Large-size high-uniformity coil design method based on adaptive PSOGWO fusion optimization

Abstract

The invention discloses a large-size high-uniformity coil design method based on adaptive PSOGWO fusion optimization, and the method comprises the steps: carrying out the Taylor expansion of a central magnetic field, and converting the solving of the axial position of a coil into a multivariable nonlinear optimization problem; and under geometric and unified manufacturing constraints, a self-adaptive PSOGWO fusion optimization algorithm is provided to obtain the optimal axial position of each pair of coils. According to the algorithm, particle swarm global exploration and grey wolf hunting type local mining are combined, and adaptive factors and weight proportions are introduced, so that the search precision and robustness in a complex multi-peak problem are improved, and the convergence stability and the local extremum resistance of the algorithm are improved. Under the background of a large-size coil, the uniform interval and the center uniformity of the coil designed by the novel optimization algorithm are obviously superior to those of a traditional coil and a coil designed by a single intelligent algorithm. The design method is suitable for scenes of SERF atom magnetometer compensation / modulation coils and the like, and can be used in cooperation with a multi-channel measurement scheme to improve the spatial resolution.

Description

TECHNICAL FIELD

[0001] The application relates to a large-size high-uniformity coil design method based on adaptive PSOGWO fusion optimization, belongs to the technical field of magnetic field generation and compensation, and can be used for providing a high-uniformity magnetic field working environment in an atomic magnetometer, and is favorable for improving the response amplitude, signal-to-noise ratio and measurement sensitivity of the atomic magnetometer. BACKGROUND

[0002] With the development of optical pumping technology, a spin-exchange relaxation-free (SERF) atomic magnetometer has become an important research direction and mainstream device for low-frequency ultra-high sensitivity magnetic field measurement. In recent years, the sensitivity of such sensors in the low-frequency band has been significantly improved, and the expected performance is expected to further approach orders of magnitude. Compared with traditional SQUID magnetometers (SQUID, superconducting quantum interference device), the SERF scheme does not need to rely on a complex liquid nitrogen refrigeration system and has a lower operation and maintenance cost, and is more suitable for engineering deployment. At the same time, benefiting from the characteristics of easy miniaturization, wearability and portability of the device, it has been widely used in dynamic measurement of biomagnetic signals such as magnetoencephalography, magnetocardiography and muscle magnetic field.

[0003] With the development of atomic sensing technology, SERF atomic magnetometers and other ultra-high sensitivity devices have put forward more stringent requirements for large-space high-uniformity magnetic fields. Existing engineering practices usually rely on magnetic shielding and compensation coils to obtain the target magnetic field, but the intrinsic performance of the magnetic shielding material and the structure coupling limit the compensation effect, and higher field uniformity and longer uniformity interval still need to be obtained on the coil system side. Traditional Helmholtz, Lee-Whiting, saddle and Rogowski coils have deficiencies in the uniformity length, adaptability to large-size cavities and integrability of arrayed systems. Simply increasing the number of coils to improve uniformity will significantly increase the design difficulty and assembly complexity, and is not conducive to heat dissipation and cost.

[0004] On the existing coil design method, the target field / inverse method and the positive method based on Biot-Savart law have their own limitations: the former needs to first calculate the current density and then land on discrete coils, and the calculation chain is long and the compatibility with mechanical boundaries is poor; the latter can perform Taylor expansion in the central region to suppress low-order non-uniform terms, but it is difficult to analytically close in the high-order case, and when the number of coils increases and multiple constraints such as light transmission holes, minimum spacing, and skeleton size are introduced, a multi-variable strongly nonlinear parameter solving problem is easily formed. Such problems have a large number of local extrema, and are highly sensitive to initial values, boundaries and search strategies, resulting in a deviation between "theoretical optimal" and "manufacturable optimal". Therefore, in order to solve the multi-variable nonlinear optimization problem, an intelligent optimization algorithm is introduced for coil design, but the current single intelligent optimization algorithm is prone to local optimization when designing large-size coils, resulting in poor optimization results and low uniformity.

[0005] In summary, for large-size, high-uniformity and engineering manufacturability coil systems, there are currently: traditional coils are difficult to maintain long uniformity under large size and multiple constraint conditions; analytical design is not suitable for high-order and multiple coils, and parameter solving is strongly nonlinear; the optimization effect of single intelligent optimization algorithm is not good. The existing scheme cannot meet the application requirements of high-uniformity magnetic field under large-size application background, and a design route that can complete multi-variable nonlinear optimization under unified geometric and engineering constraints and consider manufacturing and testing processes is urgently needed. SUMMARY

[0006] The purpose of the present application is to overcome the shortcomings of the prior art, and to provide a large-size high-uniformity coil design method based on adaptive PSOGWO fusion optimization, which is beneficial to obtaining a longer uniformity interval and a flatter central magnetic field distribution under the engineering constraints of large size, as few coil pairs as possible and manufacturability, while shortening the design-prototyping-calibration cycle, considering manufacturing feasibility and experimental repeatability, and being suitable for atomic magnetometers and other scenes with rigid requirements for weak magnetic field high uniformity.

[0007] The technical solution of the present application is as follows:

[0008] The large-size high-uniformity coil design method based on adaptive PSOGWO fusion optimization comprises the following steps:

[0009] Step 1, under the cylindrical symmetric multi-pair coil topology, based on the magnetic field model of the bipolar symmetric cylindrical coil system, the axial magnetic field, i.e. the Z-axis magnetic field, is calculated according to the Biot-Savart law, and Taylor expansion is performed at z=0, a layered weighted objective function is established, and a relative uniformity threshold is set;

[0010] Step 2, set geometric-technological constraints including symmetry, minimum spacing, upper and lower limits, skeleton radius, number of coil pairs N and number of turns, using unit current method to normalize magnetic field, ensure different schemes are comparable under the same electromagnetic reference;

[0011] Step 3, search for optimal solution of axial position using adaptive PSOGWO fusion optimization algorithm, initialize population and calculate fitness after coil configuration, the algorithm fuses particle swarm speed-position update and grey wolf leadership hunting update according to adaptive coefficient in each iteration, and adjusts inertia weight and learning factor according to fitness;

[0012] Step 4, realize coil entity on the outer surface of the cylindrical skeleton using flexible printed circuit (FPC) technology, build AC modulation-PLL demodulation platform, assemble and correct the prototype or fine-tune the weight according to the measured results until the engineering application requirements are met.

[0013] Step 1 includes the following expressions:

[0014]

[0015]

[0016]

[0017]

[0018] Where ε(z) is the relative uniformity, B z (z) is the Taylor expansion of Z-axis magnetic field Bz at z=0, B z (0) is the Z-axis magnetic field at z=0, B0 is the initial term, k is the serial number, K is the Taylor expansion order, 2k is the even order, f is the hierarchical weighted objective function, j is the serial number, M is the number of layers, B z (Z) is the magnetic field generated by multiple pairs of coils in the central region of Z-axis direction, μ0 is the vacuum permeability, i is the current of each coil, R is the coil radius, N is the number of symmetrically distributed coils, n i is the number of turns, z' is the intermediate quantity, z is the z-axis coordinate value, d i ' is the intermediate quantity, d i is the position of the i-th coil on the Z-axis.

[0019] Step 2 includes the following expressions:

[0020]

[0021] Where d min is the minimum value of the coil on the Z-axis, d max is the maximum value of the coil on the Z-axis.

[0022] Step 3 includes the following expression:

[0023]

[0024]

[0025] Where X(t+1) is the overall iteration position, t is the iteration number, and λ(t) is the adaptive weight coefficient. GWO (t+1) is the position of the (t+1)th GWO iteration, X PSO (t+1) is the PSO iteration position at the (t+1)th iteration, ω(t) is the adaptive inertia weight, X(t) is the current position, c1(t) and c2(t) are both adaptive learning factors, r1' and r2' are both PSO random vectors, and p i g is the individual historical optimum of the PSO, g is the population optimum of the PSO, and ω is the PSO population optimum. max It is the preset maximum weight, ω min It is the preset minimum weight, T is the maximum number of iterations, and c1 max c2 max All are the preset maximum values ​​of the adaptive learning factor, c1 min c2 min All are preset minimum values ​​of the adaptive learning factor.

[0026] Step 4 includes scanning along the axial direction at fixed intervals to obtain the magnetic field profile, converting it into the measured curve of relative uniformity, and calibrating the coil constant through B–I linear fitting at multiple current points, where B is the magnetic field and I is the current.

[0027] Adaptive PSOGWO fusion optimization is adopted to suppress the central even-order non-uniform term and smooth the boundary field gradient under engineering constraints such as large-size geometric requirements and finite number of coil pairs. This significantly expands the axial uniform region and makes the central magnetic field distribution flatter, which is beneficial to improving the response amplitude, signal-to-noise ratio and measurement sensitivity of the atomic magnetometer.

[0028] By integrating global particle swarm optimization (PSO) with local mining by multiple leaders of gray wolves, and adaptively adjusting the inertia weight, learning factor, and scaling factor based on population diversity, this algorithm achieves higher optimization efficiency and convergence stability compared to single PSO or GWO algorithms. It can reduce parameter trial and error and prototype iterations, shorten the design cycle, and reduce debugging costs.

[0029] The coils are arranged symmetrically along the axis and have standardized positional constraints, which makes them robust to manufacturing and assembly tolerances. Under common conditions of small axis deviations and small spacing errors, the flatness of the uniform area and the central field remains stable, which is beneficial for large-scale production and long-term reliable operation.

[0030] For large-scale applications such as compensation or modulation coils of SERF atomic magnetometers, large-diameter magnetometer cavities, and multi-channel measurement systems, it can achieve stable uniformity evaluation and coil calibration under normal experimental conditions by combining AC modulation-phase-locked demodulation measurement, which is convenient for field integration and maintenance.

[0031] The technical effects of this invention are as follows: This invention is based on an adaptive PSOGWO fusion optimization method for designing large-size, highly uniform coils. By performing a Taylor expansion on the central magnetic field, the solution for the axial position of the coil is transformed into a multivariable nonlinear optimization problem. Under geometric and unified manufacturing constraints, an adaptive PSOGWO (Particle Swarm Optimization–Grey Wolf Optimizer) fusion optimization algorithm is proposed to obtain the optimal axial position of each pair of coils. The algorithm combines global particle swarm exploration with grey wolf-style local mining and introduces adaptive factors and weight ratios to improve the accuracy and robustness of the search in complex multi-peak problems, which helps to improve the convergence stability and resistance to local extrema of the algorithm. In the context of large-size coils, the uniformity of the coils designed by the novel optimization algorithm is significantly better than that of traditional coils and coils designed by a single intelligent algorithm. This design method is applicable to scenarios such as SERF atomic magnetometer compensation / modulation coils and can be used in conjunction with multi-channel measurement schemes to improve spatial resolution. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating the design method for large-size, highly uniform coils based on adaptive PSOGWO fusion optimization, as described in this invention. PSOGWO stands for Particle Swarm Optimization – Grey Wolf Optimizer (PSO stands for Particle Swarm Optimization, and GWO stands for Grey Wolf Optimizer). Figure 1The process includes: Step 1: Under a cylindrical symmetric multi-coil topology, based on the magnetic field model of the bipolar symmetric cylindrical coil system, the axial magnetic field (i.e., the Z-axis magnetic field) is calculated according to the Biot-Savart law, and a Taylor expansion is performed at z=0 to establish a hierarchical weighted objective function and set a relative uniformity threshold; Step 2: Using the axial position of each pair of coils as design variables, geometric and technological constraints such as symmetry, minimum spacing, upper and lower limits, skeleton radius, number of coil pairs N, and number of turns are set, and the magnetic field is normalized using the unit current method to ensure that different schemes are comparable under the same electromagnetic reference; Step 3: The adaptive PSOGWO fusion optimization algorithm is used to search for the optimal solution of the axial position, coil configuration, initialize the population, and calculate the fitness. In each iteration, the algorithm integrates particle swarm velocity-position update and gray wolf leadership encirclement update according to the adaptive coefficient, and adaptively adjusts the inertia weight and learning factor according to the fitness; Step 4: The coil entity is realized on the outer surface of the cylindrical skeleton using flexible printed circuit technology, an AC modulation-phase-locked demodulation platform is built, and the prototype is subjected to necessary assembly correction or weight fine-tuning based on the measured results until it meets the engineering application requirements.

[0033] Figure 2 This is a schematic diagram illustrating the principle of the adaptive PSOGWO fusion algorithm in this invention. Figure 2 In this context, C1, C2, and C3 are all GWO random vectors, a1, a2, and a3 are all GWO convergence factors, and α, β, and δ are the three wolves with the best current fitness in the GWO. X GWO (t+1) is the position of the (t+1)th GWO iteration, where t is the iteration number, and D α D β D δ Both are GWO distance vectors, p i The PSO is the individual historical best, λ(t) is the adaptive weight coefficient, prey is the global best position, c1(t) and c2(t) are both adaptive learning factors, r1' and r2' are both PSO random vectors, V is the PSO velocity, ω(t) is the adaptive inertia weight, X(t+1) is the global iteration position, and X... PSO (t+1) is the position of the PSO iteration in the (t+1)th iteration, X(t) is the current position, and g is the PSO population optimum. Detailed Implementation

[0034] The following is in conjunction with the attached diagram ( Figures 1-2 The present invention will be described in conjunction with the examples.

[0035] Figure 1 This is a flowchart illustrating the implementation of the large-size, highly uniform coil design method based on adaptive PSOGWO fusion optimization of the present invention. Figure 2 This is a schematic diagram illustrating the principle of the adaptive PSOGWO fusion algorithm in this invention. (Reference) Figures 1-2As shown, the design method for large-size, highly uniform coils based on adaptive PSOGWO fusion optimization includes the following steps: Step 1, under a cylindrically symmetric multi-pair coil topology, based on the magnetic field model of the bipolar symmetric cylindrical coil system, according to the Biot–Savart... The algorithm calculates the axial magnetic field (Z-axis magnetic field) using the law, performs a Taylor expansion at z=0, establishes a hierarchical weighted objective function, and sets a relative uniformity threshold. Step 2 involves setting geometric-process constraints using the axial position of each pair of coils as design variables. These constraints include symmetry, minimum spacing, upper and lower limits, frame radius, number of coil pairs N, and number of turns. The magnetic field is normalized using the unit current method to ensure comparability of different schemes under the same electromagnetic reference. Step 3 uses an adaptive PSOGWO fusion optimization algorithm to search for the optimal solution for the axial position and coil configuration. After initializing the population and calculating fitness, the algorithm integrates particle swarm velocity-position updates and wolf-led encirclement updates in each iteration using adaptive coefficients, and adaptively adjusts the inertia weight and learning factor based on fitness. Step 4 uses flexible printed circuit (FPC) technology to realize the coil entity on the outer surface of the cylindrical frame, builds an AC modulation-phase-locked demodulation platform, and performs assembly correction or weight fine-tuning on the prototype based on actual measurement results until it meets engineering application requirements.

[0036] Step 1 includes the following expression:

[0037]

[0038]

[0039]

[0040]

[0041] Where ε(z) is the relative uniformity, B z (z) is the Taylor expansion of the Z-axis magnetic field Bz at z=0, B z (0) is the Z-axis magnetic field at z=0, B0 is the initial term, k is the index number, K is the Taylor expansion order, 2k is an even order, f is the layered weighted objective function, j is the index number, M is the layer number, B z (Z) represents the magnetic field generated by multiple pairs of coils along the Z-axis in the central region, μ0 is the free permeability, i is the current in each coil, R is the coil radius, N is the number of symmetrically distributed coils, and n i It is the number of turns, z' is an intermediate quantity, z is the z-axis coordinate value, and d i ' is an intermediate quantity, d i It is the position of the i-th coil on the Z-axis.

[0042] Step 2 includes the following expression:

[0043]

[0044] Where d min It is the minimum value of the coil on the Z-axis, d max It is the maximum value of the coil on the Z-axis.

[0045] Step 3 includes the following expression:

[0046]

[0047]

[0048] Where X(t+1) is the overall iteration position, t is the iteration number, and λ(t) is the adaptive weight coefficient. GWO (t+1) is the position of the (t+1)th GWO iteration, X PSO (t+1) is the PSO iteration position at the (t+1)th iteration, ω(t) is the adaptive inertia weight, X(t) is the current position, c1(t) and c2(t) are both adaptive learning factors, r1' and r2' are both PSO random vectors, and p i g is the individual historical optimum of the PSO, g is the population optimum of the PSO, and ω is the PSO population optimum. max It is the preset maximum weight, ω min It is the preset minimum weight, T is the maximum number of iterations, and c1 max c2 max All are the preset maximum values ​​of the adaptive learning factor, c1 min c2 min All are preset minimum values ​​of the adaptive learning factor.

[0049] Step 4 includes scanning along the axial direction at fixed intervals to obtain the magnetic field profile, converting it into the measured curve of relative uniformity, and calibrating the coil constant through B–I linear fitting at multiple current points, where B is the magnetic field and I is the current.

[0050] The technical solution of this invention is: a design method for large-size, highly uniform coils based on adaptive PSOGWO fusion optimization, the implementation method and steps of which are as follows:

[0051] (1) Based on the magnetic field model of the bipolar symmetric cylindrical coil system, calculate the axial magnetic field according to the Biot-Savart law. And perform a Taylor expansion at z=0 to construct the relative uniformity. ;

[0052] (2) Under geometric constraints Given a fixed number of coil pairs N, establish the objective function. Or its weighted form, to minimize the sum of even-order derivative coefficients in the central region;

[0053] (3) Adaptive PSOGWO fusion optimization algorithm is used for search The optimal solution, where the algorithm adjusts the coefficients adaptively in each iteration. The particle swarm velocity-position update is integrated with the gray wolf α / β / δ leadership and encirclement update, and the inertia weight and learning factor are adaptively adjusted according to the fitness changes.

[0054] (4) The coil entity is constructed on the outer surface of the cylindrical skeleton using flexible printed circuit (FPC) technology, an AC modulation-phase lock demodulation platform is built, the magnetic field profile is obtained by scanning along the axial fixed step distance, the relative uniformity is calculated and the coil constant is calibrated by B-I linear fitting at multiple current points; the prototype is then assembled and corrected or its weights are finely adjusted according to the measured results until the requirements of engineering applications are met.

[0055] Adaptive PSOGWO fusion optimization is adopted to suppress the central even-order non-uniform term and smooth the boundary field gradient under engineering constraints such as large-size geometric requirements and finite number of coil pairs. This significantly expands the axial uniform region and makes the central magnetic field distribution flatter, which is beneficial to improving the response amplitude, signal-to-noise ratio and measurement sensitivity of the atomic magnetometer.

[0056] By integrating global particle swarm optimization (PSO) with local mining by multiple leaders of gray wolves, and adaptively adjusting the inertia weight, learning factor, and scaling factor based on population diversity, this algorithm achieves higher optimization efficiency and convergence stability compared to single PSO or GWO algorithms. It can reduce parameter trial and error and prototype iterations, shorten the design cycle, and reduce debugging costs.

[0057] The coils are arranged symmetrically along the axis and have standardized positional constraints, which makes them robust to manufacturing and assembly tolerances. Under common conditions of small axis deviations and small spacing errors, the flatness of the uniform area and the central field remains stable, which is beneficial for large-scale production and long-term reliable operation.

[0058] The method is applicable to large-scale applications such as SERF atomic magnetometer compensation / modulation coils, large-diameter magnetometer cavities, and multi-channel measurement systems. Under normal experimental conditions, it can be combined with AC modulation-phase-locked demodulation measurement to obtain stable uniformity evaluation and coil calibration, which is convenient for field integration and maintenance.

[0059] A design method for large-size, highly uniform coils based on adaptive PSOGWO fusion optimization is described below, including the following implementation method and steps:

[0060] (1) Model and calibrate the design object. Under the topology of cylindrical symmetric multi-pair coils, calculate the axial magnetic field according to the Biot-Savart law based on the magnetic field model of the bipolar symmetric cylindrical coil system. And perform a Taylor expansion at z=0 to construct the relative uniformity. And set a uniformity threshold. The target working interval is defined. To suppress the central even-order non-uniform term, a hierarchical weighted objective function is established. .

[0061] (2) Based on the axial position of each pair of coils As design variables, geometric and technological constraints such as symmetry, minimum spacing, upper and lower limits, skeleton radius, number of coil pairs N and number of turns are set; the magnetic field is normalized using the unit current method to ensure that different schemes are comparable under the same electromagnetic reference.

[0062] (3) The coil configuration is optimized based on the adaptive PSOGWO fusion optimization algorithm. After initializing the population and calculating the fitness, the PSO and GWO update channels are executed synchronously in each iteration. The PSO generates candidate solutions based on the velocity-position model and uses inertia weights. and individual / social learning factors , An adaptive update mechanism that dynamically adjusts with iterations is adopted to regulate the exploration-convergence balance. GWO follows this principle. The multi-leader encirclement mechanism is locally refined and the leader set is dynamically updated. The results from the two channels are weighted and fused using an adaptive weight coefficient λ(t), while feasible region projection and elite retention are employed to ensure manufacturability and convergence stability. The objective function threshold, uniformity constraint satisfaction, and maximum iteration number are used as stopping criteria. Convergence determination is based on the current optimal... Substitute the magnetic field model back to calculate the uniformity error. If the threshold condition or boundary gradient smoothness requirement is not met, the weights and fusion strategy are adaptively adjusted and iterated until the condition is met.

[0063] (4) The coil body is realized on the outer surface of the cylindrical skeleton using flexible printed circuit (FPC) technology. An AC modulation-phase lock demodulation platform is built. The magnetic field profile is obtained by scanning along the axial fixed step distance. The relative uniformity is calculated and the coil constant is calibrated by B-I linear fitting at multiple current points. Based on the measured results, the prototype is corrected or the weight is fine-tuned until it meets the requirements of engineering application.

[0064] The principle of this invention is as follows:

[0065] Taking multiple pairs of circular coils of the same radius, symmetrically arranged about z=0, as the object, a magnetic field model on the axis is established based on Biot–Savart's law, and the axial position of the coils is determined. The solution is transformed into a nonlinear optimization problem involving the suppression of even-order terms.

[0066] To simplify the formula and enhance the model's applicability to similar coils with different radii, the lengths in the formula are expressed as relative values ​​of the radii. The magnetic field generated by multiple pairs of coils in the central region along the Z-axis can be represented as:

[0067]

[0068] In the formula, N is the number of symmetrically distributed coils. This indicates the position of the i-th coil on the Z-axis. The current in each coil is i, and the number of turns is... .

[0069] Perform a dual-order Taylor expansion at z=0:

[0070]

[0071] Based on this, construct the optimization function:

[0072]

[0073] when At that time, the even-order terms in the central region are close to zero. To achieve the desired uniformity within the target interval. (This is the goal of the solution.) The optimal combination is found by using adaptive PSOGWO fusion optimization as the global optimizer: PSO channel candidate solutions and GWO channel candidate solutions are generated in parallel within a unified population evolution framework, and then adaptive weight coefficients are used to optimize the combination. Fusion of two-channel results:

[0074]

[0075] Unlike traditional fixed-parameter PSO velocity correction, the new algorithm uses inertia weights. and individual / social learning factors , An adaptive update mechanism is adopted, which dynamically adjusts with each iteration.

[0076]

[0077] in, Let T be the velocity vector of the current individual, and T be the maximum number of iterations. This represents the inertia weight, used to adjust the intensity of exploration and development. , These are individual / social learning factors, used to guide particles towards their historical best position and global best position, respectively. In the initial stage, the search space is vast and information is scarce, requiring "large inertia + strong individual term" (…). big, big, (Small) to differentiate populations and cover multimodal peaks and valleys; as the understanding of the solution space gradually accumulates, it gradually switches to "weak inertia + strong social terms" ( Small, Small, (Large), guided by group consensus, it rapidly converges to excellent areas and refines the search. , It is an independently generated random vector, ensuring the randomness of the search process.

[0078] by Threshold, The constraint satisfaction and maximum algebraic sum are used as stopping conditions. This algorithm balances global exploration and local refinement in a multi-peaked, strongly coupled design space, and can obtain the optimal axial arrangement of coils that satisfies the constraints of large-size applications.

[0079] like Figure 1 As shown, the specific implementation steps of the present invention are as follows:

[0080] (1) Model and calibrate the design object. Under the topology of cylindrical symmetric multi-pair coils, calculate the axial magnetic field according to the Biot-Savart law based on the magnetic field model of the bipolar symmetric cylindrical coil system. And perform a Taylor expansion at z=0 to construct the relative uniformity. And set a uniformity threshold. The target working interval is defined. To suppress the central even-order non-uniform term, a hierarchical weighted objective function is established. .

[0081] (2) Based on the axial position of each pair of coils As design variables, geometric and technological constraints such as symmetry, minimum spacing, upper and lower limits, skeleton radius, number of coil pairs N and number of turns are set; the magnetic field is normalized using the unit current method to ensure that different schemes are comparable under the same electromagnetic reference.

[0082] (3) The coil configuration is optimized based on the adaptive PSOGWO fusion optimization algorithm. After initializing the population and calculating the fitness, the PSO and GWO update channels are executed synchronously in each iteration. The PSO generates candidate solutions based on the velocity-position model and uses inertia weights. and individual / social learning factors , An adaptive update mechanism that dynamically adjusts with iterations is adopted to regulate the exploration-convergence balance. GWO follows this principle. The multi-leader encirclement mechanism is locally refined and the leader set is dynamically updated; the two-channel results are adjusted using adaptive coefficients. Weighted fusion, combined with feasible region projection and elite preservation, ensures manufacturability and convergence stability. The stopping criteria are the objective function threshold, uniformity constraint satisfaction, and maximum number of iterations; convergence is determined by selecting the current optimal... Substitute the magnetic field model back to calculate the uniformity error. If the threshold condition or boundary gradient smoothness requirement is not met, the weights and fusion strategy are adaptively adjusted and iterated until the condition is met.

[0083] (4) The coil body is realized on the outer surface of the cylindrical skeleton using flexible printed circuit (FPC) technology. An AC modulation-phase lock demodulation platform is built. The magnetic field profile is obtained by scanning along the axial fixed step distance. The uniformity measured curve is calculated. The coil constant (B is the magnetic field and I is the current) is calibrated by B-I linear fitting at multiple current points. Based on the measured results, the prototype is subjected to necessary assembly correction or weight fine adjustment until it meets the requirements of engineering application.

[0084] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, and / or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A design method of large-size high-uniformity coil based on adaptive PSOGWO fusion optimization, characterized in that, Comprising the following steps: Step 1, under the cylindrical symmetry multi-pair coil topology, based on the magnetic field model of the bipolar symmetry cylindrical coil system, the axial magnetic field, i.e. the Z-axis magnetic field, is calculated according to the Biot-Savart law, Taylor expansion is performed at z=0, a layered weighted objective function is established and a relative uniformity threshold is set; Step 2, taking the axial position of each pair of coils as the design variable, setting the geometric-technological constraints, the geometric-technological constraints include symmetry, minimum spacing, upper and lower limits, skeleton radius, number of coil pairs N and number of turns, using the unit current method to normalize the magnetic field, ensuring that different schemes are comparable under the same electromagnetic reference; Step 3, using the adaptive PSOGWO fusion optimization algorithm to search for the optimal solution of the axial position, after initializing the population and calculating the fitness, the algorithm updates the particle swarm speed-position and the grey wolf hunting in each iteration according to the adaptive coefficient, and adjusts the inertia weight and learning factor according to the fitness; Step 4, using the flexible printed circuit (FPC) process to realize the coil entity on the outer surface of the cylindrical skeleton, building an alternating current modulation-locked demodulation platform, assembling and correcting the prototype or fine-tuning the weight according to the measured results until the engineering application requirements are met.

2. The large size high uniformity coil design method based on adaptive PSO GWO fusion optimization according to claim 1, characterized in that, In step 1, the following expressions are included: ； ； ； ； where ε(z) is the relative homogeneity, B z (z) is the Taylor expansion of the Z-axis magnetic field Bz at z = 0, B z (0) is the Z-axis magnetic field at z = 0, B0 is the initial term, k is the order number, K is the Taylor expansion order, 2k is the even order, f is the layered weighting objective function, j is the order number, M is the layer number, B z (Z) is the magnetic field generated by the multiple pairs of coils in the central region of the Z-axis direction, μ0 is the vacuum permeability, i is the current of each coil, R is the coil radius, N is the number of symmetrically distributed coils, n i is the number of turns, z' is the intermediate quantity, z is the z-axis coordinate value, d i ' is the intermediate quantity, d i is the position of the i-th coil on the Z-axis.

3. The large size high uniformity coil design method based on adaptive PSO GWO fusion optimization according to claim 1, characterized in that, In step 2, the following expressions are included: ； where d min is the minimum value of the coil in the Z axis, d max is the maximum value of the coil in the Z axis.

4. The large size high uniformity coil design method based on adaptive PSO GWO fusion optimization according to claim 1, characterized in that, In step 3, the following expressions are included: ； ； where X(t+1) is the overall iteration position, t is the iteration number, λ(t) is the adaptive weight coefficient, X GWO (t+1) is the GWO iteration position of the t+1 time, X PSO (t+1) is the PSO iteration position of the t+1 time, ω(t) is the adaptive inertia weight, X(t) is the current position, c1(t), c2(t) are adaptive learning factors, r1', r2' are PSO random vectors, p i is the PSO individual historical optimum, g is the PSO group optimum, ω max is the preset weight maximum value, ω min is the preset weight minimum value, T is the maximum iteration number, c1 max , c2 max are adaptive learning factor preset maximum values, c1 min , c2 min are adaptive learning factor preset minimum values.

5. The large size high uniformity coil design method based on adaptive PSO GWO fusion optimization according to claim 1, characterized in that, In step 4, the magnetic field profile is obtained by scanning along the axial step distance, the relative uniformity measured curve is converted, and the coil constant is calibrated by B-I linear fitting of multiple current points, B is the magnetic field, and I is the current.

6. The large size high uniformity coil design method based on adaptive PSO GWO fusion optimization according to claim 1, characterized in that, Using adaptive PSOGWO fusion optimization, under the engineering constraints of large size geometric requirements and limited number of coil pairs, the central even-order non-uniform terms and the smooth boundary field gradient are suppressed, the axial uniformity region is significantly expanded, and the central magnetic field distribution is more flat, which is beneficial to improve the response amplitude, signal-to-noise ratio and measurement sensitivity of the atomic magnetometer.

7. The large size high uniformity coil design method based on adaptive PSO GWO fusion optimization according to claim 1, characterized in that, By fusing the global search of particle swarm and the local exploitation of grey wolf multi-leaders, and adjusting the inertia weight, learning factor and proportion coefficient according to the group diversity, compared with single PSO or GWO algorithm, it has higher optimization efficiency and convergence stability, can reduce parameter trial and error and prototype iteration times, shorten design cycle and reduce debugging cost.

8. The large size high uniformity coil design method based on adaptive PSO GWO fusion optimization according to claim 1, characterized in that, The coils are arranged symmetrically along the axial direction and subject to standardized position constraints, which are robust to manufacturing and assembly tolerances; under the condition of common axial small deviation and small spacing error, the uniformity region and the flatness of the central field remain stable, which is beneficial to large-scale production and long-term reliable operation.

9. The large size high uniformity coil design method based on adaptive PSO GWO fusion optimization according to claim 1, characterized in that, For large-size application scenarios such as SERF atomic magnetometer compensation or modulation coils, large-aperture magnetometer cavities, and multi-channel measurement systems, in a conventional experimental environment, combined with alternating current modulation-locked demodulation measurement, stable uniformity evaluation and coil calibration can be obtained, which is convenient for on-site integration and operation.

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