A multi-physical field multi-objective optimization method and device for active magnetic bearing

Abstract

The application belongs to the technical field of active magnetic bearing control and optimization, and discloses a kind of active magnetic bearing multi-physical field multi-objective optimization method and device, method includes through proximal strategy optimization decision algorithm, the result under different parameter combinations is analyzed and evaluated, and guided feedback is carried out using reward function and penalty function;In the proximal strategy optimization decision algorithm and the main algorithm of the third generation non-dominated sorting genetic algorithm, the proximal strategy optimization stagnation perception guiding mechanism and the third generation non-dominated sorting genetic algorithm adaptive evolution factor are added as a hybrid algorithm;After the optimization iteration of the hybrid algorithm ends, the final Pareto solution set is output, and the optimal solution is selected by the approximation ideal solution sorting method.The application can solve the problems of low efficiency of multi-objective optimization of active magnetic bearing, complex coupling of multi-physical field, and difficulty in balancing control performance and energy consumption.

Description

Technical Field

[0001] This invention belongs to the field of active magnetic bearing control and optimization technology, specifically relating to an active magnetic bearing multi-physics field multi-objective optimization method and device. Background Technology

[0002] Active magnetic bearings (AMBs) are widely used in high-speed rotating machinery due to their non-contact and adjustable stiffness characteristics. Existing magnetic bearing optimization methods are mostly based on single-objective or static models, which makes it difficult to simultaneously consider multiple objective performances such as system stability, power consumption, and temperature rise. Furthermore, they suffer from low optimization efficiency and slow convergence speed under multi-physics coupling conditions.

[0003] Chinese patent publication number CN120562271A, entitled "Multi-mode Progressive Constraint Integrated Optimization Method for Fault-Tolerant Magnetic Bearings," describes a multi-physics simulation analysis of magnetic bearings under different modes. Based on sensitivity analysis, it constructs surrogate models for levitation force, loss, and stress under different modes, completing multi-objective optimization of the normal mode to obtain the optimal solution set. For light, medium, and heavy fault-tolerant modes, a progressive constraint optimization framework is adopted. This patent application uses the set of variables coupled with the current mode in the solution set of the previous mode optimization as constraints, combines them with independent variable samples to generate a potential solution space, and conducts multi-objective optimization under various fault-tolerant modes based on a surrogate model. It then filters the independent variable solution sets of each mode by inversely matching coupled variables, conducts simulations and experimental verification, determines the optimal sensitivity parameter, and designs a magnetic bearing based on this optimal sensitivity parameter. However, this patent application cannot solve the problems of stagnation and low optimization efficiency in multi-objective optimization algorithms. Summary of the Invention

[0004] To overcome the problems existing in the prior art, the present invention aims to provide a multi-physics multi-objective optimization method and device for active magnetic bearings. By combining a proximal strategy optimization decision algorithm and a third-generation non-dominated sorting genetic algorithm as a hybrid algorithm, the various structural parameters of the active magnetic bearing are continuously iteratively designed. Furthermore, a proximal strategy optimization stagnation perception guidance mechanism is introduced to evaluate the bearing performance under different parameter combinations. This solves the problems of low efficiency in multi-objective optimization, complex multi-physics coupling, and difficulty in balancing control performance and energy consumption in the prior art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides a multi-physics multi-objective optimization method for active magnetic bearings, comprising the following steps: The target variable to be optimized for the active magnetic bearing is set, and the optimization objective and the optimization variable are analyzed by proximal strategy optimization and third-generation non-dominated sorting genetic algorithm. The results under different parameter combinations are analyzed and evaluated through a proximal policy optimization decision algorithm, and the reward function and penalty function are used for guidance feedback. The multi-physics multi-objective problem is constructed as a Markov decision quintuple, and a state space vector and an action space vector are constructed. The action space vector is mapped to the proximal policy optimization guidance evolution factor parameters. A proximal strategy optimization stagnation awareness guidance mechanism and a third-generation non-dominated sorting genetic algorithm adaptive evolutionary factor are added to the main algorithms of the proximal strategy optimization decision algorithm and the third-generation non-dominated sorting genetic algorithm as a hybrid algorithm. After initializing the population with the hybrid algorithm, adaptive updates are performed. The proximal strategy optimization stagnation awareness guidance mechanism determines the population evolution status in real time and dynamically determines the evolutionary factor parameters for adaptive update iteration accordingly. After the hybrid algorithm optimization iteration is completed, the final Pareto solution set is output. The optimal solution is selected by the approximation ideal solution sorting method and used for the multiphysics field optimization design of the active magnetic bearing.

[0006] Optionally, the formulas for optimizing the objective x, the optimization variable F(x), and the constraints on the optimization variable are as follows:

[0007] in, N The number of coil turns. l For bearing thickness, d The outer diameter of the rotor. d 0 represents the rotor's inner diameter. t The width of the magnetic pole. h For the depth of the groove, F max For the maximum electromagnetic force, V For bearing volume, P This represents the total bearing loss. D Stator outer diameter δ The length of the air gap. A 0 represents the air gap area. A c The area of ​​the coil cavity, N p For extreme logarithms, I max For maximum operating current, μ 0 is the permeability of free space. T max For the maximum temperature, Δ T total For the total temperature rise, T 0 represents the ambient temperature.

[0008] Optionally, the state space vector st and the action space vector at are:

[0009] In the formula, Norm Represents state normalization, G t It is algebra. FR t It is the proportion of feasible solutions. It is the average constraint violation rate. HVImp t It is the relative improvement rate of two adjacent generations of supervolume. NDS t The proportion of non-dominated solutions. Spread t It is a measure of the spatial distribution of the target. μ x ( t )and σ x ( t ) are two scalar statistics obtained by compressing the normalized design variables; The reward and penalty functions are set to evaluate each set of parameters. The feedback formula is as follows:

[0010] In the formula, For the dominant function, γ As a discount factor, r t For real-time rewards, λ GAE It's a GAE parameter. δ t It is a timing difference error. V ( s t ) is the Critic network estimation function.

[0011] Optionally, the initial population for the hybrid algorithm is:

[0012] in, It is the initialized population. It is a deterministic solution for the near-end policy optimization decision algorithm. It is a stochastic solution of the near-end policy optimization decision algorithm. It is a random solution of the third-generation non-dominated sorting genetic algorithm.

[0013] Optionally, the adaptive update formula for the hybrid algorithm is:

[0014] in, For crossover probability, The mutation probability, N i It is the current iteration number.N max It is the maximum number of iterations. G p It is the non-dominated ranking of individuals. G pm It is the largest nondominated sort.

[0015] Optionally, the formula for the proximal strategy optimization stagnation-aware guidance mechanism is:

[0016] Where I is the indicator function, L is the window length, and τ is the stagnation threshold.

[0017] Secondly, the present invention provides an active magnetic bearing multiphysics multi-objective optimization system, characterized in that it comprises: The variable setting module is used to set the target variables to be optimized for the active magnetic bearing. The optimization target and optimization variables are analyzed using proximal strategy optimization and third-generation non-dominated sorting genetic algorithm. The vector construction module is used to analyze and evaluate the results under different parameter combinations through the proximal policy optimization decision algorithm, and to guide the feedback with reward and penalty functions; it constructs the multi-physics multi-objective problem into a Markov decision quintuple, constructs the state space vector and action space vector, and maps the action space vector to the proximal policy optimization guidance evolution factor parameters; The hybrid algorithm computation module is used to add a proximal strategy optimization stagnation awareness guidance mechanism and a third-generation non-dominated sorting genetic algorithm adaptive evolutionary factor to the main algorithms of the proximal strategy optimization decision algorithm and the third-generation non-dominated sorting genetic algorithm as a hybrid algorithm. After initializing the population with the hybrid algorithm, adaptive updates are performed. The proximal strategy optimization stagnation awareness guidance mechanism determines the population evolutionary state in real time and dynamically determines the evolutionary factor parameters for adaptive update iteration based on this. The optimal parameter generation module is used to output the final Pareto solution set after the hybrid algorithm optimization iteration is completed. The optimal solution is selected by the approximation ideal solution sorting method and used for the multiphysics field optimization design of active magnetic bearings.

[0018] Thirdly, the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computer program.

[0019] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0020] Fifthly, the present invention provides a computer program product comprising a computer-readable medium, wherein computer-readable program code is included on the computer-readable medium, the program code performing the method.

[0021] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a multi-physics multi-objective optimization method and device for active magnetic bearings. By combining multi-physics modeling, reinforcement learning-assisted evolutionary search and intelligent decision-making, it systematically solves key technical problems in the design of high-speed active magnetic bearings, such as conflicting performance indicators, low optimization efficiency and difficulty in thermal performance evaluation.

[0022] This invention addresses the problem of low early-stage population quality caused by random initialization in the standard NSGA-III (Non-dominated Sorting Genetic Algorithm III). It employs a hybrid initialization strategy, combining pre-generated feasible solutions from PPO (Proximal Policy Optimization) with randomized solutions to form the initial population, ensuring a strong foundation of feasible solutions from the outset. To address the issue of standard algorithms easily stagnating in later evolutionary stages, this invention introduces a stagnation-aware mechanism. This mechanism monitors the hypervolume improvement in the population's target space in real time. When stagnation is detected, the PPO policy network is automatically triggered to adaptively adjust evolutionary parameters such as crossover probability, mutation probability, and distribution index, allowing the algorithm to regain search vitality during stagnation. This mechanism ensures stable convergence performance throughout the entire evolutionary process.

[0023] This invention introduces the Policy Optimizer (PPO) into the NSGA-III framework, establishing a master-slave collaborative relationship: NSGA-III acts as the master optimizer, responsible for environmental selection and non-dominated ranking of the population, while PPO serves only as an auxiliary module, outputting adaptive evolutionary parameters when the algorithm stagnates. This design retains NSGA-III's excellent Pareto front distribution capability in multi-objective optimization while leveraging the sequential decision-making advantages of reinforcement learning to compensate for its insufficient search efficiency in complex engineering problems. The PPO's policy network continuously optimizes its decision quality through reward signals, making the auxiliary intervention increasingly precise and effective.

[0024] Furthermore, this invention integrates electromagnetic force calculation, volume calculation, and total loss calculation into the same optimization framework. Five key structural parameters—coil turns N, bearing thickness l, rotor magnetic sleeve outer diameter d, magnetic pole width t, and slot depth h—are used as design variables. The three optimization objectives are maximizing electromagnetic force, minimizing volume, and minimizing total loss. Geometric, electromagnetic, and thermal constraints are introduced to ensure that all solutions meet engineering feasibility requirements. This model uses total loss as a surrogate index for thermal performance, avoiding the direct use of time-consuming finite element thermal simulations in iterative loops. This fundamentally solves the problem of excessively high computational costs in thermal evaluation, enabling multiphysics coupling optimization to be achieved within an engineering-acceptable timeframe. Attached Figure Description

[0025] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way.

[0026] In the attached diagram: Figure 1 This is a schematic diagram of the overall system framework of an embodiment of the present invention; Figure 2 This is a flowchart of the PPO-NSGA-Ⅲ algorithm according to an embodiment of the present invention; Figure 3 This is a comparison of electromagnetic simulation results before and after optimization in an embodiment of the present invention; where (a) is before optimization; and (b) is after optimization. Figure 4 This is a comparison of bearing stiffness results before and after optimization in an embodiment of the present invention; where (a) is before optimization; and (b) is after optimization. Figure 5 This is a comparison of bearing temperature simulation results before and after optimization in an embodiment of the present invention; where (a) is before optimization and (b) is after optimization. Detailed Implementation

[0027] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0028] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0029] It should be noted that any reference signs placed between parentheses in the claims should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. This application can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In a unit claim enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third, etc., does not indicate any order. These words can be interpreted as names.

[0030] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0031] The present invention will now be described in detail with reference to the accompanying drawings.

[0032] As a key support component of high-speed rotating machinery, the design of active magnetic bearings must simultaneously consider electromagnetic force output capacity, structural compactness, and thermal reliability. However, there is an inherent conflict among these three aspects: increasing the electromagnetic force usually requires increasing the number of coil turns or bearing volume, but this exacerbates losses and temperature rise; pursuing a compact structure limits the magnetic circuit area and reduces force output. Traditional design methods often rely on empirical trial and error or single-objective optimization, which cannot effectively handle the aforementioned multi-objective coupling contradictions. Furthermore, standard multi-objective evolutionary algorithms are prone to search stagnation or premature convergence when facing high-dimensional constrained engineering problems, and frequent calls to finite element thermal simulations for iterative evaluation lead to excessively high computational costs.

[0033] The present invention provides a multi-physics, multi-objective optimization method for active magnetic bearings, comprising the following steps: The target variable to be optimized for the active magnetic bearing is set, and the optimization objective and the optimization variable are analyzed by proximal strategy optimization and third-generation non-dominated sorting genetic algorithm. The results under different parameter combinations are analyzed and evaluated through a proximal policy optimization decision algorithm, and the reward function and penalty function are used for guidance feedback. The multi-physics multi-objective problem is constructed as a Markov decision quintuple, and a state space vector and an action space vector are constructed. The action space vector is mapped to the proximal policy optimization guidance evolution factor parameters. A proximal strategy optimization stagnation awareness guidance mechanism and a third-generation non-dominated sorting genetic algorithm adaptive evolutionary factor are added to the main algorithms of the proximal strategy optimization decision algorithm and the third-generation non-dominated sorting genetic algorithm as a hybrid algorithm. After initializing the population with the hybrid algorithm, adaptive updates are performed. The proximal strategy optimization stagnation awareness guidance mechanism determines the population evolution status in real time and dynamically determines the evolutionary factor parameters for adaptive update iteration accordingly. After the hybrid algorithm optimization iteration is completed, the final Pareto solution set is output. The optimal solution is selected by the approximation ideal solution sorting method and used for the multiphysics field optimization design of the active magnetic bearing.

[0034] This invention combines a proximal strategy optimization decision-making algorithm and a third-generation non-dominated sorting genetic algorithm as a hybrid algorithm to iteratively design various structural parameters of an active magnetic bearing. It also introduces a proximal strategy optimization stagnation perception guidance mechanism to evaluate the bearing performance under different parameter combinations. This solves the problems of low efficiency in multi-objective optimization, complex multi-physics coupling, and difficulty in balancing control performance and energy consumption in the prior art.

[0035] Example 1 The present invention provides a multi-physics, multi-objective optimization method for active magnetic bearings, comprising the following steps: Step 1: Establish a multiphysics model of the magnetic bearing. This step involves establishing an electromagnetic model, a thermal model, and a structural dynamics model to achieve a multiphysics description of the magnetic bearing system.

[0036] Based on the structural design principle of active magnetic bearings (AMB), the NSGA-Ⅲ algorithm is used for algorithm modeling, and the optimization objectives and optimization variables are analyzed. Establish a PPO decision module to analyze and evaluate the results under different parameter combinations, and use reward and penalty functions to guide feedback; A PPO-NSGA-Ⅲ multiphysics multi-objective optimization algorithm was established, and a PPO stagnation perception guidance module and an NSGA-Ⅲ adaptive evolution factor were added to the NSGA-Ⅲ main algorithm.

[0037] After the hybrid algorithm optimization iteration is completed, the final Pareto solution set is output, and the optimal solution is selected by the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) decision method.

[0038] Step 2: Construct a multi-objective optimization function. Based on Step 1, define multiple optimization objectives to comprehensively evaluate the performance of the magnetic bearing system.

[0039]

[0040] in, N The number of coil turns. l For bearing thickness, d The outer diameter of the rotor. d 0 represents the rotor's inner diameter. t The width of the magnetic pole. h For the depth of the groove, F max For the maximum electromagnetic force, V For bearing volume, P This represents the total bearing loss. D Stator outer diameter δ The length of the air gap. A 0 represents the air gap area. A c The area of ​​the coil cavity, N p For extreme logarithms, I max For maximum operating current, μ 0 is the permeability of free space. T max For the maximum temperature, Δ T total For the total temperature rise, T 0 represents the ambient temperature.

[0041] Step 3: Introduce a PPO policy network to improve search efficiency. A reinforcement learning-based PPO policy network is introduced. The input to the policy network is the current system state, and the output is the PPO guiding evolution factor parameters. The reward function design, combined with a multi-objective optimization function, guides the policy network to select actions beneficial to multi-objective optimization during iteration, causing the population to converge towards the Pareto front.

[0042] The multiphysics multi-objective problem is constructed as a Markov decision quintuple, and the constructed state space vector and action space vector are expressed as follows:

[0043] The action space vector is mapped to PPO guided evolutionary factor parameters, specifically described as follows:

[0044] in, and These represent the crossover probability and the distribution index, respectively. and These represent the mutation probability and the mutation distribution index, respectively. It is the PPO guiding probability. Set up reward and penalty functions to evaluate and provide feedback for each set of parameters:

[0045] In the formula, For the dominant function, γ As a discount factor, r t For real-time rewards, λ GAE These are GAE (Generalized Advantage Estimation) parameters. δ t It is a timing difference error. V ( s t ) is the Critic network estimation function.

[0046] Step four: First, initialize the NSGA-III population: Based on the multi-objective optimization function and system constraints, initialize the NSGA-III algorithm population. The initial population consists of a set of feasible solutions, with each individual corresponding to a set of parameters to be optimized. The initial population uses a mixed population setting. Second, PPO stagnation awareness guides population evolution: In this step, the output of the PPO policy network is used to guide the evolutionary process of the NSGA-III population. Each generation of population individuals adjusts their parameters according to the suggestions of the policy network, and selects the next generation of population through non-dominated sorting and crowding distance calculation. At the same time, the policy network updates its policy based on the population performance, continuously improving the quality of decision-making. Through this evolutionary mechanism combined with reinforcement learning, the convergence speed of multi-objective optimization can be accelerated, while maintaining the diversity of the solution set. Hybrid NSGA-Ⅲ initial population:

[0047] in, It is a deterministic solution for PPO. It is a PPO stochastic solution. It is a stochastic solution of NSGA-III.

[0048] Adaptive Subgeneration Update Strategy

[0049] in, and These represent the crossover and mutation probabilities, respectively. N i It is the current iteration number. N max It is the maximum number of iterations. G p It is the non-dominated ranking of individuals. G pm It is the largest nondominated sort.

[0050] PPO stagnation perception:

[0051] Where I(·) is the indicator function, L is the window length, and τ is the stagnation threshold. If I t = 1, then the algorithm is considered to be in a stagnant phase.

[0052] Step 5: Output the Pareto optimal solution set. After several iterations, the algorithm generates a Pareto optimal solution set, where each solution achieves a balance between different objectives. Based on the TOPSIS decision, one or more sets of optimal parameters can be selected for the actual design and control of the magnetic bearing system, achieving the goals of performance improvement, power consumption reduction, and temperature rise control.

[0053] This invention integrates electromagnetic force calculation, volume calculation, and total loss calculation into the same optimization framework, using five key structural parameters: number of coil turns. N Bearing thickness l Rotor magnetic sleeve outer diameter d Magnetic pole width t trench depth h As design variables, the model aims to maximize electromagnetic force, minimize volume, and minimize total loss as three optimization objectives. Geometric, electromagnetic, and thermal constraints are introduced to ensure all solutions meet engineering feasibility requirements. The model uses total loss as a surrogate index for thermal performance, avoiding the direct invocation of time-consuming finite element thermal simulations in iterative loops. This fundamentally solves the problem of excessively high computational costs in thermal evaluation, enabling multiphysics coupling optimization to be achieved within an engineering-acceptable timeframe.

[0054] Example 2 This invention uses Python and Ansys Maxwell to verify the superiority of the proposed PPO-NSGA-Ⅲ algorithm and compare bearing performance before and after optimization. The multiphysics, multi-objective optimization design framework based on PPO-NSGA-Ⅲ proposed in this invention is as follows: Figure 1 As shown.

[0055] To verify the effectiveness of the proposed multiphysics, multi-objective optimization method for active magnetic bearings based on PPO-NSGA-Ⅲ, this invention constructs an optimization algorithm based on the Python platform and establishes an electromagnetic field simulation model using Ansys Maxwell electromagnetic field simulation software. The system performance before and after optimization is compared and analyzed. The overall simulation process and design framework are as follows: Figure 1 As shown.

[0056] like Figure 1As shown, a multiphysics optimization design framework for active magnetic bearings is established, including electromagnetic field modeling, structural response analysis, and a multi-objective optimization process based on PPO-NSGA-Ⅲ. During simulation, optimization variables are input into the electromagnetic model to obtain parameters such as electromagnetic force, losses, and temperature, which are then fed back to the optimization algorithm to achieve closed-loop iterative calculation. Detailed steps are as follows: Step 1: Establish a multiphysics model for the magnetic bearing Before optimization begins, the electromagnetic, thermal, and structural models of the active magnetic bearing are first established. Specifically, this involves: determining fundamental parameters such as the number of pole pairs, air gap length, and rotor magnetic sleeve outer diameter range; deriving the electromagnetic force calculation formula using the equivalent magnetic circuit method; determining the volume calculation formula based on the bearing's geometry; and using the sum of copper loss, iron loss, and windage loss as the total loss to characterize thermal performance. The output of this step is a set of mathematical expressions that relate the structural parameters to be optimized to three objective functions.

[0057] Step 2: Define optimization variables, objective function, and constraints. The design variables for this optimization are clearly defined as five: number of coil turns. N Bearing thickness l Rotor magnetic sleeve outer diameter d Magnetic pole width t trench depth h The optimization objectives are threefold: maximizing the maximum electromagnetic force. F max Minimize bearing volume V Minimize total loss P total Simultaneously, three types of constraints are set: geometric constraints (ensuring that the dimensions of each component do not interfere with each other and the coil area does not exceed the slot area), electromagnetic constraints (ensuring that the electromagnetic force is sufficient to support the rotor's unbalanced force and the magnetic flux density does not exceed the material saturation value), and thermal constraints (ensuring that the temperature rise does not exceed the upper limit allowed by the winding material). The above variables, objectives, and constraints are input into the optimization algorithm as the basis for solving the problem.

[0058] Step 3: Initialize the population by mixing Before starting the NSGA-III algorithm, a hybrid strategy is used to generate the initial population. Specifically, the population size is set to 100, with 30% of individuals deterministically generated by the PPO policy network, 30% randomly sampled by the PPO policy network, and the remaining 40% generated using traditional random sampling. These three are combined to form the complete initial population. The purpose of this is to ensure that the initial solution set contains feasible solutions of a certain quality while maintaining sufficient exploration diversity, avoiding the slow early convergence caused by purely random initialization.

[0059] Step 4: Set the basic parameters of the NSGA-III algorithm The maximum number of generations is set to 100. The Das-Dennis uniform reference point generation method is used to generate 100 reference points, ensuring the uniform distribution of individuals in the target space. Scheduling curves for the basic crossover and mutation probabilities are set: as the number of generations increases, the crossover and mutation probabilities are adaptively adjusted according to a cosine law, balancing early-stage global exploration with later-stage local refinement.

[0060] Step 5: Entering the main optimization loop – evaluation, stagnation detection, and PPO intervention decision-making. After each generation of optimization begins, the three objective function values ​​and three types of constraint violations are calculated sequentially for all individuals in the current population. After evaluation, the stagnation detection phase begins: the average improvement in target space hypervolume (HV) over the last five generations is calculated. If this value is less than a preset threshold (10... - If ³), then the algorithm is considered to have entered a stalled state.

[0061] If the population is determined to be stagnant, a certain guidance probability (determined by the PPO policy network based on the current population state output) is used to decide whether to activate PPO intervention. If intervention is triggered, the PPO policy network outputs a set of adaptive evolutionary parameters; if intervention is not triggered, the NSGA-III basic parameters from step four are used. If the population is determined to be non-stagnant, the basic parameters are used directly for this generation's evolution.

[0062] Step Six: Generate offspring population and calculate reward feedback Using the evolutionary parameters determined in step five, simulated binary crossover and polynomial mutation operations are performed on the parent population to generate a offspring population of the same size as the parent population. After the offspring are generated, the reward value for this generation's optimization process is calculated. This reward comprehensively considers the improvement of the objective function and the change in constraint violation: the greater the improvement of the objective function and the smaller the constraint violation, the higher the reward value. This reward value is only used for subsequent parameter updates of the PPO policy network and does not participate in the population selection process of NSGA-III.

[0063] Step 7: Merge parent and child generations, and perform NSGA-Ⅲ environment selection. The parent and offspring populations are merged into a temporary population (size 200). A non-dominated sort is performed on the merged population, stratifying individuals according to their non-dominated level. Then, following the reference point association mechanism of NSGA-III, individuals are sequentially selected from the non-dominated layers until the next generation population is filled (size restored to 100). Simultaneously, the reward value and population state obtained in this generation are fed back to the PPO policy network to update its network parameters, making its subsequent intervention actions more accurate.

[0064] Step 8: Loop Termination and Output of Optimal Solution Repeat steps five through seven until the maximum number of generations (100) is reached. After iteration terminates, output all non-dominated solutions from the final generation, forming the Pareto optimal solution set. Using the TOPSIS decision method, each solution in the solution set is sorted according to its relative proximity to the ideal and negative ideal solutions, and the compromise solution with the best overall performance is selected as the final design parameters. This set of parameters can then be used for the actual engineering design and prototype manufacturing of the active magnetic bearing.

[0065] Additional notes on the optimized verification process: The entire optimization process described above was completed within the Python numerical computation platform without invoking finite element simulation. After optimization, the optimal parameter combination selected by TOPSIS was input into Ansys Maxwell electromagnetic field simulation software and temperature field simulation software for independent finite element verification to confirm the validity of the optimization results. Verification included: magnetic flux density distribution, electromagnetic force magnitude, current stiffness and displacement stiffness, total losses, and steady-state temperature distribution; rotor dynamic modal analysis was supplemented as necessary.

[0066] like Figure 2 As shown, this invention presents the specific process of the PPO-NSGA-Ⅲ algorithm. First, the population is initialized. Then, the individuals are guided and updated through the PPO policy network, and non-dominated sorting and selection are performed using the NSGA-Ⅲ algorithm to obtain a multi-objective Pareto solution set. Through multiple iterations, the optimization variables gradually converge.

[0067] like Figure 3 The image shows a comparison of electromagnetic simulation results before and after optimization. The comparison reveals that the optimized magnetic field distribution is more uniform, and the magnetic flux utilization rate is improved, thereby enhancing the electromagnetic force output capability.

[0068] like Figure 4 The figure shows a comparison of bearing stiffness results before and after optimization. The results indicate that the system stiffness is improved after optimization, which is beneficial to enhancing rotor operating stability.

[0069] like Figure 5 The image shows a comparison of the temperature field simulation results before and after optimization. It can be seen that the optimized temperature distribution is more reasonable, local temperature rise is suppressed, and this helps improve the reliability of the system operation.

[0070] In summary, through simulation verification, the optimization method proposed in this invention can achieve comprehensive optimization of the performance of active magnetic bearings under multi-objective constraints, and has good application effects.

[0071] After optimization by this invention, the bearing volume is reduced by approximately 17%, from 441,326 mm³ to 364,602 mm³; the maximum electromagnetic force increases from 600 N to 1,002 N, an improvement of approximately 67%; and the total loss is reduced by approximately 44%, from 675 W to 378 W. This achieves a synergistic improvement in force density and thermal performance. Finite element electromagnetic simulation shows that the optimized magnetic flux density increases from 1.34 T to 1.95 T, resulting in more efficient utilization of the magnetic circuit; temperature field simulation shows that the peak temperature decreases from 109.17 ℃ to 74.33 ℃, effectively suppressing temperature rise.

[0072] Under the same computational budget, this invention achieves a higher hypervolume (HV) index and a lower generational distance (GD) compared to NSGA-II, standard NSGA-III, and adaptive NSGA-III, indicating superior Pareto front quality. Faster constraint violation convergence and a higher proportion of feasible solutions demonstrate the algorithm's advantages in constraint handling. Ablation experiments further verify that the hybrid initialization, stagnation sensing, and PPO gating intervention modules each independently contribute observable performance gains.

[0073] The optimized prototype achieved stable levitation across the entire speed range of 0–24,000 rpm, with the peak-to-peak value of the four-degree-of-freedom vibration remaining stable at 0.06 mm. The control current did not exceed 3 A throughout the entire range, far below the design limit. Rotor modal analysis showed that the translational and conical modes improved from 30.9 Hz and 55.0 Hz to 77.1 Hz and 143.9 Hz, respectively, indicating a significant enhancement in support stiffness. The first-order bending mode (2,537 Hz) remained well above the highest operating frequency (400 Hz), with no risk of bending resonance.

[0074] In summary, this invention effectively solves three core problems in the design of active magnetic bearings—multi-objective conflict, low optimization search efficiency, and high thermal assessment cost—by combining multi-physics unified modeling, reinforcement learning-assisted evolutionary search, and intelligent decision-making. It achieves comprehensive optimization goals of increasing electromagnetic force, reducing volume, and suppressing temperature rise, providing an efficient and reliable integrated solution for the design of high-performance support components for high-speed electric drive systems. It has clear industrial application value and promising prospects for promotion.

[0075] Example 3 Based on the multi-physics multi-objective optimization method for active magnetic bearings in Embodiment 1, a multi-physics multi-objective optimization system for active magnetic bearings is disclosed, comprising: The variable setting module is used to set the target variables to be optimized for the active magnetic bearing. The optimization target and optimization variables are analyzed using proximal strategy optimization and third-generation non-dominated sorting genetic algorithm. The vector construction module is used to analyze and evaluate the results under different parameter combinations through the proximal policy optimization decision algorithm, and to guide the feedback with reward and penalty functions; it constructs the multi-physics multi-objective problem into a Markov decision quintuple, constructs the state space vector and action space vector, and maps the action space vector to the proximal policy optimization guidance evolution factor parameters; The hybrid algorithm computation module is used to add a proximal strategy optimization stagnation awareness guidance mechanism and a third-generation non-dominated sorting genetic algorithm adaptive evolutionary factor to the main algorithms of the proximal strategy optimization decision algorithm and the third-generation non-dominated sorting genetic algorithm as a hybrid algorithm. After initializing the population with the hybrid algorithm, adaptive updates are performed. The proximal strategy optimization stagnation awareness guidance mechanism determines the population evolutionary state in real time and dynamically determines the evolutionary factor parameters for adaptive update iteration based on this. The optimal parameter generation module is used to output the final Pareto solution set after the hybrid algorithm optimization iteration is completed. The optimal solution is selected by the approximation ideal solution sorting method and used for the multiphysics field optimization design of active magnetic bearings.

[0076] Example 4 The purpose of this embodiment is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the active magnetic bearing multiphysics multi-objective optimization method.

[0077] Example 5 The purpose of this embodiment is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the active magnetic bearing multiphysics multi-objective optimization method.

[0078] Example 6 The purpose of this embodiment is to provide a computer program product including a computer-readable medium, wherein the computer-readable medium contains computer-readable program code that executes the active magnetic bearing multiphysics multi-objective optimization method.

[0079] The steps and methods involved in the apparatuses of the above embodiments 3, 4, 5 and 6 correspond to those in embodiment 1. For specific implementation details, please refer to the relevant description section of embodiment 1.

[0080] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0081] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0082] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0083] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0084] Unless otherwise specified, the working methods or control methods involved in the above embodiments are conventional working methods or control methods in the art.

[0085] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Any other modifications or equivalent substitutions made by those skilled in the art to the technical solutions of the present invention, as long as they do not depart from the spirit and scope of the technical solutions of the present invention, should be covered within the scope of the claims of the present invention.

Claims

1. A multi-physics, multi-objective optimization method for active magnetic bearings, characterized in that, Includes the following steps: The target variable to be optimized for the active magnetic bearing is set, and the optimization objective and the optimization variable are analyzed by proximal strategy optimization and third-generation non-dominated sorting genetic algorithm. The results under different parameter combinations are analyzed and evaluated through a proximal policy optimization decision algorithm, and the reward function and penalty function are used for guidance feedback. The multi-physics multi-objective problem is constructed as a Markov decision quintuple, and a state space vector and an action space vector are constructed. The action space vector is mapped to the proximal policy optimization guidance evolution factor parameters. A proximal strategy optimization stagnation awareness guidance mechanism and a third-generation non-dominated sorting genetic algorithm adaptive evolutionary factor are added to the main algorithms of the proximal strategy optimization decision algorithm and the third-generation non-dominated sorting genetic algorithm as a hybrid algorithm. After initializing the population with the hybrid algorithm, adaptive updates are performed. The proximal strategy optimization stagnation awareness guidance mechanism determines the population evolution status in real time and dynamically determines the evolutionary factor parameters for adaptive update iteration accordingly. After the hybrid algorithm optimization iteration is completed, the final Pareto solution set is output. The optimal solution is selected by the approximation ideal solution sorting method and used for the multiphysics field optimization design of the active magnetic bearing.

2. The multi-physics, multi-objective optimization method for active magnetic bearings according to claim 1, characterized in that, The formulas for the optimization objective x, the optimization variable F(x), and the constraints on the optimization variable are as follows: in, N The number of coil turns. l For bearing thickness, d The outer diameter of the rotor. d 0 represents the rotor's inner diameter. t The width of the magnetic pole. h For the depth of the groove, F max For the maximum electromagnetic force, V For bearing volume, P This represents the total bearing loss. D Stator outer diameter δ The length of the air gap. A 0 represents the air gap area. A c The area of ​​the coil cavity, N p For extreme logarithms, I max For maximum operating current, μ 0 is the permeability of free space. T max For the maximum temperature, Δ T total For the total temperature rise, T 0 represents the ambient temperature.

3. The multi-physics, multi-objective optimization method for active magnetic bearings according to claim 1, characterized in that, The state space vector st and the action space vector at are: In the formula, Norm Represents state normalization, G t It is algebra. FR t It is the proportion of feasible solutions. It is the average constraint violation rate. HVImp t It represents the relative improvement rate between two adjacent generations of hypervolume. NDS t The proportion of non-dominated solutions. Spread t It is a measure of the spatial distribution of the target. μ x ( t )and σ x ( t ) are two scalar statistics obtained by compressing the normalized design variables; The reward and penalty functions are set to evaluate each set of parameters. The feedback formula is as follows: In the formula, For the dominant function, γ As a discount factor, r t For real-time rewards, λ GAE It's a GAE parameter. δ t It is a timing difference error. V ( s t ) is the Critic network estimation function.

4. The multi-physics, multi-objective optimization method for active magnetic bearings according to claim 1, characterized in that, The initial population for the hybrid algorithm is: in, It is the initialized population. It is a deterministic solution for the near-end policy optimization decision algorithm. It is a stochastic solution of the near-end policy optimization decision algorithm. It is a random solution of the third-generation non-dominated sorting genetic algorithm.

5. The multi-physics, multi-objective optimization method for active magnetic bearings according to claim 1, characterized in that, The adaptive update formula for the hybrid algorithm is: in, For crossover probability, The mutation probability, N i It is the current iteration number. N max It is the maximum number of iterations. G p It is the non-dominated ranking of individuals. G pm It is the largest nondominated sort.

6. The multi-physics, multi-objective optimization method for active magnetic bearings according to claim 1, characterized in that, The formula for the stagnation-aware guidance mechanism for near-end strategy optimization is: Where I is the indicator function, L is the window length, and τ is the stagnation threshold.

7. A multi-physics, multi-objective optimization system for an active magnetic bearing, characterized in that, include: The variable setting module is used to set the target variables to be optimized for the active magnetic bearing. The optimization target and optimization variables are analyzed by using proximal strategy optimization and third-generation non-dominated sorting genetic algorithm. The vector construction module is used to analyze and evaluate the results under different parameter combinations through the proximal policy optimization decision algorithm, and to guide the feedback with reward and penalty functions; it constructs the multi-physics multi-objective problem into a Markov decision quintuple, constructs the state space vector and action space vector, and maps the action space vector to the proximal policy optimization guidance evolution factor parameters; The hybrid algorithm computation module is used to add a proximal strategy optimization stagnation awareness guidance mechanism and a third-generation non-dominated sorting genetic algorithm adaptive evolutionary factor to the main algorithms of the proximal strategy optimization decision algorithm and the third-generation non-dominated sorting genetic algorithm as a hybrid algorithm. After initializing the population with the hybrid algorithm, adaptive updates are performed. The proximal strategy optimization stagnation awareness guidance mechanism determines the population evolutionary state in real time and dynamically determines the evolutionary factor parameters for adaptive update iteration based on this. The optimal parameter generation module is used to output the final Pareto solution set after the hybrid algorithm optimization iteration is completed. The optimal solution is selected by the approximation ideal solution sorting method and used for the multiphysics field optimization design of active magnetic bearings.

8. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method of any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1-6.

10. A computer program product comprising a computer-readable medium, characterized in that, The computer-readable medium contains computer-readable program code that performs the method according to any one of claims 1-6.

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