CN113051735A - Proportional electromagnet electromagnetic force linear characteristic optimization method - Google Patents
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Abstract
The invention discloses a method for optimizing the electromagnetic force linear characteristic of a proportional electromagnet, and belongs to the field of proportional electromagnet optimization design. The method firstly determines design parameters and constraint conditions, and defines a complex correlation coefficient between current and electromagnetic forceR 2As an optimization objective; then, establishing a functional relation between the design parameters and the optimization target; re-determining the ratioAn electromagnetic force linear characteristic optimization mathematical model of the electromagnet is described; and finally, solving an optimized mathematical model of the electromagnetic force linear characteristic of the proportional electromagnet to obtain an optimized design solution. The optimization method adopts a method of combining numerical simulation and an approximate model, can optimize the linear characteristic of the electromagnetic force of the proportional electromagnet with low cost and high efficiency, and is beneficial to improving the product performance of the proportional electromagnet.
Description
Technical Field
The invention belongs to the field of proportional electromagnet optimization design, and particularly relates to a method for optimizing electromagnetic force linear 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 electromagnetic force of the proportional electromagnet is required to have good linear characteristic, that is, the control current and the output electromagnetic force have good linear relation. The optimization of the linear characteristic of the electromagnetic force of the proportional electromagnet at present 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 linear 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 linear characteristic of the proportional electromagnet faces certain challenges.
Disclosure of Invention
In order to solve the problems, the invention provides a high-efficiency and low-cost optimization method for the electromagnetic force linear characteristic of the proportional electromagnet.
The purpose of the invention is realized as follows:
a proportional electromagnet electromagnetic force linear characteristic optimization method comprises the following steps:
step 1, determining design parameters;
step 2, determining constraint conditions;
step 3, defining a complex correlation coefficient R between the current and the electromagnetic force2As an optimization objective;
step 4, constructing a functional relation between the design parameters and the optimization target;
step 5, determining a proportional electromagnet electromagnetic force linear characteristic optimization mathematical model;
and 6, solving a proportional electromagnet electromagnetic force linear characteristic optimization mathematical model to obtain 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 optimization problem of the electromagnetic force linear characteristic of the proportional electromagnet are as follows:
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, in step 3, the complex correlation coefficient R between the current and the electromagnetic force2The 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]Is divided into any corresponding onesOperating current, xmIs 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)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(X,in)a) Wherein
In the above formula, F (X, i)n,xm) Represents the discrete operating point (i) under the design parameter Xn,xm) Corresponding electromagnetic force, f represents the number of equally divided working strokes;
3.4 sample points (i) using least squaresn,F(X,in)a) Linear regression is carried out to obtain a complex correlation coefficient R2(X)。
Further, the specific method for constructing the functional relationship between the design parameters and the optimization target in the step 4 comprises the following steps:
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 corresponding complex correlation coefficient R2Forming 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 a complex correlation coefficient R2And selecting the approximate model with the highest precision as the final functional relation by using a Leave-one-out cross-validation (LOOCV), namely the design parameter and the optimization targetFunctional relationship R of2(X)。
Further, the linear characteristic optimization mathematical model of the proportional electromagnet in the step 5 is expressed as:
further, in step 6, the linear characteristic optimization mathematical model of the electromagnetic force of the proportional electromagnet is solved, and the obtained optimization design solution is as follows:
solving a proportional electromagnet electromagnetic force linear characteristic optimization mathematical model by adopting a genetic algorithm, an ant colony algorithm or other optimization algorithms, and taking the maximum R2And (X) taking the corresponding X as an optimization design solution.
The invention has the advantages that: the method for optimizing the electromagnetic force linear characteristic of the proportional electromagnet adopts a method of combining numerical simulation and an approximate model and uses a complex correlation coefficient R between current and electromagnetic force2As an optimization target, a functional relation between a design variable and the optimization target is constructed based on an approximate model, a complex numerical simulation model or a physical test is replaced, the linear characteristic of the electromagnetic force of the proportional electromagnet can be optimized with low cost and high efficiency, and the product performance of the proportional electromagnet is improved.
Drawings
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 method for optimizing the electromagnetic force linear characteristic of the proportional electromagnet according to the present embodiment 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 optimization problem of the electromagnetic force linearity of the proportional electromagnetThe parameter is measured as
X＝(α,r1,l1,r2,l2)。
Step two, determining constraint conditions
The constraint is specifically the value range of each design parameter, i.e.
Xl≤X≤Xu；
Wherein, XlTo lower limit of design parameter, XuThe upper limit of the design parameter.
Step three, defining complex correlation coefficient R between current and electromagnetic force2As optimization objectives
Complex correlation coefficient R between current and electromagnetic force2The 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]Any working stroke corresponding to the equal division and dispersion is shown in figure 3;
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)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(X,in)a) Wherein
In the formula, F (X, i)n,xm) Representing discrete work under design parameter XPoint of Condition (i)n,xm) Corresponding electromagnetic force, f represents the number of equally divided working strokes;
3.4 sample points (i) using least squaresn,F(X,in)a) Linear regression is carried out to obtain a complex correlation coefficient R2(X)。
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 corresponding complex correlation coefficient R2Forming 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 a complex correlation coefficient R2And 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 R between the design parameters and the optimization target2(X)。
Step five, determining proportion electromagnet electromagnetic force linear characteristic optimization mathematical model
The proportional electromagnet electromagnetic force linear characteristic optimization mathematical model is specifically expressed as follows:
and step six, solving a proportional electromagnet electromagnetic force linear characteristic optimization mathematical model to obtain an optimization design solution.
Solving a proportional electromagnet electromagnetic force linear characteristic optimization mathematical model by adopting a genetic algorithm, an ant colony algorithm or other optimization algorithms, and taking the maximum R2And (X) taking the corresponding X as an optimization design solution.
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 (7)
1. A method for optimizing the electromagnetic force linear characteristic of a proportional electromagnet is characterized by comprising the following steps:
step 1, determining design parameters;
step 2, determining constraint conditions;
step 3, defining a complex correlation coefficient R between the current and the electromagnetic force2As an optimization objective;
step 4, constructing a functional relation between the design parameters and the optimization target;
step 5, determining a proportional electromagnet electromagnetic force linear characteristic optimization mathematical model;
and 6, solving a proportional electromagnet electromagnetic force linear characteristic optimization mathematical model to obtain an optimization design solution.
2. The method for optimizing the electromagnetic force linear characteristic of the proportional electromagnet according to claim 1, wherein the design parameters in the 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 problem of optimizing the electromagnetic force linear characteristic of the proportional electromagnet are
X＝(α,r1,l1,r2,l2)。
3. The method for optimizing the electromagnetic force linear characteristic of the proportional electromagnet according to claim 1, wherein the method comprises the following steps: the constraint condition in step 2 is specifically the value range of each design parameter, that is to say
Xl≤X≤Xu，
Wherein, XlTo lower limit of design parameter, XuThe upper limit of the design parameter.
4. The method as claimed in claim 1, wherein the step 3 is performed by using a complex correlation coefficient R between the current and the electromagnetic force2The 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)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(X,in)a) Wherein
In the formula, F (X, i)n,xm) Represents the discrete operating point (i) under the design parameter Xn,xm) Corresponding electromagnetic force, f represents the number of equally divided working strokes;
3.4 sample points (i) using least squaresn,F(X,in)a) Linear regression is carried out to obtain a complex correlation coefficient R2(X)。
5. The method for optimizing the linear characteristic of the electromagnetic force of the proportional electromagnet according to claim 1, wherein the step 4 of constructing the functional relationship between the design parameters and the optimization target comprises the following specific steps:
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 corresponding complex correlation coefficient R2Forming 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 a complex correlation coefficient R2And selecting the approximate model with the highest precision as the functional relation R between the design parameters and the optimization target by using a Leave-one-out cross-validation (LOOCV) method2(X)。
6. The method for optimizing the linear characteristic of the electromagnetic force of the proportional electromagnet as claimed in claim 1, wherein the mathematical model for optimizing the linear characteristic of the proportional electromagnet in the step 5 is expressed as:
7. the method for optimizing the linear characteristic of the electromagnetic force of the proportional electromagnet according to claim 1, wherein the step 6 of solving the mathematical model for optimizing the linear characteristic of the electromagnetic force of the proportional electromagnet is characterized in that the specific method for obtaining the optimal design solution is as follows: solving a proportional electromagnet electromagnetic force horizontal characteristic optimization mathematical model by adopting a genetic algorithm, an ant colony algorithm or other optimization algorithms, and taking the maximum R2And (X) taking the corresponding X as an optimization design solution.
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