Electromagnetic scattering field calculation method for underwater cylindrical metal small target

Abstract

Aiming at the detection and identification problems of an underwater target, the invention discloses an electromagnetic scattering field calculation method for an underwater cylindrical metal small target, which comprises the following steps of: 1, carrying out geometric and physical modeling on the underwater cylindrical metal small target to be detected, carrying out numerical discretization preprocessing, calculating information of network nodes of geometric and physical models, and calculating the electromagnetic scattering field of the underwater cylindrical metal small target to be detected; constructing a grid model of the underwater cylindrical metal small target; 2, an electromagnetic scattering field of the grid model is calculated through an improved moment method, and electromagnetic scattering field curves of the underwater cylindrical metal small target in different scenes are obtained; 3, an electromagnetic scattering field of the grid model is calculated through an equivalent surface current method, and electromagnetic scattering field curves of the underwater cylindrical metal small target in different scenes are obtained; and 4, comparing the electromagnetic scattering field curves in the two steps, verifying that the shapes and the amplitudes of the two curves are basically consistent in an allowable error range, and detecting and identifying the underwater metal small target according to the action distance and the intersection situation of the target.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater target detection and recognition, and in particular to a method for calculating the electromagnetic scattering field of small underwater metal targets. Background Art

[0002] With the development of underwater low-frequency detection technology, many scholars have begun to attempt to use low-frequency electromagnetic signals for the detection of small underwater metal targets, and low-frequency electromagnetic detection has gradually become the main detection means of non-acoustic detection. Underwater low-frequency electromagnetic detection includes passive detection and active detection. Passive detection generally involves towing various magnetic detection system devices from a ship on the sea surface into the water, and detecting by measuring the magnetic anomaly behavior caused by the target through a magnetic sensor. The typical representative of active electromagnetic detection at present is the Marine Controlled Source Electromagnetic Method (MCSEM). The basic idea of this low-frequency artificial source electromagnetic method for detecting underwater targets is as follows: A low-frequency electromagnetic wave is emitted by a transmitting device. When the electromagnetic wave is incident on a metal target, induced currents will be generated inside it, and these induced currents will form a scattering field near the underwater target. The field collected by a receiving device is the sum of the scattering field and the incident field. The underwater target is located and recognized based on the result of normalizing the scattering field to the incident field. The calculation of the electromagnetic scattering field of small underwater metal targets is the core basic problem of underwater active electromagnetic detection, which directly affects the detection and recognition effects of metal small targets.

[0003] As early as the 1970s, the theoretical research on applying electromagnetic methods to the ocean began. The horizontal electric dipole model was first used for the design of transmitters and receivers, and the corresponding MCSEM research was carried out. Since the 21st century, several foreign oil companies have made breakthroughs in electromagnetic detection, and have successfully carried out marine magnetotelluric method and marine MCSEM method detections in the North Atlantic and off the west coast of Africa, with the exploration water depth exceeding one thousand meters. Most of the research in the field of marine exploration using MCSEM is aimed at large-scale targets (various oil and gas and mineral resources) in deep waters (water depth greater than 300m), and it is severely restricted when the water depth is relatively shallow or small-scale targets are detected. At present, some domestic institutions have also carried out some research work on marine electromagnetic detection. For example, Northwestern Polytechnical University has carried out a series of research on the underwater electromagnetic field characteristics of submarines, the cross-interface propagation characteristics of underwater extremely low-frequency electromagnetic fields, and high-sensitivity and low-noise sensors, and has achieved remarkable results. In 2010, the axial frequency electromagnetic field of a submarine was detected for the first time in China. Generally speaking, the currently detected targets basically belong to large-scale targets such as oil and gas and mineral resources. The low-frequency detection research on small-scale underwater targets based on the marine controlled source electromagnetic method in China is almost blank. In order to narrow the gap with the international level, it is urgent to vigorously develop this detection technology to meet the urgent needs of underwater small target detection in China. Summary of the Invention

[0004] Aiming at the shortcomings of the above-mentioned existing technologies, the present invention proposes a method for calculating the electromagnetic scattering field of small underwater metal targets. By improving the classical method of moments and introducing an augmented electric field integral equation, the problem of low-frequency breakdown of the traditional method of moments is solved, and accurate numerical calculation of the electromagnetic scattering field of small metal targets is carried out. Under the condition that the accuracy can meet the requirements of engineering applications, in order to improve the calculation efficiency and simplify the electromagnetic scattering field model of the target, an equivalent surface current method that can calculate quickly is designed.

[0005] A method for calculating the electromagnetic scattering field of small underwater metal targets adopted by the present invention includes the following steps:

[0006] Step 1: Conduct geometric and physical modeling on the small underwater cylindrical metal target to be detected, and perform numerical discretization preprocessing. Calculate the information of the network nodes of the geometric and physical models, and construct a grid model of the small underwater cylindrical metal target;

[0007] Step 2: Use the improved method of moments to calculate the electromagnetic scattering field of the grid model, and obtain the electromagnetic scattering field curves of the small underwater cylindrical metal target in different scenarios;

[0008] Step 3: Use the equivalent surface current method to calculate the electromagnetic scattering field of the grid model, and obtain the electromagnetic scattering field curves of the small underwater cylindrical metal target in different scenarios;

[0009] Step 4: Compare the electromagnetic scattering field curves in Step 2 and Step 3, verify whether the shapes and amplitudes of the two curves are basically the same within the allowable error range, and realize the detection and identification of the small underwater cylindrical metal target according to the action distance and intersection posture of the target to be detected.

[0010] Further, the specific steps of Step 2 include:

[0011] Step 2.1: Using the RWG basis function, approximate the current density J(r) on the target surface S as:

[0012]

[0013] where N is the number of internal edges, I n is the current coefficient associated with the nth edge, and f n is the vector basis function defined on the adjacent triangles associated with the nth edge, and f n is:

[0014]

[0015] In the formula, l n is the nth pair of adjacent triangles and The common side, is the surface area of triangle ; is the surface area of triangle . The vector starts from the vertex of and reaches the surface element. The vector starts from an arbitrary point on the surface element and points to the endpoint. These two vectors can be used to simulate the current flow direction on the surface element;

[0016] Step 2.2: Obtain the current continuity condition according to the current continuity theorem:

[0017]

[0018] where ω is the angular frequency, r' is the coordinate of the source point position, is the divergence operator with respect to the source point coordinate r', i is the imaginary unit, and ρ s is the source charge density, representing the charge density distribution at the source point r'.

[0019] Step 2.3: Establish the surface electric field integral equation of the target according to the boundary conditions and the surface equivalence principle:

[0020]

[0021] where η b is the wave impedance in free space, is the wave number in free space,

[0022] Step 2.4: Define the matrices and

[0023]

[0024] In the formula, ε r is the relative permittivity, μ r is the relative conductivity; the matrices V, S, and P are all symmetric; the subscripts m and n respectively represent different basis function numbers, corresponding to different triangles T m and T n ;

[0025] Step 2.5: Discretize the electric field integral equation using the basis function f n to obtain:

[0026]

[0027] Where, η0 is the wave impedance of free space, k0 is the wave number of free space, J represents the current density vector on the target surface S, b is a known vector, and i is the imaginary unit;

[0028] S in the above formula is:

[0029] S = D T In the formula of PD, D represents the divergence operator;

[0030] Step 2.6: Then use the basis function f n Discretize the current continuity condition to obtain:

[0031] D·J = ik0c0ρ;

[0032] In the formula, c0 represents the speed of light in vacuum, and ρ represents the charge density;

[0033] Step 2.7: Combine the formulas in Steps 2.5 - 2.6 to obtain the augmented electric field integral equation set:

[0034]

[0035] Among them, is the impedance matrix;

[0036] Step 2.8: Obtain the electromagnetic scattering field curve according to the augmented electric field integral equation set obtained in Step 2.7.

[0037] Furthermore, the specific steps of Step 3 include:

[0038] Step 3.1: Calculate the equivalent surface current on the surface of a cylinder with radius a through the following formula:

[0039]

[0040] Among them, and H z respectively represent the tangential component of the magnetic field intensity on the cylinder surface; j z respectively represent z and the equivalent surface current of the primary field on the cylinder surface;

[0041] Step 3.2: Since the vector potential A is coaxial with the current density vector, at the observation point with secondary field coordinates p2, z2, obtain the three components of vector A:

[0042]

[0043] Among them, μ a represents the magnetic permeability, and ds represents the unit area of the cylinder surface;

[0044] The distance R2 from the surface of the cylinder to the secondary field receiving point is:

[0045]

[0046] Step 3.3: After completing the operation of the curl according to the receiving point coordinates, the components of the secondary field magnetic field intensity vector are obtained:

[0047]

[0048] Among them, H r2 , H z2 are the r- and z-direction components of the secondary field magnetic field intensity vector respectively;

[0049] Step 3.4: Calculate the primary field magnetic field intensity components on the surface of the cylinder;

[0050] Step 3.5: Based on the primary field magnetic field intensity components on the surface of the cylinder, obtain the three components of the primary field generated by the axial dipole of the transmitting antenna on the cylinder surface:

[0051]

[0052] Step 3.6: Calculate the components of the primary field magnetic field intensity vector components on the surface of the cylinder in the cylindrical coordinate system through the following formula:

[0053]

[0054] Among them, R1 2 = x 2 + y 2 + z 2 represents the distance from the transmitting dipole to the surface ds of the cylinder;

[0055] represents the coordinates of the transmitting dipole;

[0056] Step 3.7: Convert the components of the secondary electromagnetic field intensity vector reflected by the cylindrical target into components in the rectangular coordinate system according to the following formula:

[0057]

[0058] Among them, x2, y2, z2 represent the receiving antenna coordinates; the distance R2 from the surface of the cylinder to the observation point is:

[0059]

[0060] Step 3.8: Calculate the electromagnetic scattering field of the cylindrical metal target based on the components in the rectangular coordinate system.

[0061] Furthermore, when calculating the magnetic field strength component of the primary field on the surface of the cylinder in step 3.4, the following two cases are considered:

[0062] 1) For the radial magnetic dipole of the transmitting antenna with a distance p1 from the axis of the cylinder and the beam the magnetic field strength component of the primary field on the surface of the cylinder is obtained by the following formula:

[0063]

[0064] where is the magnetic moment of the transmitting magnetic dipole;

[0065] 2) For the radial magnetic dipole of the transmitting antenna with the magnetic dipole oriented along an arc and located at a distance p1 from the axis of the cylinder in the beam the magnetic field strength component of the primary field on the surface of the cylinder is obtained by the following formula:

[0066]

[0067] Therefore, the electromagnetic scattering field calculation method for small underwater metal targets adopted in the present invention has the following technical effects:

[0068] The present invention first accurately numerically calculates the electromagnetic scattering field of small metal targets by improving the classical moment method. Then, on the premise of meeting the accuracy requirements of engineering applications, in order to further improve the calculation efficiency and simplify the target electromagnetic scattering field model, a surface current method is proposed. This method can not only significantly improve the calculation speed but also effectively reduce the consumption of calculation resources while ensuring the calculation accuracy. The moment method has high calculation accuracy, while the surface current method has a fast calculation speed. Both have important theoretical significance and engineering application value in the calculation of the electromagnetic scattering field of small underwater metal targets. The combined scheme of the present invention provides an effective numerical calculation means for the electromagnetic scattering analysis of underwater targets and has strong practicability and popularization.

[0069] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Brief Description of the Drawings

[0070] Figure 1 is the magnetic dipole model.

[0071] Figure 2 is the grid model of the cylinder target.

[0072] Figure 3 is the electromagnetic scattering field in the x-component when the intersection angle θ changes.

[0073] Figure 4 is the electromagnetic scattering field in the y-component when the intersection angle θ changes.

[0074] Figure 5 It is the electromagnetic scattering field in the z-component when the intersection angle θ changes.

[0075] Figure 6 It is the electromagnetic scattering field in the x-component when the operating distance h changes.

[0076] Figure 7 It is the electromagnetic scattering field in the y-component when the operating distance h changes.

[0077] Figure 8 It is the electromagnetic scattering field in the z-component when the operating distance h changes.

[0078] Figure 9 It is the schematic diagram of electromagnetic scattering of a cylindrical target.

[0079] Figures 10a - 10c They are the magnetic induction intensities of the cylindrical target in the x, y, and z directions respectively.

[0080] Figure 11 It is the on-site picture of the electromagnetic scattering field experiment in the embodiment.

[0081] Figure 12 It is the picture of the physical small magnetic bar.

[0082] Figure 13 It is the picture of the physical cylindrical barrel.

[0083] Figure 14 It is the experimental scene picture drawn according to the test scenario.

[0084] Figures 15a - 15c They are the results in the x-component, y-component, and z-component respectively when the intersection angle θ is 30°.

[0085] Figures 16a - 16c They are the results in the x-component, y-component, and z-component respectively when the intersection angle θ is 60°.

[0086] Figures 17a - 17c They are the results in the x-component, y-component, and z-component respectively when the intersection angle θ is 90°.

[0087] Figures 18a - 18c They are the results in the x-component, y-component, and z-component respectively when the operating distance h is 0.2 m.

[0088] Figures 19a - 19c They are the results in the x-component, y-component, and z-component respectively when the operating distance h is 0.3 m.

[0089] Figures 20a - 20c They are the results in the x-component, y-component, and z-component respectively when the operating distance h is 0.4 m.

[0090] Figures 21a - 21c They are the results in the x, y, and z components when the magnetic moment direction is horizontal, respectively.

[0091] Figures 22a - 22c They are the results in the x, y, and z components when the magnetic moment direction is vertical, respectively.

[0092] Figures 23a - 23b It is a schematic diagram of the equivalence principle. Figure 23a It is the actual electromagnetic distribution before equivalence. Figure 23b It is the electromagnetic distribution after equivalence. Specific implementation manners

[0093] In the description of the present invention, it should also be noted that unless otherwise clearly specified and limited, these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims of this application.

[0094] 1. Introduction to the electromagnetic radiation field of the transmitting antenna

[0095] In marine electromagnetic exploration, the magnetic dipole is widely used as a radiator. The present invention intends to use a current-carrying circular coil as the transmitting antenna. When the distance between the observation point and the transmitting antenna is much larger than the size of the transmitting antenna itself, the minor details of the transmitting antenna can be ignored and replaced by a circular current loop. At this time, this current loop is called a magnetic dipole, and its intensity is represented by the magnetic dipole moment M, and the direction is determined by the right-hand screw rule, as Figure 1 shown.

[0096] In engineering, the receiving coil and the transmitting coil often adopt coils wound with multiple turns, and ferromagnetic materials with very high magnetic permeability, such as pure iron, ferrite, silicon steel, etc., are added at the center of the coil. Usually, the multi-turn coil is also equivalent to a magnetic dipole for analysis, and the radiation magnetic moment of the multi-turn coil can be expressed by Equation (1):

[0097] M = μ0μ r NIS (1)

[0098] where μ0 represents the magnetic permeability of air or seawater; μ r represents the relative magnetic permeability of the magnetic core; N represents the number of turns of the coil; I represents the current intensity (A) in the coil; S represents the cross-sectional area (m 2 ) of the current loop.

[0099] Solve the Maxwell equations, and then obtain the expression of the radiation source with a vertical magnetic dipole as the model:

[0100]

[0101] where, ω represents the angular frequency of the alternating magnetic dipole electromagnetic field; R represents the distance from the wave source to the observation point; K represents the complex wave number, which is a complex number in a conducting medium;

[0102] The above equations all contain the KR term. According to the comparison between the distance R from the wave source to the observation point and the wavelength λ of the radiated electromagnetic wave in the propagation medium, the radiation electromagnetic field of the magnetic dipole can be divided into three regions:

[0103] (1) When KR << 1, it is called the near field region, also known as the quasi-static region or the quasi-stationary region;

[0104] (2) When KR >> 1, it is called the far field region;

[0105] (3) The region between (1) and (2) is called the intermediate region.

[0106] The working frequency band of active electromagnetic detection usually satisfies the condition of R << 0.1λ. Therefore, active electromagnetic detection uses the near field region generated by the excitation of a magnetic dipole source. The distribution of its near field region is approximately the same as that of a static magnetic dipole (ω = 0, that is, K = 0) field, that is, approximately the nature of a constant field. From the perspective of energy, the near field (E×H) is an imaginary number, which indicates that the spatial field only exchanges energy with the field source and does not radiate away from the field source.

[0107] 2. The electromagnetic scattering field calculation method proposed by the present invention

[0108] The present invention proposes an electromagnetic scattering field calculation method for a small underwater cylindrical metal target, which includes the following steps:

[0109] Step 1: Perform geometric and physical modeling on the small underwater cylindrical metal target to be detected, and perform numerical discretization preprocessing, calculate the information of the network nodes of the geometric and physical models, and construct a grid model of the small underwater cylindrical metal target;

[0110] Step 2: Use the improved method of moments to calculate the electromagnetic scattering field of the grid model to obtain the electromagnetic scattering field curves of the small underwater cylindrical metal target in different scenarios;

[0111] Step 3: Use the equivalent surface current method to calculate the electromagnetic scattering field of the grid model to obtain the electromagnetic scattering field curves of the small underwater cylindrical metal target in different scenarios;

[0112] Step 4: Compare the electromagnetic scattering field curves in Step 2 and Step 3, verify that the shapes and amplitudes of the two curves are basically the same within the allowable error range, and realize the detection and identification of small underwater metal targets according to the action distance and intersection situation of the target to be detected.

[0113] In the embodiments, relevant electromagnetic scattering field experiments are carried out to verify the feasibility and effectiveness of the two methods proposed by the present invention (the improved method of moments and the equivalent surface current method) in the detection and identification of small underwater cylindrical metal targets. The experimental results provide sufficient experimental basis and support for the further popularization and application of these two methods in practical applications.

[0114] The calculation of the electromagnetic scattering field of small metal targets based on the method of moments and the calculation of the electromagnetic scattering field of small metal targets based on the surface current method are introduced below respectively.

[0115] (1) Calculation of the electromagnetic scattering field of typical small metal targets based on the improved method of moments

[0116] ① Introduction to the method of moments (MOM)

[0117] The basic idea of the method of moments is to transform the boundary value problem into a problem of solving a system of linear equations. In this process, it is necessary to discretize the electromagnetic field problem to be solved and select a set of basis functions to represent it in the form of a linear combination. Then, the unknown function in the operator equation is replaced with the linear combination form, and by selecting appropriate weight functions, the residual of the equation is made zero in the sense of weighted average, thus transforming the problem into solving algebraic equations. Finally, by solving these algebraic equations, the solution of the electromagnetic field distribution is obtained.

[0118] When solving the linear non-homogeneous equation, it can be expressed in the following form:

[0119] L(f) = g (5)

[0120] Among them, L is a linear operator, g is a known excitation function, and f is an unknown response function. Define f and g into two different spaces F and G respectively, so the meaning of equation (5) is that through the operator L, a set of functions in the F space is mapped onto the G space.

[0121] To solve the numerical solution of the above equation (5), expand the response function f in its domain into a linear combination of f1, f2,..., f N :

[0122]

[0123] Among them, define {a n} as a set of scalar coefficients to be solved, and f n is the selected basis function.

[0124] It can be seen that this is an approximate idea of limit approximation. When N → ∞ and {f n} is a complete set, the solution value of this formula is actually accurate.

[0125] However, infinity is an ideal and perfect situation. In the process of solving practical problems, N is always a finite value. Therefore, the above equation (6) is a relatively accurate approximate solution. Thus, in order to further solve a more accurate result of equation (6), substituting equation (6) into (5) gives:

[0126]

[0127] In the above equation (7), it is necessary to solve for the scalar coefficients {a n}, and define a vector set w m = {w1, w2,..., w N} of the same number N within the domain of the operator L. This is the so-called test function, also known as the weight function. In the treatment of practical problems, considering the accuracy of the final result, the Galerkin method is generally used to select the weight function, that is, the test function and the basis function use the same function.

[0128] Taking the inner product of both sides of equation (7) using the weight function gives:

[0129]

[0130] Equation (8) can be rewritten in the following matrix form:

[0131] In the above equation:

[0132]

[0133] In the above equation (11), if the [l mn of the impedance matrix is non-singular, it can be divided to the right-hand side of the equation, and after deformation, it has the following form:

[0134] [a n = [l mn -1 [g m (12)

[0135] Substituting the known excitation function g into the above equation (12), and solving by multiplying with the inverse matrix of the impedance matrix, the matrix of coefficients a can be obtained. Substituting the obtained coefficients a into (6) can obtain the numerical solution of the original response function f, that is, the solution of the target electromagnetic field distribution.

[0136] ② Improved method of moments

[0137] Using the RWG basis function, the current density J(r) on the target surface S is approximated as:

[0138]

[0139] Among them, N is the number of internal edges, I​n is the current coefficient associated with the nth edge, f n is the vector basis function defined on the adjacent triangles associated with the nth edge, and f n is expressed as:

[0140]

[0141] where l n is the common edge of the nth pair of adjacent triangles and ; is the surface area of triangle ; is the surface area of triangle ; the vector starts from the vertex of to the surface element; the vector points from an arbitrary point on the surface element to the endpoint. These two vectors can be used to simulate the flow direction of the current on the surface element.

[0142] The surface integral equation of the conductor target is established based on the boundary conditions and the surface equivalence principle, and is often used to analyze homogeneous dielectric targets and perfect conductor targets. The surface equivalence principle simplifies the solution of complex electromagnetic scattering field problems to the solution of the surface current and magnetic current of the target, and then obtains the spatial distribution of the electromagnetic field excited by the current and magnetic current.

[0143] Let the background space be K1, with its related parameters being ε b and μ b . Assume that the ideal metal region is K2, and S is the outer surface of K2. Assume that the current J1 and magnetic current M1 excite the electromagnetic field E i and magnetic field H i in K1. E and H represent the total electric field and magnetic field at r in K1, as shown in Figures 23a - 23b .

[0144] According to the surface equivalence principle, the electromagnetic scattering of the metal target can be replaced by the radiation excited by the current J S on the closed space surface S. The scattered electric field E S and magnetic field H s excited by the current source J s can be derived based on the spatial Green's function, and then combined with the boundary conditions to obtain the surface integral equation. The relationship between the incident, scattered, and total electromagnetic field parameters is:

[0145] E(r) = E i (r) + E s (r) (15)

[0146] H(r) = Hi (r) + H s (r)(16)

[0147] Introduce the scalar potential Φ S and the magnetic vector potential A S We can obtain:

[0148] Φ s (r) = ε b -1 ∫ S ρ s (r′)G(r, r′)dS′ (17)

[0149] A s (r) = μ0∫ S J S (r′)G(r, r′)dS′ (18)

[0150] Wherein, the Green's function represents a spherical wave generated by a point source at r′, and R = |r - r′| represents the distance between these two points, is the wavenumber in free space.

[0151] Obtained from the current continuity theorem:

[0152]

[0153] On the boundary surface S, according to the ideal conductor boundary condition, it can be known that:

[0154] n × [E i (r) + E s (r)] = 0, r ∈ S (20)

[0155] Since K2 is an ideal metal region, the internal electric and magnetic field components are zero, and there is no accumulation of magnetic current on its surface S. Therefore, M S = 0, so only J S exists:

[0156] J S (r) = n × [H i (r) + H s (r)], r ∈ S (21)

[0157] The source J on the surface of the ideal conductor S generates the electromagnetic field in space as:

[0158]

[0159] Wherein, ω is the angular frequency.

[0160] Substituting Equation (19) into Equation (17), we can obtain:

[0161]

[0162] Finally, substituting Equation (23) into Equation (20), the electric field integral equation can be obtained:

[0163]

[0164] Substituting Equations (18) and (24) into Equation (25), the electric field integral equation can be expressed as:

[0165]

[0166] where η b is the wave impedance in free space.

[0167] The improved method of moments, i.e., the augmented electric field integral equation, combines the current continuity condition with the electric field integral equation. The solution vector selects both current and charge simultaneously, and the vector potential function and scalar potential function balance their contributions by normalizing the frequency. After normalizing the RWG basis function, the solution current is expanded as shown in Equation (14), and the solution charge is expanded by the pulse basis function as:

[0168]

[0169] where h n is the pulse basis function, h n is the triangular element, and A n is the surface area of the triangular element.

[0170] The electric field integral equation and the current continuity condition can be discretized using the basis function f n , and the integral equation is transformed into a matrix equation using the matrices V, S, P, and D. The definitions of the matrices and are respectively:

[0171]

[0172]

[0173] where ε r is the relative permittivity, μ r is the relative conductivity; the matrices V, S, and P are all symmetric; the subscripts m and n respectively represent different basis function numbers, corresponding to different triangles T m and T n ;

[0174] Discretizing the integral equation (Equation 26), we get:

[0175]

[0176] Where η0 is the free space wave impedance, k0 is the free space wave number, J is the current density vector to be solved, b is a known vector, and i is an imaginary unit;

[0177] S=D T PD (33)

[0178] Where D represents the divergence operator.

[0179] The current continuity condition (Equation 19) is also discretized to obtain:

[0180] D·J=ik0c0ρ (34)

[0181] Where c0 is the speed of light in a vacuum and ρ is the charge density.

[0182] By combining equation (32) to equation (34), we can obtain the augmented electric field integral equation group:

[0183]

[0184] The impedance matrix Since the augmented electric field integral equation is electrically neutral, the impedance matrix A in the low-frequency domain is not full rank. This problem can be solved by combining the electrical neutrality condition, thereby reducing the matrix dimension by reducing the unknowns, and further ensuring that the matrix A of the augmented electric field integral equation is full rank.

[0185] Specifically, let the number of targets be t. After discretizing the targets with triangular face elements, the sum of face elements is Among them, p i represents the number of face elements after each target is discretized, and p represents the sum of the number of face elements after all targets are discretized. According to the electrical neutrality condition, we can get:

[0186]

[0187] In the formula, Q n is the nth charge, N t is the triangle face element on the t-th target, the N-th t The charge can be expressed as:

[0188]

[0189] In order to make the matrix A a full rank matrix, equation (35) can be rewritten as:

[0190]

[0191] Among them, the vector I ris the identity matrix with dimensions (p - t)×(p - t). The high sparse matrix are the projection matrices respectively, and:

[0192] ρ r = F·ρ, ρ = B·ρ r (39)

[0193] In the formula, the matrix F transforms the original solution charge vector into a charge vector ρ with dimensions r , while the matrix B restores the vector ρ r to the original solution charge vector ρ.

[0194] The matrix V is a symmetric matrix and when k0→0, k0 2 I r is approximately a zero matrix. By constructing a constrained preconditioner, the system can converge quickly, avoiding convergence problems.

[0195]

[0196] The present invention uses the diagonal matrices of matrices V and P to construct a preconditioner, which can also be inverted quickly when dealing with problems containing more unknowns, solving the low-frequency collapse problem.

[0197] ③ Calculation and simulation of the electromagnetic scattering field of a cylindrical target

[0198] In order to numerically simulate the electromagnetic response characteristics of an underwater cylindrical metal target, it is first necessary to construct the geometric and physical models of the target and perform numerical discretization preprocessing. Then, the improved method of moments calculation steps are used to calculate the information of the model grid nodes, obtaining the final electromagnetic response results of the cylindrical target.

[0199] In this simulation, the meshed grid was divided into 3788 grids using the triangular grid meshing method in HyperMesh software. The meshed grid model of the underwater cylindrical metal small target after meshing is as Figure 2 shown. The height of the model is 1.8 m and the diameter is 50 cm.

[0200] As Figure 2 shown, the transmitting and receiving coils are located at a certain depth h (i.e., the operating distance) below the target, along the target axis from -2 m to 2 m. The transmitting antenna is equivalent to a magnetic dipole, and its magnetic dipole moment is set to 0.1 A·m 2 in the simulation. The frequency of the radiated electromagnetic wave is 500 Hz. The distance between the transmitting antenna and the receiving antenna is 0.266 m. During the calculation, due to the extremely large computational amount of the method of moments, a supercomputer platform is used for the calculation. When calculating the electromagnetic scattering characteristic curve of the cylindrical target, 81 sampling points are selected.

[0201] The following uses the method of moments to calculate the characteristic curves of the electromagnetic scattering field of a cylindrical target under different intersection angles θ, action distances h, and directions (horizontal or vertical) of the magnetic moment generated by the magnetic dipole. The specific results are as follows:

[0202] i) When the action distance h is 0.1 m, the direction of the magnetic moment generated by the magnetic dipole is horizontal, and the magnitude of the magnetic moment is 0.1 A·m 2 The simulation results when the intersection angle θ takes 0, 30°, 60°, and 90° respectively are as Figures 3 - 5 shown. It can be seen from the figure that when the intersection angle changes, the electromagnetic scattering curve also changes regularly. This general rule is that as the intersection angle increases, the trajectory of the transceiver device and the action range of the target become smaller, and the corresponding scattering signal width becomes narrower.

[0203] ii) When the intersection angle θ is 90°, the direction of the magnetic moment generated by the magnetic dipole is horizontal, and the magnitude of the magnetic moment is 0.1 A·m 2 The simulation results when the action distance h is 0.1 m, 0.2 m, 0.3 m, and 0.4 m respectively are as Figures 6 - 8 shown. It can be seen from the figure that when the action distance changes, the electromagnetic scattering curve also changes regularly. This general rule is that as the action distance increases, the amplitude of the corresponding electromagnetic scattering field also becomes smaller.

[0204] (2) Calculation of the electromagnetic scattering field of a typical small metal target based on the surface current method

[0205] ① Introduction to the surface current method

[0206] The equivalent principle of the surface current method is that within a free space range of area S that is not affected by the field source body, the current and magnetic current distributed on this surface may generate an electromagnetic field. In this sense, the actual field source body can be replaced by an equivalent surface current. The surface current density j and the magnetic current density j * can be calculated using the tangential components of the electromagnetic field strength:

[0207] j = [n × H], j * = [E × n] (41)

[0208] In the formula, H and E respectively represent the magnetic field strength and electric field strength vectors of the combined field on the surface S; n represents the normal line of the surface S pointing to the spatial region, and this space is the equivalent current field;

[0209] In other words, the equivalent surface current is calculated through the tangential components of the magnetic field strength and electric field strength on the surface S. Under the condition of high metal conductivity, more precisely, ideal conductivity, the tangential component of the magnetic field strength will be doubled and enhanced relative to a slightly curved surface, while the tangential component of the electric field strength tends to zero. Thus, on a slightly curved and ideally conductive surface, the equivalent current density is equal to:

[0210] j = 2[n×H1] (42)

[0211] where H1 represents the primary magnetic field of a point alternating magnetic dipole with magnetic moment P M of the point alternating magnetic dipole;

[0212] This current generates an electric field in the surrounding space, and its vector potential A is equal to:

[0213]

[0214] where μ a represents the magnetic permeability and R represents the distance from the spatial point to the magnetic dipole.

[0215] According to Huygens' theorem, when the surface equivalent current density is equal to j, each unit ds of this surface constitutes the basic field source body of a spherical wave. Through the vector potential A, the magnetic field strength vector H2 of the secondary electromagnetic field in the surrounding space of the object is obtained. According to formulas (42), (43) and the quasi-steady state approximation method, the vector of the secondary reflection field is calculated by the surface integral method as follows:

[0216]

[0217] where rot is calculated as the curl according to the coordinates of the receiving point of the magnetic field H2, and R 2 is the distance from the ds unit on the object surface to the field receiving point.

[0218] The primary magnetic field H1 of a point alternating magnetic dipole with magnetic moment P M is calculated by the quasi-steady state approximation method as follows:

[0219]

[0220] where R1 is the distance from the magnetic dipole (actual magnetic source body) to the ds point on the surface of the detection target, and P M is the magnetic moment.

[0221] When we are detecting, we first need a transmitting antenna, which is generally replaced by a magnetic dipole. The receiving antenna can receive the components in the three directions of x, y, and z. The electromagnetic wave radiated by the transmitting antenna is called the primary field B1. After the primary field reaches the target, the equivalent surface current induced at each point on the target is calculated. These equivalent surface currents will radiate an electromagnetic field outward, which is the secondary field B2 we need.

[0222] ② Calculation of the electromagnetic scattering field of a cylindrical target

[0223] Set the radius of the cylinder as a, and the axis of the cylinder coincides with the z-axis of the cylindrical coordinate system r, z. The tangential component of the magnetic field strength on the cylinder surface and H zdetermines the corresponding equivalent surface current:

[0224]

[0225] where H z1 、 respectively represent the magnetic field intensity z of the primary field on the surface of the cylinder and the tangential component; j z respectively represent z and the equivalent surface current of the primary field on the surface of the cylinder;

[0226] Since the vector potential A is coaxial with the current density vector, at the observation point with secondary field coordinates p2, z2, the three components of vector A are:

[0227]

[0228] where μ a represents the magnetic permeability, and ds represents the unit area of the cylinder surface.

[0229] The distance R2 from the cylinder surface to the secondary field receiving point is:

[0230]

[0231] After performing the curl operation according to the receiving point coordinates, the components of the secondary field magnetic field intensity vector can be obtained:

[0232]

[0233] where H r2 、 H z2 are respectively the r and z direction components of the secondary field magnetic field intensity vector;

[0234] For a radial magnetic dipole of the transmitting antenna with a distance p1 from the axis of the cylinder and a beam , the magnetic field intensity component of the primary field on the cylinder surface is obtained as follows:

[0235]

[0236] where R1 represents the distance from the transmitting magnetic dipole to the cylinder surface, is the magnetic moment of the transmitting magnetic dipole.

[0237] When the magnetic dipole is oriented along an arc and is located at a distance p1 from the axis of the cylinder in the beam , the primary field component on the cylinder surface is calculated as follows:

[0238]

[0239] In the formula, represents the azimuthal component of the magnetic dipole.

[0240] The axial dipole of the transmitting antenna generates the following components of the primary field on the cylindrical surface:

[0241]

[0242] where p MZ represents the axial component of the magnetic dipole.

[0243] The vector components of the magnetic field intensity of the primary field on the cylindrical surface are calculated by the following formula in the cylindrical coordinate system:

[0244]

[0245] In the formula, R1 2 = x 2 + y 2 + z 2 , R1 is the distance from the transmitting dipole to the surface ds of the cylinder, P Mx is the x - direction component of the magnetic dipole in the Cartesian coordinate system, P My is the y - direction component of the magnetic dipole in the Cartesian coordinate system; represents the coordinates of the transmitting dipole.

[0246] The vector components of the secondary electromagnetic field intensity reflected by the cylindrical target, when converted to the Cartesian coordinate system for calculation, are given by the formula:

[0247]

[0248] x2, y2, z2 are the coordinates of the receiving point, i.e., the coordinates of the receiving antenna. The distance from the cylindrical surface to the observation point of the secondary field:

[0249]

[0250] In this way, the calculation formulas for the three components of the electromagnetic scattering field of the cylindrical metal target calculated by the surface current method are obtained (i.e., Equation 55).

[0251] ③ Electromagnetic Scattering Field Simulation Results of the Cylindrical Target

[0252] For the Figure 9 scene schematic diagram shown below, select the parameters (including cylinder size, operating frequency, transceiver spacing, operating distance, magnetic moment, intersection angle, antenna radiation direction, etc.), program the above calculation method in MATLAB, and finally the electromagnetic scattering characteristic curve of the cylindrical metal target can be obtained.

[0253] During the simulation process, both the transmitting antenna and the receiving antenna are replaced by magnetic dipoles, with their coordinates being (x1, y1, z1) and (z2, y2, z2) respectively. The length b of the cylinder is 1.8 m, the diameter 2a is 0.533 m, the transceiver distance d is 0.25 m, the operating distance h is 0.9 m, the intersection angle θ is 0°, the frequency f is 1111 Hz, and the directions of the magnetic moments generated by the magnetic dipoles are perpendicular, with the magnitudes of the magnetic moments all being 0.1 A·m 2 of the signal.

[0254] The code is written into MATLAB, and the results obtained from the simulation are as Figures 10a - 10c shown. The curves in the figure are the electromagnetic scattering curves of the cylinder target calculated by the surface current method.

[0255] Embodiment

[0256] The present invention proposes a method for calculating the electromagnetic scattering field of a small underwater metal target. Taking the cylinder model as an example, an electromagnetic scattering field experiment is carried out for verification.

[0257] 1. Test scenario

[0258] As Figure 11 shown, install the cylinder model and use different transceiver devices (transceiver distance, magnitude of the transmitting magnetic moment, scaling ratio, perpendicular or parallel magnetic moment direction), and move the model along -2 m to 2 m.

[0259] 2. Transceiver device

[0260] As Figure 12 shown, the transceiver device in this embodiment is a small magnetic rod, the transceiver distance is 0.266 m, and it is configured perpendicular or parallel.

[0261] 3. Magnetic sensor

[0262] What the magnetic sensor actually collects is the voltage value, with the unit being V. The conversion coefficient of the sensor sensitivity used in this experiment is 0.5 nT / mV. Therefore, to convert it to the magnetic field unit, first multiply by 1000 to mV, and then multiply by 0.5, which is the magnetic induction intensity, with the unit being nT.

[0263] 4. Cylindrical barrel model

[0264] The thickness of the cylindrical barrel used in this experiment is 2.7 mm, the diameter is 50 cm, and the length is 1.8 m. The physical diagram is as Figure 13 shown.

[0265] 5. Data collection device

[0266] In this experiment, the experimental data is transmitted to the computer for further processing through a data acquisition box connected to a power amplifier. According to the test scenario of this experiment, an experimental scenario diagram as Figure 14 shown can be drawn.

[0267] 6. Experimental Procedures

[0268] The experimental process of this experiment can be divided into the following steps: (1) First, test the entire system on land to ensure normal communication; (2) Hang the target surface ship on the hoisting point of the traveling crane, and use the host computer to adjust the depth, intersection angle, and moving distance; (3) Place the transceiver equipment on the ladder and set the transmission signal parameters; (4) The surface ship moves along the established trajectory and passes under the target; (5) Process the received data and draw the target passing characteristic curve.

[0269] Transmit the experimental data to the computer for recording, and compare and process it with the results of the surface current method and the method of moments simulation, and the following results can be obtained:

[0270] (1) When the action distance h is 0.1 m, the direction of the magnetic moment generated by the magnetic dipole is horizontal, and the magnitude of the magnetic moment is 0.1 A·m 2 , the comparison results of the intersection angle θ at 30°, 60°, and 90° are as Figures 15a - 15c , Figures 16a - 16c and Figures 17a - 17c ;

[0271] (2) When the intersection angle θ is 90°, the direction of the magnetic moment generated by the magnetic dipole is horizontal, and the magnitude of the magnetic moment is 0.1 A·m 2 , the comparison results of the action distance h at 0.2 m, 0.3 m, and 0.4 m are as Figures 18a - 18c , Figures 19a - 19c and Figures 20a - 20c :

[0272] (3) When the intersection angle θ is 90°, the action distance h is 0.5 m, and the magnetic dipole generates magnetic moments with horizontal and vertical directions and the magnitude of the magnetic moment is 0.1 A·m 2 respectively, the comparison results are as Figures 21a - 21c , Figures 22a - 22c :

[0273] It can be clearly seen from the comparison graph of the results that the curve shapes and amplitudes obtained by the surface current method simulation, the method of moments simulation, and the experiment are consistent within the error allowable range. Therefore, it can prove the effectiveness of the surface current method and the method of moments in calculating the electromagnetic scattering field.

[0274] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for calculating the electromagnetic scattering field of a small metallic underwater cylindrical target, characterized in that It includes the following steps: Step 1: Geometrically and physically model the small underwater cylindrical metal target to be detected, perform numerical discretization preprocessing, calculate the information of the network nodes of the geometric and physical models, and construct a grid model of the small underwater cylindrical metal target; Step 2: Use the improved method of moments to calculate the electromagnetic scattering field of the grid model, and obtain the electromagnetic scattering field curves of the small underwater cylindrical metal target in different scenarios; Step 3: Use the equivalent surface current method to calculate the electromagnetic scattering field of the grid model, and obtain the electromagnetic scattering field curves of the small underwater cylindrical metal target in different scenarios; Step 4: Compare the electromagnetic scattering field curves in Step 2 and Step 3, verify whether the shapes and amplitudes of the two curves are basically the same within the allowable error range, and realize the detection and identification of the small underwater cylindrical metal target according to the electromagnetic scattering field curves of the target to be detected under different operating distances and encounter postures.

2. The electromagnetic scattering field calculation method for a small underwater cylindrical metal target according to claim 1, characterized in that, The specific steps of Step 2 include: Step 2.1: Using the RWG basis function, approximate the current density J(r) on the target surface S as: where N is the number of internal edges, I n is the current coefficient associated with the n-th edge, and f n is the vector basis function defined on the adjacent triangles associated with the n-th edge, and f n is given by: where \(l\) n is the common side of the \(n\)th pair of adjacent triangles and , is the surface area of triangle , is the surface area of triangle . The vector starts from the vertex of to the surface element. The vector starts from an arbitrary point on the surface element and points to the endpoint. These two vectors can be used to simulate the flow direction of the current on the surface element; Step 2.2: Obtain the current continuity condition according to the current continuity theorem: where ω is the angular frequency, r′ is the coordinate of the source point position, is the divergence operator for the source point coordinate r', i is the imaginary unit, ρ s is the source charge density, representing the charge density distribution located at the source point r'. Step 2.3: Establish the surface electric field integral equation of the target according to the boundary condition and the surface equivalence principle: where η b is the wave impedance in free space, is the wave number of free space, Step 2.4: Define the matrix and where ε r is the relative permittivity, μ r is the relative conductivity; the matrices V, S, and P are all symmetric; the subscripts m and n respectively represent different basis function numbers, corresponding to different triangles T m and T n ; Step 2.5: Using the basis function f n discretize the electric field integral equation to obtain: In the formula, η0 is the free space wave impedance, k0 is the free space wave number, J represents the current density vector on the target surface S, b is a known vector, and i is the imaginary unit; S in the above formula is: S = D T PD In the formula, D represents the divergence operator; Step 2.6: Then, using the basis function f n discretize the current continuity condition to obtain: D·J = ik0c0ρ; In the formula, c0 represents the speed of light in vacuum, and ρ represents the charge density; Step 2.7: Combine the formulas in Steps 2.5 - 2.6 to obtain an augmented electric field integral equation system: Among them, is the impedance matrix; Step 2.8: Obtain the electromagnetic scattering field curve according to the augmented electric field integral equation system obtained in Step 2.

7.

3. The electromagnetic scattering field calculation method for a small underwater cylindrical metal target according to claim 1, wherein The specific steps of Step 3 include: Step 3.1: Calculate the equivalent surface current on the surface of a cylinder with radius a through the following formula: Among them, and H z respectively represent the tangential component of the magnetic field intensity on the cylindrical surface; j z respectively represent z and the equivalent surface current of the primary field on the cylindrical surface; Step 3.2: Since the vector potential A is coaxial with the current density vector, at the observation point with secondary field coordinates p2, z2, the three components of the vector A are obtained: where μ a represents the magnetic permeability, and ds represents the surface element area of the cylinder; The distance R2 from the cylinder surface to the secondary field receiving point is: Step 3.3: After performing the curl operation according to the receiving point coordinates, obtain the components of the secondary field magnetic field intensity vector: Among them, H r2 , H z2 are respectively the secondary field magnetic field intensity vector r and the z-direction component; Step 3.4: Calculate the primary field magnetic field intensity component on the cylinder surface; Step 3.5: Based on the primary field magnetic field intensity component on the cylinder surface, obtain the three components of the primary field generated by the axial dipole of the transmitting antenna on the cylinder surface: Step 3.6: Calculate the components of the primary field magnetic field intensity vector on the cylinder surface in the cylindrical coordinate system through the following formula: Among them, R1 2 = x 2 + y 2 + z 2 represents the distance from the emitting dipole to the surface ds of the cylinder; z = z - z1, z1, y1, z1 represent the coordinates of the emitting dipole; Step 3.7: Convert the components of the secondary electromagnetic field intensity vector reflected by the cylinder target into components in the Cartesian coordinate system according to the following formula: Among them, x2, y2, z2 represent the receiving antenna coordinates; the distance R2 from the cylinder surface to the observation point is: Step 3.8: Calculate the electromagnetic scattering field of the cylindrical metal target according to the components in the Cartesian coordinate system.

4. The electromagnetic scattering field calculation method for a small underwater cylindrical metal target according to claim 3, wherein When calculating the primary field magnetic field intensity component on the cylinder surface in Step 3.4, it is divided into the following two cases: 1) For a radial magnetic dipole of the transmitting antenna of the beam at a distance p1 from the axis of the cylinder, the magnetic field strength component of the primary field on the cylinder surface is obtained by the following formula: ​ Among them, is the magnetic moment of the emitted magnetic dipole; 2) For the magnetic dipole oriented along an arc and located in the beam For the radial magnetic dipole of the transmitting antenna with a distance p1 from the axis of the cylinder, the magnetic field intensity component of the primary field on the cylinder surface is obtained by the following formula:

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