CN112966389A - Multi-objective optimization method for electromagnetic force horizontal characteristics of proportional electromagnet - Google Patents

Multi-objective optimization method for electromagnetic force horizontal characteristics of proportional electromagnet Download PDF

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CN112966389A
CN112966389A CN202110279721.0A CN202110279721A CN112966389A CN 112966389 A CN112966389 A CN 112966389A CN 202110279721 A CN202110279721 A CN 202110279721A CN 112966389 A CN112966389 A CN 112966389A
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欧阳宇文
刘鹏
邓家福
吴钢
胡林
刘玉玲
涂洪涛
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Changsha University of Science and Technology
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Abstract

The invention discloses a multi-objective optimization method for the electromagnetic force horizontal characteristics of a proportional electromagnet, and belongs to the field of proportional electromagnet optimization design. The method adopts a method of combining numerical simulation and an approximate model, simultaneously considers the influence of the all-condition of the proportional electromagnet, takes the integral average value of the electromagnetic force and the integral standard deviation of the electromagnetic force as optimization targets, constructs a functional relation between design variables and the optimization targets based on the approximate model, replaces a complex numerical simulation model or a physical test, can implement optimization with low cost and high efficiency, simultaneously screens an optimized solution according to the integral optimization degree of the electromagnetic force level characteristic of the proportional electromagnet, avoids the blindness of subjective solution selection, can effectively improve the electromagnetic force level characteristic of the proportional electromagnet, and improves the performance of proportional electromagnet products.

Description

Multi-objective optimization method for electromagnetic force horizontal characteristics of proportional electromagnet
Technical Field
The invention belongs to the field of proportional electromagnet optimization design, and particularly relates to a multi-objective optimization method for the electromagnetic force horizontal characteristics of a proportional electromagnet.
Background
The proportional electromagnet as the electro-mechanical converter of electro-hydraulic proportional control element is an automatic control element with wide application, can make the liquid pressure and flow change continuously and proportionally with the control signal, and has the advantages of low cost, simple structure, good universality and strong anti-pollution capability. In order to realize the proportional control characteristic of the proportional electromagnet, the proportional electromagnet is required to have good horizontal displacement-force characteristic (horizontal characteristic for short), namely, in the working stroke of the armature, when the working current is kept stable, the output electromagnetic force of the electromagnet is kept constant. The optimization of the electromagnetic force horizontal characteristic of the prior proportional electromagnet usually depends on the experience of a designer, the structural parameters are repeatedly modified, and a limited number of parameter combinations are arranged for experiment or numerical simulation analysis so as to select the parameter combination with the best performance, so that the optimization efficiency and the optimization degree are low; on the other hand, the relationship among the performance target, the constraint and the design variable of the electromagnetic force level characteristic of the proportional electromagnet cannot be expressed explicitly, the optimization problem may be non-convex and strong non-linear, the global optimal solution is difficult to search for by directly optimizing based on the system numerical simulation analysis, and meanwhile, the calculation analysis cost is high, so that the improvement of the electromagnetic force level characteristic of the proportional electromagnet faces certain challenges.
Disclosure of Invention
In order to solve the problems, the invention provides a simple, reliable and efficient multi-objective optimization method for the electromagnetic force horizontal characteristics of the proportional electromagnet.
The purpose of the invention is realized as follows:
step 1, determining design parameters;
step 2, determining constraint conditions;
step 3, defining an optimization objective function;
step 4, constructing a functional relation between the design parameters and each optimization target;
step 5, determining a multi-objective optimization mathematical model of the electromagnetic force horizontal characteristic of the proportional electromagnet;
and 6, solving the multi-objective optimization mathematical model of the electromagnetic force horizontal characteristic of the proportional electromagnet, and screening and determining an optimization design solution.
As a further elaboration of the above optimization method:
further, the setting of the design parameters in step 1 includes:
cone angle alpha, cone radius r1Length of cone l1Radius of skeleton r2End face gap l when armature reaches maximum displacement2The design parameters of the multi-objective optimization problem of the electromagnetic force horizontal characteristics of the proportional electromagnet are
X＝(α,r1,l1,r2,l2)。
Further, the constraint condition in step 2 is specifically a value range of each design parameter:
Xl≤X≤Xu；
Xlto lower limit of design parameter, XuThe upper limit of the design parameter.
Further, the optimization objective function in step 3 is specifically:
maximum proportion electromagnet electromagnetic force integral average value
Figure BDA0002977664930000021
Minimum proportion electromagnet electromagnetic force integral standard deviation
Figure BDA0002977664930000022
Namely, it is
Figure BDA0002977664930000023
Further, in step 3The integral average value of the electromagnetic force
Figure BDA0002977664930000024
Integral standard deviation of electromagnetic force
Figure BDA0002977664930000025
The specific calculation method comprises the following steps:
3.1 determining the working current of the proportional electromagnet and the working stroke range of the armature, the working range of the working current is marked as [ ia,id]The working stroke of the armature is denoted as [ x ]a,xd]And equally dividing and dispersing the full working condition plane formed by the working current and the working stroke to further obtain corresponding discrete working condition points (i) in the full working condition planen,xm) Wherein inExpressed as the operating current ia,id]Any working current, x, corresponding to the discrete halvingmIs a working stroke range [ xa,xd]Equally dividing any corresponding working stroke;
3.2 obtaining the electromagnetic force corresponding to each discrete operating point under the design parameter X through numerical simulation;
3.3 calculating the average value F (X, i) of the electromagnetic force of the discrete operating points with the same working current and different working strokes under the design parameter Xn)a，
Figure BDA0002977664930000026
Wherein F (X, i)n,xm) Representing discrete operating points (i) at a design parameter Xn,xm) Corresponding electromagnetic force, f represents the number of equally divided working strokes;
3.4 calculating the integral average value of the electromagnetic force of the proportional electromagnet under the design parameter X
Figure BDA0002977664930000027
Figure BDA0002977664930000028
Figure BDA00029776649300000215
Wherein e represents the number of equally divided portions of the operating current, knRepresents the average value F (X, i) of the electromagnetic force for each operating currentn)aAnd k is not less than 0n≤1，
Figure BDA0002977664930000029
3.5 calculating the standard deviation F (X, i) of the electromagnetic force of the discrete operating points with the same working current and different working strokes under the design parameter Xn)s，
Figure BDA00029776649300000210
3.6 calculating the integral standard deviation of the electromagnetic force of the proportional electromagnet under the design parameter X
Figure BDA00029776649300000211
Figure BDA00029776649300000212
Figure BDA00029776649300000214
wnRepresents the standard deviation F (X, i) of the electromagnetic force at each operating currentn)sAnd 0 is not less than wn≤1，
Figure BDA00029776649300000213
Further, the specific method for constructing the functional relationship between the design parameters and the optimization objectives in step 4 includes:
4.1 sampling a design space by adopting an optimal Latin hypercube test design method to obtain a sample point set A;
4.2 obtaining the electromagnetic force of each sample point corresponding to the discrete working point in the sample point set A through numerical simulation, and further calculating to obtain the integral average value of the corresponding electromagnetic force
Figure BDA0002977664930000031
Electromagnetic force integrationStandard deviation of
Figure BDA0002977664930000032
Forming a response point set B;
4.3 respectively adopting a radial basis function model, a neural network model, a Kriging model and a quadratic polynomial model to interpolate or fit data taking the sample point set A and the response point set B as samples, and constructing a design parameter X and an electromagnetic force integral average value
Figure BDA0002977664930000033
Integral standard deviation of electromagnetic force
Figure BDA0002977664930000034
And selecting the approximate model with the highest precision as a final functional relation by using a Leave-one-out cross-validation (LOOCV), namely the functional relation between the design parameters and each optimization target
Figure BDA0002977664930000035
Further, the multi-objective optimization mathematical model of the horizontal characteristics of the proportional electromagnet in the step 5 is specifically expressed as follows:
Figure BDA0002977664930000036
further, the step 6 of solving the multi-objective optimization mathematical model of the electromagnetic force horizontal characteristic of the proportional electromagnet and screening and determining the optimization design solution specifically comprises the following steps:
6.1 solving a proportional electromagnet electromagnetic force horizontal characteristic multi-target optimization mathematical model by adopting a genetic algorithm, an ant colony algorithm or other optimization algorithms to obtain a Pareto solution set;
6.2 calculating to obtain the integral standard deviation of the electromagnetic force of each solution in the Pareto solution set
Figure BDA0002977664930000037
Degree of reduction and overall average value of electromagnetic force
Figure BDA0002977664930000038
And is defined as the overall optimization degree P (X) of the electromagnetic force level characteristic of the proportional electromagnett) Screening for Overall optimization degree P (X)t) The maximum time corresponding solution is used as the optimization design solution, wherein the overall optimization degree P (X)t) The concrete expression is as follows:
Figure BDA0002977664930000039
wherein the content of the first and second substances,
Figure BDA00029776649300000310
in order to optimize the integral standard deviation of the front electromagnetic force,
Figure BDA00029776649300000311
in order to optimize the overall standard deviation after optimization,
Figure BDA00029776649300000312
in order to optimize the overall average value of the front electromagnetic force,
Figure BDA00029776649300000313
for optimizing the overall average value of the post-electromagnetic force, X0Representing electromagnet design parameters, X, before optimizationtRepresents any electromagnet design parameter of the Pareto solution set optimization front edge.
The invention has the advantages that: the multi-objective optimization method for the electromagnetic force horizontal characteristics of the proportional electromagnet adopts a method of combining numerical simulation and an approximate model, simultaneously considers the influence of all working conditions of the proportional electromagnet, takes the integral average value of the electromagnetic force and the integral standard deviation of the electromagnetic force as optimization targets, constructs a functional relation between design variables and the optimization targets based on the approximate model, replaces a complex numerical simulation model or a physical test, can implement optimization with low cost and high efficiency, screens optimization solutions according to the integral optimization degree of the electromagnetic force horizontal characteristics of the proportional electromagnet, avoids the blindness of subjective solution selection, can effectively improve the electromagnetic force horizontal characteristics of the proportional electromagnet, and improves the performance of proportional electromagnet products.
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FIG. 1 is an inventive flow chart;
FIG. 2 is a schematic diagram of design parameters;
FIG. 3 is a schematic view of the full operating face of a proportional electromagnet.
Detailed Description
The embodiment is described in detail with reference to fig. 1, and a specific embodiment of the multi-objective optimization method for the electromagnetic force level characteristics of the proportional electromagnet is as follows.
Step one, determining design parameters
The design parameters mainly include: cone angle alpha, cone radius r1Length of cone l1Radius of skeleton r2End face gap l when armature reaches maximum displacement2As shown in fig. 2, the design parameters of the multi-objective optimization problem of the horizontal characteristics of the proportional electromagnet are as follows:
X＝(α,r1,l1,r2,l2)。
step two, determining constraint conditions
The determined constraint condition is specifically the value range of each design parameter, namely
Xl≤X≤Xu，
Wherein, XlTo lower limit of design parameter, XuThe upper limit of the design parameter.
Step three, defining an optimization objective function
The overall average value of the electromagnetic force of the electromagnet with maximized proportion
Figure BDA0002977664930000041
Minimum proportion electromagnet electromagnetic force integral standard deviation
Figure BDA0002977664930000042
As an objective function, i.e.
Figure BDA0002977664930000043
Wherein the electromagnetic force is an integral average value
Figure BDA0002977664930000044
Integral standard deviation of electromagnetic force
Figure BDA0002977664930000045
The specific calculation method comprises the following steps:
3.1 determining the working current of the proportional electromagnet and the working stroke range of the armature, the working range of the working current is marked as [ ia,id]The working stroke of the armature is denoted as [ x ]a,xd]And equally dividing and dispersing the full working condition plane formed by the working current and the working stroke to further obtain corresponding discrete working condition points (i) in the full working condition planen,xm) Wherein inExpressed as the operating current ia,id]Any working current, x, corresponding to the discrete halvingmIs a working stroke range [ xa,xd]Equally dividing any corresponding working stroke;
3.2 obtaining the electromagnetic force corresponding to each discrete operating point under the design parameter X through numerical simulation;
3.3 calculating the average value F (X, i) of the electromagnetic force of the discrete operating points with the same working current and different working strokes under the design parameter Xn)a，
Figure BDA0002977664930000046
Wherein F (X, i)n,xm) Representing discrete operating points (i) at a design parameter Xn,xm) Corresponding electromagnetic force, f represents the number of equally divided working strokes;
3.4 calculating the integral average value of the electromagnetic force of the proportional electromagnet under the design parameter X
Figure BDA0002977664930000051
Figure BDA0002977664930000052
Figure BDA00029776649300000515
Wherein e represents the number of equally divided portions of the operating current, knRepresents the average value F (X, i) of the electromagnetic force for each operating currentn)aAnd k is not less than 0n≤1，
Figure BDA0002977664930000053
3.5 calculating the standard deviation F (X, i) of the electromagnetic force of the discrete operating points with the same working current and different working strokes under the design parameter Xn)s，
Figure BDA0002977664930000054
3.6 calculating the integral standard deviation of the electromagnetic force of the proportional electromagnet under the design parameter X
Figure BDA0002977664930000055
Figure BDA0002977664930000056
Figure BDA00029776649300000516
wnRepresents the standard deviation F (X, i) of the electromagnetic force at each operating currentn)sAnd 0 is not less than wn≤1，
Figure BDA0002977664930000057
Step four, constructing a functional relation between the design parameters and the optimization target
4.1 sampling a design space by adopting an optimal Latin hypercube test design method to obtain a sample point set A;
4.2 obtaining the electromagnetic force of each sample point corresponding to the discrete working point in the sample point set A through numerical simulation, and further calculating to obtain the integral average value of the corresponding electromagnetic force
Figure BDA0002977664930000058
Electromagnetic forceIntegral standard deviation
Figure BDA0002977664930000059
Forming a response point set B;
4.3 respectively adopting a radial basis function model, a neural network model, a Kriging model and a quadratic polynomial model to interpolate or fit data taking the sample point set A and the response point set B as samples, and constructing a design parameter X and an electromagnetic force integral average value
Figure BDA00029776649300000510
Integral standard deviation of electromagnetic force
Figure BDA00029776649300000511
And selecting the approximate model with the highest precision as a final functional relation by using a Leave-one-out cross-validation (LOOCV), namely the functional relation between the design parameters and each optimization target
Figure BDA00029776649300000512
Step five, determining proportion electromagnet electromagnetic force horizontal characteristic multi-objective optimization mathematical model
The multi-objective optimization mathematical model of the horizontal characteristics of the proportional electromagnet is specifically expressed as follows:
Figure BDA00029776649300000513
step six, solving the multi-objective optimization mathematical model of the electromagnetic force horizontal characteristic of the proportional electromagnet, and screening and determining an optimization design solution
6.1 solving a proportional electromagnet electromagnetic force horizontal characteristic multi-target optimization mathematical model by adopting a genetic algorithm, an ant colony algorithm or other optimization algorithms to obtain a Pareto solution set;
6.2 calculating to obtain the integral standard deviation of the electromagnetic force of each solution in the Pareto solution set
Figure BDA00029776649300000514
Degree of reduction and overall average value of electromagnetic force
Figure BDA0002977664930000061
And is defined as the overall optimization degree P (X) of the electromagnetic force level characteristic of the proportional electromagnett) Screening for Overall optimization degree P (X)t) The maximum time corresponding solution is used as the optimization design solution, wherein the overall optimization degree P (X)t) The concrete expression is as follows:
Figure BDA0002977664930000062
wherein the content of the first and second substances,
Figure BDA0002977664930000063
in order to optimize the integral standard deviation of the front electromagnetic force,
Figure BDA0002977664930000064
in order to optimize the overall standard deviation after optimization,
Figure BDA0002977664930000065
in order to optimize the overall average value of the front electromagnetic force,
Figure BDA0002977664930000066
for optimizing the overall average value of the post-electromagnetic force, X0Representing electromagnet design parameters, X, before optimizationtRepresents any electromagnet design parameter of the Pareto solution set optimization front edge.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (9)

1. The multi-objective optimization method for the electromagnetic force horizontal characteristics of the proportional electromagnet is characterized by comprising the following steps:
step 1, determining design parameters;
step 2, determining constraint conditions;
step 3, defining an optimization objective function;
step 4, constructing a functional relation between the design parameters and each optimization target;
step 5, determining a multi-objective optimization mathematical model of the electromagnetic force horizontal characteristic of the proportional electromagnet;
and 6, solving the multi-objective optimization mathematical model of the electromagnetic force horizontal characteristic of the proportional electromagnet, and screening and determining an optimization design solution.
2. The method for multi-objective optimization of electromagnetic force level characteristics of proportional electromagnets according to claim 1, wherein the design parameters in step 1 comprise: cone angle alpha, cone radius r1Length of cone l1Radius of skeleton r2End face gap l when armature reaches maximum displacement2The design parameters of the multi-objective optimization problem of the electromagnetic force horizontal characteristics of the proportional electromagnet are
X＝(α,r1,l1,r2,l2)。
3. The method for multi-objective optimization of electromagnetic force level characteristics of proportional electromagnets according to claim 1, wherein the constraint condition in the step 2 is a value range of each design parameter, that is, a value range of each design parameter
Xl≤X≤Xu；
Wherein, XlTo lower limit of design parameter, XuThe upper limit of the design parameter.
4. The multi-objective optimization method for the electromagnetic force level characteristics of the proportional electromagnet according to claim 1, wherein the optimization objective function in the step 3 is specifically as follows: maximum proportion electromagnet electromagnetic force integral average value
Figure FDA0002977664920000011
Minimum proportion electromagnet electromagnetic force integral standard deviation
Figure FDA0002977664920000012
Namely, it is
Figure FDA0002977664920000013
5. The method as claimed in claim 4, wherein the electromagnetic force level characteristic of the proportional electromagnet is optimized by multiple targets, and the electromagnetic force integral average value is
Figure FDA0002977664920000014
Integral standard deviation of electromagnetic force
Figure FDA0002977664920000015
The specific calculation method comprises the following steps:
firstly, determining the working current of proportional electromagnet and the working stroke range of armature, and recording the working range of working current as [ ia,id]The working stroke of the armature is denoted as [ x ]a,xd]And equally dividing and dispersing the full working condition plane formed by the working current and the working stroke to further obtain corresponding discrete working condition points (i) in the full working condition planen,xm) Wherein inExpressed as the operating current ia,id]Any working current, x, corresponding to the discrete halvingmIs a working stroke range [ xa,xd]Equally dividing any corresponding working stroke;
obtaining electromagnetic force corresponding to each discrete operating point under the design parameter X through numerical simulation;
thirdly, calculating the average value F (X, i) of the electromagnetic force of discrete operating points with equal working current and different working strokes under the design parameter Xn)aThe expression is
Figure FDA0002977664920000016
Wherein F (X, i)n,xm) Indicates separation at design parameter XFree operating point (i)n,xm) Corresponding electromagnetic force, f represents the number of equally divided working strokes;
fourthly, calculating the integral average value of the electromagnetic force of the proportional electromagnet under the design parameter X
Figure FDA0002977664920000021
The expression is
Figure FDA0002977664920000022
Figure FDA0002977664920000023
Wherein e represents the number of equally divided portions of the operating current, knRepresents the average value F (X, i) of the electromagnetic force for each operating currentn)aAnd k is not less than 0n≤1，
Figure FDA0002977664920000024
Fifthly, calculating the standard deviation F (X, i) of the electromagnetic force of discrete operating points with equal working current and different working strokes under the design parameter Xn)sThe expression is
Figure FDA0002977664920000025
Sixthly, calculating the integral standard deviation of the electromagnetic force of the proportional electromagnet under the design parameter X
Figure FDA0002977664920000026
The expression is
Figure FDA0002977664920000027
Figure FDA0002977664920000028
Wherein wnRepresents the standard deviation F (X, i) of the electromagnetic force at each operating currentn)sAnd 0 is not less than wn≤1，
Figure FDA0002977664920000029
6. The multi-objective optimization method for the electromagnetic force level characteristics of the proportional electromagnet according to claim 1, wherein the specific method for establishing the functional relationship between the design parameters and the optimization objectives in the step 4 is as follows:
4.1 sampling a design space by adopting an optimal Latin hypercube test design method to obtain a sample point set A;
4.2 obtaining the electromagnetic force of each sample point corresponding to the discrete working point in the sample point set A through numerical simulation, and further calculating to obtain the integral average value of the corresponding electromagnetic force
Figure FDA00029776649200000210
Integral standard deviation of electromagnetic force
Figure FDA00029776649200000211
Forming a response point set B;
4.3 respectively adopting a radial basis function model, a neural network model, a Kriging model and a quadratic polynomial model to interpolate or fit data taking the sample point set A and the response point set B as samples, and constructing a design parameter X and an electromagnetic force integral average value
Figure FDA00029776649200000212
Integral standard deviation of electromagnetic force
Figure FDA00029776649200000213
And selecting the approximate model with the highest precision as a final functional relation by using a Leave-one-out cross-validation (LOOCV), namely the functional relation between the design parameters and each optimization target
Figure FDA00029776649200000214
7. The method for multi-objective optimization of the electromagnetic force horizontal characteristics of the proportional electromagnet according to claim 1, wherein the multi-objective optimization mathematical model of the horizontal characteristics of the proportional electromagnet in the step 5 is specifically expressed as follows:
Figure FDA00029776649200000215
8. the method for multi-objective optimization of the electromagnetic force level characteristics of the proportional electromagnet according to claim 1, wherein the specific method for solving the multi-objective optimization mathematical model of the electromagnetic force level characteristics of the proportional electromagnet in the step 6 comprises the following steps: and solving the proportional electromagnet electromagnetic force horizontal characteristic multi-objective optimization mathematical model by adopting a genetic algorithm, an ant colony algorithm or other optimization algorithms to obtain a Pareto solution set of the optimization design.
9. The multi-objective optimization method for the electromagnetic force horizontal characteristics of the proportional electromagnet according to claim 1, wherein the specific method for screening and determining the optimal design solution in the step 6 is as follows:
6.1 solving a proportional electromagnet electromagnetic force horizontal characteristic multi-target optimization mathematical model by adopting a genetic algorithm, an ant colony algorithm or other optimization algorithms to obtain a Pareto solution set;
6.2 calculating to obtain the integral standard deviation of the electromagnetic force of each solution in the Pareto solution set
Figure FDA0002977664920000031
Degree of reduction and overall average value of electromagnetic force
Figure FDA0002977664920000032
And is defined as the overall optimization degree P (X) of the electromagnetic force level characteristic of the proportional electromagnett) Screening for Overall optimization degree P (X)t) The maximum time corresponding solution is used as the optimization design solution, wherein the overall optimization degree P (X)t) The concrete expression is as follows:
Figure FDA0002977664920000033
wherein the content of the first and second substances,
Figure FDA0002977664920000034
in order to optimize the integral standard deviation of the front electromagnetic force,
Figure FDA0002977664920000035
in order to optimize the overall standard deviation after optimization,
Figure FDA0002977664920000036
in order to optimize the overall average value of the front electromagnetic force,
Figure FDA0002977664920000037
for optimizing the overall average value of the post-electromagnetic force, X0Representing electromagnet design parameters, X, before optimizationtRepresents any electromagnet design parameter of the Pareto solution set optimization front edge.
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