CN106407509B - Modeling method and calculating method for electromagnetic characteristics of load switch electromagnetic mechanism - Google Patents
Modeling method and calculating method for electromagnetic characteristics of load switch electromagnetic mechanism Download PDFInfo
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Abstract
The invention provides a modeling method and a calculation method for electromagnetic characteristics of a load switch electromagnetic mechanism, which comprises the steps of firstly, preliminarily selecting a plurality of key interpolation nodes according to suction curve characteristics, and determining a form of a custom function reflecting the relation between the output characteristics of the load switch electromagnetic mechanism and process variables based on an interpolation idea; and then, determining unknown coefficients in the constructed custom function through Latin hypercube sampling, a finite element method and an optimization algorithm, and establishing an approximate model of the electromagnetic characteristics of the load switch electromagnetic mechanism. The calculation method is that according to the established model, when the design parameters of the load switch electromagnetic mechanism change within the tolerance range, the electromagnetic output characteristics of any process variable node of the electromagnetic mechanism are calculated.
Description
Technical Field
The invention relates to a modeling method and a calculating method for electromagnetic characteristics of an electromagnetic mechanism of a load switch.
Background
The load switch is an important component widely applied to the fields of industry, aerospace and the like, and is mainly used for realizing the functions of switching on and off, protecting and the like of load current. Modeling is carried out on the electromagnetic mechanism of the load switch so as to analyze the electromagnetic attraction characteristic of the load switch, and the method has important significance on design verification, performance evaluation and product optimization of the load switch.
The modeling of the load switch electromagnetic mechanism relates to the analysis of electric, magnetic and force multi-field coupling, and in the prior art, a finite element method is generally adopted to calculate the electromagnetic attraction characteristics at each interpolation node in the modeling process. Although the finite element method has high calculation precision, the finite element method has poor timeliness, and therefore a method needs to be found: on the premise of ensuring the precision of the approximate model, the number of interpolation nodes calculated by a finite element method is reduced.
Disclosure of Invention
The invention discloses a modeling method and a calculating method for electromagnetic characteristics of a load switch electromagnetic mechanism, which effectively solve the contradiction between modeling precision and the number of interpolation nodes needing to be calculated in the modeling process of the load switch electromagnetic mechanism.
A modeling method for electromagnetic characteristics of an electromagnetic mechanism of a load switch comprises the following steps:
1) selecting at least six key nodes influencing the transient process of the electromagnetic mechanism, establishing a functional relation between output characteristics of the nodes, and determining a specific form of a custom function reflecting the relation between the output characteristics of the load switch electromagnetic mechanism and a process variable;
2) selecting m multiplied by n interpolation nodes (U) according to the inflection point position of the suction curve of the load switchi,αj) Wherein (U)i,αj) The voltage and the armature rotation angle of a certain point on an attraction curve of the electromagnetic mechanism are represented by m and n respectively representing the number of the voltage and the rotation angle, i belongs to (1,2, …, m), and j belongs to (1,2, …, n); at each key design parameter x of electromagnetic mechanismk∈(x1,x2,…,xp) Within the tolerance range of (1), q nodes are uniformly selected, delta xklDenotes x at node l ∈ (1,2, …, q)kThe amount of change in (c);
3) calculating key design parameter x by using finite element methodkIn (U)i,αj,Δxkl) Obtaining an interpolation node (U) by the electromagnetic torque of the electromagnetic mechanism under the condition and by a spline interpolation methodi,αj) Variation Δ x of each key design parameterklA relation with an electromagnetic torque variation;
4) reselecting at least six sampling points in each interpolation node forming area, calculating the electromagnetic torque at the reselected sampling points by using a finite element method, taking the electromagnetic torque as an actual value of the electromagnetic torque, substituting the reselected sampling points into the self-defined function determined in the step 1), calculating unknown coefficients in the self-defined function by taking 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 as a target function, and finishing the establishment of the load switch electromagnetic mechanism model.
The method also comprises an optimization process of the established model, which specifically comprises the following steps:
a) regenerating a plurality of random samples within a parameter tolerance range, and calculating the output characteristics of the electromagnetic mechanism corresponding to each sample through a finite element method and the model determined in the step 4) respectively;
b) taking the calculation result of the finite element method as a true value, evaluating the error and precision of the established model, judging whether the precision requirement is met, and if so, completing modeling;
c) if not, re-acquiring m 'x n' new sample points (U) based on the cross-validation sequential sampling strategyi',αj') Wherein i 'belongs to (1,2, …, m'), and j 'belongs to (1,2, …, n'), and x is calculated by applying finite element methodkIn (U)i',αj',Δxkl) The electromagnet under the condition attracts the torque and goes to step 4).
Further, in step 1), an interpolation method is adopted to establish a functional relationship between output characteristics of each node, and an expression is as follows:
wherein, F (U)i,αj) Is (U)i,αj) Output characteristics of the load switch electromagnetic mechanism; (U)i,αj) For any process variable node, at a selected process variable node (U)i0,αj0)、(Ui1,αj0)、(Ui0,αj1) And (U)i1,αj1) Within the enclosed area;
to characterize the interpolation function for each point weight coefficient, the mathematical expression thereof depends on the functional relationship between the process variable and the output characteristic of the electromagnetic mechanism, and includes influence coefficients with respect to the voltage U and the rotation angle α.
Further, in the step 4), sampling points are selected by Latin hypercube sampling.
Further, the objective function in the step 4) is
Wherein G isiA finite element calculation result representing output characteristics corresponding to the ith sampling point in the N new sampling points; f (X)i) An approximate model of the load switch electromagnetic mechanism containing unknown coefficients.
Further, the indexes for evaluating the error and the accuracy of the established model in the step b) are as follows: root mean square error RMSE and complex correlation coefficient R2The calculation formulas are respectively as follows:
where k is the sample size for model validation, yiIn response to the actual value of the value,
for the predicted values obtained from the approximation model,
is the true response mean.
Further, the interactive verification sequential sampling strategy in the step c) is
Wherein CVE (U)i',αj') Represents the interactive proof error function, d ((U)i',αj'),(Ui,αj) Represents the distance of the new sample point from the original sample point, i ' e (1,2, …, m '), j '∈(1,2,…,n')。
Meanwhile, the invention also comprises a method for calculating the electromagnetic property of the load switch electromagnetic mechanism, which comprises the following steps:
1) selecting at least six key nodes influencing the transient process of the electromagnetic mechanism, establishing a functional relation between output characteristics of the nodes, and determining a specific form of a custom function reflecting the relation between the output characteristics of the load switch electromagnetic mechanism and a process variable;
2) selecting m multiplied by n interpolation nodes (U) according to the inflection point position of the suction curve of the load switchi,αj) Wherein (U)i,αj) The voltage and the armature rotation angle of a certain point on an attraction curve of the electromagnetic mechanism are represented by m and n respectively representing the number of the voltage and the rotation angle, i belongs to (1,2, …, m), and j belongs to (1,2, …, n); at each key design parameter x of electromagnetic mechanismk∈(x1,x2,…,xp) Within the tolerance range of (1), q nodes are uniformly selected, delta xklDenotes x at node l ∈ (1,2, …, q)kThe amount of change in (c);
3) calculating key design parameter x by using finite element methodkIn (U)i,αj,Δxkl) Obtaining an interpolation node (U) by the electromagnetic torque of the electromagnetic mechanism under the condition and by a spline interpolation methodi,αj) Variation Δ x of each key design parameterklA relation with an electromagnetic torque variation;
4) reselecting at least six sampling points in each interpolation node forming area, calculating the electromagnetic torque at the reselected sampling points by using a finite element method, taking the electromagnetic torque as an actual value of the electromagnetic torque, substituting the reselected sampling points into the self-defined function determined in the step 1), calculating unknown coefficients in the self-defined function by taking 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 as a target function, and finishing the establishment of the load switch electromagnetic mechanism model;
5) and (4) substituting the variable quantity of each design parameter of the electromagnetic mechanism and the process variable node parameter to be calculated into the model determined in the step 4) for calculation to obtain the electromagnetic moment of the process variable node.
In order to ensure the accuracy of the established model, the calculation method further comprises the step of optimizing the established model, which specifically comprises the following steps:
a) regenerating a plurality of random samples within a parameter tolerance range, and calculating the output characteristics of the electromagnetic mechanism corresponding to each sample through a finite element method and the model determined in the step 4) respectively;
b) taking the calculation result of the finite element method as a true value, evaluating the error and precision of the established model, judging whether the precision requirement is met, and if so, completing modeling;
c) if not, re-acquiring m 'x n' new sample points (U) based on the cross-validation sequential sampling strategyi',αj') Wherein i 'belongs to (1,2, …, m'), and j 'belongs to (1,2, …, n'), and x is calculated by applying finite element methodkIn (U)i',αj',Δxkl) The electromagnet under the condition attracts the torque and goes to step 4).
Further, the objective function in step 4) of the modeling method is
Wherein G isiA finite element calculation result representing output characteristics corresponding to the ith sampling point in the N new sampling points; f (X)i) An approximate model of the load switch electromagnetic mechanism containing unknown coefficients.
The method comprises the steps of preliminarily selecting key interpolation nodes according to suction curve characteristics, and constructing a load switch electromagnetic mechanism approximate model based on a user-defined interpolation function through Latin hypercube sampling and a finite element method based on an interpolation idea; and then verifying the established model, and if the modeling precision evaluation result does not meet the requirement, gradually increasing the number of interpolation nodes by an interactive verification sequential sampling strategy until the established approximate model meets the precision requirement. The invention reduces the number of interpolation nodes calculated by a finite element method, and effectively balances the contradiction between the approximate modeling precision and the modeling time.
Meanwhile, sampling points are selected by a Latin hypercube sampling method, and the randomness and the independence of the sampling points are guaranteed.
Drawings
FIG. 1 is a flow chart of a modeling method according to the present invention;
FIG. 2 is a schematic flow chart illustrating the optimization of the modeling model according to the present invention.
Detailed Description
The invention provides a modeling method and a calculation method for electromagnetic characteristics of a load switch electromagnetic mechanism, which comprises the steps of firstly, preliminarily selecting a plurality of key interpolation nodes according to suction curve characteristics, and determining a form of a self-defined function reflecting the relation between the output characteristics of the load switch electromagnetic mechanism and process variables based on an interpolation idea; and then, determining unknown coefficients in the constructed custom function through Latin hypercube sampling, a finite element method and a particle swarm algorithm, and establishing an approximate model of the load switch electromagnetic mechanism.
The invention is further described below with reference to the accompanying drawings.
As shown in the first figure, the modeling method of the load switch electromagnetic mechanism comprises the following steps:
1) selecting six key nodes influencing the transient process of the electromagnetic mechanism, establishing a functional relation between output characteristics of all the nodes by an interpolation method, and determining a specific form of a custom function reflecting the relation between the output characteristics of the load switch electromagnetic mechanism and a process variable:
wherein, F (U)i,αj) Is (U)i,αj) Output characteristics of the load switch electromagnetic mechanism; (U)i,αj) For any process variable node, at a selected process variable node (U)i0,αj0)、(Ui1,αj0)、(Ui0,αj1) And (U)i1,αj1) Within the enclosed area;
for characterizing the interpolation function of the weight coefficients of each point, its mathematical tableThe expression depends on the functional relationship between the process variable and the output characteristic of the electromagnetic mechanism and includes an influence coefficient with respect to the voltage U and the rotation angle α.
2) Selecting m multiplied by n interpolation nodes (U) according to the inflection point position of the suction curve of the load switchi,αj) Wherein (U)i,αj) The voltage and the armature rotation angle of a certain point on an attraction curve of the electromagnetic mechanism are represented by m and n respectively representing the number of the voltage and the rotation angle, i belongs to (1,2, …, m), and j belongs to (1,2, …, n); at each key design parameter x of electromagnetic mechanismk∈(x1,x2,…,xp) Within the tolerance range of (1), q nodes are uniformly selected, delta xklDenotes x at node l ∈ (1,2, …, q)kThe amount of change in (c);
3) calculating key design parameter x by using finite element methodkIn (U)i,αj,Δxkl) Obtaining an interpolation node (U) by an electromagnetic torque of the electromagnetic mechanism under the condition and a cubic spline interpolation methodi,αj) Variation Δ x of each key design parameterklA relation with an electromagnetic torque variation;
4) and (2) reselecting six sampling points in each interpolation node forming area by a Latin hypercube method, calculating the electromagnetic torque at the reselected sampling points by using a finite element method, taking the electromagnetic torque as an actual value of the electromagnetic torque, substituting the reselected sampling points into the custom function determined in the step 1), taking the minimum error between the calculated value of the electromagnetic torque of the custom function and the actual value calculated by the finite element method as a target function, optimally calculating an unknown coefficient in the custom function by a particle swarm algorithm, and finishing the establishment of the load switch electromagnetic mechanism model.
Wherein the objective function is
In the formula, GiA finite element calculation result representing output characteristics corresponding to the ith sampling point in the N new sampling points; f (X)i) An approximate model of the load switch electromagnetic mechanism containing unknown coefficients.
Sampling points are selected by a Latin hypercube method, and the randomness and relative independence of sampling are effectively guaranteed.
In addition, in order to ensure the accuracy and precision of the built model, the invention also provides an optimization process of the built model, which specifically comprises the following steps:
a) regenerating a plurality of random samples within a parameter tolerance range by using a Latin hypercube sampling method, and calculating the output characteristics of the electromagnetic mechanism corresponding to each sample by using a finite element method and the model determined in the step 4) respectively;
b) taking the calculation result of the finite element method as a true value, evaluating the error and precision of the established model, judging whether the precision requirement is met, and if so, completing modeling; the indexes for evaluating the error and the precision of the established model are as follows: root mean square error RMSE and complex correlation coefficient R2The calculation formulas are respectively as follows:
where k is the sample size for model validation, yiIn response to the actual value of the value,
for the predicted values obtained from the approximation model,
is the mean of the true responses;
c) if not, re-acquiring m 'x n' new sample points (U) based on the cross-validation sequential sampling strategyi',αj') Wherein i 'belongs to (1,2, …, m'), and j 'belongs to (1,2, …, n'), and x is calculated by applying finite element methodkIn (U)i',αj',Δxkl) Electromagnetic attraction torque under the condition, and turning to the step 4); wherein, the interactive verification sequential sampling strategy is
In the formula, CVE (U)i',αj') Represents the interactive proof error function, d ((U)i',αj'),(Ui,αj) Represents the distance of the new sample point from the original sample point, i 'e (1,2, …, m'), and j 'e (1,2, …, n').
The method for calculating the electromagnetic property of the load switch electromagnetic mechanism only uses the model established by the modeling method to calculate the electromagnetic property of the load switch electromagnetic mechanism, and the embodiment of the method is not repeated herein.
Claims (7)
1. A modeling method for electromagnetic characteristics of an electromagnetic mechanism of a load switch is characterized by comprising the following steps:
1) selecting at least six key nodes influencing the transient process of the electromagnetic mechanism, establishing a functional relation between output characteristics of the nodes, and determining a specific form of a custom function reflecting the relation between the output characteristics of the load switch electromagnetic mechanism and a process variable;
2) selecting m multiplied by n interpolation nodes (U) according to the inflection point position of the suction curve of the load switchi,αj) Wherein (U)i,αj) The voltage and the armature rotation angle of a certain point on an attraction curve of the electromagnetic mechanism are represented by m and n respectively representing the number of the voltage and the rotation angle, i belongs to (1,2, …, m), and j belongs to (1,2, …, n); at each key design parameter x of electromagnetic mechanismk∈(x1,x2,…,xp) Within the tolerance range of (1), q nodes are uniformly selected, delta xklDenotes x at node l ∈ (1,2, …, q)kThe amount of change in (c);
3) calculating key design parameter x by using finite element methodkIn (U)i,αj,Δxkl) Obtaining an interpolation node (U) by the electromagnetic torque of the electromagnetic mechanism under the condition and by a spline interpolation methodi,αj) Variation Δ x of each key design parameterklA relation with an electromagnetic torque variation;
4) reselecting at least six sampling points in each interpolation node forming area, calculating the electromagnetic torque at the reselected sampling points by using a finite element method, taking the electromagnetic torque as an actual value of the electromagnetic torque, substituting the reselected sampling points into the self-defined function determined in the step 1), calculating unknown coefficients in the self-defined function by taking 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 as a target function, and finishing the establishment of the load switch electromagnetic mechanism model;
in the step 1), an interpolation method is adopted to establish a functional relation among output characteristics of each node, and the expression is as follows:
wherein, F (U)i,αj) Is (U)i,αj) Output characteristics of the load switch electromagnetic mechanism; (U)i,αj) For any process variable node, at a selected process variable node (U)i0,αj0)、(Ui1,αj0)、(Ui0,αj1) And (U)i1,αj1) Within the enclosed area;
an interpolation function for representing each point weight coefficient, the mathematical expression of which depends on the functional relationship between the process variable and the output characteristic of the electromagnetic mechanism and comprises influence coefficients related to the voltage U and the rotation angle α;
the method also comprises an optimization process of the established model, which specifically comprises the following steps:
a) regenerating a plurality of random samples within a parameter tolerance range, and calculating the output characteristics of the electromagnetic mechanism corresponding to each sample through a finite element method and the model determined in the step 4) respectively;
b) taking the calculation result of the finite element method as a true value, evaluating the error and precision of the established model, judging whether the precision requirement is met, and if so, completing modeling;
c) if not, re-acquiring m 'based on the interactive verification sequential sampling strategy'X n' new sample points (U)i',αj') Wherein i 'belongs to (1,2, …, m'), and j 'belongs to (1,2, …, n'), and x is calculated by applying finite element methodkIn (U)i',αj',Δxkl) The electromagnet under the condition attracts the torque and goes to step 4).
2. The modeling method of claim 1, wherein: and 4) sampling points are selected by Latin hypercube sampling in the step 4).
3. The modeling method of claim 1, wherein: the objective function in the step 4) is
Wherein G isiA finite element calculation result representing output characteristics corresponding to the ith sampling point in the N new sampling points; f (X)i) An approximate model of the load switch electromagnetic mechanism containing unknown coefficients.
4. The modeling method of claim 1, wherein: the indexes for evaluating the error and the precision of the established model in the step b) are as follows: root mean square error RMSE and complex correlation coefficient R2The calculation formulas are respectively as follows:
where k is the sample size for model validation, yiIn response to the actual value of the value,
for the predicted values obtained from the approximation model,
is the true response mean.
5. The modeling method of claim 1, wherein: the interactive verification sequential sampling strategy in the step c) is
Wherein CVE (U)i',αj') Represents the interactive proof error function, d ((U)i',αj'),(Ui,αj) Represents the distance of the new sample point from the original sample point, i 'e (1,2, …, m'), and j 'e (1,2, …, n').
6. A method for calculating the electromagnetic property of a load switch electromagnetic mechanism is characterized by comprising the following steps: the method comprises the following steps:
1) selecting at least six key nodes influencing the transient process of the electromagnetic mechanism, establishing a functional relation between output characteristics of the nodes, and determining a specific form of a custom function reflecting the relation between the output characteristics of the load switch electromagnetic mechanism and a process variable;
2) selecting m multiplied by n interpolation nodes (U) according to the inflection point position of the suction curve of the load switchi,αj) Wherein (U)i,αj) The voltage and the armature rotation angle of a certain point on an attraction curve of the electromagnetic mechanism are represented by m and n respectively representing the number of the voltage and the rotation angle, i belongs to (1,2, …, m), and j belongs to (1,2, …, n); at each key design parameter x of electromagnetic mechanismk∈(x1,x2,…,xp) Within the tolerance range of (1), q nodes are uniformly selected, delta xklDenotes x at node l ∈ (1,2, …, q)kThe amount of change in (c);
3) calculating key design parameter x by using finite element methodkIn (U)i,αj,Δxkl) Obtaining an interpolation node (U) by the electromagnetic torque of the electromagnetic mechanism under the condition and by a spline interpolation methodi,αj) Variation Δ x of each key design parameterklAnd electromagnetic forceThe relationship of the moment variation;
4) reselecting at least six sampling points in each interpolation node forming area, calculating the electromagnetic torque at the reselected sampling points by using a finite element method, taking the electromagnetic torque as an actual value of the electromagnetic torque, substituting the reselected sampling points into the self-defined function determined in the step 1), calculating unknown coefficients in the self-defined function by taking 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 as a target function, and finishing the establishment of the load switch electromagnetic mechanism model;
5) substituting the variable quantity of each design parameter of the electromagnetic mechanism and the process variable node parameter to be calculated into the model determined in the step 4) for calculation to obtain the electromagnetic moment of the process variable node;
in the step 1), an interpolation method is adopted to establish a functional relation among output characteristics of each node, and the expression is as follows:
wherein, F (U)i,αj) Is (U)i,αj) Output characteristics of the load switch electromagnetic mechanism; (U)i,αj) For any process variable node, at a selected process variable node (U)i0,αj0)、(Ui1,αj0)、(Ui0,αj1) And (U)i1,αj1) Within the enclosed area;
an interpolation function for representing each point weight coefficient, the mathematical expression of which depends on the functional relationship between the process variable and the output characteristic of the electromagnetic mechanism and comprises influence coefficients related to the voltage U and the rotation angle α;
the method also comprises an optimization process of the established model, which specifically comprises the following steps:
a) regenerating a plurality of random samples within a parameter tolerance range, and calculating the output characteristics of the electromagnetic mechanism corresponding to each sample through a finite element method and the model determined in the step 4) respectively;
b) taking the calculation result of the finite element method as a true value, evaluating the error and precision of the established model, judging whether the precision requirement is met, and if so, completing modeling;
c) if not, re-acquiring m 'x n' new sample points (U) based on the cross-validation sequential sampling strategyi',αj') Wherein i 'belongs to (1,2, …, m'), and j 'belongs to (1,2, …, n'), and x is calculated by applying finite element methodkIn (U)i',αj',Δxkl) The electromagnet under the condition attracts the torque and goes to step 4).
7. The method for calculating the electromagnetic property of the electromagnetic mechanism of the load switch according to claim 6, wherein the method comprises the following steps: the objective function in the step 4) is
Wherein G isiA finite element calculation result representing output characteristics corresponding to the ith sampling point in the N new sampling points; f (X)i) An approximate model of the load switch electromagnetic mechanism containing unknown coefficients.
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| CN101354978A (en) * | 2007-12-31 | 2009-01-28 | 唐华山 | Wetness contact intelligence control power load switch |
| CN103576121A (en) * | 2013-10-31 | 2014-02-12 | 惠州学院 | Smart electric meter constant magnetic detecting system and method |
| CN105353246A (en) * | 2015-11-18 | 2016-02-24 | 中国电力科学研究院 | Load elements and testing method of low voltage releasing characteristics of load switching elements |
| CN105429131A (en) * | 2015-12-07 | 2016-03-23 | 中国电力科学研究院 | Load model building method of considering load frequency characteristics |
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| CN101354978A (en) * | 2007-12-31 | 2009-01-28 | 唐华山 | Wetness contact intelligence control power load switch |
| CN103576121A (en) * | 2013-10-31 | 2014-02-12 | 惠州学院 | Smart electric meter constant magnetic detecting system and method |
| CN105353246A (en) * | 2015-11-18 | 2016-02-24 | 中国电力科学研究院 | Load elements and testing method of low voltage releasing characteristics of load switching elements |
| CN105429131A (en) * | 2015-12-07 | 2016-03-23 | 中国电力科学研究院 | Load model building method of considering load frequency characteristics |
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