CN113051734B - Electromagnetic force average variation coefficient-based electromagnetic force horizontal characteristic optimization method for proportional electromagnet - Google Patents
Electromagnetic force average variation coefficient-based electromagnetic force horizontal characteristic optimization method for proportional electromagnet Download PDFInfo
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Abstract
The invention discloses a method for optimizing electromagnetic force horizontal characteristics of a proportional electromagnet based on an electromagnetic force average variation coefficient, and belongs to the field of optimal design of proportional electromagnets. Firstly, determining design parameters and constraint conditions, and defining an electromagnetic force average variation coefficient as an optimization target; then constructing a functional relation between the design parameters and the optimization targets; determining an electromagnetic force horizontal characteristic optimization mathematical model of the proportional electromagnet; and finally, solving an electromagnetic force horizontal characteristic optimization mathematical model of the proportional electromagnet to obtain an optimal design solution. The optimization method combines a numerical simulation method and an approximate model method, can efficiently optimize electromagnetic force horizontal characteristics of the proportional electromagnet at low cost, and is beneficial to improving product performance of the proportional electromagnet.
Description
Technical Field
The invention belongs to the field of optimization design of proportional electromagnets, and particularly relates to a method for optimizing electromagnetic force horizontal characteristics of proportional electromagnets based on electromagnetic force average variation coefficients.
Background
The electro-mechanical conversion device using the proportional electromagnet as the electro-hydraulic proportional control element is an automatic control element with very wide application, can enable the pressure and the flow of liquid flow to continuously and proportionally follow the control signal to change, and has the advantages of low cost, simple structure, good universality, strong pollution resistance and the like. In order to realize the proportional control characteristic of the proportional electromagnet, it is required to have a good horizontal displacement-force characteristic (abbreviated as horizontal characteristic), that is, the output electromagnetic force of the electromagnet is kept constant while the operating current is kept stable during the operating stroke of the armature. The optimization of electromagnetic force horizontal characteristics of the proportional electromagnet at present often depends on experience of a designer, structural parameters are repeatedly modified, and a limited number of parameter combinations are arranged for experimental or numerical simulation analysis so as to select the parameter combination with the best performance, and the optimization efficiency and the optimization degree are low; on the other hand, the relation among the electromagnetic force horizontal characteristic performance target, constraint and design variable of the proportional electromagnet cannot be expressed explicitly, the optimization problem can be non-convex and strong nonlinear, the global optimal solution is difficult to search for by optimizing based on system numerical simulation analysis, and meanwhile, the calculation and analysis cost is high, so that the improvement of the electromagnetic force horizontal characteristic of the proportional electromagnet faces a certain challenge.
Disclosure of Invention
In order to solve the problems, the invention provides an efficient and low-cost optimization method for electromagnetic force horizontal characteristics of a proportional electromagnet based on an average variation coefficient of electromagnetic force.
The purpose of the invention is realized in the following way:
the electromagnetic force level characteristic optimization method of the proportional electromagnet based on the electromagnetic force average variation coefficient comprises the following steps:
step 1, determining design parameters;
step 2, determining constraint conditions;
step 3, defining the electromagnetic force average variation coefficient of the proportional electromagnetAs an optimization target;
step 4, constructing a functional relation between the design parameters and the optimization targets;
step 5, determining an electromagnetic force horizontal characteristic optimization mathematical model of the proportional electromagnet;
and step 6, solving a mathematical model for optimizing electromagnetic force horizontal characteristics of the proportional electromagnet to obtain an optimal design solution.
As a further illustration of the above optimization method:
further, the setting design parameters in step 1 includes:
cone angle alpha, cone radius r 1 Length of cone l 1 Radius r of skeleton 2 End face gap l when armature reaches maximum displacement 2 The design parameters of the electromagnetic force horizontal characteristic optimization problem of the proportional electromagnet are as follows
X＝(α,r 1 ,l 1 ,r 2 ,l 2 )。
Further, the constraint condition in the step 2 is specifically a value range of each design parameter:
X l ≤X≤X u ，
X l to the lower limit of design parameters, X u Is the upper limit of the design parameters.
Further, the electromagnetic force average variation coefficient of the proportional electromagnet in the step 3The specific calculation method of (1) comprises the following steps:
3.1 determining the operating current of the proportional electromagnet and the operating travel range of the armature, the operating range of the operating current being designated [ i ] a ,i d ]The working stroke of the armature is denoted as x a ,x d ]And equally dividing and dispersing the full working condition plane formed by the working current and the working stroke, thereby obtaining corresponding discrete working condition points (i) n ,x m ) Wherein i is n Represented as operating current i a ,i d ]Is equally divided into any working current and x m For working range of travel [ x ] a ,x d ]Any working stroke corresponding to the equal-divided discrete;
3.2, obtaining electromagnetic force corresponding to each discrete working point under the design parameter X through numerical simulation;
3.3 calculating the average force F (X, i) of the discrete working points with different working strokes and equal working currents under the design parameter X n ) a ，Wherein F (X, i) n ,x m ) Representing discrete operating points (i) at design parameter X n ,x m ) The corresponding electromagnetic force, f, represents the number of parts of the working stroke divided equally;
3.4 calculating the electromagnetic force standard deviation F (X, i) of the discrete working points with different working strokes and equal working currents under the design parameter X n ) s The expression is
3.5 calculating the electromagnetic force variation coefficient of the discrete working points with different working strokes and equal working currents under the design parameter X
3.6 electromagnetic force variation coefficient CV (X, i) at each operating current under the design parameter X n ) Averaging to obtain electromagnetic force average variation coefficient under design parameter XWherein e represents the number of parts in which the operating current is divided equally, k n Represents the variation coefficient CV (X, i) of electromagnetic force for each working current n ) And 0.ltoreq.k n ≤1，/>
Further, the specific method for constructing the functional relationship between the design parameters and the optimization targets in the step 4 includes:
4.1, sampling a design space by adopting an optimal Latin hypercube experimental design method to obtain a sample point set A;
4.2 obtaining electromagnetic force of each sample point in the sample point set A corresponding to the discrete working condition point through numerical simulation, and further calculating to obtain a corresponding electromagnetic force average variation coefficientConstructing a response point set B;
4.3 respectively adopting radial basis function model, neural network model, kriging model and quadratic polynomial model to respectively interpolate or fit the data using sample point set A and response point set B as sample so as to construct design parameter X and electromagnetic force average variation coefficientThe function relation between the two models is selected by using a Leave-one-out cross-validation (LOOCV) method, and the approximation model with highest precision is selected as the final function relation, namely the function relation between the design parameters and the optimization targets>
Further, in the step 5, the horizontal characteristic optimization mathematical model of the proportional electromagnet is expressed as follows:
further, in the step 6, solving a mathematical model for optimizing electromagnetic force horizontal characteristics of the proportional electromagnet, and obtaining an optimal design solution comprises the following specific steps:
adopting genetic algorithm, ant colony algorithm or other optimization algorithm to solve electromagnetic force horizontal characteristic optimization mathematical model of proportional electromagnet, and taking the minimum valueThe corresponding X is used as an optimal design solution.
The invention has the advantages that: the electromagnetic force level characteristic optimization method of the proportional electromagnet based on the electromagnetic force average variation coefficient adopts a method of combining numerical simulation and an approximate model, considers the influence of all working conditions of the proportional electromagnet, takes the electromagnetic force integral variation coefficient as an optimization target, constructs a functional relation between a design variable and the optimization target based on the approximate model, replaces a complex numerical simulation model or a physical test, can optimize the electromagnetic force level characteristic of the proportional electromagnet with low cost and high efficiency, and is beneficial to improving the product performance of the proportional electromagnet.
Drawings
FIG. 1 is a flow chart of the invention;
FIG. 2 is a schematic diagram of design parameters;
FIG. 3 is a schematic diagram of the full operating mode of the proportional electromagnet.
Detailed Description
The embodiment will be described in detail with reference to fig. 1, and the method for optimizing electromagnetic force horizontal characteristics of a proportional electromagnet based on an average variation coefficient of electromagnetic force according to the present embodiment is as follows.
Step one, determining design parameters
The design parameters mainly comprise: cone angle alpha, cone radius r 1 Length of cone l 1 Radius r of skeleton 2 End face gap l when armature reaches maximum displacement 2 As shown in fig. 2, the design parameters of the optimization problem of the horizontal characteristic of the proportional electromagnet are as follows:
X＝(α,r 1 ,l 1 ,r 2 ,l 2 )。
step two, determining constraint conditions
The constraint is specifically the range of values of the design parameters, i.e
X l ≤X≤X u ，
Wherein X is l To the lower limit of design parameters, X u Is the upper limit of the design parameters.
Step three, defining the electromagnetic force average variation coefficient of the proportional electromagnetAs an optimization target
Average coefficient of variation of electromagnetic forceThe specific calculation method of (a) is as follows:
3.1 determining the operating current of the proportional electromagnet and the operating travel range of the armature, the operating range of the operating current being designated [ i ] a ,i d ]The working stroke of the armature is denoted as x a ,x d ]And equally dividing and dispersing the full working condition plane formed by the working current and the working stroke, thereby obtaining corresponding discrete working condition points (i) n ,x m ) I.e. discrete points in the working area shown in fig. 3, where i n Represented as operating current i a ,i d ]Is equally divided into any working current and x m For working range of travel [ x ] a ,x d ]Is equally divided into any corresponding working strokes, as shown in fig. 3.
3.2, obtaining electromagnetic force corresponding to each discrete working point under the design parameter X through numerical simulation;
3.3 calculating the average force F (X, i) of the discrete working points with different working strokes and equal working currents under the design parameter X n ) a The expression is
Wherein F (X, i) n ,x m ) Representing discrete operating points (i) at design parameter X n ,x m ) The corresponding electromagnetic force, f, represents the number of parts of the working stroke divided equally;
3.4 calculating the electromagnetic force standard deviation F (X, i) of the discrete working points with different working strokes and equal working currents under the design parameter X n ) s The expression is
3.5 calculating the electromagnetic force variation coefficient CV (X, i) of the discrete working points with different working strokes and equal working currents under the design parameter X n ) The expression is
3.6 electromagnetic force variation coefficient CV (X, i) at each operating current under the design parameter X n ) Averaging to obtain electromagnetic force average variation coefficient under design parameter XThe expression is
Wherein e represents the number of parts in which the operating current is divided equally, k n Represents the variation coefficient CV (X, i) of electromagnetic force for each working current n ) And 0.ltoreq.k n ≤1，
Step four, constructing a functional relation between design parameters and optimization targets
4.1, sampling a design space by adopting an optimal Latin hypercube experimental design method to obtain a sample point set A;
4.2 obtaining electromagnetic force of each sample point in the sample point set A corresponding to the discrete working condition point through numerical simulation, and further calculating to obtain a corresponding electromagnetic force average variation coefficientConstructing 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 respectively interpolate or fit the data taking the sample point set A and the response point set B as samples, so as to construct a design parameter X and an average variation coefficientThe function relation between the two is selected by a Leave-one-out cross-validation (LOOCV) method, and the approximation model with the highest precision is selected as the final function relation, namely the design parameter and the LOOCVFunctional relation between optimization goals->
Step five, determining an optimized mathematical model of electromagnetic force horizontal characteristics of proportional electromagnet
The horizontal characteristic optimization mathematical model of the proportional electromagnet is specifically expressed as follows:
and step six, solving a mathematical model for optimizing electromagnetic force horizontal characteristics of the proportional electromagnet to obtain an optimal design solution.
Adopting genetic algorithm, ant colony algorithm or other optimization algorithm to solve electromagnetic force horizontal characteristic optimization mathematical model of proportional electromagnet, and taking the minimum valueThe corresponding X is used as an optimal design solution.
The present invention is capable of other and further embodiments and its several details are capable of modification and variation in light of the present invention, as will be apparent to those skilled in the art, without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (6)
1. The electromagnetic force horizontal characteristic optimization method of the proportional electromagnet based on the electromagnetic force average variation coefficient is characterized by comprising the following steps of:
step 1, determining a design parameter X;
step 2, determining constraint conditions;
step 3, defining the electromagnetic force average variation coefficient of the proportional electromagnetAs an optimization target;
step 4, constructing a functional relation between the design parameters and the optimization targets;
step 5, determining an electromagnetic force horizontal characteristic optimization mathematical model of the proportional electromagnet;
step 6, solving a mathematical model for optimizing electromagnetic force horizontal characteristics of the proportional electromagnet to obtain an optimal design solution;
the electromagnetic force average variation coefficient of the proportional electromagnet in the step 3The specific calculation method of (a) is as follows:
(1) determining the working current of the proportional electromagnet and the working stroke range of the armature, wherein the working range of the working current is denoted as [ i ] a ,i d ]The working stroke of the armature is denoted as x a ,x d ]And equally dividing and dispersing the full working condition plane formed by the working current and the working stroke, thereby obtaining corresponding discrete working condition points (i) n ,x m ) Wherein i is n Represented as operating current i a ,i d ]Is equally divided into any working current and x m For working range of travel [ x ] a ,x d ]Any working stroke corresponding to the equal-divided discrete;
(2) obtaining electromagnetic force corresponding to each discrete working point under the design parameter X through numerical simulation;
(3) respectively calculating the electromagnetic force average value F (X, i) of discrete working points with different working strokes and equal working currents under the design parameter X n ) a The expression isWherein F (X, i) n ,x m ) Representing discrete operating points (i) at design parameter X n ,x m ) The corresponding electromagnetic force, f, represents the number of parts of the working stroke divided equally;
(4) respectively calculating electromagnetic force standard deviation F (X, i) of discrete working points with different working strokes and equal working currents under design parameter X n ) s The expression is
(5) Respectively calculating electromagnetic force variation coefficients of discrete working points with different working strokes and equal working currents under the design parameter X
(6) Coefficient of variation CV (X, i) of electromagnetic force at each operating current under design parameter X n ) Averaging to obtain electromagnetic force average variation coefficient under design parameter XWherein e represents the number of parts in which the operating current is divided equally, k n Represents the variation coefficient CV (X, i) of electromagnetic force for each working current n ) And 0.ltoreq.k n ≤1，/>
2. The method for optimizing electromagnetic force level characteristics of a proportional electromagnet based on electromagnetic force average variation coefficient according to claim 1, wherein the design parameters in step 1 include:
cone angle alpha, cone radius r 1 Length of cone l 1 Radius r of skeleton 2 End face gap l when armature reaches maximum displacement 2 The design parameters of the electromagnetic force horizontal characteristic optimization problem of the proportional electromagnet are as follows
X＝(α,r 1 ,l 1 ,r 2 ,l 2 )。
3. The method for optimizing electromagnetic force horizontal characteristics of proportional electromagnet based on electromagnetic force average variation coefficient as set forth in claim 1, wherein said constraint condition in step 2 is specifically a range of values of each design parameter, namely
X l ≤X≤X u ，
Wherein X is l To the lower limit of design parameters, X u To design parametersThe upper limit of the number.
4. The method for optimizing electromagnetic force level characteristics of a proportional electromagnet based on electromagnetic force average variation coefficients according to claim 1, wherein the specific method for constructing a functional relation between design parameters and optimization targets in step 4 is as follows:
4.1, sampling a design space by adopting an optimal Latin hypercube experimental design method to obtain a sample point set A;
4.2 obtaining electromagnetic force of each sample point in the sample point set A corresponding to the discrete working condition point through numerical simulation, and further calculating to obtain a corresponding electromagnetic force average variation coefficientConstructing a response point set B;
4.3 respectively adopting radial basis function model, neural network model, kriging model and quadratic polynomial model to respectively interpolate or fit the data using sample point set A and response point set B as sample so as to construct design parameter X and electromagnetic force average variation coefficientThe function relation between the two models is selected by a leave-one-out cross-validation (LOOCV) method, and the approximate model with highest precision in the radial basis function model, the neural network model, the Kriging model and the quadratic polynomial model is selected as the function relation between the design parameters and the optimization targets>
5. The method for optimizing electromagnetic force horizontal characteristics of a proportional electromagnet based on electromagnetic force average variation coefficient according to claim 1, wherein the mathematical model for optimizing electromagnetic force horizontal characteristics of a proportional electromagnet in step 5 is expressed as:
6. the method for optimizing electromagnetic force horizontal characteristics of the proportional electromagnet based on the electromagnetic force average variation coefficient according to claim 1, wherein the specific method for solving the mathematical model for optimizing electromagnetic force horizontal characteristics of the proportional electromagnet to obtain the optimal design solution is as follows:
adopting genetic algorithm, ant colony algorithm or other optimization algorithm to solve electromagnetic force horizontal characteristic optimization mathematical model of proportional electromagnet, and taking the minimum valueThe corresponding X is used as an optimal design solution.
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| CN113051735A (en) * | 2021-03-16 | 2021-06-29 | 长沙理工大学 | Proportional electromagnet electromagnetic force linear characteristic optimization method |
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| CN110911084A (en) * | 2019-12-11 | 2020-03-24 | 长沙理工大学 | Series-parallel permanent magnet and electromagnetic hybrid excitation high-speed electromagnetic actuator |
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