Naval vessel far-field magnetic field inversion method based on magnetic gradient tensor

Abstract

The invention discloses a ship far-field magnetic field inversion method based on magnetic gradient tensor. According to a traditional naval vessel magnetic field inversion method based on magnetic induction intensity, in the naval vessel magnetic field separation step, an additional sensor needs to be arranged for obtaining a reference background geomagnetic field, measurement errors are difficult to control, measurement data are inaccurate, and errors are generated during naval vessel far-field magnetic field inversion. According to the method, the magnetic gradient tensor is used as data for constructing the magnetic field model, a background geomagnetic field does not need to be measured, the measurement steps are simplified, and meanwhile inversion of the far-field magnetic field of the naval vessel has high accuracy. According to the method, the ship model is solved by using the MOAEMDE algorithm, control parameters of the algorithm can be adaptively adjusted, repeated manual parameter configuration according to different measurement environments is not needed, and the method is high in adaptability and convenient to use.

Description

Technical Field

[0001] The present invention relates to the technical field of ship magnetic field inversion, and in particular to a ship far-field magnetic field inversion method based on magnetic gradient tensor. Background Art

[0002] In order to ensure that the hull of a ship is strong enough to support its navigation in the ocean, a large amount of ferromagnetic materials are usually used. Due to the properties of ferromagnetic materials and the existence of the earth's large magnetic field, a magnetic field will be formed around the ship, making it easy for the ship to be detected by magnetic detection equipment and expose its position, and be attacked by magnetic fuse mines, torpedoes, etc. Therefore, in order to ensure the safe navigation of the ship, magnetic protection measures such as demagnetization of the ship are required. How to accurately obtain the ship's magnetic field is the primary issue for effective magnetic protection of the ship.

[0003] There are two methods to obtain the ship's magnetic field, physical measurement method and numerical inversion method. However, due to the large overall size of the ship and the complex structure of the ship, the use of magnetic sensors to directly physically measure the ship's magnetic field will face difficulties in setting up the measurement platform and interference from background magnetic field environmental factors. These problems are particularly prominent when measuring the ship's far-field magnetic field. Therefore, in order to accurately and conveniently obtain the distribution of the ship's magnetic field, most of the current research uses numerical modeling methods. This type of method models the ship's magnetic field based on the magnetic field measurement data of one or more planes near the ship (these magnetic field data can be accurately and directly measured) to obtain the magnetic field distribution in a large range around the ship.

[0004] The magnet simulation method is a modeling method that is widely used in ship magnetic field modeling. It establishes a numerical model of the ship magnetic field based on the similarity of the magnetic field distribution characteristics of the real ship and the simulated magnetic object at several measurement points. However, this type of method only requires the magnetic field generated by the ship itself when modeling, so the first problem to be faced is how to separate the ship magnetic field from the background geomagnetic field in the magnetic field measurement data of the sensor. The traditional solution is to set up a geomagnetic reference sensor to measure the magnetic induction intensity of the background geomagnetic field separately, and then subtract the background geomagnetic field from the magnetic field measurement data to obtain the magnetic induction intensity of the ship magnetic field. This places high requirements on the location selection of the geomagnetic reference sensor. It needs to be far away from the influence range of the ship magnetic field to obtain a pure geomagnetic field, but it cannot be too far away, otherwise the geomagnetic field measurement value of the reference point will be greatly different from the geomagnetic field measurement value of the experimental site. At the same time, the geomagnetic field fluctuations existing in nature will also affect the value of the reference geomagnetic field. The measurement error of the reference geomagnetic field will be retained during the magnetic field calculation process, thereby affecting the modeling of the ship magnetic field. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention proposes a ship far-field magnetic field inversion method based on the magnetic gradient tensor. According to the theory that the magnetic gradient tensor of the ship is much larger than the magnetic gradient tensor of the geomagnetic field, the magnetic gradient tensor of the geomagnetic field can be completely ignored, and the magnetic gradient tensor of the ship can be considered equal to the magnetic gradient tensor of the mixed magnetic field of the ship and the geomagnetic field. Therefore, this method directly uses the magnetic gradient tensor of the mixed magnetic field without setting up a geomagnetic reference sensor to measure the geomagnetic field. Then, a ship magnetic field model is established based on the magnetic gradient tensor, avoiding the error caused by unreasonable reference sensor settings.

[0006] In a first aspect, the present invention provides a method for inverting a ship's far-field magnetic field based on a magnetic gradient tensor, which specifically includes: Step 1, setting a near-field measurement plane at a distance R from the center of the ship; setting a plurality of measurement points on the near-field measurement plane; constructing a magnetic gradient tensor measurement array for each measurement point, and then obtaining near-field magnetic gradient tensor data of each measurement point; Step 2, constructing a multi-magnetic dipole array model based on magnetic gradient tensor; Step 3, based on the multi-objective adaptive elite mutation differential evolution algorithm, solve the optimal position and corresponding magnetic moment of each magnetic dipole in the multi-magnetic dipole array model; Step 4: According to the optimal position and corresponding magnetic moment of each magnetic dipole in the multi-magnetic dipole array model in step 3, the ship magnetic field distribution is obtained.

[0007] In a second aspect, the present invention provides an electronic device, characterized in that it includes a processor and a memory, the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the method.

[0008] In a third aspect, the present invention provides a machine-readable storage medium, characterized in that the machine-readable storage medium stores machine-executable instructions, and when the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the method.

[0009] The present invention has the following beneficial effects: 1. The present invention aims at the problem that when the magnetic induction intensity of a ship is used for numerical modeling of the magnetic field in the traditional method, the extraction of the ship's magnetic field will face the difficulty in selecting the location of the geomagnetic reference sensor, and the unreasonable location setting will cause errors in magnetic field modeling. The present invention uses the magnetic gradient tensor to perform numerical modeling of the ship's magnetic field. Compared with the traditional method, the properties of the magnetic gradient tensor can be used to extract the characteristics of the ship's magnetic field without measuring the background geomagnetic field, which simplifies the measurement operation process, avoids the introduction of errors when subtracting the background geomagnetic field, and reduces the interference of geomagnetic field fluctuations on the ship's magnetic field inversion.

[0010] 2. The present invention proposes a MOAEMDE algorithm in solving and modeling the ship's magnetic field. Compared with most traditional iterative optimization algorithms, it does not require manual setting and adjustment of the control parameters of the algorithm, but adaptively optimizes the control parameters during the iteration process, making the application scenarios of the present invention more flexible and extensive. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is the overall flow chart of the present invention.

[0012] Figure 2 Schematic diagram of the magnetic gradient tensor measurement array.

[0013] Figure 3 Schematic diagram of the optimized range for magnetic dipoles.

[0014] Figure 4 This is a picture of a ship model.

[0015] Figure 5 This is a simulation area diagram.

[0016] Figure 6 Schematic diagram of experimental data collection points.

[0017] Figure 7 This is the magnetic dipole distribution map in the scenario without geomagnetic fluctuations.

[0018] Figure 8 This is the magnetic field inversion result diagram for a scenario without geomagnetic fluctuations.

[0019] Fig. 9 This is the magnetic dipole distribution map in the scenario with geomagnetic fluctuations.

[0020] Fig.10 This is the magnetic field inversion result diagram for the scenario with geomagnetic fluctuations. DETAILED DESCRIPTION

[0021] The present invention will be further explained below with reference to the accompanying drawings; The present invention provides a ship far-field magnetic field inversion method based on magnetic gradient tensor, such as Figure 1 As shown, the following steps are included: Step 1: Set a near-field measurement plane at a distance R from the center of the ship, set multiple measurement points on the near-field measurement plane, and there is a spacing between the measurement points; and construct a magnetic gradient tensor measurement array for each measurement point to measure the near-field magnetic gradient tensor data of the ship. The theoretical basis and process are as follows: With each measuring point as the origin, the length direction of the hull as the x-axis, the maximum width direction of the hull as the y-axis, and the height direction of the hull as the z-axis, an xyz coordinate system is constructed; a magnetic sensor is set in the positive and negative directions of the x and y axes respectively; a magnetic gradient tensor measurement array is constructed by the above four magnetic sensors; The magnetic gradient tensor is defined as a second-order tensor of magnetic field data in a three-dimensional coordinate space, expressed as represents the magnetic gradient tensor and can be written as follows: (1) in, represents the magnetic gradient tensor components, represents the magnetic scalar potential, represents the component of magnetic induction intensity, It means to find partial derivatives.

[0022] Each component of the magnetic gradient tensor can be represented by the partial differential of the magnetic induction intensity, but the partial differential of the magnetic induction intensity cannot be measured by a magnetic sensor in practice. Therefore, the difference of the magnetic induction intensity of two measurement points at a certain distance is used to approximate the partial differential of the magnetic induction intensity, which can conveniently and accurately calculate the components of the magnetic gradient tensor. The magnetic gradient tensor measurement array constructed according to this theory is as follows: Figure 2 As shown, the corresponding tensor components are calculated as follows:

[0023] (2) in, The magnetic induction intensity measured by two magnetic sensors located in the coaxial direction of the coordinate system in the magnetic gradient tensor measurement array The difference in quantity, For the above two magnetic sensors The distance in the direction, and generally taken .

[0024] Step 2: Construct a multi-magnetic dipole array model based on the magnetic gradient tensor, specifically: The magnetic field generated by the ship hull can be regarded as a static magnetic field without current. Therefore, the Maxwell equations can be listed as shown in equations (3)-(4): (3) (4) in is the nabla operator, is the magnetic induction intensity, , , They represent the unit vectors in the three coordinate axes of the rectangular coordinate system respectively; combined with equations (3) and (4), we can further calculate: (5) From the conclusion in equation (5), we can see that there are five elements in the magnetic gradient tensor matrix: , , , , are independent of each other. Therefore, using , , , , The five components can fully describe the physical quantity of the magnetic gradient tensor at a certain measurement point in space.

[0025] The magnetic field generated by a single magnetic dipole at a point in space can be expressed as: (6) Expanded into matrix form is as follows: (7) in, is the vector of the magnetic dipole pointing to the measurement point, , , are the three components of the magnetic moment of the magnetic dipole, To measure the magnetic permeability of the medium in the area, the magnetic permeability of water and air media can be considered to be equal to the magnetic permeability of vacuum, that is, .

[0026] According to the conclusion in formula (1), the five components of the magnetic gradient tensor can be obtained by taking the partial derivative of the magnetic induction intensity. Therefore, by taking the partial derivative of formula (7), the magnetic gradient tensor representation of a single magnetic dipole can be obtained: (8) The meanings of all symbols are the same as in formula (7).

[0027] When the distance between the measurement point and the ship is greater than 2.5 times the longest geometric dimension of the ship, the magnetic field of the ship can be equivalent to the magnetic field generated by a single magnetic dipole. When solving the ship's magnetic field model, the near-field magnetic field data of the ship is used. The distance between the measurement point and the ship must be less than 2.5 times the longest geometric dimension of the ship. At this time, the magnetic gradient tensor model of a single magnetic dipole cannot achieve satisfactory fitting accuracy for the near-field magnetic field with more complex characteristics. Therefore, the magnetic gradient tensor model of a multi-magnetic dipole array is needed to fit the target's near-field magnetic field to solve the ship's magnetic field model.

[0028] The magnetic field of the multi-magnetic dipole array model is composed of the superposition of the magnetic fields of multiple single magnetic dipoles in space. Therefore, the magnetic gradient tensor model of a single magnetic dipole in formula (8) can be combined to form the magnetic gradient tensor model of the multi-magnetic dipole array, as shown in the following formula:

[0029] (9) in, is the number of magnetic gradient tensor measurement points, is the number of dipoles in the magnetic dipole array, The expanded form is as follows: (10) Among them, the subscript Represents the measurement point number, subscript represents the magnetic dipole number, , , , .

[0030] Magnetic moment parameters The expanded form is as follows: (11) Magnetic gradient tensor The expanded form is as follows: (12) Step 3: Based on the multi-objective adaptive elite mutation differential evolution algorithm (MOAEMDE), the optimal position and corresponding magnetic moment of each magnetic dipole in the multi-magnetic dipole array model are solved.

[0031] Firstly, the problem to be solved by the MOAEMDE algorithm is described. The algorithm is used to solve the relevant parameters of the multi-magnetic dipole model that can fit the near-field magnetic field measurement data of the ship, including the position coordinate parameters and magnetic moment parameters of the magnetic dipole.

[0032] Regarding the position coordinate parameters, the optimization range of the magnetic dipole position in this model is limited to the elliptical midline plane of the ship. The coordinate system is established with the center of the midline plane as the origin of the coordinate system. The optimization range of the magnetic dipole can be expressed as follows: Figure 3 As shown, the position coordinate parameters to be solved can be expressed as , is the serial number of the magnetic dipole. In the MOAEMDE algorithm, a set of position coordinates of all magnetic dipoles constitutes the gene of an individual, and the optimal individual finally selected by the algorithm is the optimal position coordinate parameter.

[0033] Regarding the magnetic moment parameter, its composition is , represents the three components of the magnetic moment, is the serial number of the magnetic dipole. The magnetic moment is obtained by the position coordinate matrix composed of the position coordinate parameters and the near-field magnetic gradient tensor data through stepwise regression. In the MOAEMDE algorithm, each individual will obtain its own set of magnetic moment parameters in each iteration, which is used to calculate the objective function value of the individual and help the multi-objective optimization function to select individuals. The magnetic moment corresponding to the optimal individual finally selected by the algorithm is the optimal magnetic moment parameter.

[0034] The optimal position of the magnetic dipole and the corresponding magnetic moment solution based on MOAEMDE specifically include the following steps: ① Initialization of magnetic dipole position population and algorithm control parameters The first step is to initialize the population. Suppose the number of individuals in the population is , the number of genes per individual is (i.e., magnetic dipole number ), then each individual in the population can be expressed as

[0035] (13) The initialization of the population can be expressed as (14) in , , represents the number of iterations, and Separate The upper and lower limits of the gene value.

[0036] Then the control parameters are initialized. The elite mutation strategy is adopted. ", the algorithm needs to initialize three control parameters, namely the scaling factor , crossover probability factor With elite weighting factor Each individual has a separate set of control parameters ,Right now , which indicates that the evolution to Generation, individual The corresponding control parameters. The value ranges of the three parameters are defined as , the control parameter initialization can be expressed as:

[0037] (15) ②Screening the initial elite population First, determine the multi-objective optimization function used for screening.

[0038] The ship magnetic field model constructed by the present invention is described by the linear equation group shown in formula (9). The condition number of the linear equation group can be used to quantify the stability of the model. The definition of the condition number is as follows: (16) in, Represents the coefficient matrix of the linear equation system, that is, The smaller the condition number, the more stable the model will be, and the more accurate the value of the magnetic moment will be. According to the above theory, the condition number objective function is defined as follows:

[0039] (17) in, , are the horizontal and vertical coordinates of the magnetic dipoles in the array, is the number of magnetic dipoles.

[0040] In addition, a more intuitive indicator that reflects the accuracy of the model is the modeling error, which is defined as follows: (18) in is the value solved by magnetic moment inversion, which contains the three components of the magnetic moment of each magnetic dipole, indicating the magnitude of the magnetism of each magnetic dipole in the three directions of the rectangular coordinate system. The specific method of magnetic moment inversion solution will be described in detail in ⑤. The smaller the modeling error, the more accurate the solution of the magnetic moment. According to the above theory, the objective function of the modeling error is defined as follows:

[0041] (19) in, , are the horizontal and vertical coordinates of the magnetic dipoles in the array, is the number of magnetic dipoles.

[0042] The two optimization objective functions introduced above and , the constructed multi-objective optimization function is as follows: (20) Next, the initial elite population is screened. The Pareto optimal solution set in the initial population is used as the initial elite population. The solution method for the Pareto optimal solution set is as follows:

[0043] (twenty one) in, In order to optimize the number of objective functions, the number of objective functions is optimized in the present invention. , For the An optimization objective function. and are two different individuals randomly selected from the population. After traversing the entire population, all individuals satisfying formula (21) The solution set formed is the Pareto optimal solution set.

[0044] ③ Population executes elite mutation strategy Operate on the current population, elite mutation strategy " The formula for ” is as follows: (twenty two) in Represents the current individual, represents individuals randomly selected from the elite population, and is a randomly selected individual from the population, but , , Different from each other.

[0045] ④ Population gene crossover operation To operate the current population, the gene crossover operation formula is as follows: (twenty three) in, , , All represent genes, subscript Indicates individual, subscript represents the sequence number of the gene in an individual, express The random amount in . represents the first The first genes, Indicates the first The first genes, Indicates the first The first genes, is the control parameter The crossover probability factor in .

[0046] ⑤ Magnetic moment solution based on stepwise regression method In this step, each individual in the population will be solved, and the position coordinates stored by each individual and the coordinates of the near-field magnetic field measurement point together constitute the position matrix , the magnetic gradient tensor forms the vector The stepwise regression method transforms the magnetic moment vector in equation (9) into As the parameter variables to be determined, the complexity of the model is dynamically optimized in the process. Its core function is to eliminate redundant parameter variables to be determined, that is, to set some magnetic moment components to 0. The detailed steps of the stepwise regression method to solve the magnetic moment parameters are as follows:

[0047] a. Substitute the matrix in equation (9) With vector Combine to form an augmented matrix (twenty four) Among them Column correspondence , No. Column correspondence .

[0048] Next, The data in are normalized to eliminate dimension effects: (25) in For the The mean of the column, , and obtain the standardized matrix .

[0049] b. Calculate the correlation coefficient matrix: (26) c. Select the first parameter variable to enter the stepwise regression method. The selection rule is: , , (27) in, is the number of magnetic moment parameter variables to be determined, and its value is , is the correlation coefficient matrix The elements corresponding to the subscript numbers in , Subscript is the serial number of the parameter variable selected into the algorithm.

[0050] Correlation coefficient matrix do Transformation, The transformation is defined as follows: (28) After the first transformation The reconstructed matrix is ​​denoted by , the number of selected parameter variables is .

[0051] The significance level was selected as of Distribution as a significance test ( Critical value of the test : (29) in For the matrix number of rows.

[0052] conduct The calculation formula is as follows: (30) Test for judgment Is it true? If so, determine the introduction number as The parameter variable is selected and removed from the candidate pool of parameter variables. Otherwise, the stepwise regression method fails and the algorithm is exited, and it is determined that the position distribution of the magnetic dipole array at this time is unreasonable.

[0053] d. Enter the parameter variable screening loop. Set the matrix Experienced Second-rate Transformed , and introduced A parameter variable that cannot be eliminated.

[0054] The new parameter variables entering the stepwise regression method are determined by formula (23). do Transformation , ,calculate and Test. , then the introduction number is , and remove it from the candidate pool, and go to step e; if , then do Transformation Restored to , go to step f.

[0055] If this step starts , it means that all parameter variables have been selected and there are no more parameter variables to be selected, and then go to step f.

[0056] e. After successfully introducing a parameter variable, you need to parameter variables Check to see if any parameter variables need to be removed.

[0057] The previous value is calculated by formula (26): parameter variables , subscript For the front The serial number of the parameter variable, for The minimum value in . , then there is no parameter variable to be eliminated, go to step d; if , then Do Transformation, after transformation, it is still recorded as , serial number is The parameter variables are removed from the selected queue and put back into the pool to be selected, and then step e is restarted until there are no parameter variables to be removed.

[0058] f. The parameter variable screening cycle ends, let (31) in Subscript , , , ... are the serial numbers of the selected parameter variables, and are arranged from small to large. for The elements in .

[0059] The formula for restoring parameter variables is shown in formula (19): (32) in .

[0060] g. The magnetic moment vector Expand as follows (33) Fill the result into the output vector The magnetic moment vector solution is completed (34) That is, the values ​​of the selected parameter variables are filled in the corresponding positions, and the positions of the unselected parameter variables are filled with 0, indicating that they are eliminated.

[0061] ⑥ Population individual selection operation to generate the optimal population for this iteration The MOAEMDE algorithm uses a greedy algorithm to update individuals in the next generation population. For multi-objective minimization problems, individuals with lower values ​​of all objective functions are selected as individuals in the new population. The formula is as follows: (35) in, is the count of the objective function, is the objective function shown in step ②, n=1 or 2, that is , , represents the number of objective functions, where , The first Individuals, is the population after the crossover operation Individuals, For the next generation of population Individual.

[0062] After step ⑥, determine whether the maximum number of iterations of MOAEMDE has been reached. If so, jump to step ⑨, otherwise continue to step ⑦.

[0063] ⑦ Elite population update This step is the same as the screening operation of the initial elite population in ②. The Pareto optimal solution set in the population generated after step ⑥ is used as the elite population in the next iteration of the algorithm.

[0064] ⑧Adaptive update of algorithm control parameters The Min-Max method is used to normalize the objective function value of each individual in the population. The formula is as follows: (36) All individuals are sorted by the calculated values ​​according to the following formula, and are the two normalized objective functions, , : (37) The last 40% of individuals in the population are selected as individuals with poor optimization results. Parameter adaptive update will dynamically adjust the values ​​of the control parameters corresponding to these individuals. The specific operations are as follows:

[0065] The parameter adaptive update strategy is divided into two modes: overall learning and parameter reset.

[0066] Mode 1. All-person learning The optimization results of individuals with poor results are used to learn the control parameters of elite individuals. The formula is as follows: (38) in, Represents the average value of the control parameter factor of the elite population.

[0067] Mode 2. Parameter reset Reset the parameters of some individuals in the population to maintain the diversity of the population. The formula is as follows: (39) The choice between the two modes is determined by the population diversity threshold. The formula for the diversity threshold is as follows: (40) in, For this generation The optimal value of the objective function value, is the average value of the objective function.

[0068] The rules for mode selection are as follows: (41) in , .

[0069] After this step is completed, jump to step ③ to continue the cycle.

[0070] ⑨ The iteration ends and the optimal solution of the magnetic dipole position and the corresponding magnetic moment are selected The individuals in the Pareto optimal solution set of the population generated by the last iteration are sorted according to the calculated values ​​of formula (37), and the solution with the smallest value is taken as the optimal solution, that is, the optimal position coordinate parameter, and the corresponding magnetic moment is the optimal magnetic moment parameter.

[0071] Step 4: Based on the multi-magnetic dipole array model, the optimal solution of the magnetic dipole position and the corresponding magnetic moment obtained in step 3 are combined to solve the ship's magnetic field distribution.

[0072] The multi-magnetic dipole array model is shown in equation (42): (42) The expanded form is as follows: is the position coefficient of the relative position between the inversion point and the magnetic dipole, which is expanded as follows: , , , , , , , , ,in The subscript represents the inversion point, subscript Represents a magnetic dipole.

[0073] The expanded form is as follows: in is the number of inversion points; The expanded form is as follows: in is the number of magnetic dipoles in the magnetic dipole array.

[0074] According to the formula in step 3, the magnetic moment parameters and coordinate position parameters of each magnetic dipole in the array are solved, and the optimal magnetic dipole coordinate position parameters and the coordinates of the magnetic field space point to be inverted are substituted into the position matrix , substitute the optimal magnetic moment parameters into the vector , the magnetic induction intensity of the ship's magnetic field at the inversion point can be solved, and the vector It means that the distribution of the ship's magnetic field can be obtained by taking multiple groups of inversion points.

[0075] The present invention is subjected to simulation experiment analysis below, and the experimental setting and results are as follows: The simulation data used in the experiment was generated by the finite element simulation software COMSOL, and the established ship model is as follows: Figure 4 As shown, the simulation area is Figure 5 The experimental scene parameter settings are shown in Table 1.

[0076] Table 1 Simulation scenario parameters Parameter Type value Ship model length 32m Ship model radius 2.5m Ship model hull thickness 0.05m Relative magnetic permeability of ship model materials 700 Simulation scenario range 500m × 500m × 600m Geomagnetic field #timg# component -30000nT Geomagnetic field #timg# component -40000nT Geomagnetic field #timg# component -50000nT The experimental data collection points are as follows: Figure 6 As shown, the magnetic field inversion effect will be obtained by comparing the software simulation values ​​of the three measurement lines on the far field plane above the ship with the inversion values ​​of the present invention. The inversion effect of the present invention is mainly judged by the inversion accuracy, using the relative root mean square error (RRMSE), whose numerical value represents the percentage of the error between the inversion value and the true value in the entire magnetic anomaly field fluctuation range, which can be expressed as follows by formula (43):

[0077] (43) in, represents the inversion value, represents the true value, , Represent the maximum and minimum values ​​in the real value respectively.

[0078] In the inversion, the parameters used by MOAEMDE are set as follows: the number of magnetic dipoles is 20, the maximum number of iterations is 200, and the number of individuals in the population is 200.

[0079] Simulation 1 Magnetic field inversion without geomagnetic fluctuations This simulation considers the ideal situation of ship magnetic field inversion, that is, the background magnetic field in the experiment only contains a uniform and stable geomagnetic field, and there is no other environmental interference. Although the value of the geomagnetic field has been accurately given, it is not used in the method of the present invention. Figure 7The distribution of magnetic dipoles solved by the MOAEMDE algorithm is given. It can be seen that there are 19 magnetic dipoles in the figure, which is less than 20. This is because the stepwise regression method eliminates some redundant magnetic dipoles in the process of solving the magnetic moment. This not only improves the stability of the magnetic field model, but also improves the accuracy of the model parameter solution. Figure 8 The three-component values ​​of magnetic induction intensity inverted by the method of the present invention on three measurement lines in the high-altitude far field are given ( Figure 8 The dashed line shows the reference value generated by the simulation software ( Figure 8 The comparison results of the inversion results of the proposed method are shown in Table 2. The inversion error of the proposed method in this scenario is less than 10%.

[0080] Table 2 Magnetic field inversion results for scenarios without geomagnetic fluctuations Measuring Line BxRRMSE By RRMSE BZ #timg# 4.46% 4.92% 1.04% #timg# 4.42% 7.58% 1.05% #timg# 4.42% 6.86% 1.06% Simulation 2 Magnetic field inversion with geomagnetic fluctuations This simulation considers a more realistic ship magnetic field inversion scenario. In simulation 1, Gaussian white noise is added to the uniform and stable geomagnetic field to simulate the fluctuations of the geomagnetic field in the natural environment and other possible environmental interferences. The introduced magnetic field noise interference reaches 1% of the maximum amplitude of the ship magnetic field fluctuation range, varying from a few nT to hundreds of nT. At this time, the background geomagnetic field can no longer be accurately obtained. Fig. 9 The distribution of magnetic dipoles solved by the MOAEMDE algorithm is given. It can be seen that the number of magnetic dipoles in the figure is further reduced to 13. This is because the magnetic field data is affected by environmental noise. The model needs to reduce more redundant parameters to enhance stability and prevent overfitting of the model. Fig.10 The inversion value of the method of the present invention is given ( Fig.10 The dashed line shows the reference value of the simulation software ( Fig.10 The comparison of the inversion error of simulation 1 is shown in the solid line. This is due to the influence of environmental noise and the sacrifice of some inversion accuracy to maintain the stability of the model. The specific numerical evaluation results are given in Table 3. It can be seen that the inversion errors of the x and z components of the magnetic induction intensity have not increased significantly. Although the percentage result of the inversion error of the y component has increased significantly, Fig.10 It can be seen that the actual value of the error is only about 1nT, indicating that the inversion method still has a high accuracy.

[0081] Table 3 Magnetic field inversion results for scenarios with geomagnetic fluctuations Measuring Line BxRRMSE By RRMSE BZ #timg# 5.48% 15.37% 1.79% #timg# 5.44% 21.27% 1.86% #timg# 5.45% 16.77% 1.93% The above is a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements and modifications without departing from the principle of the present invention. These improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A ship far-field magnetic field inversion method based on magnetic gradient tensor, characterized in that The following steps are involved: Step 1, setting a near-field measurement plane at a distance R from the center of the ship; setting a plurality of measurement points on the near-field measurement plane; constructing a magnetic gradient tensor measurement array for each measurement point, and then obtaining near-field magnetic gradient tensor data of each measurement point; Step 2, constructing a multi-magnetic dipole array model based on magnetic gradient tensor; Step 3, based on the multi-objective adaptive elite mutation differential evolution algorithm, solve the optimal position and corresponding magnetic moment of each magnetic dipole in the multi-magnetic dipole array model; Step 4: According to the optimal position and corresponding magnetic moment of each magnetic dipole in the multi-magnetic dipole array model in step 3, the ship magnetic field distribution is obtained.

2. The method according to claim 1, characterized in that: The calculation of the near-field magnetic gradient tensor data of each measurement point in step 1 is specifically: With each measuring point as the origin, the length direction of the hull as the x-axis, the maximum width direction of the hull as the y-axis, and the height direction of the hull as the z-axis, an xyz coordinate system is constructed; a magnetic sensor is set in the positive and negative directions of the x and y axes respectively; a magnetic gradient tensor measurement array is constructed by the above four magnetic sensors; The magnetic gradient tensor G is expressed in the following form: （1） in, represents the magnetic gradient tensor components, represents the magnetic scalar potential, represents the component of magnetic induction intensity, It means to find partial derivatives; According to the magnetic gradient tensor measurement array, the magnetic gradient tensor component of each measurement point is calculated, and the calculation formula is as follows: （2） in, The magnetic induction intensity measured by the two magnetic sensors Q1 and Q2 in the magnetic gradient tensor measurement array located in the coaxial direction of the coordinate system The difference in quantity, For two magnetic sensors Q1, Q2 Distance in direction; The method according to claim 2, characterized in that Step 2 is specifically: The magnetic field generated by the ship hull is regarded as a static magnetic field without current. Therefore, the Maxwell equations are obtained as shown in equations (3)-(4): （3） （4） in is the nabla operator, is the magnetic induction intensity, , , Respectively represent the unit vectors in the three coordinate axis directions of the rectangular coordinate system; combined with equations (3) and (4), further calculation is made: （5） From formula (5), we can see that the magnetic gradient tensor matrix has , , , , are independent of each other, so using , , , , The five components formed can fully describe the magnetic gradient tensor at a certain measurement point in space; According to formula (1), , , , , It can be obtained by taking the partial derivative of the magnetic induction intensity, so the magnetic gradient tensor of a single magnetic dipole is expressed as follows: （6） in, is the vector of the magnetic dipole pointing to the measurement point, , , are the three components of the magnetic moment of the magnetic dipole, is the magnetic permeability of the medium in the measurement area; The magnetic field of the multi-magnetic dipole array model is composed of the superposition of the magnetic fields of multiple single magnetic dipoles in space; therefore, the magnetic gradient tensor model of a single magnetic dipole in formula (6) is combined to form the magnetic gradient tensor model of the multi-magnetic dipole array, as shown in the following formula: （7） Among them, the subscript is the number of measurement points of the magnetic gradient tensor, subscript is the number of magnetic dipoles in the magnetic dipole array, The expanded form is as follows:

3. Among them, the subscript Represents the measurement point number, subscript represents the magnetic dipole number, , , , ; Magnetic moment parameters The expanded form is as follows:

4. Magnetic Gradient Tensor The expanded form is as follows:

5. The method according to claim 3, characterized in that: Step 3 specifically is: 3-1 Initialization of magnetic dipole position population and algorithm control parameters; 3-2 Screening the initial elite population; 3-3 Execute the elite mutation strategy on the current population; 3-4 Perform gene crossover operation on the current population; 3-5 Solve the magnetic moment of each individual in the current population based on the stepwise regression method; 3-6 Generate the optimal population of the current iteration; determine whether the maximum number of iterations has been reached, if so, jump to step 3-9, otherwise continue to step 3-7; 3-7 elite populations updated; 3-8 Control parameters are adaptively updated and jump to step 3-3; After the 3-9 iterations, the individuals in the Pareto optimal solution set of the population generated by the last iteration are sorted according to the comprehensive objective function To sort, select The solution with the smallest value is the optimal solution, the optimal solution is the optimal position of the magnetic dipole position, and the magnetic moment corresponding to the optimal solution is the magnetic moment corresponding to the optimal position of the magnetic dipole position.

6. The method according to claim 4, characterized in that: Step 3-1 is as follows: 3-1-1 Population initialization; specifically: Individuals are represented by: （8） The population initialization is expressed as: （9） in , , is the number of individuals, is the number of genes in an individual, is the number of iterations, and Respectively The upper and lower limits of the value of each gene; 3-1-2 Control parameter initialization; specifically: The number of iterations is At that time, The control parameters corresponding to each individual Initialization is represented as: （10） in The number of iterations is At that time, The scaling factor corresponding to each individual, The number of iterations is At that time, The crossover probability factor corresponding to each individual is The number of iterations is At that time, The elite weight factor corresponding to each individual; The method according to claim 5, characterized in that Step 3-2 is specifically: 3-2-1 Define the condition number objective function and modeling error objective function , construct a multi-objective optimization function, as follows: （11） in, , are the horizontal and vertical coordinates of the magnetic dipoles in the magnetic dipole array, is the number of magnetic dipoles, are the three components of the magnetic moment of each magnetic dipole; 3-2-2 Take the Pareto optimal solution set in the initial population as the initial elite population; The method according to claim 6, characterized in that steps 3-8 are specifically: All individuals are based on the comprehensive objective function Sort, where and are the two normalized objective functions, , : （16） The last 40% of individuals in the population are selected for adaptive update of control parameters. The formula is as follows: （17） （18） in, For this generation The optimal value of the objective function value, n = 1 or 2, is the average value of the objective function, ; Represents the average value of the control parameter factor of the elite population; represents the diversity threshold.

7. An electronic device, characterized in that: The invention comprises a processor and a memory, wherein the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the method according to any one of claims 1 to 7.

8. A machine-readable storage medium, characterized in that: The machine-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the method described in any one of claims 1 to 7.

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