A method for calculating the external magnetic field of cargo based on numerical integration of boundary magnetic field

Abstract

This invention discloses a method for calculating the external magnetic field of cargo based on the numerical integration of boundary magnetic fields, relating to the field of electromagnetic detection technology. The method includes the following steps: constructing a cargo numerical model in finite element electromagnetic field calculation software and setting the dimensions of the cargo numerical model; determining the position of the initial magnetic source and setting the initial magnetic source intensity based on the cargo numerical model; calculating the magnetic field intensity at distances of 2.1m and 4.6m from the initial magnetic source intensity using the finite element electromagnetic field calculation software to obtain spatial magnetic field data, and then obtaining the attenuation coefficients of the transverse unit detection points of all boundary planes, obtaining a set of attenuation coefficients, and performing spatial interpolation and translation processing; coupling the measured magnetic field data collected by the array sensor with the attenuation coefficients at the corresponding positions to solve for the magnetic field intensity at distances of 2.1m and 4.6m from the surface of the object being measured; achieving high-precision and high-efficiency calculation of the external magnetic field of cargo, meeting the rapid and non-destructive requirements of aviation transport safety inspection.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic detection technology, and in particular to a method for calculating the external magnetic field of cargo based on the numerical integration of boundary magnetic fields. Background Technology

[0002] In recent years, with the Civil Aviation Administration of my country continuously raising its requirements for air transport safety management, especially in the field of risk prevention and control of magnetic cargo transportation, weak magnetic screening technology in airport cargo inspection has become a key link in ensuring the safety of air operations.

[0003] According to relevant regulations, the maximum magnetic field strength at a distance of 2.1m from the surface of the object being tested shall not exceed 200nT, and the magnetic field strength at any location at a distance of 4.6m from the surface of the object being tested shall not exceed 525nT. Therefore, the magnetic field strength at the above locations is the core indicator for determining whether the magnetic materials carried by the cargo exceed the standard. The accurate calculation of the magnetic field strength at these specific locations is of decisive significance for determining the compliance of magnetic cargo and is also a core requirement of the airport cargo magnetic detection process.

[0004] In the existing technology, there is still a technological gap in the dedicated magnetic field strength calculation method for magnetic detection of airport cargo. This lack makes it difficult to quickly and accurately quantify and assess the risks of magnetic materials inside various types of cargo in actual operation. It cannot meet the core requirements of rapid and non-destructive magnetic detection of cargo in the air transport scenario, resulting in efficiency bottlenecks and application limitations in the cargo magnetic compliance determination process.

[0005] Therefore, a method for calculating the external magnetic field of cargo based on the numerical integration of the boundary magnetic field is provided to solve the above problems. Summary of the Invention

[0006] The purpose of this invention is to provide a method for calculating the external magnetic field of cargo based on the numerical integration of the boundary magnetic field. Based on the measured magnetic field data of the cargo collected by the array sensor, the magnetic field strength at two key locations 2.1m and 4.6m away from the surface of the object under test is solved, and compliance judgment is completed. This method achieves high-precision detection of the magnetic strength of the cargo, shortens the magnetic field solution time, reduces the waiting time in the detection process, and reduces labor costs.

[0007] To achieve the above objectives, this invention provides a method for calculating the external magnetic field of cargo based on the numerical integration of the boundary magnetic field, comprising the following steps:

[0008] S1: Construct a numerical model of the cargo in the finite element electromagnetic field calculation software and set the dimensions of the cargo numerical model;

[0009] S2: Determine the location of the initial magnetic source and set the initial magnetic source intensity based on the cargo numerical model;

[0010] S3: The magnetic field strength at distances of 2.1m and 4.6m from the initial magnetic source intensity was calculated using finite element electromagnetic field calculation software to obtain spatial magnetic field data;

[0011] S4: Set the attenuation coefficient of the initial magnetic source based on the space magnetic field data;

[0012] S5: Repeat steps S2-S4 until the attenuation coefficients of all transverse unit detection points are obtained;

[0013] S6: Repeat steps S2-S5 until the attenuation coefficients of all transverse unit detection points on the boundary plane are obtained, thus obtaining the attenuation coefficient set;

[0014] S7: Spatial interpolation of the attenuation coefficient set is performed using cubic spline interpolation.

[0015] S8: The attenuation coefficients after spatial interpolation of each boundary plane are translated. For magnetic field components that are translated beyond the domain, zero-value boundary conditions are applied to obtain the final set of attenuation coefficients.

[0016] S9: Couple the measured magnetic field data collected by the array sensor with the attenuation coefficient at the corresponding position to solve the magnetic field strength at 2.1m and 4.6m away from the surface of the object being measured.

[0017] Preferably, step S1 specifically includes the following steps:

[0018] S11: In the finite element electromagnetic field calculation software, construct a hexahedral numerical model that matches the actual shape of the measured cargo, and determine the six boundary planes of the hexahedral numerical model. The six boundary planes include the front, back, left, right, top, and bottom.

[0019] S12: Set the length, width, and height of the hexahedral numerical model according to the physical layout length of the array sensors in the actual detection environment;

[0020] S13: Determine the number of detection points in each boundary plane based on the number of array sensors deployed. Determine the number of x-axis detection points based on the number of horizontal array sensors deployed. Determine the number of z-axis detection points based on the number of vertical array sensors deployed. Determine the number of y-axis detection points based on the width range of the actual measured goods and the spacing between adjacent array sensors.

[0021] Preferably, step S2 specifically includes the following steps:

[0022] S21: Select any x-axis detection point on any boundary plane and set it as the position of the initial magnetic source, and set the initial magnetic source intensity;

[0023] S22: Define the magnetic field strength vector of the initial magnetic source using three-dimensional components. Magnetic field strength vector Specifically set as follows:

[0024] ;

[0025] in, Represents the magnetic field strength vector The magnitude of the magnetic field in the x-axis direction, Represents the magnetic field strength vector The magnitude of the magnetic field in the y-axis direction. Represents the magnetic field strength vector The magnitude of the magnetic field in the z-axis direction;

[0026] S23: Perform three assignments of magnetic source parameters to the initial magnetic source to obtain the complete magnetic field contribution of the initial magnetic source in three-dimensional space. In a single assignment of magnetic source parameters, a non-zero initial magnetic field component is set for any direction, and a zero initial magnetic field component is set for the other two directions.

[0027] Preferably, step S3 specifically includes the following steps:

[0028] S31: Based on Maxwell's equations, the formula for solving the spatial magnetic field is derived. The specific formula for solving the spatial magnetic field is as follows:

[0029] ;

[0030] ;

[0031] ;

[0032] in, Indicates magnetic field strength. Represents the Laplace operator. Represents free current density. Represents magnetic flux density, Indicates permeability, Represents the permeability of free space. Indicates the magnetization of the material. Represents the solution to the vector Poisson equation;

[0033] S32: According to the vector identity The vector Poisson equation is obtained, and the vector Poisson equation is specifically set as follows:

[0034] ;

[0035] Solving the vector Poisson equation in free space yields the solution to the vector Poisson equation. Specifically set as follows:

[0036] ;

[0037] in, This represents the volume of the three-dimensional spatial region occupied by the free current. Indicates the current detection location. Indicates the initial magnetic source position;

[0038] Solution of the vector Poisson equation The simplification process yields a simplified result, which is specifically set as follows:

[0039] ;

[0040] in, Represents the dipole moment. Indicates the current detection position relative to the initial magnetic source position The distance between them;

[0041] S33: Based on the solution of the vector Poisson equation Calculate magnetic flux density magnetic flux density Specifically set as follows:

[0042] ;

[0043] For magnetic flux density The simplification process yields a simplified result, which is specifically set as follows:

[0044] ;

[0045] S34: Based on magnetic flux density Calculate the magnetic field strength magnetic field strength Specifically set as follows:

[0046] ;

[0047] S35: Calculate the magnetic field strength respectively x-axis direction component y-axis component and z-axis direction component x-axis component y-axis component and z-axis direction component Specifically set as follows:

[0048] ;

[0049] ;

[0050] ;

[0051] in, Represents dipole moment Component in the x-axis direction, Represents dipole moment Component in the y-axis direction Represents dipole moment Component in the z-axis direction Indicates the current detection position Component in the x-axis direction, Indicates the current detection position Component in the y-axis direction Indicates the current detection position Component in the z-axis direction.

[0052] Preferably, step S4 specifically includes the following steps:

[0053] S41: Using the dataset function of the finite element electromagnetic field calculation software, extract spatial magnetic field data that are parallel to the xy plane, yz plane and xz plane, and at distances of ±2.1m and ±4.6m from the corresponding reference planes, respectively;

[0054] S42: Set the extracted spatial magnetic field data as the attenuation coefficient of the initial magnetic source.

[0055] Preferably, step S7 specifically includes the following steps:

[0056] S71: Perform spatial interpolation on the set of attenuation coefficients. The specific interpolation algorithm is set as follows:

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] ;

[0063] in, Indicates the measurement point. This represents the magnetic field component of the interpolation along the x-axis. This represents the magnetic field component interpolated along the y-axis. This represents the magnetic field component of the interpolation along the z-axis. Indicates the first in the x-axis direction One known measured magnetic field component Indicates the first in the y-axis direction One known measured magnetic field component Indicates the first position in the z-axis direction One known measured magnetic field component Indicates the first in the x-axis direction One known measured magnetic field component Indicates the first in the y-axis direction One known measured magnetic field component Indicates the first in the z-axis direction One known measured magnetic field component Represents the normalization parameter. This represents the boundary conditions, i.e., the size range of the cargo numerical model. Indicates the interval in the size range The lower limit, Indicates the interval in the size range The upper limit, Indicates the interval in the size range Equally spaced interpolation points generated within the area. Indicates the length of the interpolation interval. Indicates the first in the x-axis direction A known measured second derivative Indicates the first in the y-axis direction A known measured second derivative Indicates the first in the z-axis direction A known measured second derivative Indicates the first in the x-axis direction A known measured second derivative Indicates the first in the y-axis direction A known measured second derivative Indicates the first position in the z-axis direction One known measured second derivative;

[0064] S72: Using the visualization function of MATLAB software, draw the three-dimensional spatial distribution maps of the original and interpolated magnetic field data respectively;

[0065] S73: Compare the spatial coordinates of the magnetic source and the distribution characteristics of the magnetic field strength in the distribution map to verify the effectiveness of the interpolation.

[0066] Preferably, in step S8, the translation method is specifically set as follows:

[0067] ;

[0068] in, This represents the attenuation coefficient after interpolation. This represents the attenuation coefficient after translation. This indicates the total number of interpolations. Indicates the number of displacement steps.

[0069] Preferably, step S9 specifically includes the following steps:

[0070] S91: Introducing a Filtering Threshold Based on the filtering threshold The space magnetic field data is filtered, and only those data that are not less than the filtering threshold are included. The space magnetic field data is coupled with the measured magnetic field data, specifically set as follows:

[0071] ;

[0072] ;

[0073] in, Data representing the magnetic field strength of the space magnetic field. Indicates the selected A dataset of intensity values Indicates the proportionality coefficient;

[0074] S92: Couple the measured magnetic field data collected by the array sensor with the attenuation coefficient at the corresponding location to solve for the magnetic field strength at distances of 2.1m and 4.6m from the surface of the object being measured. The specific method for solving the magnetic field strength is set as follows:

[0075] ;

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] in, This represents the magnetic field strength value at any location in space. This represents the magnetic field strength component along the x-axis at any location in space. This represents the magnetic field strength component along the y-axis at any location in space. This represents the magnetic field strength component along the z-axis at any location in space. Indicates measurement point Measured magnetic field data in the x-axis direction. Indicates measurement point Attenuation coefficient in the x-axis direction Indicates measurement point Measured magnetic field data in the y-axis direction. Indicates measurement point Attenuation coefficient in the y-axis direction Indicates measurement point Measured magnetic field data in the z-axis direction Indicates measurement point Attenuation coefficient in the z-axis direction;

[0081] S93: Evaluate the accuracy of the attenuation coefficient solution by quantitatively verifying it using both space magnetic field data and measured magnetic field data. The specific verification method is set as follows:

[0082] ;

[0083] in, This represents the percentage deviation relative to the global average. Indicates measurement point The magnetic field strength value in the x-axis direction is the magnetic field strength component. Indicates measurement point The magnetic field strength value in the y-axis direction is the magnetic field strength component. Indicates measurement point The magnetic field strength value in the z-axis direction is the magnetic field strength component. Indicates measurement point The spatial magnetic field strength component in the x-axis direction Indicates measurement point Components of the spatial magnetic field intensity in the y-axis direction Indicates measurement point The spatial magnetic field strength component in the z-axis direction;

[0084] S94: Extract the extreme values ​​from the solutions for the magnetic field strength at 2.1m and 4.6m respectively, and determine the maximum magnetic field strength values ​​at 2.1m and 4.6m;

[0085] S95: Compare the maximum magnetic field strength values ​​at 2.1m and 4.6m with the magnetic field strength limits specified in relevant international air transport standards, and determine the air transport safety status of the cargo based on the comparison results.

[0086] Therefore, the above-mentioned method for calculating the external magnetic field of cargo based on the numerical integration of the boundary magnetic field has the following beneficial effects:

[0087] (1) This scheme is based on the finite element method. It uses the finite element electromagnetic field calculation software to construct a numerical model for magnetic field calculation. Using the numerical solution function of the software, the initial calculation of the magnetic field strength at the detection positions of 2.1m and 4.6m is completed. Then, the initial data is spatially constrained by the cubic spline interpolation method, and the data coverage is limited to the effective size range of the cargo. This reduces the influence of invalid information on the subsequent calculation of the attenuation coefficient and improves the accuracy of the attenuation coefficient calculation.

[0088] (2) In order to reduce the overall data computation complexity and improve the solution efficiency, this scheme does not repeat the complete calculation process for each detection point. Instead, based on the uniformity of the magnetic field spatial distribution, it performs a translation operation on the interpolated magnetic field strength data. Through this operation, the final attenuation coefficient of each detection point in all planes is quickly obtained, which greatly reduces the number of repeated calculations and significantly shortens the overall calculation time.

[0089] The method of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0090] Figure 1 This is a flowchart of a method for calculating the external magnetic field of cargo based on the numerical integration of the boundary magnetic field according to the present invention;

[0091] Figure 2 This is a flowchart for solving the attenuation coefficient in this invention;

[0092] Figure 3 A flowchart for verifying the accuracy of this invention;

[0093] Figure 4 The diagram shows the results of the accuracy verification of the present invention, in which (a) simulated magnetic field distribution with a single magnetic source, (b) calculated magnetic field distribution with a single magnetic source, (c) simulated magnetic field distribution with two magnetic sources, (d) calculated magnetic field distribution with two magnetic sources, (e) simulated magnetic field distribution with three magnetic sources, and (f) calculated magnetic field distribution with three magnetic sources. Detailed Implementation

[0094] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0095] Unless otherwise defined, the methodological or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0096] The terms "comprising" or "including" as used in this invention mean that the element preceding the term encompasses the element listed after the term, and do not exclude the possibility of encompassing other elements. Terms such as "inner," "outer," "upper," and "lower" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. When the absolute position of the described object changes, the relative positional relationship may also change accordingly. In this invention, unless otherwise explicitly specified and limited, the term "attached" and similar terms should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can refer to a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication of two elements or the interaction relationship between two elements. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0097] Example

[0098] like Figures 1-3 As shown, this invention provides a method for calculating the external magnetic field of cargo based on the numerical integration of the boundary magnetic field, including the following steps:

[0099] S1: Construct a numerical model of the cargo in the finite element electromagnetic field calculation software and set the dimensions of the cargo numerical model;

[0100] Step S1 specifically includes the following steps:

[0101] S11: In the finite element electromagnetic field calculation software, construct a hexahedral numerical model that matches the actual shape of the measured cargo, and determine the six boundary planes of the hexahedral numerical model. The six boundary planes include the front, back, left, right, top, and bottom.

[0102] S12: Based on the physical deployment length of the array sensors in the actual detection environment, set the length, width, and height of the hexahedral numerical model to ensure that the model is geometrically similar to the actual detection scene, thereby reducing the magnetic field calculation error caused by scale deviation. In this embodiment, the width of the cargo is less than 3.3m, the height is less than 3.3m, and the length is less than 3m. Therefore, the length, width, and height of the designed array sensor model are x=3.295m, y=3m, and z=3.22m, respectively.

[0103] S13: Based on the number of array sensors deployed, determine the number of detection points in each boundary plane. Based on the number of horizontal array sensors deployed, determine the number of x-axis detection points. Based on the number of vertical array sensors deployed, determine the number of z-axis detection points. Based on the width range of the actual measured goods and the spacing between adjacent array sensors, determine the number of y-axis detection points. In this embodiment, the number of x-axis, y-axis, and z-axis detection points are 16, 200, and 16, respectively.

[0104] Within a certain range, the density of measurement and detection points is positively correlated with the accuracy of solving the spatial magnetic field. That is, the more detection points there are and the higher the degree of grid discretization, the higher the accuracy of subsequent spatial magnetic field strength calculation will be in theory. However, computational efficiency must be taken into account to avoid excessive discretization leading to excessive computation time.

[0105] S2: Determine the location of the initial magnetic source and set the initial magnetic source intensity based on the cargo numerical model;

[0106] Step S2 specifically includes the following steps:

[0107] S21: Select any x-axis detection point on any boundary plane and set it as the position of the initial magnetic source, and set the initial magnetic source intensity;

[0108] S22: Define the magnetic field strength vector of the initial magnetic source using three-dimensional components. Magnetic field strength vector Specifically set as follows:

[0109] ;

[0110] in, Represents the magnetic field strength vector The magnitude of the magnetic field in the x-axis direction, Represents the magnetic field strength vector The magnitude of the magnetic field in the y-axis direction. Represents the magnetic field strength vector The magnitude of the magnetic field in the z-axis direction;

[0111] S23: Perform three parameter assignments on the initial magnetic source to obtain the complete magnetic field contribution of the initial magnetic source in three-dimensional space. In each parameter assignment, a non-zero initial magnetic field component is set for any direction, and a zero initial magnetic field component is set for the other two directions. In this embodiment, the non-zero initial magnetic field component is set to 700. .

[0112] S3: The magnetic field strength at distances of 2.1m and 4.6m from the initial magnetic source intensity was calculated using finite element electromagnetic field calculation software to obtain spatial magnetic field data;

[0113] Step S3 specifically includes the following steps:

[0114] S31: Based on Maxwell's equations, the formula for solving the spatial magnetic field is derived. The specific formula for solving the spatial magnetic field is as follows:

[0115] ;

[0116] ;

[0117] ;

[0118] in, Indicates magnetic field strength. Represents the Laplace operator. Represents free current density. Represents magnetic flux density, Indicates permeability, Represents the permeability of free space. Indicates the magnetization of the material. Represents the solution to the vector Poisson equation;

[0119] S32: According to the vector identity The vector Poisson equation is obtained, and the vector Poisson equation is specifically set as follows:

[0120] ;

[0121] Solving the vector Poisson equation in free space yields the solution to the vector Poisson equation. Specifically set as follows:

[0122] ;

[0123] in, This represents the volume of the three-dimensional spatial region occupied by the free current. Indicates the current detection location. Indicates the initial magnetic source position;

[0124] Solution of the vector Poisson equation The simplification process yields a simplified result, which is specifically set as follows:

[0125] ;

[0126] in, Represents the dipole moment. Indicates the current detection position relative to the initial magnetic source position The distance between them;

[0127] S33: Based on the solution of the vector Poisson equation Calculate magnetic flux density magnetic flux density Specifically set as follows:

[0128] ;

[0129] For magnetic flux density The simplification process yields a simplified result, which is specifically set as follows:

[0130] ;

[0131] S34: Based on magnetic flux density Calculate the magnetic field strength magnetic field strength Specifically set as follows:

[0132] ;

[0133] S35: Calculate the magnetic field strength respectively x-axis direction component y-axis component and z-axis direction component x-axis component y-axis component and z-axis direction component Specifically set as follows:

[0134] ;

[0135] ;

[0136] ;

[0137] in, Represents dipole moment Component in the x-axis direction, Represents dipole moment Component in the y-axis direction Represents dipole moment Component in the z-axis direction Indicates the current detection position Component in the x-axis direction, Indicates the current detection position Component in the y-axis direction Indicates the current detection position Component in the z-axis direction.

[0138] Finite element electromagnetic field calculation software solves for the magnetic field strength at any location in space based on the above principle. Therefore, after selecting the initial magnetic source placement location and setting the initial magnetic field component parameters, the magnetic field calculation function of the finite element electromagnetic field calculation software can be used directly to solve for the spatial magnetic field strength distribution generated by the initial magnetic source in the entire calculation domain.

[0139] The magnetic field calculation results of the finite element electromagnetic field calculation software cover the entire simulation space by default, and can characterize the magnetic field intensity vector and component information of the initial magnetic source at any position in space. Since the core objective is to obtain magnetic field data at positions 2.1m and 4.6m away from the surface of the object being measured, targeted data extraction is required after the magnetic field calculation is completed through the software's post-processing function.

[0140] S4: Set the attenuation coefficient of the initial magnetic source based on the space magnetic field data;

[0141] Step S4 specifically includes the following steps:

[0142] S41: Using the dataset function of the finite element electromagnetic field calculation software, extract spatial magnetic field data that are parallel to the xy plane, yz plane and xz plane, and at distances of ±2.1m and ±4.6m from the corresponding reference planes, respectively;

[0143] S42: Set the extracted spatial magnetic field data as the attenuation coefficient of the initial magnetic source.

[0144] S5: Repeat steps S2-S4 until the attenuation coefficients of all transverse unit detection points are obtained;

[0145] After calculating the attenuation coefficient of the initial target detection point, the remaining transverse detection points are selected one by one as new calculation objects. Following the established magnetic field data extraction and processing methods in steps S2-S4, the attenuation coefficient corresponding to each transverse detection point is solved, and finally the complete calculation of the attenuation coefficient of a certain row of transverse detection points in the plane is achieved.

[0146] S6: Repeat steps S2-S5 until the attenuation coefficients of all transverse unit detection points on the boundary plane are obtained, thus obtaining the attenuation coefficient set;

[0147] After calculating the attenuation coefficient of a certain row of transverse detection points in a certain plane, the same calculation process needs to be performed on any row of transverse detection points in the other 5 planes according to the established magnetic field data extraction and processing methods in steps S2-S5. That is, by solving the magnetic field distribution and extracting coefficients through standardized magnetic field distribution, the attenuation coefficients corresponding to the transverse detection points in each plane are obtained. After the calculation of the transverse detection points of all planes is completed, all calculation results are integrated to finally construct a complete set of attenuation coefficients covering all plane information.

[0148] S7: Spatial interpolation of the attenuation coefficient set is performed using cubic spline interpolation.

[0149] Since the finite element electromagnetic field calculation software calculates the magnetic field intensity distribution at any location in space, even if the attenuation coefficient limits the distance in a certain direction, for example, the attenuation coefficient of the xy plane is 1, and the magnetic field intensity dataset of the xy plane at a distance of 2.1m from the surface of the object being measured, the spatial coverage of the original data in other directions still far exceeds the size range of the boundary plane. The data dimension includes magnetic field components in the x, y, and z directions, and the unit of magnetic field intensity is Tesla.

[0150] Since the spatial range of the original data does not match the effective size of the cargo, in order to ensure the accuracy of subsequent analysis, the original magnetic field data needs to be interpolated to constrain its spatial range to the effective size range of the cargo.

[0151] Cubic spline interpolation has advantages such as high smoothness of interpolation function, prominent locality features, and strong numerical stability. When processing multi-node, large-scale magnetic field datasets in three-dimensional space, it is not prone to numerical oscillations and can stably output interpolation results that conform to physical reality. Moreover, its computational complexity is moderate, balancing accuracy and efficiency. Therefore, this method is used to interpolate the original data.

[0152] Step S7 specifically includes the following steps:

[0153] S71: Perform spatial interpolation on the set of attenuation coefficients. The specific interpolation algorithm is set as follows:

[0154] ;

[0155] ;

[0156] ;

[0157] ;

[0158] ;

[0159] ;

[0160] in, Indicates the measurement point. This represents the magnetic field component of the interpolation along the x-axis. This represents the magnetic field component interpolated along the y-axis. This represents the magnetic field component of the interpolation along the z-axis. Indicates the first in the x-axis direction One known measured magnetic field component Indicates the first in the y-axis direction One known measured magnetic field component Indicates the first position in the z-axis direction One known measured magnetic field component Indicates the first in the x-axis direction One known measured magnetic field component Indicates the first in the y-axis direction One known measured magnetic field component Indicates the first position in the z-axis direction One known measured magnetic field component Represents the normalization parameter. This represents the boundary conditions, i.e., the size range of the cargo numerical model. Indicates the interval in the size range The lower limit, Indicates the interval in the size range The upper limit, Indicates the interval in the size range Equally spaced interpolation points generated within the area. Indicates the length of the interpolation interval. Indicates the first in the x-axis direction A known measured second derivative Indicates the first in the y-axis direction A known measured second derivative Indicates the first position in the z-axis direction A known measured second derivative Indicates the first in the x-axis direction A known measured second derivative Indicates the first in the y-axis direction A known measured second derivative Indicates the first position in the z-axis direction One known measured second derivative;

[0161] The cubic spline interpolation method divides the entire interpolation interval into several smaller intervals. In each smaller interval, a cubic polynomial is used to approximate the original function. Since the magnetic field data includes magnetic field components in the x, y, and z directions, the above algorithm provides interpolation polynomials for these three directions.

[0162] S72: In order to verify the reliability of the magnetic field distribution data after interpolation, that is, the consistency between the interpolated data and the original data, the visualization function of MATLAB software was used to draw the three-dimensional spatial distribution map of the original and interpolated magnetic field data respectively.

[0163] S73: Compare the spatial coordinates of the magnetic source and the distribution characteristics of the magnetic field strength in the distribution map to verify the effectiveness of the interpolation.

[0164] S8: The attenuation coefficients after spatial interpolation of each boundary plane are translated. For magnetic field components that are translated beyond the domain, zero-value boundary conditions are applied to obtain the final set of attenuation coefficients.

[0165] After interpolation, the dataset size of all horizontal detection points is unified. To obtain the attenuation coefficients of all detection points in all planes, a row of detection points can be selected as the starting calculation object in any target plane: starting from the first horizontal detection point in the row, the attenuation coefficient of the detection point is calculated according to the magnetic field data extraction, interpolation and coefficient solving process established in steps S2-S7; then the remaining detection points in the row are processed in sequence until the calculation of all detection points in the row is completed; repeat this row and column traversal logic until the attenuation coefficients of all detection points in the plane are calculated. Referring to the above calculation process of the attenuation coefficients of all detection points in the same plane, the attenuation coefficients of all detection points in the other 5 planes can be solved one by one.

[0166] However, while the above method can ensure the accuracy of the attenuation coefficient calculation, it has significant limitations in practical applications: due to the large number of detection points in the model, and the fact that each detection point needs to perform three independent repeated calculations to obtain complete magnetic field information, the overall number of calculations increases significantly, resulting in problems such as huge calculation time and low solution efficiency, which is not conducive to the subsequent realization of efficient and fast large-scale data processing.

[0167] Given the uniformity of magnetic field distribution in space and the continuous variation of magnetic field strength between adjacent detection points, the calculation process was optimized based on this characteristic: the interpolated magnetic field strength data was directly translated to quickly obtain the magnetic field distribution information of adjacent detection points; for magnetic field data that exceeds the boundary plane size after translation, zero-value boundary conditions were used for supplementary processing, that is, by setting the constraint that the magnetic field strength in the region outside the boundary is zero, the spatial integrity and physical rationality of the data are ensured, thereby significantly reducing the amount of calculation and improving the solution efficiency while ensuring the calculation accuracy.

[0168] In step S8, the translation method is specifically set as follows:

[0169] ;

[0170] in, This represents the attenuation coefficient after interpolation. This represents the attenuation coefficient after translation. This indicates the total number of interpolations. Indicates the number of displacement steps.

[0171] Therefore, the attenuation coefficients of all detection points can be quickly solved using the shift algorithm described above.

[0172] S9: Couple the measured magnetic field data collected by the array sensor with the attenuation coefficient at the corresponding position to solve the magnetic field strength at 2.1m and 4.6m away from the surface of the object being measured.

[0173] Specifically, the array sensor can acquire the measured magnetic field data at each measurement point. By multiplying the measured data with the attenuation coefficient at the corresponding spatial position 2.1m away from the surface of the object, the magnetic field strength in the plane at that distance can be obtained. Similarly, by multiplying the same set of measured data with the attenuation coefficient at the corresponding spatial position 4.6m away, the magnetic field strength in the plane at a distance of 4.6m can be obtained.

[0174] Step S9 specifically includes the following steps:

[0175] S91: Due to the large number of detection points, and the fact that the attenuation coefficient and simulated magnetic field data for each detection point are both 3×n matrices, the calculation of the spatial magnetic field strength is highly complex and time-consuming. Statistical results show that the calculation time for a 2.1m spatial magnetic field is about 1 hour. This time consumption is difficult to meet the efficiency requirements of actual freight inspection. Therefore, a screening threshold is introduced. Based on the filtering threshold The space magnetic field data is filtered, and only those data that are not less than the filtering threshold are included. The measured magnetic field data is coupled with the attenuation coefficient at the corresponding location, specifically set as follows:

[0176] ;

[0177] ;

[0178] in, Data representing the magnetic field strength of the space magnetic field. Indicates the selected A dataset of intensity values This represents the proportionality coefficient, which needs to be determined based on the actual scenario.

[0179] To evaluate the impact of applying the screening threshold on computational accuracy, this embodiment compares and analyzes the deviation between the calculated magnetic field and the simulated magnetic field before and after threshold screening. The results show that the deviation is about 4% when the threshold is not applied, while the deviation increases by only 1% after applying the threshold. The difference between the two is small, indicating that the screening threshold can maintain high computational accuracy while significantly improving computational efficiency, thus verifying the effectiveness of the strategy.

[0180] S92: Couple the measured magnetic field data collected by the array sensor with the attenuation coefficient at the corresponding location to solve for the magnetic field strength at distances of 2.1m and 4.6m from the surface of the object being measured. The specific method for solving the magnetic field strength is set as follows:

[0181] ;

[0182] ;

[0183] ;

[0184] ;

[0185] ;

[0186] in, This represents the magnetic field strength value at any location in space. This represents the magnetic field strength component along the x-axis at any location in space. This represents the magnetic field strength component along the y-axis at any location in space. This represents the magnetic field strength component along the z-axis at any location in space. Indicates measurement point Measured magnetic field data in the x-axis direction. Indicates measurement point Attenuation coefficient in the x-axis direction Indicates measurement point Measured magnetic field data in the y-axis direction. Indicates measurement point Attenuation coefficient in the y-axis direction Indicates measurement point Measured magnetic field data in the z-axis direction Indicates measurement point Attenuation coefficient in the z-axis direction;

[0187] In the above calculations, special attention should be paid to the matching of the detection point location data. Since there are many detection points, and each detection point contains measured data and attenuation data in the x, y, and z directions, the principle of "detection point correspondence" must be strictly followed in the product calculation of the measured magnetic field data and the attenuation coefficient. That is, the measured x-axis magnetic field component of the detection point is only multiplied by the "attenuation coefficient solved when the initial component in the x direction is not zero", the y-axis component is only multiplied by the "attenuation coefficient solved when the initial component in the y direction is not zero", and the z-axis component is the same.

[0188] In the actual scenario of airport cargo inspection, a preliminary preparation process needs to be completed before each batch of cargo is inspected, such as cargo size estimation and cargo information entry. This process takes about 20-30 seconds. For airport cargo inspection systems, in addition to the accuracy of spatial magnetic field strength calculation, magnetic field solution efficiency is also a key indicator affecting cargo inspection speed, inspection process continuity and personnel work efficiency. Excessive solution time will lead to congestion in the inspection queue and reduce overall inspection efficiency. If the solution time can be matched with the time of the preliminary preparation process, seamless connection of the inspection process can be achieved, and the system operation efficiency can be improved.

[0189] S93: Evaluate the accuracy of the attenuation coefficient solution by quantitatively verifying it using both space magnetic field data and measured magnetic field data. The specific verification method is set as follows:

[0190] ;

[0191] in, This represents the percentage deviation relative to the global average. Indicates measurement point The magnetic field strength value in the x-axis direction is the magnetic field strength component. Indicates measurement point The magnetic field strength value in the y-axis direction is the magnetic field strength component. Indicates measurement point The magnetic field strength value in the z-axis direction is the magnetic field strength component. Indicates measurement point The spatial magnetic field strength component in the x-axis direction Indicates measurement point Components of the spatial magnetic field intensity in the y-axis direction Indicates measurement point The spatial magnetic field strength component in the z-axis direction;

[0192] The calculation results show that the deviation between the measured magnetic field and the space magnetic field is less than 5%, indicating that the accuracy of the attenuation coefficient calculation meets the application requirements.

[0193] S94: Extract the extreme values ​​from the solutions for the magnetic field strength at 2.1m and 4.6m respectively, and determine the maximum magnetic field strength values ​​at 2.1m and 4.6m;

[0194] S95: Compare the maximum magnetic field strength values ​​at 2.1m and 4.6m with the magnetic field strength limits specified in relevant international air transport standards, and determine the air transport safety status of the cargo based on the comparison results.

[0195] The solution time of the spatial magnetic field proposed in this embodiment was statistically analyzed. The results show that the solution time of the spatial magnetic field of this method can be controlled within 20 seconds, which can be completed simultaneously in the early preparation stage of cargo inspection. From the perspective of time, the solution efficiency can fully meet the actual process requirements of airport cargo inspection.

[0196] like Figure 4 As shown, under different magnetic source configurations of single, two, and three magnetic sources, the comparison results of the simulated and calculated magnetic fields at a distance of 2.1m from the cargo surface show that the simulated and calculated magnetic fields maintain good consistency in terms of the spatial distribution of the magnetic sources and the amplitude of the magnetic field intensity, further verifying the reliability of the attenuation coefficient solution method and the magnetic field calculation results in this study.

[0197] Therefore, the present invention adopts the above-mentioned method for calculating the external magnetic field of cargo based on the numerical integration of the boundary magnetic field, which not only achieves efficient and non-destructive testing of the magnetic strength of transported cargo, but also further improves the safety of air transport, reduces operational risks, and provides technical support for ensuring the economic performance of air transport.

[0198] Finally, it should be noted that the above embodiments are only used to illustrate the method of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the method of the present invention, and these modifications or equivalent substitutions should not cause the modified method to deviate from the spirit and scope of the method of the present invention.

Claims

1. A method for calculating the external magnetic field of cargo based on numerical integration of boundary magnetic field, characterized in that, Includes the following steps: S1: Construct a numerical model of the cargo in the finite element electromagnetic field calculation software and set the dimensions of the cargo numerical model; S2: Determine the location of the initial magnetic source and set the initial magnetic source intensity based on the cargo numerical model; S3: The magnetic field strength at distances of 2.1m and 4.6m from the initial magnetic source intensity was calculated using finite element electromagnetic field calculation software to obtain spatial magnetic field data; S4: Set the attenuation coefficient of the initial magnetic source based on the space magnetic field data; S5: Repeat steps S2-S4 until the attenuation coefficients of all transverse unit detection points are obtained; S6: Repeat steps S2-S5 until the attenuation coefficients of all transverse unit detection points on the boundary plane are obtained, thus obtaining the attenuation coefficient set; S7: Spatial interpolation of the attenuation coefficient set is performed using cubic spline interpolation. S8: The attenuation coefficients after spatial interpolation of each boundary plane are translated. For magnetic field components that are translated beyond the domain, zero-value boundary conditions are applied to obtain the final set of attenuation coefficients. S9: Couple the measured magnetic field data collected by the array sensor with the attenuation coefficient at the corresponding position to solve the magnetic field strength at 2.1m and 4.6m away from the surface of the object being measured.

2. The method for calculating the external magnetic field of cargo based on numerical integration of boundary magnetic field according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11: In the finite element electromagnetic field calculation software, construct a hexahedral numerical model that matches the actual shape of the measured cargo, and determine the six boundary planes of the hexahedral numerical model. The six boundary planes include the front, back, left, right, top, and bottom. S12: Set the length, width, and height of the hexahedral numerical model according to the physical layout length of the array sensors in the actual detection environment; S13: Determine the number of detection points in each boundary plane based on the number of array sensors deployed. Determine the number of x-axis detection points based on the number of horizontal array sensors deployed. Determine the number of z-axis detection points based on the number of vertical array sensors deployed. Determine the number of y-axis detection points based on the width range of the actual measured goods and the spacing between adjacent array sensors.

3. The method for calculating the external magnetic field of cargo based on numerical integration of boundary magnetic field according to claim 2, characterized in that, Step S2 specifically includes the following steps: S21: Select any x-axis detection point on any boundary plane and set it as the position of the initial magnetic source, and set the initial magnetic source intensity; S22: Define the magnetic field strength vector of the initial magnetic source using three-dimensional components. Magnetic field strength vector Specifically set as follows: ； in, Represents the magnetic field strength vector The magnitude of the magnetic field in the x-axis direction, Represents the magnetic field strength vector The magnitude of the magnetic field in the y-axis direction. Represents the magnetic field strength vector The magnitude of the magnetic field in the z-axis direction; S23: Perform three assignments of magnetic source parameters to the initial magnetic source to obtain the complete magnetic field contribution of the initial magnetic source in three-dimensional space. In a single assignment of magnetic source parameters, a non-zero initial magnetic field component is set for any direction, and a zero initial magnetic field component is set for the other two directions.

4. The method for calculating the external magnetic field of cargo based on numerical integration of boundary magnetic field according to claim 3, characterized in that, Step S3 specifically includes the following steps: S31: Based on Maxwell's equations, the formula for solving the spatial magnetic field is derived. The specific formula for solving the spatial magnetic field is as follows: ； ； ； in, Indicates magnetic field strength. Represents the Laplace operator. Represents free current density. Represents magnetic flux density, Indicates magnetic permeability, Represents the permeability of free space. Indicates the magnetization of the material. Represents the solution to the vector Poisson equation; S32: According to the vector identity The vector Poisson equation is obtained, and the vector Poisson equation is specifically set as follows: ； Solving the vector Poisson equation in free space yields the solution to the vector Poisson equation. Specifically set as follows: ； in, This represents the volume of the three-dimensional spatial region occupied by the free current. Indicates the current detection location. Indicates the initial magnetic source position; Solution to the vector Poisson equation The simplification process yields a simplified result, which is specifically set as follows: ； in, Represents the dipole moment. Indicates the current detection position relative to the initial magnetic source position The distance between them; S33: Based on the solution of the vector Poisson equation Calculate magnetic flux density magnetic flux density Specifically set as follows: ； For magnetic flux density The simplification process yields a simplified result, which is specifically set as follows: ； S34: Based on magnetic flux density Calculate the magnetic field strength magnetic field strength Specifically set as follows: ； S35: Calculate the magnetic field strength respectively x-axis component y-axis component and z-axis direction component x-axis component y-axis component and z-axis direction component Specifically set as follows: ； ； ； in, Represents dipole moment Component in the x-axis direction, Represents dipole moment Component in the y-axis direction Represents dipole moment Component in the z-axis direction Indicates the current detection position Component in the x-axis direction, Indicates the current detection position Component in the y-axis direction Indicates the current detection position Component in the z-axis direction.

5. The method for calculating the external magnetic field of cargo based on numerical integration of boundary magnetic field according to claim 4, characterized in that, Step S4 specifically includes the following steps: S41: Using the dataset function of the finite element electromagnetic field calculation software, extract spatial magnetic field data that are parallel to the xy plane, yz plane and xz plane, and at distances of ±2.1m and ±4.6m from the corresponding reference planes, respectively; S42: Set the extracted spatial magnetic field data as the attenuation coefficient of the initial magnetic source.

6. The method for calculating the external magnetic field of cargo based on numerical integration of boundary magnetic field according to claim 5, characterized in that, Step S7 specifically includes the following steps: S71: Perform spatial interpolation on the set of attenuation coefficients. The specific interpolation algorithm is set as follows: ； ； ； ； ； ； in, Indicates the measurement point. This represents the magnetic field component of the interpolation along the x-axis. This represents the magnetic field component of the interpolation along the y-axis. This represents the magnetic field component of the interpolation along the z-axis. Indicates the first in the x-axis direction One known measured magnetic field component Indicates the first in the y-axis direction One known measured magnetic field component Indicates the first in the z-axis direction One known measured magnetic field component Indicates the first in the x-axis direction One known measured magnetic field component Indicates the first in the y-axis direction One known measured magnetic field component Indicates the first position in the z-axis direction One known measured magnetic field component Represents the normalization parameter. This represents the boundary conditions, i.e., the size range of the cargo numerical model. Indicates the interval in the size range The lower limit, Indicates the interval in the size range The upper limit, Indicates the interval in the size range Equally spaced interpolation points generated within. Indicates the length of the interpolation interval. Indicates the first in the x-axis direction A known measured second derivative Indicates the first in the y-axis direction A known measured second derivative Indicates the first position in the z-axis direction A known measured second derivative Indicates the first in the x-axis direction A known measured second derivative Indicates the first in the y-axis direction A known measured second derivative Indicates the first position in the z-axis direction One known measured second derivative; S72: Using the visualization function of MATLAB software, draw the three-dimensional spatial distribution maps of the original and interpolated magnetic field data respectively; S73: Compare the spatial coordinates of the magnetic source and the distribution characteristics of the magnetic field strength in the distribution map to verify the effectiveness of the interpolation.

7. The method for calculating the external magnetic field of cargo based on numerical integration of boundary magnetic field according to claim 6, characterized in that, In step S8, the translation method is specifically set as follows: ； in, This represents the attenuation coefficient after interpolation. This represents the attenuation coefficient after translation. This indicates the total number of interpolations. Indicates the number of displacement steps.

8. The method for calculating the external magnetic field of cargo based on numerical integration of boundary magnetic field according to claim 7, characterized in that, Step S9 specifically includes the following steps: S91: Introducing a screening threshold Based on the filtering threshold The space magnetic field data is filtered, and only those data that are not less than the filtering threshold are included. The space magnetic field data is coupled with the measured magnetic field data, specifically set as follows: ； ； in, Data representing the magnetic field strength in space. Indicates the selected A dataset of intensity values, Indicates the proportionality coefficient; S92: Couple the measured magnetic field data collected by the array sensor with the attenuation coefficient at the corresponding location to solve for the magnetic field strength at distances of 2.1m and 4.6m from the surface of the object being measured. The specific method for solving the magnetic field strength is set as follows: ； ； ； ； ； in, This represents the magnetic field strength value at any location in space. This represents the magnetic field strength component along the x-axis at any location in space. This represents the magnetic field strength component along the y-axis at any location in space. This represents the magnetic field strength component along the z-axis at any location in space. Indicates measurement point Measured magnetic field data in the x-axis direction. Indicates measurement point Attenuation coefficient in the x-axis direction Indicates measurement point Measured magnetic field data in the y-axis direction. Indicates measurement point Attenuation coefficient in the y-axis direction Indicates measurement point Measured magnetic field data in the z-axis direction Indicates measurement point Attenuation coefficient in the z-axis direction; S93: Evaluate the accuracy of the attenuation coefficient solution by quantitatively verifying it using both space magnetic field data and measured magnetic field data. The specific verification method is set as follows: ； in, This represents the percentage deviation relative to the global average. Indicates measurement point The magnetic field strength value in the x-axis direction is the magnetic field strength component. Indicates measurement point The magnetic field strength value in the y-axis direction is the magnetic field strength component. Indicates measurement point The magnetic field strength value in the z-axis direction is the magnetic field strength component. Indicates measurement point The spatial magnetic field strength component in the x-axis direction Indicates measurement point Components of the spatial magnetic field intensity in the y-axis direction Indicates measurement point The spatial magnetic field intensity component in the z-axis direction; S94: Extract the extreme values ​​from the solutions for the magnetic field strength at 2.1m and 4.6m respectively, and determine the maximum magnetic field strength values ​​at 2.1m and 4.6m; S95: Compare the maximum magnetic field strength values ​​at 2.1m and 4.6m with the magnetic field strength limits specified in relevant international air transport standards, and determine the air transport safety status of the cargo based on the comparison results.

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