A sinusoidal excitation signal is sequentially applied to the common coil Ca. The changing electric field generates a changing magnetic field around the coil, inducing eddy currents in the non-ferromagnetic metal plate to be tested, thereby generating a changing electric field. The first electric field intensity value distribution data set is obtained at the inverse problem meshing node of the non-ferromagnetic metal plate to be tested. Sinusoidal excitation signals of the same amplitude and frequency are sequentially fed into the virtual coils, and the second electric field intensity distribution data set is obtained at the inverse problem mesh node. Step 3: According to the electromagnetic tomography sensitivity matrix calculation method based on the reciprocity theorem, the voltage sensitivity matrix S of the virtual coil is obtained. V (k,i); Step 4: According to Faraday's law of electromagnetic induction, establish the induced voltage peak U2 of the virtual coil and the magnetic flux density passing through the cross section of the virtual coil The relationship between the virtual coil cross section and the magnetic flux density in the simulation is approximately uniformly distributed, and the magnetic flux passing through the virtual coil cross section is expressed as the product of the z-axis component of the magnetic flux density and the cross-sectional area of ​​the virtual coil, thereby obtaining the expression of the induced voltage peak value U2 of the virtual coil; Step 5: Based on the expression of the induced voltage peak value U2 of the virtual coil obtained in step 4, the magnetic field sensitivity matrix is ​​expressed by the voltage sensitivity matrix as follows: Where A2 is the cross-sectional area of ​​the virtual coil; ω is the angular frequency of the sinusoidal excitation.

2. The method for rapidly acquiring a magnetic field sensitivity matrix based on a magnetic sensor array according to claim 1 is characterized in that: In step 1, the center of the magnetic sensor coincides with the center of the virtual coil, and the direction of the magnetic field detected by the magnetic sensor coincides with the central axis of the virtual coil.

3. The method for rapidly acquiring a magnetic field sensitivity matrix based on a magnetic sensor array according to claim 1 is characterized in that In, In step 3, the voltage sensitivity matrix S of the virtual coil V(k,i) for: Where k represents the excitation-detection pair when the common coil Ca is used as the excitation coil and the virtual coil cb is used as the detection coil; I is the amplitude of the sinusoidal excitation current passed into the common coil; is the electric field intensity at node i of the inverse problem mesh when the ordinary coil Ca is excited; is the electric field intensity at node i of the inverse problem mesh when the virtual coil cb is excited; △v is the mesh volume of the inverse problem.

4. The method for rapidly acquiring a magnetic field sensitivity matrix based on a magnetic sensor array according to claim 3 is characterized in that: In step 3, the voltage sensitivity matrix of the virtual coil is expressed as: Where m is the number of excitation-detection pairs, and n is the number of grids used to divide the inverse problem.

5. The method for rapidly acquiring a magnetic field sensitivity matrix based on a magnetic sensor array according to claim 1, wherein: In step 4, the induced voltage peak value U2 of the virtual coil established is related to the magnetic flux density passing through the cross section of the virtual coil. The relationship between them is: Where N2 is the number of turns of the virtual coil; is the surface element of the virtual coil cross section; The expression of the induced voltage peak U2 of the virtual coil is: U2=-jN2A2ωB Z (4) Where j is the imaginary unit; B Z is the z-axis component of the magnetic flux density of the virtual coil.

6. The method for rapidly acquiring a magnetic field sensitivity matrix based on a magnetic sensor array according to claim 1, wherein: In step 1, a sinusoidal excitation signal with a frequency of 10 kHz is sequentially supplied to the common coil Ca.

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