CN108508281B - Depth conversion method of ship electrostatic field based on point power supply frequency domain method - Google Patents

Depth conversion method of ship electrostatic field based on point power supply frequency domain method Download PDF

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CN108508281B
CN108508281B CN201810222855.7A CN201810222855A CN108508281B CN 108508281 B CN108508281 B CN 108508281B CN 201810222855 A CN201810222855 A CN 201810222855A CN 108508281 B CN108508281 B CN 108508281B
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史建伟
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Jiangsu Fubo Ocean Exploration Technology Co ltd
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    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract

Ship static electricityA depth conversion method of a field based on a point power supply frequency domain method belongs to the technical field of electric field measurement of ships. The method comprises the following steps: setting a measuring interval below the ship body, and measuring the ship potential U on a measuring line; calculating a sinusoidal transformation B (omega) of the potential U at different frequency points omega according to the potential U actually measured in the step S1); calculating equivalent source intensity P by using sine transformation B (omega) and combining measurement informationx(ii) a Based on equivalent source intensity PxAnd calculating the potential U of any measuring point. The advantages are that: under the condition of ensuring the conversion precision, the measuring points are minimum, the depth conversion can be realized by only one measuring line, the calculation is simple, the method is suitable for shallow sea environment and infinite deep sea area, and the point source intensity can be obtained.

Description

Depth conversion method of ship electrostatic field based on point power supply frequency domain method
Technical Field
The invention belongs to the technical field of ship electric field measurement, and particularly relates to a depth conversion method of a ship electrostatic field based on a point power supply frequency domain method.
Background
The electrostatic field of the ship is an important exposure source of the ship target and an attack source of weapons in water. In order to prevent the strike of a mine installed with an electric field fuse, electric field suppression technology is generally applied to ship design and manufacture in various countries. On the other hand, when the electrostatic field suppression effect is evaluated to be effective, the potential or the electric field peak-to-peak value at a certain depth is generally used as an evaluation index. In fact, it is difficult to accurately obtain the maximum peak-peak value of the electrostatic field signal on a certain plane under the limitation of the measurement conditions, and the maximum peak-peak value of the electric field on the plane when the electric field is hidden is not on the same measurement line as the maximum peak-peak value of the electric field when the hidden is not adopted, so that certain measurement data is required to be used for depth conversion. The connotation of ship electric field depth conversion is to obtain ship electric field data on another depth plane by analyzing ship electric field measurement data in a certain area on a certain depth plane and carrying out proper calculation. The existing ship electrostatic field depth conversion mainly comprises a large plane conversion algorithm and an iterative conversion algorithm.
In the large plane conversion algorithm, the depth conversion method based on the large plane measurement data is based on the following steps: the electrostatic field in the seawater is generated by corrosion and corrosion-resistant currents near the surface of the ship, and there is no free charge in the seawater space below the ship, so the electrostatic field in this region satisfies the laplace equation. When the target plane is located below the conversion plane, a space surrounded by the conversion plane and infinity can be selected as a conversion space, and the electrostatic field data of the conversion plane and the infinity boundary are used as boundary conditions to solve the laplace equation satisfied by the electrostatic field to obtain the electrostatic field on any plane in the conversion space. The method has the disadvantages that the conversion precision can be ensured only when the plane is large enough, namely, the measuring points are large enough, theoretically, the conversion can be accurately converted when the conversion plane is infinite, and in practice, the conversion error is larger when the plane is smaller. In the iterative conversion algorithm, when the point source superposition method is used for inverting the electrostatic field, more unknown parameters need to be calculated, so that the algorithm difficulty is increased.
In view of the above-mentioned prior art, the applicant has made an advantageous design, and the technical solutions described below have been made in this context.
Disclosure of Invention
The invention aims to provide a depth conversion method of a ship electrostatic field based on a point power supply frequency domain method, which has the advantages of few measuring points, high conversion precision and capability of obtaining source intensity information.
The invention aims to achieve the aim, and the depth conversion method of the ship electrostatic field based on the point power supply frequency domain method is characterized by comprising the following steps:
s1) setting a measuring interval below the ship body, and measuring the ship potential U on a measuring line;
s2) calculating the sine transformation B (omega) of the potential signal U at different frequency points omega according to the potential U measured in the step S1),
Figure GDA0001668155720000021
s3) calculating equivalent source intensity P by using sine transformation B (omega) and combining measurement informationx；
S4) based on the equivalent source intensity PxAnd calculating the potential U of any measuring point.
In a specific embodiment of the invention, let the coordinates of the measurement interval under the hull be ([ -L, L)]，y0，z0) The coordinates of the measuring points are (x, y, z), and the different frequency points omega are respectively taken as omega1、ω2And, wherein, L is greater than or equal to one-half of the ship length, the equivalent source intensity PxThe calculation formula of (2) is as follows:
Figure GDA0001668155720000022
wherein the content of the first and second substances,
Figure GDA0001668155720000023
K0for the second class of zero-order modified Bessel functions, ω τ is a variable,
Figure GDA0001668155720000024
sigma is the seawater conductivity and f (omega) is the correction function.
In another specific embodiment of the present invention, under the two-layer model of air and seawater, the correction function f (ω) is:
Figure GDA0001668155720000025
in another embodiment of the present invention, under the three-layer model of air, sea water and seabed, the correction function f (ω) is:
Figure GDA0001668155720000026
wherein
Figure GDA0001668155720000027
Figure GDA0001668155720000028
Figure GDA0001668155720000029
Figure GDA0001668155720000031
k is the sea bottom reflection coefficient, m is the number of reflection layers, and H is the depth of the seawater.
Due to the adoption of the structure, compared with the prior art, the invention has the beneficial effects that: under the condition of ensuring the conversion precision, the measuring points are minimum, the depth conversion can be realized by only one measuring line, the calculation is simple, the method is suitable for shallow sea environment and infinite deep sea area, and the point source intensity can be obtained.
Drawings
Fig. 1 is a schematic view of the current lines under the two-layer model.
Detailed Description
So that the public can fully understand the technical spirit and the beneficial effects of the invention, the applicant will describe the detailed description of the specific embodiments of the invention in conjunction with the drawings, but the description of the embodiments is not a limitation of the technical solution, and any changes made according to the inventive concept without substantial changes should be considered as the protection scope of the invention.
The invention relates to a depth conversion method of a ship electrostatic field based on a point power supply frequency domain method, which mainly comprises the following steps:
s1) setting a measuring interval below the ship body, and measuring the ship potential U on a measuring line;
s2) calculating the sine transformation B (omega) of the potential signal U at different frequency points omega according to the potential U measured in the step S1),
Figure GDA0001668155720000032
s3) calculating equivalent source intensity P by using sine transformation B (omega) and combining measurement informationx；
S4) based on the equivalent source intensity PxAnd calculating the potential U of any measuring point.
The above steps will be described in detail below.
Firstly, two-layer model conditions are considered, namely, two-layer media of air and seawater are considered, and the influence of the seabed media is ignored. Setting an interval [ -L, L ] below the hull]The coordinates are ([ -L, L)]，y0，z0) The current line in this interval, as shown in FIG. 1, measures the magnitude of the potential generated at an arbitrary measurement point P (x, y, z) as
Figure GDA0001668155720000033
Where ρ (ξ) is the current linear density, σ is the seawater conductivity, and ξ is the position of the source point.
If the potential values along the x direction are fourier transformed, there are:
Figure GDA0001668155720000034
will be provided with
Figure GDA0001668155720000035
Expressed in real and imaginary parts, i.e.
Figure GDA0001668155720000036
In the formula, a (ω) is cosine fourier transform, and B (ω) is sine fourier transform.
For B (ω), sin (ω ξ) is expressed as a sum of powers, which is
Figure GDA0001668155720000041
In the formula (I), the compound is shown in the specification,
Figure GDA0001668155720000042
for the second class of zero-order modified bessel functions,
Figure GDA0001668155720000043
defining:
Figure GDA0001668155720000044
comprises the following steps:
C(ω)＝Px+ω2D+O(ω4) (6)
in the formula, O (omega)4) Is omega4A high order small quantity of (D) is ω2The coefficient of (a).
If take omega2＝2ω1(
Figure GDA0001668155720000045
L is greater than or equal to one-half of the ship's length), and ω is equal to or greater than ω2、ω1When substituted into formula (6), then have
Figure GDA0001668155720000046
As can be seen from equation (7), the potential signal on one line can be used to measure ω at different frequencies1、ω2And calculating the equivalent source intensity of the current line by the Fourier transform.
In the following, the case of a three-layer model medium is explained, i.e. considering an air-seawater-seabed three-layer medium.
For three layers of model media, the distribution is in the interval [ -L, L]Upper (coordinates of ([ -L, L)]，y0，z0) A current line of) at an arbitrary measurement point P (x, y, z) generates a potential of magnitude
Figure GDA0001668155720000047
In the formula (I), the compound is shown in the specification,
Figure GDA0001668155720000048
wherein k is the sea bottom reflection coefficient, m is the number of reflection layers, and H is the depth of the sea water.
The sine transformation is calculated for U to obtain
Figure GDA0001668155720000051
In the formula (I), the compound is shown in the specification,
Figure GDA0001668155720000052
wherein the content of the first and second substances,
Figure GDA0001668155720000053
Figure GDA0001668155720000054
Figure GDA0001668155720000055
defining:
Figure GDA0001668155720000056
the two-layer model has the following characteristics:
C(ω)＝Px+ω2D+O(ω4) (13)
get omega2＝2ω1And will be ω2、ω1Substituting into equation (13) can also obtain equation (7), and calculate the equivalent source intensity of the current line.
In summary, under the condition of two or three model media, the potential signal on one line can be used at different frequency points ω2、ω1Sine transformation of B (omega), omega K0(ω τ) or ω E (ω) the equivalent source intensity of the current line is calculated. However, as can be seen from the formula (2), when the sinusoidal transformation is calculated using the actual measurement data, the integration interval is [ - ∞, + ∞ [ ]]And in actual measurement, the measurement interval is a finite space [ -L, + L [ -L ]]I.e. B (ω) calculated using measured data is actually:
Figure GDA0001668155720000057
c (ω) in equation (12) is actually:
Figure GDA0001668155720000058
this can lead to errors in the inversion.
Definitions of C (ω) and C1The error of (ω) is Δ (ω), then:
Figure GDA0001668155720000059
in the formula of UgThe potential values outside the measurement interval.
Under the far field condition, the electrostatic field of the ship can be regarded as a dipole field, and the coordinate of the dipole center is (0, y)0,z0) And then Δ (ω) can be expressed as ship equivalent dipole source intensity PxI.e.:
Δ(ω)＝Pxf(ω) (17)
this results in the equation (13) changing to:
C1(ω)+Pxf(ω)＝Px+ω2D+O(ω4) (18)
if take omega2＝2ω1And will be ω2、ω1Substituting equation (18) and performing a simple calculation yields:
Figure GDA0001668155720000061
under the two layers of mediums, the medium layer is a hollow layer,
Figure GDA0001668155720000062
as can be seen from the formula (20), when the measurement interval is limited, the error caused by the limited measurement interval can be compensated by the potential continuation method.
C under three-layer medium1(ω) and f (ω) are respectively:
Figure GDA0001668155720000063
Figure GDA0001668155720000064
therefore, after the equivalent dipole strength Px is calculated according to the measurement value of one measuring line, the two-layer model is calculated according to the following formula:
Figure GDA0001668155720000065
the electric field value of an arbitrary field point P (x, y, z) can be calculated.
For the three-layer model according to:
Figure GDA0001668155720000066
wherein the content of the first and second substances,
Figure GDA0001668155720000067
the electric field value of an arbitrary field point P (x, y, z) can be calculated.
Under the condition of ensuring the conversion precision, the invention has the advantages of minimum measuring points, simple calculation, capability of realizing depth conversion by one measuring line theoretically, suitability for shallow sea environment (air-seawater-seabed three-layer model) and infinite deep sea area (air-seawater two-layer model) and capability of obtaining point source intensity.

Claims (3)

1. A depth conversion method of a ship electrostatic field based on a point power supply frequency domain method is characterized by comprising the following steps:
s1) setting a measuring interval below the ship body, and measuring the ship potential U on a measuring line;
s2) calculating the sine transformation B (omega) of the potential U at different frequency points omega according to the potential U measured in the step S1),
Figure FDA0002362517320000011
s3) calculating equivalent source intensity P by using sine transformation B (omega) and combining measurement informationxSetting the coordinate of the measuring interval below the ship body as ([ -L, L)]，y0，z0) The coordinates of the measuring points are (x, y, z), and the different frequency points omega are respectively taken as omega1、ω2And is and
Figure FDA0002362517320000012
wherein, L is more than or equal to one-half of the ship length, the equivalent source intensity P isxThe calculation formula of (2) is as follows:
Figure FDA0002362517320000013
wherein the content of the first and second substances,
Figure FDA0002362517320000014
K0for the second class of zero-order modified bessel functions,
Figure FDA0002362517320000015
sigma is the seawater conductivity, and f (omega) is a correction function;
s4) based on the equivalent source intensity PxAnd calculating the potential U of any measuring point.
2. The method for converting the depth of the electrostatic field of the ship based on the point power supply as claimed in claim 1, wherein under a two-layer model of air and seawater, the correction function f (ω) is:
Figure FDA0002362517320000016
3. the method for converting the depth of the electrostatic field of the ship based on the point power supply as claimed in claim 1, wherein under the three-layer model of air, seawater and seabed, the correction function f (ω) is:
Figure FDA0002362517320000017
wherein
Figure FDA0002362517320000018
Figure FDA0002362517320000019
Figure FDA00023625173200000110
Figure FDA00023625173200000111
k is the sea bottom reflection coefficient, m is the number of reflection layers, and H is the depth of the seawater.
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