CN116973817A - Ship magnetic field modeling inversion and confidence interval determination method thereof - Google Patents
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Abstract
The application belongs to the technical field of ship magnetic field modeling inversion methods, and particularly relates to a ship magnetic field modeling inversion and a confidence interval determining method thereof, which comprises the following steps: obtaining inversion measurement data; establishing a ship magnetic field model; establishing a magnetic field equation set of a ship magnetic field model; conversion processing of an overdetermined equation; establishing a ship magnetic field model; substituting the ship magnetic field measurement data into a ship magnetic field model to finish ship magnetic field inversion. The application also provides a confidence interval determining method for inverting the measured data. The ship magnetic field model and the inversion method thereof have good stability, inversion can be completed without an intelligent algorithm, a depth conversion result with higher precision is obtained, the conversion error is less than 10%, and the engineering requirements are met; meanwhile, by using the magnetic field data confidence interval determining method based on the T distribution principle, the magnetic field confidence area can be accurately obtained, the probability of inverting the correctness of input data is improved, and the effectiveness of multiple groups of magnetic field data is rapidly discriminated and judged.
Description
Technical Field
The application belongs to the technical field of ship magnetic field modeling inversion methods, and particularly relates to a ship magnetic field modeling inversion and a confidence interval determining method thereof
Background
In order to comprehensively understand the magnetic field distribution of the ship under the conditions of different ocean areas and different depths, the magnetic source targets are required to be modeled on the basis of measured data, the magnetic field distribution of other depths is converted, the distribution rule and data of the ship magnetic field under the different depths at different positions are determined, the effective inversion of the magnetic source targets according to the measured data is the basis of some series of works such as depth conversion, and how to build an inversion model with high stability and how to determine the correctness of the magnetic field measured data are the problems which must be considered for solving the related problems. The currently used magnet simulation method utilizes a group of equivalent magnetic sources to replace a real magnetic target, and an equivalent source model is built by fully fitting magnetic field measurement data, so that reconstruction and conversion of a ship magnetic field are realized by utilizing forward modeling of the equivalent source model.
Disclosure of Invention
The application aims to improve a mathematical model of magnetic field inversion modeling based on a point magnetic charge theory based on actual requirements, and provides ship magnetic field modeling inversion with high model stability and a confidence interval determining method thereof
In order to achieve the above purpose, the present application adopts the following technical scheme.
The application relates to a ship magnetic field modeling method, which comprises the following steps:
s1, establishing a magnetic field point magnetic charge matrix model
In the magnetic field point magnetic charge matrix model, the magnetic charges of each point are distributed in a linear equidistant manner along the longitudinal direction of the ship to form s point magnetic charge measuring lines, the number of the point magnetic charges on each point magnetic charge measuring line is N, and a point magnetic charge array containing N=s×n point magnetic charges is formed;
s2, establishing a magnetic field equation set of a point magnetic charge matrix model
The coordinates of the point charges P (i) in the point charge array are (x) i ,y i ,z i ) I=1, 2, … N; the coordinates of the measurement point S (j) are (x) j ,y j ,z j ) J=1, 2, … M; the magnetic induction B generated at the measurement point S (j) j The expression is as follows:
wherein A is x (P i ,S j )、A y (P i ,S j )、A z (P i ,S j ) For measuring the distance function on three coordinate axes of the point S (j) and the point magnetic charge P (i), two position variables in the distance function are the space position coordinates S corresponding to the measuring point S (j) j Spatial position coordinates P corresponding to point charges P (i) i ；Q i The magnetic charge amount being the i-th point magnetic charge; r is the distance between the point charges P (i) at the measurement point S (j),the magnetic field equation set generated by the point magnetic charge array at all measuring points is obtained:
B＝AQ
B＝(B x1 B y1 B z1 …B xM B yM B zM ) T
Q＝(Q 1 Q 2 … Q N ) T
s3, conversion processing of overdetermined equation of magnetic field equation set of ship magnetic field model
The least square method is adopted to convert the formula (1) into a least-squares function:
introducing penalty functionsObtained by the constraint formula (2): />Wherein beta is penalty factor, which is self-fixed constant; let A x (P i ,S j )＝η ij ，A y (P i ,S j )＝l ij ，A z (P i ,S j )＝ν ij ，
The matrix coefficient a of formula (6) in the magnetic field equation set is converted into an expression:
the magnetic field linear equation set is converted into (n+1) × (n+1) th order matrix equation:
s4, establishing a ship magnetic field model
According to the natural physical law, establishing a point magnetic charge overall distribution neutral equation of a magnetic source:
according to the principle of the minimum value, the method comprises the following steps:
and (3) and (4) and (5) are combined to obtain the ship magnetic field model.
The application also provides an inversion method based on the ship magnetic field model, which comprises the following steps:
step 1, obtaining inversion measurement data
Setting M measuring points around the ship to be measured; acquiring partial ship magnetic field measurement data at a certain depth; the ship magnetic field measurement number comprises ship magnetic field distribution data;
step 2, establishing a ship magnetic field model
In the ship magnetic field model, each point magnetic charge is distributed in a linear equidistant manner along the longitudinal direction of the ship to form s point magnetic charge measuring lines, the number of the point magnetic charges on each point magnetic charge measuring line is N, and a point magnetic charge array containing N=s×n point magnetic charges is formed; the combined type (3), (4) and (5) establishes a ship magnetic field model;
and 3, substituting the ship magnetic field measurement data into a ship magnetic field model to finish ship magnetic field inversion.
Further expanding the ship magnetic field inversion method, wherein the step 3 further comprises the step of calculating magnetic field data of any position below the ship based on the magnetic charge amount obtained by ship magnetic field inversion and the corresponding magnetic charge position instead of the forward modeling of the magnetic field completed by the formula (1).
The method for inverting the ship magnetic field is further improved or expanded, and the step 3 further comprises the step of calculating the magnetic field data of any depth below the ship to complete depth conversion based on the magnetic load obtained by inverting the ship magnetic field and the position of the corresponding magnetic load instead of the step (1) to complete forward modeling of the magnetic field.
The application also provides a confidence interval determining method for inverting the measured data, which comprises the following steps:
step A) obtaining magnetic field distribution of a certain number of groups, and respectively obtaining n groups of magnetic field data under continuous time windows based on m equidistant measurement points under a certain depth under ship keels;
step B), regarding each measuring point on the measuring line as one sample set, so that m sample sets are total, and each sample set contains n sample data formed by magnetic field data; based on the sample set and the internal sample data thereof, constructing n rows and m columns of matrix to be estimated X= [ X ] 1 ,X 2 ,…,X m ]Wherein X is i ＝[x i1 ,x i2 ,…x in ] T I=1, 2, …, m, j=1, 2, …, n; i.e.
Step C) calculating the sample mean value of each column of the matrix X:as the overall mean μ of each column;
step D) calculating the sample variance of each column of the matrix X:obtaining the overall variance:
step E) obtaining confidence intervals of each column of the matrix according to the T distribution principlet is a confidence parameter;
and F) calculating to obtain confidence intervals corresponding to each column of samples according to the steps (1) and (5), obtaining confidence intervals of m measurement points after n times of measurement, connecting the m confidence intervals to obtain confidence areas of overall distribution of the magnetic field, and setting the confidence degree to be D), wherein the distribution in the confidence areas can be considered, and the reliability of the D% of the distribution of the magnetic field in the areas accords with the actual magnetic field distribution of the ship.
The beneficial effects are that:
the ship magnetic field model and the inversion method thereof have good stability, inversion can be completed without an intelligent algorithm, a depth conversion result with higher precision is obtained, the conversion error is less than 10%, and the engineering requirements are met; meanwhile, by using the magnetic field data confidence interval determining method based on the T distribution principle, the magnetic field confidence area can be accurately obtained, the probability of inverting the correctness of input data is improved, and the effectiveness of multiple groups of magnetic field data is rapidly discriminated and judged.
Drawings
FIG. 1 is a point magnetic charge model;
FIG. 2 is a measurement coordinate system and dot magnetic charge array layout;
FIG. 3 magnetic field distribution at depth 1.5 b;
FIG. 4 magnetic field distribution at depth 2.0 b;
FIG. 5 shows the magnetic field distribution at a depth of 3.0 b;
FIG. 6 1.5B to a depth of 2.0B y Conversion results;
fig. 7B y Distribution of measured values and energy spectrogram;
FIG. 8B of 10 samplings x A distribution map;
FIG. 9 confidence level of 95% B x A confidence region;
fig. 10 is a graph of magnetic field data confidence assessment.
Detailed Description
The present application will be described in detail with reference to specific examples.
Aiming at the problems that the stability of a magnetic field equivalent source inversion method model cannot be guaranteed and the correctness of magnetic field measurement data cannot be guaranteed, the application provides a ship magnetic field model with high stability, high modeling efficiency and high ship magnetic field inversion accuracy and an inversion method thereof based on a point magnetic load model theory.
The basic principle and effectiveness of the ship magnetic field model in the application are explained based on the point magnetic charge basic theory.
In the theory of point magnetic charges, the physical model of the point magnetic charges can be regarded as a planar current-carrying loop, as shown in fig. 1; the scalar magnetic bits generated by the point magnetic charges are:
wherein M is the magnetization intensity of the magnetized medium and represents the magnetic moment of the magnetized medium in unit volume; vector r points from volume element dV to the measurement point;
the former formula is transformed according to the vector identity to obtain:
wherein S is the magnetic medium boundary surface of the volume V; ρ m Is the bulk density of the magnetic charge; sigma (sigma) m The magnetic field generated by the magnetized magnetic medium can be regarded as being generated by the volume magnetic charge and the surface magnetic charge with certain density in space.
From maxwell's equations, the magnetic field strength can be found from the scalar magnetic potential of the magnetic medium when no free current is present in the field:
the algebraic sum of bulk and surface charges in a uniformly magnetized magnetic medium is zero, namely:
when the volume element dVThe volume or area element dS has an infinitesimal small area and when approaching a point ρ m dV or sigma m dS becomes a point magnetic charge with concentrated magnetic charge quantity Q, and scalar magnetic bit and magnetic field intensity at a certain place are:
the application provides a ship magnetic field model and a modeling method thereof, wherein the ship magnetic field model can be used for ship magnetic field inversion based on the point magnetic charge theory.
Assuming that there is a point magnetic charge with a magnetic charge quantity Q at the origin of coordinates [25] ：
The magnetic induction intensity generated by the point magnetic charge in space is as follows:
wherein mu 0 For vacuum permeability, vector r points from the point charge P to the measurement point S, r being the distance between the point charge and the measurement point.
Based on the above-mentioned basis, in the ship magnetic field modeling process of the present application, the point charges are firstly linearly arranged along the ship longitudinal direction to form a plurality of measurement lines, and the number of the measurement lines is S, and the number of the point charges on each line is N, so that n=sn point charges are contained in total, and the coordinates of the point charges S (i) are (x) i ,y i ,z i )，i＝1,2,…N。
At the same time, M sensor measuring points are included around the ship, and the coordinates of the measuring point P (j) are set as (x) j ,y j ,z j ) J=1, 2, … M. The magnetic induction B generated at the measuring point P (j) j ＝[B xj ,B yj ,B zj ]Can be calculated according to the following formula:
wherein A is x (P i ,S j )、A y (P i ,S j )、A z (P i ,S j ) For measuring the distance function in three coordinate axis directions of the point S (j) and the point magnetic charge P (i), two position variables in the distance function are the space position coordinates S corresponding to the measuring point S (j) j Spatial position coordinates P corresponding to point charges P (i) i ；
Suppose Q i The magnetic charge amount being the i-th point magnetic charge; r is the distance between the point charges P (i) at the measurement point S (j),the magnetic field equation set generated by the point magnetic charge array at all the measurement points can be obtained:
B＝AQ
B＝(B x1 B y1 B z1 …B xM B yM B zM ) T
Q＝(Q 1 Q 2 … Q N ) T
the magnetic charge Q can be obtained by solving a magnetic field equation set i However, in actual measurement, the number of measurement points is often larger than the number of point charges, i.e. M>N, the equation to be solved is an overdetermined equation, and the equation can be solved by adopting a least square method, namely, the equation (1) is converted into a least-squares function by adopting the least square method:
in order to solve the problem of unstable solution of the overdetermined equation, the application introduces a penalty functionSo as to restrict the original equation,then there are: />Wherein beta is penalty factor, which is self-fixed constant;
let A x (P i ,S j )＝η ij ，A y (P i ,S j )＝l ij ，A z (P i ,S j )＝ν ij The matrix coefficient a of formula (6) in the magnetic field equation set can be converted into an expression:
meanwhile, the magnetic field linear equation set is converted into an (N+1) x (N+1) order matrix equation:
according to the natural physical law, the point magnetic charge overall distribution of the magnetic source satisfies the magnetic neutral equation:
according to the principle of the minimum value, the method comprises the following steps:
based on the steps, the ship magnetic field model can be obtained by the combined type (3), (4) and (5);
substituting the real magnetic field data of the ship into the ship magnetic field model to finish the inversion of the ship magnetic field;
replacing the calculated magnetic charge quantity and the corresponding magnetic charge position with the magnetic return type (1) so as to calculate a magnetic field at any distance below; and (5) completing conversion of any depth of the ship magnetic field.
From the foregoing, in the present application, the inversion and depth conversion of the ship magnetic field are not only based on the ship magnetic field model, but also the validity of the input measurement data directly affects the validity of the ship magnetic field inversion, and only if the sample data accords with the real magnetic field distribution of the magnetic source, the inversion and conversion are valid. In particular, in the magnetic field measurement process, conditions such as rolling pitching, noise interference, uneven alignment of heading and ideal heading may exist in the ship, so that only one set of magnetic field data is collected and whether the actual magnetic field distribution of the ship can be correctly reflected cannot be evaluated, therefore, multiple sets of data are generally collected and averaged to eliminate errors, but if the data with larger errors exist in the data sets, the obtained magnetic field distribution and the actual distribution have larger difference, and the correct effectiveness of inversion and depth conversion is affected.
In order to ensure the effectiveness of the ship magnetic field inversion method, the application provides a confidence interval determination method of ship magnetic field data in an inversion process, which is used for providing basis for inversion input data screening, by calculating confidence areas of multiple groups of magnetic field distribution to obtain magnetic field distribution with higher reliability and effectively evaluating the reliability of magnetic field data.
In magnetic field measurement, a group of magnetic field distribution can be obtained once, the two measurements are mutually independent, the total measurement times are generally less than 30 times (N is less than 30) due to engineering application requirements, and the method belongs to small samples. The method comprises the following specific steps:
(1) A certain number of sets of magnetic field distributions are obtained. Assuming that the measuring line at the depth of 1.5b right below the ship keel comprises m equidistant measuring points, respectively acquiring measured n (n < 30) groups of magnetic field data under a continuous time window;
(2) Considering each measuring point on the measuring line as one sample set, one measuring line comprises m sample sets, each sample set comprises n samples, and n rows and m columns of matrix to be estimated X= [ X ] are formed 1 ,X 2 ,…,X m ]Wherein X is i ＝[x i1 ,x i2 ,…x ij ] T ，i＝1,2,…,m，j＝1,2,…,n；
(3) Calculating a sample mean value of each column of the matrix X:as the overall mean μ of each column;
(4) Calculating the sample variance of each column of matrix X:thereby obtaining the overall variance:
(5) According to the principle of T distribution, the confidence interval of each column of the matrix can be obtained as follows:t is a confidence parameter;
(6) And (3) calculating according to the steps (1) - (5) to obtain confidence intervals corresponding to each column of samples, namely after n times of measurement, connecting the m confidence intervals to obtain confidence areas of overall distribution of the magnetic field, and evaluating the distribution of the magnetic field. If the confidence level is selected as D%, the distribution in the confidence area can be considered that the reliability of the distribution of the magnetic field in the area with the D% accords with the actual distribution of the magnetic field of the ship.
To verify the inversion algorithm, in this embodiment, a three-axis fluxgate sensor is used to measure the magnetic field of a typical ship model in a laboratory, where the typical ship model has a ship length l=4.2m and a ship width b=0.467m, and a measurement coordinate system Oxyz is established by taking the ship center as the origin O, the x positive direction is along the longitudinal direction of the ship bow, the y positive direction is along the port side of the ship model, and the z positive direction is perpendicular to the ship model downwards. As shown in fig. 2, the dot magnetic charge simulation array is longitudinally arranged on the axial surface in the ship model and consists of three lines, 9 dot magnetic charges are longitudinally and equidistantly arranged on each simulation line, and the positive transverse distance between the simulation lines is 0.53b.
To better illustrate, magnetic field signals of different depths around the ship model are acquired, the measurement depth H is respectively set to be three depths of 1.5b, 2.0b and 3.0b, four sensors (three measurement sensors and one reference sensor) are adopted for measurement for simplifying experiments, the transverse distance of each measurement sensor is 0.53b, the ship model is measured point by point in a uniform speed passing mode from above the sensors, the coordinates of the three measurement sensors are respectively (0, -0.53b, H), (0, H), (0, 53b and H), the measurement range is [ -4.2m,4.2m ], the measurement point distance is 0.1m, 3 measurement lines are arranged at each measurement depth, the total of 85 points on each measurement line is 255 measurement points, and the coordinate distribution of the measurement points is shown in table 1.
Table 1 measurement point coordinate distribution table
| x j /m | y j /m | z j /m | j |
| 0.42+0.1(i-1) | -0.25 | H | 1,2,....85 |
| -0.42+0.1(i-86) | 0 | H | 86,87,...,170 |
| -0.42+0.1(i-171) | 0.25 | H | 171,172,...,255 |
In order to test the inversion algorithm, the magnetic field distribution of a certain depth is used as a learning sample, and the magnetic field distribution of other depths is used as a test sample, so that the inversion algorithm is verified.
The magnetic field distributions of the ship model at the depths of 1.5b, 2.0b and 3.0b are shown in fig. 3, 4 and 5.
And performing depth conversion according to the position distribution of the point magnetic charges and the calculated magnetic charge quantity so as to verify the accuracy of the inversion result. The concrete conversion process is divided into three parts:
(1) 1.5b depth to 1.5b, 2.0b and 3.0b depth;
(2) 2.0b depth to 2.0b and 3.0b depth;
(3) 3.0b depth to 3.0b depth conversion;
in order to better represent the inversion precision, the application adopts relative peak-to-peak value error and root mean square error to judge inversion and conversion effects at the same time, and the definition of the two errors is as follows:
a. the relative peak-to-peak error calculates the peak-to-peak value between the curves, representing the similarity in shape between the scaled magnetic field distribution and the measured value for the corresponding depth. The relative peak-to-peak error is defined as:
B c calculating magnetic field data of a certain depth for inverting the obtained point magnetic charges, B m Magnetic field measurement data for the same depth.
b. The relative root mean square error represents the degree of difference between the scaled result and the measured data. The relative root mean square error is defined as:
the conversion errors are shown in tables 2 and 3.
TABLE 2 depth scaled relative peak to peak error table
TABLE 3 depth scaling versus root mean square error table
As is clear from tables 2 and 3, the relative peak-to-peak error is 10% or less in the depth conversion from shallow to deep, indicating that the similarity between the conversion curve and the corresponding depth curve is high, B x 、B y And B z The magnetic field conversion of the model is relatively smaller in root mean square error, the fitting degree is higher, and the stability of the model and the effectiveness of the algorithm are proved. But B is y The larger error of (B) relative to the magnetic field in the other two directions, especially the relative root mean square error, indicates that the conversion curves have larger difference, and B is taken to study the problem y The case where the relative root mean square error is the largest, i.e., the 1.5b depth is converted to 2.0b depth is studied, and the conversion result is shown in fig. 6.
As can be seen in fig. 6, under the keel B y Poor fitting degree, two sides B y Has better fitting degree to B y The measured values were subjected to energy spectrum analysis as shown in fig. 7, and the depth conversion errors of the three lines were calculated as shown in table 4, respectively.
Table 4.1.5B when converting to 2.0B depth y Error calculation result table
| Positive transverse distance | y＝-0.53b | y＝0 | y＝0.53b |
| Relative peak-to-peak error/% | 3.28 | 71.45 | 0.91 |
| Relative root mean square error/% | 8.15 | 237.55 | 5.00 |
From FIG. 7 and Table 4, it can be derived that B y The reason for the larger relative root mean square error is due to the lower B of the ship keel y The magnitude of the original distribution of the magnetic field is far smaller than that of the magnetic field in the directions of the positive transverse direction and the two sides, the energy is very small relative to the other two measuring lines, the point magnetic charges obtained by inversion cannot be considered with data with two orders of magnitude which are too different, and B is caused y Relatively large root mean square error, from B x 、B z And B in the right-lateral direction y Under keel B y The fitting error of (2) belongs to acceptable errors, and the errors do not affect the stability of the inversion model and the effectiveness of depth conversion.
In order to reproduce the magnetic field bias caused by the aforementioned errors, laboratory simulations were performed with the following steps:
(1) Because the ship model is large in volume and heavy in weight, the shaking conditions of the ship body such as rolling, pitching and the like are difficult to simulate, in the measurement process, the ship movement is changed into the sensor movement, and a certain small shaking is applied to the sensor so as to simulate the magnetic field distribution change under the shaking condition of the ship body;
(2) Besides placing the sensors under the ship model keels, a part of sensors are placed at positions deviating from the keels so as to simulate the condition that the heading and the sensors are not standard.
To facilitate the observation methodAvailability, taking B with depth of 1.5B below the keel of the ship model in the laboratory x The measured values are analyzed by taking an example, 10 groups of data are measured, and the area of the measuring line under the keel is [ -4.2m,4.2m]A total of 127 equidistant measurement points resulted in 10 sets of distributions as shown in figure 8.
As can be seen from fig. 8, the 10 groups have the same distribution shape, but different magnitudes of the deviations exist, and even the individual distributions fluctuate greatly, which means that the two errors have a significant effect on the authenticity of the magnetic field measurement, and it cannot be estimated by naked eyes which group of magnetic fields is closest to the correct distribution.
According to the confidence interval determining method for inverting the measured data, 10 groups of data are calculated, the confidence coefficient is taken to be 95%, and confidence intervals at 127 measured points are calculated respectively as shown in table 5.
TABLE 5 confidence interval calculation of measurement points
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The upper and lower limits of the confidence intervals are connected according to the confidence interval distribution of each measurement point in table 5, and the constructed region is the magnetic field confidence region distribution with the confidence degree of 95%, as shown in fig. 9. Comparing 10 sets of measurement data with confidence regions yields fig. 10. As can be seen from fig. 10, due to the lower side B of the keel x The distribution is approximately symmetrical about the Y-axis, and the left and right peaks are the same, so the magnetic field evaluation is performed from the left half peak and the middle trough. Different distributions can be easily distinguished after the confidence regions are drawn, and curves contained in the left half-wave peak confidence regions are as follows: (4) (7) and (9), the trough confidence region comprising a curve: (7) and (9).
It can be deduced that there is 95% reason for the magnetic field distributions numbered (7) and (9) to believe that they correspond to the correct magnetic field distribution at a depth of 1.5b directly below the ship's keel.
The validity of the method for evaluating the magnetic field is verified through ship model experiments, the confidence region of the magnetic field distribution can be obtained from a plurality of groups of measurement data, the magnetic field distribution conforming to the confidence region under the selected confidence degree can be obtained rapidly through comparison with the measurement data, and the correctness and the validity of the magnetic field data input in inversion are guaranteed to the greatest extent from the source.
In order to ensure the stability of a ship magnetic field inversion model, the application provides a ship magnetic field model and an inversion method algorithm based on a point magnetic load model and adopting a minimum mean square error principle, solves the problem of overdetermined model equation from the construction of a mathematical model, effectively avoids the algorithm from sinking into local minimum, can achieve better conversion precision without adding intelligent algorithms such as a genetic algorithm and the like based on the depth conversion verification of the embodiment, meets engineering requirements, and has the advantage of high model stability. The magnetic field evaluation method based on the T distribution theory can obtain confidence regions from a plurality of groups of measurement data, selects the magnetic field measurement samples meeting the confidence requirements, ensures inversion correctness from the source to the greatest extent, and provides a new thought for evaluation of magnetic field measurement.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present application, and not for limiting the scope of the present application, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made to the technical solution of the present application without departing from the spirit and scope of the technical solution of the present application.
Claims (5)
1. The ship magnetic field modeling method is characterized by comprising the following steps of:
s1, establishing a magnetic field point magnetic charge matrix model
In the magnetic field point magnetic charge matrix model, the magnetic charges of each point are distributed in a linear equidistant manner along the longitudinal direction of the ship to form s point magnetic charge measuring lines, the number of the point magnetic charges on each point magnetic charge measuring line is N, and a point magnetic charge array containing N=s×n point magnetic charges is formed;
s2, establishing a magnetic field equation set of a point magnetic charge matrix model
Midpoint of magnetic charge array with pointsThe coordinates of the magnetic charge P (i) are (x) i ,y i ,z i ) I=1, 2, … N; the coordinates of the measurement point S (j) are (x) j ,y j ,z j ) J=1, 2, … M; the magnetic induction B generated at the measurement point S (j) j The expression is as follows:
wherein A is x (P i ,S j )、A y (P i ,S j )、A z (P i ,S j ) For measuring the distance function on three coordinate axes of the point S (j) and the point magnetic charge P (i), two position variables in the distance function are the space position coordinates S corresponding to the measuring point S (j) j Spatial position coordinates P corresponding to point charges P (i) i ；Q i The magnetic charge amount being the i-th point magnetic charge; r is the distance between the point charges P (i) at the measurement point S (j),the magnetic field equation set generated by the point magnetic charge array at all measuring points is obtained:
B＝AQ
B＝(B x1 B y1 B z1 …B xM B yM B zM ) T
Q＝(Q 1 Q 2 …Q N ) T
s3, conversion processing of overdetermined equation of magnetic field equation set of ship magnetic field model
The least square method is adopted to convert the formula (1) into a least-squares function:
introducing penalty functionsObtained by the constraint formula (2): />Wherein beta is penalty factor, which is self-fixed constant; let A x (P i ,S j )＝η ij ，A y (P i ,S j )＝l ij ，A z (P i ,S j )＝ν ij ，
The matrix coefficient a of formula (6) in the magnetic field equation set is converted into an expression:
the magnetic field linear equation set is converted into (n+1) × (n+1) th order matrix equation:
s4, establishing a ship magnetic field model
According to the natural physical law, establishing a point magnetic charge overall distribution neutral equation of a magnetic source:
according to the principle of the minimum value, the method comprises the following steps:
and (3) and (4) and (5) are combined to obtain the ship magnetic field model.
2. The ship magnetic field inversion method based on the ship magnetic field model of claim 1, which is characterized by comprising the following steps:
step 1, obtaining inversion measurement data
Setting M measuring points around the ship to be measured; acquiring partial ship magnetic field measurement data at a certain depth; the ship magnetic field measurement number comprises ship magnetic field distribution data;
step 2, establishing a ship magnetic field model
In the ship magnetic field model, each point magnetic charge is distributed in a linear equidistant manner along the longitudinal direction of the ship to form s point magnetic charge measuring lines, the number of the point magnetic charges on each point magnetic charge measuring line is N, and a point magnetic charge array containing N=s×n point magnetic charges is formed; the combined type (3), (4) and (5) establishes a ship magnetic field model;
and 3, substituting the ship magnetic field measurement data into a ship magnetic field model to finish ship magnetic field inversion.
3. The ship magnetic field inversion method according to claim 2, wherein the step 3 further comprises the step of calculating magnetic field data of any position under the ship based on the magnetic charge amount obtained by ship magnetic field inversion and the position of the corresponding magnetic charge, and replacing the forward modeling of the magnetic field with the formula (1).
4. The ship magnetic field inversion method according to claim 2, wherein the step 3 further comprises the step of calculating the magnetic field data of any depth below the ship to complete depth conversion based on the magnetic charge amount obtained by ship magnetic field inversion and the position of the corresponding magnetic charge instead of the formula (1) to complete forward modeling of the magnetic field.
5. A confidence interval determination method for inverting measurement data as claimed in claim 2, comprising the steps of:
step A) obtaining magnetic field distribution of a certain number of groups, and respectively obtaining n groups of magnetic field data under continuous time windows based on m equidistant measurement points under a certain depth under ship keels;
step B) regarding each measuring point on the measuring line as one sample set, then m sample sets are total, each sample set contains n sample data composed of magnetic field data, and based on the sample set and the internal sample data thereof, n rows and m columns of matrix to be estimated X= [ X ] are constructed 1 ,X 2 ,…,X m ]Wherein X is i ＝[x i1 ,x i2 ,…x in ] T I=1, 2, …, m, j=1, 2, …, n; i.e.
Step C) calculating the sample mean value of each column of the matrix X:as the overall mean μ of each column;
step D) calculating the sample variance of each column of the matrix X:obtaining the overall variance:
step E) obtaining confidence intervals of each column of the matrix according to the T distribution principlet is a confidence parameter;
and F) calculating to obtain confidence intervals corresponding to each column of samples according to the steps (1) and (5), obtaining confidence intervals of m measurement points after n times of measurement, connecting the m confidence intervals to obtain confidence areas of overall distribution of the magnetic field, and setting the confidence degree to be D), wherein the distribution in the confidence areas can be considered, and the reliability of the D% of the distribution of the magnetic field in the areas accords with the actual magnetic field distribution of the ship.
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