CN116975991A - Magnetic target three-dimensional optimizing inversion positioning method based on particle swarm optimization - Google Patents
Magnetic target three-dimensional optimizing inversion positioning method based on particle swarm optimization Download PDFInfo
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Abstract
The application belongs to the technical field of ship magnetic field inversion, and particularly relates to a magnetic target three-dimensional optimizing inversion positioning method based on a particle swarm algorithm. The method comprises the following steps: acquiring ship reference magnetic field data; constructing a three-dimensional magnetic dipole and ellipsoid mixed model; performing magnetic dipole search based on a particle swarm algorithm; determining fitting accuracy errors; setting a weight value to screen the optimal number of magnetic dipoles; in the prior art, the magnetic dipoles are generally arranged on the horizontal plane of the central axis of the ship, the modeling of the magnetic dipole distribution is expanded to the three-dimensional space of the whole ellipsoid, the magnetic dipole distribution position is determined by adopting a method which is faster in convergence and more robust to a large-capacity sample, the obtained magnetic dipole distribution is closer to the magnetic distribution characteristics of the actual ship, the fitting precision is higher, and the magnetic dipole spatial distribution can be obtained only by changing the long axis and the short axis of the ellipsoid for ships with different sizes, so that the method has convenience and size universality.
Description
Technical Field
The application belongs to the technical field of ship magnetic field inversion, and particularly relates to a magnetic target three-dimensional optimizing inversion positioning method based on a particle swarm algorithm.
Background
The safe sailing of the ship is an important guarantee of the vitality of the ship. In recent years, the rapid development of mines has made underwater protection of ships particularly important. Due to various factors such as the special hull structure, construction materials, power systems, anti-corrosion systems, loading equipment, electromechanical equipment and the like, ships can generate various physical fields in the course of navigation, wherein the magnetic signal is one of the signals which are most easily collected by enemy as a target characteristic signal. However, due to factors such as complex ship structure, uneven magnetic substance distribution and the like, how to accurately model a ship magnetic field becomes a primary problem of ship magnetic protection. The magnet simulation method is a modeling method which is more in use, and comprises three models, namely: a magnetic dipole model, a uniformly magnetized ellipsoid of revolution and a magnetic dipole array mixed model. However, these schemes have problems that magnetic targets have complex shapes and difficult model construction. At present, most of researches on magnetic targets adopt a modeling method of uniformly magnetized ellipsoids and magnetic dipole mixtures, but the magnetic dipoles are only arranged on the central axis plane of the ellipsoids, so that the problem that the magnetic field distribution characteristics of the magnetic targets cannot be reflected truly exists.
Disclosure of Invention
The application aims to provide a particle swarm algorithm-based magnetic target three-dimensional optimizing inversion positioning method which is flexible to use, high in simulation precision, more accurate in magnetic field inversion result and more consistent with a real ship magnetic field and is based on a particle swarm algorithm.
In order to achieve the above purpose, the present application adopts the following technical scheme.
A magnetic target three-dimensional optimizing inversion positioning method based on a particle swarm algorithm comprises the following steps:
step 1, acquiring ship reference magnetic field data
Based on classical rotating ellipsoids and magnetic dipole array model theory, the induction magnetic field generated in the geomagnetic field under the ideal condition of the ship is determined and used as a reference value.
Step 2, constructing a three-dimensional magnetic dipole and ellipsoid mixed model
Cutting the ellipsoid of rotation and the magnetic dipole array model by using a plurality of planes perpendicular to the long axis to obtain slice spaces with the same number as the magnetic dipoles, wherein the thickness of each slice space is consistent; the slicing space is equivalent to a cuboid space with a square cross section;
step 3, magnetic dipole searching is carried out based on particle swarm algorithm
(1) Establishing a feasible solution space based on three-dimensional magnetic dipole and ellipsoid mixed model parameters, initializing n particles in the feasible solution space to form a population X= (X) 1 ,X 2 ,...,X n ) Wherein X is i Is a vector of D dimension: x is X i ＝(x i1 ,x i2 ,...,x iD )，i＝1,2,...,n；X iD Representing the long axis coordinates of a certain magnetic dipole obtained after cutting;
in this patent, x= (X) 1 ,X 2 ,...,X n ) Representing a possible n magnetic dipole distribution schemes; each scheme comprises D magnetic dipole coordinates X i ＝(x i1 ,x i2 ,...,x iD ) The method comprises the steps of carrying out a first treatment on the surface of the Setting a search upper limit of magnetic dipole number, starting increasing from 2 magnetic dipoles, making every increment undergo the process of one-time algorithm, calculating position and error result, thenFrom this an optimal solution is derived;
(2) the particle characteristics are represented by three indexes of position, speed and fitness value, wherein the position refers to the space of each cutting block limited by the ellipsoid after cutting, and the fitness value is obtained by calculating a fitness function;
(3) moving the particles in the solution space, the movement speed of the ith particle being set as V i ＝(V i1 ,V i2 ,...，V iD ) By tracking, the individual extremum P is searched i ＝(P i1 ,P i2 ,...,P iD ) Is adapted to the optimal position P best And population extremum G i ＝(G i1 ,G i2 ,...,G iD ) The fitness optimal position G in (1) best Updating individual position and velocity:
wherein ω is inertial weight; d=1, 2,. -%, D; i=1, 2,. -%, n; k is the current iteration number; v (V) id Is the speed of the ith particle; c 1 And c 2 Is acceleration factor, is non-negative constant; r is (r) 1 And r 2 Is distributed in [0,1 ]]Random numbers of intervals;
(4) calculating fitness value once every time the particle is updated, and updating individual extremum P by comparing fitness value of new particle with fitness value of individual extremum and population extremum best And population extremum G best Position until all iterations are completed;
step 4, determining fitting accuracy errors
Based on the magnetic dipole space position coordinate scheme X obtained in the step 3 i Calculating a magnetic field generated by a magnetic dipole in an ellipsoid in a three-dimensional space, fitting the magnetic field with a reference value, and representing error calculation fitting precision by using two norms of errors/two norms of original data:
the fitting accuracy error calculation formula is:
wherein h is xcal 、h ycal 、h zcal Is based on the magnetic dipole position coordinate scheme X i Performing inversion to obtain a magnetic field calculated value; h is a x 、h y 、h z Is a reference value;
step 5, setting weight to screen the optimal magnetic dipole number
The weight calculation mode is as follows:
E best ＝min{0.4×errx i +0.1×erry i +0.4×errz i +0.1×t i },(i＝1,…,N)；
wherein E is best Determining the optimal magnetic dipole number according to the optimal weight; errx (r x) i 、erry i 、errz i Fitting errors of three components when the number of magnetic dipoles is i respectively; t is t i The calculation time is the calculation time when the number of magnetic dipoles is i.
The optimal weight in the application is selected according to the proportion of three components of the magnetic field when the ship sails, and is set according to empirical data.
The method for positioning the magnetic target by three-dimensional optimizing inversion based on the particle swarm algorithm is further improved or a preferred embodiment, and the following specific method is adopted in the step 1:
a1, simplifying a ship into an ellipsoid with uniform magnetization, and longitudinally arranging magnetic dipoles with equal strength on the horizontal plane of the central axis of the ellipsoid, wherein the arrangement positions and the specific number of the magnetic dipoles are determined according to the specific magnetic field distribution of the ship;
a2, the magnetic field generated by the magnetic dipole in the ellipsoid is approximately simulated into a real magnetic field generated by a ship, a calculation model is simplified, and magnetic field conversion with different depths is carried out;
a3, fitting the magnetic field distribution of the ship with the magnetic dipoles through known magnetic field distribution of the ship, and calculating the magnetic field distribution of the space around the ship as a reference value according to a mixed model of the magnetic dipoles and ellipsoids.
In the step 3, the parameters of the particle swarm algorithm are set as follows:
a. maximum number of iterations: 100; number of individuals in population: 50; acceleration parameters: 2;
b. weight at the beginning of the algorithm: 0.9; weight at the end of algorithm: 0.4;
c. algorithm termination threshold: 10 -5 The method comprises the steps of carrying out a first treatment on the surface of the Terminating the algorithm when the variation of the optimal value of the corresponding population in two successive iterations is smaller than the value;
d. threshold for terminating the iteration: 1000; when the gradient value of the function is unchanged in the continuous 1000 iterations, the iteration is exited;
(5) and after the updating calculation is finished, outputting a magnetic dipole space position calculation result when the number of the magnetic dipoles is different.
In the step 3, the fitness function refers to:
in the step 2, the square corresponding to the cuboid space is determined based on the following manner: and determining a middle plane perpendicular to the long axis in the slice space, determining a circle formed by intersecting the middle plane and the shell surface of the ellipsoid of revolution, and taking the inscribed square of the circle as the square of the section of the cuboid space.
A further improvement or a preferred embodiment of the magnetic target three-dimensional optimizing inversion positioning method based on the particle swarm algorithm, wherein the a2 specifically comprises:
a20, designing a uniformly magnetized rotary ellipsoid with the geometrical size equivalent to that of a ship, arranging N magnetic dipoles along the longitudinal direction of the ellipsoid at the same distance d, wherein a long half shaft is a, a short half shaft is b, the geometrical center of the ellipsoid and the geometrical center of the ship are overlapped, and the geometrical centers are respectively recorded as 1,2 and N from left to right;
a21 is based on the coordinates of the ith magnetic dipole:has (x) 0 ,y 0 ,z 0 ) = (0, 0); magnetic target at P j (x j ,y j ,z j ) The three components of the magnetic field generated at the position are H xij 、H yij 、H zij The method comprises the following steps:
b xji ＝a yji
a zij ＝c xij
b xij ＝c yij
magnetic moment components of the ith magnetic dipole along the directions of an x axis, a y axis and a z axis respectively;
a22, synthesizing equations satisfied by each magnetic dipole in the rotating ellipsoid and the magnetic dipole array to obtain a magnetic field equation at a measuring point:
FM＝H
M＝[M x M y M z M x1 M y1 M z1 … M xm M ym M zm ] T
a23, fitting the magnetic dipole according to the known magnetic field distribution of the ship, and calculating the magnetic field distribution of the space around the ship as a reference value according to a mixed model of the magnetic dipole and the ellipsoid.
The beneficial effects are that:
in the prior art, the magnetic dipoles are generally arranged on the horizontal plane of the central axis of the ship, the modeling of the magnetic dipole distribution is expanded to the three-dimensional space of the whole ellipsoid, the magnetic dipole distribution position is determined by adopting a method which is faster in convergence and more robust to a large-capacity sample, the obtained magnetic dipole distribution is closer to the magnetic distribution characteristics of the actual ship, the fitting precision is higher, and the magnetic dipole spatial distribution can be obtained only by changing the long axis and the short axis of the ellipsoid for ships with different sizes, so that the method has convenience and size universality.
Drawings
FIG. 1 is a schematic diagram of a model of a ellipsoid of revolution and a magnetic dipole array;
FIG. 2 1B three-dimensional spatial distribution of magnetic dipoles at depth;
FIG. 3 1B is a graph of the change in the optimal weight with increasing magnetic dipole number at depth;
FIG. 4 is a graph of the change in the optimal weight with increasing magnetic dipole number at depth 1B;
FIG. 5 1B is a graph of the X component fit of the magnetic dipole inversion calculation to a baseline value at depth;
FIG. 6 1B is a graph of the Y component fit of the magnetic dipole inversion calculation to a baseline value at depth;
FIG. 7 1B is a plot of Z-component fit of magnetic dipole inversion calculations to baseline values at depth;
FIG. 8 5B is a three-dimensional spatial distribution of magnetic dipoles at depth;
FIG. 9 5B is a graph showing the change in the optimal weight with increasing magnetic dipole number at depth;
FIG. 10 5B is a graph showing the change in the optimal weight with increasing magnetic dipole number;
FIG. 11 5B is a graph of the Y component fit of the magnetic dipole inversion calculation to a baseline value at depth;
FIG. 12 5B is a graph of the Y component fit of the magnetic dipole inversion calculation to a baseline value at depth;
FIG. 13 5B is a plot of Z component fit of the magnetic dipole inversion calculation to a baseline value at depth;
FIG. 14 10B is a three-dimensional spatial distribution of magnetic dipoles at depth;
FIG. 15 10B is a plot of the change in optimal weight with increasing magnetic dipole number at depth;
fig. 16 (10 b) change in optimum weight with increasing magnetic dipole number (local));
FIG. 17 10B is a graph of the X component fit of the magnetic dipole inversion calculation at depth versus baseline;
FIG. 18 10B is a graph of the Y component fit of the magnetic dipole inversion calculation at depth versus the baseline value;
FIG. 19 10B is a plot of Z-component fit of magnetic dipole inversion calculations to baseline values at depth.
Detailed Description
The present application will be described in detail with reference to specific examples.
The magnetic target has the problems of complex shape and difficult model construction. At present, most of researches on magnetic targets adopt a modeling method of uniformly magnetized ellipsoids and magnetic dipole mixtures, but the magnetic dipoles are only arranged on the central axis plane of the ellipsoids, so that the problem that the magnetic field distribution characteristics of the magnetic targets cannot be reflected truly exists. On the basis of a uniformly magnetized ellipsoid and magnetic dipole mixed modeling method, the method carries out slice processing on an ellipsoid three-dimensional model, searches the position of a magnetic dipole by adopting a particle swarm algorithm, sets a weight to find the number of dipoles with both operation time and calculation precision, obtains the optimal three-dimensional spatial distribution of the magnetic dipole in the ellipsoid, and inverts to obtain magnetic field data with different depths below the ellipsoid.
The magnetic target three-dimensional optimizing inversion positioning method based on the particle swarm optimization can realize the automatic optimizing of the magnetic dipole in the three-dimensional ellipsoid, obtain the optimal position distribution of the magnetic dipole with both calculation time and calculation precision, realize the high-precision fitting of the near field and the far field with a reference field, ensure that the fitting precision is up to 99.99 percent, and solve the problem that the magnetic dipole is inaccurate for near field simulation; meanwhile, as the fitting depth is increased, the number of the optimal dipoles is gradually reduced, and high-precision coupling of the magnetic field can be realized by only a small number of dipoles; the fitting precision with the ship model measured data is higher than 99%, the effectiveness and the correctness of the modeling method are checked, and the high-precision automatic optimizing inversion positioning of the magnetic target is realized.
The method comprises the following specific steps:
step 1, acquiring ship reference magnetic field data
Based on classical rotating ellipsoids and magnetic dipole array model theory, the induction magnetic field generated in the geomagnetic field along the north-south heading under the ideal condition of the ship is determined and used as a reference value.
The principle of the classical rotating ellipsoid and the magnetic dipole array model is shown in figure 1, a ship is simplified into a uniformly magnetized ellipsoid, magnetic dipoles with equal strength are longitudinally arranged on the horizontal plane of the central axis of the ellipsoid, the arrangement positions and the specific number of the magnetic dipoles are determined according to the specific magnetic field distribution of the ship, the magnetic field generated by the magnetic dipoles in the ellipsoid is approximately simulated into a real magnetic field generated by the ship, a calculation model is simplified, and the magnetic field conversion of different depths is carried out.
Assuming that the geometry of a uniformly magnetized ellipsoid of revolution is comparable to that of a ship, N (N is an odd number) magnetic dipoles are arranged along the longitudinal direction of the ellipsoid at the same distance d, the major half axis is a, the minor half axis is b, the geometric center of the ellipsoid and the geometric center of the ship coincide, and are respectively recorded as 1,2 from left to right,..n, then the coordinates of the ith (i=1, 2,..n) magnetic dipole are:(i=0 corresponds to a rotational ellipsoid, there is (x) 0 ,y 0 ,z 0 ) = (0, 0); set magnetic target at P j (x j ,y j ,z j ) The three components of the magnetic field generated at the position are H xij 、H yij 、H zij The following steps are:
when i is more than or equal to 1 and less than or equal to N,magnetic moment components of the ith magnetic dipole along the directions of an x axis, a y axis and a z axis respectively;
b xji ＝a yji
a zij ＝c xij
b xij ＝c yij
the equation satisfied by each magnetic dipole in the combined rotational ellipsoid and magnetic dipole array can be obtained as the equation that the magnetic field at the measurement point should satisfy:
FM＝H
M＝[M x M y M z M x1 M y1 M z1 … M xm M ym M zm ] T
fitting the known magnetic field distribution of the ship with magnetic dipoles, and calculating the magnetic field distribution of the space around the ship as a reference value according to a mixed model of the magnetic dipoles and ellipsoids;
step 2, constructing a three-dimensional magnetic dipole and ellipsoid mixed model
Cutting the ellipsoid of rotation and the magnetic dipole array model by using a plurality of planes perpendicular to the long axis to obtain slice spaces with the same number as the magnetic dipoles, wherein the thickness of each slice space is consistent;
the slice space is equivalent to a cuboid space with a square cross section, and the square cross section is an inscribed square with a round tangential plane corresponding to the magnetic dipole;
step 3, magnetic dipole searching is carried out based on particle swarm algorithm
(1) Based on three-dimensional magnetic dipoles and ellipsesThe sphere mixed model parameters establish a feasible solution space, n particles are generated in the feasible solution space in an initializing mode, and a population X= (X) is formed 1 ,X 2 ,...,X n ) Wherein, the i (i=1, 2,) th particle X i A vector representing one D dimension: x is X i ＝(x i1 ,x i2 ,...,x iD )；
X i Representing the set of long axis direction coordinates of the magnetic dipole obtained after cutting.
(2) The particle characteristics are represented by three indexes of position, speed and fitness value, wherein the position refers to the space of each cutting block limited by the ellipsoid after cutting, the fitness value is calculated by a fitness function, and the fitness value is obtained by adopting a Griwang function:
(3) moving the particles in the solution space, the movement speed of the ith particle being set as V i ＝(V i1 ,V i2 ,...，V iD ) By tracking, the individual extremum P is searched i ＝(P i1 ,P i2 ,...,P iD ) Is adapted to the optimal position P best And population extremum G i ＝(G i1 ,G i2 ,...,G iD ) The fitness optimal position G in (1) best Updating individual location and speed:
wherein ω is inertial weight; d=1, 2,. -%, D; i=1, 2,. -%, n; k is the current iteration number; v (V) id Is the speed of the ith particle; c 1 And c 2 Is acceleration factor, is non-negative constant; r is (r) 1 And r 2 Is distributed in [0,1 ]]Random numbers of intervals;
(4) every time a particle is updatedThe position, the fitness value is calculated once, and the fitness value of the new particle is compared with the fitness value of the individual extremum and the population extremum to update the individual extremum P best And population extremum G best Position until all iterations are completed;
in this embodiment, parameters of the particle swarm algorithm are set as follows:
e. maximum number of iterations: 100;
f. number of individuals in population: 50;
g. acceleration parameters: 2;
h. weight at the beginning of the algorithm: 0.9;
i. weight at the end of algorithm: 0.4;
j. algorithm termination threshold: 10 -5 The method comprises the steps of carrying out a first treatment on the surface of the Namely, stopping the algorithm when the change of the optimal value of the corresponding population in two continuous iterations is smaller than the value;
k. threshold for terminating the iteration: 1000; i.e. when the gradient value of the function has not changed in 1000 consecutive iterations, the iteration is exited.
(5) And after the updating calculation is finished, outputting a magnetic dipole space position calculation result when the number of the magnetic dipoles is different.
Step 4, determining fitting accuracy errors
Based on the magnetic dipole space position coordinate scheme obtained in the step 3, calculating a magnetic field generated by a magnetic dipole in an ellipsoid in a three-dimensional space, fitting with a reference value, and calculating fitting accuracy by representing errors by two norms of errors/two norms of original data (since the reference value of a Y component is 0, absolute errors are adopted for calculation when calculating the fitting accuracy of the Y component).
The fitting accuracy error calculation formula is:
wherein h is xcal 、h ycal 、h zcal A magnetic field calculation value for magnetic dipole inversion; h is a x 、h y 、h z Is a reference value;
step 5, setting corresponding weights to screen the optimal number of magnetic dipoles, wherein the specific weight calculation mode is as follows: (since the ship heading Y component is ideally 0, the fitting accuracy of the X and Z components is emphasized.
E best ＝min{0.4×errx i +0.1×erry i +0.4×errz i +0.1×t i }；
Wherein E is best The optimal weight is used for finding out the corresponding optimal magnetic dipole number according to the optimal weight;
errx i 、erry i 、errz i fitting errors of three components when the number of magnetic dipoles is i respectively; t is t i The calculation time is the calculation time when the number of magnetic dipoles is i.
The following describes the verification of the foregoing scheme based on simulation calculations:
ideally, the ship has no geomagnetic field Y component along the north-south heading, and the geomagnetic field X component is 33500nT, and the Z component is 36500nT. The ellipsoid has the length of 4m and the width of 0.467m, the depths of 1B, 5B and 10B of the reference plane, namely 0.437m, 2.185m and 4.37m are respectively calculated, 201 fitting field points are set, the optimal magnetic dipole quantity is automatically optimized by adopting an algorithm and calculated according to the weight, the optimal magnetic dipole space distribution is finally generated, and the fitting result is calculated as shown in figures 2-19.
Fitting results of the calculated value and the standard value of the magnetic dipole inversion can be obtained: when the depth is 1B, the optimal magnetic dipole numbers of models with different sizes are 24, the fitting error of the X component of the model A is 0.048%, and the fitting precision is 99.952%; the maximum absolute error of the Y component is 22.356nT; the fitting error of the Z component is 0.0097%, and the fitting precision is 99.99%; when the depth is 5B, the number of optimized optimal magnetic dipoles is 24, the fitting error of the X component is 0.0034%, and the fitting precision is 99.997%; the maximum absolute error of the Y component is 0.0124nT; the fitting error of the Z component is 0.007%, and the fitting precision is 99.993%; when the depth is 10B, the number of optimized optimal magnetic dipoles is 8, the fitting error of the X component is 0.0018%, and the fitting precision is 99.998%; the maximum absolute error of the Y component is 0.931nT; the fitting error of the Z component was 0.00076%, and the fitting accuracy was 99.999%.
Therefore, based on the scheme of the application, under different depths, the magnetic dipoles can successfully realize automatic optimizing and three-dimensional space distribution of the quantity in the ellipsoid, and the distribution situation of the magnetic dipoles reflects the magnetic characteristics of the ellipsoid; when the depth is shallower, the distribution of magnetic dipoles in the ellipsoidal space can also realize the high-precision inversion of the near field; with the increase of inversion depth, the number of required magnetic dipoles is reduced, namely, high-precision fitting of an inversion calculated value and a reference value can be realized by only a small number of magnetic dipoles; meanwhile, the optimizing process takes account of calculation time, the calculation time of 52 magnetic dipoles is 14.11s, the calculation time of 24 magnetic dipoles is 4.41s, the calculation time of 8 magnetic dipoles is 0.41s, high-precision inversion calculation is guaranteed on the premise of short calculation time, the calculation time is short, the efficiency is high, the effectiveness of the magnetic target three-dimensional optimizing inversion positioning method based on the particle swarm algorithm is fully demonstrated, and the defect that the inversion precision of the magnetic dipoles in the near is low is overcome.
And measuring the induction magnetic fields of the three models with different sizes at the same depth, and verifying the magnetic dipole three-dimensional inversion model by taking the measured data as a reference value. The A-type ship model has the length of 4.4m, the width of 0.43m, the B-type ship model has the length of 3.4m and the width of 0.3m; c-shaped ship model is 4.8m long and 0.5m wide; the measuring depth of the sensor is one time of the ship width, and the measured value is subjected to inversion fitting by adopting a magnetic dipole automatic optimizing algorithm. By comparing the data, the algorithm can realize the automatic optimization of the optimal distribution and number of the magnetic dipoles under the depth of 1B for models with different sizes, the spatial arrangement is realized in the ellipsoids, and the high-precision fitting of the three-component inversion value and the measured value of the magnetic field can be realized. When the fitting depth is 1B, the optimal number of magnetic dipoles for ship optimization in three sizes is 24. The fitting error of the X component of the A-shaped ship is 0.014%, and the fitting precision is 99.986%; the maximum absolute error of the Y component is 0.129nT; the fitting error of the Z component is 0.0059%, and the fitting precision is 99.994%; the fitting error of the X component of the B-type ship is 0.0025%, and the fitting precision is 99.998%; the maximum absolute error of the Y component is 0.0322nT; the fitting error of the Z component is 0.007%, and the fitting precision is 99.993%; the fitting error of the X component of the C-shaped ship is 3.19×10 -7 % and fitting accuracy is approximate100%; the maximum absolute error of the Y component is 3.82×10 -4 pT, the magnitude reaches the Pitty level; the fitting error of the Z component is 4.9X10 -7 The fitting accuracy is approximately 100%.
Similarly, the inversion calculation time of the three ship models is 7.72s, 4.24s and 4.29s respectively, so that the calculation efficiency is high, and the high efficiency and the calculation advantage of the algorithm are proved. For ellipsoids with different sizes, the fitting precision of inversion calculation of 1B depth is high, and the magnetic target three-dimensional optimizing inversion positioning method based on the particle swarm algorithm is verified to enable the magnetic dipoles to realize high-precision inversion calculation of magnetic field distribution in the vicinity of the ellipsoids, is suitable for the ellipsoids with different sizes, and has model universality and algorithm convenience.
On the basis of uniformly magnetized ellipsoids and magnetic dipole mixed modeling, the application carries out slice processing on the ellipsoids, and improves the planar distribution of the magnetic dipoles into three-dimensional distribution in the internal space of the ellipsoids. And adopting a PSO algorithm, automatically optimizing the number of magnetic dipoles by setting a weight which gives consideration to calculation time and inversion precision, and automatically generating three-dimensional spatial distribution in an ellipsoid. Simulation results prove that the magnetic target three-dimensional optimizing inversion positioning method based on the particle swarm algorithm can realize automatic optimizing of the quantity and position distribution of magnetic dipoles in an ellipsoidal space, and the magnetic field three-component fitting accuracy obtained by inversion calculation is very high and can reach 99.99% under the condition of considering calculation time; meanwhile, inversion calculation of different depths shows that the magnetic target three-dimensional optimizing inversion positioning method based on the particle swarm algorithm is not limited by the depths, overcomes the defect that the magnetic dipole has low inversion precision in the near field, and can realize high-precision inversion fitting calculation of different depths. The fitting result of the ship model test data with three different sizes can be obtained, the magnetic dipoles can be fitted with high precision of the magnetic field, the magnetic dipoles can be arranged differently in space according to the magnetic field condition, the fitting degree of the three components of the magnetic field obtained by space distribution inversion and the reference magnetic field is high, the fitting error is within 0.02%, and the inversion precision of the magnetic dipoles is greatly improved.
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 (6)
1. A magnetic target three-dimensional optimizing inversion positioning method based on a particle swarm algorithm is characterized by comprising the following steps:
step 1, acquiring ship reference magnetic field data
Based on classical rotating ellipsoids and magnetic dipole array model theory, determining an induced magnetic field generated in a geomagnetic field under the ideal condition of a ship as a reference value;
step 2, constructing a three-dimensional magnetic dipole and ellipsoid mixed model
Cutting the ellipsoid of rotation and the magnetic dipole array model by using a plurality of planes perpendicular to the long axis to obtain slice spaces with the same number as the magnetic dipoles, wherein the thickness of each slice space is consistent; the slicing space is equivalent to a cuboid space with a square cross section;
step 3, magnetic dipole searching is carried out based on particle swarm algorithm
(1) Establishing a feasible solution space based on three-dimensional magnetic dipole and ellipsoid mixed model parameters, initializing n particles in the feasible solution space to form a population X= (X) 1 ,X 2 ,...,X n ) Wherein X is i Is a vector of D dimension: x is X i ＝(x i1 ,x i2 ,...,x iD )，i＝1,2,...,n；X iD Representing the long axis coordinates of a certain magnetic dipole obtained after cutting;
(2) the particle characteristics are represented by three indexes of position, speed and fitness value, wherein the position refers to the space of each cutting block limited by the ellipsoid after cutting, and the fitness value is obtained by calculating a fitness function;
(3) moving the particles in the solution space, the movement speed of the ith particle being set as V i ＝(V i1 ,V i2 ,...，V iD ) By trackingSearching for an individual extremum P i ＝(P i1 ,P i2 ,...,P iD ) Is adapted to the optimal position P best And population extremum G i ＝(G i1 ,G i2 ,...,G iD ) The fitness optimal position G in (1) best Updating individual position and velocity:
wherein ω is inertial weight; d=1, 2,. -%, D; i=1, 2,. -%, n; k is the current iteration number; v (V) id Is the speed of the ith particle; c 1 And c 2 Is acceleration factor, is non-negative constant; r is (r) 1 And r 2 Is distributed in [0,1 ]]Random numbers of intervals;
(4) calculating fitness value once every time the particle is updated, and updating individual extremum P by comparing fitness value of new particle with fitness value of individual extremum and population extremum best And population extremum G best Position until all iterations are completed;
step 4, determining fitting accuracy errors
Based on the magnetic dipole space position coordinate scheme X obtained in the step 3 i Calculating a magnetic field generated by a magnetic dipole in an ellipsoid in a three-dimensional space, fitting the magnetic field with a reference value, and representing error calculation fitting precision by using a two-norm of an error:
the fitting accuracy error calculation formula is:
wherein h is xcal 、h ycal 、h zcal Is based on the magnetic dipole position coordinate scheme X i Performing inversion to obtain a magnetic field calculated value; h is a x 、h y 、h z Is a reference value;
step 5, setting weight to screen the optimal magnetic dipole number
The weight calculation mode is as follows:
E best ＝min{0.4×errx i +0.1×erry i +0.4×errz i +0.1×t i },(i＝1,…,N)；
wherein E is best Determining the optimal magnetic dipole number according to the optimal weight; errx (r x) i 、erry i 、errz i Fitting errors of three components when the number of magnetic dipoles is i respectively; t is t i The calculation time is the calculation time when the number of magnetic dipoles is i.
2. The method for three-dimensional optimizing inversion positioning of magnetic targets based on particle swarm optimization according to claim 1, wherein the following steps are adopted in step 1:
a1, simplifying a ship into an ellipsoid with uniform magnetization, and longitudinally arranging magnetic dipoles with equal strength on the horizontal plane of the central axis of the ellipsoid, wherein the arrangement positions and the specific number of the magnetic dipoles are determined according to the specific magnetic field distribution of the ship;
a2, the magnetic field generated by the magnetic dipole in the ellipsoid is approximately simulated into a real magnetic field generated by a ship, a calculation model is simplified, and magnetic field conversion with different depths is carried out;
a3, fitting the magnetic field distribution of the ship with the magnetic dipoles through known magnetic field distribution of the ship, and calculating the magnetic field distribution of the space around the ship as a reference value according to a mixed model of the magnetic dipoles and ellipsoids.
3. The method for three-dimensional optimizing inversion positioning of magnetic targets based on particle swarm optimization according to claim 1, wherein in the step 3, parameters of the particle swarm optimization are set as follows:
a. maximum number of iterations: 100; number of individuals in population: 50; acceleration parameters: 2;
b. weight at the beginning of the algorithm: 0.9; weight at the end of algorithm: 0.4;
c. algorithm termination thresholdValue: 10 -5 The method comprises the steps of carrying out a first treatment on the surface of the Terminating the algorithm when the variation of the optimal value of the corresponding population in two successive iterations is smaller than the value;
d. terminating the iteration threshold: 10 3 The method comprises the steps of carrying out a first treatment on the surface of the When the gradient value of the function is unchanged in the continuous 1000 iterations, the iteration is exited;
(5) and after the updating calculation is finished, outputting a magnetic dipole space position calculation result when the number of the magnetic dipoles is different.
4. The method for three-dimensional optimizing inversion positioning of magnetic targets based on particle swarm optimization according to claim 1, wherein in the step 3, the fitness function is:
5. the method for three-dimensional optimizing inversion positioning of magnetic targets based on particle swarm optimization according to claim 1, wherein in the step 2, the square corresponding to the cuboid space is determined based on the following manner: and determining a middle plane perpendicular to the long axis in the slice space, determining a circle formed by intersecting the middle plane and the shell surface of the ellipsoid of revolution, and taking the inscribed square of the circle as the square of the section of the cuboid space.
6. The method for three-dimensional optimizing inversion positioning of a magnetic target based on a particle swarm optimization according to claim 2, wherein a2 specifically comprises:
a20, designing a uniformly magnetized rotary ellipsoid with the geometrical size equivalent to that of a ship, arranging N magnetic dipoles along the longitudinal direction of the ellipsoid at the same distance d, wherein a long half shaft is a, a short half shaft is b, the geometrical center of the ellipsoid and the geometrical center of the ship are overlapped, and the geometrical centers are respectively recorded as 1,2 and N from left to right;
a21 is based on the coordinates of the ith magnetic dipole:has (x) 0 ,y 0 ,z 0 ) = (0, 0); magnetic target at P j (x j ,y j ,z j ) The three components of the magnetic field generated at the position are H xij 、H yij 、H zij The method comprises the following steps:
b xji ＝a yji
a zij ＝c xij
b xij ＝c yij
magnetic moment components of the ith magnetic dipole along the directions of an x axis, a y axis and a z axis respectively;
a22, synthesizing equations satisfied by each magnetic dipole in the rotating ellipsoid and the magnetic dipole array to obtain a magnetic field equation at a measuring point:
FM＝H
M＝[[M x M y M z M x1 M y1 M z1 …M xm M ym M zm ]] T
a23, fitting the magnetic dipole according to the known magnetic field distribution of the ship, and calculating the magnetic field distribution of the space around the ship as a reference value according to a mixed model of the magnetic dipole and the ellipsoid.
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