A multi-objective optimization method for structure parameters of a differential excitation coil

Abstract

The application belongs to the technical field of electromagnetic nondestructive testing, and particularly relates to a multi-target optimization method for structure parameters of a differential excitation coil; the method comprises the following steps: setting a range of structure parameters of the differential excitation coil to be optimized and actual engineering constraint conditions; constructing a solid coil spatial microelement model; calculating high-precision spatial magnetic field distribution of a single-sided excitation coil according to the solid coil spatial microelement model; calculating total excitation magnetic field distribution of the differential excitation coil according to the high-precision spatial magnetic field distribution of the single-sided excitation coil; constructing a first target function for representing magnetic field radial distribution uniformity and a second target function for representing magnetic field intensity according to the total excitation magnetic field distribution; and solving the first target function and the second target function based on the actual engineering constraint conditions to obtain the structure parameters of the differential excitation coil; the application realizes multi-target optimization of excitation magnetic field uniformity and absolute intensity, and improves the design precision and engineering practicability of a particle sensor.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic nondestructive testing technology, specifically relating to a multi-objective optimization method for the structural parameters of a differential excitation coil. Background Technology

[0002] In the field of modern industrial electromagnetic nondestructive testing (such as eddy current testing, fluxgate sensing, and online monitoring of abrasive particles in oil), differential excitation coils are widely used in the core excitation source design of various precision sensing devices because they can establish alternating magnetic fields in opposite directions, effectively cancel common-mode interference, and form a high-sensitivity detection zone. For example, in a high-precision three-coil oil abrasive particle sensor, the spatial distribution characteristics of the magnetic field excited by the differential excitation coil (radial magnetic field uniformity and peak absolute intensity) directly determine the spatial distribution characteristics of the excited magnetic field inside the sensor and the signal-to-noise ratio and consistency of the final induced signal.

[0003] However, existing methods for optimizing differential excitation coil structures generally have shortcomings. Regarding near-field spatial calculation models, existing analytical methods often employ approximate models such as "thin-walled coils," neglecting the spatial distribution effect of thick coil cross-sections in practical applications. This leads to calculation distortion and even divergence when evaluating the magnetic field in near-field regions such as the inner wall of the flow channel, resulting in extremely low fidelity of the underlying physical model. Simultaneously, because the spatial uniformity and absolute strength of the excitation magnetic field are mutually constrained, traditional empirical trial-and-error or single-objective optimization often blindly pursue extreme field strength values ​​at the expense of uniformity, leading to severe deterioration of the radial gradient of the magnetic field. This "one-sided approach" results in significant differences in signals generated by abrasive particles of the same size at different locations, easily causing missed or false positives. Furthermore, existing purely theoretical optimization solutions often lack engineering constraints, remaining largely at the level of ideal geometry. They fail to deeply incorporate industrial baseline limitations such as the physical diameter of standard enameled wire and the physical fill rate of the winding, making the "optimal size" output by the algorithm impossible to achieve in actual manufacturing, resulting in a disconnect between theoretical deduction and engineering manufacturing.

[0004] In summary, a multi-objective optimization design method for differential excitation coils is urgently needed. This method aims to eliminate spatial calculation errors of thick coils from a physical perspective and, under the premise of introducing real engineering manufacturing constraints, achieve the globally optimal configuration of radial uniformity and magnetic field strength of the excitation magnetic field. This will provide reliable technical support for the customized development of high-performance sensors. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a multi-objective optimization method for the structural parameters of differential excitation coils, which includes:

[0006] S1: Set the range of structural parameters of the differential excitation coil to be optimized and the actual engineering constraints;

[0007] S2: Construct a spatial micro-element model of a thick coil;

[0008] S3: Calculate the high-precision spatial magnetic field distribution of a single-sided excitation coil based on the spatial micro-element model of the thick coil;

[0009] S4: Calculate the total excitation magnetic field distribution of the differential excitation coil based on the high-precision spatial magnetic field distribution of the single-sided excitation coil; construct a first objective function to characterize the radial distribution uniformity of the magnetic field and a second objective function to characterize the magnetic field strength based on the total excitation magnetic field distribution;

[0010] S5: Solve the first objective function and the second objective function based on the actual engineering constraints to obtain the structural parameters of the differential excitation coil.

[0011] Preferably, in step S1, the range of structural parameters of the differential excitation coil is expressed as follows: ,in The inner diameter of the coil. The outer diameter of the coil. This refers to the axial length of a single-sided excitation coil. The distance between the inner sides of the two symmetrical differential excitation coils is denoted as ... denoted as denoted denoted denoted as denoted denoted denoted denoted

[0012] Preferably, step S2 specifically includes: setting the number of radial divisions as... The number of axial divisions is The single-sided thick rectangular cross-section of the differential excitation coil is discretized radially and axially as follows: The system generates a micro-mesh and extracts the geometric center coordinates of each micro-mesh.

[0013] Preferably, in step S3, the process of calculating the high-precision spatial magnetic field distribution of a single-sided excitation coil includes:

[0014] By traversing the micro-element mesh of the solid coil spatial micro-element model, the magnetic field component generated by each micro-element mesh at the observation point in the target space is calculated using complete elliptic integral. The magnetic field components of all micro-element meshes are vector-superimposed to obtain the high-precision spatial magnetic field distribution of a single-sided excitation coil.

[0015] Furthermore, the formula for calculating the magnetic field component generated by each micro-grid element at the observation point in the target space is expressed as:

[0016]

[0017] in, This represents the observation point of the infinitesimal mesh in the target space. The generated magnetic field components, This represents the equivalent magnetic field coefficient of the infinitesimal element. Indicates the excitation current. Indicates the number of micro-element meshes. Indicates the first The first kind of complete elliptic integral of a infinitesimal mesh. Indicates the first The second kind of complete elliptic integral of a infinitesimal grid; Indicates the first The modulus of a complete elliptic integral of a infinitesimal mesh is expressed in Cartesian coordinates as follows:

[0018]

[0019] in, The coordinates of the spatial observation point, Indicates the first The radial center coordinates of each infinitesimal grid element. Indicates the first The axial center coordinates of a micro-element mesh;

[0020] When the observation point in the target space is located within the smallest neighborhood of the central axis of the micro-element grid, the calculation is automatically switched to the analytical formula of the magnetic field of the circular coil axis.

[0021] Preferably, in step S4, the formula for calculating the total excitation magnetic field distribution of the differential excitation coil is expressed as:

[0022]

[0023] in, Indicates the total excitation magnetic field strength. This indicates the magnetic field strength of the left excitation coil. This indicates the magnetic field strength of the excitation coil on the right. Represents the coordinates of a spatial observation point. Indicates the first The radial center coordinates of each infinitesimal grid element. Indicates the first The axial center coordinates of a micro-element mesh. Indicates the first The radial center coordinates of each infinitesimal grid element. Indicates the first The axial center coordinates of a micro-element mesh.

[0024] Preferably, in step S4, the process of constructing the first objective function and the second objective function based on the total excitation magnetic field distribution includes:

[0025] Based on the total excitation magnetic field distribution, the plane containing the maximum absolute value of the total excitation magnetic field is taken as the target cross section; the wall thickness boundary of the actual oil pipe is set, and multiple radial test points are extracted from the center of the target cross section to the pipe wall. A first objective function and a second objective function are established based on the magnetic field distribution of these multiple radial test points; the first objective function and the second objective function are expressed as follows:

[0026]

[0027]

[0028] in, The objective function representing the radial uniformity of the magnetic field distribution is... The objective function representing the absolute peak intensity of the magnetic field is... This indicates the number of discrete test points. Indicates the first The absolute value of the axial magnetic flux density at each test point It represents the absolute peak intensity of the average magnetic field.

[0029] Preferably, in step S5, the first objective function and the second objective function are solved using a non-dominated sorting genetic algorithm. A fixed random seed mechanism is introduced in the process of solving the objective function to ensure the stability and reproducibility of the Pareto front solution set output, and to output the optimal differential excitation coil structure parameters.

[0030] The beneficial effects of this invention are as follows:

[0031] Compared with existing technologies, this invention abandons the traditional coarse approximation model and constructs a solid coil discretized infinitesimal element model combined with a complete elliptic integral. This eliminates the computational truncation error in the near-field region from a physical level, providing a high-fidelity analytical model for magnetic field evaluation. Based on this, addressing the mutual constraints between the "spatial uniformity" and "magnetic field strength" of the excitation magnetic field, this invention establishes a dual-objective evaluation function and employs a multi-objective optimization algorithm for global optimization, intuitively revealing the physical trade-offs between performance indicators. Simultaneously, the optimization framework incorporates manufacturing constraints such as the actual enameled wire diameter and the physical fill rate of the winding, ensuring the manufacturability and engineering application value of the output structural parameters from the source. Compared to computationally time-consuming finite element numerical simulations and "black box" optimization algorithms that lack insight into patterns, the purely analytical optimization framework of this invention not only reduces time costs but also clearly reveals the physical relationship between structural deformation and performance leaps, providing efficient and reliable technical support for the customized development of high-performance electromagnetic sensors. This invention can reduce the calculation error of the near-field magnetic field, improve computational efficiency, and, combined with actual engineering processing constraints, achieve multi-objective optimization of the uniformity and absolute strength of the excitation magnetic field, thereby improving the design accuracy and engineering practicality of abrasive sensors. Attached Figure Description

[0032] Figure 1 This is a flowchart of the multi-objective optimization method for the structural parameters of the differential excitation coil in this invention;

[0033] Figure 2 This is a schematic diagram of the discretized spatial element model of the differential coil cross section in this invention;

[0034] Figure 3 This is a comparison diagram of the axial and radial non-uniformity of the differential excitation magnetic field with different structural parameters of the coil in a preferred embodiment of the present invention;

[0035] Figure 4 This is a two-dimensional Pareto front scatter plot of radial non-uniformity of the excitation magnetic field and absolute peak magnetic field intensity output by the multi-objective optimization algorithm in a preferred embodiment of the present invention.

[0036] Figure 5 This is a three-dimensional physical coupling diagram showing the relationship between coil structure dimensional parameters and multi-objective performance in a preferred embodiment of the present invention;

[0037] Figure 6 This is a comparison diagram of the theoretical magnetic field distribution of a set of structural parameters and ANSYS simulation in a preferred embodiment of the present invention. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] This invention proposes a multi-objective optimization method for the structural parameters of a differential excitation coil, such as... Figure 1 As shown, the method includes the following:

[0040] S1: Set the range of structural parameters of the differential excitation coil to be optimized and the actual engineering constraints.

[0041] In some preferred embodiments of the present invention, the differential excitation coil for an inductive abrasive sensor is optimized. A set of macroscopic geometric parameters to be optimized, i.e., a range of differential excitation coil structural parameters, is set. ,in The inner diameter of the coil. The outer diameter of the coil. This refers to the axial length of a single-sided excitation coil. The distance between the inner sides of the two symmetrical differential excitation coils is denoted as .

[0042] To ensure the manufacturability of the purely theoretical optimization solution in a real workshop, this embodiment introduces engineering manufacturing constraints. The physical diameter of the standard enameled wire used to wind the coil is set to be... The physical fill rate of the coil winding Based on this constraint, the effective total number of turns of a single-sided excitation coil is... Strictly defined as:

[0043]

[0044] This constraint restricts the algorithm from using spurious extreme structural parameter combinations that cannot be circumvented in practical engineering situations during optimization.

[0045] S2: Construct a spatial micro-element model of a thick coil.

[0046] Based on the induction detection mechanism, an optimization criterion for magnetic field uniformity is established, and a micro-element model of a thick coil is constructed. Specifically:

[0047] Based on the fundamental principles of electromagnetic induction, when metal abrasive particles pass through the internal flow channel of the sensor, they are magnetized and exhibit eddy current effects under the influence of an external time-harmonic alternating magnetic field. This disturbs the original magnetic flux and induces a voltage. Assuming the induction coil is centered on the axis, and the abrasive particles move along... If the axis moves uniformly, the induced voltage signal can be expressed as:

[0048]

[0049] in, Indicates the total number of turns of the induction coil. Represents the changing vector magnetic potential. express Axial unit vector, This represents the cross-sectional area of ​​the induction coil. Indicates the volume of worn abrasive particles. This represents the magnetic coefficient determined by the physical parameters of the abrasive particles (such as radius, relative permeability, and permeability). Indicates the intensity of the excitation magnetic field. and These represent the position vector of any field point and the particle center, respectively.

[0050] Since the physical parameters of the abrasive grains remain constant, and their velocity can be considered uniformly distributed during the extremely short time they pass through the sensor, and considering that sensors typically have a symmetrical structure, and the abrasive grains move along... Since the abrasive grains move along the axial direction, the voltage signal generated by them at any given moment can be considered to depend primarily on their radial position. Therefore, although it is difficult to determine the trajectory of the abrasive grains in a real-world environment, improving the uniformity of the radial distribution of the excitation magnetic field can effectively reduce the impact of radial position variations on the consistency of the detection results.

[0051] Construct a thick coil micro-element model, specifically:

[0052] To achieve high-precision calculation of the near-field magnetic field distribution, this invention abandons the approximate model of thin-walled coils, which has significant errors. Under ideal conditions, the current elements in the coil are uniformly distributed, and the frequency of the input current is typically in the range of 50-100kHz. Under these conditions, the size of the coil system is much smaller than the electromagnetic wavelength; therefore, the entire system can be considered quasi-static. Based on this, the winding can be equivalent to a stack of multiple thin coils. By regularly dividing the coil into... A tightly stacked fine coil, specifically, such as Figure 2 As shown, the radial division number is set to... The number of axial divisions is The single-sided thick rectangular cross-section of the differential excitation coil is discretized radially and axially as follows: A micro-mesh is generated, and the geometric center coordinates (radial center coordinates) of each micro-mesh are extracted. and axial center coordinates The divided coil can be represented as:

[0053] ,

[0054] in, This indicates the position of the left end of the coil. This indicates the position of the right end of the coil. Indicates the axial thickness of the micro-element. Indicates the radial element thickness. and They represent the first The axial center coordinates and radial center coordinates of each micro-element mesh.

[0055] S3: Calculate the high-precision spatial magnetic field distribution of a single-sided excitation coil based on the spatial micro-element model of the thick coil.

[0056] Based on the Biot-Savart law and infinitesimal Taylor expansion, a high-fidelity spatial analytical magnetic field of a single-sided coil is derived, specifically:

[0057] In cylindrical coordinates, the magnetic induction produced by a monopole Defined as According to the Biot-Savart law, the magnetic field generated by a current element is:

[0058]

[0059] in, Represents the permeability of free space. Indicates the excitation current. Represents the source point cylindrical coordinates. This represents the relative azimuth angle between the source point and the field point. The magnetic field strength at that point is expressed as:

[0060]

[0061] in, This indicates the density intensity of the excitation coil.

[0062] Under the quasi-static field approximation, the magnetic induction intensity generated by a single-sided coil at any observation point in space can be obtained by integral of infinitesimal elements. Quantity in The integral over the range is 0, therefore The effective component is:

[0063]

[0064] In these equations, This represents a first-kind elliptic integral. This represents a complete elliptic integral of the second kind. Furthermore, ,

[0065] Represents the coordinate field function. Represents the modulus of the complete elliptic integral.

[0066] Since the wear particles move in the same direction as the oil, only the following needs to be considered. The axial components, based on the infinitesimal model established by S2, traverse the infinitesimal mesh and calculate the magnetic field components generated by each infinitesimal mesh at the observation point in the target space using complete elliptic integrals. Then, the magnetic field components of all infinitesimal meshes are vector-superimposed.

[0067]

[0068] in, Because the integration process and and These two variables are irrelevant and have been omitted. For the... A thin coil, the integration interval of the first-order term is symmetrical. Therefore: and Through the At point against and Performing a bivariate Taylor expansion, we obtain:

[0069]

[0070] in, This represents a second-order term.

[0071] Under these conditions, the approximate error determined by the coil thickness parameter starts from the second-order term, and the standard error function can be defined as follows: and The entire error can be further expressed as: When the coil thickness parameter and When it is small enough, we can assume and ,then and At the same time, due to the field With source At sufficiently large distances, the near-field effect-induced approximate failure can be ignored. Therefore, higher-order errors dominated by second-order terms can be approximately ignored. Furthermore, there is... Under the approximate condition of stacked thin coils, coil 1's No. The expression for each component can be represented as: ,but It can be approximated as:

[0072]

[0073] because Therefore, the magnetic flux density The components can ultimately be represented as:

[0074]

[0075] in, This represents the equivalent magnetic field coefficient of the infinitesimal element. , , Indicates the excitation current. This represents a first-kind elliptic integral. This represents a complete elliptic integral of the second kind. The modulus of a complete elliptic integral is expressed in Cartesian coordinates as follows:

[0076]

[0077] in, The coordinates of the spatial observation point, For the first The radial center coordinates of each infinitesimal grid element. For the first The axial center coordinates of a micro-element mesh.

[0078] In the high-precision magnetic field calculation model of this invention, to solve the nonlinear magnetic field generated by a single micro-grid in space, a first-type and a second-type complete elliptic integral are introduced. The parameters are... Let be the modulus of the complete elliptic integral. This modulus, as a dimensionless spatial coupling coefficient, physically characterizes the relative position and geometric approximation of the target spatial observation point and the center of the field source micro-grid in three-dimensional space. By establishing this modulus, this invention successfully reduces the complexity of three-dimensional spatial integration to a standard numerical calculation, thereby significantly improving the iterative optimization efficiency of subsequent multi-objective optimization algorithms while ensuring high fidelity in near-field magnetic field distribution calculation.

[0079] Specifically, when calculating the magnetic field components of the micro-element mesh, this invention introduces an axis singularity protection mechanism. Specifically, when the target spatial observation point is located within the minimum neighborhood of the central axis of the micro-element mesh (i.e., ... When this happens, the algorithm automatically switches to the analytical formula for the magnetic field along the axis of a standard circular coil: This avoids the division-to-zero divergence of the elliptic integral matrix caused by the denominator approaching zero, thus ensuring the absolute stability and continuity of the global spatial magnetic field assessment.

[0080] S4: Calculate the total excitation magnetic field distribution of the differential excitation coil based on the high-precision spatial magnetic field distribution of the single-sided excitation coil; construct a first objective function to characterize the radial distribution uniformity of the magnetic field and a second objective function to characterize the magnetic field strength based on the total excitation magnetic field distribution.

[0081] From step S3, the magnetic induction intensity of coil 2 can be obtained. Combined with the magnetic induction intensity of coil 1, the magnetic induction intensity of the differential excitation coil, i.e., the total excitation magnetic field distribution of the differential excitation coil, can be obtained.

[0082]

[0083] in, Indicates the total excitation magnetic field strength. This indicates the magnetic field strength of the left excitation coil. This indicates the magnetic field strength of the excitation coil on the right. The parameter order of coil 2.

[0084] like Figure 3 As shown, the total excitation magnetic field at the symmetry center plane of the dual coils strictly cancels out to zero, while positive and negative magnetic field peak planes are formed in the internal regions of the two coils respectively. Furthermore, due to the different coil structures, the generated magnetic field strength varies radially, causing radial magnetic field inhomogeneity. Simultaneously, because the differential coil structure and its excited magnetic field possess strict spatial symmetry (i.e., the absolute values ​​and radial distribution of the magnetic fields on both peak planes are completely identical), this embodiment employs a single-sided peak-finding acceleration strategy based on physical symmetry to significantly reduce computational redundancy in the multi-objective optimization iteration process.

[0085] Specifically: Using only the physical boundary of a single-sided coil (e.g., the right-side coil) as a reference, the axial scanning range is set to encompass the edge effect of that coil (i.e., the scanning range is set as...). To balance peak capture accuracy and iterative calculation efficiency, multiple discrete scanning points (preferably 41 in this embodiment) are set along the axis within this range. The plane containing the maximum absolute value of the total excitation magnetic field is calculated and locked as the target evaluation section. Next, the wall thickness boundary of the actual oil pipe is set. Within this target evaluation section, the wall thickness is uniformly extracted radially from the center of the flow channel to the inner wall of the oil pipe. Discrete test points (preferred in this embodiment) ), and record the first Absolute value of axial magnetic induction intensity at each test point Finally, a multi-objective function was established based on the magnetic field distribution data of the aforementioned radial test point group. :

[0086] Establish a first objective function to characterize the radial uniformity of the magnetic field distribution:

[0087]

[0088] Establish a second objective function to characterize the absolute peak intensity of the magnetic field:

[0089]

[0090] in, The objective function representing the radial uniformity of the magnetic field distribution is... The objective function representing the absolute peak intensity of the magnetic field is... This indicates the number of discrete test points. Indicates the first The absolute value of the axial magnetic flux density at each test point It represents the absolute peak intensity of the average magnetic field.

[0091] S5: Solve the first objective function and the second objective function based on the actual engineering constraints to obtain the structural parameters of the differential excitation coil.

[0092] The first objective function is the relative standard deviation of the absolute magnetic field strength at multiple radial test points. The multi-objective optimization algorithm optimizes the magnetic field uniformity by minimizing this relative standard deviation. The second objective function is the average value of the magnetic field strength at the multiple radial test points. The multi-objective optimization algorithm optimizes the absolute peak magnetic field strength by maximizing this average value.

[0093] The physical search boundary of the decision variables set in step S1. In step S4, the first objective function and the second objective function are optimization-oriented. In some preferred embodiments of the present invention, a fast non-dominated sorting genetic algorithm (NSGA-II) with an elite retention strategy is preferably used as a multi-objective optimization algorithm to perform global optimization, generate a Pareto front solution set that reflects the balance between magnetic field uniformity and signal strength, and output the optimal differential excitation coil structure parameters.

[0094] In practice, the structural parameters are set within a limited range. , , , The unit is mm, the tube wall is 0.5 mm, and the excitation current is 1 A. During the iterative optimization process, the algorithm is strictly constrained by physical manufacturing constraints such as the effective wire filling rate. The effective wire filling rate is usually set in the range of 0.60 to 0.85 according to the winding process accuracy. To balance the high-precision alignment and winding process with the loss of the insulating varnish film, the preferred filling rate is 0.75. This constraint ensures that the dimensional parameters of the optimized output can meet the physical manufacturability of the actual workshop, and the constraint of the effective total number of turns of the single-sided excitation coil avoids the pure mathematical optimization from falling into false extreme values ​​where the theoretical number of turns cannot be physically realized. The control parameters of the genetic algorithm are initialized (in this embodiment, the population size is preferably set to 300 and the maximum number of generations is 200). At the same time, the radial non-uniformity error is minimized. And maximize the peak magnetic field strength (Internally, this is converted to finding the minimum value) as the fitness evaluation criterion, and the population is continuously evolved through crossover, mutation, and non-dominated sorting operators.

[0095] Under these constrained parameters, after optimization convergence, the algorithm outputs a set of non-dominated Pareto front optimal solutions (e.g., Figure 4 As shown). Extreme pursuit of uniformity: R I =2.51mm, R O =5.03mm, L z=9.98mm, D=8.68mm, radial non-uniformity error 0.9185%, peak magnetic field strength 47.15mT. It was found that by sacrificing only a small amount of uniformity, the peak magnetic field strength can be significantly increased to nearly 110mT. Furthermore, deep data mining of the Pareto front solution set output by the multi-objective optimization algorithm revealed that the optimization model exhibits a typical "non-uniqueness" (i.e., many-to-one mapping) physical characteristic in the inverse electromagnetic problem. In practical implementation, for a selected extreme electromagnetic performance target point on the Pareto front curve (e.g., a specific comprehensive performance point satisfying extremely low radial non-uniformity error and extremely high absolute peak magnetic field), the optimization framework of this invention can output multiple sets of coil physical size combinations with structural differences but equivalent electromagnetic performance in parallel. For example, there are the same performance target points for long flat coil combinations and short tall coil combinations, and both exhibit a high degree of size compensation and performance consistency in the core magnetic field evaluation index. Based on this feature, this invention provides designers with significant engineering design margins in practical engineering implementation. When extracting the final manufacturing dimensions, designers can use external physical assembly constraints as a secondary screening boundary: if there are physical barriers to the radial space dimensions of the target sensor installation environment, the sensor can be selected from the above equivalent parameter combinations for processing.

[0096] Multidimensional feature extraction and physical coupling analysis of the optimal solution set of the Pareto front (e.g.) Figure 5 As shown), there is a strong trade-off between structural parameters and multi-objective performance: during the optimization process, the inner diameter... With length Rapid convergence approaches the physical boundary limit; while the outer diameter Spacing with the inner side This exhibits a very clear gradient evolution, becoming a core sensitive parameter that dominates performance. With... Expanding from the lower limit (e.g., 5.0 mm) to the upper limit (e.g., 10.0 mm), due to the dispersion effect of the spatial magnetic field excited by the thick coil, the system has reached the uniformity limit under this specific spatial size constraint. Further increasing uniformity (to the left), the radial non-uniformity error of the sensor... Deterioration is inevitable, with the central peak magnetic field strength... It achieved leapfrog growth. For example... Figure 6 As shown, the calculated fit evaluation index, Rfit 2 =0.9931. The theoretical analytical model and the finite element simulation results are highly consistent in terms of spatial distribution and extreme point location, but there is a certain deviation in absolute amplitude, RMSE=1.42mT. This is due to reasonable errors caused by simulation condition settings and mesh generation. In actual engineering optimization, this analytical model has sufficient relative accuracy to guide structural parameter optimization and selection.

[0097] Ultimately, designers no longer need to rely on experience to trial and error in parameter setting. They can directly select the optimal compromise parameters (e.g., a parameter set that balances extremely low error and a moderate magnetic field) from the Pareto front solution set based on the constraints in actual engineering and the preferred weights for "target signal sensitivity" and "magnetic field radial uniformity." This optimal parameter is then output as the final manufacturing dimensions of the differential excitation coil, thus completing the customized design of the sensor. The differential excitation coil manufactured based on these final dimensions can effectively reduce the "trajectory sensitivity" interference caused by radial position from a physical source, thereby improving the quantitative detection accuracy and operational reliability of the sensor.

[0098] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-objective optimization method for the structural parameters of a differential excitation coil, characterized in that, Includes the following steps: S1: Set the range of structural parameters of the differential excitation coil to be optimized and the actual engineering constraints; S2: Construct a spatial micro-element model of a thick coil; S3: Calculate the high-precision spatial magnetic field distribution of a single-sided excitation coil based on the spatial micro-element model of the thick coil; S4: Calculate the total excitation magnetic field distribution of the differential excitation coil based on the high-precision spatial magnetic field distribution of the single-sided excitation coil; construct a first objective function to characterize the radial distribution uniformity of the magnetic field and a second objective function to characterize the magnetic field strength based on the total excitation magnetic field distribution; S5: Solve the first objective function and the second objective function based on the actual engineering constraints to obtain the structural parameters of the differential excitation coil.

2. The multi-objective optimization method for the structural parameters of a differential excitation coil according to claim 1, characterized in that, In step S1, the range of structural parameters of the differential excitation coil is expressed as follows: ,in The inner diameter of the coil. The outer diameter of the coil. This refers to the axial length of a single-sided excitation coil. The distance between the inner sides of the two symmetrical differential excitation coils is denoted as ... denoted deno denoted deno denoted deno denoted deno denoted deno deno denoted deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno deno 3. The multi-objective optimization method for the structural parameters of a differential excitation coil according to claim 1, characterized in that, Step S2 specifically includes: setting the number of radial divisions as... The number of axial divisions is The single-sided thick rectangular cross-section of the differential excitation coil is discretized radially and axially as follows: The system generates a micro-mesh and extracts the geometric center coordinates of each micro-mesh.

4. The multi-objective optimization method for the structural parameters of a differential excitation coil according to claim 1, characterized in that, In step S3, the process of calculating the high-precision spatial magnetic field distribution of a single-sided excitation coil includes: By traversing the micro-element mesh of the solid coil spatial micro-element model, the magnetic field component generated by each micro-element mesh at the observation point in the target space is calculated using complete elliptic integral. The magnetic field components of all micro-element meshes are vector-superimposed to obtain the high-precision spatial magnetic field distribution of a single-sided excitation coil.

5. The multi-objective optimization method for the structural parameters of a differential excitation coil according to claim 4, characterized in that, The formula for calculating the magnetic field component generated by each micro-grid element at the observation point in the target space is expressed as: ； in, Represents the observation point of the infinitesimal mesh in the target space. The generated magnetic field components, This represents the equivalent magnetic field coefficient of the infinitesimal element. Indicates the excitation current. Indicates the number of micro-element meshes. Indicates the first The first kind of complete elliptic integral of a infinitesimal mesh. Indicates the first The second kind of complete elliptic integral of a infinitesimal grid; Indicates the first The modulus of a complete elliptic integral of a infinitesimal mesh is expressed in Cartesian coordinates as follows: ； in, The coordinates of the spatial observation point, Indicates the first The radial center coordinates of each infinitesimal grid element. Indicates the first The axial center coordinates of a micro-element mesh; When the observation point in the target space is located within the smallest neighborhood of the central axis of the micro-element grid, the calculation is automatically switched to the analytical formula of the magnetic field of the circular coil axis.

6. The multi-objective optimization method for the structural parameters of a differential excitation coil according to claim 1, characterized in that, In step S4, the formula for calculating the total excitation magnetic field distribution of the differential excitation coil is expressed as: ； in, Indicates the total excitation magnetic field strength. This indicates the magnetic field strength of the left excitation coil. This indicates the magnetic field strength of the excitation coil on the right. Represents the coordinates of a spatial observation point. Indicates the first The radial center coordinates of each infinitesimal grid element. Indicates the first The axial center coordinates of a micro-element mesh. Indicates the first The radial center coordinates of each infinitesimal grid element. Indicates the first The axial center coordinates of a micro-element mesh.

7. The multi-objective optimization method for the structural parameters of a differential excitation coil according to claim 1, characterized in that, In step S4, the process of constructing the first objective function and the second objective function based on the total excitation magnetic field distribution includes: Based on the total excitation magnetic field distribution, the plane containing the maximum absolute value of the total excitation magnetic field is taken as the target cross section; the wall thickness boundary of the actual oil pipe is set, and multiple radial test points are extracted from the center of the target cross section to the pipe wall. A first objective function and a second objective function are established based on the magnetic field distribution of these multiple radial test points; the first objective function and the second objective function are expressed as follows: ； ； in, The objective function representing the radial uniformity of the magnetic field distribution is... The objective function representing the absolute peak intensity of the magnetic field is... This indicates the number of discrete test points. Indicates the first The absolute value of the axial magnetic flux density at each test point It represents the absolute peak intensity of the average magnetic field.

8. The multi-objective optimization method for the structural parameters of a differential excitation coil according to claim 1, characterized in that, In step S5, the first objective function and the second objective function are solved using a non-dominated sorting genetic algorithm. A fixed random seed mechanism is introduced in the process of solving the objective function to ensure the stability and reproducibility of the Pareto front solution set output, and to output the optimal differential excitation coil structure parameters.

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