Multi-objective optimization method and system for cylindrical permanent magnet linear motor based on NSGA-Ⅱ

Abstract

The present invention discloses a multi-objective optimization method and system for a cylindrical permanent magnet linear motor based on NSGA-II. A sensitive parameter algorithm is used to construct a motor optimization objective function. A two-dimensional motor model is constructed according to the motor optimization objective function and the motor size. Then, motor-related data is derived from the two-dimensional motor model. A bagging algorithm is used for fitting training to obtain a training model with a higher degree of fit between training values ​​and target values. Finally, an optimal value interval of the motor optimization objective is determined according to the training model, and the NSGA-II algorithm is used to optimize the optimal interval to obtain an optimal solution for multi-objective optimization, thereby realizing multi-objective optimization of the motor and outputting a Pareto front solution set of the optimized output power and efficiency, as well as various optimization parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of motor optimization, and more particularly to a multi-objective optimization method and system for a cylindrical permanent magnet linear motor based on NSGA-II. Background Art

[0002] Tubular Permanent Magnet Linear Motor (TPMLM) has the characteristics of simple structure, easy processing and assembly, high air gap magnetic field and no lateral end effect. It is widely used in industrial fields such as wave power generation, oscillation systems, high-precision CNC machine tools and robots.

[0003] To improve the output power and operating efficiency of motor systems, numerous optimization methods have been proposed, the most prominent of which are structural optimization and algorithm optimization. Structural optimization can be achieved by reducing magnetic drag and increasing permanent magnet utilization. Algorithmic optimization can employ various motor optimization analysis methods, such as the response surface methodology, genetic algorithms, and simulated annealing. However, these optimization objectives are often relatively simple. As the application of cylindrical permanent magnet linear motors expands, various applications require both excellent individual performance and good overall performance. Therefore, multi-objective optimization of the motor is an effective method for improving its overall performance. However, since the parameters to be considered in motor optimization design are not unique and are often coupled to each other, the optimization results obtained for a single parameter cannot reflect the overall optimal solution. Comprehensive consideration of the motor's performance indicators and economic efficiency is necessary.

[0004] Maximizing motor output power and efficiency is a multi-objective problem in motor optimization. Common multi-objective optimization approaches include optimizing the average electromagnetic torque and effective motor cost, optimizing motor thrust, thrust-to-volume ratio, and efficiency. To improve the output power and operating efficiency of motor systems, motor optimization can be applied at both the structural and algorithmic levels. For structural optimization, a partially segmented Halbach structure can be used to address the high cogging torque and eddy current losses of permanent magnets in high-power-density permanent magnet synchronous motors, but this approach has limited applicability. Alternatively, secondary length optimization and slot phase shifting can be employed for permanent magnet linear motors, which can reduce end and slot effects, but have limitations in suppressing thrust fluctuations. For algorithmic optimization, a multi-objective particle swarm optimization algorithm with a black hole mechanism and chaotic search has been proposed to prevent premature algorithm development. This algorithm can increase population diversity and improve algorithm optimization accuracy, but it is computationally complex and challenging. Overall, current multi-objective motor optimization methods still suffer from long optimization times, low efficiency, and unsatisfactory results.

[0005] Therefore, how to improve the efficiency and effect of motor multi-objective optimization and reduce time consumption is an urgent problem that technicians in this field need to solve. Summary of the Invention

[0006] In view of this, the present invention provides a multi-objective optimization method and system for a cylindrical permanent magnet linear motor based on NSGA-Ⅱ. NSGA-Ⅱ is used to explore the multi-objective optimization of a cylindrical permanent magnet linear motor (TPMLM), and the output power and operating efficiency of the TPMLM are maximized.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A multi-objective optimization method for a cylindrical permanent magnet linear motor based on NSGA-II includes the following steps:

[0009] Step 1: Preset motor performance indicators, use the sensitive parameter method to select the optimization variables that have the greatest impact on the motor output power and efficiency from the preset motor performance indicators, and construct the motor optimization objective function based on the optimization variables;

[0010] Step 2: Obtain the motor dimensions and construct a two-dimensional motor model based on the optimization objectives and optimization variables in the motor's optimization objective function. The motor dimensions are the measured dimensions before optimization. The optimization objectives include power and efficiency, and the optimization variables include pole arc coefficient, air gap length, back iron thickness, permanent magnet thickness, and slot width. The optimization objective is to maximize power and efficiency, expressed as an optimization objective function.

[0011] Step 3: Exporting motor-related data from the two-dimensional motor model, the motor-related data includes optimization targets and optimization variables, processing the data into the form of the first five columns as optimization variables and the last two columns as optimization targets, and processing the exported current, voltage, and loss data into a distribution form in which the optimization variables and the optimization targets correspond one to one; wherein the optimization variables are used as features and the optimization targets are used as labels, and the motor-related data are fitted and trained using the bagging algorithm to obtain a fitting model with the highest fit between the training value and the target value;

[0012] The software is used to export motor-related data. Because the amount of data is large, machine learning is used to process the data first, and then a fitting model is obtained. This fitting model is then optimized using a multi-objective optimization algorithm.

[0013] Step 4: Based on the fitting model fitted by Bagging, determine the interval of the optimal value of the motor's optimization target, use the NSGA-Ⅱ algorithm for optimization, obtain the optimal solution of multi-objective optimization, realize the multi-objective optimization of the motor, obtain the optimal solution of the optimization target and the optimal parameter values ​​of the optimization variables, and the optimal solution of the optimization target includes the Pareto front solution set of output power and efficiency.

[0014] Preferably, the specific process of building a two-dimensional model of a motor in ANASYS Maxwell includes:

[0015] Step 21: Construct a two-dimensional motor model of TPMLM in ANASYS Maxwell based on the motor size, optimization objectives, optimization variables, and constraints of the optimization variables.

[0016] Step 22: Determine the material properties of each part of the motor in the two-dimensional model of the motor;

[0017] Step 23: setting the boundary conditions of the two-dimensional model of the motor and providing an excitation source;

[0018] Step 24: Select the parameters of the motor two-dimensional model to be calculated, such as output power, operating efficiency, etc.

[0019] Step 25: Determine the parameters required to solve the two-dimensional model of the motor, including determining the initial velocity, boundary, external load, time step, etc. of the TPMLM.

[0020] Preferably, the specific process of using the Bagging algorithm to perform fitting training on the motor-related data in step 3 is:

[0021] Step 31: Using the motor-related data as the original sample set, training samples are extracted from the original sample set. In each round of training, n training samples are extracted from the original sample set using the Bootstraping method to form a training sample set. A total of k rounds of extraction are performed to obtain k training sample sets.

[0022] Step 32: Each time a training sample set is trained to obtain a model, k training sets are trained to obtain k models in total;

[0023] Step 33: For classification problems, the obtained k models are voted to obtain the classification results; for regression problems, the mean of the k models is calculated as the final training result to obtain the fitting model with the highest fit between the training value and the target value.

[0024] Preferably, in step 4, the NSGA-II algorithm is used for optimization, the population and parameters are set, and the algorithm is called to perform population evolution. The specific process is as follows:

[0025] Step 41: Randomly generate an initial parent population P of size N, set G = 1, perform fast non-dominated sorting, and obtain the first generation offspring population Q through the three basic operations of selection, crossover, and mutation of the genetic algorithm;

[0026] Step 42: Starting from the second generation, merge the parent population with the child population to define a temporary population P* , P * =P+Q, then P * Perform fast non-dominated sorting and calculate the crowding degree of individuals in each non-dominated layer. Then select appropriate individuals to form a new parent population based on the non-dominated relationship and the crowding degree of the individuals, and set G = G + 1.

[0027] Step 43: Generate a new offspring population through the basic operations of the genetic algorithm, and return to step 42 until G reaches the preset maximum number of iterations, then the population optimization ends.

[0028] The multi-objective optimization system for cylindrical permanent magnet linear motors based on NSGA-II includes a sensitive parameter analysis module, a two-dimensional modeling module, a training and fitting module, and an NSGA-II optimization module.

[0029] Sensitive parameter analysis module, which obtains preset motor performance indicators and constructs optimization objective functions based on the motor performance indicators;

[0030] The two-dimensional modeling module constructs a two-dimensional model of the motor according to the optimization objective function and the motor performance index, and derives motor-related data from the two-dimensional model of the motor and transmits it to the training and fitting module;

[0031] The training and fitting module uses the Bagging algorithm to perform fitting training based on motor-related data, obtains the fitting model, and transmits it to the NSGA-Ⅱ optimization module;

[0032] The NSGA-Ⅱ optimization module optimizes the fitting model using the NSGA-Ⅱ algorithm to obtain the optimal solution of the optimization target and the optimized parameter values ​​of the optimization variables.

[0033] The above technical solution shows that, compared with the prior art, the present invention provides a multi-objective optimization method and system for a cylindrical permanent magnet linear motor based on NSGA-II. The method uses a sensitive parameter algorithm to construct a motor optimization objective function, constructs a two-dimensional motor model based on the motor optimization objective function and motor dimensions, then derives motor-related data from the two-dimensional motor model and uses a bagging algorithm for fitting training to obtain a training model with a higher degree of fit between the training value and the target value. Finally, the optimal value range of the motor optimization objective is determined based on the training model, and the NSGA-II algorithm is used to optimize the optimal range to obtain the optimal solution for multi-objective optimization, thereby achieving multi-objective optimization of the motor and outputting the Pareto front solution set of optimized output power and efficiency, as well as various optimized parameters. The present invention fully utilizes the multi-data training capability of bagging and the global search capability of NSGA-II to optimize the objectives; uses NSGA-II optimization to ensure the diversity of solutions and improve the quality of solutions through dynamic crowding and adaptive hybrid crossover operators; obtains the optimal solution for motor structural parameters through global optimization, and achieves the best operating performance of TPMLM; and through the optimization of motor parameter structure, the optimized power density and efficiency are improved under different conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0035] Figure 1 The accompanying drawing is a schematic diagram of the overall optimization process of the present invention provided by the present invention;

[0036] Figure 2 The accompanying drawing is a schematic diagram of the two-dimensional model structure provided by the present invention;

[0037] Figure 3 The accompanying drawing is a schematic diagram of the NSGA-II optimization process provided by the present invention;

[0038] Figure 4 The accompanying drawing is a schematic diagram showing the comparison of power before and after optimization provided by the present invention;

[0039] Figure 5 The accompanying drawing is a schematic diagram showing the comparison of the optimization efficiency before and after the present invention. DETAILED DESCRIPTION

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0041] The embodiment of the present invention discloses a multi-objective optimization method for cylindrical permanent magnet linear motor based on NSGA-Ⅱ, the process is as follows Figure 1 shown.

[0042] The main influencing factors of the cylindrical permanent magnet linear motor (TPMLM) include: pole arc coefficient, air gap length, permanent magnet thickness, slot width, and back iron thickness. The constraints of the optimization variables are as follows: the pole arc coefficient range is 0.5≤α≤0.8; the air gap length range is 1≤g≤2; the back iron thickness range is 2≤H b ≤5; Permanent magnet thickness range: 3≤H pm ≤6; Slot width range: 9≤W slot ≤ 11. The optimization goal is to maximize output power and efficiency.

[0043] According to the optimization variables and optimization targets, the mathematical function of the motor multi-objective optimization of the present invention can be obtained as follows:

[0044]

[0045]

[0046] Where P is the output power; η is the efficiency; α is the pole arc coefficient; g is the air gap length; H b is the back iron thickness; H pm is the thickness of the permanent magnet; W slot is the slot width.

[0047] The system of the present invention includes a two-dimensional modeling part, a sensitive parameter analysis part, a machine learning training and fitting part, and an NSGA-II optimization part;

[0048] The two-dimensional modeling part is used to establish the two-dimensional model of the cylindrical permanent magnet linear motor and construct the two-dimensional model of the optimization object;

[0049] The sensitive parameter analysis section is used to obtain the motor's optimization variables and construct the motor's optimization objective function. Based on the obtained optimization objective function, the sensitive parameter analysis is performed to determine the motor's main influencing factors - pole arc coefficient, air gap length, back iron thickness, permanent magnet thickness, and slot width - as optimization variables. The sensitive parameter analysis is performed based on the motor's optimization objectives (power and efficiency).

[0050] The machine learning fitting training part is used to perform fitting analysis on the data. It fits the relevant variables and target data derived from the two-dimensional model to obtain a result with a higher degree of fit between the training value and the target value.

[0051] The NSGA-II optimization part is based on the training data obtained by machine learning fitting training, and uses MOPs to obtain the Pareto optimal solution set that meets the constraints, as well as the final values ​​of the optimization objectives and optimization variables, to achieve multi-objective motor optimization.

[0052] The steps of the method of the present invention are:

[0053] S1: Use the sensitive parameter method to find the variable parameters that have the greatest impact on the motor output power and efficiency as the main influencing factors, and use the obtained main influencing factors as optimization variables to construct the optimization objective function of the motor;

[0054] S2: Obtain the motor size and build a two-dimensional model of the motor based on the motor optimization target and optimization variables;

[0055] S21: Draw the 2D model of TPMLM in ANASYS Maxwell according to the size parameters of TPMLM;

[0056] S22: Give material properties to each part of TPMLM;

[0057] S23: Set the boundary conditions of TPMLM and give the excitation source;

[0058] S24: Select the parameters to be calculated, such as output power, operating efficiency, etc.;

[0059] S25: Determine the parameters required to be solved, including the initial velocity, boundary, external load, time step, etc. of the TPMLM;

[0060] S3: Export relevant data from the 2D model and use Bootstrap Aggregating (Bagging) to fit and train the data. Process the current, voltage, and hysteresis loss data obtained from ANASYS Maxwell into efficiency and power data distributions. This data is then processed into feature (optimization variable) and label (optimization target) distributions. Bagging is used for model training, data fitting, and model saving.

[0061] S31: Extract a training set from the original sample set. In each round, use the Bootstraping method to extract n training samples from the original sample set to form a sample set. Perform k rounds of extraction to obtain k training sets.

[0062] S32: Each time a training set is trained, a model is obtained. K training sets are trained to obtain k models in total.

[0063] S33: For classification problems, the k models obtained in the previous step are voted to obtain the classification result. For regression problems, the mean of the above models is calculated as the final result.

[0064] S4: Based on the model fitted by bagging, determine the optimal value range of the motor's optimization objectives, use NSGA-II to obtain the optimal solution for multi-objective optimization, implement multi-objective optimization of the motor, and obtain the Pareto front solution set of the optimized output power and efficiency and the values ​​of each optimization parameter; read the machine learning fitting model trained using bagging, namely the efficiency and power models; use NSGA-II for parameter optimization, set the population and parameters, and call the algorithm to perform population evolution;

[0065] S41: Randomly generate an initial population of size N, perform fast non-dominated sorting, and obtain the first generation of offspring population through the three basic operations of genetic algorithm: selection, crossover, and mutation;

[0066] S42: Starting from the second generation, the parent population and the child population are merged and fast non-dominated sorting is performed again. At the same time, the crowding degree of the individuals in each non-dominated layer is calculated, and suitable individuals are selected to form a new parent population based on the non-dominated relationship and the crowding degree of the individuals.

[0067] S43: Generate a new offspring population through the basic operations of the genetic algorithm, and so on, until G reaches the preset maximum number of iterations, then the population optimization ends. Determine whether the set program end conditions are met. If so, the program ends; if not, return to S3 to continue fitting.

[0068] Simulation verification:

[0069] Based on the optimized variable values, the optimized variable values ​​are brought into the simulation model to obtain the output power and efficiency values, and compared with those before optimization to determine whether the optimization target has been improved.

[0070] Based on the optimized motor dimensions, an ANASYS Maxwell simulation model of the TPMLM was established. The instantaneous power was calculated at a speed of 0.5 m / s, a hysteresis loss internal resistance of 0.8 Ω, and a load of 10 Ω. The efficiency was calculated at a speed of 0.1-1.0 m / s. The average power and average efficiency were calculated using the instantaneous power and efficiency values ​​before and after optimization. The optimized parameters were obtained from the optimized Pareto front solution set. The results of the present invention are compared. The comparison of variables before and after optimization is shown in Table 1 below, and the comparison of target values ​​before and after optimization is shown in Table 2 below.

[0071] Table 1 Comparison of variables before and after optimization

[0072]

[0073] Table 2 Comparison of target values ​​before and after optimization

[0074]

[0075] Figure 2 The two-dimensional model in the figure is based on the basic dimensions of the motor, including the air gap 1, stator 2, back iron 3, auxiliary slot 4, stator convex 5, and permanent magnet 6. A two-dimensional simulation was performed on ANASYS Maxwell based on the basic dimensions and constraints of the TPMLM. The establishment of the simulation model provides basic data for the next step of training and optimization. The simulation model derives data related to the optimization variables: pole arc coefficient, air gap length, permanent magnet thickness, slot width, back iron thickness, and the optimization objectives: output power and efficiency. The basic dimensions of the motor are shown in Table 3 below:

[0076] Table 3 Basic dimensions of motors

[0077]

[0078]

[0079] Figure 3 The figure shows the NSGA-II optimization process of the present invention. NSGA-II is an improvement of the genetic algorithm. Its main idea is the non-dominated sorting genetic algorithm, which mainly uses fast non-dominated sorting and elitism to preserve excellent individuals. The main steps of the optimization are as follows:

[0080] First, randomly generate an initial parent population P of size N, set G = 1, and after fast non-dominated sorting, obtain the first generation offspring population Q through the three basic operations of selection, crossover, and mutation of the genetic algorithm;

[0081] Secondly, starting from the second generation, the parent population and the child population are merged to define a temporary population P * , P * =P+Q, then P * Perform fast non-dominated sorting and calculate the crowding degree of individuals in each non-dominated layer. Select appropriate individuals to form a new parent population based on the non-dominated relationship and the crowding degree of the individuals, and set G = G + 1.

[0082] Finally, a new offspring population is generated through the basic operations of the genetic algorithm; and so on, until the conditions for the end of the program are met.

[0083] Figure 4This is a comparison chart of the instantaneous power of the motor before and after motor optimization. The output power is calculated when the speed is 0.5m / s and the load is 10Ω. The instantaneous power of TPMLM is related to the internal circuit being a three-phase circuit. The output power P of TPMLM out Calculated as P out =I A U A +I B U B +I C U C ;

[0084] Among them, I A , I B , I C 、U A 、U B 、U C They are the current and voltage values ​​of each phase of the three-phase circuit respectively. It can be seen from the figure that the output power of the optimized TPMLM is increased compared with that before optimization. The average power of TPMLM is changed from 401.52W before optimization to 454.02W after optimization, achieving the optimization effect.

[0085] Figure 5 This is a comparison chart of motor efficiency before and after optimization. The efficiency is calculated when the winding resistance is 0.8Ω. Calculate, where P core is the hysteresis loss, the hysteresis loss data is derived from the simulation model, P out is the output power, P cu use Perform calculations.

[0086] As can be seen from the figure, the working efficiency of the optimized motor is significantly improved compared to that before optimization. The average efficiency of the motor increases from 82.83% before optimization to 90.18% after optimization, achieving the optimization effect. The above prototype measurement demonstrates the effectiveness of the proposed method for optimizing the TPMLM structure.

[0087] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0088] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-objective optimization method for cylindrical permanent magnet linear motor based on NSGA-Ⅱ, characterized by: The following steps are involved: Step 1: Preset motor performance indicators, select optimization variables from the preset motor performance indicators using a sensitive parameter method, and construct an optimization objective function of the motor based on the optimization variables; Step 2: Obtain the motor size and build a two-dimensional model of the motor based on the optimization objectives and optimization variables in the motor optimization objective function; Step 3: Exporting motor-related data from the motor two-dimensional model, and performing fitting training on the motor-related data using a bagging algorithm to obtain a fitting model with the highest degree of fit between the training value and the target value; Step 4: Optimize using the NSGA-II algorithm based on the fitted model to obtain the optimal solution of the optimization objective and the optimal parameter values ​​of the optimization variables. The optimal solution of the optimization objective includes the Pareto front solution set of output power and efficiency. In step 4, the NSGA-Ⅱ algorithm is used for optimization. The population and parameters are set, and the algorithm is called to perform population evolution. The specific process is as follows: Step 41: Randomly generate an initial parent population P of size N, set G = 1, perform fast non-dominated sorting, and obtain the first generation offspring population Q through the three basic operations of selection, crossover, and mutation of the genetic algorithm; Step 42: Starting from the second generation, merge the parent population with the child population and set a temporary population P * , P * =P+Q, then P * Perform fast non-dominated sorting and calculate the crowding degree of individuals in each non-dominated layer. Then select appropriate individuals to form a new parent population based on the non-dominated relationship and the crowding degree of the individuals, and set G = G + 1. Step 43: Generate a new offspring population through the basic operations of the genetic algorithm, and return to step 42 until G reaches the preset maximum number of iterations, then the population optimization ends.

2. The multi-objective optimization method for cylindrical permanent magnet linear motor based on NSGA-II according to claim 1 is characterized in that: The specific process of building a 2D motor model in ANASYS Maxwell includes: Step 21: Build a 2D motor model in ANASYS Maxwell based on the motor size, optimization objectives, optimization variables, and constraints. Step 22: Determine the material properties of each part of the motor in the two-dimensional model of the motor; Step 23: setting the boundary conditions of the two-dimensional model of the motor and providing an excitation source; Step 24: Select parameters of the motor two-dimensional model to be calculated; Step 25: Determine the number of parameters required to solve the two-dimensional model of the motor.

3. The multi-objective optimization method for cylindrical permanent magnet linear motor based on NSGA-II according to claim 1 is characterized in that: The specific process of using the Bagging algorithm to fit the motor-related data in step 3 is as follows: Step 31: Using the motor-related data as the original sample set, training samples are extracted from the original sample set. In each round of training, n training samples are extracted from the original sample set using the Bootstraping method to form a training sample set. A total of k rounds of extraction are performed to obtain k training sample sets. Step 32: Each time a training sample set is trained to obtain a model, k training sets are trained to obtain k models in total; Step 33: The obtained k models are voted to obtain the classification results, and the mean of the k models is calculated as the final training result.

4. A multi-objective optimization system for a cylindrical permanent magnet linear motor multi-objective optimization method based on NSGA-II according to claims 1-3, characterized in that: It includes sensitive parameter analysis module, two-dimensional modeling module, training and fitting module and NSGA-Ⅱ optimization module; Sensitive parameter analysis module, which obtains preset motor performance indicators and constructs optimization objective functions based on the motor performance indicators; The two-dimensional modeling module constructs a two-dimensional model of the motor according to the optimization objective function and the motor performance index, and derives motor-related data from the two-dimensional model of the motor and transmits it to the training and fitting module; The training and fitting module uses the Bagging algorithm to perform fitting training based on motor-related data, obtains the fitting model, and transmits it to the NSGA-Ⅱ optimization module; The NSGA-Ⅱ optimization module optimizes the fitting model using the NSGA-Ⅱ algorithm to obtain the optimal solution of the optimization target and the optimized parameter values ​​of the optimization variables.

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