Optimization design method of wind power controllable magnetic gear box

Abstract

The invention relates to an optimal design method of a wind power controllable magnetic gearbox, and belongs to the field of wind power. The controllable magnetic gear box comprises an inner rotor, an outer rotor, a magnetism adjusting ring and a stator, an inner rotor average torque and torque pulsation, a stator no-load back electromotive force amplitude and a distortion rate are selected as optimization targets, ten parameters such as inner and outer rotor iron core thicknesses, a permanent magnet thickness, a magnetic adjusting ring thickness, a stator iron core outer radius and a stator winding turn number are selected as design variables to be optimized, an LHS experiment is carried out, and a BPNN proxy model is established and trained; performing Sobol 'global sensitivity analysis on the trained agent model to screen out key design variables to be optimized; optimizing the key design variables to be optimized by adopting NSGA-II to obtain an optimal solution set; and the optimal solution set is evaluated by adopting TOPSIS, and a group of optimal design variables are accurately selected, so that the optimization target is optimal. According to the method, the optimization precision and efficiency can be remarkably improved, and the purposes of reducing the cost and improving the performance are achieved.

Description

Technical Field

[0001] The present invention relates to a multi-objective optimization design method, in particular to an optimization design method for a wind power controllable magnetic gearbox, and belongs to the technical field of wind power generation. Background Art

[0002] Wind turbine gearboxes are core components of semi-direct-drive and doubly-fed wind turbines. Traditional mechanical gearboxes have drawbacks such as the need for lubrication, high failure rates, and high maintenance costs, hindering the development of the wind power industry. Existing magnetic gearboxes, while offering advantages such as no lubrication and overload protection, are uncontrollable.

[0003] Because the wind power controllable magnetic gearbox adopts armature winding and concentrated magnetic core, it can not only be used as a motor when the wind speed is low, thereby reducing the starting torque, but also be used as a speed-increasing gearbox and generator when the wind speed exceeds the rated wind speed, thereby making full use of wind energy and increasing power generation. This is of great significance to promoting the development of my country's wind power industry.

[0004] However, the wind power controllable magnetic gearbox has multiple air gaps. In addition to the inner and outer rotors and magnetic regulating rings, there are also stator magnetic cores and windings. Its design parameters are relatively large and there is a strong coupling and strong nonlinear relationship between the variables. Therefore, the performance of the wind power controllable magnetic gearbox is significantly affected by the structural parameters. Its optimization design is extremely challenging because it is essentially a system optimization problem with complex constraints, multiple objectives, and strong nonlinearity. It is necessary to obtain a design solution that optimizes the various performance indicators of the controllable magnetic gearbox while satisfying various conditions at the same time. The selection of optimization objectives and optimization strategies for the controllable magnetic gearbox will seriously affect the quality of the magnetic gearbox design solution, and thus determine its operating performance.

[0005] Existing multi-objective optimization algorithms, such as the hybrid genetic algorithm (MOGA), multi-objective particle swarm optimization (MOPSO), ant colony algorithm (ACA), and tabu search (TS), are prone to falling into local optima for high-dimensional, nonlinear, and multimodal problems, making it difficult to obtain the optimal design solution and resulting in high computational costs. When neural networks are used as surrogate models, improper sample selection can lead to insufficient model accuracy. Back-propagation neural networks (BPNNs) are powerful nonlinear modeling tools capable of approximating complex functional relationships. The Sobol's method is a variance-based Monte Carlo method that first samples model parameters and then calculates the partial and total variances of the model's output response to obtain the global sensitivity of each parameter. The second-generation non-dominated sorting genetic algorithm (NSGA-II) inherits many of the advantages of genetic algorithms, such as simplicity, robustness, versatility, and scalability. It uses fast non-dominated sorting to partition the population into multiple Pareto frontier levels, ensuring the algorithm can simultaneously optimize multiple objectives and generate a set of high-quality non-dominated solutions. However, all solutions in the Pareto optimal solution set are in a non-dominated relationship, that is, in the absence of decision maker preference information, there is theoretically no absolute ranking of superiority or inferiority. Usually, the Pareto optimal solution set contains a large number of solutions (from hundreds to thousands), which will cause the dimension of the decision space to increase dramatically, making the decision process very complex and difficult. It can be seen that the existing optimization methods are difficult to cope with the complex optimization problems brought about by the multi-objective, strong nonlinear and high-dimensional characteristics of wind power controllable magnetic gearboxes, resulting in low optimization efficiency and difficulty in meeting design requirements. Therefore, there is an urgent need for an efficient and accurate optimization design method to improve its performance. Summary of the Invention

[0006] The main purpose of the present invention is to address the shortcomings and gaps in the existing technology and provide an optimization design method for a wind power controllable magnetic gearbox. By adopting Latin hypercube sampling (LHS) and integrating multiple advanced optimization technologies such as BP neural network (BPNN), Sobol' global sensitivity analysis, NSGA-Ⅱ and TOPSIS (topic ideal solution sorting method), the optimal solution is accurately selected to achieve efficient optimization of the structural parameters of the magnetic gearbox, thereby significantly improving its torque stability and electromagnetic performance, reducing torque pulsation and harmonic distortion rate, and meeting the technical requirements of the wind power generation field for high-performance magnetic gearboxes.

[0007] To achieve the above objectives, the wind turbine controllable magnetic gearbox described in the present invention comprises an inner rotor, a magnetic adjustment ring, an outer rotor, a stator, and a rotating shaft. The inner rotor comprises inner rotor permanent magnets and an inner rotor core; the magnetic adjustment ring comprises magnetic adjustment magnet blocks and non-magnetic material; the outer rotor comprises outer rotor permanent magnets and an outer rotor iron block; and the stator comprises three-phase windings and a stator core. The outer rotor is fixed to the wind turbine main shaft; the inner rotor core is fixed to the rotating shaft, and the other end of the rotating shaft is connected to the rotating shaft of the wind turbine generator via a coupling.

[0008] The present invention provides a wind power controllable magnetic gearbox optimization design method, comprising the following steps:

[0009] Step 1: Select the average torque T of the inner rotor of the wind power controllable magnetic gearbox. avg , inner rotor torque pulsation T rip , the no-load back electromotive force amplitude of the stator winding V EMF And the distortion rate THD of the no-load back electromotive force of the stator winding EMF To optimize the target, the vector y of the optimization target is defined as:

[0010] y=[y1,y2,y3,y4]=[|T avg -T s |,T rip ,|V EMF -V N |,THD EMF ] (1)

[0011] Where, T s is the inner rotor stall torque, V N is the stator winding phase voltage amplitude.

[0012] Step 2: Select the following 10 parameters as the design variables to be optimized for the wind turbine controllable magnetic gearbox: inner rotor core thickness h1, inner rotor permanent magnet thickness h2, magnetic adjustment ring thickness h3, outer rotor permanent magnet thickness h4, stator core thickness h5, stator core outer radius r2, outer rotor permanent magnet proportional coefficient N a , magnetic block span coefficient K p , axial length L, number of stator winding turns Z, then the vector x of the design variables to be optimized is defined as:

[0013] x=[x1,x2,x3,x4,x5,x6,x7,x8,x9,x 10 ]=[h1,h2,h3,h4,h5,r2,N a ,K p ,L,Z] (2)

[0014] Step 3: Determine the constraints of the design variable x to be optimized:

[0015]

[0016] In the formula, l and u in the subscripts of each design variable x to be optimized represent the lower bound and upper bound of the variable, respectively.

[0017] Step 4: Perform Latin Hypercube Sampling (LHS) experiment to establish the initial sample space:

[0018] 41) Determine the size of the sampling dimension d of the sample, that is, the number of design variables to be optimized; determine the value range of each design variable to be optimized.

[0019] 42) Divide the interval: divide the value range of each variable into [a j ,b j ] is divided into n equal-width intervals, and the width of each area is

[0020] 43) Random permutation: Randomly arrange the intervals after each variable is divided to generate a random order.

[0021] 44) Sampling in subintervals: Randomly select sample points in each subinterval. For the sampling point of the i-th sample in the j-th dimension, the calculation formula is:

[0022] x ij =a j +Δ×(π j (i)-1+u ij ) (4)

[0023] Where, π j (i) is the subinterval number of the i-th sample in the j-th dimension, i = 1, 2, ..., n, u ij is a random number uniformly distributed in the interval [0,1].

[0024] 45) Generate a sample matrix: Combine the sample points of all dimensions to form an n×d sample matrix. Each row of this matrix represents a sample point, and each column corresponds to a dimension.

[0025] Step 5: Use BPNN to establish a proxy model between each optimization target y of the wind power controllable magnetic gearbox and the design variable to be optimized x.

[0026] 51) The BPNN includes 1 input layer, 1 hidden layer, and 1 output layer, wherein the input layer has 10 neurons, which are 10 design variables to be optimized x1~x 10 ; The hidden layer has 150 neurons; the output layer has 4 neurons, which are 4 optimization targets y1, y2, y3, and y4 respectively.

[0027] 52) Perform feedforward calculations. For a given input sample, the output value of the neuron is calculated layer by layer to achieve information transfer. The output value of the sth neuron in the hidden layer is calculated as follows:

[0028]

[0029] Where w is is the connection weight between the jth neuron in the input layer and the sth neuron in the hidden layer, a s is the bias of the sth neuron in the hidden layer, f(·) is the activation function of the hidden layer, and the Sigmoid function is used, that is:

[0030] The output of the lth neuron in the output layer is the predicted value of the optimization target for:

[0031]

[0032] Where w sl is the connection weight coefficient between the sth neuron of the hidden layer and the lth neuron of the output layer, b l is the threshold of the lth neuron in the output layer, l = 1, 2, 3, 4;

[0033] 53) Error calculation: The output prediction value of the BPNN obtained in step 52) and the expected output y l , calculate the prediction error e l :

[0034]

[0035] 54) Weight update: According to the prediction error e obtained in step 53) l Update the network connection weight w is and w sl :

[0036]

[0037] Where η is the learning rate.

[0038] 55) Threshold update: According to the network prediction error e obtained in step 53) l Update network node threshold a s and b l :

[0039]

[0040] 56) Model evaluation and validation: using the coefficient of determination R 2, root mean square error RMSE and mean absolute error MAE are used to evaluate the model prediction performance, and their expressions are:

[0041]

[0042] Where m is the number of test set samples, m = 15% × n × d; y i is the actual value of the i-th sample, is the predicted value of the i-th sample, is the mean value of the i-th sample.

[0043] 57) Analyze the prediction effect, when the determination coefficient R 2 >0.9, and the root mean square error RMSE<ε1 and the mean absolute error MAE<ε2, then go to step 6, otherwise return to step 52); ε1 and ε2 are both positive real numbers close to 0.

[0044] Step 6: Based on the Sobol' global sensitivity analysis, select the key design variables to be optimized that have a greater impact on the optimization objective. The specific method is as follows:

[0045] 61) Calculate the partial variance and total variance of the model output response to obtain the global sensitivity of each parameter. d =(X|x j ; j=1,2,…,d), the function f(x) is decomposed into 2 d Sum of increasing polynomials:

[0046]

[0047] Where f0 is a constant term, f j (x j ) is dependent only on x j The first-order term, f j,k (x j ,x k ) is x j and x k interaction term; k is a positive integer, 1≤k≤d;

[0048] Then the total variance V and partial variance V 1,2, ... ,j They are:

[0049]

[0050] Then the total variance V and sensitivity index S 1,2, ... ,j for:

[0051]

[0052] Where, the sensitivity index S 1,2, ... ,j is the ratio of variance, indicating the degree of influence of changes in each design variable to be optimized on the optimization objective; h is a positive integer, 1≤h≤j.

[0053] 62) Perform Sobol' global sensitivity analysis on the BPNN proxy model according to step 61) to screen out key design variables to be optimized.

[0054] 63) Repeat the operation process of steps 4 and 5 for the key design variables to be optimized obtained in step 62), wherein the range of the design variables to be optimized and the optimization objectives remain unchanged, and the retrained BPNN agent model is used as the fitness function of the second-generation non-dominated sorting genetic algorithm (NSGA-II) to carry out the optimization work.

[0055] In step 7, the second-generation non-dominated sorting genetic algorithm NSGA-II is used to perform fast non-dominated solution set sorting using the Pareto dominance mechanism, and a population update mechanism is established based on the elite strategy and individual crowding distance selection to generate the Pareto optimal solution set of the key design variables to be optimized obtained in step 6.

[0056] Step 8: Use the TOPSIS method to evaluate the Pareto optimal solution set and select a set of optimal key design variables to be optimized according to the design requirements. The specific steps are as follows:

[0057] 81) Construct a decision matrix: Construct a decision matrix: Determine the corresponding decision matrix H based on the number of solutions t and the number of optimization targets l:

[0058]

[0059] Where h tl Represents the lth optimization target value of the tth solution, t = 1, 2…, r, l = 1, 2, 3, 4.

[0060] 82) Normalize the original data:

[0061] All optimization target values ​​h tl Perform the same-direction processing as follows:

[0062]

[0063] Using the vector normalization method, we get the normalized matrix Q, where the unit q in Q is tl for:

[0064]

[0065] 83) Determine the weights and construct the weighting matrix:

[0066] Introducing the weight vector w l :

[0067]

[0068] Unit q in Q tl Multiply by the corresponding weights to reflect the importance of different indicators in decision-making, and calculate the weighted normative matrix U, the unit u in U tl for:

[0069] u tl =q tl w l (20)

[0070] 84) Determine positive and negative ideal solutions: Find the optimal value (positive ideal solution) and the worst value (negative ideal solution) of each optimization objective as a reference for evaluating the solution.

[0071] Positive ideal solution U + :

[0072]

[0073] Negative ideal solution U - :

[0074]

[0075] Where U + and U - denote the positive ideal solution set and the negative ideal solution set respectively; They represent the positive ideal solutions of the four optimization objectives, They represent the negative ideal solutions of the four optimization objectives respectively.

[0076] 85) Calculate the distance between each solution and the positive / negative ideal solution:

[0077] Distance to positive ideal solution

[0078]

[0079] Distance to negative ideal solution

[0080]

[0081] 86) Calculate the proximity index A t , the proximity index of each solution is calculated by distance, reflecting the relative closeness between the solution and the ideal solution:

[0082]

[0083] 87) Comprehensive evaluation and ranking: According to the proximity index A t Sort all the solutions, A t The larger the value, the better the solution, thus the order of advantages and disadvantages of the solutions can be obtained, providing a basis for decision-making.

[0084] Step 9: Substitute the optimal solution value selected in step 8 into the designed model for simulation analysis. If all four optimization target values ​​meet the design requirements, the optimization is terminated; otherwise, return to step 4.

[0085] The beneficial effects of the present invention are:

[0086] 1) In continuous dimensional parameter optimization, the combination of Latin Hypercube Sampling (LHS), BP neural network, and Sobol's analysis offers significant advantages. LHS efficiently generates uniform samples, BP neural network accurately builds surrogate models, and Sobol's analysis precisely screens key parameters. This collaborative approach effectively reduces the number of finite element experiments and computational costs, while improving optimization accuracy and efficiency and ensuring a cost-effective and practical optimization process.

[0087] 3) In multi-objective optimization, the Pareto optimal solution set provides a large number of non-dominated solutions. After comprehensive evaluation using the TOPSIS method, it can effectively overcome the problem of a sharp increase in the dimensionality of the decision space and reduce the complexity of decision making. In addition, when there are manufacturing constraints, cost restrictions, and implicit preferences, the variable parameter combination with the best overall performance can still be selected. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 This is a schematic diagram of the wind power system topology of the wind power controllable magnetic gearbox of the present invention.

[0089] Figure 2 This is a structural cross-sectional view of the wind power controllable magnetic gearbox of the present invention.

[0090] Figure 3 Schematic diagram of the process of optimizing the design method of the present invention.

[0091] Figure 4 Schematic diagram of some design variables to be optimized for the wind power controllable magnetic gearbox of the present invention.

[0092] Figure 5 This is the BPNN agent model for the optimization design method of the present invention.

[0093] Figure 6 This is a comparison curve between the actual value and the predicted value of the BPNN prediction optimization target of the present invention.

[0094] Figure 7 It is a sensitivity analysis diagram of each design variable to be optimized and each optimization target of the present invention.

[0095] Figure 8 This is the Pareto frontier diagram of the optimization target generated after the wind power controllable magnetic gearbox of the present invention is optimized by NSGA-Ⅱ.

[0096] Figure 9 This is the no-load back electromotive force waveform of the wind power controllable magnetic gearbox of the present invention before optimization.

[0097] Figure 10 This is the no-load back electromotive force harmonic spectrum of the wind power controllable magnetic gearbox before optimization.

[0098] Figure 11 This is the no-load back electromotive force waveform diagram of the optimized wind power controllable magnetic gearbox of the present invention.

[0099] Figure 12 This is the no-load back electromotive force harmonic spectrum of the optimized wind power controllable magnetic gearbox of the present invention.

[0100] Figure 13 This is a torque-time curve diagram of the wind power controllable magnetic gearbox before optimization.

[0101] Figure 14 This is the torque-time curve of the optimized wind power controllable magnetic gearbox of the present invention.

[0102] Among them, 1-wind wheel; 2-wind wheel main shaft; 3-rotating shaft; 4-stator; 5-outer rotor; 6-magnetic adjustment ring; 7-inner rotor; 8-wind turbine; 9-casing; 10-base; 11-stator core; 12-stator winding; 13-outer rotor permanent magnet; 14-outer rotor iron block; 15-magnetic adjustment magnet block; 16-inner rotor permanent magnet; 17-inner rotor core. DETAILED DESCRIPTION

[0103] The present invention will be described in further detail below with reference to the accompanying drawings.

[0104] like Figure 1 、 Figure 2 As shown, the wind power controllable magnetic gearbox described in the present invention includes: a stator 4, an outer rotor 5, a magnetic adjustment ring 6, an inner rotor 7, a rotating shaft 3, a shell 9, and a base 10; the stator 4 includes a stator core 11 and a stator winding 12, the outer rotor 5 includes an outer rotor permanent magnet 13 and an outer rotor iron block 14; the magnetic adjustment ring 6 includes a magnetic adjustment block 15 and a non-magnetic material; the inner rotor 7 includes an inner rotor permanent magnet 16 and an inner rotor core 17; the outer rotor 5 is fixed to the wind wheel main shaft 2; the inner rotor core 17 is fixed to the rotating shaft 3, and the other end of the rotating shaft 3 is connected to the rotating shaft of the wind turbine 8 through a coupling.

[0105] like Figure 3 As shown, the present invention provides an optimization design method for a wind power controllable magnetic gearbox, comprising the following steps:

[0106] Step 1: Select the average torque T of the inner rotor 7 of the wind power controllable magnetic gearbox avg , inner rotor torque pulsation T rip , the no-load back electromotive force amplitude V of the stator winding 12 EMF And the distortion rate THD of the no-load back electromotive force of the stator winding EMF To optimize the target, the vector y of the optimization target is defined as:

[0107] y=[y1,y2,y3,y4]=[|T avg -T s |,T rip ,|V EMF -V N |,THD EMF ] (1)

[0108] Where, T s is the inner rotor stall torque, V N is the stator winding phase voltage amplitude.

[0109] Step 2: Select the following 10 parameters as the design variables to be optimized for the wind turbine controllable magnetic gearbox: inner rotor core thickness h1, inner rotor permanent magnet thickness h2, magnetic adjustment ring thickness h3, outer rotor permanent magnet thickness h4, stator core thickness h5, stator core outer radius r2, outer rotor permanent magnet proportional coefficient N a , magnetic block span coefficient K p , axial length L, number of stator winding turns Z (some variables are Figure 4 (indicated in the middle), then the vector x of the design variables to be optimized is defined as:

[0110] x=[x1,x2,x3,x4,x5,x6,x7,x8,x9,x 10 ]=[h1,h2,h3,h4,h5,r2,N a ,K p ,L,Z] (2)

[0111] Step 3: Determine the constraints of the design variable x to be optimized:

[0112]

[0113] In the formula, l and u in the subscripts of each design variable x to be optimized represent the lower bound and upper bound of the design variable, respectively.

[0114] Step 4: Perform Latin Hypercube Sampling (LHS) experiment to establish the initial sample space:

[0115] 41) Determine the value range of each design variable to be optimized and the size of the sampling dimension d (i.e., the number of design variables to be optimized).

[0116] 42) Divide the interval: divide the value range of each variable into [a j ,b j ] is divided into n equal-width intervals, and the width of each area is

[0117] 43) Random permutation: Randomly arrange the intervals after each variable is divided to generate a random order.

[0118] 44) Sampling in subintervals: Randomly select sample points in each subinterval. For the sampling point of the i-th sample in the j-th dimension, the calculation formula is:

[0119] x ij =a j +Δ×(π j (i)-1+u ij ) (4)

[0120] Where, π j (i) is the subinterval number of the i-th sample in the j-th dimension, i = 1, 2, ..., n, u ij is a random number uniformly distributed in the interval [0,1].

[0121] 45) Generate a sample matrix: Combine the sample points of all dimensions to form an n×d sample matrix. Each row of this matrix represents a sample point, and each column corresponds to a dimension.

[0122] Sampling is performed according to the above process. Based on the given design variables to be optimized and their value ranges, the sampling dimension d = 10 and the number of sampling intervals n = 1000 are determined, providing data samples for subsequent BP neural network training.

[0123] Step 5: Use BPNN to establish a proxy model between each optimization target y of the wind power controllable magnetic gearbox and the design variable to be optimized x.

[0124] 51) The BPNN includes 1 input layer, 1 hidden layer, and 1 output layer, wherein the input layer has 10 neurons, which are 10 design variables to be optimized x1~x 10 ; The hidden layer has 150 neurons; the output layer has 4 neurons, which are 4 optimization targets y1, y2, y3, and y4 respectively.

[0125] 52) Perform feedforward calculations. For a given input sample, the output value of the neuron is calculated layer by layer to achieve information transfer. The output value of the sth neuron in the hidden layer is calculated as follows:

[0126]

[0127] Where w is is the connection weight between the jth neuron in the input layer and the sth neuron in the hidden layer, a s is the bias of the sth neuron in the hidden layer, f(·) is the activation function of the hidden layer, and the Sigmoid function is used, that is:

[0128] The output of the lth neuron in the output layer is the predicted value of the optimization target for:

[0129]

[0130] Where w sl is the connection weight coefficient between the sth neuron of the hidden layer and the lth neuron of the output layer, b l is the threshold of the lth neuron in the output layer, l = 1, 2, 3, 4;

[0131] 53) Error calculation: The output prediction value of the BPNN obtained in step 52) and the expected output y l , calculate the prediction error e l :

[0132]

[0133] 54) Weight update: According to the prediction error e obtained in step 53) l Update the network connection weight w is and w sl :

[0134]

[0135] Where η is the learning rate.

[0136] 55) Threshold update: According to the network prediction error e obtained in step 53) l Update network node threshold a s and b l :

[0137]

[0138] 56) Model evaluation and validation: After multiple rounds of iterative training, the model is finally evaluated using the test set. The coefficient of determination R is used. 2 , root mean square error RMSE and mean absolute error MAE are used to evaluate the model prediction performance, and their expressions are:

[0139]

[0140] Where m is the number of test set samples, m = 15% × n × d; y i is the actual value of the i-th sample, is the predicted value of the i-th sample, is the mean value of the i-th sample.

[0141] 57) Analyze the prediction effect, when the determination coefficient R 2 If the error is >0.9, and the root mean square error (RMSE) is <ε1 and the mean absolute error (MAE) is <ε2, then proceed to step 6; otherwise, return to step 52. ε1 and ε2 are both positive real numbers close to 0. If the error is small, it means that the BPNN prediction effect is very good and the next step of optimization can be carried out.

[0142] Step 6: Based on the Sobol' global sensitivity analysis, select the key design variables to be optimized that have a greater impact on the optimization objective. The specific method is as follows:

[0143] 61) Calculate the partial variance and total variance of the model output response to obtain the global sensitivity of each parameter. d =(X|x j ; j=1,2,…,d), the function f(x) is decomposed into 2 d Sum of increasing polynomials:

[0144]

[0145] Where f0 is a constant term, f j (x j ) is dependent only on x j The first-order term, f j,k (x j ,x k ) is x j and x k interaction terms;

[0146] Then the total variance V and partial variance V 1,2,,j They are:

[0147]

[0148] Then the total variance V and sensitivity index S 1,2,,j for:

[0149]

[0150] Where, the sensitivity index S 1,2,…,j is the ratio of variance, indicating the degree of influence of changes in each design variable to be optimized on the optimization objective; h is a positive integer, 1≤h≤j.

[0151] The larger the sensitivity index, the stronger the impact; S j represents the first-order sensitivity of the j-th design variable to be optimized, indicating the impact of the j-th design variable to be optimized on the dependent variable when it acts alone; S j,k It represents the second-order global sensitivity index under the joint action of the j-th design variable to be optimized and the k-th design variable to be optimized. The sum of the sensitivity indices of all orders of a certain design variable to be optimized is the total sensitivity index of the design variable to be optimized, which reflects the comprehensive influence of the change of the design variable to be optimized itself and the change caused by the interaction with other design variables to be optimized.

[0152] 62) Perform a Sobol' global sensitivity analysis on the BPNN proxy model according to step 61) to screen out key design variables to be optimized. As an example, the present invention screens out six key design variables to be optimized: inner rotor core thickness h1, inner rotor permanent magnet thickness h2, outer rotor permanent magnet thickness h4, stator core thickness h5, stator core outer radius r2, and armature winding turns Z.

[0153] 63) Repeat the operation process of steps 4 and 5 for the key design variables to be optimized obtained in step 62), wherein the range of the design variables to be optimized and the optimization objectives remain unchanged, and the retrained BPNN agent model is used as the fitness function of the second-generation non-dominated sorting genetic algorithm (NSGA-II) to carry out the optimization work.

[0154] Step 7: Use the second-generation non-dominated sorting genetic algorithm NSGA-II and the Pareto dominance mechanism to quickly sort the non-dominated solution set. Based on the elite strategy and individual crowding distance selection, establish a population update mechanism to generate the Pareto optimal solution set of the key design variables to be optimized obtained in step 6. The details are as follows:

[0155] 71) Initialize the population: Randomly generate an initial population P0 of size M. Each individual in the population represents a possible solution with a specific set of decision variable values.

[0156] 72) Fast Non-Dominated Sorting: Perform fast non-dominated sorting on the individuals in P0 to form multiple non-dominated frontiers. The individuals at the first frontier are the best and have better fitness.

[0157] 73) Crowding Calculation: For each individual in the non-dominated front, the crowding degree between individuals is calculated. The crowding degree reflects the distribution of individuals in the target space. The greater the distance, the lower the crowding degree, indicating that the solutions around the individual are sparser and the diversity is better.

[0158] 74) Selection operation: Based on the non-dominated level and crowding degree, select some individuals as the parent population Pt , used to generate the next generation. Usually, methods such as tournament selection are used to give priority to individuals with high non-dominated ranks (i.e., low levels) and high crowding.

[0159] 75) Crossover and mutation operations: for the selected parent population P t The individuals in the population undergo crossover and mutation operations to generate the offspring population Q t The crossover operation is to exchange some genes of two parent individuals to produce new offspring; the mutation operation is to randomly change the genes of an individual to increase the diversity of the population.

[0160] 76) Population merging: merge the parent population P t and the offspring population Q t Merge to form a new population R of size 2M t .

[0161] 77) Update population: generate new population R t Perform non-dominated sorting and crowding calculation, and then select M individuals from the mixed population according to the sorting results and crowding to form a new population P t+1 , as the next generation population. The selection process prioritizes retaining individuals on a better non-dominated frontier. Within the same non-dominated frontier, individuals with a smaller crowding degree are prioritized to maintain the diversity of the population and its tendency to converge to the Pareto frontier.

[0162] 78) Termination judgment: Check whether the termination conditions are met, such as reaching the maximum number of iterations, population convergence, or meeting specific performance indicators. If the termination conditions are met, the optimal individual in the current population is output as the Pareto optimal solution set for the multi-objective optimization problem; otherwise, return to step 74) and continue iterative optimization.

[0163] As an example, set the initial population P0 to 2000, then perform a non-dominated quick sort operation and calculate the congestion degree. The crossover probability is 0.8, the mutation probability is 0.05, and the number of iterations is 50.

[0164] Step 8: Use the TOPSIS method to evaluate the Pareto optimal solution set and select a set of optimal key design variables to be optimized according to the design requirements. The specific steps are as follows:

[0165] 81) Construct a decision matrix: Construct a decision matrix: Determine the corresponding decision matrix H based on the number of solutions t and the number of optimization targets l:

[0166]

[0167] Where h tlRepresents the lth optimization target value of the tth solution, t = 1, 2…, r, l = 1, 2,…, 4; as an example, assume r = 10.

[0168] 82) Normalize the original data: The TOPSIS method uses distance to measure sample differences, so all evaluation indicators need to be normalized before calculating the distance. The smaller the optimization target, the better. This is a negative indicator, so it needs to be converted to a positive value as follows:

[0169]

[0170] Using the vector normalization method, we get the normalized matrix Q, where the unit q in Q is tl for:

[0171]

[0172] 83) Determine the weights and construct the weighting matrix:

[0173] Introducing the weight vector w l :

[0174]

[0175] Each unit q in Q tl Multiply by the corresponding weights to reflect the importance of different indicators in decision-making, and calculate the weighted normative matrix U, the unit u in U tl for:

[0176] u tl =q tl w l (20)

[0177] 84) Determine the positive ideal solution and negative ideal solution: Find the optimal value (positive ideal solution) and the worst value (negative ideal solution) of each indicator as a reference for the evaluation plan.

[0178] Positive ideal solution U + :

[0179]

[0180] Negative ideal solution U - :

[0181]

[0182] Where U + and U - denote the positive ideal solution set and the negative ideal solution set respectively; They represent the positive ideal solutions of the four optimization objectives, They represent the negative ideal solutions of the four optimization objectives respectively.

[0183] 85) Calculate the distance between each solution and the positive / negative ideal solution:

[0184] Distance to positive ideal solution

[0185]

[0186] Distance to negative ideal solution

[0187]

[0188] 86) Calculate the proximity index A t :

[0189]

[0190] Proximity Index A t The size of reflects the relative closeness between the solution and the ideal solution: A t The larger the value, the closer it is to the ideal solution U + The closer, the distance to the negative ideal solution U - The farther away, the better the solution.

[0191] 87) Comprehensive evaluation and ranking: According to the proximity index A t Sort all the solutions, A t The larger the value, the better the solution, thus the order of advantages and disadvantages of the solutions can be obtained, providing a basis for decision-making.

[0192] Step 9: Substitute the optimal solution value selected in step 8 into the designed model for simulation analysis. If all four optimization target values ​​meet the design requirements, the optimization is terminated; otherwise, return to step 4.

[0193] The present invention is further described below with reference to a preferred embodiment.

[0194] Taking a 3kW wind power controllable magnetic gearbox according to the present invention as an example, its technical parameters are shown in Table 1.

[0195] Table 1 Technical data of wind power controllable magnetic gearbox

[0196]

[0197] According to the design requirements in Table 1, the preliminary main dimensions and design variable parameters to be optimized of the wind power controllable magnetic gearbox are shown in Table 2.

[0198] Table 2 Preliminary determination of main dimensions

[0199]

[0200]

[0201] First, Latin hypercube sampling is performed on the model, where the initial values ​​and value ranges of the design variables to be optimized are shown in Table 3.

[0202] Table 3 Initial values ​​and value ranges of design variables to be optimized

[0203]

[0204] Construct the BNPP proxy model for the sampled samples. Figure 5 This is the BPNN agent model structure diagram, Figure 6 The comparison curve between the actual value and the predicted value of the BPNN prediction optimization target is shown in Table 4. The error values ​​predicted by the BP neural network model are shown in Table 4. It can be seen from Table 4 that the correlation R 2 Both are greater than 0.95, and the RMSE and MAE values ​​are small, indicating that the prediction effect of BPNN is very good and the next step of optimization can be carried out.

[0205] Table 4 BPNN proxy model error

[0206]

[0207] Perform Sobol′ global sensitivity analysis on the surrogate model. Figure 7 Figure 2 shows the sensitivity analysis of each design variable to be optimized. Based on the Sobol's method analysis, the six key parameters to be optimized were: inner rotor core thickness h1, inner rotor permanent magnet thickness h2, outer rotor permanent magnet thickness h4, stator core thickness h5, stator core outer radius r2, and armature winding turns Z.

[0208] Repeat the operation process of steps 4 and 5 for the six selected parameters to be optimized, where the range of the design variables to be optimized and the optimization target remain unchanged, and the retrained BPNN prediction model is used as the NSGA-II fitness function to carry out the optimization work.

[0209] Figure 8 The Pareto frontier diagram of different optimization target error values ​​after NSGA-Ⅱ optimization. The optimal data set selected by TOPSIS evaluation method is shown in Table 5.

[0210] Table 5 Structural parameters of the controllable magnetic gearbox after optimization

[0211]

[0212] Figure 9 、 10 They are respectively the waveform diagram of the no-load back electromotive force before optimization and the harmonic spectrum diagram of the no-load back electromotive force; Figure 11 、 12The following are the waveform and harmonic spectrum of the optimized no-load back EMF. As can be seen from the figures, the harmonic distortion rates of phases A, B, and C have dropped from 11.23%, 11.74%, and 11.36% before optimization to 4.01%, 4.29%, and 4.11%, respectively, all below 5%, meeting the design requirements.

[0213] Figure 13 and Figure 14 The torque-time curves before and after optimization are shown. As can be seen from the figure, the torque pulsation of the inner rotor has been significantly reduced from the original 8.01% to 4.39%, a decrease of 45.19%. The torque pulsation of the outer rotor has also been reduced from 3.84% to 2.51%, a decrease of 34.63%. The optimized torque pulsation is less than 5%, which meets the stringent design requirements and means that the controllable magnetic gearbox can provide smoother and more continuous torque output during operation. This plays a key role in improving the efficiency of the entire drive system and extending its service life in application scenarios requiring high precision and high reliability.

Claims

1. A wind power controllable magnetic gearbox optimization design method, the wind power controllable magnetic gearbox comprising: An inner rotor, a magnetic adjustment ring, an outer rotor, a stator, and a rotating shaft; the inner rotor includes an inner rotor permanent magnet and an inner rotor iron core; the magnetic adjustment ring includes a magnetic adjustment magnet block; the outer rotor includes an outer rotor permanent magnet and an outer rotor iron block; the stator includes a three-phase winding and a stator iron core; characterized in that the following steps are adopted: Step 1: Select the average torque T of the inner rotor of the wind power controllable magnetic gearbox. avg , inner rotor torque pulsation T rip , the no-load back electromotive force amplitude of the stator winding V EMF And the distortion rate THD of the no-load back electromotive force of the stator winding EMF To optimize the target, the vector y of the optimization target is defined as: y=[y1,y2,y3,y4]=[|T avg -T s |,T rip ,|V EMF -V N |,THD EMF ] (1) Where, T s is the inner rotor stall torque, V N is the stator winding phase voltage amplitude; Step 2: Select the following 10 parameters as the design variables to be optimized for the wind turbine controllable magnetic gearbox: inner rotor core thickness h1, inner rotor permanent magnet thickness h2, magnetic adjustment ring thickness h3, outer rotor permanent magnet thickness h4, stator core thickness h5, stator core outer radius r2, outer rotor permanent magnet proportional coefficient N a , magnetic block span coefficient K p , axial length L, number of stator winding turns Z, then the vector x of the design variables to be optimized is defined as: x=[x1,x2,x3,x4,x5,x6,x7,x8,x9,x 10 ]=[h1,h2,h3,h4,h5,r2,N a ,K p ,L,Z] (2); Step 3: Determine the constraints of the design variable x to be optimized: In the formula, l and u in the subscripts of each design variable x to be optimized represent the lower bound and upper bound of the variable respectively; Step 4: Perform Latin Hypercube Sampling (LHS) experiment to establish the initial sample space: Step 5: Using BPNN to establish a proxy model between each optimization objective y of the wind power controllable magnetic gearbox and the design variable to be optimized x; Step 6: Based on Sobol's global sensitivity analysis, the key design variables to be optimized that have a greater impact on the optimization objective are screened out; Step 7: Using the second-generation non-dominated sorting genetic algorithm NSGA-II, using the Pareto dominance mechanism, to quickly sort the non-dominated solution set, establish a population update mechanism based on the elite strategy and individual crowding distance selection, and generate the Pareto optimal solution set of the key design variables to be optimized obtained in step 6; Step 8: Use the TOPSIS method to evaluate the Pareto optimal solution set and select a set of optimal key design variables to be optimized according to the design requirements; Step 9: Substitute the optimal solution value selected in step 8 into the designed model for simulation analysis. If all four optimization target values ​​meet the design requirements, the optimization is terminated; otherwise, return to step 4.

2. According to claim 1, an optimization design method for a wind power controllable magnetic gearbox is characterized in that: The specific steps of step 4 are: 41) Determine the size of the sampling dimension d of the sample, that is, the number of design variables to be optimized; determine the value range of each design variable to be optimized; 42) Divide the interval: divide the value range of each variable into [a j ,b j ] is divided into n equal-width intervals, and the width of each area is 43) Random permutation: Randomly permuting the intervals after each variable is divided to generate a random order; 44) Sampling in subintervals: Randomly select sample points in each subinterval. For the sampling point of the i-th sample in the j-th dimension, the calculation formula is: x ij =a j +Δ×(π j (i)-1+u ij ) (4) Where, π j (i) is the subinterval number of the i-th sample in the j-th dimension, i = 1, 2, ..., n, u ij is a random number uniformly distributed in the interval [0,1]; 45) Generate a sample matrix: Combine the sample points of all dimensions to form an n×d sample matrix; each row of this matrix represents a sample point, and each column corresponds to a dimension.

3. According to claim 1, a method for optimizing the design of a wind power controllable magnetic gearbox is characterized in that: The specific steps of step 5 are: 51) The BPNN includes 1 input layer, 1 hidden layer, and 1 output layer, wherein the input layer has 10 neurons, which are 10 design variables to be optimized x1~x 10 The hidden layer has 150 neurons; the output layer has 4 neurons, which are the 4 optimization targets y1, y2, y3, and y4 respectively; 52) Perform feedforward calculation, and the output value of the sth neuron in the hidden layer is calculated as follows: Where w is is the connection weight between the jth neuron in the input layer and the sth neuron in the hidden layer, a s is the bias of the sth neuron in the hidden layer, f(·) is the activation function of the hidden layer, and the Sigmoid function is used, that is: The output of the lth neuron in the output layer is the predicted value of the optimization target for: Where w sl is the connection weight coefficient between the sth neuron of the hidden layer and the lth neuron of the output layer, b l is the threshold of the lth neuron in the output layer, l = 1, 2, 3, 4; 53) Error calculation: The output prediction value of the BPNN obtained in step 52) and the expected output y l , calculate the prediction error e l : 54) Weight update: According to the prediction error e obtained in step 53) l Update the network connection weight w is and w sl : Where η is the learning rate; 55) Threshold update: According to the network prediction error e obtained in step 53) l Update network node threshold a s and b l : 56) Model evaluation and validation: using the coefficient of determination R 2 , root mean square error RMSE and mean absolute error MAE are used to evaluate the model prediction performance, and their expressions are as follows: Where m is the number of test set samples, m = 15% × n × d; y i is the actual value of the i-th sample, is the predicted value of the i-th sample, is the average value of the i-th sample; 57) Analyze the prediction effect, when the determination coefficient R 2 >0.9, and the root mean square error RMSE<ε1 and the mean absolute error MAE<ε2, then go to step 6, otherwise return to step 52); ε1 and ε2 are both positive real numbers close to 0.

4. According to claim 1, a method for optimizing the design of a wind power controllable magnetic gearbox is characterized in that: The specific steps of step 6 are: 61) Calculate the partial variance and total variance of the model output response to obtain the global sensitivity of each parameter; for the parameter domain I with d dimensions d =(X|x j ; j=1,2,…,d), the function f(x) is decomposed into 2 d Sum of increasing polynomials: Where f0 is a constant term, f j (x j ) depends only on x j The first-order term, f j,k (x j ,x k ) is x j and x k interaction term; k is a positive integer, 1≤k≤d; Then the total variance V and partial variance V 1,2,...,j They are: Then the total variance V and sensitivity index S 1,2,...,j for: Where, the sensitivity index S 1,2,...,j is the ratio of variance, indicating the degree of influence of each design variable to be optimized on the optimization target; h is a positive integer, 1≤h≤j; 62) performing a Sobol' global sensitivity analysis on the BPNN proxy model according to step 61) to screen out key design variables to be optimized; 63) Repeat the operation process of steps 4 and 5 for the key design variables to be optimized obtained in step 62), wherein the range of the design variables to be optimized and the optimization target remain unchanged, and use the retrained BPNN agent model as the fitness function of the second-generation non-dominated sorting genetic algorithm NSGA-II to carry out the optimization work.

5. According to claim 1, a method for optimizing the design of a wind power controllable magnetic gearbox is characterized in that: The specific steps of step 8 are: 81) Construct a decision matrix: Construct a decision matrix: Determine the corresponding decision matrix H based on the number of solutions t and the number of optimization targets l: Where h tl represents the lth optimization target value of the tth solution, t=1,2…,r; l=1,2,3,4; 82) Normalize the original data: All optimization target values ​​h tl Perform the same-direction processing as follows: Using the vector normalization method, we get the normalized matrix Q, where the unit q in Q is tl for: 83) Determine the weights and construct the weighting matrix: Introducing the weight vector w l : Each unit q in Q tl Multiply by the corresponding weight to reflect its importance in decision making, and calculate the weighted normative matrix U, where unit u in U is tl for: u tl =q tl ·w l (20); 84) Determine the positive and negative ideal solutions: Find the optimal value of each optimization objective, i.e., the positive ideal solution, and the worst value, i.e., the negative ideal solution: Positive ideal solution U + : Negative ideal solution U - : Where U + and U - denote the positive ideal solution set and the negative ideal solution set respectively; They represent the positive ideal solutions of the four optimization objectives, Represent the negative ideal solutions of the four optimization objectives respectively; 85) Calculate the distance between each solution and the positive and negative ideal solutions: Distance to positive ideal solution Distance to negative ideal solution 86) Calculate the proximity index A t : 87) Comprehensive evaluation and ranking: According to the proximity index A t Sort all the solutions, A t The larger the value, the better the solution, thus the order of advantages and disadvantages of the solutions can be obtained, providing a basis for decision-making.

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