A multi-objective optimization method and system for radial permanent magnet motor considering end leakage flux

Abstract

The present invention discloses a multi-objective optimization method and system for a radial permanent magnet motor considering end magnetic leakage. Firstly, a two-dimensional radial permanent magnet motor model is constructed based on a three-dimensional radial permanent magnet motor model, and then a magnetic permeability coefficient is introduced into a main magnetic leakage region in the two-dimensional radial permanent magnet motor model to construct a two-dimensional equivalent model. Then, the optimization target, design parameters and the value range of the design parameters are determined according to the obtained two-dimensional equivalent model. The present invention realizes the function of multi-objective optimization of the radial permanent magnet motor considering end magnetic leakage, and in the main magnetic leakage region, the magnetic permeability coefficient is iteratively calculated by each air domain radius and the number of divisions to construct a two-dimensional equivalent model, thereby ensuring the calculation accuracy. The hierarchical optimization of the design parameters using comprehensive sensitivity analysis can not only solve the problem that the number of design variables is large, resulting in reduced accuracy of the proxy model and difficulty in converging the optimization algorithm, but also shorten the calculation time, and is suitable for being widely promoted and used.

Description

Technical Field

[0001] The present invention relates to the technical field of radial permanent magnet motor optimization, and in particular to a multi-objective optimization method and system for a radial permanent magnet motor taking end magnetic leakage into consideration. Background Art

[0002] With the proposal of the dual carbon goals, new energy vehicle technology has achieved rapid development. Permanent magnet motors have become an important choice for new energy vehicles due to their simple structure, high efficiency, high torque density and high dynamic performance. In order to improve the comprehensive performance of energy vehicles, multi-objective optimization of permanent magnet motors is an indispensable part.

[0003] At present, the multi-objective optimization of radial permanent magnet motors is mostly aimed at two-dimensional finite element models, which generally cannot take into account the end magnetic leakage of the motor. When the end magnetic leakage of the motor is large, there will be large errors in the two-dimensional finite element calculation results. As the armature current increases, the phenomenon of end magnetic leakage becomes more and more obvious, and the error becomes larger and larger. At the same time, although the three-dimensional finite element model takes into account the end magnetic leakage, its modeling cycle is long and the calculation cost is high. Therefore, it is necessary to design a multi-objective optimization method and system for radial permanent magnet motors that takes into account end magnetic leakage. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and to better and effectively solve the multi-objective optimization of radial permanent magnet motors. Since most of the current multi-objective optimization methods are aimed at two-dimensional finite element models, the end magnetic leakage of the motor cannot be generally considered. When the end magnetic leakage of the motor is large, there is a large error in the two-dimensional finite element calculation result. As the armature current increases, the phenomenon of end magnetic leakage becomes more and more obvious, and the error becomes larger and larger. At the same time, although the three-dimensional finite element model takes the end magnetic leakage into account, its modeling cycle is long and the calculation cost is high. A multi-objective optimization method and system for radial permanent magnet motors considering end magnetic leakage are provided, which realizes the function of multi-objective optimization of radial permanent magnet motors considering end magnetic leakage, and in the main magnetic leakage area, the permeability coefficient is iteratively calculated by each air domain radius and the number of divisions to construct a two-dimensional equivalent model, thereby ensuring the calculation accuracy. The hierarchical optimization of design parameters using comprehensive sensitivity analysis can not only solve the problem that the number of design variables is large, resulting in reduced accuracy of the proxy model and difficulty in convergence of the optimization algorithm, but also shortens the calculation time.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A multi-objective optimization method for a radial permanent magnet motor considering end magnetic leakage comprises the following steps:

[0007] Step A, constructing a two-dimensional radial permanent magnet motor model based on the three-dimensional radial permanent magnet motor model, then introducing a magnetic permeability coefficient into a main magnetic leakage region in the two-dimensional radial permanent magnet motor model and constructing a two-dimensional equivalent model;

[0008] Step B, determining the optimization target, design parameters and value ranges of the design parameters according to the obtained two-dimensional equivalent model;

[0009] Step C, performing comprehensive sensitivity analysis on the optimization target and the design parameters, and dividing the design parameters into high-sensitivity parameters and low-sensitivity parameters according to the size of the comprehensive sensitivity coefficient;

[0010] Step D, using Latin hypercube sampling to establish high-sensitivity design parameter sample points for high-sensitivity parameters, and then using extreme learning to obtain an optimized proxy model;

[0011] Step E, using the optimization agent model to obtain the Pareto solution set;

[0012] Step F, based on the Pareto solution set, the final parameters of the optimization target are selected by using the approximate ideal solution sorting method;

[0013] Step G, optimizing the low-sensitivity parameters using parameter scanning and obtaining the optimal parameters;

[0014] Step H, based on the final parameters of the optimization target and the optimal parameters, the optimized motor model is established and the finite element analysis is performed on the optimized motor. The comprehensive performance of the optimized motor and the original motor is compared and the optimization effectiveness is verified to complete the multi-objective optimization operation of the radial permanent magnet motor.

[0015] The aforementioned multi-objective optimization method of a radial permanent magnet motor considering end leakage flux, step A, constructs a two-dimensional radial permanent magnet motor model based on a three-dimensional radial permanent magnet motor model, then introduces the magnetic permeance coefficient into the main leakage flux area in the two-dimensional radial permanent magnet motor model and constructs a two-dimensional equivalent model, the specific steps are as follows,

[0016] Step (A1), according to the magnetic flux density distribution of the three-dimensional permanent magnet motor model, assuming that the axial leakage flux is a semicircle, define P m is the permeance of the main leakage flux in the two-dimensional permanent magnet motor model, where the permeance of the main leakage flux in the nth air domain is P m_n As shown in formula (1),

[0017]

[0018] Among them, μ 0 represents the vacuum permeability, W s_n represents the width of the nth air domain, H s_n represents the length of the nth air domain, L stk Indicates the axial length;

[0019] Step (A2), define P s and P t are the axial leakage flux permeance and the axial leakage flux permeance between stator teeth, respectively. The nth air domain axial leakage flux permeance P s_n Axial leakage flux permeance P between the nth stator tooth t_n As shown in formulas (2) and (3),

[0020] P s_n =0.264μ 0 ×H s_n (2)

[0021]

[0022] Among them, N slot Indicates the number of stator slots, R out_n and R in_n denote the inner and outer diameters of the nth air domain, respectively;

[0023] Step (A3), based on the symmetry of the end leakage flux, the total permeance P at both ends of the nth air domain leakage flux Total_n As shown in formula (4),

[0024] P Total_n =2(P s_n +P t_n )+P m_n (4);

[0025] Step (A4), define μ rf is the magnetic permeability coefficient of the leakage flux, where the magnetic permeability coefficient μ of the nth air domain leakage flux is rf_n As shown in formula (5),

[0026]

[0027] Step (A5), the magnetic permeability coefficient is calculated iteratively by the radius of each air domain and the number of divisions, so as to complete the construction of the two-dimensional equivalent model.

[0028] The aforementioned multi-objective optimization method for radial permanent magnet motor considering end leakage flux, step B, determines the optimization target, design parameters and the value range of the design parameters according to the obtained two-dimensional equivalent model, wherein the optimization target is to maximize the motor efficiency η and the output torque T avg Maximum torque ripple T rip Minimum, design parameters include slot width B s0 、Notch height H s0 、Tooth width B s1 , slot wedge height H s1 , Groove depth H s2 , pole arc coefficient α and permanent magnet thickness T pm.

[0029] In the aforementioned multi-objective optimization method for radial permanent magnet motor considering end magnetic leakage, step C performs comprehensive sensitivity analysis on the optimization objectives and design parameters, and divides the design parameters into high-sensitivity parameters and low-sensitivity parameters according to the size of the comprehensive sensitivity coefficient, wherein the sensitivity index G j (x i ) and comprehensive sensitivity S(x i ) are shown in formula (6) and formula (7) respectively,

[0030]

[0031] S(x i )=λ j |G j (x i )|(7)

[0032] Among them, x i represents the i-th design parameter, y j represents the jth optimization objective, E(y j / x i ) represents the average value, V(E(y j / x i )) represents E(y j / x i ), V(y j ) represents y j The variance of j represents the weight of the jth optimization objective.

[0033] The aforementioned multi-objective optimization method for radial permanent magnet motor considering end magnetic leakage, step D, uses Latin hypercube sampling to establish high-sensitivity design parameter sample points for high-sensitivity parameters, and then uses extreme learning to obtain the optimization agent model. The specific steps are as follows:

[0034] Step D1, determining the sampling range of the design parameters, specifically dividing the sampling range of the design parameters into M identical sampling intervals, and determining the total number of samples to be sampled;

[0035] Step D2, randomly sampling with Latin hypercube in the divided interval to obtain a data set, and then dividing the data set into a training set and a test set in proportion, and then using the design parameters as the input layer and the optimization target as the output layer, and then building a proxy model based on extreme learning using the data of the training set;

[0036] Step D3, using the coefficient of determination R 2 Measures the accuracy of the proxy model, where the coefficient of determination R 2 As shown in formula (8),

[0037]

[0038] Where n represents the number of experiments, Y i represents the true value of the test set, represents the surrogate model fitting value;

[0039] Step D4, judging whether the accuracy of the proxy model meets the requirements, if not, returning to step D2 and increasing the number of sampling of high-sensitivity design parameters, if it meets the requirements, obtaining the final proxy model of the optimization target.

[0040] The aforementioned multi-objective optimization method for radial permanent magnet motor considering end magnetic leakage, step E, uses the optimization agent model to obtain the Pareto solution set, the specific steps are as follows:

[0041] Step E1, initialize parameters and generate an initial population, then perform non-dominated sorting and crowding calculation and sort the population;

[0042] Step E2, divide the sorted population into the upper half with good Pareto rank and the lower half with poor Pareto rank and process them separately. The specific processing steps are as follows:

[0043] Step E21: For the upper part with good Pareto rank, dynamic crossover and mutation probability based on population crowding is used to update the population so as to increase the convergence of the population, where the crossover rate P c and mutation rate P m As shown in formulas (9) and (10),

[0044]

[0045]

[0046] Among them, p c_avg , p c_max and p c_min Respectively represent the crossover rate P c The average, maximum and minimum values ​​of p m_avg , p m_max and p m_min Represents the mutation rate P m The average, maximum and minimum values ​​of iter represent the current number of iterations, MaxIt represents the maximum number of iterations, d(i) represents the crowding degree of the i-th individual, and d avg (i) represents the average crowding degree of the i-th individual at the frontier;

[0047] Step E22, introduce nonlinear learning factors to update the population for the lower half with poor Pareto rank. The specific updating steps are as follows:

[0048] Step E221, updated speed Vi (t+1) and position X i (t+1) are shown in formulas (11) and (12), respectively.

[0049] V i (t+1)=ωV i (t)+c 1 γ 1 (p best_i (t)-X i (t))+c 2 γ 2 (g NSGA-Ⅱ_i (t)-X i (t))(11)

[0050] X i (t+1)=X i (t)+V i (t+1)(12)

[0051] Among them, X i (t) is the position variable, V i (t) is the velocity vector, X i (t) and V i (t) represent the position and velocity of particle i at time t, p best_i (t) and g NSGA-Ⅱ_i (t) represent the historical optimal position of particle i at time t and the randomly selected individual in the NSGA-Ⅱ population, ω represents the inertia weight factor, γ 1 and γ 2 Both represent random numbers in [0, 1], c 1 and c 2 All represent learning factors greater than zero;

[0052] Step E222, nonlinear learning factor c 1 and c 2 As shown in formulas (13) and (14),

[0053]

[0054]

[0055] Among them, c 1 and c 2 Both represent nonlinear learning factors greater than zero, c 1_max 、c 1_min 、c 2_max and c 2_min They are the nonlinear learning factors c 1 and c 2 The maximum and minimum values ​​of ;

[0056] Step E3, combining the dynamic crossover and mutation probability of the population crowding degree to update the population and the nonlinear learning factor to update the population, and performing non-dominated sorting.

[0057] The aforementioned multi-objective optimization method for radial permanent magnet motor considering end magnetic leakage, step F, based on the Pareto solution set, adopts the approximate ideal solution sorting method to select the final parameters of the optimization target, the specific steps are as follows:

[0058] Step (F1), determine the distance D from each objective function value to the positive ideal solution t + And the distance D from each objective function value to the negative ideal solution t - As shown in formulas (15) and (16),

[0059]

[0060]

[0061] Where N represents the number of targets, λ j represents the weight of the jth optimization objective, Y j + and Y j - represent the positive ideal solution and negative ideal solution of the jth optimization objective, respectively, and f j,k represents the kth function value of the jth optimization objective;

[0062] Step (F2), determine the comprehensive distance between each optimization objective function value and the ideal solution As shown in formula (17),

[0063]

[0064] In the aforementioned multi-objective optimization method for a radial permanent magnet motor taking into account end magnetic leakage, step G uses parameter scanning to optimize the low-sensitivity parameters and obtain the optimal parameters, wherein the low-sensitivity parameter optimization is performed after the high-sensitivity parameter optimization is completed.

[0065] A multi-objective optimization system for a radial permanent magnet motor considering end magnetic leakage, comprising an equivalent model building module, an optimization determination module, a sensitivity analysis module, a proxy model building module, a Pareto solution set acquisition module, an optimization target final parameter selection module, an optimal parameter acquisition module and an optimization verification module;

[0066] The equivalent model construction module is used to construct a two-dimensional radial permanent magnet motor model based on a three-dimensional radial permanent magnet motor model, and then introduce a magnetic permeability coefficient into a main magnetic leakage region in the two-dimensional radial permanent magnet motor model to construct a two-dimensional equivalent model;

[0067] The optimization determination module is used to determine the optimization target, design parameters and the value range of the design parameters according to the obtained two-dimensional equivalent model;

[0068] The sensitivity analysis module is used to perform comprehensive sensitivity analysis on the optimization target and the design parameters and divide the design parameters into high-sensitivity parameters and low-sensitivity parameters according to the size of the comprehensive sensitivity coefficient;

[0069] The proxy model building module is used to establish high-sensitivity design parameter sample points using Latin hypercube sampling for high-sensitivity parameters, and then use extreme learning to obtain an optimized proxy model;

[0070] The Pareto solution set acquisition module is used to obtain the Pareto solution set by using the optimization agent model;

[0071] The optimization target final parameter selection module is used to select the optimization target final parameter by using the approximate ideal solution sorting method;

[0072] The optimal parameter acquisition module is used to optimize the low-sensitivity parameters by parameter scanning and obtain the optimal parameters;

[0073] The optimization verification module is used to establish an optimized motor model based on the final parameters of the optimization target and the optimal parameters and perform finite element analysis on the optimized motor, then compare the comprehensive performance of the optimized motor and the original motor and verify the effectiveness of the optimization, thereby completing the multi-objective optimization operation of the radial permanent magnet motor.

[0074] The beneficial effects of the present invention are as follows: a multi-objective optimization method and system for a radial permanent magnet motor considering end magnetic leakage of the present invention, firstly, a two-dimensional radial permanent magnet motor model is constructed based on a three-dimensional radial permanent magnet motor model, then a magnetic permeability coefficient is introduced into the main magnetic leakage area in the two-dimensional radial permanent magnet motor model and a two-dimensional equivalent model is constructed, then the optimization target, design parameters and the value range of the design parameters are determined according to the obtained two-dimensional equivalent model, then a comprehensive sensitivity analysis is performed on the optimization target and the design parameters, and the design parameters are divided into high-sensitivity parameters and low-sensitivity parameters according to the size of the comprehensive sensitivity coefficient, then Latin hypercube sampling is used to establish high-sensitivity design parameter sample points for the high-sensitivity parameters, and then extreme learning is used to obtain an optimization proxy model, and then the optimization proxy model is used to obtain a Pareto solution set, and then the approximate ideal solution sorting method is used based on the Pareto solution set to select the final parameters of the optimization target, and then the low-sensitivity parameters are optimized by parameter scanning and the optimal parameters are obtained, and then the optimized motor model is established based on the final parameters of the optimization target and the optimal parameters, and the optimized motor is subjected to finite element analysis, and finally compared. The comprehensive performance of the motor after optimization and the original motor is calculated and the effectiveness of the optimization is verified, and the multi-objective optimization operation of the radial permanent magnet motor is completed; the function of the present invention to perform multi-objective optimization on the radial permanent magnet motor while considering the end magnetic leakage is effectively realized, and the magnetic permeability coefficient is iteratively calculated by each air domain radius and the number of divisions in the main magnetic leakage area to construct a two-dimensional equivalent model, which not only shortens the calculation time, but also ensures the calculation accuracy. The hierarchical optimization of the design parameters using comprehensive sensitivity analysis can not only solve the problem of reduced accuracy of the proxy model and difficulty in convergence of the optimization algorithm due to the large number of design variables, but also shorten the calculation time. The present invention can effectively solve the problem of insufficient multi-variable optimization accuracy by constructing a proxy model of the optimization target through extreme learning, and the use of the optimized proxy model to generate a Pareto solution set can effectively improve the robustness, convergence accuracy and search efficiency of the optimization algorithm, and the final design parameters are selected using the approximate ideal solution sorting method, which not only takes into account the subjective will of the decision maker, but also reflects the importance of the objective function, so that the optimal solution has a strong theoretical basis and has a good application prospect. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is an overall flow chart of a multi-objective optimization method of a radial permanent magnet motor considering end magnetic leakage of the present invention;

[0076] Figure 2 It is a schematic diagram of modeling of a two-dimensional equivalent model of the present invention;

[0077] Figure 3 It is a two-dimensional finite element equivalent iteration flow chart of the present invention;

[0078] Figure 4 1 is a schematic diagram of a torque versus current curve of the present invention;

[0079] Figure 5 is the optimization proxy model diagram of the present invention;

[0080] Figure 6 is the Pareto diagram of the present invention;

[0081] Figure 7 It is a comparison diagram of the peak torque waveform of the motor before and after the optimization of the present invention. DETAILED DESCRIPTION

[0082] The present invention will be further described below in conjunction with the accompanying drawings.

[0083] like Figure 1 As shown, a multi-objective optimization method of a radial permanent magnet motor considering end magnetic leakage of the present invention comprises the following steps:

[0084] like Figure 2 As shown, step A, based on the three-dimensional radial permanent magnet motor model, construct a two-dimensional radial permanent magnet motor model, then introduce the magnetic permeance coefficient into the main leakage magnetic region in the two-dimensional radial permanent magnet motor model and construct a two-dimensional equivalent model. The specific steps are as follows:

[0085] Step (A1), according to the magnetic flux density distribution of the three-dimensional permanent magnet motor model, assuming that the axial leakage flux is a semicircle, define P m is the permeance of the main leakage flux in the two-dimensional permanent magnet motor model, where the permeance of the main leakage flux in the nth air domain is P m_n As shown in formula (1),

[0086]

[0087] Among them, μ 0 represents the vacuum permeability, W s_n represents the width of the nth air domain, H s_n represents the length of the nth air domain, L stk Indicates the axial length;

[0088] Step (A2), define P s and P t are the axial leakage flux permeance and the axial leakage flux permeance between stator teeth, respectively. The nth air domain axial leakage flux permeance P s_n Axial leakage flux permeance P between the nth stator tooth t_n As shown in formulas (2) and (3),

[0089] P s_n =0.264μ 0 ×H s_n (2)

[0090]

[0091] Among them, Nslot Indicates the number of stator slots, R out_n and R in_n denote the inner and outer diameters of the nth air domain, respectively;

[0092] Step (A3), based on the symmetry of the end leakage flux, the total permeance P at both ends of the nth air domain leakage flux Total_n As shown in formula (4),

[0093] P Total_n =2(P s_n +P t_n )+P m_n (4);

[0094] Step (A4), define μ rf is the magnetic permeability coefficient of the leakage flux, where the magnetic permeability coefficient μ of the nth air domain leakage flux is rf_n As shown in formula (5),

[0095]

[0096] like Figure 3 As shown, in step (A5), the permeability coefficient is calculated iteratively by the radius of each air domain and the number of divisions to complete the construction of the two-dimensional equivalent model.

[0097] Step B, determining the optimization target, design parameters and the value range of the design parameters according to the obtained two-dimensional equivalent model, wherein the optimization target is to maximize the motor efficiency η and the output torque T avg Maximum torque ripple T rip Minimum, design parameters include slot width B s0 、Notch height H s0 、Tooth width B s1 , slot wedge height H s1 , Groove depth H s2 , pole arc coefficient α and permanent magnet thickness T pm .

[0098] like Figure 4 As shown in step C, a comprehensive sensitivity analysis is performed on the optimization target and the design parameters, and the design parameters are divided into high-sensitivity parameters and low-sensitivity parameters according to the size of the comprehensive sensitivity coefficient, where the sensitivity index G j (x i ) and comprehensive sensitivity S(x i ) are shown in formula (6) and formula (7) respectively,

[0099]

[0100] S(x i )=λ j |G j (x i)|(7)

[0101] Among them, x i represents the i-th design parameter, y j represents the jth optimization objective, E(y j / x i ) represents the average value, V(E(y j / x i )) represents E(y j / x i ), V(y j ) represents y j The variance of j represents the weight of the jth optimization objective.

[0102] like Figure 5 As shown, step D uses Latin hypercube sampling to establish high-sensitivity design parameter sample points for high-sensitivity parameters, and then uses extreme learning to obtain the optimization agent model. The specific steps are as follows:

[0103] Step D1, determining the sampling range of the design parameters, specifically dividing the sampling range of the design parameters into M identical sampling intervals, and determining the total number of samples to be sampled;

[0104] Step D2, randomly sampling with Latin hypercube in the divided interval to obtain a data set, and then dividing the data set into a training set and a test set in proportion, and then using the design parameters as the input layer and the optimization target as the output layer, and then constructing a proxy model based on extreme learning using the data of the training set;

[0105] Step D3, using the coefficient of determination R 2 Measures the accuracy of the proxy model, where the coefficient of determination R 2 As shown in formula (8),

[0106]

[0107] Where n represents the number of experiments, Y i represents the true value of the test set, represents the surrogate model fitting value;

[0108] Step D4, judging whether the accuracy of the proxy model meets the requirements, if not, returning to step D2 and increasing the number of sampling of high-sensitivity design parameters, if it meets the requirements, obtaining the final proxy model of the optimization target.

[0109] like Figure 6 As shown, step E uses the optimization agent model to obtain the Pareto solution set. The specific steps are as follows:

[0110] Step E1, initialize parameters and generate an initial population, then perform non-dominated sorting and crowding calculation and sort the population;

[0111] Step E2, divide the sorted population into the upper half with good Pareto rank and the lower half with poor Pareto rank and process them separately. The specific processing steps are as follows:

[0112] Step E21: For the upper part with good Pareto rank, dynamic crossover and mutation probability based on population crowding is used to update the population so as to increase the convergence of the population, where the crossover rate P c and mutation rate P m As shown in formulas (9) and (10),

[0113]

[0114]

[0115] Among them, p c_avg , p c_max and p c_min Respectively represent the crossover rate P c The average, maximum and minimum values ​​of p m_avg , p m_max and p m_min Represents the mutation rate P m The average, maximum and minimum values ​​of iter represent the current number of iterations, MaxIt represents the maximum number of iterations, d(i) represents the crowding degree of the i-th individual, and d avg (i) represents the average crowding degree of the i-th individual at the frontier;

[0116] Step E22, introduce nonlinear learning factors to update the population for the lower half with poor Pareto rank. The specific updating steps are as follows:

[0117] Step E221, updated speed V i (t+1) and position X i (t+1) are shown in formulas (11) and (12), respectively.

[0118] V i (t+1)=ωV i (t)+c 1 γ 1 (p best_i (t)-X i (t))+c 2 γ 2 (g NSGA-Ⅱ_i (t)-X i (t)) (11)

[0119] X i(t+1)=X i (t)+V i (t+1)(12)

[0120] Among them, X i (t) is the position variable, V i (t) is the velocity vector, X i (t) and V i (t) represent the position and velocity of particle i at time t, p best_i (t) and g NSGA-Ⅱ_i (t) represent the historical optimal position of particle i at time t and the randomly selected individual in the NSGA-Ⅱ population, ω represents the inertia weight factor, γ 1 and γ 2 Both represent random numbers in [0, 1], c 1 and c 2 All represent learning factors greater than zero;

[0121] Step E222, nonlinear learning factor c 1 and c 2 As shown in formulas (13) and (14),

[0122]

[0123]

[0124] Among them, c 1 and c 2 Both represent nonlinear learning factors greater than zero, c 1_max 、c 1_min 、c 2_max and c 2_min They are the nonlinear learning factors c 1 and c 2 The maximum and minimum values ​​of ;

[0125] Step E3, combining the dynamic crossover and mutation probability of the population crowding degree to update the population and the nonlinear learning factor to update the population, and performing non-dominated sorting.

[0126] Step F, based on the Pareto solution set, the approximate ideal solution sorting method is used to select the final parameters of the optimization target. The specific steps are as follows:

[0127] Step (F1), determine the distance D from each objective function value to the positive ideal solution t + And the distance D from each objective function value to the negative ideal solution t - As shown in formulas (15) and (16),

[0128]

[0129]

[0130] Where N represents the number of targets, λ j represents the weight of the jth optimization objective, Y j + and Y j - represent the positive ideal solution and negative ideal solution of the jth optimization objective, respectively, and f j,k represents the kth function value of the jth optimization objective;

[0131] Step (F2), determine the comprehensive distance between each optimization objective function value and the ideal solution As shown in formula (17),

[0132]

[0133] Step G, using parameter scanning to optimize the low-sensitivity parameters and obtain the optimal parameters, wherein the low-sensitivity parameter optimization is performed after the high-sensitivity parameter optimization is completed.

[0134] like Figure 7 As shown, in step H, based on the final parameters of the optimization target and the optimal parameters, an optimized motor model is established and a finite element analysis is performed on the optimized motor. Then, the comprehensive performance of the optimized motor and the original motor is compared and the effectiveness of the optimization is verified, thus completing the multi-objective optimization operation of the radial permanent magnet motor.

[0135] A multi-objective optimization system for a radial permanent magnet motor considering end magnetic leakage comprises an equivalent model construction module, an optimization determination module, a sensitivity analysis module, a proxy model construction module, a Pareto solution set acquisition module, an optimization target final parameter selection module, an optimal parameter acquisition module and an optimization verification module; the equivalent model construction module is used to construct a two-dimensional radial permanent magnet motor model based on a three-dimensional radial permanent magnet motor model, and then introduce a magnetic permeability coefficient into a main magnetic leakage region in the two-dimensional radial permanent magnet motor model and construct a two-dimensional equivalent model; the optimization determination module is used to determine the optimization target, design parameters and the value range of the design parameters according to the obtained two-dimensional equivalent model; the sensitivity analysis module is used to perform a comprehensive sensitivity analysis on the optimization target and the design parameters and divide the design parameters into high sensitivity and low sensitivity according to the size of the comprehensive sensitivity coefficient. The method comprises the following steps: the first step is to use a plurality of optimization methods to optimize the radial permanent magnet motor, and the second step is to use a plurality of optimization methods to optimize the radial permanent magnet motor. The method comprises the following steps: a) optimize the radial permanent magnet motor, and b) optimize the radial permanent magnet motor. The method comprises the following steps: a) optimize the radial permanent magnet motor, and c) optimize the radial permanent magnet motor. The method comprises the following steps: a) optimize the radial permanent magnet motor, and c) optimize the radial permanent magnet motor. The method comprises the following steps: a) optimize the radial permanent magnet motor, and c) optimize the radial permanent magnet motor.

[0136] In order to better illustrate the use effect of the present invention, a specific embodiment of the present invention is described below;

[0137] The main structural parameters of the radial permanent magnet motor used in this embodiment are shown in Table 1.

[0138] Table 1 Main structural parameters of the motor

[0139]

[0140] like Figure 2 As shown, it is a schematic diagram of modeling a two-dimensional equivalent model of the radial permanent magnet motor of this embodiment. It can be seen that the main leakage magnetic area of ​​the motor is divided into n areas, and the magnetic permeability coefficient of each area is calculated by the stator parameters.

[0141] In order to ensure the accuracy of the two-dimensional equivalent model, the radial division layer number n and the inner and outer radius R of each air domain are out_n and R in_n Determined by iteration, the specific iteration flow chart is as follows Figure 3 shown.

[0142] like Figure 4As shown, in this embodiment, by introducing the magnetic permeability coefficient in the main leakage magnetic region, the torque of the two-dimensional equivalent model, the traditional two-dimensional model and the three-dimensional model are obtained as a function of current. It can be seen that at the maximum current, the errors between the two-dimensional equivalent model and the traditional two-dimensional model and the three-dimensional model are 1.6% and 20.5%, respectively, and the error is reduced by 18.9%.

[0143] The range of motor design parameters is shown in Table 2. The sensitivity analysis of the design parameters is carried out within the range of design parameters, and the high-sensitivity design parameter B is obtained. s0 , B s1 , H s2 , α and T pm , low sensitivity design parameter H s0 and H s1 .

[0144] Table 2 Motor design parameter range

[0145]

[0146]

[0147] In this embodiment, according to the value range of the high-sensitivity design parameter, Latin hypercube sampling is used to establish 200 groups of sample points, and finite element software is used to calculate the optimization target results of different sample points; and the 200 groups of sample points are randomly grouped in a ratio of 4:1, that is, 160 groups of training sample points and 40 groups of test sample points are obtained.

[0148] The design parameters of the training sample points are used as the input layer, the optimization target is used as the output layer, and the proxy model of the optimization target is constructed based on the extreme learning machine fitting data. Table 3 shows the determination coefficient R of each optimization target proxy model 2 ,The determination coefficients of the three models are close to 1, which are 0.9994, 0.9978 and 0.9986 respectively, indicating that the prediction accuracy of each proxy model is high and the prediction results can be close to the actual values.

[0149] Table 3 Determination coefficient of optimized proxy model

[0150]

[0151] like Figure 5 As shown, it is a schematic diagram of the optimization agent model adopted in this embodiment, which solves the problems that the existing optimization agent model has difficulty in handling large-scale problems and is prone to falling into local optimal solutions.

[0152] like Figure 6 As shown, this embodiment uses the optimization agent model to optimize the optimization target to obtain the Pareto solution set, and selects the final parameters of the optimization target based on the approximate ideal solution sorting method;

[0153] like Figure 7 As shown in the figure, it is a comparison diagram of the peak torque waveform of the motor before and after optimization in this embodiment. Compared with the original motor, the torque of the optimized motor is increased from 298.9Nm to 329.7Nm, an increase of 10.3%; the efficiency is increased from 92.5% to 93.3%, an increase of 0.8%; the torque pulsation is reduced from 5.33% to 3.12%, a decrease of 2.21%, and the optimization effect is obvious.

[0154] In summary, the present invention provides a multi-objective optimization method and system for a radial permanent magnet motor considering end magnetic leakage. First, a two-dimensional radial permanent magnet motor model is constructed based on a three-dimensional radial permanent magnet motor model. Then, the magnetic permeability coefficient is introduced into the main magnetic leakage area in the two-dimensional radial permanent magnet motor model and a two-dimensional equivalent model is constructed. Then, the optimization target, design parameters and the value range of the design parameters are determined according to the obtained two-dimensional equivalent model. Then, a comprehensive sensitivity analysis is performed on the optimization target and the design parameters, and the design parameters are divided into high-sensitivity parameters and low-sensitivity parameters according to the size of the comprehensive sensitivity coefficient. Subsequently, Latin hypercube sampling is used to establish high-sensitivity design parameter sample points for the high-sensitivity parameters, and then extreme learning is used to obtain an optimization proxy model. Then, the optimization proxy model is used to obtain a Pareto solution set, and then the approximate ideal solution sorting method is used based on the Pareto solution set to select the final parameters of the optimization target. Then, parameter scanning is used to optimize the low-sensitivity parameters and obtain the optimal parameters. Then, based on the final parameters of the optimization target and the optimal parameters, an optimized motor model is established and a finite element analysis is performed on the optimized motor. Finally, the optimized motor is compared. The comprehensive performance of the motor and the original motor is evaluated and the optimization effectiveness is verified, and the multi-objective optimization operation of the radial permanent magnet motor is completed; the function of the present invention to perform multi-objective optimization on the radial permanent magnet motor while considering the end magnetic leakage is effectively realized, and the magnetic permeability coefficient is iteratively calculated by each air domain radius and the number of divisions in the main magnetic leakage area to construct a two-dimensional equivalent model, which not only shortens the calculation time, but also ensures the calculation accuracy. The hierarchical optimization of the design parameters using comprehensive sensitivity analysis can not only solve the problem of reduced accuracy of the proxy model and difficulty in convergence of the optimization algorithm due to the large number of design variables, but also shortens the calculation time. The present invention can effectively solve the problem of insufficient multi-variable optimization accuracy by constructing a proxy model of the optimization target through extreme learning, and the use of the optimized proxy model to generate a Pareto solution set can effectively improve the robustness, convergence accuracy and search efficiency of the optimization algorithm, and the final design parameters are selected using the approximate ideal solution sorting method, which not only takes into account the subjective will of the decision maker, but also reflects the importance of the objective function, so that the optimal solution has a strong theoretical basis and has good application prospects.

[0155] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A multi-objective optimization method for radial permanent magnet motor considering end leakage flux, characterized in that: The following steps are included: Step A, constructing a two-dimensional radial permanent magnet motor model based on the three-dimensional radial permanent magnet motor model, then introducing the magnetic permeance coefficient in the main leakage magnetic region of the two-dimensional radial permanent magnet motor model and constructing a two-dimensional equivalent model. The specific steps are as follows: Step (A1), according to the magnetic flux density distribution of the three-dimensional permanent magnet motor model, assuming that the axial leakage flux is a semicircle, define P m is the permeance of the main leakage flux in the two-dimensional permanent magnet motor model, where the permeance of the main leakage flux in the nth air domain is P m_n As shown in formula (1), Where μ0 represents the vacuum magnetic permeability, W s_n represents the width of the nth air domain, H s_n represents the length of the nth air domain, L stk Indicates the axial length; Step (A2), define P s and P t are the axial leakage flux permeance and the axial leakage flux permeance between stator teeth, respectively. The axial leakage flux permeance of the nth air domain is P s_n The axial leakage flux permeance P between the nth stator tooth t_n As shown in formulas (2) and (3), P s_n =0.264μ0×H s_n (2) Among them, N slot Indicates the number of stator slots, R out_n and R in_n denote the inner and outer diameters of the nth air domain, respectively; Step (A3), based on the symmetry of the end leakage flux, the total permeance P at both ends of the nth air domain leakage flux Total_n As shown in formula (4), P Total_n =2(P s_n +P t_n )+P m_n (4); Step (A4), define μ rf is the magnetic permeability coefficient of the leakage flux, where the magnetic permeability coefficient μ of the nth air domain leakage flux is rf_n As shown in formula (5), Step (A5), the magnetic permeability coefficient is calculated iteratively by the radius of each air domain and the number of divisions, so as to complete the construction of the two-dimensional equivalent model; Step B, determining the optimization target, design parameters and the value range of the design parameters according to the obtained two-dimensional equivalent model, wherein the optimization target is to maximize the motor efficiency η and the output torque T avg Maximum torque ripple T rip Minimum, design parameters include slot width B s0 、Notch height H s0 、Tooth width B s1 , slot wedge height H s1 , Groove depth H s2 , pole arc coefficient α and permanent magnet thickness T pm ; Step C: Perform comprehensive sensitivity analysis on the optimization target and design parameters, and divide the design parameters into high-sensitivity parameters and low-sensitivity parameters according to the size of the comprehensive sensitivity coefficient. The sensitivity index G j (x i ) and comprehensive sensitivity S(x i ) are shown in formula (6) and formula (7) respectively, S(x i )=λ j |G j (x i )| (7) Among them, x i represents the i-th design parameter, y j represents the jth optimization objective, E(y j / x i ) represents the average value, V(E(y j / x i )) represents E(y j / x i ), V(y j ) represents y j The variance of j represents the weight of the jth optimization objective; Step D, Latin hypercube sampling is used to establish high-sensitivity design parameter sample points for high-sensitivity parameters, and then extreme learning is used to obtain the optimization proxy model. The specific steps are as follows: Step D1, determining the sampling range of the design parameters, specifically dividing the sampling range of the design parameters into M identical sampling intervals, and determining the total number of samples to be sampled; Step D2, randomly sampling with Latin hypercube in the divided interval to obtain a data set, and then dividing the data set into a training set and a test set in proportion, and then using the design parameters as the input layer and the optimization target as the output layer, and then constructing a proxy model based on extreme learning using the data of the training set; Step D3, using the coefficient of determination R 2 Measures the accuracy of the proxy model, where the coefficient of determination R 2 As shown in formula (8), Where n represents the number of experiments, Y i represents the true value of the test set, represents the surrogate model fitting value; Step D4, judging whether the accuracy of the proxy model meets the requirements, if not, returning to step D2 and increasing the number of samples of the high-sensitivity design parameters, if it meets the requirements, obtaining the final proxy model of the optimization target; Step E: Use the optimization agent model to obtain the Pareto solution set. The specific steps are as follows: Step E1, initialize parameters and generate an initial population, then perform non-dominated sorting and crowding calculation and sort the population; Step E2, divide the sorted population into the upper half with good Pareto rank and the lower half with poor Pareto rank and process them separately. The specific processing steps are as follows: Step E21: For the upper part with good Pareto rank, dynamic crossover and mutation probability based on population crowding is used to update the population so as to increase the convergence of the population, where the crossover rate P c and mutation rate P m As shown in formulas (9) and (10), Among them, p c_avg , p c_max and p c_min Respectively represent the crossover rate P c The average, maximum and minimum values ​​of p m_avg , p m_max and p m_min Represents the mutation rate P m The average, maximum and minimum values ​​of iter represent the current number of iterations, MaxIt represents the maximum number of iterations, d(i) represents the crowding degree of the i-th individual, and d avg (i) represents the average crowding degree of the i-th individual at the frontier; Step E22, introduce nonlinear learning factors to update the population for the lower half with poor Pareto rank. The specific updating steps are as follows: Step E221, updated speed V i (t+1) and position X i (t+1) are shown in formulas (11) and (12), respectively. V i (t+1)=ωV i (t)+c1γ1(p best_i (t)-X i (t))+c2γ2(g NSGA-Ⅱ_i (t)-X i (t)) (11) X i (t+1)=X i (t)+V i (t+1) (12) Among them, X i (t) is the position variable, V i (t) is the velocity vector, X i (t) and V i (t) represent the position and velocity of particle i at time t, p best_i (t) and g NSGA-Ⅱ_i (t) represents the historical optimal position of particle i at time t and the randomly selected individual in the NSGA-Ⅱ population, ω represents the inertia weight factor, γ1 and γ2 both represent random numbers in [0, 1], and c1 and c2 both represent learning factors greater than zero; In step E222, the nonlinear learning factors c1 and c2 are respectively as shown in formulas (13) and (14), Among them, c1 and c2 both represent nonlinear learning factors greater than zero, c 1_max 、c 1_min 、c 2_max and c 2_min are the maximum and minimum values ​​of the nonlinear learning factors c1 and c2 respectively; Step E3, combining the dynamic crossover and mutation probability of population crowding and the nonlinear learning factor to update the population, and performing non-dominated sorting; Step F, based on the Pareto solution set, the final parameters of the optimization target are selected by using the approximate ideal solution sorting method; Step G, optimizing the low-sensitivity parameters using parameter scanning and obtaining the optimal parameters; Step H, based on the final parameters of the optimization target and the optimal parameters, the optimized motor model is established and the finite element analysis is performed on the optimized motor. The comprehensive performance of the optimized motor and the original motor is compared and the optimization effectiveness is verified to complete the multi-objective optimization operation of the radial permanent magnet motor.

2. A multi-objective optimization method for a radial permanent magnet motor considering end magnetic leakage according to claim 1, characterized in that: Step F, based on the Pareto solution set, the approximate ideal solution sorting method is used to select the final parameters of the optimization target. The specific steps are as follows: Step (F1), determine the distance D from each objective function value to the positive ideal solution k + And the distance D from each objective function value to the negative ideal solution k - As shown in formulas (15) and (16), Where N represents the number of targets, λ j represents the weight of the jth optimization objective, Y j + and Y j - represent the positive ideal solution and negative ideal solution of the jth optimization objective, respectively, and f j,k represents the kth function value of the jth optimization objective; Step (F2), determine the comprehensive distance between each optimization objective function value and the ideal solution As shown in formula (17), 3. The multi-objective optimization method of a radial permanent magnet motor considering end magnetic leakage according to claim 2 is characterized in that: Step G, using parameter scanning to optimize the low-sensitivity parameters and obtain the optimal parameters, wherein the low-sensitivity parameter optimization is performed after the high-sensitivity parameter optimization is completed.

4. A multi-objective optimization system for a radial permanent magnet motor taking into account end magnetic leakage, the multi-objective optimization system for a radial permanent magnet motor being based on the multi-objective optimization method for a radial permanent magnet motor according to any one of claims 1 to 3, characterized in that: It includes equivalent model construction module, optimization determination module, sensitivity analysis module, proxy model construction module, Pareto solution set acquisition module, optimization target final parameter selection module, optimal parameter acquisition module and optimization verification module; The equivalent model construction module is used to construct a two-dimensional radial permanent magnet motor model based on a three-dimensional radial permanent magnet motor model, and then introduce a magnetic permeability coefficient into a main magnetic leakage region in the two-dimensional radial permanent magnet motor model to construct a two-dimensional equivalent model; The optimization determination module is used to determine the optimization target, design parameters and the value range of the design parameters according to the obtained two-dimensional equivalent model; The sensitivity analysis module is used to perform comprehensive sensitivity analysis on the optimization target and the design parameters and divide the design parameters into high-sensitivity parameters and low-sensitivity parameters according to the size of the comprehensive sensitivity coefficient; The proxy model building module is used to establish high-sensitivity design parameter sample points using Latin hypercube sampling for high-sensitivity parameters, and then use extreme learning to obtain an optimized proxy model; The Pareto solution set acquisition module is used to obtain the Pareto solution set by using the optimization agent model; The optimization target final parameter selection module is used to select the optimization target final parameter by using the approximate ideal solution sorting method; The optimal parameter acquisition module is used to optimize the low-sensitivity parameters by parameter scanning and obtain the optimal parameters; The optimization verification module is used to establish an optimized motor model based on the final parameters of the optimization target and the optimal parameters and perform finite element analysis on the optimized motor, then compare the comprehensive performance of the optimized motor and the original motor and verify the effectiveness of the optimization, thereby completing the multi-objective optimization operation of the radial permanent magnet motor.

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