Underwater target comprehensive magnetic field time-space characteristic analysis method

Abstract

The invention discloses an underwater target comprehensive magnetic field time-space characteristic analysis method, which adopts COMSOL and MATLAB software to perform modeling research on a magnetic anomaly field and a wake flow magnetic field respectively, and utilizes App Designer of MATLAB to construct a unified user interface to integrate two magnetic field simulation results, thereby realizing enhancement of target comprehensive magnetic field model precision and improvement of simulation analysis efficiency. Full-automatic solution of the target magnetic field is realized through interactive operation, so that acquisition of space-time characteristics and attenuation laws of the magnetic field under different parameters is more concise and visual, and then the efficiency of underwater target magnetic detection is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater target detection, and in particular relates to a method for analyzing the spatiotemporal characteristics of the comprehensive magnetic field of an underwater target. Background Art

[0002] Accurate modeling of the magnetic field radiated by underwater targets is of great significance for improving the accuracy and efficiency of magnetic detection. The radiated magnetic field of underwater targets is mainly divided into two types: one is the magnetic anomaly field generated by the magnetization of the target's ferromagnetic shell by the geomagnetic field, and the other is the wake magnetic field generated by the seawater's wake disturbance cutting through the geomagnetic field when the target moves. In actual detection scenarios, magnetic sensors receive the total magnetic field signal, but current simulations and analyses of the magnetic anomaly field and wake magnetic field are mostly performed independently. There is a lack of systematic research on the radiation mechanism, propagation model, spatiotemporal characteristics, and attenuation law of the integrated magnetic field, making it difficult to effectively promote the development and application of underwater target magnetic detection technology.

[0003] To accurately assess the spatiotemporal characteristics of the magnetic field radiated by underwater targets, it is necessary to integrate the magnetic anomaly field model with the wake magnetic field model, comprehensively analyze the spatiotemporal characteristics and attenuation patterns of the target's radiated magnetic field, and deeply explore the impact of target motion parameters and ocean environment parameters on the magnetic field, laying a research foundation for improving magnetic detection technology. The combined use of MATLAB and COMSOL software can achieve these goals and has the following advantages:

[0004] (1) COMSOL software has powerful three-dimensional dynamic modeling and post-processing capabilities, which can accurately calculate the spatiotemporal distribution characteristics of the magnetic anomaly field;

[0005] (2) MATLAB software is capable of complex numerical calculations and graphics processing, and is suitable for simulation analysis of wake magnetic fields, providing detailed magnetic field distribution and variation patterns.

[0006] (3) MATLAB's App Designer can integrate the simulation results of COMSOL and MATLAB, provide a unified user interface, realize fully automated solution of magnetic fields, and improve model accuracy and simulation efficiency. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this paper provides a method for analyzing the spatiotemporal characteristics of the integrated magnetic field of underwater targets. This method uses COMSOL and MATLAB software to model the magnetic anomaly field and wake magnetic field, respectively. MATLAB's AppDesigner is then used to create a unified user interface to integrate the two magnetic field simulation results. This method enhances the accuracy of the integrated magnetic field model and improves the efficiency of simulation analysis. This interactive operation enables fully automated solution of the target magnetic field, making the spatiotemporal characteristics and attenuation patterns of the magnetic field under different parameters more concise and intuitive, thereby improving the efficiency of underwater target magnetic detection.

[0008] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0009] Step 1: Set and unify the physical parameters of the background field;

[0010] Step 2: Create a geometric model of the underwater target in COMSOL;

[0011] Step 3: Solve the underwater target magnetic anomaly field using COMSOL;

[0012] Step 4: Save the result data in COMSOL;

[0013] Step 5: Establish the wake velocity field model in MATLAB;

[0014] Step 6: Solve the magnetic field of the underwater target wake using MATLAB;

[0015] Step 7: Save the result data in MATLAB;

[0016] Step 8: Use APP Designer to design the interface;

[0017] Step 9: Integrate underwater target magnetic anomaly field and wake magnetic field data for simulation and solution;

[0018] Step 10: Perform data processing and analysis based on the calculation results.

[0019] Furthermore, the step 1 is specifically as follows:

[0020] Step 1-1: Set the background magnetic field inside the underwater target calculation domain to a uniform magnetic field; The positive axis points to geographic north. The positive axis points to geographic west. Positive axis perpendicular to Facing upward; geomagnetic induction intensity exist The projection on the plane is , and The angle between them is the magnetic inclination , downward inclination is positive; The angle between the magnetic declination and geographic north is the magnetic declination. , the east declination is positive; then the geomagnetic induction intensity is expressed as:

[0021] (1)

[0022] Where, is the magnitude of the Earth's magnetic field, 、 、 Represent the unit vectors along the x, y, and z axes respectively;

[0023] Using the IGRF-14 world geomagnetic field model, according to the formula The magnetic induction intensity of the Earth's magnetic field in the x, y, and z directions is further calculated;

[0024] Step 1-2: Solve the magnetic anomaly field and wake magnetic field of the underwater target, and divide the entire calculation domain into sea water and air domain; set the sea level height to , the sea area below the sea level is expressed as ; Above the sea level is the air domain, represented by .

[0025] Furthermore, the step 2 is specifically as follows:

[0026] Step 2-1: Open COMSOL Multiphysics, select the Model Wizard, set the spatial dimension to 3D, and the physical field to "Magnetic Field, No Current." Treat the underwater target as a simplified rotating ellipsoid model. First, create an ellipse on the "Work Plane" with the major axis equal to the total length of the underwater target and the minor axis equal to the maximum diameter. Then, convert the 2D plane into a 3D solid.

[0027] Step 2-2: Select "User Controlled Mesh" as the meshing method, where the underwater target is a "Free Triangle" mesh and the computational domain is a "Free Tetrahedron" mesh; the shell material of the underwater target uses the steel material in the built-in material library, and it is assumed that the target has been demagnetized.

[0028] Furthermore, the step 3 is specifically as follows:

[0029] Step 3-1: Assume the aircraft is flying above sea level at the initial moment When the underwater target is at point O, its x-coordinate and y-coordinate are both 0, and the z-coordinate is the depth below the sea level. Target at speed Move in a straight line with uniform speed from north to south along the negative x-axis;

[0030] Step 3-2: Set up the solver in COMSOL, select the "steady state" method to solve the spatial distribution of the magnetic anomaly field, and add a "parametric sweep" step to solve the time domain characteristics of the underwater target magnetic anomaly field; according to Gauss's magnetic law, we can obtain:

[0031]

[0032] In the formula, ” is the divergence operator; is the magnetic anomaly magnetic induction intensity, expressed as:

[0033]

[0034] Where, is the magnetic anomaly field intensity, is the vacuum permeability, , is the relative magnetic permeability of the ferromagnetic target housing material, ;

[0035] Step 3-3: The formula Substitution have to:

[0036]

[0037] Magnetic anomaly field strength Defined as:

[0038]

[0039] Where, is the scalar magnetic potential, is the Earth's magnetic field strength;

[0040] General Substitution Get the differential equation to be solved:

[0041]

[0042] Where, the geomagnetic induction intensity ;

[0043] Step 3-4: The external boundary conditions of the computational domain are insulating from the Earth's magnetic field, as follows:

[0044]

[0045] Where, is the boundary normal vector of the target shell surface;

[0046] By Get the magnetic anomaly field that needs to be solved:

[0047]

[0048] After the solution is completed, add a "1D Plot Group" to the "Results" in the main screen bar to obtain the magnetic anomaly field vector field in the x, y, and z directions on the detection path.

[0049] Furthermore, the step 4 is specifically as follows:

[0050] In the COMSOL menu bar, click "Results" → "Export", select "Export Data", export the magnetic anomaly field vector field data on the detection plane, detection path and detection point respectively, specify the data save path and save format; select "Grid" as the data export format, and set the sampling points uniformly.

[0051] Furthermore, the step 5 is specifically as follows:

[0052] Step 5-1: The underwater target moves at a constant speed in the sea water Moving along the negative direction of the x-axis, the disturbed seawater generates free surface waves composed of diffusion waves and shear waves, namely the Kelvin wake;

[0053] The underwater target is equivalent to a rotating ellipsoid, and its volume formula is:

[0054]

[0055] Where, is the total target length, is the maximum diameter of the target;

[0056] Free spectral function of underwater target wake Expressed as:

[0057]

[0058] Where, is the target speed, is the angle between the propagation direction of the wake wave and the x-axis, is the wake wave number, expressed as:

[0059]

[0060] Where, is the acceleration due to gravity, ;

[0061] Step 5-2: The wake velocity field of the underwater target is:

[0062]

[0063] Where, is the angular frequency, , For time, is the harmonic component of the wake velocity field, where the vector Expressed as:

[0064]

[0065] Where, is the diving depth of the underwater target, is the unit vector of the wake wave propagation direction, and:

[0066]

[0067] After solving, the wake velocity vector field in the x, y, and z directions on the detection plane is obtained.

[0068] Furthermore, the step 6 is specifically as follows:

[0069] Step 6-1: According to Faraday's law of electromagnetic induction, a time-varying magnetic field generates an electric field, namely:

[0070]

[0071] In the formula, ” is the curl operator, is the wake electric field intensity, is the wake magnetic induction intensity, expressed as:

[0072]

[0073] From Ampere's circuit law, we know that the current and the time-varying electric field generate a magnetic field, that is:

[0074]

[0075] Where, is the magnetic permeability of seawater, is the dielectric constant of seawater, is the current density, expressed as:

[0076] (18)

[0077] Where, is the electrical conductivity of seawater, ,Will is approximately regarded as 0, so the formula Simplified to:

[0078]

[0079] Step 6-2: The formula Substitution and Further simplifying the solution, we get Maxwell's equations:

[0080]

[0081] (twenty one)

[0082] General Substitution ,get:

[0083]

[0084] Reference , wake magnetic field strength Satisfies the relationship:

[0085]

[0086] Step 6-3: Assume that seawater is an incompressible fluid whose volume remains constant during flow, without compression or expansion, that is:

[0087] (twenty four)

[0088] Considering that the wave height of the seawater free surface wave is much smaller than its wavelength, the free surface is approximately regarded as a plane, that is, ;Introduction of Laplace operator , then the wake magnetic field strength The identity is:

[0089]

[0090] According to the formula and ,Mode Simplified to:

[0091]

[0092] General Substitution In, we get:

[0093]

[0094] Step 6-4: The wake magnetic field strength generated by the underwater target is:

[0095]

[0096] Where, is the harmonic component of the wake magnetic field, where Expressed as:

[0097]

[0098] In the formula, the introduced vector and Respectively expressed as:

[0099]

[0100]

[0101] Where, is the complex parameter of electromagnetic wave propagation in the medium, , subscript Corresponding to the air domain and sea water domain respectively; is the parameter of electromagnetic wave propagation in air, ;

[0102] A point on the aircraft detection path is taken as the detection point, and the wake magnetic field vector field in the x, y, and z directions at the detection point is obtained after solving.

[0103] Furthermore, the step 7 is specifically as follows:

[0104] In MATLAB, the "fprintf" command is used to export the wake magnetic field data on the detection plane, detection path, and detection point, respectively, and the data saving path and format are specified; the data is exported in the form of a "grid", and the sampling points are uniformly set to ensure the consistency and comparability of the data.

[0105] Furthermore, the step 8 is specifically as follows:

[0106] Use MATLAB's App Designer to design the interface of the visual simulation system, including parameter input module, result solution module and data analysis module;

[0107] The parameter input module includes the settings of underwater targets, calculation domain, geomagnetic field, seawater and detection parameters; for geomagnetic field parameters, the IGRF model is automatically calculated to obtain the corresponding magnetic induction intensity, magnetic inclination and magnetic declination values, which are displayed synchronously in the interface; detection parameters include detection height and sensitivity;

[0108] The result solution module displays a basic model including a geometric model and a wake velocity field model, and also displays the spatial distribution of the magnetic field radiated by several underwater targets on the detection plane or detection path, as well as the time domain characteristics at the detection point;

[0109] The data analysis module solves the maximum amplitude of the magnetic field based on the detection plane, detection path and detection point respectively, and displays the coordinates of the aircraft detection position at this time.

[0110] Furthermore, the step 9 is specifically as follows:

[0111] The magnetic anomaly field calculated by COMSOL software Wake magnetic field calculated with MATLAB software Vector superposition to obtain the comprehensive magnetic field , expressed as:

[0112]

[0113] Livelink for MATLAB enables real-time connectivity between COMSOL and MATLAB.

[0114] The result solution module in the simulation interface consists of three parts: "Basic Model" displays the geometric model of the underwater target and the model diagram of the wake velocity field vector field; "Spatial Distribution" displays the distribution diagram of the magnetic anomaly field, wake magnetic field and comprehensive magnetic field vector field on the detection plane or detection path; "Time Domain Characteristics" displays the characteristic diagram of the magnetic anomaly field, wake magnetic field and comprehensive magnetic field vector field at the detection point.

[0115] Furthermore, the step 10 is specifically as follows:

[0116] After integrating the magnetic anomaly field and wake magnetic field data according to step 9, the maximum amplitudes of the magnetic anomaly field, wake magnetic field, and comprehensive magnetic field are calculated. The data analysis module determines the detection possibility through three methods: detection plane, detection path, and detection point. If the maximum amplitude of any vector field of the same magnetic field type is higher than or equal to the sensitivity, it means that the target can be detected, and the text box displays "Yes", otherwise it displays "No", thus completing the entire process of underwater target comprehensive magnetic field simulation analysis.

[0117] The beneficial effects of the present invention are as follows:

[0118] (1) The present invention is based on the Windows platform and uses MATLAB's APP Designer as a development tool. By simply selecting options and inputting key parameters, the design of a method for analyzing the spatiotemporal characteristics of the integrated magnetic field of underwater targets can be efficiently completed, and the simulation results can be intuitively displayed in one-dimensional, two-dimensional, and three-dimensional visual images.

[0119] (2) Through the joint simulation and magnetic field integration of COMSOL and MATLAB, the solution objects of the magnetic anomaly field and the wake magnetic field are unified, the solution speed of the comprehensive magnetic field is accelerated, and the consistency of the relevant parameters of the two magnetic fields is ensured, thereby improving the model accuracy of the comprehensive magnetic field. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] Figure 1 It is a flow chart of the method of the present invention.

[0121] Figure 2 Schematic diagram of the relationship between the direction of the geomagnetic field and the target motion coordinate system according to an embodiment of the present invention.

[0122] Figure 3 It is a geometric model diagram of the equivalent rotating ellipsoid of the underwater target in an embodiment of the present invention.

[0123] Figure 4 Schematic diagram of the spatial position of the aircraft detection plane and detection path according to an embodiment of the present invention.

[0124] Figure 5 It is a spatial distribution diagram of the x component of the magnetic anomaly field on the detection path of an embodiment of the present invention.

[0125] Figure 6 It is a spatial distribution diagram of the y component of the magnetic anomaly field on the detection path of an embodiment of the present invention.

[0126] Figure 7 It is a spatial distribution diagram of the z component of the magnetic anomaly field on the detection path of an embodiment of the present invention.

[0127] Figure 8 Schematic diagram of the wake generated during the motion of an underwater target according to an embodiment of the present invention.

[0128] Figure 9 3 is a spatial distribution diagram of the x-component of the wake velocity field on the detection plane according to an embodiment of the present invention.

[0129] Figure 10 3 is a spatial distribution diagram of the y component of the wake velocity field on the detection plane according to an embodiment of the present invention.

[0130] Figure 11 3 is a spatial distribution diagram of the z component of the wake velocity field on the detection plane according to an embodiment of the present invention.

[0131] Figure 12 Schematic diagram of the spatial position of the relationship between the aircraft detection point and the target according to an embodiment of the present invention.

[0132] Figure 13 3 is a time domain characteristic diagram of the x component of the wake magnetic field at the detection point according to an embodiment of the present invention.

[0133] Figure 143 is a time domain characteristic diagram of the y component of the wake magnetic field at the detection point according to an embodiment of the present invention.

[0134] Figure 15 3 is a time domain characteristic diagram of the z component of the wake magnetic field at the detection point according to an embodiment of the present invention.

[0135] Figure 16 It is a schematic diagram of the simulation interface of the comprehensive magnetic field of an underwater target according to an embodiment of the present invention.

[0136] Figure 17 It is a basic model effect diagram displayed on the simulation interface of the embodiment of the present invention.

[0137] Figure 18 3. It is a rendering of the spatial distribution of the target magnetic field on the detection plane according to an embodiment of the present invention.

[0138] Figure 19 It is a rendering of the spatial distribution of the target magnetic field on the detection path of an embodiment of the present invention.

[0139] Figure 20 It is a rendering of the time domain characteristics of the target magnetic field at the detection point according to an embodiment of the present invention. DETAILED DESCRIPTION

[0140] The present invention will be further described below with reference to the accompanying drawings and examples.

[0141] The purpose of the present invention is to address the problem of independent analysis of magnetic anomaly fields and wake magnetic fields in the existing technology and the lack of systematic research, and to propose a method for analyzing the spatiotemporal characteristics of the integrated magnetic field of underwater targets. This method uses COMSOL and MATLAB software to model the magnetic anomaly field and wake magnetic field respectively, and uses MATLAB's App Designer to build a unified user interface to integrate the two magnetic field simulation results, thereby enhancing the accuracy of the integrated magnetic field model of the target and improving the efficiency of simulation analysis. Through interactive operations, the target magnetic field is fully automated, making the acquisition of the spatiotemporal characteristics and attenuation laws of the magnetic field under different parameters more concise and intuitive, thereby improving the efficiency of underwater target magnetic detection.

[0142] The present invention is used to solve the problems of low solution efficiency and model accuracy in the prior art when analyzing the target magnetic anomaly field or wake magnetic field alone, and provides a new idea for the comprehensive magnetic field characteristic analysis of underwater targets.

[0143] This embodiment provides a joint simulation method for the temporal and spatial characteristics of the comprehensive magnetic field of an underwater target. Figure 1 As shown, the joint simulation method includes: steps S1 to S10.

[0144] Step S1: setting and unifying the physical parameters of the background field;

[0145] Step S2: Establishing the underwater target geometric model in COMSOL;

[0146] Step S3: solving the underwater target magnetic anomaly field by COMSOL;

[0147] Step S4: Save the result data in COMSOL;

[0148] Step S5: Establish a wake velocity field model in MATLAB;

[0149] Step S6: solving the underwater target wake magnetic field using MATLAB;

[0150] Step S7: Save the result data in MATLAB;

[0151] Step S8: Use APP Designer to design the interface;

[0152] Step S9: Integrate underwater target magnetic anomaly field and wake magnetic field data for simulation and solution;

[0153] Step S10: Perform data processing and analysis based on the calculation results.

[0154] Reference below Figures 2 to 20 Each step of the method for joint simulation of underwater target magnetic anomaly characteristics in this embodiment is described in more detail.

[0155] Step S1: setting and unifying the physical parameters of the background field;

[0156] Assume that the background magnetic field inside the underwater target calculation domain is a uniform magnetic field. The relationship between the direction of the geomagnetic field and the underwater target motion coordinate system is as follows: Figure 2 As shown; The positive axis points to geographic north. The positive axis points to geographic west. Positive axis perpendicular to Facing upward; geomagnetic induction intensity exist The projection on the plane is , and The angle between them is the magnetic inclination , downward inclination is positive; The angle between the magnetic declination and geographic north is the magnetic declination. , the east declination is positive; then the geomagnetic induction intensity is expressed as:

[0157]

[0158] Where, is the magnitude of the Earth's magnetic field, 、 、 Represent the unit vectors along the x, y, and z axes respectively;

[0159] The IGRF-14 global geomagnetic field model is used. In this embodiment, the geographical coordinates of a certain observation point are used as an example to set the parameters. The input parameters and output parameters of the geomagnetic field are as follows: As shown; according to the formula Further calculations yield the magnetic induction intensities of the Earth's magnetic field in the x, y, and z directions, which are: , , ;

[0160] surface Geomagnetic field input and output parameters

[0161]

[0162] The magnetic anomaly field and wake magnetic field of the underwater target are solved, and the entire calculation domain is divided into sea water and air domain; the height of the sea level is set to , the sea area below the sea level is expressed as ; Above the sea level is the air domain, represented by ; The basic physical quantities of seawater and air are set as follows shown.

[0163] surface Basic physical quantity settings of the computational domain

[0164]

[0165] Step S2: Establishing the underwater target geometric model in COMSOL;

[0166] Open COMSOL Multiphysics software, select the model wizard, set the spatial dimension to 3D, and the physical field to "magnetic field, no current". Equivalently treat the underwater target as a simplified rotating ellipsoid model. First, create an ellipse on the "working plane" with the major axis as the total length of the underwater target and the minor axis as the maximum diameter. Then, convert the two-dimensional plane into a three-dimensional entity. The constructed rotating ellipsoid model is as follows: Figure 3 As shown;

[0167] The meshing method is "User Controlled Mesh", where the underwater target is a "Free Triangle" mesh and the computational domain is a "Free Tetrahedron" mesh; the shell material of the underwater target is the steel material in the built-in material library, and it is assumed that the target has been demagnetized; a set of basic parameters of the target are set as follows shown.

[0168] surface Basic parameter settings for underwater targets

[0169]

[0170] Step S3: solving the underwater target magnetic anomaly field by COMSOL;

[0171] Assume the aircraft is flying above sea level at the initial moment When the underwater target is at point O, its x-coordinate and y-coordinate are both 0, and its z-coordinate is a certain depth below the sea level. Target at speed Make a uniform straight motion from north to south along the negative x-axis; the spatial position of the detection plane and the detection path is as follows Figure 4 As shown;

[0172] In COMSOL, set up the solver, select the "steady state" method to solve the spatial distribution of the magnetic anomaly field, and add the "parametric sweep" step to solve the time domain characteristics of the underwater target magnetic anomaly field. According to Gauss's magnetic law, we can get:

[0173]

[0174] In the formula, ” is the divergence operator, is the magnetic anomaly magnetic induction intensity, expressed as:

[0175]

[0176] Where, is the magnetic anomaly field intensity, is the vacuum permeability, , is the relative magnetic permeability of the ferromagnetic target housing material, ;

[0177] General Substitution We can get:

[0178]

[0179] Magnetic anomaly field strength Defined as:

[0180]

[0181] Where, is the scalar magnetic potential, is the Earth's magnetic field strength;

[0182] General Substitution The differential equation to be solved is:

[0183]

[0184] Where, the geomagnetic induction intensity ;

[0185] The external boundary conditions of the computational domain are insulating to the Earth's magnetic field, and are:

[0186]

[0187] Where, is the boundary normal vector of the target shell surface;

[0188] By The magnetic anomaly field that needs to be solved can be obtained:

[0189]

[0190] After the solution is completed, add a "one-dimensional plot group" to the "results" in the main screen bar to obtain the magnetic anomaly field vector field in the x, y, and z directions on the detection path, as shown below: Figure 5 、 Figure 6 and Figure 7 As shown; the x-axis represents the abscissa of the detection path, and the y-axis represents the magnetic field intensity of each vector field.

[0191] Step S4: Save the result data in COMSOL;

[0192] In the COMSOL menu bar, click "Results" → "Export" and select "Export Data". Export the wake magnetic field data on the detection plane, detection path, and detection points respectively, and specify the data save path and format. Select "Grid" as the data export format and set the sampling points uniformly to ensure data consistency and comparability. In this example, the sampling points are uniformly set to 1000 points along the x-axis.

[0193] Step S5: Establish a wake velocity field model in MATLAB;

[0194] The underwater target moves at a constant speed in the sea water. Moving along the negative direction of the x-axis, the disturbed seawater generates free surface waves composed of diffusion waves and shear waves, namely the Kelvin wake, as shown in Figure 8 As shown;

[0195] The underwater target is equivalent to a rotating ellipsoid, and its volume formula is:

[0196]

[0197] Where, is the total target length, is the maximum diameter of the target;

[0198] Free spectral function of underwater target wake Expressed as:

[0199]

[0200] Where, is the target speed, is the angle between the propagation direction of the wake wave and the x-axis, is the wake wave number, expressed as:

[0201]

[0202] Where, is the acceleration due to gravity, ;

[0203] The wake velocity field of the underwater target is:

[0204]

[0205] Where, is the angular frequency, , For time, is the harmonic component of the wake velocity field, where the vector Expressed as:

[0206]

[0207] Where, is the diving depth of the underwater target, is the unit vector of the wake wave propagation direction, and:

[0208]

[0209] After solving, the wake velocity vector fields in the x, y, and z directions on the detection plane are obtained, as follows: Figure 13 、 Figure 14 and Figure 15 As shown; the x-axis and y-axis represent the horizontal and vertical coordinates of the detection plane respectively, and the color bar represents the vector field strength.

[0210] Step S6: solving the underwater target wake magnetic field using MATLAB;

[0211] According to Faraday's law of electromagnetic induction, a time-varying magnetic field generates an electric field, namely:

[0212]

[0213] In the formula, ” is the curl operator, is the wake electric field intensity, is the wake magnetic induction intensity, expressed as:

[0214]

[0215] From Ampere's circuit law, we know that the current and the time-varying electric field generate a magnetic field, that is:

[0216]

[0217] Where, is the magnetic permeability of seawater, is the dielectric constant of seawater, is the current density, expressed as:

[0218]

[0219] Where, is the electrical conductivity of seawater, ,Will is approximately regarded as 0, so the formula Simplified to:

[0220]

[0221] General Substitution and Further simplifying the solution, we get Maxwell's equations:

[0222]

[0223]

[0224] General Substitution ,get:

[0225]

[0226] Reference , wake magnetic field strength Satisfies the relationship:

[0227]

[0228] Assume that seawater is an incompressible fluid, and its volume remains constant during the flow process without compression or expansion, that is:

[0229]

[0230] Considering that the wave height of the seawater free surface wave is much smaller than its wavelength, the free surface is approximately regarded as a plane, that is, ;Introduction of Laplace operator , then the wake magnetic field strength The identity is:

[0231]

[0232] According to the formula and ,Mode Simplified to:

[0233]

[0234] General Substitution In the above equation, we can get:

[0235]

[0236] The wake magnetic field strength generated by the underwater target is:

[0237]

[0238] Where, is the harmonic component of the wake magnetic field, where Expressed as:

[0239]

[0240] In the formula, the introduced vector and Respectively expressed as:

[0241]

[0242] (63)

[0243] Where, is the complex parameter of electromagnetic wave propagation in the medium, , subscript Corresponding to the air domain ( ) and sea waters ( ); is the parameter of electromagnetic wave propagation in air, ;

[0244] Take a point on the aircraft detection path as the detection point, such as Figure 12 As shown; after solving, the wake magnetic field vector fields in the x, y, and z directions at the detection point are obtained, respectively as Figure 13 、 Figure 14 and Figure 15 As shown; the left y-axis represents the detection distance between the aircraft and the underwater target, and the right y-axis represents the magnetic field strength of each vector field.

[0245] Step S7: Save the result data in MATLAB;

[0246] In MATLAB, use the "fprintf" command to export the wake magnetic field data on the detection plane, detection path, and detection point, respectively, and specify the data save path and format. Export the data in the form of a "grid" and set the sampling points uniformly to ensure data consistency and comparability. In this example, the sampling points are uniformly set to 1000 points along the x-axis.

[0247] Step S8: Use APP Designer to design the interface;

[0248] Use MATLAB's APP Designer to design the interface of the visual simulation system, including parameter input module, result solution module and data analysis module, such as Figure 16 As shown;

[0249] The parameter input module includes settings for underwater targets, calculation domain, geomagnetic field, seawater, and detection parameters (detection height and sensitivity). Geomagnetic field parameters are automatically calculated based on the IGRF model to obtain corresponding magnetic induction intensity, magnetic inclination, and magnetic declination values, which are displayed synchronously on the interface. This is a set of parameters entered by default in the simulation interface. The output geomagnetic field strength is , the magnetic inclination is , the magnetic declination is ;

[0250] surface Simulation interface default parameter settings

[0251]

[0252] The result solving module displays the basic model including the geometric model and the wake velocity field model, and can also display the spatial distribution of the magnetic field radiated by several underwater targets on the detection plane or detection path, as well as the time domain characteristics at the detection point;

[0253] The data analysis module solves the maximum amplitude of the magnetic field based on the detection plane, detection path and detection point, and displays the coordinates of the aircraft detection position at this time, and further determines the detection possibility of the magnetic anomaly field, wake magnetic field and comprehensive magnetic field.

[0254] Step S9: integrating the two sets of magnetic field data for simulation and solution;

[0255] The magnetic anomaly field calculated by COMSOL software Wake magnetic field calculated with MATLAB software Vector superposition to obtain the comprehensive magnetic field , expressed as:

[0256]

[0257] To achieve the goal of automatically solving two magnetic fields and their combined magnetic field in the same interface after inputting a set of parameters, a real-time connection between COMSOL and MATLAB is implemented through Livelink for MATLAB.

[0258] The result solution module in the simulation interface consists of three parts; the “basic model” displays the underwater target geometric model and the model diagram of the wake velocity field vector field, such as Figure 17 As shown in the figure; “Spatial distribution” shows the distribution of magnetic anomaly field, wake magnetic field and integrated magnetic field vector field on the detection plane or detection path, as shown in the figure. Figure 18 and 19 As shown in the figure; “Time domain characteristics” shows the characteristics of the magnetic anomaly field, wake magnetic field and comprehensive magnetic field vector field at the detection point, as shown in the figure. Figure 20 As shown, the dotted line represents the detection distance between the aircraft and the underwater target, and the solid line represents the intensity of each magnetic field vector field.

[0259] Step S10: performing data processing and analysis based on the calculation results;

[0260] After integrating the two sets of magnetic field data according to step S9, the maximum amplitudes of the magnetic anomaly field, the wake magnetic field, and the comprehensive magnetic field are calculated. The data analysis module determines the detection possibility by three methods: detection plane, detection path, and detection point. If the maximum amplitude of any vector field of the same magnetic field type is higher than or equal to the sensitivity (set in step S8), it means that the target can be detected, and the text box displays "Yes", otherwise it displays "No", thus completing the whole process of underwater target comprehensive magnetic field simulation analysis. It can be seen that in this example, based on the three detection methods, the "Detection Possibility" text box all displays "Yes", indicating that the target can be detected.

[0261] surface Detection possibility determination example

[0262]

Claims

1. A method for analyzing the spatiotemporal characteristics of the integrated magnetic field of an underwater target, characterized in that: The steps include: Step 1: Set and unify the physical parameters of the background field; Step 2: Create a geometric model of the underwater target in COMSOL; Step 3: Solve the underwater target magnetic anomaly field using COMSOL; Step 4: Save the result data in COMSOL; Step 5: Establish the wake velocity field model in MATLAB; Step 6: Solve the magnetic field of the underwater target wake using MATLAB; Step 7: Save the result data in MATLAB; Step 8: Use APP Designer to design the interface; Step 9: Integrate underwater target magnetic anomaly field and wake magnetic field data for simulation and solution; Step 10: Perform data processing and analysis based on the calculation results.

2. The method for analyzing the spatiotemporal characteristics of the comprehensive magnetic field of an underwater target according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1-1: Set the background magnetic field inside the underwater target calculation domain to a uniform magnetic field; The positive axis points to geographic north. The positive axis points to geographic west. Positive axis perpendicular to Facing upward; geomagnetic induction intensity exist The projection on the plane is , and The angle between them is the magnetic inclination , downward inclination is positive; The angle between the magnetic declination and geographic north is the magnetic declination. , the east declination is positive; then the geomagnetic induction intensity is expressed as: （1） Where, is the magnitude of the Earth's magnetic field, 、 、 Represent the unit vectors along the x, y, and z axes respectively; Using the IGRF-14 world geomagnetic field model, according to the formula The magnetic induction intensity of the Earth's magnetic field in the x, y, and z directions is further calculated; Step 1-2: Solve the magnetic anomaly field and wake magnetic field of the underwater target, and divide the entire calculation domain into sea water and air domain; set the sea level height to , the sea area below the sea level is expressed as ; Above the sea level is the air domain, represented by .

3. The method for analyzing the spatiotemporal characteristics of the comprehensive magnetic field of an underwater target according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2-1: Open COMSOL Multiphysics, select the Model Wizard, set the spatial dimension to 3D, and the physical field to "Magnetic Field, No Current." Treat the underwater target as a simplified rotating ellipsoid. First, create an ellipse on the "Work Plane" with the major axis equal to the total length of the underwater target and the minor axis equal to the maximum diameter. Then, convert the 2D plane into a 3D solid. Step 2-2: Select "User Controlled Mesh" for the meshing method, with the underwater target as the "Free Triangle" mesh and the computational domain as the "Free Tetrahedron" mesh; The shell material of the underwater target adopts the steel material in the built-in material library, and it is assumed that the target has been demagnetized.

4. The method for analyzing the spatiotemporal characteristics of the comprehensive magnetic field of an underwater target according to claim 3, characterized in that: The step 3 is specifically as follows: Step 3-1: Assume the aircraft is flying above sea level at the initial moment When the underwater target is at point O, its x-coordinate and y-coordinate are both 0, and the z-coordinate is the depth below the sea level. Target at speed Move in a straight line with uniform speed from north to south along the negative x-axis; Step 3-2: Set up the solver in COMSOL, select the "steady state" method to solve the spatial distribution of the magnetic anomaly field, and add a "parametric sweep" step to solve the time domain characteristics of the underwater target magnetic anomaly field; according to Gauss's magnetic law, we can obtain: （2） Where, ” is the divergence operator; is the magnetic anomaly magnetic induction intensity, expressed as: （3） Where, is the magnetic anomaly field intensity, is the vacuum permeability, , is the relative magnetic permeability of the ferromagnetic target housing material, ; Step 3-3: The formula Substitution have to: （4） Magnetic anomaly field strength Defined as: （5） Where, is the scalar magnetic potential, is the Earth's magnetic field strength; General Substitution Get the differential equation to be solved: （6） Where, the geomagnetic induction intensity ; Step 3-4: The external boundary conditions of the computational domain are insulating from the Earth's magnetic field, as follows: （7） Where, is the boundary normal vector of the target shell surface; By Get the magnetic anomaly field that needs to be solved: （8） After the solution is completed, add a "1D Plot Group" to the "Results" tab on the main screen to obtain the magnetic anomaly vector field in the x, y, and z directions along the detection path.

5. The method for analyzing the spatiotemporal characteristics of the comprehensive magnetic field of an underwater target according to claim 4, characterized in that: The step 4 is specifically as follows: In the COMSOL menu bar, click "Results" → "Export", select "Export Data", and export the magnetic anomaly field vector data on the detection plane, detection path, and detection point respectively, and specify the data save path and save format; select "Grid" as the data export format and set the sampling points uniformly.

6. The method for analyzing the spatiotemporal characteristics of the integrated magnetic field of an underwater target according to claim 5, characterized in that: The step 5 is specifically as follows: Step 5-1: The underwater target moves at a constant speed in the sea water Moving along the negative direction of the x-axis, the disturbed seawater generates free surface waves composed of diffusion waves and shear waves, namely the Kelvin wake; The underwater target is equivalent to a rotating ellipsoid, and its volume formula is: （9） Where, is the total target length, is the maximum diameter of the target; Free spectral function of underwater target wake Expressed as: （10） Where, is the target speed, is the angle between the propagation direction of the wake wave and the x-axis, is the wake wave number, expressed as: （11） Where, is the acceleration due to gravity, ; Step 5-2: The wake velocity field of the underwater target is: （12） Where, is the angular frequency, , For time, is the harmonic component of the wake velocity field, where the vector Expressed as: （13） Where, is the diving depth of the underwater target, is the unit vector of the wake wave propagation direction, and: （14） After solving, the wake velocity vector field in the x, y, and z directions on the detection plane is obtained.

7. The method for analyzing the spatiotemporal characteristics of the integrated magnetic field of an underwater target according to claim 6, characterized in that: The step 6 is specifically as follows: Step 6-1: According to Faraday's law of electromagnetic induction, a time-varying magnetic field generates an electric field, namely: （15） Where, ” is the curl operator, is the wake electric field intensity, is the wake magnetic induction intensity, expressed as: （16） From Ampere's circuit law, we know that the current and the time-varying electric field generate a magnetic field, that is: （17） Where, is the magnetic permeability of seawater, is the dielectric constant of seawater, is the current density, expressed as: （18） Where, is the electrical conductivity of seawater, ,Will is approximately regarded as 0, so the formula Simplified to: （19） Step 6-2: The formula Substitution and Further simplifying the solution, we get Maxwell's equations: （20） （21） General Substitution ,get: （22） Reference , wake magnetic field strength Satisfies the relationship: （23） Step 6-3: Assume that seawater is an incompressible fluid whose volume remains constant during flow, without compression or expansion, that is: （24） Considering that the wave height of the seawater free surface wave is much smaller than its wavelength, the free surface is approximately regarded as a plane, that is, ;Introduction of Laplace operator , then the wake magnetic field strength The identity is: （25） According to the formula and ,Mode Simplified to: （26） General Substitution In, we get: （27） Step 6-4: The wake magnetic field strength generated by the underwater target is: （28） Where, is the harmonic component of the wake magnetic field, where Expressed as: （29） In the formula, the introduced vector and Respectively expressed as: （30） （31） Where, is the complex parameter of electromagnetic wave propagation in the medium, , subscript Corresponding to the air domain and sea water domain respectively; is the parameter of electromagnetic wave propagation in air, ; A point on the aircraft detection path is taken as the detection point, and the wake magnetic field vector field in the x, y, and z directions at the detection point is obtained after solving.

8. The method for analyzing the spatiotemporal characteristics of the comprehensive magnetic field of an underwater target according to claim 7, characterized in that: The steps 7 and 8 are as follows: In MATLAB, the "fprintf" command was used to export the wake magnetic field data on the detection plane, detection path, and detection points, respectively, and the data save path and format were specified. The data was exported in the form of a "grid", and the sampling points were uniformly set to ensure data consistency and comparability. Use MATLAB's App Designer to design the interface of the visual simulation system, including parameter input module, result solution module and data analysis module; The parameter input module includes the settings of underwater targets, calculation domain, geomagnetic field, seawater and detection parameters; for geomagnetic field parameters, the IGRF model is automatically calculated to obtain the corresponding magnetic induction intensity, magnetic inclination and magnetic declination values, which are displayed synchronously in the interface; detection parameters include detection height and sensitivity; The result solution module displays a basic model including a geometric model and a wake velocity field model, and also displays the spatial distribution of the magnetic field radiated by several underwater targets on the detection plane or detection path, as well as the time domain characteristics at the detection point; The data analysis module solves the maximum amplitude of the magnetic field based on the detection plane, detection path and detection point respectively, and displays the coordinates of the aircraft detection position at this time.

9. The method for analyzing the spatiotemporal characteristics of the integrated magnetic field of an underwater target according to claim 8, characterized in that: The step 9 is specifically as follows: The magnetic anomaly field calculated by COMSOL software Wake magnetic field calculated with MATLAB software Vector superposition to obtain the comprehensive magnetic field , expressed as: （32） Livelink for MATLAB enables real-time connectivity between COMSOL and MATLAB. The result solution module in the simulation interface consists of three parts: "Basic Model" displays the geometric model of the underwater target and the model diagram of the wake velocity field vector field; "Spatial Distribution" displays the distribution diagram of the magnetic anomaly field, wake magnetic field, and integrated magnetic field vector field on the detection plane or detection path; and "Time Domain Characteristics" displays the characteristic diagrams of the magnetic anomaly field, wake magnetic field, and integrated magnetic field vector field at the detection point.

10. The method for analyzing the spatiotemporal characteristics of the comprehensive magnetic field of an underwater target according to claim 9, characterized in that: The step 10 is specifically as follows: After integrating the magnetic anomaly field and wake magnetic field data according to step 9, the maximum amplitudes of the magnetic anomaly field, wake magnetic field, and combined magnetic field are calculated. The data analysis module then determines the detection possibility using three methods: detection plane, detection path, and detection point. If the maximum amplitude of any vector field of the same magnetic field type is greater than or equal to the sensitivity, the target can be detected and the text box displays "Yes". Otherwise, "No" is displayed, completing the entire process of underwater target comprehensive magnetic field simulation analysis.

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