Method for calculating electromagnetic scattering field of underwater cylindrical metal small target

Abstract

Aiming at the detection and identification problem of underwater target, the application discloses a kind of electromagnetic scattering field calculation method of underwater cylindrical metal small target, including step 1: the underwater cylindrical metal small target to be detected is geometrically and physically modeled, and numerical discretization preprocessing is carried out, the information of geometric and physical model network node is calculated, and the grid model of underwater cylindrical metal small target is constructed;Step 2: the electromagnetic scattering field of grid model is calculated using improved moment method, and the electromagnetic scattering field curve of underwater cylindrical metal small target under different scenes is obtained;Step 3: the electromagnetic scattering field of grid model is calculated using equivalent surface current method, and the electromagnetic scattering field curve of underwater cylindrical metal small target under different scenes is obtained;Step 4: compare the electromagnetic scattering field curves in the above two steps, verify that the curve shape and amplitude of the two are basically consistent within the error allowed range, and realize the detection and identification of underwater metal small target according to the action distance and intersection situation of target.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of detection and identification of underwater targets, and particularly to a method for calculating electromagnetic scattering field of underwater small metal targets. BACKGROUND

[0002] With the development of underwater low-frequency detection technology, many scholars have begun to try to use low-frequency electromagnetic signals to detect underwater small metal targets, and low-frequency electromagnetic detection has gradually become the main detection method of non-acoustic detection. Underwater low-frequency electromagnetic detection includes passive detection and active detection. Passive detection generally involves dragging various magnetic detection system devices into the water from a ship on the sea surface, and detecting the target by measuring the magnetic anomaly behavior caused by the target. The typical representative of active electromagnetic detection is the Marine Controlled Source Electromagnetic Method (MCSEM). The basic idea of this low-frequency artificial source electromagnetic method for detecting underwater targets is that when low-frequency electromagnetic waves are emitted by a transmitter, an induced current is generated inside the metal target when the electromagnetic waves enter the metal target, and the induced current forms a scattering field near the underwater target. The field collected by the receiver is the sum of the scattering field and the incident field, and the underwater target is located and identified according to the normalized result of the scattering field to the incident field. The calculation of the electromagnetic scattering field of underwater small metal targets is a core problem of underwater active electromagnetic detection, which directly affects the detection and identification of small metal targets.

[0003] As early as the 1970s, research on the application of electromagnetic methods to the ocean in the theoretical aspect began, and the horizontal electric dipole model was first used to design the transmitter and receiver, and corresponding MCSEM research was carried out. Since the 21st century, several foreign oil companies have made breakthroughs in electromagnetic detection, and have successfully conducted marine magnetotelluric and MCSEM detection in the North Atlantic and West Africa, with a water depth of more than one kilometer. Most of the research on the use of MCSEM for marine exploration is aimed at large-scale targets (various oil and gas and mineral resources) in deep water (water depth greater than 300m), which is severely restricted in shallow water or when detecting small-scale targets. At present, some domestic institutions have also conducted some research on marine electromagnetic detection, such as the Northwest Industrial University, which has carried out a series of research on the characteristics of submarine underwater electromagnetic fields, the transmission characteristics of underwater extremely low-frequency electromagnetic fields across interfaces, and high-sensitivity low-noise sensors, and has made significant achievements in detecting the shaft frequency electromagnetic field of a submarine for the first time in China in 2010. However, in general, the targets detected at present are basically large-scale targets such as oil and gas and mineral resources, and the research on low-frequency detection of small-scale underwater targets based on MCSEM is almost blank in China. In order to narrow the gap with the international community, it is urgent to develop this detection technology, so as to meet the urgent needs of underwater small target detection in China. SUMMARY

[0004] The present application is directed to the above-mentioned shortcomings of the prior art, and proposes a method for calculating the electromagnetic scattering field of a small underwater metal target, which improves the classical method of moments, introduces an augmented electric field integral equation, solves the problem of low-frequency collapse of the traditional method of moments, and accurately numerically calculates the electromagnetic scattering field of a small metal target. In order to improve the calculation efficiency and simplify the model of the electromagnetic scattering field of the target, an equivalent surface current method is designed to quickly calculate the electromagnetic scattering field of the target under the condition of ensuring the accuracy to meet the engineering application.

[0005] The method for calculating the electromagnetic scattering field of a small underwater metal target adopted by the present application comprises the following steps:

[0006] Step 1: geometric and physical modeling of the underwater cylindrical small metal target to be detected, numerical discretization pretreatment, calculation of the information of the geometric and physical model network nodes, and construction of the grid model of the underwater cylindrical small metal target;

[0007] Step 2: calculating the electromagnetic scattering field of the grid model by using the improved method of moments to obtain the electromagnetic scattering field curve of the underwater cylindrical small metal target under different scenarios;

[0008] Step 3: calculating the electromagnetic scattering field of the grid model by using the equivalent surface current method to obtain the electromagnetic scattering field curve of the underwater cylindrical small metal target under different scenarios;

[0009] Step 4: comparing the electromagnetic scattering field curves in steps 2 and 3 to verify whether the curve shapes and amplitudes are basically consistent within the error allowable range, and realizing the detection and identification of the underwater cylindrical small metal target according to the action distance and intersection situation of the target to be detected.

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

[0011] Step 2.1: using the RWG basis function to approximate the current density J(r) of 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, f n is a vector basis function defined on the adjacent triangle associated with the nth edge, and f n is:

[0014]

[0015] where l n is the nth pair of adjacent triangles andthe public edge of is a triangle is the surface area of is a triangle is the surface area of is a vector from a vertex of a surface element, is a vector from an arbitrary point of an end point, these two vectors can be used to simulate the current flow direction on the surface element;

[0016] Step 2.2: According to the current continuity theorem, the current continuity condition is obtained:

[0017]

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

[0019] Step 2.3: According to the boundary conditions and the surface equivalent principle, the surface electric field integral equation of the target is established:

[0020]

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

[0022] Step 2.4: Define matrix and

[0023]

[0024] In the formula, ε r is the relative dielectric constant, μ r is the relative conductivity; matrix V, S and P have symmetry; subscripts m and n represent different base function numbers, corresponding to different triangles T m and T n ;

[0025] Step 2.5: Discretize the electric field integral equation using base function f n , get:

[0026]

[0027] where η0is the wave impedance in free space, k0is the wave number in free space, J represents the current density vector of 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 D represents a divergence operator in the formula of PD;

[0030] Step 2.6: Reuse the base function f n Discretize the current continuity condition to obtain:

[0031] D·J = ik0c0ρ;

[0032] In the formula, c0represents the speed of light in a vacuum, and ρ represents the charge density;

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

[0034]

[0035] where, is an 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] Further, the specific steps of step 3 include:

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

[0039]

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

[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, the three components of the vector A are obtained:

[0042]

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

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

[0045]

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

[0047]

[0048] where H r2 , H z2 are the r, z direction components of the secondary field magnetic field strength vector, respectively.

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

[0050] Step 3.5: Based on the primary field magnetic field strength 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 strength vector on the surface of the cylinder in the cylindrical coordinate system by the following formula:

[0053]

[0054] where 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 strength vector reflected by the cylindrical target into components in the rectangular coordinate system according to the following formula:

[0057]

[0058] where x2, y2, z2 represent the coordinates of the receiving antenna; 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 according to the components in the rectangular coordinate system.

[0061] Furthermore, in step 3.4, the calculation of the primary magnetic field intensity components on the cylinder surface is divided into the following two cases:

[0062] 1) For a distance p1 from the axis of the cylinder, the beam The radial magnetic dipole of the transmitting antenna is used to obtain the primary field magnetic field intensity components on the surface of the cylinder using the following formula:

[0063]

[0064] in, The magnetic moment for emitting magnetic dipoles;

[0065] 2) The magnetic dipole is oriented in a circular arc and located in the beam. The radial magnetic dipole of the transmitting antenna at a distance p1 from the axis of the cylinder is used to obtain the primary field magnetic field intensity components on the surface of the cylinder using the following formula:

[0066]

[0067] Therefore, the present invention employs the above-mentioned method for calculating the electromagnetic scattering field of small underwater metallic targets, and has the following technical advantages:

[0068] This invention first improves the classical method of moments (MoM) to accurately calculate the electromagnetic scattering field of small metallic targets. Then, while meeting the accuracy requirements for engineering applications, a surface current method is proposed to further improve computational efficiency and simplify the target's electromagnetic scattering field model. This method not only significantly improves computational speed but also effectively reduces computational resource consumption while maintaining accuracy. The MoM offers high computational accuracy, while the surface current method boasts fast computational speed; both have significant theoretical and engineering application value in calculating the electromagnetic scattering field of small underwater metallic targets. The combined approach of this invention provides an effective numerical calculation method for electromagnetic scattering analysis of underwater targets, possessing strong practicality and scalability.

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

[0070] Figure 1 This is a magnetic dipole model.

[0071] Figure 2 The target mesh model is a cylinder.

[0072] Figure 3 This represents the electromagnetic scattering field on the x-component as the intersection angle θ changes.

[0073] Figure 4 This represents the electromagnetic scattering field on the y-component as the intersection angle θ changes.

[0074] Figure 5 Electromagnetic scattering field in z component for intersection angle θ change.

[0075] Figure 6 Electromagnetic scattering field in x component for action distance h change.

[0076] Figure 7 Electromagnetic scattering field in y component for action distance h change.

[0077] Figure 8 Electromagnetic scattering field in z component for action distance h change.

[0078] Figure 9 Schematic diagram of electromagnetic scattering of cylindrical target.

[0079] Figures 10a-10c Magnetic induction intensity of cylindrical target in x, y, z directions respectively.

[0080] Figure 11 On-site diagram of electromagnetic scattering field experiment in embodiment.

[0081] Figure 12 Physical diagram of small magnet.

[0082] Figure 13 Physical diagram of cylindrical barrel.

[0083] Figure 14 Experimental scene diagram drawn according to test scene.

[0084] Figures 15a-15c Results of x component, y component, z component respectively when intersection angle θ is 30°.

[0085] Figures 16a-16c Results of x component, y component, z component respectively when intersection angle θ is 60°.

[0086] Figures 17a-17c Results of x component, y component, z component respectively when intersection angle θ is 90°.

[0087] Figures 18a-18c Results of x component, y component, z component respectively when action distance h is 0.2m.

[0088] Figures 19a-19c Results of x component, y component, z component respectively when action distance h is 0.3m.

[0089] Figures 20a-20c Results of x component, y component, z component respectively when action distance h is 0.4m.

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

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

[0092] Figures 23a-23b An equivalent principle diagram, Figure 1 An actual electromagnetic distribution before equivalence, Figure 23a-23b An electromagnetic distribution after equivalence. DETAILED DESCRIPTION

[0093] In the description of the present application, it is also necessary to point out that, unless otherwise explicitly specified and limited, these embodiments are only used for illustrating the present application but not for limiting the scope of the present application. In addition, it should be understood that, after reading the content taught by the present application, those skilled in the art can make various alterations or modifications to the present application, and these equivalent forms also fall within the scope defined by the appended claims of the present application.

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

[0095] In marine electromagnetic detection, magnetic dipole is widely used as a radiator. The present application intends to use a current loop as a transmitting antenna, and when the distance between the observation point and the transmitting antenna is much larger than the size of the transmitting antenna itself, the small details of the transmitting antenna can be ignored, and a circular current loop is used instead. At this time, this current loop is called a magnetic dipole, the strength of which is represented by a magnetic dipole moment M, and the direction is determined by the right-hand screw rule, as shown in Figure 2

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

[0097] M = μ0μ r NIS (1)

[0098] Wherein, 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] Solving Maxwell equation, and then obtaining the expression of the radiation source with a vertical magnetic dipole as a 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 the conductive medium;

[0102] KRterm is contained in the above formula, according to 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 magnetic dipole radiated electromagnetic field can be divided into three regions:

[0103] (1) When KR<<1, it is called the near zone, also called the quasi-static zone or quasi-stable zone;

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

[0105] (3) Between (1) and (2) is called the intermediate zone.

[0106] The working frequency band of active electromagnetic detection usually satisfies the condition of R<<0.1λ. Therefore, the active electromagnetic detection is a near field zone generated by using a magnetic dipole source. The distribution of the near field zone is approximately the same as that of the static magnetic dipole (ω=0, that is, K=0) field, that is, approximately the same as the constant field. From the energy point of view, the near zone field (E x H) is a virtual number, which indicates that the space 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 provided in the present application

[0108] The present application provides an electromagnetic scattering field calculation method for an underwater cylindrical metal small target, which comprises the following steps:

[0109] Step 1, geometric and physical modeling is performed on the underwater cylindrical metal small target to be detected, and numerical discretization pretreatment is performed, the information of the geometric and physical model network nodes is calculated, and a grid model of the underwater cylindrical metal small target is constructed;

[0110] Step 2, the electromagnetic scattering field of the grid model is calculated by using the improved method of moments, and the electromagnetic scattering field curve of the underwater cylindrical metal small target under different scenes is obtained;

[0111] Step 3, the electromagnetic scattering field of the grid model is calculated by using the equivalent surface current method, and the electromagnetic scattering field curve of the underwater cylindrical metal small target under different scenes is obtained;

[0112] Step 4, the electromagnetic scattering field curves in steps 2 and 3 are compared, the curve shape and amplitude of the two curves are verified to be basically consistent within the error allowable range, and the detection and identification of the underwater metal small target are realized according to the action distance and intersection situation of the target to be detected.

[0113] In the embodiment, the electromagnetic scattering field experiment is carried out, and the feasibility and effectiveness of the two methods (the improved moment method and the equivalent surface current method) proposed in the application in the detection and identification of the underwater cylindrical metal small target are verified. The experimental results provide sufficient experimental basis and support for further popularization and application of the two methods in practical application.

[0114] Next, the calculation of the electromagnetic scattering field of the metal small target based on the moment method and the calculation of the electromagnetic scattering field of the metal small target based on the surface current method are introduced respectively.

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

[0116] ① Introduction of the moment method (MOM)

[0117] The basic idea of the moment method is to convert the boundary value problem into a problem of solving a linear equation set. In this process, the electromagnetic field problem to be solved needs to be discretized, and a set of basis functions is selected to represent it in the form of linear combination. Then, the unknown function in the operator equation is replaced by the linear combination form, and the residual of the equation is made zero in the sense of weighted average by selecting appropriate weight functions, so that the problem is converted into solving algebraic equations. Finally, by solving these algebraic equations, the solution of the electromagnetic field distribution is obtained.

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

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

[0120] Where L is a linear operator, g is a known excitation function, and f is an unknown response function. Define f and g in two different spaces F and G, so that the meaning of formula (5) is to map a set of functions in F space to G space through operator L.

[0121] In order to solve the numerical solution of the above formula (5), the response function f is expanded in its definition domain as a linear combination of f1, f2,..., fN: N

[0122]

[0123] Where {a n} is 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 of this formula is actually accurate.

[0125] ​But infinite is a kind of ideal perfect condition, in the process of solving practical problems, N is always a finite value, so the above formula (6) is a relatively accurate approximate solution. In order to further solve formula (6) more accurate results, formula (6) into (5) can be obtained:

[0126]

[0127] In the above formula (7), the scalar coefficient {a n} needs to be solved, and a vector set w m = {w1, w2,..., w N} of the same number N is defined in the definition domain of the operator L, which is commonly known as the test function, also known as the weight function. In the actual problem, considering the accuracy of the final result, Galileo's method is generally used to select the weight function, that is, the test function and the basis function use the same function.

[0128] Using the weight function to take the inner product of both sides of formula (7) can be obtained:

[0129]

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

[0131] In the above formula, there are:

[0132]

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

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

[0135] Substitute the known excitation function g into formula (12), and solve it by multiplying the inverse matrix of the impedance matrix to obtain the coefficient matrix a. Substitute the obtained coefficient a into formula (6) to obtain the numerical solution of the initial response function f, that is, the solution of the target electromagnetic field distribution.

[0136] ②Improved moment method

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

[0138]

[0139] where N is the number of internal edges, In It is the current coefficient associated with the nth edge, f n It is a vector basis function defined on the adjacent triangles associated with the nth edge, and f n Represented as:

[0140]

[0141] In the formula, l n For the nth pair of adjacent triangles and public side, It is a triangle Surface area, It is a triangle Surface area, vector from Starting from the vertex, to Surface element, vector from Any point of the face element points to The endpoints, these two vectors, can be used to simulate the direction of current flow on a surface element.

[0142] The surface integral equation for a conductor target is established based on boundary conditions and the surface equivalence principle, and is often used to analyze targets in homogeneous media and ideal conductors. The surface equivalence principle simplifies the solution of complex electromagnetic scattering field problems to solving for the current and magnetic current on the target surface, thereby obtaining the spatial distribution of the electromagnetic field excited by the current and magnetic current.

[0143] Let the background space be K1, and its relevant parameter be ε. b and μ b Assume the ideal metallic region is K2, and S is the outer surface of K2. Assume that current J1 and magnetic current M1 excite electromagnetic E in K1. i and magnetic field H i E and H represent the total electric and magnetic fields at point r in K1, such as Figure 2 As shown.

[0144] Based on the principle of surface equivalence, the current J on the surface S of a closed space can be used as an example. S The excited radiation replaces the electromagnetic scattering of the metallic target, generated by the current source J. S Excited scattered electric field E s and magnetic field H s The surface integral equation can be derived from the spatial Green's function and then combined with boundary conditions. The relationship between the incident, scattered, and total electromagnetic field parameters is as follows:

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

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

[0147] Introducing scalar potential Φ S and magnetic potential vector 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] In the formula, the Green's function represents The spherical wave generated by the point source at point r′, where R = |rr′| represents the distance between the two points. It is the wavenumber of free space.

[0151] From the current continuity theorem, we get:

[0152]

[0153] On the boundary surface S, according to the boundary conditions of an ideal conductor, we know that:

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

[0155] Since K2 is an ideal metallic region, its 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 exists. S :

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

[0157] Source J on the surface of an ideal conductor S The electromagnetic field generated in space is:

[0158]

[0159] In the formula, ω is the angular frequency.

[0160] Substituting equation (19) into equation (17), we get:

[0161]

[0162] Finally, substituting equation (23) into equation (20) yields the electric field integral equation:

[0163]

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

[0165]

[0166] In the formula, η b It is the wave impedance in free space.

[0167] The improved method of moments, namely the augmented electric field integral equation, combines the current continuity condition with the electric field integral equation. The solution vector simultaneously selects both current and charge, and the vector potential function and scalar potential function are balanced by normalizing the frequency. After normalizing the RWG basis functions, the solution current is expanded as shown in equation (14), and the solution charge is expanded using the pulse basis functions as follows:

[0168]

[0169] In the formula, h n It is the impulse basis function, h n It is a triangular unit, A n It is the surface area of ​​the triangular unit.

[0170] The electric field integral equation and the current continuity condition can be obtained using the basis function f. n Discretize the equations and transform the integral equations into matrix equations using matrices V, S, P, and D. and The definitions are as follows:

[0171]

[0172]

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

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

[0175]

[0176] In the formula, 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 the imaginary unit.

[0177] S = D T PD (33)

[0178] In the formula, D represents the divergence operator.

[0179] Discretizing the current continuity condition (Equation 19) in the same way, we get:

[0180] D·J=ik0c0ρ (34)

[0181] In the formula, c0 represents the speed of light in a vacuum, and ρ represents the charge density.

[0182] Combining equations (32) to (34) yields the augmented electric field integral equations:

[0183]

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

[0185] Specifically, assuming the number of targets is t, after discretizing the targets using triangular facets, the sum of the facets is... Where, p i Let represent the number of surface elements after discretizing each target, and p represent the total number of surface elements after discretizing all targets. According to the electroneutrality condition, we can obtain:

[0186]

[0187] In the formula, Q n For the nth charge, N t For the triangular element on the t-th target, the N-th t A charge can be represented as:

[0188]

[0189] To make matrix A a full-rank matrix, equation (35) can be rewritten as:

[0190]

[0191] Where, vector I rThis is an identity matrix with dimensions (pt) × (pt). It is a highly sparse matrix. Let be the projection matrices, and:

[0192] ρ r =F·ρ, ρ=B·ρ r (39)

[0193] In the formula, matrix F transforms the original solution charge vector into a vector with dimension F. The charge vector ρ r Matrix B will then convert vector ρ r The original charge vector ρ is restored.

[0194] Matrix V is a symmetric matrix and k0 → 0. 2 I r For a near-zero matrix, constrained preconditions can be constructed to enable the system to converge quickly and avoid convergence problems.

[0195]

[0196] This invention uses the diagonal matrices of matrices V and P to construct preconditions, which can quickly invert problems with many unknowns and solve the low-frequency collapse problem.

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

[0198] To numerically simulate the electromagnetic response characteristics of an underwater cylindrical metallic target, a geometric and physical model of the target is first constructed and preprocessed using numerical discretization. Then, an improved method of moments (MoM) is used to calculate the information of the model's mesh nodes, yielding the final electromagnetic response results for the cylindrical target.

[0199] The meshing used in this simulation was performed in HyperMesh software using a triangular meshing method, resulting in 3788 meshes. The meshed model of the underwater cylindrical metal target is shown below. Figures 3-5 As shown, the model is 1.8m high and 50cm in diameter.

[0200] like Figures 6-8 As shown, the transceiver coil is located at a certain depth h (i.e., the effective distance) below the target, extending along the target axis from -2m to 2m. The transmitting antenna is equivalent to a magnetic dipole, and its magnetic dipole moment is set to 0.1 A·m in the simulation. 2 The frequency of the radiated electromagnetic waves is 500Hz. The distance between the transmitting and receiving antennas is 0.266m. Due to the extremely large computational load of the method of moments, a supercomputer platform was used for the calculation. When calculating the electromagnetic scattering characteristic curve of the cylindrical target, 81 sampling points were selected.

[0201] The characteristic curves of the electromagnetic scattering field of a cylindrical target are calculated below using the method of moments (MoM) for different intersection angles θ, interaction distances h, and directions of magnetic moments generated by the magnetic dipoles (horizontal or vertical). The specific results are as follows:

[0202] i) The effective distance h is 0.1 m, the magnetic dipole generates a magnetic moment in a horizontal direction with a magnitude of 0.1 A·m. 2 Simulation results for intersection angles θ of 0°, 30°, 60°, and 90° are as follows: Figure 9 As shown in the figure, the electromagnetic scattering curve changes in a certain way as the intersection angle changes. The general rule is that as the intersection angle increases, the effective range between the transceiver's trajectory and the target decreases, and the corresponding width of the scattered signal becomes narrower.

[0203] ii) The intersection angle θ is set to 90°, the magnetic dipole generates a magnetic moment in a horizontal direction, and the magnitude of the magnetic moment is 0.1 A·m. 2 Simulation results for action distances h of 0.1m, 0.2m, 0.3m, and 0.4m are as follows: Figures 10a-10c As shown in the figure, the electromagnetic scattering curve changes in a certain way as the effective distance changes. The general rule is that as the effective distance increases, the amplitude of the corresponding electromagnetic scattering field decreases.

[0204] (2) Calculation of electromagnetic scattering field of typical small metallic targets based on surface current method

[0205] ① Introduction to Surface Current Method

[0206] The equivalent principle of the surface current method is that within a free space of area S, unaffected by the source body, currents and magnetic currents distributed on that surface can generate an electromagnetic field. In this sense, the actual source body can be replaced by an equivalent surface current. The surface current density j and magnetic current density j... * The electromagnetic field strength can be calculated using the tangential component:

[0207] j = [n × H], j * = [E×n] (41)

[0208] In the formula, H and E represent the combined magnetic field strength and electric field strength vector on surface S, respectively; n represents the normal to the spatial region pointed to by surface S, which is the equivalent current field.

[0209] In other words, the equivalent surface current is calculated using the tangential components of the magnetic and electric field strengths on surface S. Under conditions of high metallic conductivity, or more precisely, ideal conductivity, the tangential component of the magnetic field strength is doubled relative to a slightly curved surface, while the tangential component of the electric field strength approaches zero. Therefore, 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 a magnetic moment of P M The primary magnetic field of the 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 R represents the permeability, and R represents the distance from the spatial point to the magnetic dipole.

[0215] According to Huygens' theorem, when the equivalent current density on the surface is equal to j, each element ds on the surface constitutes the basic source of a spherical wave. The magnetic field strength vector H2 of the secondary electromagnetic field around the object is obtained using the vector potential A. Based on formulas (42), (43), and the quasi-steady-state approximation, the vector of the secondary reflected field is calculated using the surface integral method as follows:

[0216]

[0217] In the formula, rot is calculated based on the coordinates of the receiving point of the magnetic field H2, and R... 2 The distance is the distance from the ds element on the object surface to the field receiving point.

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

[0219]

[0220] In the formula, R1 is the distance from the magnetic dipole (the actual magnetic source) to point ds on the surface of the target being detected, and P M It is the magnetic moment.

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

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

[0223] Let the radius of the cylinder be a, and the cylinder axis be r in the cylindrical coordinate system. The z-axis coincides with the z-axis. The tangential component of the magnetic field intensity on the cylindrical surface. and H zThis determines the corresponding equivalent surface current:

[0224]

[0225] In the formula, H z1 , Let z and z represent the magnetic field strength of the primary field on the surface of the cylinder, respectively. Tangential component; j z Represent z and The equivalent surface current of a primary field on the surface of a cylinder;

[0226] Because the vector potential A is coaxial with the current density vector, its coordinate in the secondary field is p2. The observation point of z2, the three components of vector A are:

[0227]

[0228] In the formula, μ a ds represents the permeability, and ds represents the area of ​​a single unit surface on the cylinder.

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

[0230]

[0231] After calculating the curl based on the coordinates of the receiving point, the components of the secondary field magnetic field strength vector can be obtained:

[0232]

[0233] In the formula, H r2 , H z2 These are the secondary field magnetic field intensity vectors r and r, respectively. z-direction component;

[0234] For a distance p1 from the axis of the cylinder, the beam The radial magnetic dipole of the transmitting antenna, and the primary field magnetic field strength components on the cylindrical surface are obtained by the following formula:

[0235]

[0236] In the formula, R1 represents the distance from the emitted magnetic dipole to the surface of the cylinder. The magnetic moment that emits the magnetic dipole.

[0237] When the magnetic dipole is oriented in a circular arc and located in the beam When the distance from the cylinder axis is p1, the primary field components on the cylinder surface are calculated using the following formula:

[0238]

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

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

[0241]

[0242] Where, p MZ This represents the axial component of the magnetic dipole.

[0243] The vector components of the primary magnetic field intensity on the surface of a cylinder are calculated in cylindrical coordinates using the following formula:

[0244]

[0245] In the formula, R1 2 =x 2 +y 2 +z 2 R1 is the distance from the emitted dipole to the surface ds of the cylinder, and P Mx Let P be the x-component of the magnetic dipole in Cartesian coordinates. My y is the y-component of the magnetic dipole in Cartesian coordinates; This represents the coordinates of the emitted dipole.

[0246] The formula for calculating the vector components of the secondary electromagnetic field intensity reflected by a cylindrical target in Cartesian coordinates is as follows:

[0247]

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

[0249]

[0250] This yields the formulas for calculating the three components of the electromagnetic scattering field of a cylindrical metallic target using the surface current method (Equation 55).

[0251] ③ Simulation results of electromagnetic scattering field of cylindrical target

[0252] Targeting the following Figure 11 The schematic diagram of the scene is shown. By selecting parameters (including cylinder size, operating frequency, transmit / receive distance, operating range, magnetic moment, intersection angle, and antenna radiation direction), the above calculation method is programmed in MATLAB, and finally the electromagnetic scattering characteristic curve of the cylindrical metal target can be obtained.

[0253] In the simulation, both the transmitting and receiving antennas are represented by magnetic dipoles, with coordinates (x1, y1, z1) and (z2, y2, z2), respectively. The cylinder has a length b of 1.8 m, a diameter 2a of 0.533 m, a transmitter-receiver spacing d of 0.25 m, an operating distance h of 0.9 m, a collision angle θ of 0°, a frequency f of 1111 Hz, and a magnetic dipole that generates a perpendicular magnetic moment with a magnitude of 0.1 A·m. 2 The signal.

[0254] The code was written into MATLAB, and the simulation results are as follows. Figure 12 As shown in the figure, the curve is the electromagnetic scattering curve of the cylindrical target calculated by the surface current method.

[0255] Example

[0256] This invention proposes a method for calculating the electromagnetic scattering field of small underwater metallic targets, and uses a cylindrical model as an example to conduct experimental verification of the electromagnetic scattering field.

[0257] 1. Test Scenario

[0258] like Figure 13 As shown, a cylindrical model is installed, and different transceiver devices are used (transceiver spacing, magnitude of transmitting magnetic moment, scaling ratio, and whether the magnetic moment direction is perpendicular or parallel). The model is moved along a distance from -2m to 2m.

[0259] 2. Transceiver device

[0260] like Figure 14 As shown, the transceiver device in this embodiment is a small magnetic rod with a transceiver spacing of 0.266m, and is configured vertically or in parallel.

[0261] 3. Magnetic sensor

[0262] The magnetic sensor actually collects voltage values, in units of V. The sensor sensitivity conversion coefficient used in this experiment is 0.5 nT / mV. Therefore, to convert it to magnetic field units, first multiply by 1000 to mV, then multiply by 0.5 to get the magnetic induction intensity, in units of nT.

[0263] 4. Cylindrical barrel model

[0264] The cylindrical barrel used in this experiment has a thickness of 2.7 mm, a diameter of 50 cm, and a length of 1.8 m. A picture of the actual barrel is shown below. Figures 15a-15c As shown.

[0265] 5. Data collection device

[0266] This experiment involves transmitting experimental data to a computer via a data acquisition box connected to a power amplifier for further processing. Based on the test scenario of this experiment, the following graphs can be plotted: Figures 16a-16c The experimental scenario diagram is shown.

[0267] 6. Experimental Procedure

[0268] The experimental process can be divided into the following steps: (1) Test the entire system on land to ensure normal communication; (2) Mount the target surface ship on the crane hoisting point and adjust the depth, intersection angle and movement distance using the host computer; (3) Place the transceiver equipment on the ladder and set the transmission signal parameters; (4) The surface ship moves along the predetermined trajectory and passes under the target; (5) Process the received data and draw the target passage characteristic curve.

[0269] The experimental data was transferred to a computer for recording and compared with the results of simulations using the surface current method and the method of moments. The following results were obtained:

[0270] (1) The effective distance h is 0.1 m, the magnetic dipole generates a magnetic moment in the horizontal direction and the magnitude of the magnetic moment is 0.1 A·m. 2 When the intersection angle θ is 30°, 60° and 90° respectively, the results are compared as follows: Figures 17a-17c , Figures 18a-18c and Figures 19a-19c ;

[0271] (2) The intersection angle θ is taken as 90°, the magnetic dipole generates a magnetic moment in the horizontal direction and the magnitude of the magnetic moment is 0.1 A·m. 2 The results for the action distance h being 0.2m, 0.3m, and 0.4m are compared as follows: Figures 20a-20c , Figures 21a-21c and Figures 22a-22c :

[0272] (3) The intersection angle θ is 90°, the action distance h is 0.5m, and the magnetic dipoles generate magnetic moments in the horizontal and vertical directions, respectively, with a magnitude of 0.1 A·m. 2 The result in the case of, for example ​ , ​ :

[0273] The results comparison chart clearly shows that the curves obtained from the surface current method simulation, the method of moments simulation, and the experiment are consistent in shape and amplitude within the allowable error range. Therefore, it can be proven that the surface current method and the method of moments are effective 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 and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to 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 underwater cylindrical metallic target, characterized in that, Includes the following steps: Step 1: Perform geometric and physical modeling of the underwater cylindrical metal target to be detected, and perform numerical discretization preprocessing to calculate the information of the network nodes of the geometric and physical model and construct the mesh model of the underwater cylindrical metal target. Step 2: Calculate the electromagnetic scattering field of the mesh model using the improved method of moments to obtain the electromagnetic scattering field curves of the underwater cylindrical metal target under different scenarios; Step 3: Calculate the electromagnetic scattering field of the mesh model using the equivalent surface current method to obtain the electromagnetic scattering field curves of the underwater cylindrical metal target under different scenarios; Step 4: Compare the electromagnetic scattering field curves in Step 2 and Step 3 to verify whether the shape and amplitude of the two curves are basically consistent within the allowable error range. Based on the electromagnetic scattering field curves of the target under different action distances and intersection situations, the detection and identification of small cylindrical metal targets underwater can be achieved. Step 2 includes the following specific steps: Step 2.1: Using the RWG basis function, the current density J(r) of the target surface S is: Where N is the number of internal edges, I n It is the current coefficient associated with the nth edge, f n f is a vector basis function defined on the adjacent triangles associated with the nth edge, and f n for: In the formula, l n For the nth pair of adjacent triangles and public side, It is a triangle Surface area, It is a triangle Surface area, vector from Starting from the vertex, to Surface element, vector from Any point of the face element points to At the endpoints, these two vectors can be used to simulate the direction of current flow on a surface element; Step 2.2: Obtain the current continuity condition according to the current continuity theorem: Where ω is the angular frequency, and r′ is the coordinate of the source point. It is the divergence operator over the source point coordinates r', where i is the imaginary unit, and ρ is the divergence operator. s It is the source charge density, representing the charge density distribution at the source point r'; Step 2.3: Establish the surface electric field integral equation of the target based on the boundary conditions and the principle of surface equivalence: Where, η b It is the wave impedance in free space. It is the wavenumber of free space. Step 2.4: Define the matrix and In the formula, ε r μ is the relative permittivity. r The relative conductivity; matrices V, S, and P are all symmetric; subscripts m and n represent different basis function indices, corresponding to different triangles T. m and T n ; Step 2.5: Using basis functions f n Discretizing the electric field integral equation yields: In the formula, η0 is the free space wave impedance, k0 is the free space wave number, J represents the current density vector of the target surface S, b is a known vector, and i is the imaginary unit. In the above formula, S is: S=D T PD In the formula, D represents the divergence operator; Step 2.6: Reuse the basis function f n Discretizing the current continuity condition yields: D·J=ik0c0ρ In the formula, c0 represents the speed of light in a vacuum, and ρ represents the charge density; Step 2.7: Combining the equations from Steps 2.5 and 2.6, we obtain the augmented electric field integral equations: in, Here is the impedance matrix; Step 2.8: Obtain the electromagnetic scattering field curve based on the augmented electric field integral equations obtained in Step 2.7; Step 3 includes the following specific steps: Step 3.1: Calculate the equivalent surface current of the cylinder with radius a using the following formula: in, and H z These represent the tangential components of the magnetic field intensity on the surface of the cylinder; j z Represent z and The equivalent surface current of a primary field on the surface of a cylinder; Step 3.2: Since the vector potential A and the current density vector are coaxial, their coordinates in the secondary field are p2. From the observation point of z2, we obtain the three components of vector A: Where, μ a ds represents the permeability, and ds represents the area of ​​a single unit surface of the cylinder. The distance R2 from the surface of the cylinder to the secondary field receiving point is: Step 3.3: After calculating the curl based on the receiver point coordinates, the components of the secondary field magnetic field strength vector are obtained: Among them, H r2 , H z2 These are the secondary field magnetic field intensity vectors r and r, respectively. z-direction component; Step 3.4: Calculate the primary field magnetic field intensity components on the surface of the cylinder; Step 3.5: Based on the primary field strength components on the cylindrical surface, obtain the three components of the primary field generated by the axial dipole of the transmitting antenna on the cylindrical surface: Step 3.6: Calculate the components of the primary magnetic field intensity vector on the cylindrical surface in cylindrical coordinates using the following formula: Among them, R1 2 =x 2 +y 2 +z 2 This represents the distance ds from the emitted dipole to the surface of the cylinder. z = z - z1, x1, y1, z1 represents the coordinates of the emitted dipole; Step 3.7: Convert the vector components of the secondary electromagnetic field intensity reflected by the cylindrical target into components in a rectangular coordinate system according to the following formula: Where x2, y2, z2 represent the coordinates of the receiving antenna; the distance R2 from the surface of the cylinder to the observation point is: Step 3.8: Calculate the electromagnetic scattering field of the cylindrical metal target based on the components in the rectangular coordinate system.

2. The method for calculating the electromagnetic scattering field of a small underwater cylindrical metal target as described in claim 1, characterized in that, In step 3.4, the calculation of the primary magnetic field intensity components on the surface of the cylinder is divided into the following two cases: 1) For a distance p1 from the axis of the cylinder, the beam The radial magnetic dipole of the transmitting antenna is used to obtain the primary field magnetic field intensity components on the surface of the cylinder using the following formula: in, The magnetic moment for emitting magnetic dipoles; 2) The magnetic dipole is oriented in a circular arc and located in the beam. The radial magnetic dipole of the transmitting antenna at a distance p1 from the axis of the cylinder is used to obtain the primary field magnetic field intensity components on the surface of the cylinder using the following formula:

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