Optimization design method of modularized axial magnetic flux permanent magnet synchronous wind driven generator

Abstract

The invention relates to an optimization design method of a modularized axial magnetic flux permanent magnet synchronous wind driven generator, and belongs to the field of wind power generation. The generator comprises a stator and a rotor. The torque pulsation and the torque density are taken as optimization targets, and the stator slot depth, the rotor permanent magnet thickness and the rotor permanent magnet pole-arc coefficient are taken as design variables to be optimized; determining constraint conditions of each design variable, performing a Latin hypercube sampling experiment, and establishing a DNN proxy model of the optimization target and the to-be-optimized design variable; a Bayesian optimization algorithm is adopted, hyper-parameters of the agent model are optimized, and optimal hyper-parameters are obtained; and training the agent model adopting the optimal hyper-parameter to obtain an optimal agent model, and based on the optimal agent model, optimizing the design variables to be optimized by adopting an NSGA-II optimization algorithm, and finally determining an optimal combination of the design variables to be optimized. According to the method, the modeling error can be reduced, the calculation efficiency can be improved, multi-target balancing under the complex parameter coupling condition can be robustly processed, and the performance of the modular generator can be effectively improved.

Description

Technical Field

[0001] The present invention relates to an optimization design method for an axial flux permanent magnet synchronous wind generator, in particular to an optimization design method for a modular axial flux permanent magnet synchronous wind generator, and belongs to the technical field of wind power generation. Background Art

[0002] Permanent magnet synchronous wind turbines have become a mainstream model in the wind power generation sector due to their advantages: 1) they require no complex mechanical gearbox and its lubrication system, resulting in low failure rates and maintenance costs; and 2) high energy conversion efficiency. In addition to these advantages, axial flux permanent magnet synchronous wind turbines offer a compact size, light weight, excellent heat dissipation, and low operating noise. These advantages are particularly well-suited to meeting the environmental protection requirements of wind farms, and they hold broad market potential.

[0003] However, traditional axial flux permanent magnet synchronous wind turbine generators (AFPMSG) mostly adopt an integral iron core structure, and the iron core cannot adopt the radial motor laminated iron core. The manufacturing process is complex and the cost is high, which limits the development of axial flux motors.

[0004] Therefore, modularizing the AFPMSG presents a promising alternative solution to these problems. Modular AFPMSGs offer advantages such as easy and quick maintenance, requiring only replacement of faulty modules, and strong fault tolerance. Consequently, the modular axial flux permanent magnet synchronous wind turbine generator (MAFPMSG) is gaining increasing attention in the wind power sector and is a key area of ​​future wind power development.

[0005] However, modularization also introduces new challenges, such as contact magnetic resistance between modules, which reduces magnetic flux density and power density, as well as magnetic field distortion, which in turn leads to increased harmonics. Therefore, the optimal design of modular AFPMSGs is particularly important. However, it is worth noting that these new challenges make the optimization process more difficult and complex, as the optimal design of modular axial flux permanent magnet synchronous wind turbines involves multi-dimensional, discrete parameter optimization. This is essentially a complex, nonlinear, multi-objective optimization problem with multiple constraints, and there is usually no optimal solution that simultaneously satisfies multiple performance indicators.

[0006] In the existing literature, some design methods based on the equivalent magnetic circuit method and multi-objective optimization have been proposed, but their accuracy is insufficient when dealing with the coupling effects of multiple permanent magnets and the dynamic changes in magnetic properties. Some have adopted a multi-level optimization strategy combined with the response surface method to optimize the design of modular motors to balance torque performance and fault tolerance. However, the optimization process requires careful weighting of different objectives and may not fully capture all complex parameter interactions. Some have proposed a novel semi-analytical method combined with artificial intelligence to suppress the cogging torque of modular permanent magnet motors. However, due to the complexity of the finite element model and the number of design variables, the optimization process using genetic algorithms and artificial neural networks can be computationally expensive. Some have proposed a modular motor design method based on analytical methods and genetic algorithms to optimize geometric parameters for maximum volumetric and gravimetric torque density. However, this method does not fully address parameter interdependencies and constraints, limiting its applicability under different conditions. Another has proposed a modular motor multi-objective optimization method based on the surrogate-assisted multi-objective optimization (SAMOO) algorithm to achieve an accurate Pareto frontier. However, its high computational cost and sensitivity to the initial sampling point distribution can lead to unsatisfactory results in large-scale designs. In summary, existing methods still face significant challenges in solving the nonlinear changes in air gap contact magnetoresistance caused by modular structures and optimizing multi-physics coupling.

[0007] To this end, the present invention proposes an optimization design method for modular axial flux permanent magnet synchronous wind turbines that combines deep neural network (DNN), Bayesian optimization and the second-generation non-dominated sorting genetic algorithm (NSGA-II). The method integrates three key components, namely DNN, Bayesian optimization and NSGA-II, to handle complex nonlinear multi-objective optimization problems. The structural parameters of the modular axial flux permanent magnet synchronous wind turbine are optimized to maximize its torque density and minimize its torque ripple. In this way, while ensuring the performance of the modular axial flux permanent magnet synchronous wind turbine, the design efficiency is improved, the calculation time is reduced, the design and manufacturing costs are reduced, and the continuous progress of wind power generation technology is promoted. Summary of the Invention

[0008] The main purpose of the present invention is to: in response to the shortcomings of the existing technology, the present invention provides an optimization design method for a modular axial flux permanent magnet synchronous wind turbine, taking into account the performance, efficiency and cost of the optimization process, effectively improving the performance of the modular AFPMSG, meeting the design requirements, and providing a new solution for the optimization design of the modular AFPMSG.

[0009] To achieve the above objectives, the modular axial flux permanent magnet synchronous wind turbine described in the present invention comprises a stator and a rotor. The stator comprises a stator core and stator windings, and the rotor comprises rotor permanent magnets and a rotor core. Both the stator and rotor employ a modular design, with both the stator core module and the rotor core module being trapezoidal modules, and permanent magnets affixed to the rotor core module.

[0010] The present invention provides an optimization design method for a modular axial flux permanent magnet synchronous wind turbine, comprising the following steps:

[0011] Step 1: According to the performance requirements of the modular axial flux permanent magnet synchronous wind turbine, select the average torque density T a , torque ripple T ri As the optimization target, three structural parameters of the modular axial flux permanent magnet synchronous wind turbine are selected as the design variables to be optimized. The three structural parameters are: stator slot depth h s , rotor permanent magnet thickness h c , rotor permanent magnet pole arc coefficient α p , then the vector x of the design variables to be optimized can be expressed as: x=[x1,x2,x3]=[h s ,h c ,α p ];

[0012] Step 2: determine the constraints of the design variables to be optimized for the modular axial flux permanent magnet synchronous wind turbine, namely:

[0013]

[0014] Among them, h sl 、h su are the lower and upper bounds of the stator slot depth respectively; h cl 、h cu are the lower and upper limits of the thickness of the rotor permanent magnet respectively; α pl , α pu are the lower and upper bounds of the rotor permanent magnet pole arc coefficient, respectively.

[0015] Step 3: Perform Latin Hypercube Sampling (LHS) experiment to establish the required sample space:

[0016] 31) Divide each design variable into M subintervals between the upper and lower bounds of its own constraints (i.e., the range of values), and then randomly select a point in each subinterval;

[0017] 32) Randomly combine the points selected from all subintervals of each design variable to obtain a total of M sample data groups (h sm ,h cm ,α pm), that is, M design variable combinations, where m = 1, 2, 3, ..., M;

[0018] 33) The actual value T of the optimization target of each sample data group is obtained through finite element simulation a,m and T ri,m .

[0019] Step 4: Establish a deep neural network DNN agent model. The deep neural network DNN contains an input layer, a hidden layer, and an output layer. The input layer has three neurons, i.e., three design variables to be optimized; the output layer has two neurons, i.e., two optimization targets (T a ,、T ri ); the number of hidden layers is 3.

[0020] The input H of the sth neuron in the first hidden layer s , output HO s They are:

[0021]

[0022]

[0023] Where w is is the i-th neuron x in the input layer i The connection weight between the sth neuron and the first hidden layer, a s is the threshold of the sth neuron in the first hidden layer, s=1,2,…,N (1) f1(·) is the activation function of the first hidden layer, which is the ReLU function (rectified linear unit function), and has: f(x) = max(x, 0);

[0024] The input H of the jth neuron in the second hidden layer is j , output HO j They are:

[0025]

[0026] Where w sj is the connection weight between the sth neuron of the first hidden layer and the jth neuron of the second hidden layer, a j is the threshold of the jth neuron in the second hidden layer, j = 1, 2, ..., N (2) ; f2(·) is the activation function of the second hidden layer, which is the ReLU function (rectified linear unit function);

[0027] The input H of the u-th neuron in the third hidden layer is u , output HO u They are:

[0028]

[0029] Where w ju is the connection weight between the jth neuron of the second hidden layer and the uth neuron of the third hidden layer, a u is the threshold value of the u-th neuron in the third hidden layer, u=1,2,…,N (3) ; f3(·) is the activation function of the third hidden layer, which is the ReLU function (rectified linear unit function);

[0030] The input of the lth neuron in the output layer is:

[0031]

[0032] The output of the lth neuron in the output layer is the predicted value of the optimization target for:

[0033]

[0034] Where w ul is the connection weight coefficient between the uth neuron in the third hidden layer and the lth neuron in the output layer, b l is the threshold of the lth neuron in the output layer, l = 1, 2; f o (·) is the activation function of the output layer, which is the ReLU function (rectified linear unit function);

[0035] Step 5: Use the Bayesian optimization algorithm to tune the hyperparameters of the DNN proxy model to obtain the optimal hyperparameters.

[0036] Step 6: Based on the optimal hyperparameters obtained in step 5, train the DNN proxy model.

[0037] Step 7: Based on the optimal DNN agent model obtained in step 6, the NSGA-II optimization algorithm is used to optimize the design variables to be optimized of the modular axial flux permanent magnet synchronous wind turbine, and the optimal combination of the design variables to be optimized of the modular axial flux permanent magnet synchronous wind turbine is determined so that the modular axial flux permanent magnet synchronous wind turbine obtains optimal performance.

[0038] The specific method of step 5 is:

[0039] 51) Design the objective function of Bayesian optimization as:

[0040] ObjectiveFunction:{max[T a(x)],min[T ri (x)]} (10)

[0041]

[0042] where T N is the rated torque of the modular axial flux permanent magnet synchronous wind generator.

[0043] 52) defining the hyperparameter vector of Bayesian optimization of the modular axial flux permanent magnet synchronous wind generator:

[0044] The hyperparameter vector h has 8 parameters, defined as: h = {η, B, N (1) , N (2) , N (3) , p, γ, T drop}; wherein η is the initial learning rate, B is the batch size, i.e. the number of samples, N (1) , N (2) , N (3) are the number of nodes of the first layer, the second layer and the third layer of the hidden layer of the DNN respectively; p is the signal loss probability, γ is the learning rate, and T drop is the learning rate decay period.

[0045] 53) initializing the sample set, i.e. initializing the hyperparameter space:

[0046] Determine the value range of each hyperparameter, based on Latin hypercube sampling (LHS) experiment, divide each hyperparameter into M subintervals in its value range, then randomly select a point in each subinterval, obtain M-dimensional components, and establish an 8×M initial sample space of the required hyperparameters; set the maximum number of iterations T;

[0047] 54) using an improved Marton 5 / 2-ARD (Automatic Relevance Determination) mixed kernel function as the covariance function of the Gaussian process GP to construct a Gaussian process surrogate model:

[0048] f(h) ~ GP(μ(h), k(h p ,h q ))(12)

[0049] where f(h) is the target value corresponding to h, μ(h) is the expectation function of the Gaussian process, and k(h p ,h q ) is the covariance function of the Gaussian process, defined as:

[0050]

[0051] where hp 、h q are two different hyperparameters, p = 1, 2, ..., 8, q = 1, 2, ..., 8; σ f is the signal variance; r 2 Defined as:

[0052]

[0053] Among them, l m is the Hamming distance correction term, l m =αδ(h p,m ,h q,m ), which is applicable to discrete parameters; α is the scaling factor of the discrete parameters; δ is the difference function associated with the discrete parameters; h p,m and h q,m Respectively represent h p 、h q The component value of the mth dimension.

[0054] 55) Calculate the expected function EI(h):

[0055]

[0056] ξ t =0.01(1-t / T) 2 (16)

[0057] Where, σ(h) are the predicted mean and predicted standard deviation of the Gaussian process surrogate model for the objective function; f(h + ) is the currently observed optimal target value; t and T are the current cycle number and the maximum cycle number, respectively; ξ t is the dynamic exploration factor; Φ(Z) and φ(Z) are the cumulative distribution function and probability density function of the standard normal distribution respectively; Z is the degree of improvement of the predicted value of the current target value for the current optimal target value, which is:

[0058]

[0059] 56) Evaluating the Performance of Gaussian Process Surrogate Models: Calculating the Coefficient of Determination R 2 , root mean square error RMSE, its expression is:

[0060]

[0061] 57) If the coefficient of determination R 2 >0.9, and the root mean square error RMSE < ε, where ε is a positive real number close to 0, then output the optimal hyperparameters and proceed to step 6; otherwise, proceed to step 58);

[0062] 58) Determine whether the maximum number of cycles has been reached. If so, output the optimal hyperparameters and proceed to step 6; otherwise, update the value of the sample point h and return to step 54).

[0063] The specific method of step 6 is:

[0064] 61) Initialize DNN, including: initializing connection weights w is 、w sj 、w ju 、w ul and threshold a s 、a j 、a u 、b l ;

[0065] 62) Define the loss function J as:

[0066]

[0067] 63) Use Adam optimizer to update connection weights and thresholds:

[0068] A1. Create an Adam optimizer object: DNN proxy model parameters, and set the initial learning rate η;

[0069] A2. Data loading and preprocessing;

[0070] A3. Set the gradient of the loss function to zero;

[0071] A4. Perform forward propagation calculation according to formula (2) to formula (9) to obtain the predicted value of the optimization target l=1,2, that is: and

[0072] A5. Calculate the loss function J according to formula (20);

[0073] A6. Perform backpropagation to calculate the gradient g of the loss function J with respect to the connection weights t (W) and the gradient of the threshold g t (B):

[0074]

[0075] Where W is the connection weight vector, defined as: W = {w is ,w sj ,w ju ,w ul}; B is the threshold vector, defined as: B = {a s ,a j ,a u ,b l};

[0076] A7. Update the connection weight W and threshold B:

[0077]

[0078] Where, the variables with subscripts t+1, t, and t-1 represent the values ​​of the variable in the next cycle, the current cycle, and the previous cycle, respectively; β1 and β2 are exponential decay rates, with β1,β2∈[0,1].

[0079] A8. Does the number of cycles t reach the maximum number of cycles T? If so, then terminate and proceed to step 7; otherwise, proceed to step A9.

[0080] A9. Does the loss function J no longer decrease? If so, then terminate and proceed to step 7. Otherwise, return to step A2.

[0081] The specific method of step 7 is:

[0082] 71) Parameter initialization, including: setting population size; selection, crossover, and mutation parameters; and maximum number of iterations K.

[0083] 72) Randomly generate the initial parent population P0 and modify the infeasible solution through constraint processing.

[0084] 73) Through iterative evolution, objective function value sorting, feasible solution judgment, fast non-dominated sorting, and congestion calculation are performed.

[0085] 74) Selection operation: Based on the non-dominated level and crowding degree, select some individuals as the parent population P k .

[0086] 75) Crossover and mutation operations: for the selected parent population P k The individuals in the population undergo crossover and mutation operations to generate the offspring population Q k , and correct infeasible solutions.

[0087] 76) Population merging: The parent population and the offspring population form a population R k , for R k Reapply fast non-dominated sorting and crowding comparison to determine the new parent population P k+1 .

[0088] 77) If the number of iterations k does not reach the maximum number of iterations K and the accuracy does not meet the preset value, the number of iterations k is increased by 1, that is, k=k+1, and return to step 73); otherwise, the Pareto optimal solution set is output and the optimal solution is determined.

[0089] The beneficial effects of the present invention are:

[0090] 1) The physical constraint model based on deep neural network (DNN) reduces the modeling error; Bayesian hyperparameter optimization improves the search efficiency by probabilistic exploration of the optimization space, thereby minimizing redundant evaluation and improving computational efficiency; the dynamic constraint of NSGA-II algorithm preserves the diversity of Pareto frontier and can robustly handle the multi-objective trade-off under complex parameter coupling conditions.

[0091] 2) The performance, efficiency and cost during optimization are considered, which effectively improves the performance of the modular AFPMSG and provides a new solution for the design of the modular AFPMSG. BRIEF DESCRIPTION OF DRAWINGS

[0092] Figure 1 It is a schematic diagram of the stator and rotor topology structure of the modular axial flux permanent magnet synchronous wind generator of the application.

[0093] Figure 2 It is a schematic diagram of the stator core module of the modular axial flux permanent magnet synchronous wind generator of the application.

[0094] Figure 3 It is a DNN-Bayesian-NSGA-II collaborative optimization framework of the application.

[0095] Figure 4 It is a flowchart of the optimization design method of the application.

[0096] Figure 5 It is a Bayesian hyperparameter optimization flowchart used by the application.

[0097] Figure 6 It is a NSGA-II multi-objective optimization design flowchart used by the application.

[0098] Figure 7 It is a Latin hypercube sampling experimental result graph of the application.

[0099] Figure 8 It is a DNN proxy model of the optimization design method of the application.

[0100] Figure 9 It is an optimization target Pareto frontier graph generated by the modular axial flux permanent magnet wind generator of the application after NSGA-II optimization.

[0101] Figure 10 It is a torque curve graph of the modular axial flux permanent magnet synchronous wind generator of the application before and after optimization.

[0102] Wherein, 1-stator; 2-rotor; 11-stator core; 12-stator winding; 21-rotor permanent magnet; 22-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 modular axial flux permanent magnet synchronous wind turbine of the present invention comprises a stator 1 and a rotor 2. The stator 1 includes a stator core 11 and a stator winding 12, while the rotor 2 includes rotor permanent magnets 21 and a rotor core 22. The inner and outer diameters of the stator core 11 and the rotor core 22 are identical. Both the stator 1 and the rotor 2 are modular in design, with both the stator and rotor core modules being trapezoidal. Permanent magnets are affixed to the rotor core modules.

[0105] like Figure 3 、 Figure 4 As shown, the present invention provides an optimization design method for a modular axial flux permanent magnet synchronous wind turbine, comprising the following steps:

[0106] Step 1: According to the performance requirements of the modular axial flux permanent magnet synchronous wind turbine, select the average torque density T a , torque ripple T ri As the optimization target, three structural parameters of the modular axial flux permanent magnet synchronous wind turbine are selected as the design variables to be optimized, namely: stator slot depth h s , rotor permanent magnet thickness h c , rotor permanent magnet pole arc coefficient α p , the vector x of the design variables to be optimized is expressed as: x=[x1,x2,x3]=[h s ,h c ,α p ];

[0107] Step 2: Determine the constraints of each design variable to be optimized for the modular axial flux permanent magnet synchronous wind turbine, namely:

[0108]

[0109] Among them, h sl 、h su are the lower and upper bounds of the stator slot depth respectively; h cl 、h cu are the lower and upper limits of the thickness of the rotor permanent magnet respectively; α pl , α pu are the lower and upper bounds of the rotor permanent magnet pole arc coefficient, respectively.

[0110] Step 3: Perform Latin Hypercube Sampling (LHS) experiment to establish the required sample space:

[0111] 31) divide each design variable to be optimized into M sub-intervals between the upper and lower bounds of its own constraint condition (i.e. the value range), and then randomly select a point in each sub-interval;

[0112] 32) randomly combine the points selected in all sub-intervals of each design variable to be optimized to obtain a total of M sample data groups (h sm ,h cm ,α pm ), i.e. M combinations of design variables to be optimized, where m = 1, 2, 3, …, M;

[0113] 33) obtain the optimization target values T a,m and T ri,m corresponding to each sample data group through finite element simulation.

[0114] Step 4, establish a deep neural network DNN proxy model, which contains an input layer, a hidden layer and an output layer; the input layer has three neurons, i.e. three design variables to be optimized; the output layer has two neurons, which are the predicted values of two optimization targets (T a , T ri ); the number of layers of the hidden layer is 3.

[0115] The input H s and output HO s of the s-th neuron of the first hidden layer are respectively:

[0116]

[0117] In the formula, w is is the connection weight between the i-th neuron x i of the input layer and the s-th neuron of the first hidden layer, a s is the threshold value of the s-th neuron of the first hidden layer, s = 1, 2, …, N (1) ; f1(·) is the excitation function of the first hidden layer, which is a ReLU function (Rectified Linear Unit function), and has: f(x) = max(x, 0);

[0118] The input H j and output HO j of the j-th neuron of the second hidden layer are respectively:

[0119]

[0120] In the formula, w sj is the connection weight between the s-th neuron of the first hidden layer and the j-th neuron of the second hidden layer, a j is the threshold value of the j-th neuron of the second hidden layer, j = 1, 2, …, N (2); f2(·) is the activation function of the second hidden layer, which is the ReLU function (rectified linear unit function);

[0121] The input H of the u-th neuron in the third hidden layer u , output HO u They are:

[0122]

[0123] Where w ju is the connection weight between the jth neuron in the second hidden layer and the uth neuron in the third hidden layer, a u is the threshold of the u-th neuron in the third hidden layer, u=1,2,…,N (3) ; f3(·) is the activation function of the third hidden layer, which is the ReLU function (rectified linear unit function);

[0124] The input of the lth neuron in the output layer is:

[0125]

[0126] The output of the lth neuron in the output layer is the predicted value of the optimization target for:

[0127]

[0128] Where w ul is the connection weight coefficient between the uth neuron in the third hidden layer and the lth neuron in the output layer, b l is the threshold of the lth neuron in the output layer, l = 1, 2; f o (·) is the activation function of the output layer, which is the ReLU function (rectified linear unit function);

[0129] Step 5: To achieve the optimal performance of the modular axial flux permanent magnet synchronous wind turbine, the torque ripple is reduced while the average torque is increased. Figure 5 As shown in the figure, the Bayesian optimization algorithm is used to tune the hyperparameters of the established DNN agent model to obtain the optimal hyperparameters. The specific method is as follows:

[0130] 51) Design the objective function of Bayesian optimization as:

[0131] ObjectiveFunction:{max[T a (x)],min[T ri (x)]} (10)

[0132]

[0133] Where, T N is the rated torque of the modular axial flux permanent magnet synchronous wind turbine.

[0134] 52) Define the Bayesian optimization hyperparameter vector of the modular axial flux permanent magnet synchronous wind turbine:

[0135] The hyperparameter vector h has 8 parameters, which are defined as: h = {η, B, N (1) ,N (2) ,N (3) ,p,γ,T drop}; where η is the initial learning rate, B is the batch size, i.e. the number of samples, and N (1) 、N (2) 、N (3) are the number of nodes in the first, second and third layers of the hidden layer of the DNN respectively; p is the signal loss probability, γ is the learning rate, T drop is the learning rate decay period.

[0136] 53) Initialize the sample set, that is, initialize the hyperparameter space:

[0137] Determine the value range of each hyperparameter. Based on the Latin Hypercube Sampling (LHS) experiment, divide each hyperparameter into M subintervals within its value range. Then randomly select a point in each subinterval to obtain M-dimensional components, and establish an 8×M initial sample space of the required hyperparameters. Set the maximum number of iterations, T.

[0138] 54) An improved Marton 5 / 2–ARD (Automatic Relevance Determination) hybrid kernel function is used as the covariance function of the Gaussian process GP to construct a Gaussian process surrogate model:

[0139] f(h)~GP(μ(h),k(h p ,h q ))(12)

[0140] Where f(h) is the target value corresponding to h, μ(h) is the expected function of the Gaussian process, and k(h p ,h q ) is the covariance function of the Gaussian process, defined as:

[0141]

[0142] Where h p 、h q are two different hyperparameters, p = 1, 2, ..., 8, q = 1, 2, ..., 8; σ f is the signal variance; r2 Defined as:

[0143]

[0144] Among them, l m is the Hamming distance correction term, l m =αδ(h p,m ,h q,m ), which is applicable to discrete parameters; α is the scaling factor of the discrete parameters; δ is the difference function associated with the discrete parameters; h p,m and h q,m Respectively represent h p 、h q The component value of the mth dimension.

[0145] 55) Calculate the expected function EI(h):

[0146]

[0147] ξ t =0.01(1-t / T) 2 (16)

[0148] Where, σ(h) are the predicted mean and predicted standard deviation of the Gaussian process surrogate model for the objective function; f(h + ) is the currently observed optimal target value; t and T are the current cycle number and the maximum cycle number, respectively; ξ t is the dynamic exploration factor; Φ(Z) and φ(Z) are the cumulative distribution function and probability density function of the standard normal distribution respectively; Z is the degree of improvement of the predicted value of the current target value for the current optimal target value, which is:

[0149]

[0150] 56) Evaluating the Performance of Gaussian Process Surrogate Models: Calculating the Coefficient of Determination R 2 , root mean square error RMSE, its expression is:

[0151]

[0152] 57) If the coefficient of determination R 2 >0.9, and the root mean square error RMSE < ε, where ε is a positive real number close to 0, then output the optimal hyperparameters and proceed to step 6; otherwise, proceed to step 58);

[0153] 58) Determine whether the maximum number of cycles has been reached. If so, output the optimal hyperparameters and proceed to step 6; otherwise, update the value of the sample point h and return to step 54).

[0154] Step 6: Based on the optimal hyperparameters obtained in step 5, train the DNN proxy model. The specific method is as follows:

[0155] 61) Initialize the DNN proxy model, including: initializing the connection weight w is 、w sj 、w ju 、w ul and threshold a s 、a j 、a u 、b l ;

[0156] 62) Define the loss function J as:

[0157]

[0158] 63) Use Adam optimizer to update connection weights and thresholds:

[0159] A1. Create an Adam optimizer object: DNN proxy model parameters, and set the initial learning rate η to 0.001;

[0160] A2. Data loading and preprocessing;

[0161] A3. Set the gradient of the loss function to zero;

[0162] A4. Perform forward propagation calculation according to formula (2) to formula (9) to obtain the predicted value of the optimization target l=1,2, that is: and

[0163] A5. Calculate the loss function J according to formula (20);

[0164] A6. Perform backpropagation to calculate the gradient g of the loss function J with respect to the connection weights t (W) and the gradient of the threshold g t (B):

[0165]

[0166] Where W is the connection weight vector, defined as: W = {w is ,w sj ,w ju ,w ul}; B is the threshold vector, defined as: B = {a s ,a j ,a u ,b l};

[0167] A7. Update the connection weight W and threshold B:

[0168]

[0169] Where, the variables with subscripts t+1, t, and t-1 represent the values ​​of the variable in the next cycle, the current cycle, and the previous cycle, respectively; β1 and β2 are exponential decay rates, with β1, β2∈[0,1], β1=0.9, β2=0.999.

[0170] A8. Does the number of cycles t reach the maximum number of cycles T? If so, then terminate and proceed to step 7; otherwise, proceed to step A9.

[0171] A9. Does the loss function J no longer decrease? If so, then end and proceed to step 7. Otherwise, return to step A2.

[0172] Step 7, such as Figure 6 As shown in FIG, based on the optimal DNN agent model obtained in step 6, the NSGA-II optimization algorithm is used to optimize the design variables to be optimized of the modular axial flux permanent magnet synchronous wind turbine, and the optimal combination of the design variables to be optimized of the modular axial flux permanent magnet synchronous wind turbine is determined, so that the modular axial flux permanent magnet synchronous wind turbine can obtain the optimal performance. The specific method is:

[0173] 71) Parameter initialization, including: setting population size; selection, crossover, and mutation parameters; maximum number of iterations K = 1000.

[0174] 72) Randomly generate the initial parent population P0 and modify the infeasible solution through constraint processing.

[0175] 73) Through iterative evolution, objective function value sorting, feasible solution judgment, fast non-dominated sorting, and congestion calculation are performed.

[0176] 74) Selection operation: Based on the non-dominated level and crowding degree, select some individuals as the parent population P k .

[0177] 75) Crossover and mutation operations: for the selected parent population P k The individuals in the population undergo crossover and mutation operations to generate the offspring population Q k , and correct infeasible solutions.

[0178] 76) Population merging: The parent population and the offspring population form a population R k , for R k Reapply fast non-dominated sorting and crowding comparison to determine the new parent population P k+1 .

[0179] 77) If the number of iterations k does not reach K and the accuracy does not meet the preset value, the number of iterations k is increased by 1, that is, k=k+1, and return to step 73); otherwise, output the Pareto optimal solution set and determine the optimal solution.

[0180] The present invention is further described below with reference to a preferred embodiment.

[0181] Taking a 2kW modular axial flux permanent magnet synchronous wind turbine generator of the present invention as an example, its technical parameters are shown in Table 1.

[0182] Table 1 Technical parameters of modular axial flux permanent magnet synchronous wind turbine generator

[0183]

[0184] Table 2 shows the initial values ​​and value ranges of the design variables to be optimized, based on which the Latin hypercube sampling experiment was carried out.

[0185] Table 2 Initial values ​​and value ranges of design variables to be optimized

[0186]

[0187] The results of the Latin hypercube sampling experiment are as follows Figure 7 As shown. Figure 7 It can be seen that the distribution of the sample points in the three-dimensional parameter space is highly uniform and independent of each other. Finite element analysis (FEA) is performed on the 50 experiments collected by the LHS method to establish a sampling sample data set.

[0188] Construct a DNN agent model for the sampled samples, and its structure is as follows Figure 8 The hyperparameters of the DNN proxy model and their value ranges are shown in Table 3.

[0189] Table 3 DNN proxy model hyperparameters and their value ranges

[0190]

[0191] The Bayesian optimization algorithm is used to tune the hyperparameters of the established DNN agent model to obtain the optimal hyperparameters and the optimal number of hidden layer neurons N. (1) 、N (2) 、N (3) are 256, 128, and 64 respectively; the signal loss probability p is 0.45; and the initial learning rate η is 0.0032.

[0192] After training the DNN agent model, RMSE(T a ) decreased from 5.4927 to 4.7984, RMSE(T ri) decreased from 0.012881 to 0.011299. The RMSE values ​​of the two optimization objectives are small, indicating that the prediction effect of the DNN proxy model is very good and the next step of optimization can be carried out.

[0193] Figure 9 The Pareto frontier plot of the optimization objective after NSGA-II optimization is shown in Table 4. The marked points in the figure are selected from the solution set as the optimal solution to the multi-objective optimization problem. The optimized values ​​of the optimized design variables and the optimization objectives are shown in Table 4.

[0194] Table 4 Optimal values ​​of design variables to be optimized and optimization target values

[0195]

[0196] The optimized design variables are used for simulation. Table 5 shows the optimized structural parameters of the modular axial flux permanent magnet synchronous wind turbine generator in Table 1. The torque curves before and after optimization are shown in Table 5. Figure 10 shown.

[0197] Table 5 Structural parameters of the optimized modular axial flux permanent magnet synchronous wind turbine

[0198]

[0199] from Figure 10 It can be seen that after optimization, the torque level is significantly improved and the torque pulsation is also significantly reduced. Table 6 shows the comparison of the relevant performance parameters of the modular axial flux permanent magnet synchronous wind turbine of the present invention before and after optimization. The results show that after optimization, T a Increased to 180N·m, an increase of 10.43%; T ri Compared with the technical requirements in Table 1, after optimization by the NSGA-II algorithm, the error of average torque is 1.22% and the error of torque ripple is 1.26%, both of which meet the design requirements.

[0200] Table 5 Comparison of results before and after optimization

[0201]

[0202] In summary, the present invention integrates the deep neural network DNN agent model, Bayesian hyperparameter tuning, and NSGA-II multi-objective optimization algorithm to provide an optimization design method for a modular axial flux permanent magnet synchronous wind turbine, taking into account the performance, efficiency, and cost in the optimization process. It can effectively improve the performance of the modular axial flux permanent magnet synchronous wind turbine and meet the design requirements, providing a new solution for the optimization design of modular axial flux permanent magnet synchronous wind turbines.

Claims

1. A method for optimizing the design of a modular axial flux permanent magnet synchronous wind turbine, the modular axial flux permanent magnet synchronous wind turbine comprising: The stator and rotor, the stator includes a stator core and a stator winding, and the rotor includes a rotor permanent magnet and a rotor core; The stator and rotor are both modularly designed. The stator core module and the rotor core module are both trapezoidal modules. Permanent magnets are attached to the rotor core module. The method is characterized by comprising the following steps: Step 1: According to the performance requirements of the modular axial flux permanent magnet synchronous wind turbine, select the average torque density T a , torque ripple T ri As the optimization target, three structural parameters of the modular axial flux permanent magnet synchronous wind turbine are selected as the design variables to be optimized. The three structural parameters are: stator slot depth h s , rotor permanent magnet thickness h c , rotor permanent magnet pole arc coefficient α p , then the vector x of the design variables to be optimized can be expressed as: x=[x1,x2,x3]=[h s ,h c ,α p ]; Step 2: determine the constraints of the design variables to be optimized for the modular axial flux permanent magnet synchronous wind turbine, namely: Among them, h sl 、h su are the lower and upper bounds of the stator slot depth respectively; h cl 、h cu are the lower and upper limits of the thickness of the rotor permanent magnet respectively; α pl , α pu are the lower and upper bounds of the rotor permanent magnet pole arc coefficient respectively; Step 3: Perform Latin Hypercube Sampling (LHS) experiment to establish the required sample space: 31) Divide each design variable to be optimized into M subintervals between the upper and lower bounds of its own constraints (i.e., the value range), and then randomly select a point in each subinterval; 32) Randomly combine the points selected from all subintervals of each design variable to be optimized to obtain a total of M sample data groups (h sm ,h cm ,α pm ), that is, M design variable combinations, where m = 1, 2, 3, ..., M; 33) The actual value T of the optimization target of each sample data group is obtained through finite element simulation a,m and T ri,m ; Step 4: Establish a deep neural network DNN agent model. The deep neural network DNN contains an input layer, a hidden layer, and an output layer. The input layer has three neurons, i.e., three design variables to be optimized; the output layer has two neurons, i.e., two optimization targets (T a ,、T ri )’s predicted value; the number of hidden layers is 3; The input H of the sth neuron in the first hidden layer s , output HO s They are: Where w is is the i-th neuron x in the input layer i The connection weight between the sth neuron and the first hidden layer, a s is the threshold of the sth neuron in the first hidden layer, s=1,2,…,N (1) f1(·) is the activation function of the first hidden layer, which is the ReLU function (rectified linear unit function), and has: f(x) = max(x, 0); The input H of the jth neuron in the second hidden layer is j , output HO j They are: Where w sj is the connection weight between the sth neuron of the first hidden layer and the jth neuron of the second hidden layer, a j is the threshold of the jth neuron in the second hidden layer, j = 1, 2, ..., N (2) ; f2(·) is the activation function of the second hidden layer, which is the ReLU function (rectified linear unit function); The input H of the u-th neuron in the third hidden layer u , output HO u They are: Where w ju is the connection weight between the jth neuron of the second hidden layer and the uth neuron of the third hidden layer, a u is the threshold value of the u-th neuron in the third hidden layer, u=1,2,…,N (3) ; f3(·) is the activation function of the third hidden layer, which is the ReLU function (rectified linear unit function); The input of the lth neuron in the output layer is: The output of the lth neuron in the output layer is the predicted value of the optimization target for: Where w ul is the connection weight coefficient between the uth neuron in the third hidden layer and the lth neuron in the output layer, b l is the threshold of the lth neuron in the output layer, l = 1, 2; f o (·) is the activation function of the output layer, which is the ReLU function (rectified linear unit function); Step 5: Using the Bayesian optimization algorithm, the hyperparameters of the DNN proxy model are tuned to obtain the optimal hyperparameters; Step 6: Based on the optimal hyperparameters obtained in step 5, train the DNN proxy model; Step 7: Based on the optimal DNN agent model obtained in step 6, the NSGA-II optimization algorithm is used to optimize the design variables to be optimized of the modular axial flux permanent magnet synchronous wind turbine, and the optimal combination of the design variables to be optimized of the modular axial flux permanent magnet synchronous wind turbine is determined so that the modular axial flux permanent magnet synchronous wind turbine obtains optimal performance.

2. The optimization design method of a modular axial flux permanent magnet synchronous wind turbine according to claim 1, characterized in that: The specific method of step 5 is: 51) Design the objective function of Bayesian optimization as: ObjectiveFunction:{max[T a (x)],min[T ri (x)]} (10) Where, T N is the rated torque of the modular axial flux permanent magnet synchronous wind turbine; 52) Define the Bayesian optimization hyperparameter vector of the modular axial flux permanent magnet synchronous wind turbine: The hyperparameter vector h has 8 parameters, which are defined as: h = {η, B, N (1) ,N (2) ,N (3) ,p,γ,T drop }; where η is the initial learning rate, B is the batch size, i.e. the number of samples, and N (1) 、N (2) 、N (3) are the number of nodes in the first, second and third layers of the hidden layer of the DNN respectively; p is the signal loss probability, γ is the learning rate, T drop is the learning rate decay period; 53) Initialize the sample set, that is, initialize the hyperparameter space: Determine the value range of each hyperparameter. Based on the Latin Hypercube Sampling (LHS) experiment, divide each hyperparameter into M subintervals within its value range. Then randomly select a point in each subinterval to obtain M-dimensional components, and establish an 8×M initial sample space of the required hyperparameters. Set the maximum number of iterations, T. 54) An improved Marton 5 / 2–ARD (Automatic Relevance Determination) hybrid kernel function is used as the covariance function of the Gaussian process GP to construct a Gaussian process surrogate model: f(h)~GP(μ(h),k(h p ,h q ))(12)In the formula, f(h) is the target value corresponding to h, μ(h) is the expected function of the Gaussian process, k(h p ,h q ) is the covariance function of the Gaussian process, defined as: Where h p 、h q are two different hyperparameters, p = 1, 2, ..., 8, q = 1, 2, ..., 8; σ f is the signal variance; r 2 Defined as: Among them, l m is the Hamming distance correction term, l m =αδ(h p,m ,h q,m ), which is applicable to discrete parameters; α is the scaling factor of the discrete parameters; δ is the difference function associated with the discrete parameters; h p,m and h q,m Respectively represent h p 、h q The component value of the mth dimension; 55) Calculate the expected function EI(h): ξ t =0.01(1-t / T) 2 (16) Where, σ(h) are the predicted mean and predicted standard deviation of the Gaussian process surrogate model for the objective function; f(h + ) is the currently observed optimal target value; t and T are the current cycle number and the maximum cycle number, respectively; ξ t is the dynamic exploration factor; Φ(Z) and φ(Z) are the cumulative distribution function and probability density function of the standard normal distribution respectively; Z is the degree of improvement of the predicted value of the current target value for the current optimal target value, which is: 56) Evaluating the Performance of Gaussian Process Surrogate Models: Calculating the Coefficient of Determination R 2 , root mean square error RMSE, its expression is: 57) If the coefficient of determination R 2 >0.9, and the root mean square error RMSE < ε, where ε is a positive real number close to 0, then output the optimal hyperparameters and proceed to step 6; otherwise, proceed to step 58); 58) Determine whether the maximum number of cycles has been reached. If so, output the optimal hyperparameters and proceed to step 6; otherwise, update the value of the sample point h and return to step 54).

3. The optimization design method of a modular axial flux permanent magnet synchronous wind turbine according to claim 1, characterized in that: The specific method of step 6 is: 61) Initialize DNN, including: initializing connection weights w is 、w sj 、w ju 、w ul and threshold a s 、a j 、a u 、b l ; 62) Define the loss function J as: 63) Use Adam optimizer to update connection weights and thresholds: A1. Create an Adam optimizer object: DNN proxy model parameters, and set the initial learning rate η; A2. Data loading and preprocessing; A3. Set the gradient of the loss function to zero; A4. Perform forward propagation calculation according to formula (2) to formula (9) to obtain the predicted value of the optimization target l=1,2, that is: and A5. Calculate the loss function J according to formula (20); A6. Perform backpropagation to calculate the gradient g of the loss function J with respect to the connection weights t (W) and the gradient of the threshold g t (B): Where W is the connection weight vector, defined as: W = {w is ,w sj ,w ju ,w ul }; B is the threshold vector, defined as: B = {a s ,a j ,a u ,b l }; A7. Update the connection weight W and threshold B: Where, the variables with subscripts t+1, t, and t-1 represent the values ​​of the variable in the next cycle, the current cycle, and the previous cycle, respectively; β1 and β2 are exponential decay rates, with β1,β2∈[0,1]; A8. Does the number of cycles t reach the maximum number of cycles T? If so, then terminate and proceed to step 7; otherwise, proceed to step A9. A9. Does the loss function J no longer decrease? If so, then terminate and proceed to step 7. Otherwise, return to step A2.

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