A Multi-Objective Optimization Method for Electromagnetic Track Armature Structure

Abstract

This application provides a multi-objective optimization method for the armature structure of an electromagnetic rail system. The method includes: determining the armature structure model and its core design variables and target value ranges; conducting experimental design on the armature structure model based on the target value ranges of the core design variables to obtain a first sample parameter matrix including multiple sets of first sample points; obtaining multiple armature structure performance parameters corresponding to each set of sample points through electromagnetic-structural coupling simulation; training an initial electromagnetic-structural response surface surrogate model to obtain a target electromagnetic-structural response surface surrogate model; and iteratively optimizing the multiple armature structure performance parameters corresponding to the armature structure model using a multi-objective optimization model to obtain the optimal solution set. This approach can simultaneously optimize multiple armature structure performance parameters, achieving synergistic and balanced optimization for different performance requirements, effectively improving problems such as localized armature ablation and insufficient mechanical properties, and enhancing the performance of the electromagnetic rail launch system.

Description

Technical Field

[0001] This application relates to the field of electromagnetic track armature structure technology, and in particular to a multi-objective optimization method for electromagnetic track armature structure. Background Technology

[0002] Electromagnetic orbital launch technology, with its advantages of high launch speed, low overload, and strong controllability, possesses extremely high engineering application value in fields such as high-speed catapults and aerospace launches. An electromagnetic orbital launch system mainly consists of a metal rail, a conductive armature, a high-power pulsed power supply, and the launch payload. The electromagnetic rail, as the core component of the electromagnetic orbital launch system for conducting and generating the magnetic field, forms an induced magnetic field by conducting strong pulsed current, which couples with the armature's conducting current to generate a Lorentz driving force, enabling the payload to accelerate at high speed. The armature, as a key component in the conversion of electrical energy to kinetic energy, plays a crucial role in conducting large pulsed currents, withstanding impact electromagnetic loads, and propelling the payload at high speed. Its structural configuration and geometric parameters directly determine the electromagnetic thrust output level, the current distribution between the armature and the electromagnetic rail, the structural mechanical load-bearing capacity, and lightweight performance. The quality of the armature structural design is a key factor affecting the service life, launch stability, and overall performance of the electromagnetic launch system.

[0003] Existing armature structure design methods are mostly experience-based fixed structure design methods. These methods often use fixed geometric configurations such as planar, concave, and convex armature structures, relying solely on engineering experience to fine-tune individual structural parameters through trial and error. This results in the armature structure being unable to be flexibly adjusted according to electromagnetic emission conditions, failing to adapt to different performance requirements, and exhibiting problems such as low optimization efficiency and limited performance improvement. Summary of the Invention

[0004] This application provides a multi-objective optimization method for electromagnetic track armature structure, which can perform multi-objective optimization of electromagnetic track armature structure, has high optimization efficiency, can adapt to different performance requirements, and improve the performance of electromagnetic track launch system.

[0005] To address the aforementioned technical problems, in a first aspect, embodiments of this application provide a multi-objective optimization method for an electromagnetic track armature structure. This method includes: determining an armature structure model, and determining the core design variables and target value ranges of the core design variables; performing experimental design on the armature structure model based on the target value ranges of the core design variables to obtain a first sample parameter matrix, the first sample parameter matrix including multiple sets of first sample points corresponding to the core design variables; performing electromagnetic-structural coupling simulation based on the multiple sets of first sample points included in the first sample parameter matrix to determine multiple armature structure performance parameters corresponding to each set of first sample points, which are then used as multiple armature structure performance parameters corresponding to the armature structure model. The step of performing electromagnetic-structural coupling simulation based on the multiple sets of first sample points included in the first sample parameter matrix to determine the multiple armature structure performance parameters corresponding to each set of first sample points includes: determining an initial electromagnetic track-armature structure model; and based on the initial electromagnetic track-armature structure model, performing electromagnetic field simulation based on the multiple sets of first sample points included in the first sample parameter matrix to obtain multiple armature structure performance parameters corresponding to each set of first sample points. The electromagnetic performance parameters of each armature structure are obtained by performing structural field simulations based on the electromagnetic performance parameters of multiple armature structures corresponding to each set of first sample points and the multiple sets of first sample points. The initial electromagnetic-structural response surface surrogate model is determined by training the initial electromagnetic-structural response surface surrogate model based on the multiple sets of first sample points and the multiple armature structure performance parameters corresponding to each set of first sample points, thus obtaining the target electromagnetic-structural response surface surrogate model. A multi-objective optimization model is then determined by iteratively optimizing the multiple armature structure performance parameters corresponding to the armature structure model based on the multi-objective optimization model and the target electromagnetic-structural response surface surrogate model, obtaining the optimal solution set as the result of the multi-objective optimization for the armature structure model. The optimal solution set includes multiple sets of target core design variables of the armature structure model and multiple target armature structure performance parameters corresponding to each set of target core design variables.

[0006] The above technical solution first establishes an armature structure model and determines the core design variables and their target value ranges. Multiple sets of sample points corresponding to the core design variables are generated through experimental design. Multiple armature structure performance parameters corresponding to each set of sample points are obtained through electromagnetic-structural coupling simulation. This completes the training of the electromagnetic-structural response surface surrogate model, resulting in a high-precision target electromagnetic-structural response surface surrogate model. Then, iterative optimization is performed using a multi-objective optimization model to solve for the optimal solution set. Compared to existing armature structure design methods, this approach overcomes the drawbacks of traditional empirical design, significantly reduces the computational load of coupled simulation, and improves design optimization efficiency. It also simultaneously considers the optimization of multiple armature structure performance parameters, effectively addressing issues such as localized armature ablation and insufficient mechanical properties. Ultimately, multiple sets of target core design variables and corresponding target armature structure performance parameters are obtained, which can be flexibly selected according to actual launch conditions, comprehensively improving the overall performance and engineering application value of the electromagnetic track and armature.

[0007] Furthermore, in the implementation method of this application, an electromagnetic-structural unidirectional sequential coupling step-by-step solution mechanism is adopted. First, electromagnetic field simulation is performed based on the initial electromagnetic track-armature structure model to extract the electromagnetic performance parameters of the armature structure. Then, the structural field is set as an external load for the electromagnetic performance parameters, and the structural performance parameters of the armature structure are solved simultaneously. This achieves decoupling and accurate calculation of electromagnetic and mechanical properties, avoids load distortion and boundary confusion problems in multi-field simultaneous solution, and ensures that the calculation benchmark of each group of sample points is unified under batch simulation, significantly improving the consistency and accuracy of performance data.

[0008] In one possible implementation of the first aspect above, the initial electromagnetic-structural response surface surrogate model is trained based on multiple sets of first sample points and multiple armature structure performance parameters corresponding to each set of first sample points to obtain a target electromagnetic-structural response surface surrogate model. This includes: dividing the multiple sets of first sample points and multiple armature structure performance parameters corresponding to each set of first sample points into a training set and a validation set; training the initial electromagnetic-structural response surface surrogate model based on the training set to obtain an intermediate electromagnetic-structural response surface surrogate model with core design variables as input independent variables and multiple armature structure performance parameters as output dependent variables; performing accuracy verification processing on the intermediate electromagnetic-structural response surface surrogate model based on the validation set to obtain accuracy verification results; and if the accuracy verification... If the results show that the intermediate electromagnetic-structural response surface surrogate model meets the accuracy requirements, then the intermediate electromagnetic-structural response surface surrogate model is determined as the target electromagnetic-structural response surface surrogate model. If the accuracy verification results show that the intermediate electromagnetic-structural response surface surrogate model does not meet the accuracy requirements, then the sparse region of the sample distribution corresponding to the first sample parameter matrix is ​​determined, and multiple sets of second sample points corresponding to the sparse region of the sample distribution and multiple armature structure performance parameters corresponding to each set of second sample points are determined. Based on the multiple sets of second sample points and the multiple armature structure performance parameters corresponding to each set of second sample points, the intermediate electromagnetic-structural response surface surrogate model is trained until the intermediate electromagnetic-structural response surface surrogate model meets the accuracy requirements, and the target electromagnetic-structural response surface surrogate model is obtained.

[0009] By employing the aforementioned technical solution, the initial electromagnetic-structural response surface surrogate model is trained by dividing the batch of simulation sample points and their corresponding armature structural performance parameters into training and validation sets. This accurately establishes the nonlinear mapping relationship between the core armature design variables and multi-dimensional structural performance parameters, enabling rapid prediction of multi-field coupling performance. Simultaneously, the model accuracy is verified through the validation set, strictly controlling the predictive reliability of the electromagnetic-structural response surface surrogate model. To address the issue of insufficient accuracy in the initial training model, sparse sample regions within the design space are precisely identified, and new sample points are added and iteratively participated in the model's secondary training. This effectively compensates for the shortcomings of traditional uniform sampling, such as insufficient spatial coverage and poor local fitting accuracy, eliminating fitting bias caused by blind spots in sample distribution and continuously optimizing the model's generalization ability and global prediction accuracy. This effectively avoids the problems of insufficient accuracy and prediction distortion in single-sampling modeling, ultimately obtaining a high-precision, high-reliability target electromagnetic-structural response surface surrogate model. This significantly reduces the repetitive computation cost of multi-field coupling simulations and ensures the accuracy and stability of performance predictions during subsequent multi-objective optimization iterations, providing reliable model support for the accurate solution of optimal armature structural parameters.

[0010] In one possible implementation of the first aspect described above, the initial electromagnetic-structural response surface surrogate model is a Kriging interpolation model, which includes a model covariance function, which is a Gaussian variogram. The initial electromagnetic-structural response surface surrogate model is trained using a training set to obtain an intermediate electromagnetic-structural response surface surrogate model with core design variables as input independent variables and multiple armature structural performance parameters as output dependent variables. This intermediate model includes: iteratively solving for the key parameters of the Gaussian variogram function based on the maximum likelihood estimation method using the training set; and fitting the initial electromagnetic-structural response surface surrogate model with the key parameters to obtain an intermediate electromagnetic-structural response surface surrogate model with core design variables as input independent variables and multiple armature structural performance parameters as output dependent variables. An intermediate electromagnetic-structural response surface surrogate model for the dependent variable is derived. The accuracy of this surrogate model is then verified using a validation set, yielding the following verification results: Based on the validation set, the predicted values ​​of the armature structure performance parameters of the intermediate electromagnetic-structural response surface surrogate model for each group of first sample points included in the validation set are determined. Based on these predicted values ​​and the corresponding armature structure performance parameters, the accuracy information of the intermediate electromagnetic-structural response surface surrogate model is determined. Finally, the accuracy verification results are obtained based on this accuracy information.

[0011] By employing the aforementioned technical solution, a Kriging interpolation model with a Gaussian variogram as the covariance function is used to construct an initial electromagnetic-structural response surface surrogate model. This model can accurately adapt to the strongly nonlinear coupling response relationship between the core design variables of the armature and multiple armature structural performance parameters, exhibiting significant local gradient changes. Compared to traditional fitting models, it possesses superior local approximation and global fitting capabilities. By iteratively solving the key parameters of the Gaussian variogram using the maximum likelihood estimation method, the core coefficients of the model can be accurately calibrated, avoiding subjective errors caused by manually set parameters. This achieves accurate fitting of the initial model and establishes a reliable mapping relationship between the core design variables of the armature and multi-dimensional armature structural performance parameters. Simultaneously, the model accuracy is quantitatively verified using validation set samples. This accurately obtains the deviation characteristics between the model's predicted values ​​and the actual simulation values, quantifies the model's accuracy information, objectively determines the reliability of the model's fit, and effectively avoids problems such as underfitting and overfitting. This ensures that the intermediate response surface surrogate model possesses high-precision predictive capabilities and generalization performance, providing accurate, stable, and reliable performance prediction basis for subsequent multi-objective optimization iterations. From the model's underlying layer, this guarantees the accuracy and engineering effectiveness of the armature structure optimization results.

[0012] In one possible implementation of the first aspect above, if the intermediate electromagnetic-structural response surface surrogate model does not meet the accuracy requirements after training the model based on multiple sets of second sample points and multiple armature structure performance parameters corresponding to each set of second sample points, then the method further includes: determining a second sample parameter matrix based on the target value range of the core design variables, the second sample parameter matrix including multiple sets of third sample points corresponding to the core design variables; determining multiple armature structure performance parameters corresponding to each set of third sample points; training the intermediate electromagnetic-structural response surface surrogate model based on the multiple sets of third sample points and multiple armature structure performance parameters corresponding to each set of third sample points until the intermediate electromagnetic-structural response surface surrogate model meets the accuracy requirements, thereby obtaining the target electromagnetic-structural response surface surrogate model.

[0013] By employing the above technical solution, when the initial sampling training of the intermediate electromagnetic-structural response surface surrogate model fails to meet the accuracy requirements, a completely new second sample parameter matrix is ​​reconstructed within the target value range of the core design variables. This allows for global supplementary sampling and iterative retraining of the model, effectively solving the problems of incomplete coverage of sparse regions, residual local fitting bias, and insufficient fitting of nonlinear responses in a single sampling. Through a closed-loop training mechanism of multiple layered sampling and iterative correction, the blank sample regions in the design space are continuously filled, the overall uniformity of sample distribution is optimized, model fitting bias is continuously corrected, and the model's ability to capture multi-parameter nonlinear coupling laws is improved. This completely avoids the defects of insufficient model generalization ability and substandard prediction accuracy caused by a single sampling method, ultimately ensuring that the response surface model fully meets the accuracy threshold requirements. This multi-level iterative optimization method ensures both the global accuracy and stability of the electromagnetic-structural coupling response fitting and avoids local fitting distortion problems, providing high-precision and highly reliable surrogate model support for subsequent multi-objective optimization iterations. From both data and model perspectives, it guarantees the accuracy and engineering practicality of the multi-objective optimization results for the armature structure.

[0014] In one possible implementation of the first aspect mentioned above, the multi-objective optimization model is obtained by: constructing a comprehensive objective evaluation function based on multiple armature structure performance parameters; determining the engineering boundary condition constraint information of the electromagnetic track armature structure; and constructing a multi-objective optimization model based on the comprehensive objective evaluation function and the engineering boundary condition constraint information.

[0015] By adopting the above technical solution, a comprehensive objective evaluation function is constructed by integrating multiple armature structure performance parameters, unifying the evaluation scale of different physical quantities, effectively balancing the conflicting relationships between various optimization objectives, and realizing a comprehensive quantitative evaluation of multi-dimensional performance. By defining the constraint range, it is ensured that the optimization process always fits the actual application scenario. The multi-objective optimization model built in this way not only clarifies the optimization direction and evaluation criteria, but also limits the feasible range of parameters. It can guide the algorithm to carry out global optimization within the compliance range, avoid optimization results that are detached from engineering reality, and provide a standardized and reliable mathematical framework for subsequent iterative optimization based on Pareto dominance, ensuring that the optimization scheme has both performance advantages and feasibility.

[0016] In one possible implementation of the first aspect described above, based on a multi-objective optimization model and a target electromagnetic-structural response surface surrogate model, iterative optimization is performed on multiple armature structure performance parameters of the electromagnetic track armature structure to obtain an optimal solution set. This includes: determining the core operating parameters of the multi-objective optimization model, which include population size, maximum number of iterations, crossover probability, mutation probability, and convergence criteria; generating an initial population based on the core design variables, target value range, and population size, where the initial population includes multiple individuals, each corresponding to a set of core design variables; iteratively optimizing the initial population based on the target electromagnetic-structural response surface surrogate model to determine the optimized armature structure performance parameters corresponding to each set of core design variables; determining the dominance relationship between each pair of individuals based on the optimized armature structure performance parameters corresponding to each set of core design variables; and optimizing the initial population based on the dominance relationship. Multiple individuals in the population are hierarchically divided to obtain a multi-level population. Based on crossover and mutation probabilities, multiple individuals in the first-level population of the multi-level population undergo crossover and parameter mutation processing to obtain multiple new individuals. A new population is generated based on these new individuals and the multiple individuals in the first-level population. Iterative optimization is performed on the new population using a multi-objective optimization model and a target electromagnetic-structural response surface surrogate model until the maximum number of iterations is reached or all individuals in the population meet the convergence criteria, resulting in the optimal solution set. The optimal solution set includes multiple sets of target core design variables corresponding to the multiple sets of core design variables of the individuals in the population that have reached the maximum number of iterations or met the convergence criteria. The optimal solution set also includes multiple target armature structure performance parameters corresponding to the core design variables of the individuals in the population that have reached the maximum number of iterations or met the convergence criteria.

[0017] By adopting the above technical solution, and through standardized configuration of core operating parameters such as population size, number of iterations, crossover and mutation probabilities, and convergence criteria, a stable and standardized algorithm operating mechanism is provided for the multi-objective optimization process, ensuring the globality and convergence stability of the optimization search. By randomly generating the initial population within the target value range of the core design variables, an initial full-coverage search of the armature structure design space is achieved. Relying on a high-precision target electromagnetic-structural response surface surrogate model, the armature structure performance parameters corresponding to each individual are quickly obtained, replacing the traditional time-consuming multi-physics coupling simulation and greatly improving the efficiency of iterative optimization. Furthermore, by determining the dominance relationship between individuals in the initial population and hierarchically sorting them, non-dominated individuals with better overall performance are accurately selected, achieving survival of the fittest in the population. Combined with crossover and parameter mutation operations, population updates are completed, which not only inherits the characteristics of high-quality structural parameters but also expands the design search space, effectively avoiding the algorithm's tendency to get trapped in local optima. Furthermore, through continuous iterative optimization combined with a dual convergence determination mechanism of maximum iteration count and population steady state, the population performance continuously converges towards the optimal frontier, ultimately obtaining an optimal solution set that balances electromagnetic propulsion performance, current uniformity, structural strength, deformation characteristics, and lightweight performance. This achieves balanced and coordinated optimization of the armature's multi-conflict performance, with all optimal solutions satisfying engineering constraints. It effectively solves the problems of one-sided performance in traditional single-objective optimization, low accuracy in empirical trial-and-error optimization, and poor iterative efficiency, providing a comprehensive and reliable optimal parameter scheme for the refined, high-performance, and engineering-oriented design of electromagnetic track armature structures.

[0018] In one possible implementation of the first aspect above, an experimental design is performed on the armature structure model according to the target value range of the core design variables to obtain a first sample parameter matrix, including: based on the target experimental design method, performing stratified random sampling on the core design variables according to the target value range of the core design variables to obtain multiple sets of first sample points; and generating a first sample parameter matrix based on the multiple sets of first sample points.

[0019] By adopting the above technical solution, based on the target experimental design method, stratified random sampling of armature structural parameters is carried out within the target value range of the core design variables, and a first sample parameter matrix is ​​constructed. This can achieve uniform and full-coverage sampling of the design space with a limited number of samples, effectively avoiding problems such as sample aggregation, local blind spots and uneven distribution.

[0020] In one possible implementation of the first aspect described above, based on the initial electromagnetic track-armature structure model, electromagnetic field simulation is performed according to multiple sets of first sample points included in the first sample parameter matrix to obtain the electromagnetic performance parameters of multiple armature structures corresponding to each set of first sample points. This includes: assigning parameter values ​​to the material parameters of the initial electromagnetic track-armature structure model and performing mesh generation on the electromagnetic track-armature structure model to obtain the target electromagnetic track-armature structure model; inputting each set of first sample points from the multiple sets of first sample points included in the first sample parameter matrix into the target electromagnetic track-armature structure model to perform electromagnetic field simulation based on the target electromagnetic track-armature structure model to obtain the electromagnetic performance parameters of multiple armature structures corresponding to each set of first sample points.

[0021] By employing the aforementioned technical solution, a unified construction and preprocessing of the target electromagnetic track-armature structure model is achieved. Standardized material parameter assignment and refined mesh generation eliminate simulation errors caused by inconsistencies in modeling, material settings, and mesh quality, ensuring the uniformity and reliability of the simulation calculation benchmarks for each group of first sample points. Furthermore, by sequentially importing each group of first sample points from the first sample parameter matrix into the standardized model for electromagnetic field simulation, electromagnetic performance parameters corresponding to different structural parameters can be accurately and in batches obtained, fully reproducing the influence of armature parameter variations on current distribution and electromagnetic thrust. This effectively avoids the randomness and repetitive workload of manual, it enhances the consistency, accuracy, and efficiency of sample performance data, providing a high-precision, high-reliability original simulation dataset for subsequent surrogate model training, and ensuring the scientific validity and accuracy of subsequent response surface fitting and multi-objective optimization results.

[0022] In one possible implementation of the first aspect described above, the electromagnetic performance parameters of the multiple armature structures include electromagnetic output force and current density uniformity, and the structural performance parameters of the multiple armature structures include maximum equivalent stress, maximum deformation, and armature volume. Electromagnetic field simulation is performed based on the target electromagnetic track-armature structure model to obtain the electromagnetic performance parameters of the multiple armature structures corresponding to each group of first sample points. This includes: setting the magnetic field environment and solution domain boundary conditions, and applying pulsed current excitation to the target electromagnetic track-armature structure model; solving the electromagnetic field based on the magnetic field environment, solution domain boundary conditions, and pulsed current excitation to obtain the electromagnetic output force and current density uniformity; performing structural field simulation based on the electromagnetic performance parameters of the multiple armature structures corresponding to each group of first sample points and the multiple groups of first sample points to obtain the structural performance parameters of the multiple armature structures corresponding to each group of first sample points. This includes: setting the electromagnetic track-armature contact conditions and introducing the electromagnetic output force; solving the structural mechanics based on the electromagnetic track-armature contact conditions and electromagnetic output force to obtain the maximum equivalent stress and maximum deformation of the armature structure; and determining the armature volume of the armature structure corresponding to each group of first sample points.

[0023] By employing the aforementioned technical solution, standardized electromagnetic field and structural field sequential coupling simulations are conducted separately. This allows for the precise step-by-step solution of multi-dimensional performance parameters, including electromagnetic output force, current density uniformity, maximum equivalent stress, maximum structural deformation, and armature volume. By uniformly setting pulsed current excitation, magnetic field environment, and solution domain boundary conditions, the electromagnetic field solution conditions accurately reflect the actual working state of electromagnetic launch, precisely reflecting the electromagnetic drive capability and current conduction uniformity under different armature structural parameters. Simultaneously, by precisely setting armature-rail contact conditions and importing real electromagnetic force loads for structural mechanics solutions, the stress distribution and deformation patterns of the armature under strong pulsed electromagnetic loads can be accurately reproduced. Combined with the model's geometric parameters, armature volume parameters are simultaneously statistically analyzed, achieving integrated, high-precision, synchronous acquisition of electromagnetic performance, structural mechanics performance, and lightweighting indicators. This effectively avoids problems such as missing solution parameters, load distortion, and inconsistent operating conditions in a single field, comprehensively, realistically, and quantitatively characterizing the integrated service performance of different armature structures. This provides comprehensive, reliable, and dimensionally complete basic performance data for subsequent high-precision fitting of response surface models and multi-objective collaborative optimization.

[0024] In one possible implementation of the first aspect mentioned above, the core design variables include the radius of the armature center hole, the radius of the drain arc profile, the length of the armature-rail contact surface, and the width of the armature-rail contact surface. Determining the target value range of the core design variables of the armature structure model includes: determining the initial value range of the core design variables of the armature structure model; determining the engineering boundary condition constraint information, and based on the initial value range and the engineering boundary condition constraint information, determining the target value range of the core design variables of the armature structure model. The engineering boundary condition constraint information includes at least one of extreme working condition load constraints, material physical property constraints, track assembly space constraints, and machining process constraints.

[0025] By adopting the above technical solution, four key geometric parameters—armature center hole radius, current-guiding arc contour radius, armature-rail contact surface length, and armature-rail contact surface width—are identified as core design variables. This allows for precise focus on key structural dimensions affecting the armature's electromagnetic conduction characteristics, mechanical load-bearing capacity, and overall structural mass, enabling refined control of armature performance. By combining multiple engineering boundary conditions, including extreme load constraints, material physical property constraints, rail assembly space constraints, and machining process constraints, the initial value range of the design variables is screened and corrected. Invalid parameter ranges such as stress exceeding limits, deformation failure, assembly interference, and inability to process are eliminated, ultimately determining a scientific, reasonable, and fully engineering-realistic target value range. This effectively avoids the defects of infeasible solutions and theoretically optimal solutions that are impractical during the optimization process, significantly reduces the invalid search space, and improves the computational efficiency and solution reliability of subsequent experimental design, surrogate model training, and multi-objective optimization. It ensures that all subsequent sample points and optimized solution sets possess mechanical safety, assembly adaptability, and manufacturability, guaranteeing the engineering practicality and feasibility of the armature structure optimization results from the outset. Attached Figure Description

[0026] To more clearly illustrate the technical solution of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below.

[0027] Figure 1 A flowchart illustrating a multi-objective optimization method for electromagnetic track armature structure provided in this application embodiment;

[0028] Figure 2 A schematic diagram of an armature structure model provided in an embodiment of this application;

[0029] Figure 3 A flowchart illustrating the target value range of core design variables for an armature structure model, provided in an embodiment of this application.

[0030] Figure 4 A flowchart illustrating the determination of a first sample parameter matrix provided in an embodiment of this application;

[0031] Figure 5 A flowchart illustrating the process for determining multiple armature structure performance parameters corresponding to each group of first sample points, as provided in an embodiment of this application.

[0032] Figure 6 A schematic diagram of a process for generating a target electromagnetic-structural response surface proxy model provided in an embodiment of this application;

[0033] Figure 7 A schematic diagram of the Pareto dominance theory provided in this application embodiment;

[0034] Figure 8This is a schematic diagram of a process for generating the optimal solution set provided in an embodiment of this application;

[0035] Figure 9 This is another flowchart illustrating the multi-objective optimization method for electromagnetic track armature structure provided in this application embodiment. Detailed Implementation

[0036] As mentioned earlier, existing armature structure optimization methods fall into two categories: one is a fixed structure design method based on experience, which does not systematically optimize the geometric parameters of the armature structure, but only adjusts individual parameters through trial and error, resulting in low optimization efficiency and limited performance improvement.

[0037] Another type is the single-objective optimization method, which establishes a fixed armature structure model and determines a single optimization objective, such as maximizing electromagnetic thrust or minimizing structural volume. Individual structural parameters are adjusted through simulation or experimentation to verify the optimization effect. If the optimization objective is not achieved, the structural parameters are repeatedly adjusted. This method ignores key performance indicators such as current density uniformity and structural stress, cannot take into account multiple performance requirements, and the optimization process relies on experience, resulting in low efficiency. It is difficult to meet the engineering requirements of complex electromagnetic rail launch systems, leading to defects such as local ablation, structural damage, and short service life in the optimized armature structure.

[0038] In summary, existing armature structure design optimization methods have the following shortcomings:

[0039] First, the experience-based fixed structure design method does not set key geometric parameters (such as the radius of the center hole and the size of the guide arc) as adjustable variables, which makes it impossible for the armature structure to be flexibly adjusted according to the electromagnetic rail launch conditions and to adapt to different thrust and lightweight requirements. This is the core reason for the performance deficiency of the armature structure.

[0040] Second, due to incomplete optimization of the armature structure, the current conduction path at the contact surface between the armature and the electromagnetic track may be unreasonable, resulting in current concentration in local areas, uneven current distribution, and excessively high current density. This may lead to local overheating, local ablation, or even exacerbate wear between the armature structure and the electromagnetic track due to local ablation, thereby reducing the armature's service life and increasing maintenance costs.

[0041] Third, single-objective optimization methods only pursue the maximum thrust or the minimum volume. If only the thrust is maximized, the armature volume will increase and the material cost will rise. If only the volume is minimized, the electromagnetic thrust will be insufficient and the current distribution will be more uneven. It is impossible to achieve the overall coordinated optimization of the armature structure and it is difficult to meet the actual engineering needs.

[0042] Fourth, both experience-based fixed structure design methods and single-objective optimization methods rely on experience for adjustments and require repeated and extensive coupled simulations. The simulation workload is large, the optimization cycle is long, and the optimization results depend on the engineer's experience, making it difficult to guarantee accuracy. They cannot be quickly adapted to different types of electromagnetic orbital launch systems such as dual-track and quad-track systems, resulting in low optimization efficiency and poor engineering practicality.

[0043] Based on this, this application proposes a multi-objective optimization method for electromagnetic track armature structure, which can perform multi-objective optimization of electromagnetic track armature structure, with high optimization efficiency, and can achieve coordinated and balanced optimization of armature electromagnetic characteristics, current distribution characteristics, structural strength deformation characteristics and lightweight characteristics, thereby improving the performance of electromagnetic track launch system.

[0044] The electromagnetic track and armature involved in this application will be described next.

[0045] The electromagnetic rail is a core component of an electromagnetic rail launch system (such as an electromagnetic railgun). It mainly consists of two parallel rigid metal rails, which together with the armature, high-power pulse power supply and launcher form a complete electromagnetic launch circuit. Its core function is to generate a magnetic field by conducting strong pulse current, and generate Lorentz force by the interaction of current in the armature, thereby driving the armature and launcher to achieve high-speed movement.

[0046] The armature is the core actuator that converts electrical energy into kinetic energy and propels the load to accelerate. Essentially, it is a conductive component that works in conjunction with the electromagnetic track or drive coil, similar to the mover in a linear motor. It is the crucial link connecting the electromagnetic driving force and the launched load. Its core function is to receive the electromagnetic energy transmitted by the electromagnetic catapult system, convert it into the kinetic energy of itself and the load, and complete the high-speed launch maneuver.

[0047] This application primarily focuses on determining the armature structure model, its core design variables, and their target value ranges. Based on these target value ranges, experimental design is performed on the armature structure model to obtain a first sample parameter matrix containing multiple sets of first sample points corresponding to the core design variables. Electromagnetic-structural coupling simulation is then conducted based on these first sample points to determine multiple armature structure performance parameters corresponding to each set of first sample points. This yields multiple armature structure performance parameters corresponding to the armature structure model and the multiple first sample points, thereby determining the initial electromagnetic-structural response surface surrogate model. Based on multiple sets of first sample points and the corresponding armature structure performance parameters, an initial electromagnetic-structural response surface surrogate model is trained to obtain a target electromagnetic-structural response surface surrogate model. Finally, a multi-objective optimization model is determined. Based on the multi-objective optimization model and the target electromagnetic-structural response surface surrogate model, iterative optimization is performed on the multiple armature structure performance parameters corresponding to the armature structure model. This yields the optimal solution set, including multiple sets of target core design variables for the armature structure model and the corresponding target armature structure performance parameters, serving as the multi-objective optimization result for the armature structure model. This achieves multi-objective optimization of the armature structure to obtain multi-objective optimized performance parameters, significantly improving the uneven current distribution in the armature and electromagnetic track, reducing the risk of localized ablation, improving design optimization efficiency, and ultimately enhancing the electromagnetic track thrust efficiency.

[0048] Next, with reference to the accompanying drawings, the multi-objective optimization method for electromagnetic track armature structure provided in this application will be described in detail.

[0049] See Figure 1 The multi-objective optimization method for electromagnetic track armature structure provided in this application specifically includes the following steps.

[0050] S100, determine the armature structure model, and determine the core design variables of the armature structure model and the target value range of the core design variables.

[0051] For example, such as Figure 2 As shown, taking a four-rail electromagnetic catapult armature as an example, a three-dimensional modeling software is used to perform a fully parametric set modeling of the armature. The fixed-size modeling method is abandoned, and the core geometric parameters that determine the electromagnetic coupling characteristics, contact conduction performance and structural load-bearing capacity of the armature are extracted as independent design variables to obtain the core design variables.

[0052] In this application, the core design variables include key structural parameters such as the radius of the armature center hole (R1), the radius of the drain arc profile (R2), the length of the armature rail contact surface (L1), and the width of the armature rail contact surface (L2) in the hollow design section.

[0053] Furthermore, such as Figure 3 As shown, the target value range of the core design variables of the armature structure model is determined in this application by the following steps.

[0054] S110, determine the initial value range of the core design variables of the armature structure model.

[0055] For example, the initial value range of core design variables can be limited based on actual engineering conditions. For instance, the floating range of each design variable can be set to the benchmark value of the existing mature armature structure, using the dimensions of the existing mature armature structure as a reference. .

[0056] S120, determine the engineering boundary condition constraint information, and determine the target value range of the core design variables of the armature structure model based on the initial value range and the engineering boundary condition constraint information.

[0057] Among them, the engineering boundary condition constraint information includes at least one of the following: extreme working condition load constraints, material physical property constraints, track assembly space constraints, and machining process constraints.

[0058] For example, by comprehensively considering the load characteristics of the armature under extreme discharge conditions, the extreme load constraints are obtained; by considering the mechanical and electrical physical properties of the structural materials from the base to the point, the material physical performance constraints are obtained; by considering the spatial constraints of the electromagnetic track-armature assembly, the track assembly spatial constraints are obtained; and by considering the feasibility of the structural processing technology, the machining process constraints are obtained.

[0059] Based on at least one of the engineering boundary condition constraints—extreme load constraints, material physical property constraints, track assembly space constraints, and machining process constraints—the upper and lower limits of each core design variable are subject to secondary correction constraints. Inappropriate parameter combinations are eliminated, and the legal value range of each core design variable is determined, resulting in the target value range for each core design variable. This ensures that each core design variable is within its legal value range, providing a standardized and iterative parameter input basis for subsequent sampling, simulation calculations, and multi-objective optimization, guaranteeing that the optimization process aligns with actual engineering application scenarios.

[0060] S200, based on the target value range of the core design variables, conduct experimental design on the armature structure model to obtain the first sample parameter matrix, which includes multiple sets of first sample points corresponding to the core design variables.

[0061] In the implementation method of this application, such as Figure 4 As shown, based on the target value range of the core design variables, an experimental design is carried out on the armature structure model to obtain the first sample parameter matrix, including the following steps.

[0062] S210, based on the target experimental design method, performs stratified random sampling on the core design variables according to the target value range of the core design variables to obtain multiple sets of first sample points.

[0063] In this application, the Design of Experiments (DOE) method is used for sample sampling. The DOE method includes orthogonal array design, central combinatorial design, traditional Latin hypercube design, and optimal Latin hypercube design.

[0064] Design of Experiments (DOE) is a systematic statistical method. Its core is to efficiently obtain experimental or simulation data by rationally designing experimental schemes, scientifically arranging experimental factors and levels, and then analyzing the influence of each factor on the target result, so as to provide reliable data support for subsequent modeling and optimization.

[0065] In this application, taking into account the characteristics of electromagnetic armature structure design variables, strong interaction and coupling between parameters, and high degree of nonlinearity of response, the limitations of orthogonal array and central combination design are abandoned, and the optimal Latin hypercube design (OptimalLHD) is selected as the target DOE experimental design method.

[0066] The optimal Latin hypercube experimental design method is a commonly used experimental design method that combines the uniformity and randomness of stratified sampling. It can uniformly cover the entire design space with a limited sample size, effectively reducing the simulation workload, while avoiding sample point clustering. It is suitable for experimental design of complex systems with many design variables and strong parameter interactions.

[0067] This application adopts the optimal Latin hypercube experimental design method because it has excellent space filling and uniform sampling capabilities, the number of experimental levels equals the number of sampling points, and satisfies the requirement that the number of experimental levels... Increasing the number of factors (i.e., the number of core design variables) by one significantly reduces the sample size and lowers the computational cost of multi-field coupling simulations compared to full-factor experiments. For example, with 2 factors and 9 experimental levels, a full-factor design requires 9*9=81 sample points, while the optimal Latin hypercube experimental design method only requires 9 sample points. These 9 sample points are evenly distributed across the entire target value range of each core design variable, greatly reducing the workload of simulation iterations and avoiding local clustering of sample points and blind spots in the design space sampling. Secondly, the optimal Latin hypercube experimental design method has a strong ability to fit nonlinear responses. For example, orthogonal experimental design methods can only allocate a small number of sample levels with limited samples, only suitable for linear or weakly nonlinear relationships within the second order. The optimal Latin hypercube experimental design method, however, can allocate more levels to each core design variable with the same number of samples, accurately capturing the high-order nonlinear and multi-parameter interactive response laws of electromagnetic-armature coupled systems, providing a data foundation for high-precision response surface modeling.

[0068] S220, Generate the first sample parameter matrix based on multiple sets of first sample points.

[0069] For example, based on the target value range of each core design variable, 5 to 10 uniform levels are set for each core design variable. Stratified random sampling is completed using the optimal Latin hypercube experimental design method to ensure that all first sample points are uniformly distributed and do not fill the entire target value range, so as to generate a standardized DOE sample matrix, which serves as the first sample parameter matrix and provides a reliable raw dataset for subsequent batch simulation calculations and model training.

[0070] S300: Perform electromagnetic-structural coupling simulation based on multiple sets of first sample points included in the first sample parameter matrix, and determine multiple armature structure performance parameters corresponding to each set of first sample points, which are used as multiple armature structure performance parameters corresponding to the armature structure model.

[0071] In the implementation method of this application, electromagnetic-structural field coupling simulation is a multi-field coupling numerical analysis method. By combining electromagnetic simulation with structural simulation, the electromagnetic force obtained from electromagnetic calculation is used as the load input for structural simulation. The electromagnetic characteristics (such as current distribution and electromagnetic output force) and structural characteristics (stress, deformation, and volume) of the armature in the electromagnetic environment are analyzed simultaneously, which can realize the collaborative analysis of multiple physical fields.

[0072] like Figure 5 As shown, electromagnetic-structural coupling simulation is performed based on multiple sets of first sample points included in the first sample parameter matrix to determine multiple armature structure performance parameters corresponding to each set of first sample points, including the following steps.

[0073] S310, Determine the initial electromagnetic track-armature structure model.

[0074] S320 assigns parameter values ​​to the material parameters of the initial electromagnetic track-armature structure model.

[0075] S330, the initial electromagnetic track-armature structure model is meshed to obtain the target electromagnetic track-armature structure model.

[0076] For example, an integrated electromagnetic track-armature structure model is established, and material properties are defined sequentially. A refined multiphysics mesh is then created, assigning physical parameters such as conductivity, permeability, elastic modulus, Poisson's ratio, and yield strength to the electromagnetic field and structural field, respectively. In other words, a unified mesh size standard, multiphysics convergence criterion, steady-state solution, and iterative convergence residual threshold are set for the electromagnetic track-armature structure model to ensure that the simulation solution accuracy and calculation rules are consistent for all sample points, eliminating interference from human-induced simulation errors.

[0077] Furthermore, the optimization objectives of the armature structure are determined to obtain multiple armature structure performance parameters.

[0078] For example, five core optimization objectives are established, taking into account electromagnetic performance, current conduction quality, structural rigidity and strength and lightweight requirements, to obtain multiple armature structural performance parameters that need to be optimized. These multiple armature structural performance parameters include electromagnetic output force, current density uniformity, maximum equivalent stress of the structure, maximum deformation of the structure and armature volume.

[0079] Among these, electromagnetic output force reflects the armature's electromagnetic driving capability, and a larger electromagnetic output force is better; therefore, the optimization objective is to maximize the electromagnetic output force. Current density uniformity characterizes the uniformity of current conduction at the contact surface between the armature and the electromagnetic track, suppressing local overheating and ablation; a higher current density uniformity is better; therefore, the optimization objective is to obtain the maximum current density uniformity. The maximum equivalent structural stress controls the armature from plastic yielding and structural failure under impact electromagnetic loads; a smaller maximum equivalent structural stress is better; therefore, the optimization objective is to obtain the minimum maximum equivalent structural stress. The maximum structural deformation ensures the dynamic fit accuracy between the armature and the electromagnetic track, avoiding jamming and contact misalignment; a smaller maximum structural deformation is better; therefore, the optimization objective is to obtain the minimum maximum structural deformation. Armature volume is a key performance parameter for achieving armature lightweighting, reducing material consumption, and minimizing moment of inertia; a smaller armature volume is better; therefore, the optimization objective is to obtain the minimum armature volume.

[0080] Furthermore, the first sample points in the multiple sets of first sample points included in the first sample parameter matrix generated by the DOE experimental design are input one by one into the target electromagnetic track-armature structure model, and the geometric dimensions of the electromagnetic track-armature structure model are automatically updated. The target electromagnetic track-armature structure model completes the electromagnetic field-structure field coupling simulation one by one, and obtains multiple armature structure performance parameters corresponding to each set of first sample points in batches.

[0081] First, based on the target electromagnetic track-armature structure model, electromagnetic field simulation is performed using multiple sets of first sample points included in the first sample parameter matrix to obtain the electromagnetic performance parameters of multiple armature structures corresponding to each set of first sample points.

[0082] S340, based on the target electromagnetic track-armature structure model, performs electromagnetic field simulation according to the first sample points included in the first sample parameter matrix.

[0083] S350 sets the magnetic field environment and solution domain boundary conditions, and applies pulsed current excitation to the target electromagnetic track-armature structure model.

[0084] S360, based on the magnetic field environment, solution domain boundary conditions and pulsed current excitation, solves the electromagnetic field to obtain the electromagnetic output force and current density uniformity.

[0085] For example, firstly, the current excitation, magnetic field boundary conditions, and insulation and conduction constraints required for electromagnetic simulation are applied. Then, the first sample points generated by the DOE experimental design are combined and sequentially substituted into the parameterized electromagnetic track-armature structure model, and the geometric dimensions of the electromagnetic track-armature structure model are automatically updated. The electromagnetic simulation (i.e., the electromagnetic field solution) is completed one by one. The global electromagnetic force distribution and current density distribution results corresponding to each group of first sample points are extracted to obtain the electromagnetic output force and current density uniformity corresponding to each group of first sample points, which are used as the electromagnetic performance parameters of multiple armature structures corresponding to each group of first sample points.

[0086] Furthermore, based on the target electromagnetic track-armature structure model, structural field simulation is performed using the electromagnetic performance parameters of multiple armature structures corresponding to each group of first sample points and multiple groups of first sample points to obtain the structural performance parameters of multiple armature structures corresponding to each group of first sample points.

[0087] S370, structural field simulation based on target electromagnetic track-armature structure model.

[0088] S380 sets the contact conditions between the electromagnetic track and the armature.

[0089] S390, introduces electromagnetic output force, performs boundary setting and load application.

[0090] S391, Coupled computation solution.

[0091] That is, based on the contact conditions between the electromagnetic track and the armature, the structural field simulation of the target electromagnetic track-armature structure model is carried out, and the electromagnetic output force obtained by the electromagnetic field simulation is imported to solve the structural mechanics, so as to obtain the maximum equivalent stress of the armature structure, the maximum deformation of the structure, and the armature volume of the armature structure corresponding to the first sample point of each group.

[0092] S392, Output the calculation results.

[0093] That is, the electromagnetic performance parameters of the armature structure, such as electromagnetic output force and current density uniformity, and the structural performance parameters of the armature structure, such as maximum equivalent stress, maximum deformation, and armature volume, are used as multiple armature structure performance parameters.

[0094] For example, the electromagnetic output force obtained from electromagnetic field calculation is imported into the structural field in a load mapping manner as the external load boundary for structural static simulation. Then, the stress field (i.e., the maximum equivalent stress of the structure) and the elastic deformation distribution (i.e., the maximum deformation of the structure) of the structural field are solved. At the same time, the geometric volume parameters of the armature entity (i.e., the armature volume) are statistically analyzed. The unidirectional coupling numerical analysis of the electromagnetic track and the armature is fully realized, and the armature structural performance parameters such as electromagnetic output force, current density uniformity, maximum equivalent stress of the structure, maximum deformation of the structure, and armature volume are obtained.

[0095] Furthermore, in the implementation of this application, data verification and anomaly removal processing are performed on multiple armature structure performance parameters.

[0096] For example, the validity of multiple armature structure performance parameters obtained from the simulation is verified, and abnormal failure sample points caused by extreme parameter combinations, mesh distortion, and non-convergence of the solution are removed. The missing sample points are then sampled and supplemented based on the DOE experimental design method, and the electromagnetic-structure coupling simulation is performed again to obtain the corresponding armature structure performance parameters, so as to ensure the integrity, validity, and absence of outlier interference in the dataset of the first sample point and its corresponding armature structure performance parameters.

[0097] Furthermore, in the implementation of this application, the armature structure performance parameters in the dataset are normalized and weighted for equalization.

[0098] For example, the five armature structural performance parameters have different dimensions and large differences in numerical magnitude, and there are mutual constraints and conflicts between the objectives. To avoid the dominance of a single objective optimization and to take all performance dimensions into account, objective normalization processing is used to perform dimensionless normalization processing on each armature structural performance parameter, eliminating the differences in dimensions and numerical ranges, and uniformly mapping them to the same evaluation interval. Furthermore, an equal weight allocation principle is adopted, setting the weights of the five armature structural performance parameters as electromagnetic output force weights. Current density uniformity weight Structural maximum equivalent stress weight Weight of maximum structural deformation Armature volume weight And the weights satisfy the normalization constraint: Based on the normalized armature structure performance parameters and fixed weight values, a comprehensive weighted objective function W is constructed:

[0099]

[0100] The comprehensive weighted objective function is used as the evaluation basis for subsequent multi-objective iterative optimization, so as to achieve simultaneous balanced optimization of electromagnetic, current, structural, and lightweight performance dimensions.

[0101] S400, determine the initial electromagnetic-structural response surface surrogate model, and train the initial electromagnetic-structural response surface surrogate model based on multiple sets of first sample points and multiple armature structure performance parameters corresponding to each set of first sample points to obtain the target electromagnetic-structural response surface surrogate model.

[0102] In one implementation of this application, the initial electromagnetic-structural response surface surrogate model is a Kriging interpolation model, and the initial electromagnetic-structural response surface surrogate model includes a model covariance function, which is a Gaussian variogram function.

[0103] The Kriging interpolation model, also known as the spatial local interpolation method, is a method based on the theory of variograms and structural analysis to make unbiased optimal estimates of regionalized variables within a finite region. It is one of the main contents of geostatistics and has the characteristics of high fitting accuracy and the ability to capture nonlinear responses. It is often used for response surface modeling of complex systems.

[0104] This application uses the Kriging interpolation model to construct an electromagnetic-structure coupled response surface surrogate model. The Kriging interpolation model belongs to the spatial local unbiased optimal interpolation method. Based on the optimal interpolation method, the theory of variogram and regional variable structure analysis, it is suitable for fitting the response of complex engineering projects with high nonlinearity and multi-parameter coupling. It is a classic surrogate model that replaces time-consuming simulation in multi-objective optimization.

[0105] The core interpolation mathematical principle of the Kriging interpolation model is: Let For the points to be observed that require valuation, , … for The surrounding observation points and the corresponding observation values ​​are: , … Unobserved points The valuation is denoted as It is obtained by weighted summation of the observations from the surrounding observation points:

[0106]

[0107] in, The point to be observed Valuation, The weighting coefficients to be determined for each observation value. Let be the observed value of the i-th observation point.

[0108] The key to Kriging interpolation lies in calculating the weighting coefficients. The weighted coefficient solution needs to satisfy two major constraints: unbiased estimation condition and minimum variance condition. The unbiased estimation condition requires that the estimated expected value is equal to the true expected value to eliminate system bias. The minimum variance condition requires that the estimated variance between the estimated expected value and the true expected value be minimized to achieve optimal interpolation fitting.

[0109] In the implementation method of this application, such as Figure 6 As shown, based on multiple sets of first sample points and multiple armature structure performance parameters corresponding to each set of first sample points, the initial electromagnetic-structural response surface surrogate model is trained to obtain the target electromagnetic-structural response surface surrogate model, including the following steps.

[0110] S410 divides multiple sets of first sample points and the multiple armature structure performance parameters corresponding to each set of first sample points into training sets and validation sets.

[0111] For example, multiple sets of first sample points and their corresponding multiple armature structure performance parameters are standardized and preprocessed to eliminate differences in dimensions and numerical magnitudes. Then, the standardized and preprocessed dataset is divided into a training set and a validation set in proportion (e.g., 8:2). The training set is used for fitting the initial electromagnetic-structural response surface surrogate model, and the validation set is used for verifying the model's generalization ability and prediction accuracy.

[0112] Furthermore, the initial electromagnetic-structural response surface surrogate model is trained based on the training set to obtain an intermediate electromagnetic-structural response surface surrogate model with core design variables as input independent variables and multiple armature structural performance parameters as output dependent variables.

[0113] S420: Based on the training set, the key parameters of the Gaussian variogram are iteratively solved using the maximum likelihood estimation method.

[0114] S430, based on key parameters, fits the initial electromagnetic-structural response surface surrogate model to obtain an intermediate electromagnetic-structural response surface surrogate model with core design variables as input independent variables and multiple armature structural performance parameters as output dependent variables.

[0115] For example, considering the strong nonlinearity and sensitivity to local gradient changes in the coupling between the electromagnetic track and the armature structure, the Gaussian variogram is selected as the covariance function. The Gaussian variogram has the characteristics of excellent curve smoothness, strong ability to capture subtle local response changes, and high fitting accuracy.

[0116] Based on the training set including multiple sets of first sample points and their corresponding armature structure performance parameters, the maximum likelihood estimation method is used to iteratively solve the key parameters of the variogram. The key parameters include process variance, spatial correlation length, etc. Then, based on the key parameters, the core parameters of the electromagnetic-structural response surface surrogate model are calibrated, and the electromagnetic-structural response surface surrogate model is optimally fitted to the response of the sample points.

[0117] Furthermore, the intermediate electromagnetic-structural response surface surrogate model is subjected to accuracy verification processing based on the verification set to obtain the accuracy verification results.

[0118] S440, Based on the validation set, determine the predicted values ​​of the armature structure performance parameters of the intermediate electromagnetic-structural response surface surrogate model corresponding to the first sample points of each group included in the validation set.

[0119] S450, based on the predicted values ​​of the armature structure performance parameters corresponding to each group of first sample points included in the validation set of the intermediate electromagnetic-structural response surface surrogate model, and the armature structure performance parameters corresponding to each group of first sample points included in the validation set of the intermediate electromagnetic-structural response surface surrogate model, determine the model accuracy information of the intermediate electromagnetic-structural response surface surrogate model.

[0120] S460, based on the model accuracy information, obtains the accuracy verification results.

[0121] For example, the multiple sets of first sample points included in the validation set are substituted into the constructed intermediate electromagnetic-structural response surface surrogate model and the armature structure performance parameters are predicted to obtain the predicted values ​​of the armature structure performance parameters of each set of first sample points included in the validation set. The predicted values ​​of the armature structure performance parameters corresponding to each set of first sample points included in the validation set and the determination coefficients of the armature structure performance parameters of the previous electromagnetic-structural coupling simulation are then determined. ) and root mean square error Equal accuracy evaluation indicators are used to obtain model accuracy information.

[0122] S470, if the intermediate electromagnetic-structural response surface surrogate model meets the accuracy requirements based on the accuracy verification results, then the intermediate electromagnetic-structural response surface surrogate model is determined as the target electromagnetic-structural response surface surrogate model.

[0123] For example, if the coefficient of determination (As an example of a preset coefficient threshold) and root mean square error (As an example of a preset error threshold), the intermediate electromagnetic-structural response surface surrogate model is considered to meet the accuracy requirements, and the intermediate electromagnetic-structural response surface surrogate model is taken as the target electromagnetic-structural response surface surrogate model.

[0124] S480, if the accuracy verification results determine that the intermediate electromagnetic-structural response surface surrogate model does not meet the accuracy requirements, then determine the sparse region of the sample distribution corresponding to the first sample parameter matrix, and determine multiple sets of second sample points corresponding to the sparse region of the sample distribution and multiple armature structure performance parameters corresponding to each set of second sample points. Based on the multiple sets of second sample points and the multiple armature structure performance parameters corresponding to each set of second sample points, train the intermediate electromagnetic-structural response surface surrogate model until the intermediate electromagnetic-structural response surface surrogate model meets the accuracy requirements, and obtain the target electromagnetic-structural response surface surrogate model.

[0125] For example, if the coefficient of determination or root mean square error If the intermediate electromagnetic-structural response surface surrogate model does not meet the accuracy requirements, a two-level optimization strategy is adopted to continue optimizing the intermediate electromagnetic-structural response surface surrogate model. The first-level optimization strategy prioritizes determining the distribution of the first sample points in the training set within the corresponding target value range, identifying sparse regions of sample distribution within the target value range, selecting multiple sets of second sample points within the sparse regions of sample distribution based on DOE experimental design methods (e.g., optimal Latin hypercube experimental design method), and performing electromagnetic-structural coupling simulations based on these sets of second sample points to determine multiple armature structure performance parameters corresponding to each set of second sample points. Based on these sets of second sample points and their corresponding armature structure performance parameters, the intermediate electromagnetic-structural response surface surrogate model is trained, and the model accuracy information of the trained intermediate electromagnetic-structural response surface surrogate model is determined. Based on the model accuracy information, accuracy verification results are obtained. If the accuracy verification results determine that the trained intermediate electromagnetic-structural response surface surrogate model meets the accuracy requirements, then the trained intermediate electromagnetic-structural response surface surrogate model is determined as the target electromagnetic-structural response surface surrogate model. If the accuracy verification results determine that the intermediate electromagnetic-structural response surface surrogate model does not meet the accuracy requirements, then step S490 is executed to implement the second-level optimization strategy.

[0126] In one implementation of this application, the number of groups of the second sample points is 15% to 20% of the number of groups of the first sample points.

[0127] S490, if the intermediate electromagnetic-structural response surface surrogate model does not meet the accuracy requirements after training the model based on multiple sets of second sample points and multiple armature structure performance parameters corresponding to each set of second sample points, then the second sample parameter matrix is ​​determined based on the target value range of the core design variables. The second sample parameter matrix includes multiple sets of third sample points corresponding to the core design variables.

[0128] For example, if the intermediate electromagnetic-structural response surface surrogate model does not meet the accuracy requirements after training the model based on multiple sets of second sample points and multiple armature structure performance parameters corresponding to each set of second sample points, then the full set of third sample points is reselected based on the DOE experimental design method (e.g., the optimal Latin hypercube experimental design method) according to the target value range of the core design variables to obtain the second sample parameter matrix.

[0129] S491, determine multiple armature structure performance parameters corresponding to the third sample points of each group, and train the intermediate electromagnetic-structure response surface surrogate model based on the multiple third sample points and the multiple armature structure performance parameters corresponding to the third sample points of each group until the intermediate electromagnetic-structure response surface surrogate model meets the accuracy requirements, and obtain the target electromagnetic-structure response surface surrogate model.

[0130] For example, electromagnetic-structural coupling simulation is performed based on multiple sets of third sample points to determine multiple armature structure performance parameters corresponding to each set of third sample points. Based on the multiple sets of third sample points and the multiple armature structure performance parameters corresponding to each set of third sample points, the trained intermediate electromagnetic-structural response surface surrogate model is trained again, and the model accuracy information of the retrained intermediate electromagnetic-structural response surface surrogate model is determined. Based on the model accuracy information, the accuracy verification result is obtained. If the accuracy verification result determines that the retrained intermediate electromagnetic-structural response surface surrogate model meets the accuracy requirements, then the retrained intermediate electromagnetic-structural response surface surrogate model is determined as the target electromagnetic-structural response surface surrogate model. If the accuracy verification result determines that the intermediate electromagnetic-structural response surface surrogate model does not meet the accuracy requirements, then the process returns to step S480, and sample points are collected again for model training until the trained electromagnetic-structural response surface surrogate model meets the accuracy requirements or the number of iterations is reached.

[0131] S500, determine the multi-objective optimization model, and based on the multi-objective optimization model and the target electromagnetic-structural response surface surrogate model, perform iterative optimization on multiple armature structure performance parameters corresponding to the armature structure model to obtain the optimal solution set, which is the result of multi-objective optimization for the armature structure model. The optimal solution set includes multiple sets of target core design variables of the armature structure model and multiple target armature structure performance parameters corresponding to each set of target core design variables.

[0132] In the implementation method of this application, the multi-objective optimization model is obtained by: constructing a comprehensive objective evaluation function based on multiple armature structure performance parameters; determining the boundary condition constraint information of the electromagnetic track armature structure; and constructing a multi-objective optimization model based on the comprehensive objective evaluation function and the boundary condition constraint information.

[0133] For example, a target electromagnetic-structural response surface surrogate model that meets the accuracy requirements is retrieved to replace time-consuming multi-field coupled simulation calculations, relying on, for example... Figure 7 The Pareto dominance theory is used to construct a standardized multi-objective optimization model. Four armature structural dimensions—armature center hole radius (R1), current-guiding arc profile radius (R2), armature rail contact surface length (L1), and armature rail contact surface width (L2)—are identified as core design variables. The previously defined target value range is strictly used as a constraint. Engineering boundary conditions such as structural strength, assembly clearance, and processing technology are also incorporated. Furthermore, sub-objective functions corresponding to five major optimization objectives—electromagnetic output force, current density uniformity, maximum equivalent stress, maximum structural deformation, and armature volume—are defined. A unified optimization solution logic is established, defining the maximization of electromagnetic thrust, current density uniformity, maximum equivalent stress, maximum elastic deformation, and overall armature volume as functions. The two types of maximization objectives are inversely transformed, and a unified algorithm for minimization is applied. Finally, a comprehensive objective evaluation function, after dimensionless normalization and equal weighting, is substituted into the model to form a complete quantitative multi-objective optimization model.

[0134] In one implementation of this application, the multi-objective optimization model is as follows:

[0135]

[0136] in, It is the first One core design variable, The total number of core design variables, For the first The target value range for each core design variable For the first Sub-objective functions, It is the total number of sub-objective functions. For the first The first core design variable Inequality constraints It is the total number of inequality constraints. For the first The first core design variable One equality constraint condition, It represents the total number of equality constraints.

[0137] Furthermore, such as Figure 8 As shown, based on a multi-objective optimization model and a target electromagnetic-structural response surface surrogate model, multiple armature structure performance parameters of the electromagnetic track armature structure are iteratively optimized to obtain the optimal solution set, including the following steps.

[0138] S510, determine the core operating parameters, which include population size, maximum number of iterations, crossover probability, mutation probability, and convergence criteria.

[0139] For example, the parameters of the non-dominated sorting genetic algorithm are set as follows: population size is 100, maximum number of iterations is 500, crossover probability is 0.8, mutation probability is 0.05, and convergence criterion is that the Pareto front distribution tends to be stable, and the optimization iteration is determined to be converged (for example, the objective optimization result remains basically unchanged after multiple consecutive iterations / the number of non-dominated solutions in the population and the distribution range of individuals no longer change significantly, the front surface morphology tends to be stable / the combination of individual parameters in the population is not significantly updated, and the multi-objective optimization model no longer searches for better performance regions).

[0140] S520 generates an initial population based on the core design variables, the target value range, and the population size. The initial population consists of multiple individuals, with each individual corresponding to a set of core design variables.

[0141] For example, an initial population of the corresponding population size is randomly generated within the target value range of each core design variable, and each individual in the initial population corresponds to a set of core design variables.

[0142] S530, based on a multi-objective optimization model and a target electromagnetic-structural response surface surrogate model, performs iterative optimization on the initial population to determine the optimized armature structure performance parameters corresponding to each set of core design variables according to the set of core design variables included in the initial population.

[0143] For example, the target electromagnetic-structural response surface proxy model is invoked to batch calculate the five optimized armature structure performance parameters corresponding to each group of core design variables in the first generation population, and the comprehensive performance score is calculated in combination with the comprehensive objective evaluation function to complete the performance assignment of all individuals in the first generation population.

[0144] S540 determines the dominance relationship between each pair of core design variables based on the optimized armature structure performance parameters corresponding to each group of core design variables.

[0145] For example, Pareto dominance relationships are determined by comparing all individuals in the first generation population pairwise based on Pareto dominance relationships.

[0146] S550, based on dominance relationships, divides multiple individuals in the initial population into population hierarchies to obtain a multi-level population.

[0147] For example, individuals that are not dominated by other individuals are divided into the first layer of non-dominated solutions. After removing individuals from the first layer, the repeated domination relationships of the remaining individuals are determined and the hierarchy is divided. The hierarchy of all individuals in the first generation population is completed layer by layer. The hierarchy ranking results affect the replication probability of individuals. The lower the individual hierarchy, the better the overall performance of the individual and the higher the replication probability, which is conducive to the transmission of superior characteristics to the next generation and promotes population evolution. This completes the ranking of the population's superiority and inferiority. The ranking hierarchy of the remaining individuals is equal to the number of individuals that dominate that individual plus 1, reflecting the relative superiority and inferiority of the individuals.

[0148] S560, based on the crossover probability and mutation probability, perform crossover recombination and parameter mutation processing on multiple individuals included in the first layer population in the multi-level population to obtain multiple new individuals, and generate a new population based on the multiple new individuals and the multiple individuals included in the first layer population.

[0149] For example, based on the hierarchical ranking results, high-quality individuals at each level are selected as the parent population. Crossover and parameter mutation operations are performed sequentially according to the set probability. Crossover and recombination are used to exchange and merge the core design variable combinations. Small parameter mutations are used to expand the search space of the core design variables and avoid the multi-objective optimization model from getting stuck in local optima. The parent population and the new offspring individuals are integrated to generate a new population.

[0150] S570, based on a multi-objective optimization model and a target electromagnetic-structural response surface surrogate model, iteratively optimizes the new population until the maximum number of iterations is reached or each individual in the population meets the convergence criteria, thus obtaining the optimal solution set.

[0151] The optimal solution set includes multiple sets of target core design variables, which are multiple sets of core design variables corresponding to multiple individuals in the population that have reached the maximum number of iterations or met the convergence criteria. The optimal solution set includes multiple sets of target armature structure performance parameters corresponding to each set of target core design variables, which are optimized armature structure performance parameters corresponding to each set of core design variables in the population that have reached the maximum number of iterations or met the convergence criteria.

[0152] For example, steps S530 to S560 are repeated for the new population to continuously iterate and update the population. If the number of iterations reaches the preset maximum number of iterations or the average value of the optimized armature structure performance parameters, Pareto front morphology, and number of non-dominated solutions of multiple generations of the population are monitored, and if the indicators remain basically stable and there is no significant optimization improvement, then the convergence judgment condition is met, the new population of the final iteration is output, and the optimal solution set is obtained.

[0153] The optimal solution set includes four core design variables of the armature structure, such as the radius of the armature center hole (R1), the radius of the current-draining arc profile (R2), the length of the armature rail contact surface (L1), and the width of the armature rail contact surface (L2), as well as five optimized armature structure performance parameters corresponding to each set of core design variables, such as electromagnetic output force, current density uniformity, maximum equivalent stress of the structure, maximum deformation of the structure, and armature volume.

[0154] Any two sets of core design variables in the optimal solution set are non-dominant to each other. There is no optimal armature structure performance parameter where one set of core design variables is superior to the other set of core design variables in all optimized armature structure performance parameters. All solution sets are trade-off solutions covering electromagnetic performance, armature structure strength, and lightweighting. The final core design variables can be selected from the optimal solution set according to the actual engineering focus, so as to achieve positive refinement driven by simulation.

[0155] For example, if the actual engineering focus is on high thrust and high conduction, then core design variables with better electromagnetic drive force and current density uniformity are selected to adapt to high-power launch scenarios. If the actual engineering focus is on high strength and high stability, then core design variables with better maximum equivalent stress and maximum deformation are selected to adapt to high-frequency and high-impact service conditions. If the actual engineering focus is on lightweight and low inertia, then core design variables with better armature volume are selected to reduce material usage and motion inertia and adapt to rapid response launch scenarios.

[0156] The optimal solution set provided by this application has all core design variables verified by load, material properties, assembly clearance, and process feasibility. It does not have problems such as geometric distortion, dimensional overrun, mechanical failure, or assembly interference, and can be directly used for modeling simulation and physical processing and trial production.

[0157] like Figure 9As shown, this application addresses the problems of existing armature structures, such as difficulty in simultaneously considering electromagnetic thrust, armature-rail contact surface current uniformity, and structural volume, leading to issues like localized overheating and ablation, structural damage, and poor economic efficiency. It proposes a multi-objective optimization method for electromagnetic track armature structures that combines parametric modeling, experimental design, multi-field coupled simulation, response surface fitting, and multi-objective optimization. By parametrically modeling the armature structure, a parametric armature structure model is obtained. The core design variables and target value ranges of the armature structure model are determined. The Design of Experiments (DOE) method is selected, and eurythmic hypercube design is used to generate experimental sample points (e.g., the first sample point). Electromagnetic-structural coupled simulation is performed on the experimental sample points to obtain the armature structure performance parameters corresponding to each group of experimental sample points. An initial electromagnetic-structural response surface surrogate model is established (e.g., constructing a Kriging model). A high-precision electromagnetic-structural response surface surrogate model is used. Based on the first sample points in the training set and their corresponding armature structural performance parameters, an initial electromagnetic-structural response surface surrogate model is obtained to generate an intermediate electromagnetic-structural response surface surrogate model. The accuracy of the intermediate electromagnetic-structural response surface surrogate model is verified to determine whether the accuracy meets the requirements. If the accuracy does not meet the requirements, DOE sample points are added (i.e., the second sample points) or DOE sample points are regenerated (i.e., the third sample points) for iterative training of the electromagnetic-structural response surface surrogate model until the accuracy requirements are met. If the accuracy meets the requirements, multi-objective optimization is performed based on a multi-objective optimization model with electromagnetic output force, current density uniformity, maximum equivalent stress of the structure, maximum deformation of the structure, and armature volume as optimization objectives to obtain the Pareto front optimal solution set. In this way, the core design variables of the optimal armature structure are obtained, which solves the problems of traditional armature structure relying on experience design, single-objective optimization easily causing other performance degradation, large amount of computation in multi-field coupled simulation iteration, and difficulty in quickly finding the global optimal parameters. It can significantly improve the problem of uneven distribution of electromagnetic track-armature current, reduce the risk of local ablation, improve electromagnetic thrust efficiency, reduce structural volume and material cost, and achieve synergistic balance optimization of armature electromagnetic characteristics, current distribution characteristics, structural strength deformation characteristics and lightweight characteristics. It can be applied to the design and optimization of armature structure of dual-rail / quad-rail electromagnetic launch systems.

[0158] It should be noted that this application can also perform multi-objective optimization of the armature structure by taking maximizing the electromagnetic output force, maximizing the current density uniformity, and minimizing the armature volume as optimization objectives.

[0159] The multi-objective optimization method for electromagnetic track armature structure provided in this application firstly establishes a multi-objective optimization system centered on "maximizing electromagnetic thrust, maximizing current density uniformity, minimizing maximum structural deformation, minimizing maximum equivalent structural stress, and minimizing armature volume." This breaks through the technical bottleneck of existing armature designs that often employ single-objective optimization, effectively resolving the contradiction between traditional schemes and the inability to simultaneously consider launch thrust efficiency, armature-rail ablation resistance, and structural lightweighting, achieving synergistic optimization of multiple key performance parameters. Simultaneously, by setting structural equivalent stress and elastic deformation as rigid constraints, this method ensures armature structural strength and service stability while pursuing improvements in electromagnetic and lightweight performance, guaranteeing that all optimization results possess good engineering feasibility and safety reliability. Second, a fully automated closed-loop optimization process was constructed, consisting of "parametric modeling of armature structure—optimal Latin hypercube DOE sampling—electromagnetic-structural coupling simulation—Kriging high-precision response surface model fitting—Pareto multi-objective model optimization." This process can eliminate the outdated design mode of traditional fixed configuration, manual trial and error, and repeated simulation debugging. By replacing massive multi-field coupling simulation with a target electromagnetic-structural response surface proxy model, it can achieve high-precision, automated global optimization of armature structure parameters, significantly reduce simulation calculation costs, shorten the structural iteration cycle, greatly reduce the dependence on engineers' design experience, and improve the scientific nature and stability of the optimization process. Third, addressing the complex characteristics of multi-parameter coupling and significant interactions between the electromagnetic passageway and armature, and the highly nonlinear structural response of the electromagnetic track and armature, a comprehensive set of optimization methods was selected and adapted accordingly. The optimal Latin hypercube experimental design method was employed to achieve uniform sampling across the entire space, avoiding sample clustering and sampling blind spots. The Gaussian variogram Kriging model was selected as a surrogate model for the electromagnetic-structural response surface to accurately fit the local nonlinear response laws, ensuring the prediction accuracy of the surrogate model. Global Pareto optimization was achieved using a non-dominated sorting genetic algorithm. The entire methodology is highly compatible with the multi-field coupling optimization scenario of the armature, balancing sampling quality, fitting accuracy, and global optimization capabilities. Fourth, the multi-objective optimization method for the electromagnetic track and armature structure proposed in this application is not limited by the track structure form and can be widely adapted to various electromagnetic launch systems such as dual-track and quad-track systems. The value ranges of all core design variables are comprehensively determined by combining actual assembly constraints, manufacturing processes, and extreme launch conditions. The optimized core design variables all meet the engineering usage boundaries. Furthermore, simulation verification shows that the optimized armature can effectively improve current concentration, suppress localized ablation of the armature rail, and extend the service life of the equipment. It also reduces structural materials and moment of inertia, demonstrating strong engineering practical value and promising application prospects. Fifth, by setting key geometric features such as the radius of the armature center hole, the dimensions of the current-guiding arc profile, and the length and width of the armature rail contact surface as independent, variable core design variables, the armature structure can be flexibly adjusted and refined for iterative upgrades, breaking through the limitations of traditional fixed structure design.Simultaneously, preprocessing operations such as removing abnormal and failed data and dimensionless standardization are performed on batch simulation samples to effectively remove distorted samples, unify data scale, and significantly improve the quality of training datasets, providing a solid data foundation for high-precision response surface model fitting and reliable optimal parameter solving.

[0160] The multi-objective optimization method for electromagnetic track armature structure provided in this application can be applied to electronic devices.

[0161] That is, the embodiments of this application also provide an electronic device, including a processor and a memory communicatively connected to the processor, wherein the memory stores computer execution instructions, and the processor executes the computer execution instructions stored in the memory to implement the multi-objective optimization method for electromagnetic track armature structure provided in the implementation of this application.

[0162] This application also provides a chip for executing instructions, which is used to execute the technical solution of the multi-objective optimization method for electromagnetic track armature structure in the above embodiments.

[0163] This application also provides a computer-readable storage medium storing computer instructions. When these computer instructions are executed on the processor of an electronic device, the processor of the electronic device executes the technical solution of the multi-objective optimization method for electromagnetic track armature structure described in the above embodiments.

[0164] In some possible implementations, various aspects of the methods provided in this application can also be implemented as a program product, which includes program code. When the program product is run on the processor of an electronic device, the program code is used to cause the processor of the electronic device to perform the steps in the methods of the various exemplary implementations of this application described above. For example, the electronic device can perform the multi-objective optimization method for electromagnetic track armature structure described in the embodiments of this application.

[0165] The program product may take the form of any combination of one or more readable media. A readable medium may be a readable data medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CDROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0166] This application also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium. When the at least one processor executes the computer program, it can implement the technical solution of the multi-objective optimization method for electromagnetic track armature structure in the above embodiments.

[0167] It should be noted that, in addition to the specific embodiments described above, those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Although the description of this application is presented in conjunction with preferred embodiments, this does not mean that the features of this application are limited to this implementation. On the contrary, the purpose of describing the application in conjunction with the implementation is to cover other options or modifications that may be derived from this application. To provide a thorough understanding of this application, many specific details are included in the above description, and this application may also be implemented without using these details. Furthermore, to avoid confusion or obscuring the focus of this application, some specific details will be omitted in the description. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other.

[0168] It should be noted that in this specification, similar reference numerals and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0169] It should be noted that the terms "first," "second," and "third" are used only to distinguish descriptions and should not be interpreted as indicating or implying relative importance.

[0170] It should be noted that some structural or methodological features may be shown in the accompanying drawings in a specific arrangement and / or order. However, it should be understood that such a specific arrangement and / or order may not be necessary. Rather, in some embodiments, these features may be arranged in a manner and / or order different from that shown in the illustrative drawings. Furthermore, including structural or methodological features in a particular figure does not imply that such features are required in all embodiments, and in some embodiments, these features may be omitted or may be combined with other features.

[0171] Although this application has been illustrated and described with reference to certain preferred embodiments, those skilled in the art should understand that the above description is a further detailed explanation of the application in conjunction with specific implementations, and should not be construed as limiting the specific implementation of the application to these descriptions. Those skilled in the art can make various changes in form and detail, including some simple deductions or substitutions, without departing from the spirit and scope of this application.

Claims

1. A multi-objective optimization method for electromagnetic track armature structure, characterized in that, The method includes: Determine the armature structure model, and determine the core design variables of the armature structure model and the target value range of the core design variables; Based on the target value range of the core design variables, an experimental design is performed on the armature structure model to obtain a first sample parameter matrix, which includes multiple sets of first sample points corresponding to the core design variables. Electromagnetic-structural coupling simulation is performed based on the multiple sets of first sample points included in the first sample parameter matrix to determine multiple armature structure performance parameters corresponding to each set of first sample points, which are then used as multiple armature structure performance parameters corresponding to the armature structure model. The process of determining multiple armature structure performance parameters corresponding to each set of first sample points through electromagnetic-structural coupling simulation includes: determining an initial electromagnetic track-armature structure model; performing electromagnetic field simulation based on the initial electromagnetic track-armature structure model and the multiple sets of first sample points included in the first sample parameter matrix to obtain electromagnetic performance parameters of multiple armature structures corresponding to each set of first sample points; performing structural field simulation based on the electromagnetic performance parameters of multiple armature structures corresponding to each set of first sample points and the multiple sets of first sample points to obtain structural performance parameters of multiple armature structures corresponding to each set of first sample points; and obtaining multiple armature structure performance parameters corresponding to each set of first sample points based on the electromagnetic performance parameters of multiple armature structures corresponding to each set of first sample points and the structural performance parameters of the multiple armature structures. An initial electromagnetic-structural response surface surrogate model is determined. Based on the multiple sets of first sample points and the multiple armature structure performance parameters corresponding to each set of first sample points, the initial electromagnetic-structural response surface surrogate model is trained to obtain the target electromagnetic-structural response surface surrogate model. A multi-objective optimization model is determined. Based on the multi-objective optimization model and the target electromagnetic-structural response surface surrogate model, the multiple armature structure performance parameters corresponding to the armature structure model are iteratively optimized to obtain the optimal solution set, which serves as the multi-objective optimization result for the armature structure model. The optimal solution set includes multiple sets of target core design variables of the armature structure model and multiple target armature structure performance parameters corresponding to each set of target core design variables.

2. The multi-objective optimization method for electromagnetic track armature structure according to claim 1, characterized in that, Based on the multiple sets of first sample points and the multiple armature structure performance parameters corresponding to each set of first sample points, the initial electromagnetic-structural response surface surrogate model is trained to obtain the target electromagnetic-structural response surface surrogate model, including: The multiple sets of first sample points and the multiple armature structure performance parameters corresponding to each set of first sample points are divided into training set and validation set; The initial electromagnetic-structural response surface surrogate model is trained based on the training set to obtain an intermediate electromagnetic-structural response surface surrogate model with the core design variables as input independent variables and the multiple armature structure performance parameters as output dependent variables. The intermediate electromagnetic-structure response surface surrogate model is subjected to accuracy verification processing based on the verification set to obtain the accuracy verification results. If the intermediate electromagnetic-structure response surface surrogate model is determined to meet the accuracy requirements based on the accuracy verification results, then the intermediate electromagnetic-structure response surface surrogate model is determined to be the target electromagnetic-structure response surface surrogate model. If the accuracy verification results indicate that the intermediate electromagnetic-structural response surface surrogate model does not meet the accuracy requirements, then the sparse region of the sample distribution corresponding to the first sample parameter matrix is ​​determined, and multiple sets of second sample points corresponding to the sparse region of the sample distribution and multiple armature structure performance parameters corresponding to each set of second sample points are determined. Based on the multiple sets of second sample points and the multiple armature structure performance parameters corresponding to each set of second sample points, the intermediate electromagnetic-structural response surface surrogate model is trained until the intermediate electromagnetic-structural response surface surrogate model meets the accuracy requirements, thus obtaining the target electromagnetic-structural response surface surrogate model.

3. The multi-objective optimization method for electromagnetic track armature structure according to claim 2, characterized in that, The initial electromagnetic-structural response surface surrogate model is a Kriging interpolation model, and the initial electromagnetic-structural response surface surrogate model includes a model covariance function, which is a Gaussian variogram function. The initial electromagnetic-structural response surface surrogate model is trained based on the training set to obtain an intermediate electromagnetic-structural response surface surrogate model with the core design variables as input independent variables and the multiple armature structural performance parameters as output dependent variables, including: Based on the training set, the key parameters of the Gaussian variogram are iteratively solved using the maximum likelihood estimation method. Based on the key parameters, the initial electromagnetic-structural response surface surrogate model is fitted to obtain an intermediate electromagnetic-structural response surface surrogate model with the core design variables as input independent variables and the multiple armature structure performance parameters as output dependent variables. The intermediate electromagnetic-structural response surface surrogate model is subjected to accuracy verification processing based on the verification set to obtain accuracy verification results, including: Based on the validation set, the predicted values ​​of the armature structure performance parameters of the intermediate electromagnetic-structural response surface surrogate model corresponding to each group of the first sample points included in the validation set are determined. Based on the predicted values ​​of the armature structure performance parameters corresponding to each group of the first sample points included in the validation set by the intermediate electromagnetic-structure response surface surrogate model, and the armature structure performance parameters corresponding to each group of the first sample points included in the validation set by the intermediate electromagnetic-structure response surface surrogate model, the model accuracy information of the intermediate electromagnetic-structure response surface surrogate model is determined. The accuracy verification result is obtained based on the model accuracy information.

4. The multi-objective optimization method for electromagnetic track armature structure according to claim 3, characterized in that, If, after training the intermediate electromagnetic-structural response surface surrogate model based on the multiple sets of second sample points and the multiple armature structure performance parameters corresponding to each set of second sample points, the intermediate electromagnetic-structural response surface surrogate model does not meet the accuracy requirements, then the method further includes: Based on the target value range of the core design variables, a second sample parameter matrix is ​​determined, which includes multiple sets of third sample points corresponding to the core design variables. Determine multiple armature structure performance parameters corresponding to each group of the third sample points. Based on the multiple groups of third sample points and the multiple armature structure performance parameters corresponding to each group of the third sample points, train the intermediate electromagnetic-structure response surface surrogate model until the intermediate electromagnetic-structure response surface surrogate model meets the accuracy requirements, and obtain the target electromagnetic-structure response surface surrogate model.

5. The multi-objective optimization method for electromagnetic track armature structure according to claim 4, characterized in that, The multi-objective optimization model is obtained in the following way: A comprehensive objective evaluation function is constructed based on the aforementioned multiple armature structure performance parameters; Determine the engineering boundary condition constraint information of the electromagnetic track armature structure; The multi-objective optimization model is constructed based on the comprehensive objective evaluation function and the engineering boundary condition constraint information.

6. The multi-objective optimization method for electromagnetic track armature structure according to claim 5, characterized in that, Based on the multi-objective optimization model and the target electromagnetic-structural response surface surrogate model, the multiple armature structure performance parameters of the electromagnetic track armature structure are iteratively optimized to obtain the optimal solution set, including: The core operating parameters of the multi-objective optimization model are determined, including population size, maximum number of iterations, crossover probability, mutation probability, and convergence criteria. Based on the core design variables, the target value range, and the population size, an initial population is generated, which includes multiple individuals, and each individual corresponds to a set of core design variables. Based on the target electromagnetic-structural response surface surrogate model, the initial population is iteratively optimized to determine the optimized armature structure performance parameters corresponding to each set of core design variables according to each set of core design variables included in the initial population. Based on the optimized armature structure performance parameters corresponding to the core design variables of each group, determine the dominance relationship between each pair of individuals; Based on the dominance relationship, the multiple individuals in the first generation population are divided into population hierarchies to obtain a multi-level population. Based on the crossover probability and the mutation probability, the multiple individuals included in the first layer population of the multi-level population are subjected to crossover recombination and parameter mutation processing to obtain multiple new individuals, and a new population is generated based on the multiple new individuals and the multiple individuals included in the first layer population. Based on the multi-objective optimization model and the target electromagnetic-structural response surface surrogate model, the new population is iteratively optimized until the maximum number of iterations is reached or each individual in the population satisfies the convergence criterion, thus obtaining the optimal solution set. The optimal solution set includes multiple sets of target core design variables corresponding to the multiple sets of core design variables of the individuals in the population that have reached the maximum number of iterations or satisfied the convergence criterion. The optimal solution set also includes multiple sets of target armature structure performance parameters corresponding to the target core design variables of each set of core design variables of the population that have reached the maximum number of iterations or satisfied the convergence criterion.

7. The multi-objective optimization method for electromagnetic track armature structure according to claim 6, characterized in that, Based on the target value range of the core design variables, experimental design is performed on the armature structure model to obtain the first sample parameter matrix, including: Based on the target experimental design method, according to the target value range of the core design variable, the core design variable is subjected to stratified random sampling to obtain multiple sets of first sample points; The first sample parameter matrix is ​​generated based on the multiple sets of first sample points.

8. The multi-objective optimization method for electromagnetic track armature structure according to any one of claims 1-7, characterized in that, Based on the initial electromagnetic track-armature structure model, electromagnetic field simulation is performed according to the multiple sets of first sample points included in the first sample parameter matrix to obtain the electromagnetic performance parameters of multiple armature structures corresponding to each set of first sample points, including: The material parameters of the initial electromagnetic track-armature structure model are assigned values, and the electromagnetic track-armature structure model is meshed to obtain the target electromagnetic track-armature structure model. The first sample points in the multiple sets of first sample points included in the first sample parameter matrix are input into the target electromagnetic track-armature structure model to perform electromagnetic field simulation based on the target electromagnetic track-armature structure model, thereby obtaining the electromagnetic performance parameters of the multiple armature structures corresponding to each set of first sample points.

9. The multi-objective optimization method for electromagnetic track armature structure according to claim 8, characterized in that, The electromagnetic performance parameters of the multiple armature structures include electromagnetic output force and current density uniformity. The structural performance parameters of the multiple armature structures include maximum equivalent stress, maximum deformation, and armature volume. Electromagnetic field simulation was performed based on the target electromagnetic track-armature structure model to obtain the electromagnetic performance parameters of the multiple armature structures corresponding to each group of first sample points, including: Set up the magnetic field environment and solution domain boundary conditions, and apply pulsed current excitation to the target electromagnetic track-armature structure model; Based on the magnetic field environment, the boundary conditions of the solution domain, and the pulsed current excitation, the electromagnetic field is solved to obtain the electromagnetic output force and the current density uniformity. Based on the electromagnetic performance parameters of the multiple armature structures corresponding to the first sample points in each group and the multiple groups of first sample points, structural field simulation is performed to obtain the structural performance parameters of the multiple armature structures corresponding to the first sample points in each group, including: Set the contact conditions between the electromagnetic track and the armature, and introduce the electromagnetic output force; Based on the contact conditions between the electromagnetic track and the armature and the electromagnetic output force, structural mechanics solutions are performed to obtain the maximum equivalent stress and maximum deformation of the armature structure; and Determine the armature volume of the armature structure corresponding to the first sample point in each group.

10. The multi-objective optimization method for electromagnetic track armature structure according to claim 9, characterized in that, The core design variables include the radius of the armature center hole, the radius of the drain arc profile, the length of the pivot rail contact surface, and the width of the pivot rail contact surface. Determining the target value range of the core design variables for the armature structural model includes: Determine the initial value range of the core design variables for the armature structure model; The engineering boundary condition constraint information is determined. Based on the initial value range and the engineering boundary condition constraint information, the target value range of the core design variables of the armature structure model is determined. The engineering boundary condition constraint information includes at least one of extreme working condition load constraints, material physical property constraints, track assembly space constraints, and machining process constraints.

Images