A multi-objective optimization method suitable for a multi-parameter coupled permanent magnet Vernier rim-propulsion motor

Abstract

The application discloses a multi-target optimization method suitable for a multi-parameter coupled permanent magnet vernier rim propulsion motor, and comprises the following steps: S1, establishing a motor no-load model; S2, taking the average torque and torque ripple of the permanent magnet vernier rim propulsion motor under load as optimization targets; S3, on the basis of completing the design of the no-load condition, determining the value range of the structural parameters related to the average torque and torque ripple; S4, bringing the value range of the structural parameters back to the motor no-load model to check whether the design requirements under the motor no-load condition are met; S5, adopting a Latin hypercube test to construct a sample library, and referring to the distribution of the sample library data, supplementing certain sample data in the sampling range with sparse samples by adopting an optimized Latin hypercube method; S6, performing sensitivity sorting and hierarchical processing on the motor structural parameters according to a parameter sensitivity analysis mode; and S7, finding a global optimal solution, and adjusting the structural parameters with weak sensitivity to complete optimization.

Description

Technical Field

[0001] This invention relates to the field of motor optimization design, and in particular to multi-objective optimization of permanent magnet vernier wheel rim propulsion motors with multi-parameter coupling. Background Technology

[0002] With increasingly frequent maritime trade exchanges between countries, higher demands are being placed on the transport and propulsion capabilities of ships. Traditional ship propulsion systems use a combination of a propulsion shaft and a propeller, which occupies a large amount of space and reduces propulsion efficiency and reliability. In recent years, a highly integrated electric propulsion device—the shaftless rim propeller—has emerged. It eliminates the propulsion shaft, directly integrating the motor rotor and propeller blades into one unit. It uses direct current drive, with the motor rotor welded to the blades, allowing the propulsion motor to directly drive the blades to perform work, thus improving the hydrodynamic performance of the propeller. Compared to traditional propulsion shaft systems, shaftless rim propellers have the advantages of smaller footprint, lower noise, lower vibration, and higher efficiency.

[0003] Permanent magnet vernier motors have the advantages of low-speed high torque output, fewer slots, high stator core utilization at low speeds, and low torque ripple. They can be combined with wheel rim propulsion motors to form permanent magnet vernier wheel rim propulsion motors, achieving low-speed high torque output and direct drive functions, thereby further improving the performance of ship propulsion systems.

[0004] However, permanent magnet vernier motors are magnetic field modulation type motors. Due to modulation behavior, their air gap magnetic field is complex, containing not only a fundamental component with large amplitude but also various higher harmonics. Furthermore, permanent magnet vernier motors have many parameters and a high degree of coupling. Traditional single-variable optimization methods have low computational cost and fast solution speed, but the optimization results obtained for a single parameter do not reflect the overall optimality. Conventional multi-objective optimization methods often employ "response surface methodology + multi-objective optimization algorithm," which has high computational accuracy, but involves a large computational load and long solution time. Moreover, once there are more than three optimization parameters, the computational difficulty increases exponentially. Currently, multi-objective optimization methods still suffer from problems such as long optimization time, low optimization efficiency, and unsatisfactory optimization results. Therefore, how to quickly and accurately find the optimal structural parameters of the motor is a problem that urgently needs to be solved. Summary of the Invention

[0005] In view of the problems existing in the prior art, the present invention discloses a multi-objective optimization method applicable to multi-parameter coupled permanent magnet vernier wheel rim propulsion motor. By performing multi-objective optimization on the permanent magnet vernier wheel rim propulsion motor, the optimization objectives of maximizing average torque and minimizing torque ripple are achieved.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] S1. A two-dimensional finite element model was built on Maxwelll software. The material properties of the motor stator, rotor, and permanent magnet were set. A winding arrangement with fractional concentrated windings and spaced-tooth winding was selected. Zero-current excitation was applied to conduct an no-load test. In the early design stage, the no-load back EMF and waveform distortion rate of the motor were mainly considered to select appropriate slot-pole fits and stator and rotor dimensions.

[0008] S2. After determining the preliminary design, based on the target rated power of the motor, apply appropriate current excitation to conduct load tests. The main optimization targets are the average torque and torque ripple of the permanent magnet vernier wheel flange propulsion motor. Combined with parametric modeling methods, analyze and screen out the structural parameters that can significantly affect the average torque and torque ripple.

[0009] S3. Based on the preliminary completion of the motor design simulation, determine the value range of the structural parameters that affect the average torque and torque ripple, thereby reducing the workload of subsequent optimization. The selection criteria for the value range are: taking the maximum average torque and minimum torque ripple achievable in step S2 as the standard, and keeping other structural parameters unchanged, changing a certain structural parameter should result in a response that is 0.9 times higher than the maximum average torque or a torque ripple that does not exceed 1.1 times the minimum torque ripple;

[0010] S4. Considering the logic before and after the design, the structural parameters determined in step S3 need to be brought back into the motor no-load model. If, within the range of values ​​determined in S3, there are values ​​that significantly reduce the no-load back EMF or significantly increase the waveform distortion rate, that range of values ​​should be eliminated to further narrow down the subsequent optimization range.

[0011] S5. Construct a sample library using Latin hypercube experimental design. At the same time, refer to the distribution of the sample library data and use the optimized Latin hypercube method to supplement a certain number of samples in the range of sparse samples, so as to ensure that the sample points are distributed as evenly as possible in the value space, which is convenient for constructing a smoother response surface.

[0012] S6: By pairwise permutations and combinations of motor structural parameters, the high-dimensional multi-objective optimization problem is reduced to multiple two-dimensional multi-objective optimization problems, and Kriging response surface models are established for each. Based on parameter sensitivity analysis, the motor structural parameters are sorted and stratified according to their sensitivity.

[0013] S7: Based on the multi-objective whale optimization algorithm, multi-objective optimization is performed on the highly sensitive structural parameters to find the global optimal solution, and then the less sensitive structural parameters are adjusted to complete the optimization.

[0014] Furthermore, step S1 mainly affects the motor's no-load back EMF and waveform distortion rate through the selection of the slot pole scheme. The permanent magnet vernier rim propulsion motor operates based on the principle of magnetic field modulation. The stator modulation pole number Zs, the permanent magnet pole pair number Pr, and the armature winding pole pair number Pw satisfy the following relationship:

[0015] Z s =P r +P w

[0016] The structural parameter block affecting the average torque and torque ripple of the motor in step S2 includes: permanent magnet thickness h. g Polar arc coefficient α, modulation tooth width f h Modulation tooth height h, isolation tooth width f s Modular air gap thickness h g .

[0017] In step S3, the thickness h of the permanent magnet is respectively... g Polar arc coefficient α, modulation tooth width f h Modulation tooth height h, isolation tooth width f s Modular air gap thickness h g Single-parameter simulations are performed, and the ranges of each structural parameter are given based on the motor's average torque and torque ripple performance, combined with the design objectives.

[0018] The parameters in step S4 are brought back to the no-load model, and some unsuitable parameters can be eliminated based on the no-load back EMF and waveform distortion rate, further narrowing the optimization selection range.

[0019] In step S5, sample points are set within the optimization range of each structural parameter using the Latin hypercube experiment. The principle behind this is stratified sampling, which approximates sampling from a multivariate parameter distribution. The mathematical formula for this principle is as follows:

[0020]

[0021] This formula describes the process of drawing n sample points from q design variables, where a ik It is matrix A = (a ik An element of ), where matrix A is an n*q matrix, a ik Let A represent the value of the k-th variable for the i-th sample point. Each column of matrix A represents a random permutation of 1 to n, with a total of n! permutations. U is also an n*q matrix. ik It follows a uniform distribution of 0-1.

[0022] However, ordinary Latin hypercube sampling can exhibit localized uneven distribution. To ensure that sample points discretely fill the entire space, additional sample points need to be added to the sparse space. Latin hypercube sampling optimized using the minimax method guarantees that the supplementary sample points can discretely fill the sparse value space. The principle and formula are as follows:

[0023]

[0024] D i =min(d i1 ,d i2 ...d in )

[0025] In the formula d ij D represents the distance between sample point i and sample point j. i Let be the eigenvalue of sample point i, representing the minimum distance to other sample points. Through iterative testing, it is possible to ensure that the eigenvalue of each sample point is as large as possible, thus guaranteeing that the supplementary sample points can fill the sparse value space.

[0026] In step S6, the Kriging model uses the covariance function to predict stochastic processes, achieving unbiased estimation. The Kriging model estimates the prediction point using known sample points, and the relationship between the sample points and the prediction point is as follows:

[0027]

[0028] Where Z is * (x) Predicted point, Z(x) i ) represents known sample points, N represents the number of sample points, and λ represents the number of sample points. i The correlation coefficient is the value of the unknown prediction point. The correlation coefficient can be expressed as:

[0029]

[0030] Where θ p To characterize the covariance coefficients that represent the influence of the Gaussian covariance function, the optimal θ p It is generally obtained through maximum likelihood estimation.

[0031] In step S6, based on the sensitivity analysis results in Optislang, the six structural parameters in S2 are sorted by sensitivity and divided into high-sensitivity parameters and low-sensitivity parameters.

[0032] In step S7, following a strong-to-weak order, the multi-objective whale optimization algorithm is used to perform multi-objective optimization on the highly sensitive structural parameters to find the global optimum. Then, the less sensitive structural parameters are adjusted to complete the optimization. The multi-objective whale optimization algorithm simulates the behavior of beluga whales in nature, which includes three stages: swimming (searching), foraging (optimization), and whale fall (selection).

[0033] The specific process of the multi-objective whale optimization algorithm is as follows: First, initialize the beluga whale population size n, the current iteration count T = 1, and the maximum iteration count T. max The initial positions of the population are randomly generated, and the population fitness is calculated according to the objective function. The balance factor B for each whale is used. fThe balance factor determines whether a creature is swimming or foraging. The formula for calculating the balance factor is as follows, where B0 is a random number between (0,1):

[0034] B f =B0(1-T / 2T) max )

[0035] When B f When the value is greater than 0.5, the whale is in the swimming phase. The algorithm's global search capability is ensured by continuously updating the position information of individual whales. The mathematical model for updating the beluga whale's position during swimming is as follows:

[0036]

[0037] d represents the dimension of the variable. This represents the new position of the i-th (i = 1, 2, ..., n) whale in dimension j (j = 1, 2, ..., d). and Let p represent the current positions of the i-th whale and the r-th whale, respectively. j r is a random number from 1 to d, r is a random number from 1 to n, and r1 and r2 are both random numbers between (0,1) to increase the randomness of the global search. The choice of odd and even dimensions reflects the synchronous behavior of beluga whales when swimming.

[0038] When B f When the value is ≤0.5, the whale is in the foraging phase. The beluga whale population cooperates in hunting by sharing location information. At the same time, a flight function is introduced to enhance convergence. The mathematical model for position update is as follows:

[0039]

[0040] and Let i and r represent the current positions of the i-th and r-th whales, respectively. Indicates the new position of the i-th whale. This represents the optimal hunting location within the beluga whale population, where r3 and r4 are random numbers between (0,1), and C1 = 2r4(1-T / T). max ), flight function L F The calculation formula is as follows:

[0041]

[0042]

[0043] u and v are random numbers that follow a normal distribution, and Γ(x) is the gamma function. Regardless of whether the whale is swimming or foraging, when a position update occurs, the population fitness is recalculated and the whales are reordered.

[0044] Since swimming and foraging can be dangerous, each change of location necessitates updating the population through whale falls. This study simulates the natural selection process of beluga whales under various threats, aiming to improve the natural adaptability of the beluga whale population. The mathematical model for this location update process is as follows:

[0045]

[0046] X step =(ab)exp(-C2T / T) max )

[0047] C2 = 2W f ×n

[0048] W f =0.1-0.05T / T max

[0049] r5, r6, and r7 are random numbers between (0, 1), X step The whale fall is short, C2 represents the step size factor, W f This represents the whale fall probability, with a and b being the upper and lower bounds of the variable. Each time whale fall data is updated, the iteration count is incremented, and the population fitness is recalculated and sorted to find the current optimal solution. This process is repeated iteratively until the current iteration count exceeds the maximum iteration count, at which point the loop terminates, and the current position is the optimal solution.

[0050] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0051] The design fully considers two operating conditions of the motor—no-load and loaded—and performs targeted optimization. Furthermore, after completing the loaded design, the parameters are reviewed, ensuring compatibility between the two parts of the design and eliminating unreasonable value ranges, thus reducing the workload for subsequent optimization, rather than relying solely on finite element software and equipment for calculations.

[0052] Based on the standard Latin hypercube sampling method to determine the sample points, a Latin hypercube method based on the minimax method is used to perform point supplementation, which makes the sample point distribution more uniform, the constructed response surface smoother, and improves the accuracy of the motor equivalent model.

[0053] Conventional multi-objective optimization methods for structures with three or more parameters suffer from enormous computational costs and long solution times. This approach constructs response surfaces by pairwise combinations of parameters and sorts them according to sensitivity analysis results, optimizing step-by-step in order of increasing strength. This fully considers the influence of each structural parameter, ensuring optimization accuracy. Simultaneously, the high-order multi-objective solution is decomposed into... This second-order multi-objective solution greatly reduces the amount of computation and shortens the solution time.

[0054] The multi-objective whale optimization algorithm is simple to operate and easy to implement. It does not rely on a large amount of computing resources, can handle large-scale complex problems, is suitable for searching for the global optimum in multi-dimensional space, and its optimization effect does not depend on the selection of the initial population. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a schematic diagram of the permanent magnet fault-tolerant vernier wheel rim propulsion motor structure of the present invention.

[0057] Figure 2 A schematic diagram of the overall optimization process provided by the present invention.

[0058] Figure 3 Comparison chart of motor parameters before and after optimization provided for this invention

[0059] Figure 4 Torque comparison chart before and after optimization provided for this invention

[0060] Figure 5 A comparison chart of torque data before and after optimization provided for this invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0062] In the accompanying drawings of specific embodiments of the present invention, in order to better and more clearly describe the working principle of each component in the system and show the connection relationship of each part in the device, only the relative positional relationship between each component is clearly distinguished. It does not constitute a limitation on the signal transmission direction, connection sequence, or size, dimension, and shape of each part within the component or structure.

[0063] like Figure 1The permanent magnet fault-tolerant vernier rim propulsion motor shown comprises a stator 1, a rotor 2, and a propeller blade 3. The stator includes a stator core 4, modulation teeth 5, fault-tolerant teeth 6, 24 stator slots 7, and a single-layer concentrated winding 8. The rotor includes a rotor core 9, core poles 10 in alternating poles, radially magnetized permanent magnet poles 11, tangentially magnetized permanent magnets 12 magnetized at a 45-degree angle to the right, and tangentially magnetized permanent magnets 13 magnetized at a 45-degree angle to the left.

[0064] The stator core 4 has 24 uniformly spaced winding slots 7, with a single-layer concentrated winding 8 embedded within them; the rotor 2 has a short-shaft flat structure, with core poles 10 and permanent magnet poles 11, 12, and 13 arranged alternately on the outer side of the rotor core, equivalent to 26 pairs of permanent magnets. The permanent magnets employ a Halbach array, with the central permanent magnet 11 radially magnetized and the two side permanent magnets 12 and 13 tangentially magnetized at a 45-degree angle; non-magnetic propeller blades 3 are directly welded to the inner side of the rotor core 9.

[0065] The flowchart of the multi-objective optimization design method for a multi-parameter coupled permanent magnet vernier wheel rim propulsion motor proposed in this invention is attached. Figure 2 As shown, the specific steps are as follows:

[0066] S1. A two-dimensional finite element model was built on Maxwelll software. The material properties of the motor stator, rotor, and permanent magnet were set. A winding arrangement with fractional slot concentrated windings and tooth-separated windings was selected, and a zero-current excitation was applied for no-load testing. According to the relevant theory of magnetic field modulation motors, the selection of slot pole scheme mainly affects the no-load back electromotive force and waveform distortion rate of the motor. The permanent magnet vernier rim propulsion motor operates based on the principle of magnetic field modulation. The stator modulation pole number Zs, the number of permanent magnet pole pairs Pr, and the number of armature winding pole pairs Pw satisfy the following relationship:

[0067] Z s =P r +P w

[0068] Based on this, a theoretically suitable slot pole matching scheme is selected, and simulation verification is carried out by building a model to select a suitable slot pole matching and main dimensions of the stator and rotor.

[0069] S2. After determining the preliminary design, based on the target rated power of the designed motor, a suitable current excitation was applied to conduct a load test, mainly optimizing the average torque and torque ripple of the permanent magnet vernier wheel flange propulsion motor. Among the many design parameters of the motor, the structural parameters that significantly affect the average torque and torque ripple of the motor were identified using parametric modeling methods. Finally, after multiple analyses and screenings, the following six motor structural parameters were determined for optimization: permanent magnet thickness h g Polar arc coefficient α, modulation tooth width f h Modulation tooth height h, isolation tooth width fs Modular air gap thickness h g ;

[0070] S3. Based on the preliminary completion of the motor design simulation, the thickness h of the permanent magnet was analyzed. g Polar arc coefficient α, modulation tooth width f h Modulation tooth height h, isolation tooth width f s Modular air gap thickness h g Single-parameter simulations were performed to determine the value range of structural parameters affecting the average torque and torque ripple based on the motor's average torque and torque ripple performance, thereby reducing the workload of subsequent optimization. The selection criteria for the value range were: taking the maximum average torque and minimum torque ripple achievable in step S2 as the standard, and keeping other structural parameters unchanged, changing a certain structural parameter should result in a response that is 0.9 times higher than the maximum average torque or a torque ripple that is no more than 1.1 times the minimum torque ripple;

[0071] S4. Considering the logical consistency before and after the design, the structural parameters determined in step S3 need to be brought back to the motor no-load model. Based on the no-load back EMF and waveform distortion rate, some unsuitable parameters should be eliminated. If, within the value range determined in S3, there are values ​​that significantly decrease the no-load back EMF or significantly increase the waveform distortion rate, that value range should be eliminated to further narrow down the subsequent optimization range.

[0072] S5. A sample library is constructed using Latin hypercube experimental design. Simultaneously, referencing the distribution of the sample library data, an optimized Latin hypercube method is used to supplement the sample number within sparse areas, ensuring that sample points are distributed as evenly as possible within the value space, facilitating the construction of a smoother response surface. The Latin hypercube experiment sets sample points within the optimized range of each structural parameter. Its principle is a stratified sampling, that is, approximating sampling from a multivariate parameter distribution. The mathematical formula for this principle is:

[0073]

[0074] This formula describes the process of drawing n sample points from q design variables, where a ik It is matrix A = (a ik An element of ), where matrix A is an n*q matrix, a ik Let A represent the value of the k-th variable for the i-th sample point. Each column of matrix A represents a random permutation of 1 to n, with a total of n! permutations. U is also an n*q matrix. ik It follows a uniform distribution of 0-1.

[0075] However, ordinary Latin hypercube sampling can exhibit localized uneven distribution. To ensure that sample points discretely fill the entire space, additional sample points need to be added to the sparse space. Latin hypercube sampling optimized using the minimax method guarantees that the supplementary sample points can discretely fill the sparse value space. The principle and formula are as follows:

[0076]

[0077] D i =min(d i1 ,d i2 ...d in )

[0078] In the formula d ij D represents the distance between sample point i and sample point j. i Let be the eigenvalue of sample point i, representing the minimum distance to other sample points. Through iterative testing, it can be ensured that the eigenvalue of each sample point is as large as possible, thus guaranteeing that the supplementary sample points can fill the sparse value space.

[0079] S6. Perform pairwise permutations and combinations of the motor structural parameters and establish Kriging response surfaces for each. Based on the sensitivity analysis results in Optislang, rank the six structural parameters in S2 according to their sensitivity. The Kriging model uses the covariance function to predict stochastic processes, achieving unbiased estimation. The Kriging model estimates predicted points using known sample points. The relationship between sample points and predicted points is as follows:

[0080]

[0081] Where Z is * (x) Predicted point, Z(x) i ) represents known sample points, N represents the number of sample points, and λ represents the number of sample points. i The correlation coefficient is the value of the unknown prediction point. The correlation coefficient can be expressed as:

[0082]

[0083] Where θ p To characterize the covariance coefficients that represent the influence of the Gaussian covariance function, the optimal θ p Generally, it is obtained through maximum likelihood estimation; based on the sensitivity analysis results in Optislang, the six structural parameters in S2 are ranked by sensitivity and divided into high-sensitivity parameters and low-sensitivity parameters.

[0084] S7. Based on the multi-objective whale optimization algorithm, multi-objective optimization is performed on the highly sensitive structural parameters to find the global optimum. Then, the less sensitive structural parameters are adjusted to complete the optimization. A comparison of motor parameters before and after optimization is shown below. Figure 3 As shown, the multi-objective whale optimization algorithm simulates the behavior of beluga whales in nature, which includes three stages: swimming (searching), foraging (optimization), and whale fall (selection).

[0085] The specific process of the multi-objective whale optimization algorithm is as follows: First, initialize the beluga whale population size n, the current iteration count T = 1, and the maximum iteration count T. max The initial positions of the population are randomly generated, and the population fitness is calculated according to the objective function. The balance factor B for each whale is used. f The balance factor determines whether a creature is swimming or foraging. The formula for calculating the balance factor is as follows, where B0 is a random number between (0,1):

[0086] B f =B0(1-T / 2T) max )

[0087] When B f When the value is greater than 0.5, the whale is in the swimming phase. The algorithm's global search capability is ensured by continuously updating the position information of individual whales. The mathematical model for updating the beluga whale's position during swimming is as follows:

[0088]

[0089] d represents the dimension of the variable. This represents the new position of the i-th (i = 1, 2, ..., n) whale in dimension j (j = 1, 2, ..., d). and Let p represent the current positions of the i-th whale and the r-th whale, respectively. j r is a random number from 1 to d, r is a random number from 1 to n, and r1 and r2 are both random numbers between (0,1) to increase the randomness of the global search. The choice of odd and even dimensions reflects the synchronous behavior of beluga whales when swimming.

[0090] When B f When the value is ≤0.5, the whale is in the foraging phase. The beluga whale population cooperates in hunting by sharing location information. At the same time, a flight function is introduced to enhance convergence. The mathematical model for position update is as follows:

[0091]

[0092] and Let i and r represent the current positions of the i-th and r-th whales, respectively. Indicates the new position of the i-th whale. This represents the optimal hunting location within the beluga whale population, where r3 and r4 are random numbers between (0,1), and C1 = 2r4(1-T / T). max ), flight function L F The calculation formula is as follows:

[0093]

[0094]

[0095] u and v are random numbers that follow a normal distribution, and Γ(x) is the gamma function. Regardless of whether the whale is swimming or foraging, when a position update occurs, the population fitness is recalculated and the whales are reordered.

[0096] Since swimming and foraging can be dangerous, each change of location necessitates updating the population through whale falls. This study simulates the natural selection process of beluga whales under various threats, aiming to improve the natural adaptability of the beluga whale population. The mathematical model for this location update process is as follows:

[0097]

[0098] X step =(ab)exp(-C2T / T) max )

[0099] C2 = 2W f ×n

[0100] W f =0.1-0.05T / T max

[0101] r5, r6, and r7 are random numbers between (0, 1), X step The whale fall is short, C2 represents the step size factor, W f This represents the whale fall probability, with a and b being the upper and lower bounds of the variable. Each time the whale fall data is updated, the iteration count is incremented, and the population fitness is recalculated and sorted to find the current optimal solution. This process is repeated iteratively until the current iteration count exceeds the maximum iteration count, at which point the loop terminates, and the current position is the optimal solution. A comparison of the motor torque waveforms before and after optimization is shown below. Figure 4 As shown, the specific values ​​of average torque and torque ripple are compared to, for example... Figure 5 As shown.

[0102] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in or transmitted through a computer-readable storage medium. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0103] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multi-objective optimization method applicable to multi-parameter coupled permanent magnet vernier wheel rim propulsion motors, characterized in that: The steps include the following: S1: Based on the no-load back EMF and waveform distortion rate of the motor, the permanent magnet vernier wheel flange propulsion motor is optimized under no-load conditions, and a no-load model of the motor is established. S2: Taking the average torque and torque ripple of the permanent magnet vernier wheel flange propulsion motor under load as the optimization target, the motor structural parameters that can significantly affect the average torque and torque ripple are analyzed and screened by combining parametric modeling methods. S3: Based on the completed no-load condition design, determine the range of values ​​for structural parameters that affect the average torque and torque pulsation; S4: Bring the range of structural parameters back to the motor no-load model to check whether it meets the design requirements under the motor no-load condition. S5: A sample library is constructed using the Latin hypercube experiment. Based on the distribution of the sample library data, an optimized Latin hypercube method is used to supplement certain sample data within the sparse sampling range. S6: By arranging the motor structural parameters in pairs, the high-dimensional multi-objective optimization problem is reduced to multiple two-dimensional multi-objective optimization problems, and Kriging models are established for each problem. The sensitivity of the motor structural parameters is sorted and hierarchically processed according to the parameter sensitivity analysis method. S7: Based on the multi-objective whale optimization algorithm, multi-objective optimization is performed on the highly sensitive structural parameters to find the global optimal solution, and the less sensitive structural parameters are adjusted to complete the optimization; Structural parameters affecting the average torque and torque ripple of a motor include: permanent magnet thickness. Polar arc coefficient Modulating tooth width Modulation tooth height , width of isolation teeth and modular air gap thickness ; The specific process of the multi-objective whale optimization algorithm is as follows: First, initialize the beluga whale population size n and the current iteration number. and maximum number of iterations The initial positions of the population are randomly generated, and the population fitness is calculated according to the objective function, based on the balance factor of each whale. The balance factor determines whether a creature is swimming or foraging. The formula for calculating the balance factor is as follows: A random number between (0,1): when At this time, the whale is in the swimming phase. The algorithm's global search capability is ensured by continuously updating the position information of individual whales. The mathematical model for updating the beluga whale's position during swimming is as follows: d represents the dimension of the variable. This represents the new position of the i-th (i=1,2…n) whale in dimension j, where j=1,2…d. and Let p represent the current positions of the i-th whale and the r-th whale, respectively. j r is a random number from 1 to d, r is a random number from 1 to n, and r1 and r2 are both random numbers between (0,1) to increase the randomness of the global search. The choice of odd and even dimensions reflects the synchronous behavior of beluga whales when swimming. when At this time, the whales are in the foraging phase. The beluga whale population cooperates to hunt by sharing location information. At the same time, a flight function is introduced to enhance convergence. The mathematical model for position update is as follows: and Let i and r represent the current positions of the i-th and r-th whales, respectively. Indicates the new position of the i-th whale. This represents the optimal hunting location within the beluga whale population, where r3 and r4 are random numbers between (0,1). Flight function L F The calculation formula is as follows: u and v are random numbers that follow a normal distribution. It is a gamma function that recalculates and sorts the population fitness when a position update occurs, regardless of whether the whale is swimming or foraging. Since swimming and foraging can be dangerous, each change of location necessitates updating the population through whale falls. This study simulates the natural selection process of beluga whales under various threats, aiming to improve the natural adaptability of the beluga whale population. The mathematical model for this location update process is as follows: r5, r6, and r7 are random numbers between (0, 1). It's the stride length of a whale fall. Indicates the step size factor. is the whale fall probability, and a and b are the upper and lower bounds of the variables. Whenever the whale fall data is updated, the iteration count is incremented by one, and the population fitness is recalculated and sorted to find the current optimal solution. The above steps are repeated until the current iteration count is greater than the maximum iteration count, at which point the loop terminates, and the current position is the optimal position solution.

2. The multi-objective optimization method for a multi-parameter coupled permanent magnet vernier wheel rim propulsion motor according to claim 1, characterized in that: The permanent magnet vernier wheel rim propulsion motor operates based on the principle of magnetic field modulation, wherein the stator modulation pole number Z s Permanent magnet pole pair number P r Armature winding pole pair number P w The following relationship must be satisfied: 。 3. The multi-objective optimization method for a multi-parameter coupled permanent magnet vernier wheel rim propulsion motor according to claim 1, characterized in that: Regarding the thickness of the permanent magnet Polar arc coefficient Modulating tooth width Modulation tooth height , width of isolation teeth Modular air gap thickness Perform single-parameter simulation and output the range of each structural parameter based on the motor's average torque and torque ripple performance, combined with the design objectives.

4. The multi-objective optimization method for a multi-parameter coupled permanent magnet vernier wheel rim propulsion motor according to claim 1, characterized in that: When the range of structural parameters is brought back to the motor no-load model, some unsuitable parameters are eliminated based on the no-load back EMF and waveform distortion rate, thereby narrowing the optimization selection range.

5. The multi-objective optimization method for a multi-parameter coupled permanent magnet vernier wheel rim propulsion motor according to claim 1, characterized in that: By setting sample points within the optimization range of various structural parameters through the Latin hypercube experiment, sampling is approximately completed from the multivariate parameter distribution. The specific formula is as follows: This formula is used to extract n sample points from q design variables, where... Is matrix A=( ) One element of matrix A, where matrix A is n q matrix, Let $\mathbf{i}$ represent the value of the $k$-th variable for the $i$-th sample point. Each column of matrix A represents a random permutation from 1 to $n$. There are a total of $\mathbf{i}$ columns. There are n possible arrangements, where U is n The matrix of q, It follows a uniform distribution of 0-1; By adding a certain number of sample points to the sparse sample space, and using Latin hypercube sampling optimized by the min-max method, the supplementary sample points are ensured to discretely fill the sparse value space. The principle formula is as follows: In the formula This represents the distance between sample point i and sample point j. Let i be the eigenvalue of sample point i, and let i represent the minimum distance from other sample points. Through repeated iterative verification, we can ensure that the supplementary sample points can fill the sparse value space.

6. The multi-objective optimization method for a multi-parameter coupled permanent magnet vernier wheel rim propulsion motor according to claim 1, characterized in that: The Kriging model uses the covariance function to predict stochastic processes and achieve unbiased estimation. The Kriging model estimates predicted points using known sample points, and the relationship between the sample points and the predicted points is as follows: Among them Prediction point Given sample points, N The number of sample points The correlation coefficient, the value of the unknown prediction point, and the correlation coefficient can be expressed as: in The optimal covariance coefficient is used to characterize the influence of the Gaussian covariance function. Obtained through maximum likelihood estimation.

7. The multi-objective optimization method for a multi-parameter coupled permanent magnet vernier wheel rim propulsion motor according to claim 1, characterized in that: Based on the sensitivity analysis results in Optislang, the six structural parameters were ranked by sensitivity and divided into high-sensitivity parameters and low-sensitivity parameters.

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