CN106407509A - Modeling method and calculating method for electromagnetic characteristic of electromagnetic mechanism of load switch - Google Patents

Abstract

The invention provides a modeling method and calculation method for the electromagnetic characteristics of the electromagnetic mechanism of the load switch. First, a number of key interpolation nodes are preliminarily selected according to the characteristics of the suction curve, and based on the idea of interpolation, the relationship between the output characteristics of the electromagnetic mechanism of the load switch and the process variables is determined. The form of the self-defined function; then the unknown coefficients in the self-defined function are determined through Latin hypercube sampling, finite element method and optimization algorithm, and an approximate model of the electromagnetic characteristics of the load switch electromagnetic mechanism is established. The calculation method is to calculate the electromagnetic output characteristics of any process variable node of the electromagnetic mechanism when the design parameters of the electromagnetic mechanism of the load switch change within the tolerance range according to the built model.

Description

A Modeling Method and Calculation Method of Electromagnetic Characteristics of Load Switch Electromagnetic Mechanism

technical field

The invention relates to a modeling method and a calculation method for the electromagnetic characteristics of a load switch electromagnetic mechanism.

Background technique

As an important component widely used in industry, aerospace and other fields, the load switch is mainly used to realize the functions of breaking and protecting the load current. Modeling the electromagnetic mechanism of the load switch and then analyzing its electromagnetic attraction characteristics is of great significance to the design verification, performance evaluation and product optimization of the load switch.

The modeling of the load switch electromagnetic mechanism involves the analysis of multi-field coupling of electricity, magnetism and force. In the modeling process of the prior art, the finite element method is usually used to calculate the electromagnetic attraction characteristics at each interpolation node. Although the finite element method has high calculation accuracy, it has poor timeliness. Therefore, it is necessary to find a method: reduce the number of interpolation nodes calculated by the finite element method under the premise of ensuring the accuracy of the approximate model.

Contents of the invention

The invention discloses a modeling method and a calculation method for the electromagnetic characteristics of a load switch electromagnetic mechanism, which effectively solves the contradictory relationship between the modeling accuracy and the number of interpolation nodes to be calculated in the modeling process of the load switch electromagnetic mechanism.

A method for modeling electromagnetic characteristics of a load switch electromagnetic mechanism, comprising the following steps:

1) Select at least six key nodes that affect the transient process of the electromagnetic mechanism, establish the functional relationship between the output characteristics of each node, and determine the specific form of the custom function that reflects the relationship between the output characteristics of the load switch electromagnetic mechanism and the process variables;

2) Select m×n interpolation nodes (U _i , α _j ) according to the position of the inflection point of the suction curve of the load switch, where (U _i , α _j ) is the voltage at a certain point on the suction curve of the electromagnetic mechanism and the armature rotation angle, and m and n are respectively Represents the number of voltage and rotation angle, i∈(1,2,…,m), j∈(1,2,…,n); each key design parameter x _k ∈(x ₁ ,x ₂ ,… ,x _p ) uniformly select q nodes within the tolerance range, and Δx _kl represents the variation of x _k at node l∈(1,2,…,q);

3) Apply the finite element method to calculate the electromagnetic moment of the electromagnetic mechanism of the key design parameter x _k under the condition of (U _i , α _j ,Δx _kl ), and use the spline interpolation method to obtain the key points at the interpolation node (U _i , α _j ). The relationship between the design parameter variation Δx _kl and the electromagnetic torque variation;

4) Re-select at least six sampling points in the area formed by each interpolation node, use the finite element method to calculate the electromagnetic torque at the re-selected sampling point, and use it as the actual value of the electromagnetic torque, and bring the re-selected sampling point into The self-defining function determined in step 1), with the minimum error between the calculated value of the electromagnetic torque of the self-defining function and the actual value calculated by the finite element method as the objective function, calculate the unknown coefficient in the self-defining function, and complete the load switch electromagnetic Establishment of institutional models.

The inventive method also includes the optimization process to the built model, specifically:

a) Regenerate some random samples within the parameter tolerance range, and calculate the corresponding electromagnetic mechanism output characteristics of each sample through the finite element method and the model determined in step 4);

b) Using the calculation results of the finite element method as the real value, evaluate the error and accuracy of the built model, judge whether the accuracy requirements are met, and complete the modeling if they are met;

c) If not satisfied, reacquire m'×n' new sample points (U _i ',α _j ') based on the interactive verification sequential sampling strategy, where i'∈(1,2,…,m'), j'∈(1,2,…,n'), apply the finite element method to calculate the electromagnetic attraction torque of x _k under the condition of (U _i ',α _j ',Δx _kl ), and go to step 4).

Further, in step 1), the interpolation method is used to establish the functional relationship between the output characteristics of each node, and the expression is:

Among them, F(U _i ',α _j ') is the output characteristic of the load switch electromagnetic mechanism at (U _i ',α _j '); (U _i ',α _j ') is any process variable node, located at the selected Process variable nodes (U _i ' ₀ ,α _j ' ₀ ), (U _i ' ₁ ,α _j ' ₀ ), (U _i ' ₀ ,α _j ' ₁ ) and (U _i ' ₁ ,α _j ' ₁ ) within the enclosed area; In order to characterize the interpolation function of the weight coefficients of each point, its mathematical expression depends on the functional relationship between the process variable of the electromagnetic mechanism and the output characteristics, and includes the influence coefficient on the voltage U and the rotation angle α.

Further, in step 4), sampling points are selected by Latin hypercube sampling.

Further, the objective function in the step 4) is

Among them, G _i represents the finite element calculation result of the output characteristic corresponding to the i-th sampling point among the N new sampling points; F(X _i ) is an approximate model of the load switch electromagnetic mechanism including unknown coefficients.

Further, the indicators for evaluating the error and precision of the built model described in step b) are: root mean square error RMSE and complex correlation coefficient R ² , and their calculation formulas are respectively:

Among them, k is the sample size for model validation, y _i is the real response value, y _i is the predicted value obtained by the approximate model, is the true response mean.

Further, the interactive verification sequential sampling strategy described in step c) is

Among them, CVE(U _i ',α _j ') represents the interactive verification error function, d((U _i ',α _j '),(U _i ,α _j )) represents the distance between the new sample point and the original sample point, i'∈(1,2,...,m'), j'∈(1,2,...,n').

Simultaneously, the present invention also includes a method for calculating the electromagnetic characteristics of the load switch electromagnetic mechanism, comprising the following steps:

1) Select at least six key nodes that affect the transient process of the electromagnetic mechanism, establish the functional relationship between the output characteristics of each node, and determine the specific form of the custom function that reflects the relationship between the output characteristics of the load switch electromagnetic mechanism and the process variables;

2) Select m×n interpolation nodes (U _i , α _j ) according to the position of the inflection point of the suction curve of the load switch, where (U _i , α _j ) is the voltage at a certain point on the suction curve of the electromagnetic mechanism and the armature rotation angle, and m and n are respectively Represents the number of voltage and rotation angle, i∈(1,2,…,m), j∈(1,2,…,n); each key design parameter x _k ∈(x ₁ ,x ₂ ,… ,x _p ) uniformly select q nodes within the tolerance range, and Δx _kl represents the variation of x _k at node l∈(1,2,…,q);

3) Apply the finite element method to calculate the electromagnetic moment of the electromagnetic mechanism of the key design parameter x _k under the condition of (U _i , α _j ,Δx _kl ), and use the spline interpolation method to obtain the key points at the interpolation node (U _i , α _j ). The relationship between the design parameter variation Δx _kl and the electromagnetic torque variation;

4) Re-select at least six sampling points in the area formed by each interpolation node, use the finite element method to calculate the electromagnetic torque at the re-selected sampling point, and use it as the actual value of the electromagnetic torque, and bring the re-selected sampling point into The self-defining function determined in step 1), with the minimum error between the calculated value of the electromagnetic torque of the self-defining function and the actual value calculated by the finite element method as the objective function, calculate the unknown coefficient in the self-defining function, and complete the load switch electromagnetic Establishment of institutional models;

5) Bring the variation of each design parameter of the electromagnetic mechanism and the process variable node parameters to be calculated into the model determined in step 4) for calculation, and obtain the electromagnetic torque of the process variable node.

In order to ensure the accuracy of the built model, the calculation method also includes the optimization of the built model, specifically:

a) Regenerate some random samples within the parameter tolerance range, and calculate the corresponding electromagnetic mechanism output characteristics of each sample through the finite element method and the model determined in step 4);

b) Using the calculation results of the finite element method as the real value, evaluate the error and accuracy of the built model, judge whether the accuracy requirements are met, and complete the modeling if they are met;

c) If not satisfied, reacquire m'×n' new sample points (U _i ',α _j ') based on the interactive verification sequential sampling strategy, where i'∈(1,2,…,m'), j'∈(1,2,…,n'), apply the finite element method to calculate the electromagnetic attraction torque of x _k under the condition of (U _i ',α _j ',Δx _kl ), and go to step 4).

Further, the objective function in step 4) of the modeling method is

Among them, G _i represents the finite element calculation result of the output characteristic corresponding to the i-th sampling point among the N new sampling points; F(X _i ) is an approximate model of the load switch electromagnetic mechanism including unknown coefficients.

In this paper, the key interpolation nodes are preliminarily selected according to the characteristics of the suction curve, and based on the idea of interpolation, the approximate model of the load switch electromagnetic mechanism based on the self-defined interpolation function is constructed through the Latin hypercube sampling and the finite element method; and then the built model is verified. If the accuracy evaluation result does not meet the requirements, the number of interpolation nodes is gradually increased through the interactive verification sequential sampling strategy until the approximate model built meets the accuracy requirements. The invention reduces the number of interpolation nodes calculated by the finite element method, and effectively balances the contradictory relationship between approximate modeling accuracy and modeling time.

At the same time, the sampling points are selected through the Latin hypercube sampling method, which ensures the randomness and independence of the sampling points.

Description of drawings

Fig. 1 is the flowchart of modeling method described in the present invention;

Fig. 2 is a schematic flow chart of optimizing the modeling model according to the present invention.

detailed description

The invention provides a modeling method and calculation method for the electromagnetic characteristics of the load switch electromagnetic mechanism. First, several key interpolation nodes are preliminarily selected according to the characteristics of the suction curve, and based on the interpolation idea, the relationship between the output characteristics of the load switch electromagnetic mechanism and the process variables is determined. Then, the unknown coefficients in the self-defined function are determined by Latin hypercube sampling, finite element method and particle swarm algorithm, and an approximate model of the load switch electromagnetic mechanism is established.

The present invention will be further described below in conjunction with the accompanying drawings.

As shown in Figure 1, a modeling method for the electromagnetic mechanism of a load switch includes the following steps:

1) Select six key nodes that affect the transient process of the electromagnetic mechanism, establish the functional relationship between the output characteristics of each node through the interpolation method, and determine the specific form of the self-defined function that reflects the relationship between the output characteristics of the load switch electromagnetic mechanism and the process variables:

Among them, F(U _{i' ,} α _{j' )} is the output characteristic of the load switch electromagnetic mechanism at (U i' ,α j'); (U _i' ,α _j' ) is any process variable node located at the selected Process variable nodes (U _i'0 ,α _j'0 ), (U _i'1 ,α _j'0 ), (U _i'0 ,α _j'1 ) and (U _i'1 ,α _j'1 ) within the enclosed area; In order to characterize the interpolation function of the weight coefficients of each point, its mathematical expression depends on the functional relationship between the process variable of the electromagnetic mechanism and the output characteristics, and includes the influence coefficient on the voltage U and the rotation angle α.

2) Select m×n interpolation nodes (U _i , α _j ) according to the position of the inflection point of the suction curve of the load switch, where (U _i , α _j ) is the voltage at a certain point on the suction curve of the electromagnetic mechanism and the armature rotation angle, and m and n are respectively Represents the number of voltage and rotation angle, i∈(1,2,…,m), j∈(1,2,…,n); each key design parameter x _k ∈(x ₁ ,x ₂ ,… ,x _p ) uniformly select q nodes within the tolerance range, and Δx _kl represents the variation of x _k at node l∈(1,2,…,q);

3) Apply the finite element method to calculate the electromagnetic torque of the electromagnetic mechanism under the condition of (U _i ,α _j ,Δx _kl ), the key design parameter x _{k ,} and _obtain each The relationship between the variation of key design parameters Δx _kl and the variation of electromagnetic torque;

4) Reselect six sampling points by Latin hypercube method in the region of each interpolation node, use the finite element method to calculate the electromagnetic moment at the reselected sampling point, and use it as the actual value of the electromagnetic moment. The sampling point is brought into the self-defined function determined in step 1), and the minimum error between the calculated value of the electromagnetic torque of the self-defined function and the actual value calculated by the finite element method is the objective function, and the self-defined function is calculated by particle swarm optimization algorithm. The unknown coefficient in the function completes the establishment of the electromagnetic mechanism model of the load switch.

Among them, the objective function is

In the formula, G _i represents the finite element calculation result of the output characteristics corresponding to the i-th sampling point among the N new sampling points; F(X _i ) is an approximate model of the load switch electromagnetic mechanism including unknown coefficients.

The sampling points are selected by the Latin hypercube method, which effectively guarantees the randomness and relative independence of sampling.

In addition, in order to ensure the accuracy and precision of the built model, the present invention also provides an optimization process for the built model, specifically:

a) Apply the Latin hypercube sampling method to regenerate some random samples within the parameter tolerance range, and calculate the corresponding electromagnetic mechanism output characteristics of each sample through the finite element method and the model determined in step 4);

b) Using the calculation results of the finite element method as the real value, evaluate the error and precision of the built model, judge whether the accuracy requirements are met, and if so, complete the modeling; among them, the indicators for evaluating the error and precision of the built model are: root mean square error RMSE and complex correlation coefficient R ² , and their calculation formulas are:

In the formula, k is the sample size for model verification, y _i is the real response value, y _i is the predicted value obtained by the approximate model, is the true response mean;

c) If not satisfied, reacquire m'×n' new sample points (U _i ',α _j ') based on the interactive verification sequential sampling strategy, where i'∈(1,2,…,m'), j'∈(1,2,…,n'), apply the finite element method to calculate the electromagnetic attraction torque of x _k under the condition of (U _i ',α _j ',Δx _kl ), and go to step 4); among them, The sequential sampling strategy for interactive verification is

In the formula, CVE(U _i ',α _j ') represents the interactive verification error function, d((U _i ',α _j '),(U _i ,α _j )) represents the distance between the new sample point and the original sample point , i'∈(1,2,...,m'), j'∈(1,2,...,n').

The method for calculating the electromagnetic characteristics of the electromagnetic mechanism of the load switch according to the present invention is only to use the model built by the above modeling method to calculate the electromagnetic characteristics of the electromagnetic mechanism of the load switch, and its embodiment will not be repeated here.

Claims (10)

1. a kind of modeling method of on-load switch electromagnetic mechanism electromagnetic property is it is characterised in that comprise the following steps：

1) choose at least six key nodes of impact electromagnetic mechanism transient process, set up the function between each node output characteristics Relation, determines the concrete form of reflection on-load switch electromagnetic mechanism output characteristics and the SQL of process variable relation；

2) m × n interpolation knot (U is chosen according to on-load switch suction knee of curve position_i,α_j), wherein (U_i,α_j) it is electromagnetic motor The voltage of certain point and armature corner on structure suction curve, m, n represent the number of voltage and corner respectively, i ∈ (1,2 ..., m), j ∈(1,2,…,n)；In electromagnetic mechanism each key design parameter x_k∈(x₁,x₂,…,x_p) the margin of tolerance in uniformly choose q Node, Δ x_klExpression node l ∈ (1,2 ..., q) place x_kVariable quantity；

3) apply Finite element arithmetic key design parameter x_kIn (U_i,α_j,Δx_kl) under the conditions of electromagnetic mechanism electromagnetic torque, and Interpolation knot (U is obtained by Spline Interpolation Method_i,α_j) place's each key design parameter variation delta x_klWith electromagnetic torque variable quantity Relation；

4) constitute in region in each interpolation knot and again choose at least six sampled points, again chosen using Finite element arithmetic The electromagnetic torque of sample point, and the actual value as electromagnetic torque, the sampled point again chosen is brought into step 1) in The SQL determining, with error between the electromagnetic torque calculated value of SQL and the actual value of Finite element arithmetic Little for object function, calculate the unknowm coefficient in described SQL, complete the foundation of on-load switch electromagnetic mechanism model.

2. modeling method according to claim 1 it is characterised in that：Also include the optimization process to institute's established model, specifically For：

A) regenerate some random samples in the range of parameter tolerance, pass through Finite Element Method and step 4 respectively) determined by Model calculates each sample corresponding electromagnetic mechanism output characteristics；

B) using Finite Element Method result of calculation as actual value, the error and precision of institute's established model is estimated, judges whether Meet required precision, if it is satisfied, then completing to model；

If c) be unsatisfactory for, m' × n' new sample point (U is reacquired based on the sequential sampling policy of validation-cross_i',α_j'), its Middle i' ∈ (1,2 ..., m'), j' ∈ (1,2 ..., n'), applies Finite element arithmetic x_kIn (U_i',α_j',Δx_kl) under the conditions of electricity Magnetic moment, and go to step 4).

3. modeling method according to claim 1 and 2 it is characterised in that：Step 1) in each node is set up using interpolation method Functional relation between output characteristics, expression formula is：

$F(U_{i^{\′}},{\mathrm{\α}}_{j^{\′}})=\underset{x_1=U_{i^{\′}0}}{\overset{U_{i^{\′}1}}{\Σ}}\underset{x_2={\mathrm{\α}}_{j^{\′}0}}{\overset{{\mathrm{\α}}_{j^{\′}1}}{\Σ}}F(x_1,x_2)\·h(U_{i^{\′}},{\mathrm{\α}}_{j^{\′}}){|}_{(x_1,x_2)}$

Wherein, F (U_i',α_j') it is (U_i',α_j') place's on-load switch electromagnetic mechanism output characteristics；(U_i',α_j') become for arbitrary process Amount node, positioned at selected process variable node (U_i'0,α_j'0)、(U_i'1,α_j'0)、(U_i'0,α_j'1) and (U_i'1,α_j'1) enclosed region Interior；For characterizing the interpolating function of each point weight coefficient, its mathematic(al) representation depends on electromagnetic mechanism process variable Functional relation and output characteristics between, and comprise the impact coefficient with regard to voltage U and corner α.

4. modeling method according to claim 1 and 2 it is characterised in that：Step 4) in selected by Latin Hypercube Sampling Take sampled point.

5. modeling method according to claim 1 and 2 it is characterised in that：Described step 4) in object function be

$\min Err=\sqrt{\frac{\underset{i=1}{\overset{N}{\Σ}}{\[G_i-F\left(X_i\right)\]}^2}{N}}$

Wherein, G_iRepresent the result of finite element of the corresponding output characteristics of ith sample point in N number of new sampled point；F(X_i) For comprising the approximate model of the on-load switch electromagnetic mechanism of unknowm coefficient.

6. modeling method according to claim 2 it is characterised in that：The error to institute's established model described in step b) and The index that precision is estimated is：Root-mean-square error RMSE and coefficient of multiple correlation R², its computing formula is respectively：

$RMSE=\frac{1}{k\stackrel{\‾}{y}}\sqrt{\underset{i=1}{\overset{k}{\Σ}}{(y_i-y_i)}^2}$

$R^2=1-\frac{\underset{i=1}{\overset{k}{\Σ}}{(y_i-y_i)}^2}{\underset{i=1}{\overset{k}{\Σ}}{(y_i-\stackrel{\‾}{y})}^2}$

Wherein, the sample size that k verifies for model, y_iFor responding actual value, y_iIt is the predicted value being obtained by approximate model,It is true Real response average.

7. modeling method according to claim 2 it is characterised in that：Validation-cross described in step c) sequential sampling plan Slightly

$\underset{U_{i^{\′}},{\mathrm{\α}}_{j^{\′}}}{max}F=\{CVE(U_{i^{\′}},{\mathrm{\α}}_{j^{\′}}),min\[d\left(\right(U_{i^{\′}},{\mathrm{\α}}_{j^{\′}}),(U_i,{\mathrm{\α}}_j\left)\right)\]\}$

Wherein, CVE (U_i',α_j') represent validation-cross error function, d ((U_i',α_j'),(U_i,α_j)) represent new sample point with original The distance of sample point, i' ∈ (1,2 ..., m'), j' ∈ (1,2 ..., n').

8. a kind of computational methods of on-load switch electromagnetic mechanism electromagnetic property it is characterised in that：Comprise the following steps：

1) choose at least six key nodes of impact electromagnetic mechanism transient process, set up the function between each node output characteristics Relation, determines the concrete form of reflection on-load switch electromagnetic mechanism output characteristics and the SQL of process variable relation；2) M × n interpolation knot (U is chosen according to on-load switch suction knee of curve position_i,α_j), wherein (U_i,α_j) inhale for electromagnetic mechanism The voltage of certain point and armature corner on force curve, m, n represent the number of voltage and corner respectively, i ∈ (1,2 ..., m), j ∈ (1, 2,…,n)；In electromagnetic mechanism each key design parameter x_k∈(x₁,x₂,…,x_p) the margin of tolerance in uniformly choose q node, Δx_klExpression node l ∈ (1,2 ..., q) place x_kVariable quantity；

3) apply Finite element arithmetic key design parameter x_kIn (U_i,α_j,Δx_kl) under the conditions of electromagnetic mechanism electromagnetic torque, and Interpolation knot (U is obtained by Spline Interpolation Method_i,α_j) place's each key design parameter variation delta x_klWith electromagnetic torque variable quantity Relation；

4) constitute in region in each interpolation knot and again choose at least six sampled points, again chosen using Finite element arithmetic The electromagnetic torque of sample point, and the actual value as electromagnetic torque, the sampled point again chosen is brought into step 1) in The SQL determining, with error between the electromagnetic torque calculated value of SQL and the actual value of Finite element arithmetic Little for object function, calculate the unknowm coefficient in described SQL, complete the foundation of on-load switch electromagnetic mechanism model；

5) variable quantity of each for electromagnetic mechanism design parameter and process variable node parameter to be calculated are brought into step 4) determined Model in calculated, obtain the electromagnetic torque of described process variable node.

9. a kind of on-load switch electromagnetic mechanism electromagnetic property according to claim 8 computational methods it is characterised in that：Also Including the optimization process to institute's established model, specially：

A) regenerate some random samples in the range of parameter tolerance, pass through Finite Element Method and step 4 respectively) determined by Model calculates each sample corresponding electromagnetic mechanism output characteristics；

B) using Finite Element Method result of calculation as actual value, the error and precision of institute's established model is estimated, judges whether Meet required precision, if it is satisfied, then completing to model；

If c) be unsatisfactory for, m' × n' new sample point (U is reacquired based on the sequential sampling policy of validation-cross_i',α_j'), its Middle i' ∈ (1,2 ..., m'), j' ∈ (1,2 ..., n'), applies Finite element arithmetic x_kIn (U_i',α_j',Δx_kl) under the conditions of electricity Magnetic moment, and go to step 4).

10. the computational methods of a kind of on-load switch electromagnetic mechanism electromagnetic property according to claim 8 or claim 9, its feature exists In：Described step 4) in object function be

$\min Err=\sqrt{\frac{\underset{i=1}{\overset{N}{\Σ}}{\[G_i-F\left(X_i\right)\]}^2}{N}}$

Wherein, G_iRepresent the result of finite element of the corresponding output characteristics of ith sample point in N number of new sampled point；F(X_i) For comprising the approximate model of the on-load switch electromagnetic mechanism of unknowm coefficient.