Permanent magnet synchronous motor multi-objective optimization method based on improved iterative Taguchi method

Abstract

The invention discloses a permanent magnet synchronous motor multi-objective optimization method based on an improved iterative Taguchi method, and the method comprises the steps: automatically matching an orthogonal table dimension according to a sensitivity analysis result, and carrying out the multi-level fine adjustment of a high-sensitivity parameter; secondly, a closed-loop iteration process including experimental design, finite element simulation and parameter weight updating is constructed, the factor step length is dynamically adjusted through the contribution degree of variance analysis parameters, step length expansion is conducted on high-contribution parameters, and the search range of the parameters is automatically compressed for low-contribution parameters; and finally, providing a dual intelligent termination criterion fusing the signal-to-noise ratio stability and the Pareto solution set coverage rate, and reducing the number of invalid iterations. Compared with the prior art, the method has the advantages that a more reasonable dynamic matching mechanism is adopted, the variable contribution degree dynamic update step length and a more accurate and rapid double iteration judgment method are combined, the number of experiments is remarkably reduced, the motor multi-target optimization rate is increased, and motor optimization is more accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-objective optimization of permanent magnet synchronous motors, and particularly relates to a multi-objective optimization method for permanent magnet synchronous motors based on an improved iterative Taguchi method. Background Technique

[0002] As an energy-efficient power device, permanent magnet synchronous motors are widely used in fields such as new energy vehicles and industrial drives. The optimization of their electromagnetic parameters plays a key role in reducing cogging torque, suppressing torque ripple, and improving multi-condition efficiency. In traditional optimization methods, the Taguchi method is often adopted due to the high efficiency of experimental design, but there are still significant limitations: on the one hand, the traditional Taguchi method uses a fixed symmetric orthogonal array and cannot dynamically adjust the number of levels according to the difference in parameter sensitivity, resulting in difficult multi-level fine adjustment of highly sensitive parameters (such as magnet thickness and air gap length), which affects the optimization accuracy; on the other hand, the fixed-step iterative mechanism is prone to falling into a local optimum, and the termination condition mostly depends on the preset number of iterations, making it difficult to balance computational efficiency and convergence stability.

[0003] In existing improvement schemes, although some scholars have proposed parameter screening based on orthogonal experiments, the problems of dynamic orthogonal array reconstruction and collaborative optimization of adaptive step sizes have not been solved; although some scholars have introduced the framework of the iterative Taguchi method, there is a lack of a sensitivity-driven orthogonal array dimension matching strategy and intelligent convergence criterion, resulting in insufficient coverage of the Pareto solution set during multi-objective optimization. In addition, the complex electromagnetic parameter coupling effect makes it difficult for traditional analysis of variance (ANOVA) to accurately quantify the parameter contribution degree, further restricting the effect of multi-objective collaborative optimization. Therefore, there are still many problems with the multi-objective optimization method for permanent magnet motors. Summary of the Invention

[0004] Object of the Invention: Aiming at the problems in the background technique, the present invention proposes a multi-objective optimization method for permanent magnet synchronous motors based on an improved iterative Taguchi method, which consists of dynamic orthogonal array reconstruction, automatic update of the iterative step size, and dual intelligent judgment, can adapt to the optimization requirements of complex electromagnetic systems, can significantly reduce the number of experiments and calculations, and can improve the parameter screening efficiency and solution set coverage ability to a certain extent.

[0005] Technical Solution: The present invention discloses a multi-objective optimization method for permanent magnet synchronous motors based on an improved iterative Taguchi method, including the following steps:

[0006] Step 1: Conduct sensitivity analysis on the optimization variables, dynamically match a mixed orthogonal array based on the sensitivity analysis results, and implement different levels of adjustment for parameters with different sensitivities;

[0007] Step 2: Construct an orthogonal experiment according to the orthogonal array dynamically matched in Step 1, conduct finite element simulation, analyze the parameter contribution degree through ANOVA variance analysis, and dynamically adjust the iterative factor step size;

[0008] Step 3: Calculate the change rate of SNR signal-to-noise ratio and the coverage rate of the Pareto solution set after iteration according to the simulation experiment data in Step 2, introduce the dual intelligent termination criteria of signal-to-noise ratio stability and Pareto solution set coverage rate into the iterative Taguchi method for iteration, and determine the final optimization variables of the permanent magnet synchronous motor.

[0009] Furthermore, the specific method for dynamically matching the asymmetric orthogonal array in Step 1 is as follows:

[0010] (1) Establish the objective function sensitivity vector F = [f1(x i ), f2(x i ), …, f k (x i )] T , where f1(x i ), f2(x i ), f k (x i ) are the optimization objectives, k is the total number of optimization objectives, x i is the optimization variable, calculate the comprehensive sensitivity of the optimization variable x i to the multi-objective system, w j is the weight, and ∑w j = 1;

[0011] (2) Calculate the parameter sensitivity difference ratio Automatically match the mixed orthogonal array. When R > R X , select the asymmetric orthogonal array. When R ≤ R X , use the traditional symmetric orthogonal array; the asymmetric orthogonal array is in the form of L(a ^ b×c ^ d), that is, b factors adopt a levels, d factors adopt c levels and a ≠ c. The highly sensitive parameters are assigned c levels, and the low sensitive parameters are assigned a levels, c > a; the symmetric orthogonal array is in the form of L(a ^ b), that is, b factors adopt a levels.

[0012] Furthermore, in Step 2, construct the objective response matrix Y[y jm k×M, where y jm represents the value of the jth objective in the mth orthogonal experiment. The matrix dimension is k×M, and m represents the serial number of the orthogonal experiment performed. Calculate the contribution degree of each optimization variable to the multi-objective S ij is the variance contribution of the optimization variable x i to the optimization objective f j . The total variance M is the total number of orthogonal experiments, is the mean value of the optimization objective f j .

[0013] Further, in step 2, according to P i multi dynamically adjust the step size where α is an adjustment factor with a value range of 0.1 to 0.3. For high contribution degree parameters, the step size increases to accelerate convergence; for low contribution degree parameters, the step size shrinks to avoid oscillation. The dynamically adjusted step size is the adjustment amount for each optimization variable during the parameter optimization process.

[0014] Further, the optimization objectives of the permanent magnet synchronous motor are output torque, torque ripple, and cogging torque, and the optimization variables are permanent magnet thickness, rotor magnetic isolation bridge circle position, tooth tip offset height, excitation initial phase angle, auxiliary slot width, and slot opening width.

[0015] Further, the optimization model of the permanent magnet synchronous motor is as follows:

[0016]

[0017] where T o ′ ut , T p ′ kavg , T c ′ og are the expected values of the motor output torque, torque ripple, and cogging torque respectively, w1, w2, and w3 are the weight coefficients of the motor output torque, torque ripple, and cogging torque respectively, and w1 + w2 + w3 = 1; T out (x i ) represents the output torque of the motor under the optimization variable x i , and is expressed as: p is the number of pole pairs of the motor, ψ pm is the magnetic flux of the motor, i d , i q are the d-axis and q-axis currents of the motor respectively, L d , L q are the d-axis and q-axis inductances of the motor respectively; T pkavg (x i ) represents the torque ripple of the motor under the optimization variable x i , and is expressed as the ratio of the peak-to-peak value of the motor output torque to the average value of the output torque as: T pk2pk , T avg are the peak-to-peak value and the average value of the motor output torque respectively; The cogging torque is the torque generated by the interaction between the permanent magnet and the iron core when the permanent magnet motor winding is not energized, and is expressed as: where z represents the number of stator teeth of the motor, L a is the axial length of the motor, R1 and R2 are the inner radius of the stator and the outer radius of the rotor, G nis the nth harmonic air-gap permeance coefficient, B r is the remanence density of the permanent magnet, μ0 is the permeability of free space, α p is the pole pitch angle, n is the harmonic order, and n1 is the pole pair correlation coefficient.

[0018] Furthermore, the dual intelligent termination criterion in step 1 includes:

[0019] (1) The change rate of the SNR signal-to-noise ratio for 3 consecutive iterations where ε is the defined change in the signal-to-noise ratio, SNR (t) 、SNR (t-1) are the signal-to-noise ratios of the tth and (t-1)th iterations respectively;

[0020] (2) The coverage rate of the Pareto solution set where ρ th is the defined coincidence rate of the Pareto solution set.

[0021] Furthermore, when both dual intelligent termination criteria are satisfied, the iteration ends and the optimal solution set is output. If only one condition is satisfied or neither is satisfied, steps 1, 2, and 3 are repeated until both dual judgment conditions are satisfied.

[0022] Beneficial effects:

[0023] 1. By grading the sensitivity of parameters, this invention automatically matches a hybrid orthogonal array according to the different sensitivities of the optimization variables, automatically adjusts the parameter levels, gives more levels to high-sensitivity parameters, and appropriately reduces the levels of low-sensitivity parameters, achieving fine adjustment of multiple levels for high-sensitivity parameters and appropriate adjustment of low-sensitivity parameters. It significantly reduces the number of experiments and improves the optimization accuracy, making it suitable for motor design and multi-objective optimization applications.

[0024] 2. By using ANOVA variance analysis to dynamically adjust the parameter step size, this invention expands the step size for high-contribution parameters and automatically compresses the search range of parameters for low-contribution parameters, reducing ineffective exploration and improving the convergence speed, saving optimization time. Using a dynamic step size can avoid the local convergence problem caused by the traditional fixed step size, saving a large amount of time for the optimization design of motors.

[0025] 3. By applying the dual criterion (SNR change rate < ε + Pareto coverage rate > ρ th ), this invention reduces the number of ineffective iterations and improves the optimization accuracy. More accurate results can be obtained with fewer experiments. Description of the Drawings

[0026] Figure 1 is a schematic flow chart of the multi-objective optimization method for a permanent magnet synchronous motor based on the improved iterative Taguchi method;

[0027] Figure 2 It is a core module diagram of the improved iterative Taguchi method. Specific implementation manners

[0028] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be described in detail below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other implementation manners obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope protected by the present invention.

[0029] Refer to Figure 1 , the present invention provides a multi-objective optimization method for permanent magnet motors based on the improved iterative Taguchi method. The optimization objectives of this embodiment are output torque, torque ripple and cogging torque, and the optimization variables are permanent magnet thickness, rotor magnetic isolation bridge circle position, tooth tip offset height, excitation initial phase angle, auxiliary slot width, and slot opening width, including the following steps:

[0030] Step 1: Parameter initialization: Determine the optimization objective f j and the optimization variable x i and the range of the optimization variable min xi ≤x i ≤max xi .

[0031] The optimization objective f j is output torque, torque ripple and cogging torque, where the output torque of the motor is expressed as:

[0032]

[0033] where p is the number of pole pairs of the motor, ψ pm is the magnetic flux of the motor, i d , i q are the d-axis and q-axis currents of the motor respectively, and L d , L q are the d-axis and q-axis inductances of the motor respectively.

[0034] The torque ripple T pkavg of the motor can generally be expressed as the ratio of the peak-to-peak value of the motor output torque to the average value of the output torque:

[0035]

[0036] where T pk2pk , T avg are the peak-to-peak value and the average value of the motor output torque respectively.

[0037] The cogging torque is the torque generated by the interaction between the permanent magnet and the iron core when the winding of the permanent magnet motor is not energized and can be expressed as:

[0038]

[0039] According to the optimization objectives and optimization variables, the optimization model of the motor can be determined as follows:

[0040]

[0041] Among them, w1, w2, and w3 are the weight coefficients of the motor output torque, torque ripple, and cogging torque respectively, and w1 + w2 + w3 = 1.

[0042] Step 2: Conduct a sensitivity analysis on the initial parameters. In order to accurately identify the influence degree of each design variable on each optimization objective, based on the sensitivity analysis method, identify the influence degree of the design variable on the optimization objective, and use the sensitivity parameter H(x i ) to represent it as:

[0043]

[0044] In the formula, E(f / x i ) represents the average value of the output of f when x i is a constant; V(E(f / x i )) is the variance of E(f / x i ); V(f) is the variance of the output value.

[0045] In order to comprehensively calculate the influence degree of each design optimization variable on the optimization objective, at the same time, considering that there are three optimization objectives in the optimization process, establish the objective function sensitivity vector F = [f1(x i ), f2(x i ), …, f k (x i )] T , and calculate the comprehensive sensitivity of the optimization variable x i to the multi-objective system.

[0046] The comprehensive sensitivity of the optimization variable x i to the multi-objective system is expressed as for calculation.

[0047] In this embodiment, k = 3, that is, F = [f1(x i ), f2(x i ), f3(x i )] T ,

[0048] After the sensitivity analysis is completed, calculate the sensitivity difference ratio of the parameters. The sensitivity difference ratio can be represented by R as:

[0049]

[0050] Automatically match the mixed orthogonal table according to the magnitude of the sensitivity difference ratio (i.e., use an asymmetric orthogonal table or a symmetric orthogonal table according to the data situation).

[0051] When R > R X , construct an asymmetric orthogonal table L(a ^ b×c ^ d), indicating that the influence differences of each optimization variable on the optimization objective are relatively large. For this, variables with larger influence differences are assigned more levels, and those with smaller differences are assigned fewer levels; the high-sensitivity parameters are assigned c levels, and the low-sensitivity parameters are assigned a levels (c > a). When R ≤ R X , use the traditional symmetric orthogonal table L(a^b), where R X is the defined sensitivity difference ratio, and different values are selected according to different application environments. In this example, R X = 5.

[0052] Construct a mixed orthogonal table through sensitivity analysis, assign different levels to different sensitivities, flexibly adapt to different parameter level requirements, and can significantly reduce the number of experiments and improve the multi-objective optimization rate in motor optimization.

[0053] Iterative feedback: Conduct orthogonal experiments according to the established orthogonal table. After the experiments are completed, analyze them and calculate the contribution degree of each optimization variable to a single optimization objective The larger it is, the more significant the influence of the optimization variable on the objective function value, and it needs to be optimized first; and the step size of the parameter with a large contribution degree needs to be enlarged to accelerate the convergence speed. Among them, the parameter contribution degree is expressed as the ratio of the total sum of squares of the parameter to the total sum of squares of differences, that is:

[0054]

[0055] SS i is the sum of squares between groups and can be expressed as: m i is the number of levels of the optimization variable x i , where n l is the number of experiments of the optimization variable x i at the l-th level, is the mean value of the optimization objective of the optimization variable x i at the l-th level, is the overall mean value of all levels of the optimization variable x i .

[0056] SST is the total sum of squares and can be expressed as: where N is the total number of orthogonal experiments in single-objective optimization, and y p is the observed value of the optimization objective function in the p-th experiment.

[0057] Calculate the contribution degree of each parameter to the multi-objective system accordingly. Total variance M is the total number of orthogonal experiments, and S ij is the optimization variable x i for the optimization objective f j variance contribution, is the mean value of the optimization objective f j

[0058] According to the contribution degree P of each optimization variable to the multi-objective system i multi dynamically adjust the step size, and the update formula of the dynamic step size can be expressed as:

[0059]

[0060] where α is the adjustment factor (it is recommended to take values from 0.1 to 0.3, and in this example, α = 0.15).

[0061] Increase the step size of the high-contribution parameters according to the calculation results to accelerate the convergence speed, and compress the step size of the low-contribution parameters to reduce ineffective exploration.

[0062] Termination judgment: Calculate the signal-to-noise ratio change rate and Pareto solution set coverage rate for 3 consecutive iterations.

[0063] where the signal-to-noise ratio change rate Δ of SNR SNR and the Pareto solution set coverage rate ρ (t) can be expressed as:

[0064]

[0065] In the formula, ε is the defined signal-to-noise ratio change amount, and here ε = 0.015; ρ th is the defined Pareto solution set coincidence rate, and here ρ th = 0.9.

[0066] Since the Taguchi method is adopted, the signal-to-noise ratio adopts the target-seeking type here, and the calculation formula is expressed as:

[0067]

[0068] where Y 2 is the mean value, and s 2 is the variance.

[0069] When the calculation result meets one of the double judgments or neither of them is met, the parameters of this iteration will repeat the steps of sensitivity analysis of the initial parameters, iterative feedback, and termination judgment until the calculation results of the iterative experiment simultaneously meet the SNR signal-to-noise ratio change rate Δ of 3 consecutive iterations.​SNR < ε and the coverage rate ρ of the Pareto solution set (t) ≥ ρ th When it is satisfied, the iteration ends and the optimal solution set is output.

[0070] An improved iterative Taguchi method for multi-objective optimization of motors disclosed by the present invention mainly consists of three modules. See Figure 2 , which are a dynamic orthogonal module, an iterative feedback module, and a termination judgment module respectively. The dynamic orthogonal module dynamically matches a hybrid orthogonal table by performing sensitivity analysis on the optimization variables. The iterative feedback module dynamically updates the iteration step size according to the contribution degree of the optimization variables to the multi-objective system by calculating the contribution degree of the optimization variables. The termination judgment module uses the change rate of the signal-to-noise ratio and the coverage rate of the Pareto solution set for double judgment.

[0071] The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly, and cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be covered within the protection scope of the present invention.

Claims

1. A multi-objective optimization method for permanent magnet synchronous motors based on an improved iterative Taguchi method, characterized in that It includes the following steps: Step 1: Conduct sensitivity analysis on the optimization variables, dynamically match the hybrid orthogonal table based on the sensitivity analysis results, and implement different levels of adjustment for different sensitivity parameters; Step 2: Construct an orthogonal experiment according to the orthogonal table dynamically matched in Step 1, conduct finite element simulation, analyze the parameter contribution degree through ANOVA variance analysis, and dynamically adjust the iteration factor step size; Step 3: Calculate the change rate of SNR signal-to-noise ratio and the coverage rate of the Pareto solution set after iteration according to the simulation experiment data in Step 2, introduce the dual intelligent termination criteria of signal-to-noise ratio stability and Pareto solution set coverage rate into the iterative Taguchi method for iteration, and determine the final optimization variables of the permanent magnet synchronous motor.

2. The multi-objective optimization method for a permanent magnet synchronous motor based on the improved iterative Taguchi method according to claim 1, wherein The specific method for dynamically matching the asymmetric orthogonal table in Step 1 is as follows: (1) Establish the objective function sensitivity vector F = [f1(x i ), f2(x i ), …, f k (x i )] T , where f1(x i ), f2(x i ), f k (x i ) are the optimization objectives, k is the total number of optimization objectives, x i is the optimization variable, calculate the comprehensive sensitivity of the optimization variable x i to the multi-objective system. w j is the weight, and ∑w j = 1; (2) Calculate the sensitivity difference ratio of parameters Automatically match the hybrid orthogonal array. When R > R X select the asymmetric orthogonal array, and when R ≤ R X use the traditional symmetric orthogonal array; the asymmetric orthogonal array is in the form of L(a ^ b×c ^ d), that is, b factors adopt a levels, d factors adopt c levels and a ≠ c, the highly sensitive parameters are assigned c levels, the low sensitive parameters are assigned a levels, and c > a; the symmetric orthogonal array is in the form of L(a ^ b), that is, b factors adopt a levels.

3. The multi-objective optimization method of the permanent magnet synchronous motor based on the improved iterative Taguchi method according to claim 2, characterized in that In step 2, the target response matrix Y[y jm k×M, where y jm represents the value of the j-th target in the m-th orthogonal experiment. The dimension of the matrix is k×M, and m represents the serial number of the orthogonal experiment performed. Calculate the contribution degrees of each optimization variable to the multi-objectives S ij is the variance contribution of the optimization variable x i to the optimization objective f j . The total variance M is the total number of orthogonal experiments is the mean value of the optimization objective f j .

4. The multi-objective optimization method for permanent magnet synchronous motors based on the improved iterative Taguchi method according to claim 3, characterized in that, In the said step 2, according to dynamically adjust the step size wherein, α is an adjustment factor with a value range of 0.1 to 0.

3. The step size of the high contribution degree parameter is increased to accelerate convergence, and the step size of the low contribution degree parameter is contracted to avoid oscillation. The dynamically adjusted step size is the adjustment amount of each optimization variable in the parameter optimization process.

5. The multi-objective optimization method of the permanent magnet synchronous motor based on the improved iterative Taguchi method according to claim 2 or 3, characterized in that The optimization objectives of the permanent magnet synchronous motor are output torque, torque ripple, and cogging torque, and the optimization variables are permanent magnet thickness, rotor magnetic isolation bridge circle position, tooth tip offset height, excitation initial phase angle, auxiliary slot width, and slot opening width.

6. The multi-objective optimization method for a permanent magnet synchronous motor based on the improved iterative Taguchi method according to claim 5, characterized in that The optimization model of the permanent magnet synchronous motor is: Among them, T o ′ ut 、T p ′ kavg 、T c ′ og are the expected values of the motor output torque, torque ripple, and cogging torque respectively. w1, w2, and w3 are the weight coefficients of the motor output torque, torque ripple, and cogging torque respectively, and w1 + w2 + w3 = 1; T out (x i ) represents the output torque of the motor under the optimization variable x i , and is expressed as: p is the number of pole pairs of the motor, ψ pm is the magnetic flux of the motor, i d , i q are the d-axis and q-axis currents of the motor respectively, L d , L q are the d-axis and q-axis inductances of the motor respectively; T pkavg (x i ) represents the torque ripple of the motor under the optimization variable x i , and is expressed as the ratio of the peak-to-peak value of the motor output torque to the average value of the output torque: T pk2pk , T avg are the peak-to-peak value and the average value of the motor output torque respectively; The cogging torque is the torque generated by the interaction between the permanent magnet and the iron core when the winding of the permanent magnet motor is not energized, and is expressed as: Among them, z represents the number of stator teeth of the motor, L a is the axial length of the motor, R1 and R2 are the inner radius of the stator and the outer radius of the rotor, G n is the nth harmonic air-gap permeance coefficient, B r is the remanence density of the permanent magnet, μ0 is the permeability of free space, α p is the pole pitch angle, n is the harmonic order, and n1 is the pole-pair correlation coefficient.

7. The multi-objective optimization method for permanent magnet synchronous motors based on the improved iterative Taguchi method according to claim 1, characterized in that, The dual intelligent termination criteria in Step 1 include: (1) Rate of change of SNR signal-to-noise ratio for three consecutive iterations where ε is the defined change in signal-to-noise ratio, SNR (t) 、SNR (t-1) are the signal-to-noise ratios of the t-th and (t - 1)-th iterations respectively; (2) Coverage rate of Pareto solution set where ρ th is the defined coincidence rate of Pareto solution sets.

8. The multi-objective optimization method for a permanent magnet synchronous motor based on the improved iterative Taguchi method according to claim 7, characterized in that, When both dual intelligent termination criteria are satisfied, the iteration ends and the optimal solution set is output. If only one condition is satisfied or neither is satisfied, repeat Step 1, Step 2, and Step 3 until both dual judgment conditions are satisfied.

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