CN115267720A

CN115267720A - Method for calculating composite electromagnetic scattering RCS (radar cross section) of marine ship target

Info

Publication number: CN115267720A
Application number: CN202210995470.0A
Authority: CN
Inventors: 王雅芬; 郭立新; 董春雷; 蔡姝; 吕亚飞; 孟肖; 张恺翊
Original assignee: Unit 91977 Of Pla
Current assignee: Unit 91977 Of Pla
Priority date: 2022-08-18
Filing date: 2022-08-18
Publication date: 2022-11-01

Abstract

The invention discloses a method for calculating a composite electromagnetic scattering RCS of a marine ship target, which specifically comprises the following steps: carrying out the motion characteristic description of the marine ship target along with the stormy waves, and constructing and solving a six-degree-of-freedom motion model of the marine ship target along with the stormy waves; establishing a dynamic sea surface and moving ship composite scene geometric model; performing surface element subdivision on geometric information of the marine ship target, dividing the marine ship target composite electromagnetic scattering RCS into four parts of RCS, specifically single scattering RCS of ships, multiple scattering RCS of ships, single scattering RCS of sea surface and multiple scattering RCS between sea surface and ship, respectively solving scattering field intensity corresponding to the four parts of RCS according to target surface elements, and performing vector superposition on the obtained scattering field intensity to obtain the marine ship target composite electromagnetic scattering RCS. The invention provides technical support for the research on the electromagnetic characteristics of the ship target in the actual complex marine environment, and has important significance for the detection, identification and research on the ship target on the sea.

Description

Method for calculating composite electromagnetic scattering RCS (radar cross section) of marine ship target

Technical Field

The invention relates to the technical field of electromagnetic fields and microwaves, in particular to a method for calculating composite electromagnetic scattering (RCS) of a marine ship target.

Background

At present, the method for estimating and calculating the composite electromagnetic scattering RCS of the marine ship target mostly only considers the motion characteristic of sea waves, and ignores the image of the motion characteristic of the ship target along with the sea waves. However, in actual situations, due to the random motion characteristic of sea waves, the attitude of the ship target changes with the sea waves under the hydrodynamic action of the sea waves, and the ship target and the coupling scattering with the sea surface also change with time. Therefore, the method for calculating the complex electromagnetic scattering RCS of the marine ship target neglecting the wave motion characteristics of the ship at the present stage has a great difference from the actual situation, so that the calculation result has a great difference from the actual complex electromagnetic scattering characteristics of the marine ship target.

In addition, the existing offshore target composite electromagnetic scattering calculation mainly comprises two schemes with wider application, one scheme is to use a ray method to consider the coupling relation between the sea surface and a ship, and the disadvantage is that if the contribution of capillary waves to a coupling field is considered, the sea surface needs to be subdivided more carefully, which undoubtedly greatly increases the calculation amount; the other scheme is to estimate the mutual coupling between the sea surface and the ship by using a complex reflection coefficient, such as a four-path method, because the shielding effect between the sea surface and the ship cannot be well considered, the supposed sea surface is a plane, the actual sea surface is a double-scale model of modulating small-scale capillary waves by large-scale fluctuating surges, and the reflection of the sea surface is not concentrated on the mirror image direction, the estimation of the coupling between the sea surface and the ship by using the complex reflection coefficient is too simple, and the scheme is not applicable in a scene with higher requirement on calculation accuracy.

Disclosure of Invention

The invention discloses a method for calculating a marine target composite electromagnetic scattering (RCS), which aims to solve the problem that the existing method for calculating the marine ship target composite scattering (RCS) is difficult to obtain the actual dynamic scene composite scattering. The RCS refers to the scattering Cross Section of the Radar, and is called Radar Cross Section in English.

The invention discloses a method for calculating a composite electromagnetic scattering RCS of a marine ship target, which comprises the following steps:

s1, establishing a coordinate system according to geometric information and scene parameters of the marine ship target, describing the motion characteristics of the marine ship target along with the stormy waves to obtain a motion characteristic description result, and constructing and solving a six-degree-of-freedom motion model of the marine ship target along with the stormy waves according to the motion characteristic description result to obtain a six-degree-of-freedom motion response variable of the ship.

The scene parameters comprise sea surface size, sea surface wind speed, sea surface wind direction, ship movement speed, ship movement direction and the like.

The method comprises the steps of establishing a global coordinate system, an inertial coordinate system and a ship body fixing coordinate system, wherein the ship body fixing coordinate system is a three-dimensional rectangular coordinate system which takes the gravity center of a ship body of a ship as an origin, takes a sea level as an XOY plane and takes the forward direction of the ship as the forward direction of an X axis, the three-dimensional rectangular coordinate system moves along with the movement of the ship, and the X axis, the Y axis and the Z axis of the ship body fixing coordinate system respectively point to the bow, the port and the bottom of the ship. The global coordinate system adopts a geodetic coordinate system, the center of the inertial coordinate system is kept consistent with the global coordinate system, the center of the inertial coordinate system does not change along with the movement of the ship body, and the X axis, the Y axis and the Z axis of the inertial coordinate system respectively point to the bow, the starboard and the bottom of the ship.

The marine ship target wave-following motion characteristic description is carried out to obtain a motion characteristic description result, and the motion characteristic description result specifically comprises the following steps: and describing the motion state of the marine ship target in the sea waves by adopting six-degree-of-freedom motion response variables, wherein the six-degree-of-freedom motion response variables comprise translational motion variables of the ship body along the coordinate axes of the fixed coordinate system and rotational motion variables around the coordinate axes of the fixed coordinate system. The translational motion variables include a surging (surge) motion variable, a swaying (sway) motion variable, and a heaving (heave) motion variable, and the rotational motion variables include a rolling (roll) motion variable, a pitching (pitch) motion variable, and a yawing (yaw) motion variable.

The position point coordinates of the marine ship target in the global coordinate system are { x, y, z }, and the position point coordinates of the marine ship target in the inertial coordinate system are { x _I ,yI,z _I And the position point coordinates of the marine ship target in the ship body fixed coordinate system are { x } _b ,y _b ,z _b The six-freedom-degree motion response variable of the ship under the ship fixed coordinate system is expressed as

u ₁ 、u ₂ 、u ₃ Respectively include surging motion variable (surge), swaying motion variable (sway) and heaving motion variable (heave) of the translational motion variable of the marine ship target ₄ 、u ₅ 、u ₆ Roll, pitch and yaw motion variables included in the rotational motion variables, respectively, and the conversion relationship between the inertial coordinate system and the hull-fixed coordinate system of the marine vessel target is expressed as

Wherein A is _roll 、A _pitch And A _yaw Are all conversion matrixes, and the expression is as follows:

the conversion relationship between the global coordinate system and the inertial coordinate system of the marine vessel target is expressed as:

wherein v is _ship In order to obtain the speed of the ship,

is the included angle between the ship motion direction and the X axis of the global coordinate system, and t represents time. The motion characteristic description result comprises a six-degree-of-freedom motion response variable, a conversion relation between an inertial coordinate system of the marine ship target and a ship body fixed coordinate system and a conversion relation between a global coordinate system of the marine ship target and the inertial coordinate system.

The method comprises the following steps of constructing a six-degree-of-freedom motion model of the marine ship target moving along with the stormy waves according to a motion characteristic description result, and specifically comprises the following steps:

calculating to obtain the encounter frequency omega taking the ship body as the reference according to the sea wave spectrum and the wave direction and ship body position relation _e (encounter frequency) and encounter wave spectrum S _e The calculation process is represented as:

wherein the content of the first and second substances,

indicating the direction of the waves and the direction of the motion of the hull

Is/are as follows the included angle is formed by the angle of inclination,

it shows that the wave direction of the sea waves is consistent with the movement direction of the ship body,

it shows that the wave direction of the sea waves is vertical to the motion direction of the ship body,

indicating that the wave direction of the sea waves is opposite to the moving direction of the ship body, omega indicates the wave period of the sea waves,

expressed at the encounter frequency ω _e Included angle

And

when encountering a wave spectrum, g is a gravity constant,

is expressed in the wave period omega and the included angle

A temporal wave spectral function;

according to the stress balance of the marine ship target on the sea surface, a linear equation of the ship moving in the regular wave is constructed, and the expression is as follows:

wherein the content of the first and second substances,

is a quality matrix, and the expression is:

where m is the mass of the marine vessel target, [ x ] _G ,y _G ,z _G ]For the seating of the center of gravity of a marine vessel target in a global coordinate systemTarget, theta _xx Representing the moment of mass inertia, theta, of the marine vessel target in translational and rotational motion along the x-axis _yy Representing the moment of mass inertia, theta, of the marine vessel target in translational and rotational motion along the x-axis _zz Representing the moment of mass inertia, theta, of the marine vessel target in translational and rotational motion along the z-axis _xy Represents the mass moment of inertia theta when the marine ship target performs translational motion along the x axis and performs rotational motion along the y axis _xz Represents the mass moment of inertia theta when the marine ship target performs translational motion along the x axis and performs rotational motion along the z axis _yz The mass moment of inertia is shown when the marine vessel target performs translational motion along the y-axis and rotational motion along the z-axis.

Representing the fluid power exerted by the sea waves on the marine target, which comprises a hydrostatic part and a fluid dynamic part generated by the ship motion, the collision of the incident waves of the sea waves on the ship body and the diffraction after the collision; decomposing and expressing a linear equation of the movement of the ship in the regular wave to obtain a six-degree-of-freedom movement model of the marine ship target along with the storm, wherein the expression is as follows:

wherein the content of the first and second substances,

a restoring force matrix for a marine vessel target, which is generated by a hydrostatic portion,

a radiation force matrix representing the motion of an offshore vessel target,

is a disturbance force amplitude matrix generated by the collision of incident waves of sea waves on a ship body and the diffraction of the incident waves after the collision.

The six-degree-of-freedom motion model of the marine ship target moving along with the storms is solved, and the six-degree-of-freedom motion model of the marine ship target moving along with the storms is solved by adopting a slicing method.

The method for solving the six-degree-of-freedom motion model of the marine ship target moving along with the wind waves by adopting the slicing method specifically comprises the following steps:

uniformly dividing the ship body into a plurality of transverse sections along the axial direction of the ship body, and solving a linear equation of the ship moving in a regular wave for each transverse section to obtain the hydrodynamic force of the ship body at the transverse section;

superposing the hydrodynamic force at each transverse section of the ship body along the axial direction of the ship body to obtain the three-dimensional hydrodynamic force of the ship body;

and constructing a sea wave spectrum superposition model by utilizing the three-dimensional fluid power of the ship body of the ship, and solving to obtain the six-degree-of-freedom motion response variable of the ship according to the sea wave spectrum superposition model.

The method is characterized in that a wave spectrum superposition model is constructed by utilizing three-dimensional fluid power of a ship body of the ship, and a six-degree-of-freedom motion response variable of the ship is obtained by solving according to the wave spectrum superposition model, and specifically comprises the following steps:

the expression of the constructed sea wave spectrum superposition model is as follows:

wherein u is _i (x, y, t) is a six-degree-of-freedom response variable of the marine vessel target at the two-dimensional wave surface (x, y) at the time t, i =1,2, _e to encounter a circular frequency omega _e Wave number of wave, S _e (,) is the two-dimensional encounter wave spectral function, R is the amplitude response operator, N _k And N _φ Number of sampling points, omega, of frequency and direction angle, respectively _e, l is the encountered circle frequency, k, at the l-th frequency sampling point _e,l To encounter a circular frequency omega _e,l The lower corresponding wave number of the sea wave,

is the jth sky of sea waveThe angle of the direction between the two sides of the body,

representing sea surface wind direction angle, Δ k _e In increments of the change in the wave number of the ocean waves,

is the incremental change of the spatial azimuth of the sea wave, epsilon _lj The initial phase corresponding to the ith frequency sampling point and the jth spatial direction angle is shown. And solving to obtain the six-degree-of-freedom motion response variable of the ship by utilizing the sea wave spectrum superposition model.

S2, establishing a dynamic sea surface and moving ship composite scene geometric model by utilizing six-degree-of-freedom motion response variables of ships;

establishing a three-dimensional dynamic sea surface geometric model of the marine ship target by using a linear superposition method, and describing the wave height of a fixed point on the sea surface at a single moment by superposing a plurality of random cosine waves, so that the wave height eta of a fixed point (x, y) on the sea surface at the moment t _L (x, y, t) is represented as:

wherein S is _e (,) is a two-dimensional encounter wave spectral function, k _l 、ω _l 、

Respectively representing wave number, circular frequency, direction angle, N, of random cosine wave _k And N _φ The number of sampling points for frequency and direction angle respectively,

representing sea surface wind direction angle, k _e,l To encounter a circular frequency omega _e,l The lower corresponding wave number of the sea wave,

the jth spatial azimuth of a wave,

is the incremental change of the spatial azimuth of the sea wave, epsilon _lj The initial phase corresponding to the ith frequency sampling point and the jth spatial direction angle is shown.

The three-dimensional dynamic sea surface geometric model comprises three-dimensional dynamic sea surface geometric information. The three-dimensional dynamic sea surface geometry information includes wave height information at each time instant for each fixed point (x, y) on the sea surface.

And linearly superposing the marine vessel target geometric information and the three-dimensional dynamic sea surface geometric information at each time sampling point to obtain a dynamic sea surface and moving vessel composite scene geometric model.

S3, calculating a composite electromagnetic scattering RCS of the marine ship target according to the dynamic sea surface and moving ship composite scene geometric model;

carrying out surface element subdivision on geometric information of a marine ship target to obtain a plurality of target surface elements, dividing the marine ship target composite electromagnetic scattering RCS into four parts of RCS, specifically, a single-scattering RCS of a ship, a multiple-scattering RCS of the ship, a single-scattering RCS of a sea surface and a multiple-scattering RCS between the sea surface and the ship, respectively solving scattering field intensities corresponding to the four parts of RCS according to the target surface elements, and carrying out vector superposition on the obtained scattering field intensities to obtain the marine ship target composite electromagnetic scattering RCS.

The calculation of the single scattering RCS of the marine ship target is realized by adopting a pure physical optical method, which specifically comprises the following steps:

local approximation is carried out on an excitation source of the scattering RCS under the tangential plane approximation condition, induced electromagnetic current of the marine ship target is obtained, near-far field extrapolation is carried out by utilizing a far-field Green function and an equivalent principle, an expression of the electromagnetic field of the marine ship target is obtained, then the surface current value and the magnetic current value of the marine ship target are obtained through the tangential plane approximation method, and single scattering RCS of the marine ship target is obtained according to the surface current value and the magnetic current value of the marine ship target.

And calculating the multiple scattering RCS of the marine ship target by adopting a bounce ray method.

When a bounce ray method is adopted to calculate the multiple scattering RCS of the marine ship target, the incident wave direction is determined, corresponding incident ray direction information is determined according to the incident wave direction, each incident ray penetrates through the center of a corresponding target surface element, shielding judgment is conducted on the target surface element according to the incident ray direction information, a shielding judgment result is obtained, the shielding judgment result comprises illumination surface element information and shielding surface element information, and for the target surface element corresponding to the illumination surface element information, the incident ray corresponding to the target surface element is tracked and the scattering field of the incident ray is calculated. The ray corresponding to the incident wave is called an incident ray, and the direction of the incident ray is called an incident ray direction.

Tracking incident rays, tracking the propagation path of each incident ray by using a geometric optical method according to a dynamic sea surface and moving ship composite scene geometric model until the incident ray is not intersected with any target surface element or the reflection times in the propagation path of the incident ray reach a preset value, and obtaining and recording the propagation path of the incident ray;

calculating the scattered field, namely acquiring intersection points of incident rays and a target surface element according to the propagation path of the incident rays, and calculating the propagation distance between two adjacent intersection points; calculating a field intensity relation between the two adjacent intersection points according to each propagation distance, taking the field intensity relation as an incident field intensity at the corresponding illumination surface element, and calculating a far-region scattering field value on the surface element at the illumination surface element by using a physical optical method; and calculating to obtain far-zone scattering field values of all the illuminated surface elements, accumulating the far-zone scattering field values of all the illuminated surface elements to obtain an accumulated value, and obtaining the multiple scattering RCS of the marine ship target by using the accumulated value.

The calculating of the field strength relationship between the two adjacent intersection points according to each propagation distance specifically includes:

in the propagation path of the incident ray, the intersection point of the incident ray and the target surface element is

I is the number of intersection points, and the propagation distance of rays between two adjacent intersection points

Obtaining the field intensity relationship at two adjacent intersection points as follows:

wherein the content of the first and second substances,

and

are respectively an intersection point

And point of intersection

At field strength, k being the wave number of the incident ray electromagnetic wave, (DF) _i And

are respectively an intersection point

Divergence factor and reflection coefficient matrix. Intersection point

Is expressed as

Where ρ is ₁ And ρ ₂ Are respectively an intersection point

At the corresponding principal radii of curvature of the incident-ray-emitting surface and the illuminated surface element, s representing the intersection point

At the reflection distance between the corresponding incident radiation-emitting surface and the illuminated surface element.

The shielding judgment of the target surface element is carried out to obtain a shielding judgment result, and the method specifically comprises the following steps:

the method comprises the steps of firstly carrying out shielding judgment on a target surface element to obtain a directly illuminated target surface element and a target surface element which is not directly illuminated, then carrying out self-shielding judgment on the directly illuminated target surface element to obtain a finally output illuminated surface element and a target surface element which is shielded by the self, wherein shielding surface element information in a shielding judgment result is formed by the target surface element information which is shielded by the self and the target surface element information which is not directly illuminated, and the finally output illuminated surface element information is formed by the illuminating surface element information in the shielding judgment result to obtain a shielding judgment result.

The shielding judgment of the other part specifically comprises the steps of judging whether the target surface element is shielded by other target surface elements or not along the direction of the incident ray, and if the target surface element is not shielded by other target surface elements, judging that the target surface element is the target surface element directly illuminated by the incident wave. And (4) carrying out other shielding judgment on all target surface elements to obtain directly illuminated target surface elements and target surface elements which are not directly illuminated.

The other shielding judgment specifically comprises that the geometric center point of a target surface element needing to be subjected to other shielding judgment is Q, if incident rays have intersection points with other target surface elements before reaching a point Q, the target surface element where the point Q is located is judged to be shielded by other target surface elements, the target surface element where the point Q is located is considered to be a target surface element which is not directly illuminated, the target surface element which is not directly illuminated belongs to a shielding surface element, if incident waves do not have intersection points with other target surface elements before reaching the point Q, the target surface element where the point Q is located is judged to be illuminated by the incident waves, and the target surface element where the point Q is located is considered to be the target surface element which is directly illuminated.

The specific implementation of the other occlusion judgment process is as follows: for a certain target surface element m on the marine ship target, if the coordinates of three vertexes of the target surface element m on the marine ship target are A, B and C, the ray starting point of the incident wave is at the point P, and the geometric center point of the target surface element m is Q. And (3) expressing the coordinate S of any point on the target surface element m as follows by using a parameter equation:

S＝αA+βB+(1-α-β)C，

wherein, alpha, beta and gamma are parameters to be solved, and let gamma = 1-alpha-beta; assuming that a point with coordinates S is also located on the line segment PQ, i.e., S is the intersection of the target bin m and the line segment PQ, the coordinates are expressed as:

S＝λP+(1-λ)Q，

according to the two expressions of the coordinate S, an equivalence equation is constructed:

α(A-C)+β(B-C)+λ(Q-P)＝Q-C，

expressing the equivalent equation as a matrix multiplication form to obtain an equivalent equation set:

where CA denotes a vector from C to a, CB denotes a vector from C to B, PQ denotes a vector from P to Q, and CQ denotes a vector from C to Q. For the equivalence equation set, if det [ CA CB PQ ] =0, the target surface element is judged to be the target surface element directly illuminated by the incident wave, if det [ CA CB PQ ] ≠ 0, the equivalence equation set is solved to obtain alpha, beta, lambda and gamma, if the values of the alpha, the beta, the lambda and the gamma are all in the interval [0,1], the target surface element is judged to be the target surface element which is not directly illuminated, and if any one of the alpha, the beta, the lambda and the gamma is not in the interval [0,1], the target surface element is judged to be the target surface element directly illuminated by the incident wave.

The self-shielding judgment of the directly illuminated target surface element specifically comprises the following steps: for a target surface element directly illuminated by incident waves and obtained through shielding judgment, calculating a normal vector of the target surface element

And the direction vector of the incident wave

Inner product of (2)

If internal product

Judging that the target surface element is the final output illumination surface element; if inner product

And judging that the target surface element is shielded by the target surface element, considering that the target surface element is the target surface element shielded by the target surface element, and enabling the target surface element shielded by the target surface element to belong to a shielding surface element.

The sea surface single scattering RCS calculation method includes the steps of discretizing the sea surface into a plurality of inclined surface elements, constructing a representation of the geometric outline of the inclined surface elements, taking each inclined surface element as a first target surface element, conducting self-shielding judgment to obtain a first sea surface illumination surface element, conducting shielding judgment on the first sea surface illumination surface element and a target surface element of a marine ship target, obtaining a second sea surface illumination surface element, illuminating all second sea surfaces to obtain a surface element, and solving to obtain the sea surface single scattering RCS by means of a semi-determination surface element method.

The self-shielding judgment of the first target surface element specifically comprises the following steps: calculating the normal vector of the first target surface element

And the direction vector of the incident wave

Inner product of (2)

If inner product

Judging that the target surface element is a first sea surface illumination surface element; if inner product

And judging that the first target surface element is shielded by the first target surface element, and considering that the first target surface element is the shielded target surface element.

The target surface element to first sea surface illumination surface element and marine naval vessel target, carry out other and shelter from the judgement, obtain second sea surface illumination surface element, it specifically includes:

and judging whether the first sea surface illumination surface element is shielded by a target surface element of the marine ship target or not along the incident ray direction, and if the first sea surface illumination surface element is not shielded by the target surface element of the marine ship target, judging that the first sea surface illumination surface element is the target surface element directly illuminated by the incident wave. And performing other shielding judgment on all the first sea surface illumination surface elements to obtain a second sea surface illumination surface element.

The shielding judgment of the ship is specifically carried out, the geometric center point of a first sea surface illumination surface element needing to be subjected to shielding judgment of the ship is Q, if incident rays have intersection points with a target surface element of a ship target at sea before reaching the Q point, the fact that the first sea surface illumination surface element where the Q point is located is shielded by the target surface element of the ship target at sea is judged, the fact that the first sea surface illumination surface element where the Q point is located is a target surface element which is not directly illuminated is considered, if incident waves do not have intersection points with the target surface element of the ship target at sea before reaching the Q point, the fact that the first sea surface illumination surface element where the Q point is located is illuminated by incident waves is judged, the fact that the first sea surface illumination surface element where the Q point is located is a target surface element which is directly illuminated is considered, and the target surface element which is directly illuminated is used as a second sea surface illumination surface element.

The sea surface discretization is processed into a plurality of inclined surface elements, the expression of the geometric profile of the inclined surface elements is constructed, the sea surface discretization is processed into a plurality of inclined surface elements, the inclined surface elements comprise rough sea surface elements and component surface elements of cosine capillary waves, the geometric profile of the inclined surface elements is expressed by superposing the rough sea surface elements and the component surface elements of the cosine capillary waves, and the expression of the geometric profile of the inclined surface elements at the moment t is as follows:

ζ(ρ _c ,t)＝B(k _c )cos(k _c ·ρ _c -ω _c t)，

where ρ is _c Representing the position coordinate vector, k, inside the tilted surface element _c Representing the wave number vector of the cosine capillary wave, B (k) _c ) Representing the amplitude, omega, of a cosine capillary wave _c Representing wave number vector k _c Corresponding angular frequency.

The illuminating surface element for all the second sea surfaces, and solving to obtain the single scattering RCS of the sea surfaces by using a semi-definite surface element method, specifically comprises the following steps:

calculating the electromagnetic scattering coefficient of each second sea surface illumination surface element by adopting a perturbation method, wherein the electromagnetic scattering coefficient of each second sea surface illumination surface element

The calculation formula of (2) is as follows:

where k is the wave number of the incident electromagnetic wave, ε is the dielectric constant of the sea surface, ψ (q) _l ) Is a spectral function of the cosine of the small-scale capillary wave component, q _l Is the projection of the scattering vector corresponding to the incident electromagnetic wave on the tilted surface element,

representing the corresponding scattering vector of the incident electromagnetic wave,

representing incident wave vector, F, corresponding to the incident electromagnetic wave _pq The scattering vector is the vector of the scattering component produced by the incident wave on the sea surface, which is the polarization factor.

The far field scattering field strength of the second sea surface illuminated surface element is expressed as

Wherein R is ₀ The distance from the starting point of the incident wave to the geometric center of the sea surface used for calculating the complex electromagnetic scattering (RCS) of the marine vessel target,

the scattering amplitude of the tilted bin is calculated by the formula:

and accumulating the far-zone scattering field intensity values of all the second sea surface illuminated surface elements to obtain an accumulated value, and obtaining the single-scattering RCS of the sea surface by using the accumulated value.

The method is characterized in that the calculation of the multiple scattering RCS between the sea surface and the marine ship target is realized by adopting a ray path tracking method, wherein the field intensity between rays is calculated by adopting a geometric optical method, when incident rays irradiate a target surface element of the marine ship target, the field intensity of a far-zone scattering field is calculated by utilizing a physical optical method, and when the incident rays irradiate an inclined surface element on the sea surface, the field intensity of the far-zone scattering field is calculated by utilizing a semi-definite surface element method. And superposing the field intensities of the far-zone scattered fields obtained by calculation to obtain the multiple scattering RCS between the sea surface and the marine vessel target. In the ray path tracking method, ray paths between the sea surface and the offshore ship target related to the ray path tracking method comprise ship-sea surface rays, sea surface-ship rays, ship-sea surface-ship rays and sea surface-ship-sea surface rays.

The invention has the beneficial effects that: the method considers the hydrodynamic force action of sea waves on a ship target, constructs a ship target wave-following six-degree-of-freedom motion model, and improves the fidelity of a dynamic sea surface and moving ship target composite scene geometric model. On the basis, the semi-definite surface element method and the ray tracing hybrid algorithm are utilized to solve the composite scattering of the sea surface and the ship target, the RCS calculation accuracy and effectiveness of the ship target on the sea can be effectively improved, meanwhile, the method greatly reduces the calculation amount and is beneficial to engineering realization. The invention provides technical support for the research of electromagnetic characteristics of ship targets in actual complex marine environments, and has important significance for the detection and identification research of the ship targets on the sea.

Drawings

FIG. 1 is a flow chart of an embodiment of the method of the present invention;

FIG. 2 is a diagram of a marine vessel target composite scattering RCS simulation result of the present invention;

FIG. 3 is a schematic view of six-degree-of-freedom ship motion according to the present invention;

FIG. 4 is a schematic view of the ship speed and the course in the global coordinate system of the present invention;

FIG. 5 is a plot of wave direction versus hull position for the present invention;

FIG. 6 is a schematic view of the slicing solution of the present invention;

FIG. 7 is a point source partitioning method for symmetric and asymmetric slice profiles according to the present invention;

FIG. 8 is a diagram of the change in sea surface geometry at different times in accordance with the present invention;

FIG. 9 is a schematic diagram of the marine vessel target composite scattering of the present invention;

FIG. 10 is a schematic view of an incident wave decomposition according to the present invention;

FIG. 11 is a schematic diagram illustrating a target bin self-occlusion determination according to the present invention;

FIG. 12 is a schematic diagram illustrating another occlusion determination of a target bin according to the present invention;

FIG. 13 is a block diagram of the flow of occlusion determination of the present invention;

FIG. 14 is a schematic view of the dual scale rough sea surface geometry of the present invention;

FIG. 15 is a schematic representation of a single bin geometric model of the present invention;

fig. 16 is a flow chart of the dynamic sea surface and moving vessel target composite electromagnetic scattering calculation of the present invention.

Detailed Description

For a better understanding of the present disclosure, an example is given here.

FIG. 1 is a flow chart of an embodiment of the method of the present invention. In specific implementation, an operation frequency threshold can be set, the operation frequency is calculated after the marine ship target composite electromagnetic scattering RCS is calculated each time, when the operation frequency exceeds the threshold, the calculation of the marine ship target composite electromagnetic scattering RCS is stopped, and the final calculation result of the RCS is output. Fig. 2 is a simulation result of the complex scattering RCS of the marine vessel target, where the sea surface size is 250m × 50m, the incident wave frequency f =33GHz, and the wind speed 10m/s above the sea surface. The ship speed is 0m/s and 60 degrees, the incident azimuth angle is 0 degree, and the polarization mode is VV polarization. The ship target geometric model is shown in fig. 2 (a), and the marine ship target composite scattering RCS curve with time is shown in fig. 2 (b). FIG. 3 is a schematic view of six-degree-of-freedom ship motion according to the present invention; FIG. 4 is a schematic view of the ship speed and the course in the global coordinate system of the present invention; FIG. 5 is a plot of wave direction versus hull position for the present invention; FIG. 6 is a schematic view of the slicing solution of the present invention; FIG. 7 is a point source partitioning method of symmetric and asymmetric slice profiles of the present invention; FIG. 8 is a diagram of the change in sea surface geometry at different times in accordance with the present invention; FIG. 9 is a schematic diagram of the marine vessel target composite scattering of the present invention; FIG. 10 is a schematic view of an incident wave decomposition according to the present invention; FIG. 11 is a schematic diagram illustrating a target bin self-occlusion determination according to the present invention; FIG. 12 is a schematic diagram illustrating another occlusion determination of a target bin according to the present invention; FIG. 13 is a block diagram of the flow of occlusion determination of the present invention; FIG. 14 is a schematic view of the dual scale rough sea surface geometry of the present invention; FIG. 15 is a schematic representation of a single bin geometric model of the present invention; fig. 16 is a flow chart of the dynamic sea surface and moving vessel target composite electromagnetic scattering calculation of the present invention.

The invention discloses a method for calculating a composite electromagnetic scattering RCS of a marine target, which is characterized in that the characteristic that a ship moves along with sea waves is considered, a ray tracing method and a surface element method are combined, a multi-path model is adopted for calculating the composite scattering of a sea surface and a ship target, a composite scattering model of the marine ship target is established, and the high-precision calculation of the composite electromagnetic scattering RCS of the marine ship target is realized. The RCS refers to the scattering Cross Section of the Radar, and is called Radar Cross Section in English.

s1, establishing a coordinate system according to geometric information and scene parameters of the marine ship target, describing wave-following motion characteristics of the marine ship target, and constructing and solving a six-degree-of-freedom motion model of the marine ship target moving along with wind and waves to obtain a six-degree-of-freedom motion response variable of the ship.

The sea surface size is the sea surface area used for calculating the composite electromagnetic scattering RCS of the marine ship target.

The establishing of the coordinate system comprises establishing of a global coordinate system, an inertial coordinate system and a ship fixing coordinate system, wherein the ship fixing coordinate system is a three-dimensional rectangular coordinate system which takes the gravity center of a ship body of the ship as an origin, takes a sea level as an XOY plane and takes the advancing direction of the ship as the forward direction of an X axis, the three-dimensional rectangular coordinate system moves along with the movement of the ship, and the X axis, the Y axis and the Z axis of the ship fixing coordinate system respectively point to the bow, the port and the bottom of the ship. Along with the different motion postures of the ship body, the fixed coordinate system of the ship body is changed continuously. The global coordinate system adopts a geodetic coordinate system, the center of the inertial coordinate system is kept consistent with the global coordinate system, the center of the inertial coordinate system does not change along with the movement of the ship body, and the X axis, the Y axis and the Z axis of the inertial coordinate system respectively point to the bow, the starboard and the bottom of the ship.

The description of the wave-following motion characteristics of the marine ship target specifically comprises the following steps: the motion state of the marine ship target in the sea wave is described by adopting six-degree-of-freedom motion response variables, as shown in fig. 3, wherein the six-degree-of-freedom motion response variables comprise translational motion variables of a ship body along coordinate axes of a fixed coordinate system and rotational motion variables around the coordinate axes of the fixed coordinate system. The translational motion variables include a surging (surge) motion variable, a swaying (sway) motion variable, and a heaving (heave) motion variable, and the rotational motion variables include a rolling (roll) motion variable, a pitching (pitch) motion variable, and a yawing (yaw) motion variable.

The position point coordinates of the marine ship target in the global coordinate system are { x, y, z }, and the position point coordinates of the marine ship target in the inertial coordinate system are { x _I ,y _I ,z _I And the position point coordinates of the marine ship target in the ship body fixed coordinate system are { x } _b ,y _b ,z _b The six-freedom-degree motion response variable of the ship under the ship fixed coordinate system is expressed as

u ₁ 、u ₂ 、u ₃ Respectively a surging motion variable (surge), a swaying motion variable (sway) and a heaving motion variable (heavie) included in the translational motion variable of the marine ship target ₄ 、u ₅ 、u ₆ Roll, pitch and yaw motion variables respectively included in the rotational motion variable, and the conversion relationship between the inertial coordinate system and the hull fixed coordinate system is expressed as

the conversion relationship between the global coordinate system and the inertial coordinate system is expressed as:

wherein v is _ship The speed of the ship is taken as the speed of the ship,

is the angle between the ship motion direction and the X-axis of the global coordinate system, and t represents time, as shown in fig. 4.

The method for constructing the six-degree-of-freedom motion model of the marine ship target moving along with the stormy waves specifically comprises the following steps:

wherein the content of the first and second substances,

The angle of inclination of the guide rail, as shown in figure 5,

expressed at the encounter frequency ω _e Included angle

And

when encountering a wave spectrum, g is a gravity constant,

is expressed in the wave period omega and the included angle

A temporal wave spectral function;

wherein the content of the first and second substances,

is a quality matrix, and the expression is:

where m is the mass of the marine vessel target, [ x ] _G ,y _G ,z _G ]Is the coordinate of the center of gravity of the marine vessel target under the global coordinate system theta _xx Representing the moment of mass inertia, theta, of the marine vessel target in translational and rotational motion along the x-axis _yy Representing the moment of mass inertia, theta, of the marine vessel target in translational and rotational motion along the x-axis _zz Representing the moment of mass inertia, θ, of the marine vessel target in translational and rotational motion along the z-axis _xy Represents the mass moment of inertia theta when the marine ship target performs translational motion along the x axis and performs rotational motion along the y axis _xz Representing marine vessel target edgesMoment of mass inertia, theta, when the x-axis performs translational motion and the z-axis performs rotational motion _yz The mass moment of inertia is shown when the marine vessel target performs translational motion along the y-axis and rotational motion along the z-axis. The mass moment of inertia is calculated by the formula:

θ _xx ＝∫(my ² (y)+mz(z) ² )dydz,θ _xy ＝∫(my ² (y)+mx(x) ² )dxdy，

θ _yy ＝∫(mx ² (x)+mz(z) ² )dxdz,θ _yz ＝∫(my ² (y)+mz(z) ² )dzdy，

θ _zz ＝∫(mx ² (x)+my ² (y))dxdy,θ _xz ＝∫mx ² (x)+mz(z) ² dxdz， (7)

wherein mx (x), my (y) and mz (z) are mass distribution functions of the marine vessel target along the x-axis, y-axis and z-axis, respectively, and θ is θ for a symmetrically mass-distributed hull _xy ＝θ _yz ＝0。

Representing the fluid power exerted by the sea waves on the marine target, which comprises a hydrostatic part and a fluid dynamic part generated by the ship motion, the collision of the incident waves of the sea waves on the ship body and the diffraction after the collision; decomposing and expressing a linear equation of the movement of the ship in the regular wave to obtain a six-degree-of-freedom movement model of the marine ship target moving along with the stormy waves, wherein the expression is as follows:

wherein the content of the first and second substances,

a radiation force matrix representing the motion of the marine vessel target,

is a disturbance amplitude matrix generated by the incident wave of the ocean waves impacting the ship body and the diffraction after the impact.

The six-degree-of-freedom motion model of the marine ship target moving along with the stormy waves is solved, and the six-degree-of-freedom motion model of the marine ship target moving along with the stormy waves is solved by adopting a slicing method.

the ship body is evenly divided into a plurality of transverse sections along the axial direction of the ship body, for each transverse section, the hydrodynamic force of the ship body at the transverse section is obtained by solving the linear equation of the ship body moving in the regular wave, the hydrodynamic force of each transverse section of the ship body is superposed along the axial direction of the ship body, the three-dimensional hydrodynamic force of the ship body is obtained, a sea wave spectrum superposition model is established by using the three-dimensional hydrodynamic force of the ship body, the six-degree-of-freedom motion vector of the marine ship target under a ship body fixed coordinate system is obtained by solving according to the sea wave spectrum superposition model, and the six-degree-of-freedom motion amplitude solving formula of the ship is used for solving the six-degree-of-freedom motion response variable of the ship.

As shown in fig. 6, according to the slicing method, the hydrodynamic force of the three-dimensional hull is obtained by superposing the two-dimensional hydrodynamic force at each section of the hull along the length of the ship, and in order to ensure the calculation accuracy of the slicing method, the number of slices is generally required to be not less than 20, the frequency range covers the whole response range, and 20 to 30 frequencies are taken between 0.20rad/s and 2.40rad/s for calculation.

The definition and basic solving method of each mechanical matrix of the linear equation of the ship moving in the regular wave are respectively introduced below.

For restoring force matrices, i.e. hydrostatic matrices

When the hull is asymmetrical, as a general caseRestoring force matrix of

Can be expressed as

Where ρ is the sea water density, the integral is the integral along the length of the hull, A is the area of the slice (below the mean surface of the water), B is the draft width, y _w (x) Is the average transverse coordinate of the slicing waterline, (x) _s ,z _s ) The coordinates of the center of the slice and the longitudinal coordinates of all cross-sectional slices are x, A _tr For dry stern section area of waterline, if the hull is not stern or stern is wet, then A _tr ＝0，y _tr ,z _tr The barycentric coordinates of the dry stern are shown.

The calculation of the additional mass, froude-Krilov force and diffraction force is described below.

Basic solution of two-dimensional streaming:

if the ship has a forward velocity v, the hull slices at an encounter frequency ω _e Oscillating, the two-dimensional flow potential satisfies the following conditions:

laplace equation (due to incompressibility of the fluid): phi is a _yy +φ _zz ＝0,z＞0；

Bottom conditions: shallow water: phi is a _z And =0, z = h, h represents water depth. Deep water:

free surface conditions: phi is a _tt -gφ _z ＝0,z＝0；

Hull boundary conditions:

which represents the speed of the hull at some point on its surface,

indicating the outward normal to the point.

Irradiation conditions:

the negative sign in the exponential term indicates that the wave propagates in the + y direction and the positive sign indicates that the wave propagates in the opposite direction.

Complex amplitude to potential

Can be obtained from the formula (10)

Shallow water:

or deep water:

according to the slicing method, the complex amplitude of the potential can be adjusted

Approximately as a superposition of point sources, i.e.

Wherein q is _i Is located at (y) _i ,z _i ) The intensity of the point source. Except for a point source (y) located within the slice outline or above z =0 _i ,z _i ) Equation (15) satisfies Laplace equation (11) everywhere.

The slice profile is defined with a given compensation point, and for the profile segment between any adjacent compensation points, a source can be generated near the midpoint between the two compensation points, generally, the source position shifts 1/20 times the profile segment length from the midpoint to the interior of the slice. Along the mean water surface z =0, grid points are automatically generated, close to the hull, the distance of the grid points being equal to 1.5 times the distance between the contour compensation points on the draft. On the more distant sides, the distance of the grid points increases by a factor of 1.5 times, until the maximum distance reaches 1/12 of the wavelength. At this point, the source point is again located at the midpoint of each free surface segment. For a symmetrical hull only half of the free surface mesh points (e.g. 55 in number) are required to be discretized, and for an asymmetrical hull the free surfaces on both sides of the slice are discretized with a mesh point number of 2 x 55. Fig. 7 shows a point source partitioning method for each hull slice profile.

For hull boundary conditions (13), the integral of the left end along each contour segment, i.e. the flow induced by the ith source S through the contour segment between points A and B, is equal to the source intensity multiplied by the angle ASB (β) _i ) Divided by 2 pi. Thus, the total flow, i.e., the sum of all the source-induced flows, is obtained

For the second term of the free surface condition (12), which can be processed in the same way as described above, the integral of the first term along the contour segment is approximated by

With the mirror image source, equation (15) can precisely satisfy the shallow water condition of the bottom condition (12). Wherein, point (y) _i ,z _i ) The mirror source of the source is located below the bottom (y) _i ,2H-z _i ) To (3). For deep water, the current potential (15) approximated by the point source method can automatically satisfy the deep water condition of the condition (12).

According to equation (17), the integral of the radiation condition (14) along the period between points A and B is

Finishing can obtain

Solving a system of linear equations consisting of boundary conditions can yield the complex amplitudes of all source intensities. Therefore, the flow potential can be determined according to equation (15).

Additional mass and drag:

according to Bernoulli's equation, the complex amplitude of the pressure is

p＝-ρφ _t (20)

Integrating the pressure amplitude along the slice profile can give complex amplitudes of horizontal forces, vertical forces and moments. For one of the forces, the force amplitude is taken into account

And amplitude of motion

Proportionally, this proportional relationship can be written as follows

Since if the sinusoidal motion occurs at the circular frequency co,

is the complex amplitude of acceleration, so

One element of the complex additive mass matrix can be understood. However, consider force amplitude

Possibly the sum of the resistance and mass terms, there are

Wherein the content of the first and second substances,

is the complex amplitude of the velocity of motion. It can be easily found that the same applies to the equations (21) and (22), and that the additional mass can be reproduced in comparison with each other

The real additional mass m and the damping coefficient d satisfy the following relationship

Froude-Krilov force:

according to the formula (20), the complex amplitude of the wave pressure is

The Froude-Krilov force can be obtained by integrating the pressure along the slice profile, and the integral of the pressure along the slice profile can be obtained by adding the integrals of the pressure along the profile segment between each two adjacent compensation points, i.e. the integral of the pressure along the profile segment between each two adjacent compensation points

Wherein Δ y = y ₂ -y ₁ ，Δz＝z ₂ -z ₁ 。

Diffraction force:

the calculation of wave diffraction forces and moments is different from the calculation of additional mass forces and moments in that only non-homogeneous terms in the boundary conditions of the hull are considered. In the diffraction force calculation, the wave current must be cancelled out by the source induced current.

Based on the flow velocity vector(s),

and

the wave flow in between can be expressed as

Using dispersion relation omega ² = gktanhkH, the first fraction in the above formula may be expressed as:

in equations (25) and (27), the direct estimation of the expression [ exp (α) -1]/α is inaccurate when α is small, and therefore, [ exp (α) -1]/α can be approximately expressed as [ exp (α) -1]/α using the Taylor expansion of the exponential function when | α | < 0.01

(3) Calculation of radiation force

Order to

Representing the complex amplitude of the forces and moments exerted by the water on the slices,

contains three components: a force in the y-direction, a force in the z-direction, and a moment about the x-axis.

Proportional to motion amplitude vector having three components

All elements in matrix A

The first table i below represents the force component and the second table j below represents this force caused by the movement of the j component. The elements of the complex additional mass matrix are understood to be contributions of real additional mass and drag and to have the same relationship as equation (23), e.g. for the first element

For ease of understanding, the formula (30) is rewritten to another form

This can be understood as the time derivative of momentum (mass times velocity). If the vessel has a forward velocity v _ship The above-mentioned motion relationship can be expressed as

Three-component cross-sectional velocity can be achieved by six-component ship motion

Is shown as

In the formula

Three component cross sectional force

And six components of force per unit length

A conversion matrix of

Force per unit length

Integration along the vessel yields a six component radiation force:

therefore, the temperature of the molten metal is controlled,

(4) Calculation of excitation force

Order to

Represents the complex amplitude of a three component force and is proportional to the complex amplitude of the wave at point (x =0, y = 0)

Including Froude-Krilov forces and diffraction forces.

In the formula, the following tables 0 and 7 represent a Froude-Krilov portion and a diffraction portion, respectively.

If the forward speed of the ship is v _ship Then diffraction force

Is extended to

For a regular wave with direction u, the complex amplitude of its wave height ζ can be expressed as

Wherein, the first and the second end of the pipe are connected with each other,

k =2 pi/λ is the wave number, λ is the wavelength, for complex amplitude at the origin. Thus, it is possible to provide

To pair

The left-multiplication transformation matrix V can convert it into a force vector of six components in the global coordinate system, and then the first partial contribution of the excitation force vector can be obtained:

for a more accurate calculation of the pitch motion and the yaw and pitch additional longitudinal forces exerted by the water on the vessel need to be taken into account. The diffraction component in this case is negligible, so that the longitudinal forces on the vessel are taken into account only for the Froude-Krilov contribution

In the formula (I), the compound is shown in the specification,

for pressure amplitude, the section center (x, y) is used here _x ,z _x ) The pressure value at (a) replaces the average value along the entire section. Pressure at the center of the cross section of

Wherein α = - ρ gexp [ -k (z) _x +T)]exp(iky _x sin(u))。

Longitudinal force per unit length

A contribution to the pitching moment can also be induced, and then a second partial contribution of the six-component excitation force vector can be obtained:

the amplitude response operator is defined as the six-freedom motion vector of the ship

And excitation regular wave complex amplitude

In a ratio of (i) to (ii)

The method is characterized in that a wave spectrum superposition model is constructed by utilizing three-dimensional fluid power of a ship body, and a six-degree-of-freedom motion vector of a marine ship target under a ship body fixed coordinate system is obtained by solving according to the wave spectrum superposition model, and specifically comprises the following steps:

according to the idea of linear superposition, the motion of the ship at a certain point of the wave surface can be considered to be formed by the excitation of waves with different frequencies and directions,

wherein u is _i (x, y, t) is the six-degree-of-freedom motion amplitude of the marine ship target at the two-dimensional wave surface (x, y) at the time t, i =1,2,.. 6, and the six-degree-of-freedom motion amplitude forms the six-degree-of-freedom motion vector of the marine ship target under the ship fixed coordinate system, and k is the six-degree-of-freedom motion vector of the marine ship target under the ship fixed coordinate system _e To encounter a circular frequency omega _e Wave number of wave, S _e (,) is the two-dimensional encounter wave spectral function, R is the amplitude response operator, N _k And N _φ Number of sampling points, omega, of frequency and direction angle, respectively _e,l Is the encountered circle frequency, k, at the l-th frequency sampling point _e,l To encounter a circular frequency omega _e,l The lower corresponding wave number of the sea wave,

being sea wavesThe (j) th spatial direction angle,

is the incremental change of the spatial azimuth of the sea wave, epsilon _lj The initial phase corresponding to the ith frequency sampling point and the jth spatial direction angle is shown. And solving to obtain the six-degree-of-freedom motion vector of the marine ship target under the ship body fixed coordinate system by utilizing the sea wave spectrum superposition model.

S2, establishing a dynamic sea surface and moving ship composite scene geometric model;

wherein S is _e (,) is a two-dimensional encounter wave spectral function, here using the Efouhaily spectrum, k _l 、ω _l 、

Respectively representing wave number, circular frequency, direction angle, N, of random cosine wave _k And N _φ Are respectively frequency and direction the number of sampling points of the corner,

the jth spatial azimuth of a wave,

representing sea surface wind direction angle, Δ k _e For incremental changes in the wavenumber of the ocean waves,

is the incremental change of the spatial azimuth of the sea wave, epsilon _lj And the initial phase corresponding to the ith frequency sampling point and the jth spatial direction angle is represented, and the initial phase is uniformly distributed between 0 pi and 2 pi.

The three-dimensional dynamic sea surface geometric model comprises three-dimensional dynamic sea surface geometric information. The three-dimensional dynamic sea surface geometry information includes wave height information at each time instant for each fixed point (x, y) on the sea surface. Fig. 8 is a diagram of the change of the geometrical profile of the sea surface at different moments.

And linearly superposing the geometric information of the marine ship target and the three-dimensional dynamic sea surface geometric information at each time sampling point to obtain a dynamic sea surface and moving ship composite scene geometric model, thereby providing effective scene information for subsequent marine ship target composite electromagnetic RCS calculation.

carrying out surface element subdivision on geometric information of a marine ship target to obtain a plurality of target surface elements, dividing the marine ship target composite electromagnetic scattering RCS into four parts of RCS, specifically, a single-scattering RCS of a ship, a multiple-scattering RCS of the ship, a single-scattering RCS of a sea surface and a multiple-scattering RCS between the sea surface and the ship, respectively solving scattering field intensities corresponding to the four parts of RCS according to the target surface elements, and carrying out vector superposition on the obtained scattering field intensities to obtain the marine ship target composite electromagnetic scattering RCS. Fig. 9 gives a schematic representation of the four parts of the scattering.

local approximation is carried out on an excitation source of the scattering RCS by adopting a tangent plane approximation condition, induced electromagnetic current of the marine ship target is obtained, near-far field extrapolation is carried out by utilizing a far-field Green function and an equivalent principle, so that an expression of the electromagnetic field of the marine ship target is obtained, then a tangent plane approximation method is adopted to obtain a surface current value and a magnetic current value of the marine ship target, and single scattering RCS of the marine ship target is obtained according to the surface current value and the magnetic current value of the marine ship target.

For the calculation of the single scattering RCS of the marine ship target, a pure Physical Optics (PO) method is adopted. It should be noted here, however, that in addition to the self-occlusion and mutual occlusion of the marine vessel targets themselves, the occlusion of the marine vessel targets by the sea surface should also be considered, and the scattering of the marine vessel target portion submerged by the sea surface as shown in fig. 9 is not calculated.

The PO method adopts tangent plane approximation conditions to carry out local approximation on an excitation source, after induction electromagnetic current is obtained, near-far field extrapolation is carried out by utilizing far field Green's function and equivalence principle, huygens' equivalence principle can be obtained, and the expression of the obtained electromagnetic field is

Then, the tangent plane is adopted to approximate the surface electromagnetic current,

the unit vector of the incident direction, the incident wave can be decomposed into parallel polarization (TM wave) by

Expressing its unit direction vector, and orthogonal polarization (TE wave) by

Showing its unit directional vector, there is a similar decomposition of the reflected wave, and figure 10 shows only a schematic diagram of the electric field vectors, which are similar.

And

the relationship between is

The relationship of the reflected field to the incident field for the TE or orthogonal polarization component can be expressed as

Wherein the relation between the propagation vector of the reflected wave and the propagation vectors of the incident wave and the normal vector is

Also the relation between the reflected field and the incident field at the TM or parallel polarization component can be expressed as

Wherein R is ^TE And R ^TM Respectively TE wave and TM wave reflection coefficients.

The equivalent electric current and magnetic current calculation formula is as follows:

formula (directional vector in original formula) for obtaining far-zone electric field by substituting formula (50)

Conversion into unit vectors of scattering direction

And assuming the amplitude of the incident wave as unity amplitude)

Wherein

The multi-scattering RCS calculation of the marine ship target is realized by adopting a bounce ray method.

When a bounce ray method is adopted to calculate the multiple scattering RCS of the marine ship target, the incident wave direction is determined, corresponding incident ray direction information is determined according to the incident wave direction, the direction of each incident ray is consistent with the incident wave direction, each incident ray penetrates through the center of a corresponding target surface element, shielding judgment is carried out on the target surface element according to the incident ray direction information, a shielding judgment result is obtained, the shielding judgment result comprises surface element illuminating information and surface element shielding information, and the incident ray corresponding to the target surface element is tracked and the scattering field of the incident ray is calculated for the target surface element corresponding to the surface element illuminating information. The ray corresponding to the incident wave is called an incident ray, and the direction of the incident ray is called an incident ray direction.

Tracking incident rays, tracking the propagation path of each incident ray by using a geometric optical method according to a dynamic sea surface and moving ship composite scene geometric model until the incident ray does not intersect any target surface element or the reflection times in the propagation path of the incident ray reach a preset value, and acquiring and recording the propagation path of the incident ray;

at the incident rayIn the propagation path, the intersection point of the incident ray and the target surface element is

and

are respectively an intersection point

And point of intersection

are respectively an intersection point

Divergence factor and reflection coefficient matrix. Intersection point

Is expressed as

Where ρ is ₁ And ρ ₂ Are respectively a crossDot

At the reflection distance between the corresponding incident radiation-emitting surface and the illuminated surface element. The divergence factor of the plane is 1, and when the target surface elements adopt the plane surface elements, the divergence factor is equal to 1.

The shielding judgment is carried out to obtain a shielding judgment result, and the method specifically comprises the following steps:

Because ship targets generally comprise a plurality of dihedral angle structures which can form a large number of multiple reflections, the ship multiple scattering is calculated by adopting a bounce ray (SBR) algorithm.

SBR is a high frequency algorithm combining Geometric Optics (GO) and PO, which uses GO to consider the energy propagation of electromagnetic waves between targets and uses PO to integrate in the far field. When the SBR is used for calculating the multiple scattering of the ship target, the incident wave direction is given, the corresponding incident rays can be determined, the direction of each incident ray is consistent with the incident wave direction, and each ray penetrates through the center of the corresponding target surface element. After the incident ray information is determined, firstly, the occlusion judgment of the target surface element is needed, which includes self-occlusion judgment and other occlusion judgment.

The other shielding judgment specifically includes judging whether the target surface element is shielded by other target surface elements along the incident ray direction, as shown in fig. 12, if the target surface element is not shielded by other target surface elements, it is judged that the target surface element is the target surface element directly illuminated by the incident wave. And performing other shielding judgment on all target surface elements to obtain the directly illuminated target surface elements and the target surface elements which are not directly illuminated.

The shielding judgment of the person is specifically performed, the geometric center point of a target surface element needing to be subjected to shielding judgment of the person is Q, if incident rays reach a Q point and intersect with other target surface elements, the target surface element where the Q point is located is judged to be shielded by other target surface elements, the target surface element where the Q point is located is considered as a target surface element which is not directly illuminated, the target surface element which is not directly illuminated belongs to a shielding surface element, if incident waves do not intersect with other target surface elements before reaching the Q point, the target surface element where the Q point is located is judged to be illuminated by the incident waves, and the target surface element where the Q point is located is considered as a target surface element which is directly illuminated.

The specific implementation of the other occlusion judgment process is as follows: for a certain target surface element m on the marine ship target, if the three vertex coordinates of the target surface element m on the marine ship target are A, B and C, the ray starting point of the incident wave is at the point P, and the geometric central point of the target surface element m is Q. And (3) expressing the coordinate S of any point on the target surface element m as follows by using a parameter equation:

S＝αA+βB+(1-α-β)C，

S＝λP+(1-λ)Q，

according to the two expressions of the coordinate S, an equivalent equation is constructed:

α(A-C)+β(B-C)+λ(Q-P)＝Q-C，

The self-shielding judgment of the directly illuminated target surface element specifically comprises the following steps: for a target surface element which is directly illuminated by incident waves and obtained through shielding judgment of the target surface element, calculating a normal vector of the target surface element

And the direction vector of the incident wave

Inner product of (2)

As shown in fig. 11. If inner product

Normal vector of target surface element

Is a direction that is directed along the hull center of gravity to the outside of the hull that satisfies the right-handed screw law.

An arbitrary point on the target bin m is expressed by a parametric equation as:

S＝αA+βB+(1-α-β)C， (66)

wherein, the values of the constants α, β and γ are all [0,1], then the point S is located inside the target bin m, otherwise the point S is located outside the target bin m, and γ =1- α - β. The three-dimensional coordinates of any point on the line segment PQ can be written as the following expression:

S＝λP+(1-λ)Q， (67)

where λ represents the distance between point S and point Q. If λ is between [0,1], then the point lies on line segment PQ, but not otherwise. When the point S is located on both the line PQ and the surface element m, that is, S is the intersection of the target surface element m and the line PQ, there are:

α(A-C)+β(B-C)+λ(Q-P)＝Q-C， (68)

recording as follows:

α(AC)+β(BC)+λ(PQ)＝CQ， (69)

the expression in matrix form is:

fig. 13 shows the flow of occlusion determination, which solves the above equation set to obtain α, β and λ, and takes γ =1- α - β, and analyzes α, β and λ to determine the occlusion condition. If det [ CA CB PQ ] =0, then expression (5) has no solution, there are no intersections and the bin is not occluded. If det [ CA CB PQ ] ≠ 0, then expression (5) has a solution with an intersection. If α, β, λ, and γ are all within the interval [0,1], the bin is occluded. If only one of α, β, λ, and γ is not in the interval [0,1], then the bin is not occluded.

And direction vector of incident wave

Inner product of (2)

As shown in fig. 11. If inner product

Judging that the target surface element is a first sea surface illumination surface element; if internal product

and judging whether the first sea surface illumination surface element is shielded by the target surface element of the marine ship target or not along the incident ray direction, and if the first sea surface illumination surface element is not shielded by the target surface element of the marine ship target, judging that the first sea surface illumination surface element is the target surface element directly illuminated by the incident wave, as shown in fig. 12. And performing other shielding judgment on all the first sea surface illumination surface elements to obtain a second sea surface illumination surface element.

He shelters from and judges, it specifically includes, the geometric center point that the first sea surface that needs to carry out his shelter from and judge illuminates the surface element is Q, if incident ray before reaching the Q point, have the intersect with the target surface element of naval vessel target, then judge that the first sea surface that Q point belongs to illuminates the surface element and is sheltered from by the target surface element of naval vessel target, consider that the first sea surface that Q point belongs to illuminates the surface element and is the target surface element that is not directly illuminated, if the incident wave is before reaching the Q point, do not have the intersect with the target surface element of naval vessel target, then judge that the first sea surface that Q point belongs to illuminates the surface element and is illuminated by the incident wave, consider that the first sea surface that Q point belongs to illuminates the target surface element that is directly illuminated, regard the target surface element that directly illuminates as the second sea surface to illuminate the surface element.

Discretizing the sea surface into a plurality of inclined surface elements, constructing a representation of the geometric profile of the inclined surface elements, and assuming that the wave number in a continuous ocean spectrum is separated into a large-scale gravity wave-dominant ocean spectrum and a small-scale tension wave-dominant ocean spectrum by using a rough sea surface dual-scale model, wherein the two wave number ranges can be completely covered by adopting two methods of kirchhoff and perturbation.

The sea surface is treated in a discretization mode to form a plurality of inclined surface elements, a representation of a geometric profile of the inclined surface elements is constructed, as shown in fig. 14, the sea surface is regarded as being formed by superposing small-scale capillary waves on large-scale gravity waves, the sea surface is treated in a discretization mode to form a plurality of inclined surface elements, each inclined surface element comprises a sea surface rough surface element and a cosine capillary wave component surface element, the geometric profile of each inclined surface element is represented by superposing the cosine capillary wave component surface elements which cause incident electromagnetic wave bragg resonance on the sea surface rough surface elements, as shown in fig. 15, the representation of the geometric profile of each inclined surface element at the time t is as follows:

ζ(ρ _c ,t)＝B(k _c )cos(k _c ·ρ _c -ω _c t)，

where ρ is _c Vector of position coordinates, k, representing the interior of the tilted bin _c Represents the wave number vector of the cosine capillary wave, B (k) _c ) Representing the amplitude, omega, of a cosine capillary wave _c Representing wave number vector k _c Corresponding angular frequency.

calculating the electromagnetism of each second sea surface illumination bin by adopting a perturbation methodScattering coefficient, electromagnetic scattering coefficient of the second sea surface illuminated surface element

The calculation formula of (2) is as follows:

Since the surface element is inclined under the action of gravity wave, the conversion problem of local coordinate and global coordinate exists. In local coordinates, the local scattering amplitude element is denoted as F _{pq_loc} I.e. by

F _{vh_loc} ＝[1-R _v (θ _{i_loc} )][1+R _h (θ _{s_loc} )]cosθ _{i_loc} sinφ _{s_loc}

F _{hv_loc} ＝[1+R _h (θ _{i_loc} )][1-R _v (θ _{s_loc} )]cosθ _{s_loc} sinφ _{s_loc}

F _{hh_loc} ＝[1+R _h (θ _{i_loc} )][1+R _h (θ _{s_loc} )]cosφ _{s_loc}

Wherein, theta _{i_loc} ，θ _{s_loc} ，φ _{i_loc} ，φ _{s_loc} The local incidence angle, scattering angle, incidence azimuth angle and scattering azimuth angle of the incident wave to the inclined surface element are respectively. The value of which is not only related to the direction of the incident wave but also to the tilt angle of the bin. R _h And R _v Are reflection coefficients of different polarizations. After the local scattering amplitude is obtained, the local scattering amplitude is converted into the global scattering amplitude by the following equation.

Wherein the content of the first and second substances,

for the global horizontal and vertical polarization vectors,

local horizontal and vertical polarization vectors.

for the scattering amplitude of the tilted bin, the formula is:

Because the small surface elements in the semi-determination method consider Bragg scattering with the largest scattering effect, each small surface element can fully reflect the contribution of capillary waves to scattering, the whole sea surface can be subdivided by adopting a larger surface element, and therefore the calculation amount can be greatly reduced by the algorithm.

The method is characterized in that the calculation of the multiple scattering RCS between the sea surface and the marine ship target is realized by adopting a ray path tracking method, wherein the field intensity between rays is calculated by adopting a geometric optical method, when incident rays irradiate a target surface element of the marine ship target, the field intensity of a far-zone scattering field is calculated by utilizing a physical optical method, and when the incident rays irradiate an inclined surface element on the sea surface, the field intensity of the far-zone scattering field is calculated by utilizing a semi-definite surface element method. And superposing the field intensities of the far-zone scattered fields obtained by calculation to obtain the multiple scattering RCS between the sea surface and the marine vessel target. In order to simplify the coupling effect between the sea surface and the marine ship target, the order of ray tracking is set to three orders, rays larger than the three orders are not considered, and in the ray path tracking method, the ray paths between the sea surface and the marine ship target comprise ship-sea surface rays, sea surface-ship rays, ship-sea surface-ship rays and sea surface-ship-sea surface rays.

Solving the scattered field intensity corresponding to the four parts, and performing vector superposition on the obtained scattered field intensity to obtain a composite total scattered field of the marine ship target, namely

Finally, fig. 16 shows a specific flow of the composite electromagnetic scattering calculation of the dynamic sea surface and the moving ship target, and it can be seen from the drawing that, in the process of the simulation calculation, a ship target geometric model file is firstly transmitted, corresponding scene parameters (such as sea surface size, wind speed, wind direction, ship movement speed, direction and the like) are set, and at each time sampling point, ship wave-following movement characteristic calculation and three-dimensional sea surface geometric modeling are respectively performed, so that a six-degree-of-freedom movement model of the ship target on the sea along with the wave is obtained, and scene information is updated. On the basis, by combining a marine ship target compound electromagnetic scattering model and by means of ray tracing and semi-determining surface element mixing methods, ship target scattering, sea surface scattering and coupling scattering between the sea surface and the ship at the time sampling point are respectively calculated, and marine ship target compound scattering RCS data are obtained. And then, updating the time sampling point, and repeating the steps until the preset maximum time sampling point is reached.

The above description is only an example of the present application and is not intended to limit the present application. Various modifications and changes may occur to those skilled in the art to which the present application pertains. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims

1. A method for calculating a marine ship target composite electromagnetic scattering (RCS) is characterized by comprising the following steps:

s1, establishing a coordinate system according to geometric information and scene parameters of the marine ship target, and describing the motion characteristics of the marine ship target along with wind waves to obtain a motion characteristic description result; according to the motion characteristic description result, a six-degree-of-freedom motion model of the marine ship target moving along with the storms is constructed and solved, and six-degree-of-freedom motion response variables of the ship are obtained;

and S3, calculating the composite electromagnetic scattering RCS of the marine ship target according to the composite scene geometric model of the dynamic sea surface and the moving ship.

2. The method of claim 1, wherein said scene parameters comprise sea surface size, sea surface wind speed, sea surface wind direction, ship motion speed, and ship motion direction;

the establishing of the coordinate system comprises establishing a global coordinate system, an inertial coordinate system and a ship body fixed coordinate system;

the ship body fixing coordinate system is a three-dimensional rectangular coordinate system which takes the gravity center of a ship body of a ship as an origin, takes a sea level as an XOY plane and takes the forward direction of the ship as the forward direction of an X axis, the three-dimensional rectangular coordinate system moves along with the movement of the ship, and the X axis, the Y axis and the Z axis of the ship body fixing coordinate system respectively point to the bow, the port and the bottom of the ship;

the global coordinate system adopts a geodetic coordinate system;

the center of the inertial coordinate system is kept consistent with the global coordinate system, the center of the inertial coordinate system does not change along with the movement of the ship body, and the X axis, the Y axis and the Z axis of the inertial coordinate system respectively point to the bow, the starboard and the bottom of the ship.

3. The method for calculating the RCS of the marine vessel target based on the complex electromagnetic scattering of the marine vessel target as recited in claim 2, wherein the model for solving the six-degree-of-freedom motion of the marine vessel target along with the stormy waves is a slice method.

4. The method for calculating the RCS of the marine vessel target complex electromagnetic scattering according to claim 3, wherein the method for solving the six-degree-of-freedom motion model of the marine vessel target moving with the wind and the waves by using the slicing method specifically comprises the following steps:

5. The method for calculating the composite electromagnetic scattering (RCS) of the marine vessel target according to claim 2, wherein the step S3 specifically comprises:

6. The method of claim 5, wherein the calculating of the multiple scattering RCS for the marine vessel target is performed by a bounce ray method; when a bounce ray method is adopted to calculate the multiple scattering RCS of the marine ship target, determining the incident wave direction, determining corresponding incident ray direction information according to the incident wave direction, enabling each incident ray to pass through the center of a target surface element corresponding to the incident ray direction information, carrying out shielding judgment on the target surface element according to the incident ray direction information to obtain a shielding judgment result, wherein the shielding judgment result comprises illumination surface element information and shielding surface element information, and for the target surface element corresponding to the illumination surface element information, tracking the incident ray corresponding to the target surface element and calculating the scattering field of the incident ray; the ray corresponding to the incident wave is called the incident ray, and the direction of the incident ray is called the incident ray direction.

7. The method for calculating the RCS of marine vessel target complex electromagnetic scattering according to claim 6, wherein the incident rays are tracked, and for each incident ray, the propagation path thereof is tracked by a geometric optical method according to the geometric model of the dynamic sea surface and moving vessel complex scene until the incident ray does not intersect any target surface element or the number of reflections in the propagation path of the incident ray reaches a preset value, and the propagation path of the incident ray is obtained and recorded.

8. The method for calculating the RCS of the marine vessel target complex electromagnetic scattering according to claim 7, wherein the scatter field calculation is performed by obtaining intersection points of incident rays and a target surface element according to propagation paths of the incident rays, and calculating propagation distances between two adjacent intersection points; calculating a field intensity relation between the two adjacent intersection points according to each propagation distance, taking the field intensity relation as an incident field intensity at the corresponding illumination surface element, and calculating a far-region scattering field value on the surface element at the illumination surface element by using a physical optical method; and calculating to obtain far-zone scattering field values of all the illuminated surface elements, accumulating the far-zone scattering field values of all the illuminated surface elements to obtain an accumulated value, and obtaining the multiple scattering RCS of the marine ship target by using the accumulated value.

9. The method for calculating the composite electromagnetic scattering (RCS) of the marine vessel target according to claim 7, wherein the determining the occlusion of the target surface element to obtain the occlusion determination result comprises:

firstly, carrying out other shielding judgment on a target surface element to obtain a directly illuminated target surface element and a target surface element which is not directly illuminated, then carrying out self-shielding judgment on the directly illuminated target surface element to obtain a final output illuminated surface element and a target surface element which is shielded by the self, wherein the information of the target surface element which is shielded by the self and the information of the target surface element which is not directly illuminated form shielding surface element information in a shielding judgment result, and the information of the final output illuminated surface element forms illuminating surface element information in the shielding judgment result to obtain a shielding judgment result;

judging whether the target surface element is shielded by other target surface elements or not along the direction of the incident ray, and if the target surface element is not shielded by other target surface elements, judging that the target surface element is the target surface element directly illuminated by the incident wave; performing other shielding judgment on all target surface elements to obtain directly illuminated target surface elements and target surface elements which are not directly illuminated;

the pair of directly illuminated target binsCarry out the self-occlusion and judge, it specifically includes: for a target surface element directly illuminated by incident waves and obtained through shielding judgment, calculating a normal vector of the target surface element

And the direction vector of the incident wave

Inner product of (2)

If inner product

10. The method for calculating the marine vessel target composite electromagnetic scattering RCS according to claim 5, wherein for calculation of the single scattering RCS of the sea surface, the sea surface is discretized into a plurality of inclined surface elements, a representation of a geometric profile of the inclined surface elements is constructed, each inclined surface element is used as a first target surface element, self-shielding judgment is carried out to obtain a first sea surface illumination surface element, the first sea surface illumination surface element and a target surface element of the marine vessel target are shielded, other shielding judgment is carried out to obtain a second sea surface illumination surface element, all second sea surface illumination surface elements are illuminated, and the single scattering RCS of the sea surface is solved by using a semi-definite surface element method.