Performance-volume-temperature multi-objective collaborative optimization method for permanent magnet synchronous motor based on response surface-thermal network agent model

Abstract

The invention relates to a permanent magnet synchronous motor performance-volume-temperature multi-objective collaborative optimization method based on a response surface-thermal network agent model, and belongs to the technical field of motor design optimization. According to the method, firstly, a response surface-thermal network combined agent model is established, specifically, losses such as iron loss and copper loss calculated by a response surface model are input into a thermal network in the form of a current source, then the voltage, namely the temperature, of each node of the thermal network is calculated according to a node voltage equation, and the temperature of each part of the permanent magnet synchronous motor can be calculated. Then, a multi-objective collaborative optimization problem based on performance-volume-temperature is constructed, and a Pareto optimal solution set of the multi-objective collaborative optimization problem is searched by adopting an NSGA-III multi-objective optimization algorithm; according to the method, calculation and optimization of the electromagnetic performance and temperature rise of the permanent magnet synchronous motor under the requirements of multiple operation working conditions can be achieved, and optimization and improvement of the volume power density and safe operation of the motor under all working conditions are achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor design optimization, and relates to a multi-objective collaborative optimization method for the performance-volume-temperature of a permanent magnet synchronous motor based on a response surface-thermal network surrogate model. Background Technique

[0002] A permanent magnet synchronous motor (PMSM) is a synchronous motor based on permanent magnet excitation, and its core structure consists of a stator, a rotor and an end cover. The stator adopts a laminated structure to reduce iron loss, and the winding can be configured in the form of concentrated full pitch or distributed short pitch; the rotor usually has permanent magnets with high magnetic energy product (such as neodymium iron boron materials) built in, and the electromechanical energy conversion is realized through the interaction between the rotating magnetic field of the stator and the magnetic field of the rotor permanent magnet. Due to its advantages such as high efficiency (no resistance loss in the rotor), close power factor and fast dynamic response, this type of motor has become the core power device in the fields of electric vehicle drive systems, industrial servo control and precision household appliances.

[0003] In the process of technological evolution, the optimal design of PMSM faces the following key challenges:

[0004] (1) Difficulty in multi-physical field coupling modeling: The actual operation of the motor involves strong coupling effects of multiple physical fields such as electromagnetic field, temperature field, stress field, etc. For example, eddy current loss of permanent magnets during high-speed operation will cause local temperature rise, resulting in magnetic performance decay; while traditional optimization methods only build surrogate models based on electromagnetic field analysis at a single operating point, and it is difficult to accurately characterize the field interaction effects within the full operating range.

[0005] (2) Bottleneck in high-dimensional objective space optimization: Comprehensive performance optimization needs to consider multiple objective parameters such as torque density, efficiency, cost, vibration and noise at the same time. Traditional multi-objective algorithms (such as genetic algorithms) have problems such as slow convergence speed and poor quality of Pareto solution sets when dealing with such high-dimensional spaces, and it is easy to weaken the trade-off relationship between some key objectives due to the curse of dimensionality.

[0006] (3) Lack of full operating range evaluation: Existing optimization processes mostly focus on improving the static performance at the rated operating point, lacking the evaluation of the dynamic characteristics of the motor during transient processes such as starting, field weakening speed increase, and load mutation, resulting in insufficient robustness of the optimization scheme under actual complex operating conditions.

[0007] To solve the above problems, the present invention urgently needs a multi-objective collaborative optimization method for the performance-volume-temperature of a permanent magnet synchronous motor. Summary of the Invention

[0008] In view of this, the purpose of the present invention is to provide a multi-objective collaborative optimization method for the performance-volume-temperature of a permanent magnet synchronous motor based on a response surface-thermal network surrogate model, which is used to solve the calculation and optimization of the electromagnetic performance and temperature rise of a permanent magnet synchronous motor under the requirements of multiple operating conditions. By constructing a high-precision surrogate model and an efficient multi-objective optimization algorithm, the best balance among the motor performance, volume, and temperature is achieved.

[0009] To achieve the above object, the present invention provides the following technical solutions:

[0010] A multi-objective collaborative optimization method for the performance-volume-temperature of a permanent magnet synchronous motor based on a response surface-thermal network surrogate model specifically includes the following steps:

[0011] S1: Establish a mathematical model and constraint conditions for the multi-objective optimization of a permanent magnet synchronous motor;

[0012] S2: Construct a response surface-thermal network combined surrogate model for calculating the temperature of each part of the permanent magnet synchronous motor;

[0013] S3: Based on the mathematical model and constraint conditions for the multi-objective optimization of the permanent magnet synchronous motor established in step S1, use the NSGA-Ⅲ multi-objective optimization algorithm to solve the Pareto optimal solution set of the response surface-thermal network combined surrogate model, and use the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) to select the optimal compromise solution from the Pareto optimal solution set, and finally obtain a relatively optimal design scheme.

[0014] Further, in step S1, establishing the mathematical model for the multi-objective optimization of a permanent magnet synchronous motor specifically includes: according to the requirements for the performance of the motor operating conditions, select the outer diameter R of the stator core sto , the torque T under the rated condition e , the amplitude U of the no-load back electromotive force line lm , the torque T under the peak condition f , and the average stator temperature T when operating at the rated condition (8.2 Nm, 7000 rpm) to the steady state st , the average winding temperature T w , and the average rotor temperature T rt as constraint indicators; Therefore, the mathematical model for the multi-objective optimization of a permanent magnet synchronous motor is expressed as:

[0015] Further, in step S2, constructing the response surface-thermal network combined surrogate model specifically combines the response surface model with the thermal network model, inputs the losses such as iron loss and copper loss calculated by the response surface model into the thermal network in the form of current sources, and then calculates the node voltages (i.e., temperatures) of each node of the thermal network according to the node voltage equation, so as to calculate the temperatures of each part of the permanent magnet synchronous motor.

[0016] Further, in step S2, constructing a response surface model specifically includes: constructing a motor response surface using a second-order polynomial model as a reduced-order surrogate model, and its mathematical expression is:

[0017]

[0018] where y is the output response (i.e., the output electromagnetic performance); x i is the input variable (i.e., the motor design parameter); β0 is the constant term, β i is the coefficient of the linear term, β ii is the coefficient of the quadratic term, β ij is the coefficient of the cross term, and ε is the model error term;

[0019] Generate training samples through experimental design, and use the least squares method to fit the response surface model.

[0020] Further, in step S2, constructing a thermal network model specifically includes: constructing a thermal network model of a permanent magnet synchronous motor based on the equivalent thermal network structure of a hollow cylinder, i.e., the T-shaped equivalent model, that is, the LPTN model.

[0021] Further, in step S3, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) evaluates the advantages and disadvantages of each solution by calculating the distances between each solution and the ideal solution and the negative ideal solution, and selects the solution that is closest to the ideal solution and farthest from the negative ideal solution.

[0022] Further, the specific steps of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) in step S3 are as follows:

[0023] 1) Construct the decision matrix X n×m : Suppose there are n solutions and m objective functions, where x ij represents the value of the i-th solution on the j-th objective function;

[0024] 2) Standardize the decision matrix X: To eliminate the influence of dimensions, use the standardization formula to standardize the decision matrix, and the standardized value r ij is:

[0025]

[0026] 3) Determine the weights: Assign weights w j to each objective function to reflect its importance, and the weights need to satisfy

[0027] 4) Calculate the weighted standardized decision matrix V: Multiply the standardized decision matrix by the weights, and its calculation formula is:

[0028] v ij = w j ·r ij

[0029] where v ij is the weighted normalized decision;

[0030] 5) Determine the positive ideal solution V + and the negative ideal solution V - : The positive ideal solution V + refers to the optimal value of each objective function. For a maximization objective, it is the maximum value in the weighted normalized matrix, and for a minimization objective, it is the minimum value in the weighted normalized matrix; the negative ideal solution V - refers to the worst value of each objective function. For a maximization objective, it is the minimum value in the weighted normalized matrix, and for a minimization objective, it is the maximum value in the weighted normalized matrix;

[0031] 6) Calculate the distance from each solution to the positive ideal solution and the distance to the negative ideal solution

[0032]

[0033] where is the j-th positive ideal solution, is the j-th negative ideal solution;

[0034] 7) Calculate the relative closeness C i :

[0035]

[0036] C i The larger C is, the closer the solution is to the ideal solution and the farther it is from the negative ideal solution;

[0037] 8) Sort and select the optimal solution: Sort the solutions according to the relative closeness C i and select the solution with the largest C i as the optimal solution.

[0038] The beneficial effects of the present invention are as follows: The multi-objective collaborative optimization method for the performance-volume-temperature of a permanent magnet synchronous motor based on a response surface-thermal network surrogate model provided by the present invention realizes the best balance of the motor performance, volume, and temperature by constructing a high-precision surrogate model and an efficient multi-objective optimization algorithm. The specific advantages are as follows:

[0039] (1) Higher-precision surrogate model: By combining the response surface with the thermal network as the surrogate model for electromagnetic-thermal calculation, the present invention can accurately describe the multi-physical field coupling characteristics of the motor compared with the traditional single-electromagnetic-field surrogate model, improving the optimization accuracy.

[0040] (2) More efficient multi-objective optimization: The NSGA-Ⅲ algorithm is adopted in the present invention, which can efficiently handle the high-dimensional objective space and generate a uniformly distributed Pareto front.

[0041] (3) Achieving full operating range optimization: The present invention comprehensively considers the relationship between the performance changes of the motor under different working conditions and the temperature and volume, and realizes the optimized design in the full torque range.

[0042] (4) Having certain engineering practicability: The optimization results are verified by finite element analysis. After optimization, the outer diameter of the stator of the permanent magnet synchronous motor is reduced by 6.1 mm, the overall volume of the motor is reduced by 9.16%, and the power density of the electric drive system is increased by 18.95%, which has high engineering application value.

[0043] Other advantages, objectives and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. Description of the Drawings

[0044] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in preferred detail below in conjunction with the drawings, where:

[0045] Figure 1 is the flow chart of the multi-objective collaborative optimization method for the performance-volume-temperature of the permanent magnet synchronous motor based on the response surface-thermal network surrogate model provided by the present invention;

[0046] Figure 2 is the thermal resistance equivalent model of a general hollow cylinder;

[0047] Figure 3 is the thermal network model of the permanent magnet synchronous motor;

[0048] Figure 4 is the NSGA-Ⅲ optimization flow chart;

[0049] Figure 5 is the Pareto front;

[0050] Figure 6 is the comparison design drawing of the motor model before and after optimization;

[0051] Figure 7The efficiency at different torques and speeds after optimization. Detailed implementation manners

[0052] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the drawings provided in the following embodiments only schematically illustrate the basic concept of the present invention. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0053] Among them, the drawings are only for illustrative purposes, showing only schematic diagrams, not physical diagrams, and cannot be understood as a limitation to the present invention; in order to better illustrate the embodiments of the present invention, some components in the drawings will be omitted, enlarged or reduced, which does not represent the size of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0054] In the drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, they are based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the drawings are only for illustrative purposes and cannot be understood as a limitation to the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0055] Please refer to Figures 1 to 7 , the embodiment of the present invention provides a multi-objective collaborative optimization method for the performance-volume-temperature of a permanent magnet synchronous motor based on a response surface-thermal network proxy model. As Figure 1 shown, it specifically includes the following steps:

[0056] 1. Establish a mathematical model for the multi-objective optimization of a permanent magnet synchronous motor

[0057] According to the requirements for the performance of the motor operating conditions, the present invention selects the outer diameter R of the stator core sto , the torque T under the rated condition e , the amplitude U of the no-load back electromotive force line lm , the torque T under the peak condition f , and the average stator temperature T when operating at the rated condition (8.2 Nm, 7000 rpm) to reach a steady state st, the average winding temperature T w , the average rotor temperature T rt As the constraint index. Therefore, the mathematical model and constraint conditions of the optimization problem of the permanent magnet synchronous motor for the integrated electric drive system can be expressed as:

[0058]

[0059] 2. Construct a response surface-thermal network proxy model

[0060] To achieve rapid calculation and analysis of the electromagnetic performance of the motor, in this embodiment, a second-order polynomial model is used to construct its response surface as a reduced-order proxy model, and its mathematical expression is:

[0061]

[0062] Among them, y is the output response (i.e., the output electromagnetic performance); x i is the input variable (i.e., the motor design parameter); β0 is the constant term, β i is the coefficient of the linear term, β ii is the coefficient of the quadratic term, β ij is the coefficient of the cross term, and ε is the model error term.

[0063] Generate training samples through experimental design and use the least squares method to fit the response surface model.

[0064] On the other hand, based on the equivalent thermal network structure of the hollow cylinder, that is, the T-type equivalent model, the LPTN model of the electric drive system is constructed. Since most of the components of the rotating motor are basically cylindrical in shape, the T-type equivalent model is very suitable for the construction of the LPTN of the motor. The housing, stator, rotor, etc. of the electric drive system can be approximately considered as Figure 2 (a) The hollow cylinder, and can be equivalent to Figure 2 (b) The circuit shown, where R1a, R2a, and R3a represent the thermal resistances in the axial direction, and R1r, R2r, and R3r represent the thermal resistances in the radial direction. The thermal resistance values are calculated by formula (1); T1 and T2 are the temperatures of the outer and inner ring surfaces respectively; T3 and T4 are the temperatures of the two axial cross-sections respectively.

[0065]

[0066] Among them, r2 and r1 represent the inner and outer ring radii respectively; k a , k r represent the axial and radial thermal conductivities respectively, and l represents the length of the hollow cylinder.

[0067] Construct the thermal network model of the permanent magnet synchronous motor based on the T-type equivalent model of the hollow cylinder as Figure 3As shown Figure 3 wherein, R1 to R2 are the thermal resistances of the driver, R3 to R4, R 11 to R 12 are the thermal resistances of the end cover, R5 to R 10 are the thermal resistances of the motor housing, R 13 to R 18 are the thermal resistances of the stator, R 19 to R 23 are the thermal resistances of the winding, R 24 to R 27 are the thermal resistances of the end winding, R 28 to R 30 are the thermal resistances of the air gap, R 31 to R 36 are the thermal resistances of the rotor and the permanent magnet, R 37 to R 39 are the thermal resistances of the shaft, R 40 to R 53 are the convective thermal resistances; T1 is the temperature of the driver, T2 and T3 are the temperatures of the end cover, T4 is the temperature of the motor housing, T5 is the temperature of the stator, T6 is the temperature of the winding, T7 and T8 are the temperatures of the end winding, T9 is the temperature of the rotor and the permanent magnet, T 10 is the temperature of the shaft; P1 is the power loss of the inverter circuit, P2 is the iron loss of the stator, P3 is the copper loss of the winding, P4 and P5 are the copper losses of the end winding, and P6 is the iron loss of the rotor and the eddy current loss of the permanent magnet.

[0068] Subsequently, the response surface model is combined with the thermal network model, and the losses such as iron loss and copper loss calculated by the response surface model are input into the thermal network in the form of current sources. Subsequently, the node voltages (i.e., temperatures) of each node of the thermal network are calculated according to the node voltage equation, and the temperatures of each part of the permanent magnet synchronous motor can be calculated.

[0069] 3. Multi-objective collaborative optimization based on performance-volume-temperature

[0070] The optimization of permanent magnet synchronous motors is a typical multi-objective optimization problem that requires a trade-off among motor performance, volume, and temperature. Traditional single-objective optimization methods are difficult to simultaneously meet multiple conflicting objectives. Therefore, it is necessary to introduce multi-objective optimization algorithms to find their Pareto optimal solution sets. GA and NSGA-II in traditional algorithms perform well in dealing with low-dimensional objective spaces. However, when the number of objective functions increases, their selection mechanism based on crowding distance is difficult to maintain the uniform distribution of the solution set, resulting in the aggregation or uneven distribution of the solution set in high-dimensional spaces and making it difficult to find a solution set with a uniform distribution and close to the true Pareto front. NSGA-III, as a multi-objective optimization algorithm improved on the basis of the genetic algorithm, aims to solve the optimization problem of high-dimensional objective spaces (i.e., a large number of objective functions). NSGA-III is an improvement of NSGA-II. Its innovation lies in introducing a reference point mechanism, which guides the evolution direction of the population by generating a set of uniformly distributed reference points, thereby maintaining the diversity and uniform distribution of the solution set in high-dimensional objective spaces. NSGA-III is mainly used to solve the problems of uneven solution set distribution and poor convergence of traditional multi-objective optimization algorithms when dealing with a large number of objective functions, and is particularly suitable for complex optimization scenarios where the number of objective functions is greater than 3. Its optimization process is as Figure 4 shown.

[0071] The NSGA-III multi-objective optimization algorithm is used to perform multi-objective optimization calculations on the established response surface-thermal network combined surrogate model to replace the electromagnetic-thermal finite element simulation of the motor. The entire optimization process can be completed in a very short time. The initial population size is set to 500, and the maximum number of iterations is set to 2000. For the constraint conditions set by formula (1), when the calculated temperature does not increase significantly, the Pareto front between the rated torque, peak torque, line back electromotive force amplitude, and stator outer diameter is as Figure 5 shown.

[0072] To select a relatively optimal design scheme from the Pareto optimal solution set, the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is used in this embodiment to select the optimal compromise solution. This method can evaluate and rank individuals based on existing data. Its core idea is to evaluate the advantages and disadvantages of each scheme by calculating the distances between each scheme and the ideal solution and the negative ideal solution, and select the scheme that is closest to the ideal solution and farthest from the negative ideal solution.

[0073] To select a relatively optimal design scheme from the Pareto optimal solution set, the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is used to select the optimal compromise solution. This method can evaluate and rank individuals based on existing data. Its core idea is to evaluate the advantages and disadvantages of each scheme by calculating the distances between each scheme and the ideal solution and the negative ideal solution, and select the scheme that is closest to the ideal solution and farthest from the negative ideal solution. The specific steps are as follows:

[0074] 1) Construct the decision matrix X n×m : Suppose there are n alternatives and m objective functions, where x ij represents the value of the i-th alternative on the j-th objective function.

[0075] 2) Standardize the decision matrix X: To eliminate the influence of dimensions, use the standardization formula to standardize the decision matrix. The standardized value r ij is:

[0076]

[0077] 3) Determine the weights: Assign weights w j to each objective function to reflect its importance. The weights need to satisfy

[0078] 4) Calculate the weighted standardized decision matrix V: Multiply the standardized decision matrix by the weights. Its calculation formula is:

[0079] v ij = w j ·r ij

[0080] where v ij is the weighted standardized decision.

[0081] 5) Determine the positive ideal solution V + and the negative ideal solution V - : The positive ideal solution V + refers to the optimal value of each objective function. For maximization objectives, it is the maximum value in the weighted standardized matrix; for minimization objectives, it is the minimum value in the weighted standardized matrix. The negative ideal solution V - refers to the worst value of each objective function. For maximization objectives, it is the minimum value in the weighted standardized matrix; for minimization objectives, it is the maximum value in the weighted standardized matrix.

[0082] 6) Calculate the distance from each alternative to the positive ideal solution and the distance to the negative ideal solution

[0083]

[0084] where is the j-th positive ideal solution, is the j-th negative ideal solution.

[0085] 7) Calculate the relative closeness C i :

[0086]

[0087] Ci The larger it is, the closer the solution is to the ideal solution and the farther it is from the negative ideal solution.

[0088] 8) Sort and select the optimal solution: According to the relative closeness C i sort the solutions and select the solution with the largest C i as the optimal solution.

[0089] Using the TOPSIS method can comprehensively consider the distances between each Pareto solution and the positive and negative ideal solutions, and by balancing the requirements of multiple objective functions shown in the mathematical model formula, select the optimal solution from the Pareto front. The finally selected optimal solution is as Figure 6 shown.

[0090] 4. Analysis and Verification of Optimization Results

[0091] To compare the change trends of various motor performances before and after optimization, a finite element simulation calculation of electromagnetic-thermal coupling was carried out on the optimized solution. Its efficiency map is as Figure 7 shown. The results show that the maximum torque of the optimized motor reaches 25 Nm, the maximum output power can reach 20 kW, and it has a wide high-efficiency range (efficiency ≥ 95%). Moreover, the outer diameter of the motor stator is reduced by 6.1 mm, the overall volume of the motor is reduced by 9.16%, the power density of the electric drive system is increased by 18.95%, and the operating temperature of the motor under rated conditions does not increase significantly, effectively achieving the optimization goal of the present invention.

[0092] To verify the accuracy and effectiveness of the electromagnetic-thermal coupling multi-objective collaborative optimization proposed by the present invention, a comparison was made with the traditional step-by-step optimization method of first optimizing the electromagnetic performance and then calculating the temperature, and finite element simulation calculations of electromagnetic-thermal coupling were carried out respectively. The calculation results are listed in Table 1. It can be seen from Table 1 that although the traditional optimization method can obtain a design solution with a peak torque of 25.5 Nm, its volume and temperature rise are significantly inferior to the collaborative optimization results. It ignores the coupling relationship between multiple objectives during the optimization process, thus falling into the trap of local optimum, resulting in its maximum torque-to-weight ratio being 6.18% lower than the optimization method proposed in this paper. The multi-objective collaborative optimization method based on the response surface-thermal network surrogate model proposed by the present invention can effectively solve this problem. By considering the coupling effect between electromagnetics and heat during the optimization process, an optimal solution is obtained among various optimization objectives, and an optimization solution with a 17.64% increase in the maximum torque-to-weight ratio and a 9.55% decrease in the rated operating temperature of the permanent magnet is successfully obtained.

[0093] Table 1 Comparison of Results between the Optimization Method of the Present Invention and the Traditional Optimization Method

[0094]

[0095] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the present technical solution, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A multi-objective collaborative optimization method for the performance-volume-temperature of a permanent magnet synchronous motor based on a response surface-thermal network surrogate model, characterized in that The method specifically includes the following steps: S1: Establish the mathematical model and constraint conditions for the multi-objective optimization of the permanent magnet synchronous motor; S2: Construct a response surface-thermal network combined surrogate model for calculating the temperatures of various parts of the permanent magnet synchronous motor; S3: Based on the mathematical model and constraint conditions for the multi-objective optimization of the permanent magnet synchronous motor established in step S1, use the NSGA-Ⅲ multi-objective optimization algorithm to solve the Pareto optimal solution set of the response surface-thermal network combined surrogate model, and use the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to select the optimal compromise solution from the Pareto optimal solution set, and finally obtain a relatively optimal design scheme.

2. The multi-objective collaborative optimization method for the performance-volume-temperature of the permanent magnet synchronous motor according to claim 1, characterized in that In step S1, establishing the mathematical model for multi-objective optimization of a permanent magnet synchronous motor specifically includes: according to the requirements for the operating condition performance of the motor, selecting the outer diameter R of the stator core sto , the torque T under rated conditions e , the amplitude U of the no-load back electromotive force line lm , the torque T under peak conditions f , the average stator temperature T when operating at rated conditions until reaching a steady state st , the average winding temperature T w and the average rotor temperature T rt as constraint indicators; therefore, the mathematical model for multi-objective optimization of a permanent magnet synchronous motor is expressed as:

3. The multi-objective collaborative optimization method for the performance-volume-temperature of the permanent magnet synchronous motor according to claim 1, characterized in that, In step S2, when constructing the response surface-thermal network combined surrogate model, specifically, the response surface model is combined with the thermal network model, and the losses calculated by the response surface model are input into the thermal network in the form of current sources, and then the node voltages of the thermal network, that is, the temperatures, are calculated according to the node voltage equation, so as to calculate the temperatures of various parts of the permanent magnet synchronous motor.

4. The multi-objective collaborative optimization method for the performance-volume-temperature of the permanent magnet synchronous motor according to claim 3, characterized in that In step S2, when constructing the response surface model, it specifically includes: using a second-order polynomial model to construct the motor response surface as a reduced-order surrogate model, and its mathematical expression is: where y is the output response, i.e., the output electromagnetic performance; x i is the input variable, i.e., the motor design parameter; β0 is the constant term, β i is the coefficient of the linear term, β ii is the coefficient of the quadratic term, β ij is the coefficient of the cross term, and ε is the model error term; Generate training samples through experimental design and use the least squares method to fit the response surface model.

5. The multi-objective collaborative optimization method for the performance-volume-temperature of a permanent magnet synchronous motor according to claim 3, wherein In step S2, when constructing the thermal network model, it specifically includes: constructing the thermal network model of the permanent magnet synchronous motor based on the equivalent thermal network structure of a hollow cylinder, that is, the T-type equivalent model, that is, the LPTN model.

6. The multi-objective collaborative optimization method for the performance-volume-temperature of the permanent magnet synchronous motor according to claim 1, characterized in that In step S3, the TOPSIS is to evaluate the advantages and disadvantages of each scheme by calculating the distances between each scheme and the ideal solution and the negative ideal solution, and select the scheme that is closest to the ideal solution and farthest from the negative ideal solution.

7. The multi-objective collaborative optimization method for the performance-volume-temperature of a permanent magnet synchronous motor according to claim 6, wherein In step S3, the specific steps of the TOPSIS are as follows: 1) Construct the decision matrix X n×m : Suppose there are n alternatives and m objective functions, where x ij represents the value of the i-th alternative on the j-th objective function; 2) Standardized decision matrix X: The decision matrix is standardized using the standardization formula, and the value r after standardization ij is as follows: 3) Determine the weights: Assign weights w to each objective function j , reflecting its importance, and the weights need to satisfy 4) Calculate the weighted normalized decision matrix V: Multiply the normalized decision matrix by the weights, and its calculation formula is: v ij = w j · r ij Among them, v ij is the weighted normalization decision; 5) Determine the positive ideal solution V + and the negative ideal solution V - : The positive ideal solution V + refers to the optimal value of each objective function. For a maximization objective, it is the maximum value in the weighted normalized matrix, and for a minimization objective, it is the minimum value in the weighted normalized matrix; the negative ideal solution V - refers to the worst value of each objective function. For a maximization objective, it is the minimum value in the weighted normalized matrix, and for a minimization objective, it is the maximum value in the weighted normalized matrix; 6) Calculate the distance from each solution to the positive ideal solution and the distance to the negative ideal solution Among them, is the j-th positive ideal solution, is the j-th negative ideal solution; 7) Calculate the relative proximity C i : C i The larger it is, the closer the solution is to the ideal solution and the farther it is from the negative ideal solution; 8) Sort and select the optimal solution: Based on the relative closeness C i Sort the solutions and select the one with i the largest C as the optimal solution.

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