Multi-objective optimization method and system of permanent magnet synchronous motor, and storage medium

Abstract

The invention relates to the technical field of permanent magnet synchronous motor design, in particular to a multi-objective optimization method and system for a permanent magnet synchronous motor and a storage medium, and the method comprises the steps: S1, building a finite element model, and selecting an optimization objective and an optimization parameter; s2, sampling based on an adaptive sampling method; s3, screening out high-sensitivity parameters based on sensitivity analysis; s4, defining an optimization objective function and constraint conditions, and fitting and simplifying the optimization objective function; s5, on the basis of a Pearson's correlation coefficient method, analyzing a coupling relationship among the optimization targets, and introducing a weight coefficient to perform normalization processing on a fitted target function to obtain a comprehensive performance index function; and S6, searching an optimal parameter combination by using a simulated annealing algorithm. The method can solve the problems of single optimization target, time-consuming calculation, poor accuracy and the like of permanent magnet synchronous motor design, and comprehensively improves the comprehensive performance of the motor.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motor design, and in particular to a multi-objective optimization method and system, and a storage medium for a permanent magnet synchronous motor. Background Art

[0002] Permanent magnet synchronous motors have many advantages such as simple structure, high efficiency, high power density and good dynamic response characteristics. They are widely used in many fields such as electric vehicles, industrial automation, household appliances, aerospace and wind power generation. The working principle of permanent magnet synchronous motors is based on the electromagnetic interaction between permanent magnets and armature windings. The rotor in the motor uses permanent magnets, while the stator is wound with three-phase windings. When the stator winding is energized, a rotating magnetic field is generated. This rotating magnetic field interacts with the permanent magnets on the rotor, thereby driving the rotor to rotate.

[0003] The design and control of permanent magnet synchronous motors involve multiple variables, which are strongly coupled and mutually influenced. At the same time, their electromagnetic characteristics are nonlinear, which makes the analysis and control of the system very complicated. It is necessary to comprehensively consider multiple factors such as electromagnetic, mechanical, and thermal design, and use advanced modeling, optimization, and control methods to adjust the determination of control parameters. Traditional motor optimization methods can only optimize a single target and cannot effectively improve the overall performance of the motor. Establishing an efficient and accurate analysis model is a key step in the optimization design of permanent magnet synchronous motors. Common methods include finite element models and analytical models, but both methods have their own advantages and disadvantages. The finite element model can accurately simulate the various characteristics of the motor, comprehensively consider the various details of the motor, and complete the coupling analysis of multiple physical fields. However, the model establishment process is relatively complicated and the calculation is time-consuming; the analytical model is based on mathematical formulas and physical laws, with fast calculation speed, and can quickly adjust parameters for iterative optimization, but its disadvantages are low accuracy and limited scope of application. At the same time, establishing an accurate analytical model requires deep theoretical knowledge and mathematical skills. Therefore, how to design a suitable optimization method is a technical problem that needs to be solved urgently in the design of permanent magnet synchronous motors. Summary of the invention

[0004] The present invention provides a multi-objective optimization method and system for a permanent magnet synchronous motor, and a storage medium, which is intended to solve the problems in the prior art of permanent magnet synchronous motor design such as single optimization target, time-consuming calculation, poor accuracy, etc., and comprehensively improve the comprehensive performance of the motor.

[0005] This application provides the following technical solutions:

[0006] A multi-objective optimization method for a permanent magnet synchronous motor comprises the following steps:

[0007] S1. Establish a finite element model and select optimization objectives and optimization parameters;

[0008] S2, sampling samples of the optimized parameters based on an adaptive sampling method;

[0009] S3. Analyze optimization parameters based on sensitivity method, select highly sensitive parameters, and introduce response surface analysis method to reflect the response relationship and change trend between each optimization target and highly sensitive parameters;

[0010] S4. Define the optimization objective function and constraint conditions, fit the functional relationship between the optimization objective and the highly sensitive parameters, and simplify the fitting function;

[0011] S5. Analyze the coupling relationship between the optimization objectives based on the Pearson correlation coefficient method, introduce the weight coefficient to normalize the fitting function, and obtain the comprehensive performance index function;

[0012] S6. Based on the simulated annealing algorithm, determine the optimal parameter combination that meets the comprehensive performance of the motor.

[0013] Technical principles: Establish a finite element model of the motor and determine the optimization objectives and optimization parameters; use the adaptive sampling method to sample the sample space; reduce the dimension of the optimization parameters based on sensitivity analysis; determine the optimization objective function through function fitting, further simplify and normalize the optimization objective function to obtain a comprehensive performance index function; use the simulated annealing algorithm to find the optimal parameter combination.

[0014] Beneficial effects: Based on sensitivity analysis, the parameters that have a greater impact on motor performance are screened out, the variables in the optimization design are reduced, and the parameter dimensions in the motor design are effectively reduced;

[0015] Secondly, the response relationship between the motor optimization parameters and the target is established based on the response surface method, and the functional relationship between each target and the variable is obtained by fitting, which avoids the need to calculate a large number of sample points in the traditional optimization method to obtain the Pareto frontier and reduces the amount of calculation;

[0016] Finally, weight coefficients are constructed to achieve normalization among multiple objectives, and optimization is performed based on the simulated annealing algorithm, which avoids a large number of finite element calculations in the sample space and improves the optimization efficiency.

[0017] Furthermore, the optimization target in S1 includes the average torque T avg , torque ripple T rip , efficiency η, salient pole ratio L r And the output power P out The optimization parameters include stator structural parameters and rotor structural parameters, and the stator structural parameters include the stator inner diameter R si 、Tooth top height h s0 、Gear shoulder height h s1 , groove depth h s2 , stator tooth width wst The rotor structural parameters include the permanent magnet length w m , permanent magnet width d m , magnetic pole angle beta v , polar cap thickness d pc , Magnetic bridge thickness W rib , Magnetic barrier chamfer radius r rb .

[0018] Beneficial effects: Different optimization objectives and constraints are fully considered during the optimization process. It is usually hoped that the motor has a large average output torque and low torque pulsation to ensure the motor's load capacity and stable operation; in addition, high output power and efficiency are also important indicators of motor high performance; a higher salient pole ratio can ensure that the motor has good speed expansion performance.

[0019] The selection of optimization parameters takes into account both the stator structural parameters and the rotor structural parameters, which can comprehensively improve the comprehensive performance of the permanent magnet synchronous motor.

[0020] Further, the steps of the adaptive sampling method include:

[0021] S21, selecting a number of optimized parameter combination design points in the motor design space as initial sample points;

[0022] S22, calculating the motor performance at the initial sample point, and constructing a feature data set of the initial sample point using the position, boundary conditions, change trend and calculation results of the motor performance of the initial sample point;

[0023] S23, constructing an evaluation model to evaluate the feature data set of the initial sample point, the evaluation result is the correlation between the initial sample point and other optimization parameter combination design points, and updating the feature data set of the initial sample point;

[0024] S24. Select an optimized parameter combination design point that has a high correlation with the feature data set of the initial sample point, and update it as a new sample point.

[0025] Beneficial effects: By identifying and leveraging high correlations between variables to improve sampling accuracy, this approach can improve sampling efficiency and accuracy in a variety of application scenarios, especially in the fields of motor design optimization, machine learning feature selection, etc.

[0026] Furthermore, the sensitivity is calculated according to the following formula:

[0027]

[0028] Among them, S i is the sensitivity of the i-th parameter, V(y|xi) is the difference between the parameters x iThe variance of other parameters relative to the optimization target, V(y) is the variance of the optimization target;

[0029] The highly sensitive parameters include the polar cap thickness d pc , magnetic pole angle beta v , permanent magnet length w m , groove depth h s2 、Stator inner diameter R si and stator tooth width w st .

[0030] Beneficial effect: The sensitivity reflects the influence of the relevant parameters on the motor performance. Setting the sensitivity threshold to filter out the highly sensitive parameters for subsequent optimization design can effectively reduce the complexity of the optimization design.

[0031] Further, the S4 comprises the following steps:

[0032] S41, define the optimization objective function and constraints, wherein the optimization objective function is defined as follows:

[0033]

[0034] where {F 1 ,F 2 ,F 3 ,F 4 ,F 5} are respectively represented as the optimization objective function, xi is the screened high sensitivity parameter;

[0035] The constraints are defined as:

[0036]

[0037] Among them, η' and T' avg They respectively represent the efficiency and output torque that the motor should meet;

[0038] S42. Fitting a functional relationship between the optimization target and the highly sensitive parameter based on the least squares method. The expression of the functional relationship is as follows:

[0039]

[0040] Among them, β0 is the first regression coefficient, βi is the second regression coefficient, βij is the third regression coefficient, βij is the fourth regression coefficient, and ε is the fitting error;

[0041] S43, simplifying the fitting function through a significance evaluation index;

[0042] S44, through the determination coefficient R 2 To verify the fitting effect of the model, the calculation formula is as follows:

[0043]

[0044] Where SSR is the regression sum of squares, which means the sum of squares of the difference between the original data and the predicted data; SST is the sum of squares of the total data, which means the sum of squares of the difference between the original data and the mean of the original data; y i , are the predicted value, actual value, and average value of each optimization objective, respectively.

[0045] Beneficial effects: Using the function fitting method to determine the relationship between each parameter and the optimization target can reduce the number of sample points required and avoid the increase in computational complexity caused by the number of optimization parameters and the value range; the fitted function relationship curve not only reflects the effect of each variable on the target alone, but also takes into account the role of the coupling terms between the variables.

[0046] The P value is introduced to reflect the influence of each item in the fitting function on the target, and the items with lower influence are screened out and eliminated, so as to further simplify the fitting function;

[0047] Introducing R 2 The determination coefficient can intuitively reflect the fitting accuracy of the model.

[0048] Further, the S5 comprises the following steps:

[0049] S51. Analyze the coupling relationship between the optimization objectives based on the Pearson correlation coefficient method. The Pearson correlation coefficient is calculated according to the following formula:

[0050]

[0051] Among them, n is the number of experimental samples, y i and j They represent the results of the two objectives in the i-th experiment respectively;

[0052] S52, introducing a weight coefficient to normalize the optimization objective function, and obtaining a comprehensive performance index function as follows:

[0053]

[0054] λ1+λ2+λ3+λ4+λ5=1

[0055] Where Y min is the comprehensive performance index function, T avg * is the output torque, T avg0 is the initial value of the output torque; P out * is the output power, P out0 is the initial value of output power; Lr* is the salient pole ratio, Lr 0 is the initial value of the salient pole ratio; T rip * is the torque ripple, T rip0 is the initial value of torque pulsation; η * is the optimal value of efficiency, η 0 is the initial value of efficiency; λ1, λ2, λ3, λ4, λ5 are the weight coefficients of each optimization objective.

[0056] Beneficial effects: The Pearson correlation coefficient can be used to help identify whether there is a strong linear correlation between optimization objectives, so as to adjust the optimization strategy in a targeted manner during the optimization process.

[0057] Furthermore, the weight coefficient of the comprehensive performance index function is adjustable.

[0058] Beneficial effect: According to the different performance requirements of the motor, the weight coefficient of each coefficient is dynamically adjusted to obtain the optimal solution.

[0059] Further, the S6 comprises the following steps:

[0060] S61, setting the initial solution, temperature, etc. of the algorithm;

[0061] S62, bringing the constructed comprehensive performance index function into solution and setting corresponding parameter constraints;

[0062] S63. Based on the comparison between the obtained solution and the initial solution, update and iterate until the optimal solution is obtained.

[0063] Beneficial effects: As a global optimization algorithm, the simulated annealing algorithm can be used to process continuous, discrete and hybrid optimization design variables and solve nonlinear optimization problems. The algorithm has low requirements on the objective function and has the advantages of strong robustness, high reliability of the optimal solution and low complexity. It is very suitable for multi-objective optimization applications of permanent magnet synchronous motors.

[0064] The present invention also provides a multi-objective optimization system for a permanent magnet synchronous motor, comprising:

[0065] Modeling module, used to establish the finite element model of the permanent magnet synchronous motor and select the optimization target and optimization parameters according to the finite element model and motor structural parameters;

[0066] A sampling module for sampling the motor sample space using an adaptive sampling method to improve sampling accuracy by identifying and utilizing high correlations between variables;

[0067] Sensitivity analysis module, which analyzes optimization parameters based on sensitivity methods and screens highly sensitive parameters;

[0068] Function construction module, used to define the optimization objective function and constraints, fit the functional relationship between the optimization objective and the highly sensitive parameters, and simplify the fitting function;

[0069] Normalization module: Based on the Pearson correlation coefficient method, the coupling relationship between the optimization objectives is analyzed, and the weight coefficient is introduced to normalize the fitting function to obtain the comprehensive performance index function;

[0070] The intelligent solution module determines the optimal parameter combination that meets the comprehensive performance of the motor based on the simulated annealing algorithm.

[0071] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the multi-objective optimization method of the permanent magnet synchronous motor as described above is implemented. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 A flowchart of a multi-objective optimization method for a permanent magnet synchronous motor;

[0073] Figure 2 The model and structural dimension diagram of the permanent magnet synchronous motor;

[0074] Figure 3 It is a process diagram of the adaptive sampling method;

[0075] Figure 4 According to W m , beta v and pc Schematic diagram of the response surface model for parameter generation;

[0076] Figure 5 It is the flowchart of simulated annealing algorithm;

[0077] Figure 6 A schematic diagram showing the comparison of the harmonic content of the magnetic flux waveform at the air gap of the motor before and after the optimization design;

[0078] Figure 7 This is a schematic diagram comparing the no-load back electromotive force waveforms before and after optimization;

[0079] Figure 8 Schematic diagram of torque comparison before and after optimization;

[0080] Fig. 9 This is a schematic diagram comparing the motor efficiency maps before and after optimization.

[0081] Fig.10 This is the structural diagram of the multi-objective optimization system of permanent magnet synchronous motor. DETAILED DESCRIPTION

[0082] The following is further described in detail through specific implementation methods:

[0083] Embodiment 1

[0084] This embodiment is a multi-objective optimization method for a permanent magnet synchronous motor. Figure 1 As shown, the following steps are included:

[0085] S1. Establish a finite element model and select optimization objectives and optimization parameters.

[0086] In this embodiment, a 6-pole 36-slot internal V-type permanent magnet synchronous motor is selected to establish a finite element model. The model and main structural parameters of the motor are as follows: Figure 2 shown.

[0087] The main structural parameters of the motor model are defined in Table 1.

[0088] Table 1

[0089]

[0090]

[0091] The parameters in the motor structure are complex and varied, and different parameters affect different performance indicators. High efficiency, low torque ripple, high torque density and good dynamic response capability are important indicators for measuring high-performance motors. avg , torque ripple T rip , efficiency η, salient pole ratio L r And the output power P out These five performance indicators are used as optimization targets. When selecting the optimization parameters, the stator structural parameters and rotor structural parameters are comprehensively considered. The stator inner diameter R is selected from the stator structural parameters. si 、Tooth top height h s0 、Gear shoulder height h s1 , groove depth h s2 , stator tooth width w st , the permanent magnet length w is selected in the rotor structural parameters m , permanent magnet width d m , magnetic pole angle beta v , polar cap thickness d pc , Magnetic bridge thickness W rib , Magnetic barrier chamfer radius r rb .

[0092] S2, based on the adaptive sampling method, samples the optimized parameters and improves the sampling accuracy by identifying and utilizing the high correlation between variables, such as Figure 3 As shown, the specific steps include:

[0093] S21, selecting a number of optimized parameter combination design points in the motor design space as initial sample points;

[0094] The selected optimization parameters and their value ranges together constitute the design space of the motor, which contains multiple optimization parameter combination design points, from which a certain number of design points are selected as initial sample points.

[0095] S22. Calculate the motor performance at the initial sample point, and construct a feature data set of the initial sample point using the position, boundary conditions, change trend and calculation results of the motor performance of the initial sample point.

[0096] S23, constructing an evaluation model to evaluate the feature data set of the initial sample point, the evaluation result is the correlation between the initial sample point and other optimization parameter combination design points, and updating the feature data set of the initial sample point;

[0097] S24. Select an optimized parameter combination design point that has a high correlation with the feature data set of the initial sample point, and update it as a new sample point.

[0098] Through the above steps, the combination design points with high correlation with the optimization target are identified and sampled first, which can effectively improve the sampling efficiency and accuracy.

[0099] S3. Analyze the optimization parameters based on the sensitivity method, screen out the highly sensitive parameters, and introduce the response surface analysis method to reflect the response relationship and change trend between each optimization objective and the highly sensitive parameters.

[0100] Considering the diversity of parameters in the optimization design of permanent magnet synchronous motors, clarifying the influence of each parameter variable on the optimization target and reducing the number of optimization variables are crucial to improving the speed of multi-objective optimization. Sensitivity analysis is used to determine the relationship and influence ratio of different parameters on the optimization target. The sensitivity of the optimization parameters can be calculated by the following formula:

[0101]

[0102] Among them, S i is the sensitivity of the i-th parameter, V(y|xi) is the difference between the parameters x i The variance of other parameters relative to the optimization target, V(y) is the variance of the optimization target.

[0103] The sensitivity of the initial optimization parameters is calculated and the sensitivity threshold is set. In this embodiment, the sensitivity threshold is set to 0.2, and the parameters with sensitivity calculation results exceeding 0.2 are defined as high sensitivity parameters for subsequent optimization design. The calculation results are shown in Table 2. The selected high sensitivity parameters include the thickness of the pole cap d pc , magnetic pole angle beta v , permanent magnet length wm , groove depth h s2 、Stator inner diameter R si and stator tooth width w st ,Through sensitivity analysis, the optimization parameters were reduced from 11 to 6, which reduced the dimension of optimization parameters.

[0104] Table 2

[0105] Goal / Parameter <![CDATA[h s0 ]]> <![CDATA[h s1 ]]> hs2 <![CDATA[w st ]]> <![CDATA[R si ]]> <![CDATA[W rib ]]> <![CDATA[W m ]]> <![CDATA[d m ]]> <![CDATA[beta v ]]> <![CDATA[d pc ]]> <![CDATA[r rb ]]> <![CDATA[T avg ]]> 0.0195 0.0135 0.5305 0.021 0.4734 0.0001 0.7981 0.0177 0.0916 0.0641 0.0001 <![CDATA[T rip ]]> 0.0001 0.0001 0.3886 0.1018 0.6567 0.079 0.6086 0.0601 0.3016 0.2016 0.0237 <![CDATA[P out ]]> 0.0159 0.0124 0.566 0.0221 0.4627 0.0001 0.8174 0.0156 0.0896 0.0616 0.0001 η 0.0001 0.0001 0.0001 0.0001 0.0001 0.000 0.8239 0.0097 0.0868 0.0524 0.0277 <![CDATA[L r ]]> 0.0195 0.0189 0.5324 0.5324 0.4279 0.0615 0.7714 0.0304 0.202 0.2218 0.0001

[0106] In order to further characterize the response relationship of the parameters with high sensitivity to the optimization target, this embodiment introduces a response surface model to intuitively reflect the influence of the highly sensitive parameters on the optimization target. m , beta v and d pc These are the parameters that have the greatest impact on the optimization objective. Based on these parameters, the corresponding response surface model is generated, such as Figure 4 shown.

[0107] S4, define the optimization objective function and constraints, fit the functional relationship between the optimization objective and the highly sensitive parameters, and simplify the fitting function. It includes the following steps:

[0108] S41. Define the optimization objective function and constraints.

[0109] Different optimization objectives and constraints are fully considered during the optimization process. It is usually hoped that the motor has a large average output torque and low torque pulsation to ensure the motor's load capacity and stable operation; in addition, high output power and efficiency are also important indicators of high performance of the motor; a higher salient pole ratio can ensure that the motor has good speed expansion performance. Therefore, this embodiment takes the maximum average torque, minimum torque pulsation, maximum output power, maximum efficiency and salient pole ratio as optimization objectives. Among them, the optimization objective function is defined as follows:

[0110]

[0111] where {F 1 ,F 2 ,F 3 ,F 4 ,F 5} are respectively represented as the optimization objective function, x i The high sensitivity parameters screened include d pc , beta v 、w m 、hs2、R si 、w st The constraint range of highly sensitive parameters is shown in Table 3:

[0112] Table 3

[0113] Optimization variables Constraint Scope <![CDATA[R si ]]> 44~50mm hs2 16~22mm <![CDATA[w st ]]> 3~5mm <![CDATA[d pc ]]> 5.5~6.2mm <![CDATA[beta v ]]> 170~175 degrees <![CDATA[w m ]]> 13~16mm

[0114] The constraints are defined as:

[0115]

[0116] Among them, η' and T' avg They represent the efficiency and output torque that the motor should meet, that is, the efficiency should not be less than 90%, and the output torque should not be less than 20N*m;

[0117] S42. Fitting a functional relationship between the optimization target and the highly sensitive parameter based on the least squares method. The expression of the functional relationship is as follows:

[0118]

[0119] Among them, β0 is the first regression coefficient, βi is the second regression coefficient, βij is the third regression coefficient, βii is the fourth regression coefficient, and ε is the fitting error;

[0120] S43. Simplify the fitting function through the significance evaluation index P value.

[0121] In order to further simplify the fitting function and improve the calculation efficiency, the P value is introduced to reflect the influence of each item in the fitting function on the target, and the items with low influence are eliminated. The P value is often used as an indicator to evaluate the significance level in statistics, and can be used to characterize the influence of each factor under a certain experimental result. If the P value coefficient is less than 0.05, it means that the item has little influence on the target function, and the item is eliminated. In this way, the function is simplified by fitting the p value coefficient before each item of the fitting function.

[0122] Taking the fitting function of output torque as an example, the initial fitting function is as follows:

[0123] T avg =1053.825+11.963*R si +20.793*d pc +2.331*beta v +5.607*w m +22.979*h s2 +17.668*w st +0.103*R s i *d pc +0.016*R si *beta v -0.054*R si *w m -0.211*R si *h s2 -0.083*R si*w st -0.165*d pc *beta v +0.145*d pc *w m +0.113*d pc *h s2 -0.049*d pc *w st +0.013*beta v *w m +0.024*beta v *h s2 -0.030*beta v *w st -0.105*w m *h s2 +0.123*w m *w st -0.158*h s2 *w st -0.057*R si 2 -0.602*d pc 2 -0.010*beta v 2 -0.044*w m ^2 -0.184*h s2 2 -0.312*w st 2

[0124] The P value coefficient is used to distinguish the higher-order terms including the second-order terms and above. After the P value is calculated and eliminated, the simplified fitting function is obtained as follows:

[0125] T avg =1053.825+11.963*R si +20.793*d pc +2.331*beta v +5.607*w m +22.979*h s2 +17.668*w st +0.103*R si *d pc -0.054*R si *w m -0.211*R si *h s2 -0.083*R si *w st-0.165*d pc *beta v +0.145*d pc *w m +0.113*d pc *h s2 -0.105*w m *h s2 +0.123*w m *w st -0.158*h s2 *w st -0.057*R si 2 -0.184*h s2 2 -0.312*w st 2

[0126] S44, through the determination coefficient R 2 To verify the fitting effect of the model.

[0127] The relationship curve of the fitting function not only reflects the effect of each variable on the target, but also considers the effect of the coupling terms between the variables. The fitting accuracy needs to be evaluated. This embodiment introduces R 2 To verify the model fitting effect. 2 The closer the value is to 1, the higher the fitting accuracy of the model is. The calculation formula is as follows:

[0128]

[0129] Where SSR is the regression sum of squares, which means the sum of squares of the difference between the original data and the predicted data; SST is the sum of squares of the total data, which means the sum of squares of the difference between the original data and the mean of the original data; y i , are the predicted value, actual value, and average value of each optimization objective, respectively.

[0130] R of the fitting curve between each optimization target 2 As shown in Table 4. It can be seen that the fitting accuracy between each objective function and the variable is more than 90%, so the motor model can be approximately replaced by this functional relationship.

[0131] Table 4

[0132] Target <![CDATA[R 2 ]]> <![CDATA[T avg ]]> 0.9970 <![CDATA[P out ]]> 0.9972 Lr 0.9598 <![CDATA[T rip ]]> 0.9231 η 0.9594

[0133] S5. Analyze the coupling relationship between the optimization objectives based on the Pearson correlation coefficient method, introduce the weight coefficient to normalize the fitting function, and obtain the comprehensive performance index function. It includes the following steps:

[0134] S51. Analyze the coupling relationship between optimization objectives based on the Pearson correlation coefficient method;

[0135] As a multi-coupled complex nonlinear system, when a certain target performance is met during the motor optimization design process, it cannot guarantee that other targets will achieve the optimal effect at the same time, and there are conflicts and constraints between the optimization targets. In order to further analyze the coupling relationship between the optimization targets, the correlation between the optimization targets is analyzed based on the Pearson correlation coefficient method. The Pearson correlation coefficient can be used to help identify whether there is a strong linear correlation between the optimization targets, so as to adjust the optimization strategy in a targeted manner during the optimization process.

[0136] The Pearson correlation coefficient was calculated as follows:

[0137]

[0138] Among them, n is the number of experimental samples, y i and j They represent the results of the two objectives in the i-th experiment respectively;

[0139] S52, introducing a weight coefficient to normalize the optimization objective function;

[0140] In order to take into account multiple performance indicators of the motor at the same time and weigh the conflicts between the various objectives, a weight coefficient is introduced to normalize the various optimization objective functions fitted above. The final comprehensive performance indicator function is as follows;

[0141]

[0142] λ1+λ2+λ3+λ4+λ5=1

[0143] Where Y min is the comprehensive performance index function, T avg * is the output torque, T avg0 is the initial value of the output torque; P out * is the output power, P out0 is the initial value of output power; Lr * is the salient pole ratio, Lr 0 is the initial value of the salient pole ratio; T rip * is the torque ripple, T rip0 is the initial value of torque pulsation; η * is the optimal value of efficiency, η 0 is the initial value of efficiency; λ1, λ2, λ3, λ4, λ5 are the weight coefficients of each optimization objective.

[0144] S6. Use simulated annealing algorithm to determine the optimal parameter combination that meets the comprehensive performance of the motor.

[0145] The simulated annealing algorithm is a global optimization algorithm that uses the annealing process of solid matter in physics and combines the probability jump characteristics to randomly find the global optimal solution of the objective function in the solution space. It can be used to process continuous, discrete and hybrid optimization design variables and solve nonlinear optimization problems. The algorithm has low requirements on the objective function and has the advantages of strong robustness, high reliability of the optimal solution and low complexity.

[0146] The process of optimizing using simulated annealing algorithm is as follows Figure 5 As shown, the following steps are included:

[0147] S61, setting the initial solution, temperature, etc. of the algorithm;

[0148] S62, bringing the constructed comprehensive performance index function into solution and setting corresponding parameter constraints;

[0149] S63. Based on the comparison between the obtained solution and the initial solution, update and iterate until the optimal solution is obtained.

[0150] The comparison of parameters before and after optimization is shown in Table 5:

[0151] Table 5

[0152] Optimization parameters Initial Value Optimized value <![CDATA[R si ]]> 44.25mm 46.96mm <![CDATA[d pc ]]> 5.64mm 5.61mm <![CDATA[beta v ]]> 171.0degree 173.8degree <![CDATA[w m ]]> 15.60mm 15.14mm <![CDATA[H s2 ]]> 19.00mm 16.37mm <![CDATA[w st ]]> 4.73mm 4.90mm

[0153] In order to verify the multi-objective optimization method of permanent magnet synchronous motor, this embodiment uses Ansys Maxwell finite element simulation to compare and analyze the electromagnetic characteristics of the motor before and after optimization. The specific process is as follows:

[0154] (1) Magnetic field performance

[0155] The harmonic content (THD) analysis of the magnetic flux waveform at the air gap of the motor before and after the optimization design is as follows: Figure 6 As shown. It can be seen that the fundamental amplitude content of the magnetic flux density at the air gap is higher after optimization, indicating a higher air gap magnetic field strength. In addition, the 5th harmonic content is low and can be ignored, and the 3 / 7 and 9th harmonic contents are reduced after optimization, and the total harmonic content is reduced, which is conducive to generating a smooth output torque.

[0156] The no-load back electromotive force waveforms before and after optimization are as follows: Figure 7 As shown in the figure, it can be seen that the optimized back electromotive force is higher and the waveform sinusoidality is improved to a certain extent. Through harmonic analysis, it can be seen that the fundamental amplitude increases from 33.58V to 35.68V after optimization, and the total harmonic distortion rate is reduced.

[0157] (2) Torque performance

[0158] The optimized torque diagram is as follows: Figure 8 As shown, it can be seen that the torque output capacity of the motor is improved to a certain extent after optimization, meeting the design requirements, and the torque pulsation is reduced by 9.9% compared with the initial design.

[0159] (3) Motor efficiency

[0160] The motor efficiency map before and after optimization is as follows Fig. 9 As shown in the figure, it can be seen that the maximum efficiency of the optimized motor can reach 92%, and the high-efficiency operating area is larger than the initial design. Under rated operating conditions, the output torque is increased from 22.9Nm to 24Nm.

[0161] Embodiment 2

[0162] Different from the first embodiment, the optimization algorithm in this embodiment uses other bionic algorithms suitable for nonlinear optimization, such as genetic algorithm, gray wolf algorithm, differential evolution algorithm, bat algorithm, seagull algorithm, etc.

[0163] Embodiment 3

[0164] This embodiment is a multi-objective optimization system for a permanent magnet synchronous motor, and its structure is as follows: Fig.10 As shown, including:

[0165] Modeling module, used to establish the finite element model of the permanent magnet synchronous motor and select the optimization target and optimization parameters according to the finite element model and motor structural parameters;

[0166] The sampling module samples the motor sample space based on an adaptive sampling method to improve sampling accuracy by identifying and utilizing high correlations between variables;

[0167] Sensitivity analysis module, which analyzes optimization parameters based on sensitivity methods and screens highly sensitive parameters;

[0168] Function construction module, used to define the optimization objective function and constraints, fit the functional relationship between the optimization objective and the highly sensitive parameters, and simplify the fitting function;

[0169] Normalization module: Based on the Pearson correlation coefficient method, the coupling relationship between the optimization objectives is analyzed, and the weight coefficient is introduced to normalize the fitting function to obtain the comprehensive performance index function;

[0170] The intelligent solution module determines the optimal parameter combination that meets the comprehensive performance of the motor based on the simulated annealing algorithm.

[0171] The specific working process of each module is as described in Example 1.

[0172] Embodiment 4

[0173] This embodiment is a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the multi-objective optimization method of the permanent magnet synchronous motor as described above is implemented. In some possible implementations, various aspects of the present invention can also be implemented in the form of a program product, which includes a program code, and when the program product is run on a terminal device, the program code is used to enable the terminal device to execute the steps of the various exemplary implementations described above in this specification.

[0174] The above are only embodiments of the present invention. The invention is not limited to the field involved in this implementation case. The common knowledge such as the known specific structure and characteristics in the scheme is not described in detail here. It should be pointed out that for those skilled in the art, several deformations and improvements can be made without departing from the structure of the present invention, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A multi-objective optimization method for a permanent magnet synchronous motor, characterized in that: The following steps are involved: S1. Establish a finite element model and select optimization objectives and optimization parameters; S2, sampling samples of the optimized parameters based on an adaptive sampling method; S3. Analyze optimization parameters based on sensitivity method, select highly sensitive parameters, and introduce response surface analysis method to reflect the response relationship and change trend between each optimization target and highly sensitive parameters; S4. Define the optimization objective function and constraint conditions, fit the functional relationship between the optimization objective and the highly sensitive parameters, and simplify the fitting function; S5. Analyze the coupling relationship between the optimization objectives based on the Pearson correlation coefficient method, introduce the weight coefficient to normalize the fitting function, and obtain the comprehensive performance index function; S6. Based on the simulated annealing algorithm, determine the optimal parameter combination that meets the comprehensive performance of the motor.

2. The multi-objective optimization method of a permanent magnet synchronous motor according to claim 1, characterized in that: The optimization objectives in S1 include the average torque T avg , torque ripple T rip , efficiency η, salient pole ratio L r And the output power P out The optimization parameters include stator structural parameters and rotor structural parameters, and the stator structural parameters include the stator inner diameter R si 、Tooth top height h s0 、Gear shoulder height h s1 , groove depth h s2 , stator tooth width w st The rotor structural parameters include the permanent magnet length w m , permanent magnet width d m , magnetic pole angle beta v , polar cap thickness d pc , Magnetic bridge thickness W rib , Magnetic barrier chamfer radius r rb .

3. The multi-objective optimization method of a permanent magnet synchronous motor according to claim 2, characterized in that: The steps of the adaptive sampling method include: S21, selecting a number of optimized parameter combination design points in the motor design space as initial sample points; S22, calculating the motor performance at the initial sample point, and constructing a feature data set of the initial sample point using the position, boundary conditions, change trend and calculation results of the motor performance of the initial sample point; S23, constructing an evaluation model to evaluate the feature data set of the initial sample point, the evaluation result is the correlation between the initial sample point and other optimization parameter combination design points, and updating the feature data set of the initial sample point; S24, selecting an optimized parameter combination design point that has a high correlation with the feature data set of the initial sample point, and updating it as a new sample point.

4. The multi-objective optimization method of a permanent magnet synchronous motor according to claim 3, characterized in that: The sensitivity is calculated according to the following formula: Among them, S i is the sensitivity of the i-th parameter, V(y|xi) is the difference between the parameters x i The variance of other parameters relative to the optimization target, V(y) is the variance of the optimization target; The highly sensitive parameters include the polar cap thickness d pc , magnetic pole angle beta v , permanent magnet length w m , groove depth h s2 、Stator inner diameter R si and stator tooth width w st .

5. The multi-objective optimization method of a permanent magnet synchronous motor according to claim 4, characterized in that: The S4 comprises the following steps: S41, define the optimization objective function and constraints, wherein the optimization objective function is defined as follows: Among them, {F1, F2, F3, F4, F5} is the optimization objective function, and xi is the screened high sensitivity parameter; The constraints are defined as: Among them, η' and T' avg They respectively represent the efficiency and output torque that the motor should meet; S42. Fitting a functional relationship between the optimization target and the highly sensitive parameter based on the least squares method. The expression of the functional relationship is as follows: Among them, β0 is the first regression coefficient, βi is the second regression coefficient, βij is the third regression coefficient, βii is the fourth regression coefficient, and ε is the fitting error; S43, simplifying the fitting function through a significance evaluation index; S44, through the determination coefficient R 2 To verify the fitting effect of the model, the calculation formula is as follows: Where SSR is the regression sum of squares, which means the sum of squares of the difference between the original data and the predicted data; SST is the sum of squares of the total data, which means the sum of squares of the difference between the original data and the mean of the original data; y i , are the predicted value, actual value, and average value of each optimization objective, respectively.

6. The multi-objective optimization method of a permanent magnet synchronous motor according to claim 5, characterized in that: The S5 comprises the following steps: S51. Analyze the coupling relationship between the optimization objectives based on the Pearson correlation coefficient method. The Pearson correlation coefficient is calculated according to the following formula: Among them, n is the number of experimental samples, y i and j They represent the results of the two objectives in the i-th experiment respectively; S52, introducing a weight coefficient to normalize the optimization objective function, and obtaining a comprehensive performance index function as follows: λ1+λ2+λ3+λ4+λ5=1 Where Y min is the comprehensive performance index function, T avg * is the output torque, T avg0 is the initial value of the output torque; P out * is the output power, P out0 is the initial value of output power; Lr * is the salient pole ratio, Lr0 is the initial value of the salient pole ratio; T rip * is the torque ripple, T rip0 is the initial value of torque pulsation; η * is the optimized value of efficiency, η0 is the initial value of efficiency; λ1, λ2, λ3, λ4, λ5 are the weight coefficients of each optimization objective.

7. The multi-objective optimization method of a permanent magnet synchronous motor according to claim 6, characterized in that: The weight coefficient of the comprehensive performance index function is adjustable.

8. The multi-objective optimization method of a permanent magnet synchronous motor according to claim 7, characterized in that: The S6 comprises the following steps: S61, setting the initial solution, temperature, etc. of the algorithm; S62, bringing the constructed comprehensive performance index function into solution and setting corresponding parameter constraints; S63. Based on the comparison between the obtained solution and the initial solution, update and iterate until the optimal solution is obtained.

9. A multi-objective optimization system for a permanent magnet synchronous motor, characterized in that: include: Modeling module, used to establish the finite element model of the permanent magnet synchronous motor and select the optimization target and optimization parameters according to the finite element model and motor structural parameters; A sampling module for sampling the motor sample space using an adaptive sampling method to improve sampling accuracy by identifying and utilizing high correlations between variables; Sensitivity analysis module, which analyzes optimization parameters based on sensitivity methods and selects highly sensitive parameters; Function construction module, used to define the optimization objective function and constraints, fit the functional relationship between the optimization objective and the highly sensitive parameters, and simplify the fitting function; Normalization module: Based on the Pearson correlation coefficient method, the coupling relationship between the optimization objectives is analyzed, and the weight coefficient is introduced to normalize the fitting function to obtain the comprehensive performance index function; The intelligent solution module determines the optimal parameter combination that meets the comprehensive performance of the motor based on the simulated annealing algorithm.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, the multi-objective optimization method for the permanent magnet synchronous motor as described in any one of claims 1-8 is implemented.

Images