Motor design method based on Kriging proxy model

Abstract

The invention discloses a motor design method based on a Kriging agent model. The method specifically comprises the steps that M motor size parameter combinations are collected to serve as input sample data S, corresponding motor performance serves as output sample data Y, S and Y form a sample set, and the Kriging agent model is trained according to the sample set; constructing an optimization model by taking minimization # imgabs0 # as a target function and taking a motor size parameter variation range in a sample of a Kriging agent model training source as a feasible region; and solving the optimization model to obtain corresponding motor parameters based on given motor performance. According to the method provided by the invention, the speed of solving the inverse mapping of the multi-performance Kriging agent model of the motor based on the coordinate descent method is improved, and the method has good practicability and economical efficiency.

Description

Technical Field

[0001] The invention belongs to the technical field of motors, and in particular relates to a motor design method based on a Kriging proxy model. Background Art

[0002] In the field of motor design, proxy models are often combined with motor simulation models to optimize the motor size parameters so that the motor's performance is still greatly improved under certain specific conditions. The proxy model can learn the mapping relationship between motor size design parameters and motor performance from a small number of samples. However, in most cases where proxy models are applied, the input variable dimension is often much higher than the output response dimension. At this time, the proxy model can only achieve unidirectional mapping, and can only use motor size design parameters as input variables and motor performance as output response, but not vice versa.

[0003] Georges Matheron systematically expounded the Kriging interpolation method in "Principles of geostatistics". This method has high prediction accuracy and can give corresponding variance estimates when predicting output responses. The principle is simple and easy to understand, and it is often used in motor size optimization design. In addition, the Kriging interpolation model expression is differentiable with respect to the independent variable, has a clear structure, is easy to combine with other optimization models, and can be flexibly applied to various scenarios. However, despite the many advantages mentioned above, the Kriging interpolation model can only predict the output response unidirectionally through a given input variable, and cannot reversely predict the value of the input variable through a given output response.

[0004] After the inverse mapping problem of the motor multi-performance Kriging proxy model is transformed into an optimization model, the objective function of the optimization model is differentiable in the feasible domain, and the constraints are linear. The projection gradient method proposed by Rosen in "The Gradient Projection Method for Nonlinear Programming" is suitable for the rapid solution of the optimization model, so that the optimization variables obtained in each iteration process are always in the feasible domain and quickly approach the optimal value. However, in practical applications, due to too many optimization variables and complex models, it is very easy for the optimization model to fall into a local optimal solution.

[0005] The coordinate gradient descent method proposed by Paul Tseng in "A coordinate gradient descent method for nonsmoothseparable minimization" is simple and efficient, and is used in high-dimensional optimization problems in many fields such as machine learning, data mining, and power system optimization. However, as the number of motor performance, that is, the dimension of the output response of the Kriging proxy model, increases, the number of extreme points of the objective function of the optimization model after the inverse mapping transformation also increases. The solution speed slows down during the solution iteration, and it is easily affected by the order of solving the components of the coordinate gradient descent method. Summary of the invention

[0006] Purpose of the invention: In order to solve the problems existing in the above-mentioned prior art, the present invention provides a motor design method based on the Kriging proxy model.

[0007] Technical solution: The present invention discloses a motor design method based on a Kriging proxy model, specifically:

[0008] Collect M motor size parameter combinations as input sample data S, use the corresponding motor performance as output sample data Y, and use S and Y to form a sample set. Train the Kriging proxy model based on the sample set. X is the input variable of the Kriging proxy model, representing the motor parameters, X = x1, x2, x3, …, x k ,…,x n ;x k represents the kth motor parameter, k = 1, 2, 3, ..., n, n represents the total number of motor parameters;

[0009] To minimize As the objective function, the optimization model is constructed with the range of motor size parameters in the samples from which the Kriging surrogate model is trained as the feasible domain; where y c For a given motor performance, y c =(y1,y2,…,y q ,…,y Q ) T , T represents transpose, y q represents the qth motor performance, q = 1, 2, ..., Q, Q represents the total number of motor performance types; Λ is the coefficient matrix, Λ = diag{λ1,λ2, ...,λ q ,…,λ Q}, diag{.} is the diagonal function, λ q represents the qth weight coefficient;

[0010] Solve the optimization model to obtain the motor parameters corresponding to the given motor performance.

[0011] Further, specifically: the Kriging proxy model The expression is as follows:

[0012]

[0013] Among them, f b (X) is the basis function of the regression model, p represents the number of basis functions, r(X) is the correlation vector between X and S, θ is a hyperparameter, The expression of the function is:

[0014]

[0015] s m,k Represents the kth motor parameter in the mth input sample data;

[0016] β * and γ * The expression is:

[0017] β * =(F T R -1 F) -1 F T R -1 Y

[0018] γ * =R -1 (Y-Fβ * )

[0019] Among them, the expressions of F and R are:

[0020]

[0021] Furthermore, a genetic algorithm is used to calculate the hyperparameter θ.

[0022] Furthermore, the expression of the optimization model is as follows:

[0023]

[0024] in, represents the qth performance of the motor predicted by the Kriging surrogate model, s m,k Represents the kth motor parameter in the mth input sample data.

[0025] Furthermore, setting λ q The expression is: and are the minimum and maximum values ​​of the qth motor performance respectively.

[0026] Furthermore, when solving the optimization model, the objective function is repeatedly iterated based on the coordinate descent method, and each descent direction is the direction of the coordinate axis corresponding to a random single component in the input variable, so that the objective function finally converges.

[0027] Furthermore, the descending iteration is specifically as follows:

[0028] After the parameters in the input variable X are combined and arranged in a preset order, descending iteration is performed.

[0029] Let the input variable at the jth iteration be X j , if the j+1th iteration needs to change X j The i-th component of Updated to:

[0030]

[0031] in, is the iteration step length, Where m j is the smallest non-negative positive integer that satisfies the following inequality:

[0032]

[0033] Among them, β∈(0,1),σ∈(0,0.5), the expression of f(.) is;

[0034] s m,i Represents the i-th motor parameter in the m-th input sample data;

[0035] Then the input variable for the j+1th iteration is

[0036] Furthermore, the Kriging proxy model needs to perform maximum value normalization on the sample data before training.

[0037] Beneficial effects:

[0038] 1. The method of the present invention is simple and easy to understand, and the objective function is differentiable with respect to the optimization variable in the feasible domain, the constraint conditions are linear, and the motor size parameters that meet multiple motor performance requirements can be easily obtained through known algorithms. The response speed of the Kriging proxy model is much faster than the calculation speed of the finite element model, which can save a lot of time consumed by the finite element model calculation.

[0039] 2. When solving the optimization model after the inverse mapping transformation of the motor multi-performance Kriging proxy model, the present invention makes the optimization variables gradually approach the optimal solution based on the improved coordinate gradient descent method, that is, only after each random selection of a component, the component is subjected to a descent iteration, that is, the number of iterations for solving the optimal value of the component at each stage is limited to 1. Compared with the general case, that is, the coordinate gradient descent algorithm is not improved, the degree of descent after replacing the component in one iterative descent is greater than the degree of descent without replacing the component in an unlimited number of iterations. The improved coordinate gradient descent method can solve complex high-dimensional optimization models faster, and because it frequently replaces components for descent iterations, the iteration order of the components has little effect on the speed of the algorithm. The improvement is simple and easy to understand, and can efficiently solve complex high-dimensional optimization models. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of the present invention.

[0041] Figure 2 It is a structural diagram of a δ-type permanent magnet flat wire motor with 48 stator slots and 8 rotor poles in an embodiment. DETAILED DESCRIPTION

[0042] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0043] In the field of motor body parameter design, it is often necessary to consider multiple motor performance application requirements to determine the motor size parameters, and it is also necessary to predict the motor performance corresponding to different motor size parameter combinations through a finite element model with a higher confidence level, establish a proxy model with motor size parameters as input variables and motor multiple performance as output response, and convert the proxy model inverse mapping problem into an optimization model solution process that can use motor multiple performance as input variables and motor size parameters as output response. The proxy model response speed is much faster than the finite element model, and introducing a proxy model instead of a finite element model calculation can save a lot of computing time. The technical solution adopted by the present invention limits the number of descending iterations after randomly selecting components in each stage during the solution process of the motor multiple performance optimization model, and can eventually quickly and stably solve the motor parameter combination corresponding to the motor multiple performance requirements.

[0044] like Figure 1 As shown, the specific process of this embodiment is as follows:

[0045] This embodiment takes a δ-type permanent magnet flat wire motor with 48 stator slots and 8 rotor poles as an example to introduce the implementation process of the present invention in detail. Figure 2 This is the structural diagram of the motor.

[0046] First, through the Latin hypercube sampling test design and combined with the finite element model, M = 100 motor size parameter combinations are collected as input sample data S. In this embodiment, the total number of motor performances Q = 2; In this embodiment, the motor average torque and average loss performance corresponding to the input sample data are used as output sample data Y. Based on the sample set, a Kriging proxy model with multiple motor size parameters as input variables and multiple motor performances as output responses is trained. The parameter adjustment process in training is solved by genetic algorithm and k-fold cross validation. Then, given the motor performance y c =(y1,y2) T ,by In order to minimize the objective function, the optimization model is constructed with the range of motor size parameters in the samples from which the Kriging proxy model is trained as the feasible domain. Finally, the objective function is repeatedly descended based on the coordinate descent method, and each descent direction is the coordinate axis direction corresponding to the random single component in the input variable, so that the objective function finally converges to 0 and obtains the performance y of the given motor. c Corresponding combinations of motor size parameters

[0047] In this embodiment, the sampling process selects 11 motor parameters as input variables X = (x1, x2, ..., x 11 )=(Rsi,Wslot,Hslot,Wslot_open,Wtip,…,Lpm2), and its initial parameter values ​​are shown in Table 1.

[0048] Table 1

[0049]

[0050]

[0051] Input any sample s in the sample data S m =(s m,1 ,s m,2 ,...,s m,k ,...,s m,n ) is an n-dimensional vector, corresponding to n motor size parameters (n=11), s m,k is the kth motor size parameter in the mth sample.

[0052] Given the motor performance requirement y c =(y1,y2) T =(120,2500) T, y1 represents the motor torque performance requirement, y1 = 120Nm, y2 represents the motor loss performance requirement, y2 = 2500W, then the objective function of the minimization optimization model is to keep the coefficient matrix of each performance value in the same dimension, Λ = diag{λ1,λ2} and the difference vector between the given performance value and the Kriging proxy model The square of the product two norm, that is Where λ1:λ2=1 / (Y1 max -Y1 min ) 2 :1 / (Y2 max -Y2 min ) 2 ,λ1+λ2=1,Y1 min and Y1 max are the minimum and maximum values ​​of the motor torque performance in the sample data set Y, Y2 min and Y2 max are the minimum and maximum values ​​of the motor loss performance in the sample data set Y. The feasible domain is determined by the range of sample values ​​in the sample data set S of the Kriging surrogate model, that is, the kth component x of the variable X k The feasible range is [x k min ,x k max ],in Then the expression of the optimization model constructed by the present invention is:

[0053]

[0054] in, represents the motor torque performance predicted by the Kriging surrogate model, represents the motor loss performance predicted by the Kriging surrogate model,

[0055] In this embodiment, the Kriging proxy model needs to perform maximum value normalization on the sample data before training, that is, scale the data to between 0 and 1 to eliminate the influence of different dimensions. The basis function of the Kriging proxy model is set to a constant basis function, and the model expression can be given by the following formula:

[0056]

[0057] Among them, the input variable X is an n-dimensional vector, f b (X) is the basis function of the regression model:

[0058] f b (X) = [f1 b (X),f2 b (X),…,fp b (X)] T

[0059] In this example, f b (X) is taken as a constant basis function, that is, p = 1, f1 b (X) = 1, r(X) is the correlation vector between X and S:

[0060]

[0061] θ is a hyperparameter, The expression of the function is:

[0062]

[0063] Among them, θ, w, x1 are The input parameters of the function. Then we can get:

[0064]

[0065] β * and γ * is the weight vector of the corresponding function:

[0066] β * =(F T R -1 F) -1 F T R -1 Y

[0067] γ * =R -1 (Y-Fβ * )

[0068] Where F and R are:

[0069]

[0070] Given a random multidimensional initial proxy model input variable In this example, it is assumed that according to Table 1, “1(x1, Rsi)→2(x2, Wslot)→3(x3, Hslot)→…→11(x 11 ,Lpm2)” is iterated in order of sequence 1, following “2(x2,Wslot)→1(x1,Rsi)→3(x3,Hslot)→…→11(x 11 ,Lpm2)” is iterated in order of sequence 2, following “3(x3,Hslot)→1(x1,Rsi)→2(x2,Hslot)→…→11(x 11, Lpm2)" is iterated in order of sequence 3, and so on, then according to "11(x 11 ,Hslot)→1(x1,Rsi)→2(x2,Hslot)→…→10(x 10 ,Wpm2)” is iterated in sequence to sequence 11.

[0071] Randomly determine the initial value X of the input variable X in the feasible domain 0 , and iterate the components in the order of 1, 2, 3, ..., 11, and repeat this step continuously, where the input variable of the jth iteration is X j =(x1 j ,x2 j ,...,x n j ), assuming that the j+1th iteration needs to change X j The i-th component of For the weight Update it to The iterative formula follows the one-dimensional projected gradient method based on the Armjio criterion, where is the iteration step length, is the descending direction, and the input variable of the j+1th iteration is That is, other components remain unchanged, only the component The one-dimensional projected gradient method based on the Armjio criterion is followed for one-step descent iteration. The descending iteration step size and descending direction The search process follows the Armjio criterion, β∈(0,1),σ∈(0,0.5) In this embodiment, β=0.5,σ=0.2, Where m k is the smallest non-negative positive integer that satisfies the following inequality:

[0072]

[0073] The expression of f(.) is; That is, f(x i ) i is a variable, There are only corresponding x i Modify, the rest remain unchanged;

[0074] The above process is repeated until the objective function of the optimization model converges to the global minimum value 0 or the total number of iterations is greater than or equal to the maximum number of iterations, and the motor performance constant y is obtained. cCorresponding motor size parameter combinations as input variables of the proxy model The objective function converges to 0 in the termination condition and is set to when the objective function is less than ε (ε is set to 1e-5 in this example), the algorithm stops.

[0075] Comparing the above improved coordinate gradient descent method with the original coordinate gradient descent method, the improved coordinate gradient descent method only performs one iteration when updating the variables, and the component Updated to After one iteration is reduced, the components are replaced in the order of loop iterations. Continue to iterate and descend; the original coordinate descent method does not limit the number of iterative descents, and performs m iterative descents on the same component in each stage. The iterative formula is still After each stage is solved, the components are updated as follows: That is, the component is not replaced until the value of the component is found that minimizes the objective function.

[0076] The initial value X for the input variable X 0 , respectively, using the original coordinate gradient descent method and the improved coordinate gradient descent method according to 1, 2,

[0077] The components are iteratively decreased in the loop sequence of 3, ..., 11, and the number of iterations required when the iteration is terminated is recorded. The results are shown in Table 2.

[0078] Table 2

[0079] order 1 2 3 4 5 6 7 8 9 10 11 average value Very bad The number of iterations of the original method 109 97 86 60 81 74 45 154 67 70 61 82 109 Improvement method iterations 20 22 26 33 31 29 21 31 23 23 22 26 13

[0080] It can be seen from the table that the original coordinate gradient descent method requires 45 iterations when iteratively solving in order 7, and 154 iterations when iteratively solving in order 8, with a range of 109, while the improved coordinate gradient descent method requires 20 iterations when iteratively solving in order 1, and 33 iterations when iteratively solving in order 4, with a range of 13. It can be seen that the influence of the component iteration order on the original coordinate gradient descent method is much greater than that of the improved coordinate gradient descent method. In addition, the original coordinate gradient descent method requires an average of 82 iterations, and the improved coordinate gradient descent method requires an average of 26 iterations. The speed of the original coordinate gradient descent method is also slower than that of the improved coordinate gradient descent method. It can be seen that the improved coordinate gradient descent method not only reduces the influence of the component order on the speed of iterative solution optimization model, but also greatly improves the solution speed.

[0081] The above implementation modes are only exemplary descriptions of the present invention and do not limit its protection scope. Those skilled in the art may also make partial changes thereto. For example, the motor type and motor performance may be selected according to actual conditions, and the type of proxy model used to fit the mapping relationship between the motor size parameter combination and the motor performance may be selected according to actual conditions. Any form of equivalent replacement that is consistent with the spirit of the invention falls within the protection scope of the present invention.

Claims

1. A motor design method based on Kriging proxy model, characterized in that: Specifically: Collect M motor size parameter combinations as input sample data S, use the corresponding motor performance as output sample data Y, and use S and Y to form a sample set. Train the Kriging proxy model based on the sample set. X is the input variable of the Kriging proxy model, representing the motor parameters, X = x1, x2, x3, …, x k ,…,x n ;x k represents the kth motor parameter, k = 1, 2, 3, ..., n, n represents the total number of motor parameters; To minimize As the objective function, the optimization model is constructed with the range of motor size parameters in the samples from which the Kriging proxy model is trained as the feasible domain; where y c For a given motor performance, y c =(y1,y2,…,y q ,…,y Q ) T , T represents transpose, y q represents the qth motor performance, q = 1, 2, ..., Q, Q represents the total number of motor performance types; Λ is the coefficient matrix, Λ = diag{λ1,λ2, ...,λ q ,…,λ Q }, diag{.} is the diagonal function, λ q represents the qth weight coefficient; Solve the optimization model to obtain the motor parameters corresponding to the given motor performance.

2. A motor design method based on Kriging proxy model according to claim 1, characterized in that: Specifically: the Kriging proxy model The expression is as follows: Among them, f b (X) is the basis function of the regression model, p represents the number of basis functions, r(X) is the correlation vector between X and S, θ is a hyperparameter, The expression of the function is: s m,k Represents the kth motor parameter in the mth input sample data; β * and γ * The expression is: β * =(F T R -1 F) -1 F T R -1 Y c * =R -1 (Y-Fβ * ) Among them, the expressions of F and R are:

3. A motor design method based on Kriging proxy model according to claim 2, characterized in that: A genetic algorithm is used to calculate the hyperparameter θ.

4. A motor design method based on Kriging proxy model according to claim 1, characterized in that: The expression of the optimization model is as follows: in, represents the qth performance of the motor predicted by the Kriging surrogate model, s m,k Represents the kth motor parameter in the mth input sample data.

5. A motor design method based on Kriging proxy model according to claim 1, characterized in that: Setting up the Lambda q The expression is: and are the minimum and maximum values ​​of the qth motor performance respectively.

6. A motor design method based on Kriging proxy model according to claim 1, characterized in that: When solving the optimization model, the objective function is repeatedly descended iteratively based on the coordinate descent method. Each descent direction is the direction of the coordinate axis corresponding to a random single component in the input variable, so that the objective function finally converges.

7. A motor design method based on Kriging proxy model according to claim 6, characterized in that: The descending iteration is specifically: After the parameters in the input variable X are combined and arranged in a preset order, descending iteration is performed. Let the input variable at the jth iteration be X j , if the j+1th iteration needs to change X j The i-th component of Updated to: in, is the iteration step length, Where m j is the smallest non-negative positive integer that satisfies the following inequality: Among them, β∈(0,1),σ∈(0,0.5), the expression of f(.) is; s m,i Represents the i-th motor parameter in the m-th input sample data; Then the input variable for the j+1th iteration is 8. A motor design method based on Kriging proxy model according to claim 1, characterized in that: The Kriging proxy model needs to perform maximum value normalization on the sample data before training.

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