Permanent magnet brushless direct current motor and parameter optimization method thereof

Abstract

The invention discloses a permanent magnet brushless direct current motor and a parameter optimization method thereof. A rotor adopts a regular hexagon structure, and permanent magnets are alternately embedded into the rotor. Seven parameters such as the maximum thickness of a permanent magnet, a pole-arc coefficient and the width of a stator notch are selected for optimization, air gap flux density, no-load back electromotive force and no-load cogging torque are taken as optimization targets, a response surface model of a multi-objective function is constructed, parameter weights of the multi-objective function are determined in combination with a CRITIC weight analysis method, the motor parameters are optimized by adopting an improved MOEA / D algorithm, and the optimal parameters of the multi-objective function are obtained. And carrying out crossover variation on the population by directional variation guided by electromagnetic characteristics, and designing a weight vector optimization Chebyshev aggregation method to find an optimal iteration population. According to the weight in the Chebyshev aggregation function designed by the invention, the problems that the traditional Chebyshev aggregation method is not smooth enough for the continuous MOP problem and the obtained solution is not uniform are solved, and the distribution uniformity of the Pareto solution set is optimized. The method has obvious advantages in the aspects of convergence speed, solution set distribution and engineering feasibility.

Description

Technical Field

[0001] The present invention relates to a method for optimizing a motor, in particular to a permanent magnet brushless DC motor and a method for optimizing its parameters, and more particularly to the field of optimizing the structural parameters of a motor by using MOEA / D. Background Art

[0002] Permanent magnet brushless DC motors are widely used in new energy vehicles (main drive motors, energy-saving accessories), industrial automation (precision control, energy-saving transformation), consumer electronics (drones, smart home appliances), aerospace (flight control systems, military drones), and renewable energy (wind turbine pitch control, energy storage temperature control) fields due to their advantages of high efficiency, high power density, and low noise. They are adapted to high dynamic response, extreme environments, and energy-saving requirements, and contribute to the intelligent and green transformation. Therefore, optimizing the structural parameters of permanent magnet brushless DC motors is extremely important.

[0003] The optimization of the structural parameters of permanent magnet brushless DC motors mainly relies on algorithms and multi-physics field coupling analysis. Traditional algorithms such as GA and PSO optimize parameters such as magnetic poles and stators through multi-objective search, but are prone to falling into local optima. Multi-physics field coupling optimization combines electromagnetic-thermal-stress simulation and surrogate models (such as Kriging) to balance performance and temperature rise, but the computational cost is high. Deep learning maps the relationship between parameters and performance through neural networks, which is suitable for high-dimensional non-linear problems (such as magnetic pole topology optimization), but relies on a large amount of data. However, these algorithms have insurmountable limitations. For example, high-precision simulation is time-consuming, and there is a problem of difficulty in optimizing the population due to its too large size, and a reduced-order model is required for acceleration.

[0004] Traditional permanent magnet brushless DC motor optimization techniques rely on single-objective empirical design and are difficult to balance the conflicts among air-gap magnetic density, back electromotive force, and cogging torque. The MOEA / D algorithm uses random crossover and mutation, has a slow convergence rate, uneven distribution of solution sets, and does not effectively embed electromagnetic constraints. The present invention proposes an improved MOEA / D method, which guides directional mutation through electromagnetic characteristics, perturbs along the gradient direction to accelerate convergence, combines dynamic weights and response surface modeling to reduce the simulation cost; and the improved Chebyshev aggregation function optimizes the solution set to be more uniform and corrects the constraints in real time, significantly improving the engineering feasibility. Summary of the Invention

[0005] Object of the Invention: Aiming at the problems in the background art, the present invention provides a permanent magnet brushless DC motor and a method for optimizing its parameters, which guide directional mutation through electromagnetic characteristics and optimize the structural parameters of the permanent magnet brushless DC motor by using MOEA / D.

[0006] Technical solution: A permanent magnet brushless DC motor of the present invention includes a rotor part and a stator part. The rotor part includes a regular hexagonal rotor core and 6 permanent magnets arranged alternately with N and S poles. The vertex positions of the hexagonal rotor core are provided with six trapezoidal wedge protrusions. The stator part includes 9 stator slots arranged in a circumferential array. There are stator teeth between every two stator slots, and circular grooves are made at the tails of the stator teeth between slots 1-2, 4-5, and 7-8.

[0007] The outer surface of the trapezoidal wedge is arc-shaped, and it is concentric with the stator part.

[0008] The permanent magnet is embedded on the side of the regular hexagon rotor between two adjacent trapezoidal wedges, and the outer surface of the permanent magnet is an arc surface, which is concentric with the stator part.

[0009] The present invention also discloses a parameter optimization method based on the above permanent magnet brushless DC motor, including the following steps:

[0010] Step 1: Determine the optimization parameters and optimization objectives of the structure of the permanent magnet brushless DC motor:

[0011] (1) The optimization parameters are: the maximum thickness h of the permanent magnet max , the pole arc coefficient α of the permanent magnet p , the width w of the stator slot opening s , the depth d of the stator slot s , the protrusion height h of the trapezoidal wedge s , the pole-slot air gap length g1 and the rotor-slot air gap length g2;

[0012] (2) The optimization objectives are: the air gap magnetic density B g , the no-load back electromotive force E0, and the no-load cogging torque T0;

[0013] (3) According to the motor design requirements, limit the range of the optimization parameters: h max = [2.8, 4]; α p = [0.6, 0.9]; w s = [2, 6]; d s = [5, 12]; h s = [0.5, 2.4]; g1 = [0.9, 1.2]; g2 = [1.2, 2.3], unit: millimeter mm;

[0014] Step 2: Use the CCD model to construct the respective response surface models of the motor air gap magnetic density, no-load cogging torque, and no-load back electromotive force;

[0015] Step 3: Use the CRITIC weight analysis method to calculate the weights of the optimization parameters of each optimization objective, and determine the objective functions of the air gap magnetic density, no-load cogging torque, and no-load back electromotive force.

[0016] Step 4: Aggregate multiple objective functions based on the objective function in Step 3, and use the improved MOEA / D algorithm to optimize the motor structure parameters to find the optimal solution as the iterative result; the improved MOEA / D algorithm performs crossover and mutation on the population with orientation mutation guided by electromagnetic characteristics.

[0017] Further, in Step 2, the CRITIC weight analysis method is used to calculate the weights of the corresponding objective functions:

[0018]

[0019] where λ 11 is the weight ratio of h max in the air-gap magnetic density, λ 12 is the weight ratio of α p in the air-gap magnetic density, λ 1k is the weight ratio of the k-th optimization parameter in the air-gap magnetic density; λ 21 , λ 22 , λ 2n , λ 31 , λ 32 , λ 3n and so on; B g (x1...x k ) is the multi-objective function of the air-gap magnetic density based on the optimization parameters, E0(x1...x k ) is the multi-objective function of the no-load back electromotive force based on the optimization parameters, and T0(x1...x k ) is the multi-objective function of the no-load cogging torque based on the optimization parameters.

[0020] Further, the steps of the improved MOEA / D algorithm in Step 4 to optimize the motor structure parameters are as follows:

[0021] (1) Initialize the population to generate an initial population with a population size of N;

[0022] (2) Perform adaptive normalization. Select the minimum value of each dimension in the population as the ideal point, construct a new coordinate system with the ideal point as the coordinate origin, then obtain the extreme points of the population on each axis of the new coordinate system to form a hyperplane, and complete the normalization of the population according to the intercepts of the hyperplane on each axis;

[0023] (3) Perform crossover and mutation on the population with orientation mutation guided by electromagnetic characteristics to generate offspring;

[0024] (4) The improved Chebyshev aggregation method is used to decompose the MOP problem of the population into multiple sub-problems. Each sub-problem converts the multi-objective into a single objective through the Chebyshev aggregation function for optimization. The weight vector and reference point are designed, and they are sorted according to the fitness to obtain the optimal solution as the iterative result;

[0025] (5) The evolutionary algorithm is continuously iterated until the termination condition is reached to obtain the finally optimized motor structure parameters.

[0026] Furthermore, for the crossover and mutation, crossover is responsible for combining the genes of parental individuals to generate offspring, while mutation introduces randomness to increase the diversity of the population; the crossover and mutation adopt the directional mutation guided by electromagnetic characteristics, and the steps are as follows:

[0027] (1) The gradient direction of the design variable for the designed calculation objective function is:

[0028]

[0029] where is the gradient direction perturbation value of the j-th optimization parameter, η is the learning rate, η = (0.05, 0.2), x j is the original value of the j-th optimization parameter, is the partial derivative of the multi-objective function with respect to the j-th optimization parameter;

[0030] F = b1B g (x1...x k ) + b2E0(x1...x n ) + b3T0(x1...x k )

[0031] where is the gradient direction perturbation value of the j-th variable; η is the learning rate, η = (0.05, 0.2); x j is the design variable, is the partial derivative of the aggregated objective function with respect to the j-th variable; where, b1 is the weight ratio of the air-gap magnetic density in the motor performance, b2 is the weight ratio of the no-load cogging torque in the motor performance, and b3 is the weight ratio of the no-load back electromotive force in the motor performance;

[0032] (2) Apply a directional perturbation along the gradient direction and superimpose a random perturbation to generate a mutated solution. The hybrid mutation formula is:

[0033]

[0034] where x' j is the value of the j-th optimization parameter after mutation; δ is the random perturbation intensity; N(0, σ 2 ) is the Gaussian distribution; σ 2is the standard deviation of the Gaussian distribution;

[0035] (3) Real-time correction is performed on the solutions that violate electromagnetic or process constraints. If the mutation is too large and causes x' j to exceed the limit, the step size is stepped back by a ratio of a:

[0036]

[0037] where a = (0, 1).

[0038] Furthermore, the improved Chebyshev aggregation method mainly includes the following parts:

[0039] The definition of the Chebyshev aggregation function is:

[0040]

[0041] where minimize g te (x|m, Z * ) is the Chebyshev aggregation value, m i are the optimization weights of the multi-objective functions of the air-gap magnetic flux density, no-load back electromotive force, and no-load cogging torque respectively, and satisfy m i ≥0, i = 1, 2, 3; x is the decision vector, including all optimization parameters to be optimized; is the ideal point, taking the minimum of the objective function values of the multi-objective functions of the air-gap magnetic flux density, no-load back electromotive force, and no-load cogging torque of the current population, that is is the ideal point of the optimized air-gap magnetic flux density population, is the ideal point of the optimized no-load cogging torque population, is the ideal point of the optimized no-load back electromotive force population; f i (x) is the value of the i-th multi-objective function; f1(x) is the value of the multi-objective function of the air-gap magnetic flux density, f2(x) is the value of the multi-objective function of the no-load cogging torque, and f3(x) is the value of the multi-objective function of the no-load back electromotive force;

[0042] Set different weight vectors Obtain all the convergence points, form the optimal Pareto optimal solution set, design the improved weight vector to obtain a more evenly distributed solution, and optimize the final solution set. The improved weight vector m * is:

[0043]

[0044] Beneficial effects:

[0045] The present invention proposes an improved MOEA / D method, which guides directional mutation through electromagnetic characteristics, perturbs along the gradient direction to accelerate convergence, and combines dynamic weights with response surface modeling to reduce the simulation time cost; by designing the weights in the Chebyshev aggregation function, it solves the problem that the traditional Chebyshev aggregation method is not smooth enough for continuous MOP problems and the obtained solutions are uneven, and optimizes the uniformity of the Pareto solution set distribution. Description of the Drawings

[0046] Figure 1 It is a structural diagram of an inner-rotor permanent magnet brushless DC motor in an embodiment of the present application.

[0047] Figure 2 It is an optimization design process of a permanent magnet brushless DC motor based on the improved MOEA / D in an embodiment of the present application.

[0048] Figure 3 It is an optimization flow chart of the improved MOEA / D in an embodiment of the present application.

[0049] Figure 4 It is a comparison diagram of the air-gap magnetic density before and after the improvement of MOEA / D in an embodiment of the present application.

[0050] Figure 5 It is a comparison diagram of the no-load cogging torque before and after the improvement of MOEA / D in an embodiment of the present application.

[0051] Figure 6 It is a comparison diagram of the no-load back electromotive force before and after the improvement of MOEA / D in an embodiment of the present application. Detailed Embodiments

[0052] The present invention will be further described below with reference to the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and cannot be used to limit the protection scope of the present invention.

[0053] As Figure 1 shown, the structure of the permanent magnet brushless DC motor disclosed by the present invention is 6 poles and 9 slots, which includes a rotor part and a stator part. The rotor part includes: a regular hexagonal rotor core with six trapezoidal wedges 10 at the vertices and 6 permanent magnets arranged alternately with N and S poles. The stator part includes: 9 stator slots arranged in a circumferential array, stator teeth are arranged between two adjacent stator slots, and circular notches are made at the tails of the stator teeth between slots 1-2, 4-5, and 7-8. Figure 1 The numbers 1 to 9 in

[0054] represent 9 slots.

[0055] The outer surface of the trapezoidal wedge 10 is arc-shaped and is concentric with the stator part.

[0056] The permanent magnet is embedded on the edge of the regular hexagon rotor core 11 between two adjacent trapezoidal wedges 10, and the outer surface of the permanent magnet is an arc surface, which is concentric with the stator part.

[0057] The design method of the structural parameters of the permanent magnet brushless DC motor is specifically as follows:

[0058] 1. Determine the optimization parameters and optimization objectives of the permanent magnet brushless DC motor structure:

[0059] (1) Set the optimization parameters of the motor as: the maximum thickness of the permanent magnet (h max ), the pole arc coefficient of the permanent magnet (α p ), the width of the stator slot opening (w s ), the depth of the stator slot (d s ), the protrusion height of the rotor wedge (h s ), the pole-slot air gap length (g1) and the rotor-slot air gap length (g2).

[0060] (2) Set the optimization objectives of the motor as: the air gap magnetic density B g , the no-load back electromotive force E0, and the no-load cogging torque T0.

[0061] (3) According to the motor size and motor design requirements, limit the range of the optimization parameters: h max = [2.8, 4]; α p = [0.6, 0.9]; w s = [2, 6]; d s = [5, 12]; h s = [0.5, 2.4]; g1 = [0.9, 1.2]; g2 = [1.2, 2.3], in millimeters (mm).

[0062] Figure 2 It is the parameter optimization design process of the permanent magnet brushless DC motor based on the improved MOEA / D algorithm.

[0063] Step 1: Determine the optimization parameters and optimization objectives of the permanent magnet brushless DC motor structure:

[0064] (1) The optimization parameters are: the maximum thickness of the permanent magnet h max , the pole arc coefficient of the permanent magnet α p , the width of the stator slot opening w s , the depth of the stator slot d s , the protrusion height of the trapezoidal wedge h s , the pole-slot air gap length g1 and the rotor-slot air gap length g2.

[0065] (2) The optimization objectives are: the air gap magnetic density B g , the no-load back electromotive force E0, and the no-load cogging torque T0.

[0066] (3) According to the motor size and motor design requirements, limit the range of optimization parameters: h max = [2.8, 4]; α p = [0.6, 0.9]; w s = [2, 6]; d s = [5, 12]; h s = [0.5, 2.4]; g1 = [0.9, 1.2]; g2 = [1.2, 2.3], in millimeters mm.

[0067] Step 2: Use Central Composite Design to construct the respective response surface models of the air-gap magnetic density, no-load cogging torque, and no-load back electromotive force of the motor.

[0068] Step 3: Calculate the weights of the optimization parameters for each optimization objective using the CRITIC weight analysis method, and determine the objective functions of the air-gap magnetic density, no-load cogging torque, and no-load back electromotive force.

[0069] Based on the response surface models of B g , E0, and T0, establish a multi-objective function for motor optimization, and calculate the corresponding weights using the CRITIC weight analysis method:

[0070]

[0071] Among them, λ 11 is the weight ratio of h max in the air-gap magnetic density, λ 12 is the weight ratio of α p in the air-gap magnetic density, λ 1k is the weight ratio of the kth optimization parameter in the air-gap magnetic density; λ 21 , λ 22 , λ 2n , λ 31 , λ 32 , λ 3n And so on; B g (x1...x k ) is the multi-objective function of the air-gap magnetic density based on the optimization parameters, E0(x1...x k ) is the multi-objective function of the no-load back electromotive force based on the optimization parameters, T0(x1...x k ) is the multi-objective function of the no-load cogging torque based on the optimization parameters.

[0072] Step 4: Aggregate the multi-objective function based on the objective function in Step 3, and use the improved MOEA / D algorithm to optimize and search for the motor structure parameters, and obtain the optimal solution as the iterative result; the improved MOEA / D algorithm performs crossover and mutation on the population with electromagnetic characteristic-guided directional mutation. As Figure 3As shown, the improved MOEA / D is used to optimize the motor structure parameters. First, initialize a population P containing N individuals. t , generate the offspring Q through crossover and mutation. t , merge the parent generation and the offspring (P t +R t ), then screen according to the constraints and perform fitness ranking. Select the top m non-dominated layer individuals to form a new population l t . If the number is less than N, supplement k individuals through adaptive adjustment; then construct a reference plane and determine the ideal point Z*, optimize the individuals through neighborhood update and aggregation function comparison, and screen the optimal individuals to add to l after correcting the reference point t until the population size reaches N; loop the above steps until the iteration times are met, and finally output the Pareto approximate solution set. The whole process integrates the environmental selection, reference point guidance and adaptive adjustment mechanisms, taking into account both convergence and diversity.

[0073] The main steps of using the improved MOEA / D to optimize the motor structure parameters are as follows:

[0074] (1) Initialize the population to generate an initial population P with a size of N t .

[0075] (2) Adaptive normalization. Select the minimum value of each dimension in the population as the ideal point, construct a new coordinate system with the ideal point as the coordinate origin, and then obtain the extreme points of the population on each axis of the coordinate system to form a hyperplane, and complete the normalization of the population according to the intercepts of the hyperplane on each axis.

[0076] (3) Use directional mutation guided by electromagnetic characteristics to perform crossover and mutation on the population to generate offspring.

[0077] Crossover and mutation. Crossover is responsible for combining the genes of parent individuals to produce offspring, while mutation introduces randomness to increase the diversity of the population. The described crossover and mutation use directional mutation guided by electromagnetic characteristics, and the main steps are as follows:

[0078] (1) Design and calculate the gradient direction of the objective function with respect to the design variables as:

[0079]

[0080] where is the gradient direction perturbation value of the j-th variable, η is the learning rate, η=(0.05, 0.2), x j is the original value of the j-th design variable, is the partial derivative of the multi-objective function with respect to the j-th variable.

[0081] F = b1B g (x1...x k ) + b2E0(x1...xn ) + b3T0(x1...x k )

[0082] Among them, is the gradient direction perturbation value of the j-th optimization parameter; η is the learning rate, η = (0.05, 0.2); x j is the design variable, is the partial derivative of the aggregated objective function with respect to the j-th optimization parameter; among them, b1 is the weight ratio of the air-gap magnetic density in the motor performance, b2 is the weight ratio of the no-load cogging torque in the motor performance, b3 is the weight ratio of the no-load back electromotive force in the motor performance, and b1, b2, and b3 are determined by the CRITIC weight analysis method.

[0083] (2) Apply a directional perturbation along the gradient direction and superimpose a random perturbation to generate a mutant solution. The hybrid mutation formula is:

[0084]

[0085] Among them, x' j is the value of the j-th design variable after mutation; δ is the random perturbation intensity; N(0, σ 2 ) is the Gaussian distribution; σ 2 is the standard deviation of the Gaussian distribution.

[0086] (3) Correct the solution that violates electromagnetic or process constraints in real time. If the mutation is too large and causes x' j to exceed the limit, then step back by a proportion a:

[0087]

[0088] Among them, a = (0, 1).

[0089] (4) Use the improved Chebyshev aggregation method to decompose the MOP problem of the population into multiple sub-problems. Each sub-problem converts the multi-objective into a single-objective for optimization through the Chebyshev aggregation function. By reasonably designing the weight vector and reference point, and sorting according to the fitness, the optimal solution is obtained as the iterative result.

[0090] The definition of the Chebyshev aggregation function is:

[0091]

[0092] Among them, minimize g te (x|m, Z * ) is the Chebyshev aggregation value, m i are the optimization weights of the multi-objective functions of the air-gap magnetic density, the no-load back electromotive force, and the no-load cogging torque respectively, and satisfy m i≥0, where i = 1, 2, 3; x is the decision vector, including all optimization parameters to be optimized; is the ideal point, taking the minimum value of the objective values of the multi-objective functions of the air-gap magnetic density, no-load back electromotive force, and no-load cogging torque of the current population, that is is the ideal point of the optimized air-gap magnetic density population, is the ideal point of the optimized no-load cogging torque population, is the ideal point of the optimized no-load back electromotive force population; f i (x) is the value of the i-th multi-objective function; f1(x) is the value of the multi-objective function of the air-gap magnetic density, f2(x) is the value of the multi-objective function of the no-load cogging torque, and f3(x) is the value of the multi-objective function of the no-load back electromotive force.

[0093] Set different weight vectors Obtain all the convergence points, form the optimal Pareto optimal solution set, design an improved weight vector to obtain a more evenly distributed solution, and optimize the final solution set. The improved weight vector m * is:

[0094] (5) Continuously iterate using an evolutionary algorithm until the termination condition is met to obtain the finally optimized motor parameters.

[0095] Step 5: Finally, construct an optimized motor finite element analysis model to demonstrate the optimized structure.

[0096] Figure 4 This is the comparison chart of the air-gap magnetic density before and after the improvement of MOEA / D in the embodiment of the present application. The harmonic content of the air-gap magnetic density optimized by the improved MOEA / D is much lower than that optimized by MOEA / D, suppressing the torque ripple of the motor and reducing the loss of the motor.

[0097] Figure 5 This is the comparison chart of the no-load cogging torque before and after the improvement of MOEA / D in the embodiment of the present application. The no-load cogging torque optimized by the improved MOEA / D is reduced by 6.7% compared with that optimized by MOEA / D, which can more effectively suppress the noise and vibration of the motor and improve the smoothness of the motor's low-speed operation.

[0098] Figure 6 This is the comparison chart of the no-load back electromotive force before and after the improvement of MOEA / D in the embodiment of the present application. The no-load back electromotive force optimized by the improved MOEA / D is reduced by 25.08% compared with that optimized by MOEA / D. The reduction of the no-load back electromotive force can more effectively reduce the eddy current and hysteresis losses in the iron core, improve the efficiency and extend the service life of the motor.

[0099] The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. It is not intended to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention shall be covered within the protection scope of the present invention.

Claims

1. A permanent magnet brushless DC motor, characterized in that, It includes a rotor part and a stator part. The rotor part includes a regular hexagon rotor core (11) and 6 permanent magnets arranged alternately with N and S poles. Six trapezoidal wedges (10) protrude at the vertex positions of the hexagonal rotor core (11). The stator part includes 9 stator slots arranged in a circular array. Stator teeth are provided between every two stator slots, and circular grooving is done at the tails of the stator teeth between slots 1 - 2, slots 4 - 5, and slots 7 - 8. The outer surface of the trapezoidal wedge (10) is arc-shaped, and it is concentric with the stator part. The permanent magnets are embedded on the sides of the regular hexagon rotor core (11) between two adjacent trapezoidal wedges (10). The outer surface of the permanent magnets is an arc surface, and it is concentric with the stator part.

2. A parameter optimization method for the permanent magnet brushless DC motor according to claim 1, characterized in that, It includes the following steps: Step 1: Determine the optimization parameters and optimization objectives of the permanent magnet brushless DC motor structure. (1) The optimized parameters are: the maximum thickness h of the permanent magnet max , the pole arc coefficient α of the permanent magnet p , the width w of the stator slot opening s , the depth d of the stator slot s , the protrusion height h of the trapezoidal wedge s , the pole-slot air gap length g1 and the rotor-slot air gap length g2; (2) The optimization objectives are: air-gap magnetic flux density B g , no-load back electromotive force E0, and no-load cogging torque T0; (3) According to the motor design requirements, limit the range of optimization parameters: h max = [2.8, 4]; α p = [0.6, 0.9]; w s = [2, 6]; d s = [5, 12]; h s = [0.5, 2.4]; g1 = [0.9, 1.2]; g2 = [1.2, 2.3], unit: millimeter (mm); Step 2: Use the CCD model to construct the respective response surface models of the air-gap magnetic density, no-load cogging torque, and no-load back electromotive force of the motor. Step 3: Use the CRITIC weight analysis method to calculate the weights of the optimization parameters of each optimization objective, and determine the objective functions of the air-gap magnetic density, no-load cogging torque, and no-load back electromotive force. Step 4: Aggregate the multi-objective functions based on the objective functions in Step 3, and use the improved MOEA / D algorithm to optimize and search for the motor structure parameters, and find the optimal solution as the iterative result. The improved MOEA / D algorithm performs crossover and mutation on the population with electromagnetic characteristic-guided directional mutation, and designs a weight vector optimization Chebyshev aggregation method to find the optimal iterative population.

3. The parameter optimization method of the permanent magnet brushless DC motor according to claim 2, wherein, In Step 2, the CRITIC weight analysis method is used to calculate the weights of the corresponding objective functions. Among them, λ 11 is the weight ratio of h max in the air-gap magnetic flux density, λ 12 is the weight ratio of α p in the air-gap magnetic flux density, λ 1k is the weight ratio of the k-th optimization parameter in the air-gap magnetic flux density; λ 21 , λ 22 , λ 2n , λ 31 , λ 32 , λ 3n and so on; B g (x1...x k ) is the multi-objective function of the air-gap magnetic flux density based on the optimization parameters, E0(x1...x k ) is the multi-objective function of the no-load back electromotive force based on the optimization parameters, T0(x1...x k ) is the multi-objective function of the no-load cogging torque based on the optimization parameters.

4. The parameter optimization method of the permanent magnet brushless DC motor according to claim 2, characterized in that The steps for the improved MOEA / D algorithm to optimize and search for the motor structure parameters in Step 4 are as follows: (1) Initialize the population to generate an initial population with a population size of N. (2) Adaptive normalization: Select the minimum value of each dimension in the population as the ideal point, construct a new coordinate system with the ideal point as the coordinate origin, then obtain the extreme points of the population on each axis of the new coordinate system to form a hyperplane, and complete the normalization of the population according to the intercepts of the hyperplane on each axis. (3) Perform crossover and mutation on the population with electromagnetic characteristic-guided directional mutation to generate offspring. (4) Use the improved Chebyshev aggregation method to decompose the MOP problem of the population into multiple sub-problems. Each sub-problem converts the multi-objective into a single objective through the Chebyshev aggregation function for optimization, designs the weight vector and reference point, and sorts according to the fitness to find the optimal solution as the iterative result. (5) Continuously iterate using the evolutionary algorithm until the termination condition is reached to obtain the finally optimized motor structure parameters.

5. The parameter optimization method of the permanent magnet brushless DC motor according to claim 4, characterized in that For the crossover and mutation, crossover is responsible for combining the genes of parental individuals to produce offspring, while mutation introduces randomness to increase the diversity of the population. The crossover and mutation use electromagnetic characteristic-guided directional mutation, and the steps are as follows: (1) Design and calculate the gradient direction of the aggregated objective function with respect to the design variables as: Among them, is the gradient direction perturbation value of the j-th optimization parameter, η is the learning rate, η = (0.05, 0.2), and x j is the original value of the j-th optimization parameter, is the partial derivative of the multi-objective function with respect to the j-th optimization parameter; F = b1B g (x1...x k ) + b2E0(x1...x n ) + b3T0(x1...x k ) Among them, is the gradient direction perturbation value of the j-th optimization parameter; η is the learning rate, η = (0.05, 0.2); x j is the design variable, is the partial derivative of the aggregated objective function with respect to the j-th optimization parameter; among them, b1 is the weight ratio of the air-gap magnetic density in the motor performance, b2 is the weight ratio of the no-load cogging torque in the motor performance, b3 is the weight ratio of the no-load back electromotive force in the motor performance, and b1, b2, and b3 are determined by the CRITIC weight analysis method; (2) Apply a directional perturbation along the gradient direction and superimpose a random perturbation to generate a mutant solution. The hybrid mutation formula is: where x' j is the value after mutation of the j-th optimization parameter; δ is the random perturbation intensity; N(0,σ 2 ) is a Gaussian distribution; σ 2 is the standard deviation of the Gaussian distribution; (3) Perform real-time correction on the solutions that violate electromagnetic or process constraints. If the variation is too large and causes x' j to exceed the limit, then step back the step size by a proportion of a: where a = (0, 1).

6. The parameter optimization method of the permanent magnet brushless DC motor according to claim 4, characterized in that The improved Chebyshev aggregation method mainly includes the following parts: The definition of the Chebyshev aggregation function is: Among them, minimizeg te (x|m,Z * ) is the Chebyshev aggregation value, and m i are the optimization weights of the multi-objective function of air-gap magnetic flux density, the multi-objective function of no-load back electromotive force, and the multi-objective function of no-load cogging torque, respectively, and satisfy m i ≥0, i = 1, 2, 3; x is the decision vector, including all optimization parameters to be optimized; is the ideal point, taking the minimum of the objective function values of the multi-objective function of air-gap magnetic flux density, the multi-objective function of no-load back electromotive force, and the multi-objective function of no-load cogging torque of the current population, that is is the ideal point of the optimized air-gap magnetic flux density population, is the ideal point of the optimized no-load cogging torque population, is the ideal point of the optimized no-load back electromotive force population; f i (x) is the value of the i-th multi-objective function; f1(x) is the value of the multi-objective function of air-gap magnetic flux density, f2(x) is the value of the multi-objective function of no-load cogging torque, and f3(x) is the value of the multi-objective function of no-load back electromotive force; Set different weight vectors Obtain all the convergence points to form the optimal Pareto optimal solution set, design an improved weight vector to obtain a more uniformly distributed solution, and optimize the final solution set. The improved weight vector m * is as follows:

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