CN112884355A - Proportional electromagnet electromagnetic force linear characteristic evaluation method based on multiple correlation coefficients - Google Patents

Proportional electromagnet electromagnetic force linear characteristic evaluation method based on multiple correlation coefficients Download PDF

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CN112884355A
CN112884355A CN202110279685.8A CN202110279685A CN112884355A CN 112884355 A CN112884355 A CN 112884355A CN 202110279685 A CN202110279685 A CN 202110279685A CN 112884355 A CN112884355 A CN 112884355A
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欧阳宇文
刘鹏
邓家福
吴钢
胡林
刘玉玲
赵晋东
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Changsha University of Science and Technology
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Abstract

The invention discloses a method for evaluating the linear characteristic of electromagnetic force of a proportional electromagnet based on a complex correlation coefficient, and belongs to the field of performance evaluation and analysis of the proportional electromagnet. Firstly, dividing a full working condition plane formed by the working current of an electromagnet and the working stroke of an armature; then obtaining the electromagnetic force output by all discrete working condition points through simulation or experiment means; calculating the average value of the electromagnetic force of the discrete working condition points under the same working current to obtain a regression sample point; performing linear regression fitting on the sample points to obtain a regression equation; obtaining the overall complex correlation coefficient between the current and the electromagnetic force according to the overall average calculation or the weighted average calculation of the working area under different working conditionsR 2(ii) a According to the overall complex correlation coefficientR 2And (4) judging the linear characteristic of the electromagnetic force of the proportional electromagnet. The method is simple and reliable, can objectively and quantitatively evaluate the linear characteristic of the electromagnetic force of the proportional electromagnet, and can be used for evaluating the electromagnetic force linear characteristic of the proportional electromagnetThe method is used for measuring the performance of the proportional electromagnet and comparing and analyzing the performance of different proportional electromagnets.

Description

Proportional electromagnet electromagnetic force linear characteristic evaluation method based on multiple correlation coefficients
Technical Field
The invention belongs to the field of performance evaluation and analysis of proportional electromagnets, and particularly relates to a method for evaluating the linear characteristics of the electromagnetic force of a proportional electromagnet based on a complex correlation coefficient.
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. However, currently, the evaluation of the linear characteristic of the electromagnetic force of the proportional electromagnet is mostly based on subjective qualitative judgment of a current-force curve diagram (chengda. research of novel disc-type proportional electromagnet [ D ]. university of zhejiang, 2009 ]), and an objective and quantitative evaluation index is lacked, so that the product performance of the proportional electromagnet is not easy to be measured, and the performance of different proportional electromagnets is not easy to compare and analyze.
Disclosure of Invention
In order to solve the problems of the existing evaluation method, the invention provides a simple, reliable, objective and quantitative evaluation method for the electromagnetic force linear characteristic of the proportional electromagnet.
The purpose of the invention is realized as follows:
the method for evaluating the electromagnetic force linear characteristic of the proportional electromagnet based on the complex correlation coefficient comprises the following steps:
step 1, dividing a full-working-condition plane;
step 2, obtaining the electromagnetic force of the discrete working condition points;
step 3, calculating the overall complex correlation coefficient R between the current and the electromagnetic force2；
Step 4, according to the integral complex correlation coefficient R between the current and the electromagnetic force2The magnitude of the value of (a) is used for judging the linearity of the electromagnetic force of the proportional electromagnetAnd (4) characteristics.
As a further explanation of the above evaluation method:
further, the dividing method of the full working condition plane in the step 1 comprises the following steps:
1.1, 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 marked as [ ia,id]The working stroke of the armature is denoted as [ x ]a,xd]；
1.2, equally dividing and dispersing the full working condition plane formed by the working current and the working stroke, and further obtaining 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]Is equally divided into corresponding arbitrary working strokes.
Further, the method for obtaining the electromagnetic force of the discrete operating point through a simulation or experiment means in the step 2 comprises the following steps:
2.1, adjusting the working stroke to a certain discrete working condition point value and then keeping the working stroke unchanged;
2.2, sequentially adjusting the working current to different discrete working condition point values, and respectively measuring corresponding electromagnetic force;
and 2.3, adjusting the working stroke to another discrete working condition point value, keeping the working stroke unchanged, and repeating the process to obtain the electromagnetic force of all the discrete working condition points.
Further, the overall complex correlation coefficient R between the current and the electromagnetic force in step 32The calculation method comprises the following steps:
3.1, respectively calculating the average value F (i) of the electromagnetic force of the discrete working points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) Wherein
Figure BDA0002977664630000021
In the formula F (i)n,xm) Representing discrete operating points (i)n,xm) Corresponding electromagnetic force, f represents the number of equally divided working strokes;
3.2 sample point (i) by least squares or partial least squaresn,F(in)a) Linear regression is carried out to obtain a linear regression equation of current-electromagnetic force
Figure BDA0002977664630000022
Wherein
Figure BDA0002977664630000023
Is inCorresponding regression average electromagnetic force predicted values, wherein k and b are regression coefficients;
3.3, calculating the average value of the electromagnetic force under different working strokes of the same current
Figure BDA0002977664630000024
The expression is
Figure BDA0002977664630000025
F(in)aThe average value of the electromagnetic force of different discrete working condition points of the working stroke under the same working current is, and e represents the number of equally divided working currents;
3.4 calculating the sum of the squares of the total deviations SST, which is expressed as
Figure BDA0002977664630000026
Wherein F (i)t)aThe average value of the electromagnetic force of discrete working condition points with different working strokes for equal working current;
3.5, calculating the regression square sum SSR, wherein the expression is
Figure BDA0002977664630000027
Wherein
Figure BDA0002977664630000028
The regression average electromagnetic force predicted value corresponding to the discrete operating point with the same working current and different working strokes;
3.6, calculating to obtain an integral complex correlation coefficient R2The expression is
Figure BDA0002977664630000029
Further, the overall complex correlation coefficient R between the current and the electromagnetic force in step 32The calculation method comprises the following steps:
3.1, respectively calculating the average value F (i) of the electromagnetic force of the discrete working points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) Wherein
Figure BDA0002977664630000031
In the formula F (i)n,xm) Representing discrete operating points (i)n,xm) Corresponding electromagnetic force, xm∈[xa,xd]F represents the number of equally divided working strokes;
3.2, defining the working area of primary and secondary current, and the interval [ ia,ib)、(ic,id]For the current minor operating region, interval [ ib,ic]Is a current main working area, wherein ia、ib、ic、id∈[ia,id]And i isa<ib<ic<id；
3.3 sample points (i) of each current working area by using least square method or partial least square methodn,F(in)a) Performing linear regression to obtain three groups of current-electromagnetic force linear regression equations:
Figure BDA0002977664630000032
Figure BDA0002977664630000033
Figure BDA0002977664630000034
wherein
Figure BDA0002977664630000035
Respectively i in different current working regionsp、iq、ijCorresponding regression mean electromagnetic force prediction value, kp、bp、kq、bq、kj、bjIs a regression coefficient;
3.4, respectively calculating the average value of the average electromagnetic force in the same current working area under the same current working condition
Figure BDA0002977664630000036
Figure BDA0002977664630000037
Wherein
Figure BDA0002977664630000038
ip∈[ia,ib) And g represents that the operating point falls within the operating stroke region [ i ]a,ib) The number of (2);
Figure BDA0002977664630000039
iq∈[ib,ic]and h represents that the operating point falls within the operating stroke region [ i ]b,ic) The number of (2);
Figure BDA00029776646300000310
ij∈(ic,id]and t represents that the operating point falls within the operating stroke region (i)c,id]The number of (2);
3.5, respectively calculating the sum of squared deviations SST of each current working areaab、SSTbc、SSTcdWherein
Figure BDA00029776646300000311
ip∈[ia,ib)；
Figure BDA00029776646300000312
iq∈[ib,ic]；
Figure BDA00029776646300000313
ij∈(ic,id]；
Wherein F (i)p)a、F(iq)a、F(ij)aThe average value of the electromagnetic force of discrete working condition points with equal working current and different working strokes in each current working area;
3.6, calculating the regression square sum SST of each current working area respectivelyab、SSTbc、SSTcdWherein
Figure BDA0002977664630000041
ip∈[ia,ib)；
Figure BDA0002977664630000042
iq∈[ib,ic]；
Figure BDA0002977664630000043
ij∈(ic,id]；
Wherein
Figure BDA0002977664630000044
Respectively obtaining regression average electromagnetic force predicted values corresponding to any current working condition point in the current working area;
3.7 respectively calculating the complex correlation coefficient R of each current working area2 ab、R2 bc、R2 cdWherein
Figure BDA0002977664630000045
Figure BDA0002977664630000046
Figure BDA0002977664630000047
3.8 setting weighting coefficients of each current working area, ia,ib)、[ib,ic]、(ic,id]The weighting coefficients of the corresponding complex correlation coefficients are respectively K1、K2、K3；
3.9, carrying out weighted calculation on the electromagnetic force complex correlation coefficient of each working current region according to the current region to obtain the electromagnetic force integral complex correlation coefficient R2The expression is R2＝K1·R2 ab+K2·R2 bc+K3·R2 cd。
Further, the overall complex correlation coefficient R between the current and the electromagnetic force in step 32The calculation method comprises the following steps:
3.1, define the working area of the primary and secondary travel, the interval [ xa,xb)、(xc,xd]For the secondary working area of the journey, interval [ xb,xc]Is the main working area of the stroke, wherein xa、xb、xc、xd∈[xa,xd]And x isa<xb<xc<xd；
3.2 setting weighting coefficients of each stroke working area, the stroke working area [ xa,xb)、[xb,xc]、(xc,xd]The weighting coefficients of the corresponding complex correlation coefficients are S1、S2、S3；
3.3, respectively calculating the electromagnetic force weighted average value F (i) of the discrete operating points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) Wherein
Figure BDA0002977664630000048
In the formula F (i)n,xm) Representing discrete operating points (i)n,xm) Corresponding electromagnetic force, xp∈[xa,xb)，xq∈[xb,xc]，xj∈(xc,xd]U, v and w each represents F (i)n,xm) Falling in the current working region [ x ]a,xb)、[xb,xc]、(xc,xd]The number of (2);
3.4 sample point (i) by least squares or partial least squaresn,F(in)a) Linear regression is carried out to obtain a linear regression equation of current-electromagnetic force
Figure BDA0002977664630000049
Wherein
Figure BDA00029776646300000410
Is inCorresponding regression average electromagnetic force predicted values, wherein k and b are regression coefficients;
3.5 calculating the difference between the same currentsAverage value of electromagnetic force weighted average value under working stroke
Figure BDA00029776646300000411
The expression is
Figure BDA0002977664630000051
Wherein F (i)n)aThe average value of the electromagnetic force of different discrete working condition points of the working stroke under the same working current is, and e represents the number of equally divided working currents;
3.6 calculating the sum of squared deviations SST, which is expressed as
Figure BDA0002977664630000052
Wherein F (i)t)aThe average value of the electromagnetic force of discrete working condition points with different working strokes for equal working current;
3.7 calculating regression Square sum SSR with the expression of
Figure BDA0002977664630000053
Wherein
Figure BDA0002977664630000054
The regression average electromagnetic force predicted value corresponding to the discrete operating point with the same working current and different working strokes;
3.8, calculating to obtain an integral complex correlation coefficient R2The expression is
Figure BDA0002977664630000055
Further, the overall complex correlation coefficient R between the current and the electromagnetic force in step 32The calculation method comprises the following steps:
3.1, define the working area of the primary and secondary travel, the interval [ xa,xb)、(xc,xd]For the secondary working area of the journey, interval [ xb,xc]Is the main working area of the stroke, wherein xa、xb、xc、xd∈[xa,xd]And x isa<xb<xc<xd；
3.2 setting weighting coefficients of each stroke working area, the stroke working area [ xa,xb)、[xb,xc]、(xc,xd]The weighting coefficients of the corresponding complex correlation coefficients are S1、S2、S3；
3.3, respectively calculating the electromagnetic force weighted average value F (i) of the discrete operating points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) The expression is
Figure BDA0002977664630000056
In the formula F (i)n,xm) Representing discrete operating points (i)n,xm) Corresponding electromagnetic force, xp∈[xa,xb)，xq∈[xb,xc]，xj∈(xc,xd]U, v and w each represents F (i)n,xm) Falling in the current working region [ x ]a,xb)、[xb,xc]、(xc,xd]The number of (2);
3.4, defining the working area of primary and secondary current, and the interval [ ia,ib)、(ic,id]For the current minor operating region, interval [ ib,ic]Is a current main working area, wherein ia、ib、ic、id∈[ia,id]And i isa<ib<ic<id；
3.5 working area of each current by least squares or partial least squaresSample point (i)n,F(in)a) Performing linear regression to obtain three groups of current-electromagnetic force linear regression equations:
Figure BDA0002977664630000057
Figure BDA0002977664630000058
Figure BDA0002977664630000061
wherein
Figure BDA0002977664630000062
Respectively i in different current working regionsp、iq、ijCorresponding regression mean electromagnetic force prediction value, kp、bp、kq、bq、kj、bjIs a regression coefficient;
3.6, respectively calculating the average value of the weighted average electromagnetic force in the same current working area under the same current working condition
Figure BDA0002977664630000063
Figure BDA0002977664630000064
Wherein
Figure BDA0002977664630000065
ip∈[ia,ib) And g represents that the operating point falls within the operating stroke region [ i ]a,ib) The number of (2);
Figure BDA0002977664630000066
iq∈[ib,ic]h represents a workerThe operating point falls within the working stroke region [ i ]b,ic) The number of (2);
Figure BDA0002977664630000067
ij∈(ic,id]and t represents that the operating point falls within the operating stroke region (i)c,id]The number of (2);
3.7, respectively calculating the sum of squared deviations SST of each current working areaab、SSTbc、SSTcdWherein
Figure BDA0002977664630000068
ip∈[ia,ib)；
Figure BDA0002977664630000069
iq∈[ib,ic]；
Figure BDA00029776646300000610
ij∈(ic,id]；
Wherein F (i)p)a、F(iq)a、F(ij)aThe average value of the electromagnetic force of discrete working condition points with equal working current and different working strokes in each current working area;
3.8, respectively calculating the regression square sum SST of each current working areaab、SSTbc、SSTcdWherein
Figure BDA00029776646300000611
ip∈[ia,ib)；
Figure BDA00029776646300000612
iq∈[ib,ic]；
Figure BDA00029776646300000613
ij∈(ic,id]；
Wherein
Figure BDA00029776646300000614
Respectively obtaining regression average electromagnetic force predicted values corresponding to any current working condition point in the current working area;
3.9 respectively calculating the complex correlation coefficient R of each current working area2 ab、R2 bc、R2 cdWherein
Figure BDA00029776646300000615
Figure BDA00029776646300000616
Figure BDA00029776646300000617
3.10 setting weighting coefficients of each current working area, current working area [ ia,ib)、[ib,ic]、(ic,id]The weighting coefficients of the corresponding complex correlation coefficients are respectively K1、K2、K3；
3.11, carrying out weighted calculation on the electromagnetic force complex correlation coefficient of each working current region according to the current region to obtain the electromagnetic force integral complex correlation coefficient R2The expression is R2＝K1·R2 ab+K2·R2 bc+K3·R2 cd。
Further, the method for determining the linear characteristic of the electromagnetic force of the proportional electromagnet in step 4 includes: overall complex correlation coefficient between current and electromagnetic forceR2The closer to 1, the better the linear characteristic of the electromagnetic force of the proportional electromagnet is; integral complex correlation coefficient R between current and electromagnetic force2The closer to 0, the worse the linear characteristic of the proportional electromagnet electromagnetic force.
The invention has the advantages that: the method for evaluating the linear characteristic of the electromagnetic force of the proportional electromagnet quantitatively judges the linear characteristic of the electromagnetic force of the proportional electromagnet by adopting the overall complex correlation coefficient between the current and the electromagnetic force, considers the influence of the proportional electromagnet under different working currents and working stroke working conditions, combines a method of regional weighting calculation, and can comprehensively, objectively and quantitatively evaluate the linear characteristic of the electromagnetic force of the proportional electromagnet. The method can be widely used for measuring the product performance of the proportional electromagnet and comparing and analyzing the performance of electromagnets with different proportions.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a flow chart of calculating a complex correlation coefficient from a ensemble averaged electromagnetic force;
FIG. 3 is a schematic view of the full operating face of a proportional electromagnet;
FIG. 4 is a flow chart of evaluation based on current partition weighting;
FIG. 5 is a schematic diagram of current-partition-based electromagnetic force complex correlation coefficient weighting;
FIG. 6 is a flow chart of evaluation based on trip partition weighting;
FIG. 7 is a schematic diagram of electromagnetic force weighting based on trip zones;
fig. 8 is a flow chart of evaluation based on current and trip partition quadratic weighting.
Detailed Description
In order to more specifically describe the present invention, the following detailed description is provided for the technical solution of the present invention with reference to the accompanying drawings and the specific embodiments.
As shown in fig. 1, an embodiment of the present invention provides a method for evaluating linear characteristics of electromagnetic force of a proportional electromagnet based on a complex correlation coefficient, and the specific implementation manner is as follows.
The first embodiment is as follows:
as shown in fig. 2, the present embodiment specifically includes the following steps:
step one, dividing a full-working-condition plane
1.1 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]As shown in fig. 3;
1.2 equally dividing and dispersing the whole working condition plane formed by the working current and the working stroke, and further obtaining corresponding discrete working condition points (i) in the whole working condition planen,xm) I.e. discrete points in the working area shown in FIG. 3, where inExpressed as the operating current ia,id]Any working current, x, corresponding to the discrete halvingmIs a working stroke range [ xa,xd]Is equally divided into corresponding arbitrary working strokes.
Step two, obtaining the electromagnetic force of the discrete operating point
The method for obtaining the electromagnetic force of the discrete working condition point by means of simulation or experiment specifically comprises the following steps:
2.1 adjusting the working stroke to a certain discrete working condition point value and then keeping the working stroke unchanged;
2.2 adjusting the working current to different discrete working condition point values in sequence, and respectively measuring corresponding electromagnetic force;
and 2.3, adjusting the working stroke to another discrete operating point value, keeping the working stroke unchanged, and repeating the process to obtain the electromagnetic force of all the discrete operating points.
Step three, calculating the integral complex correlation coefficient R between the current and the electromagnetic force2
3.1 calculating the average value F (i) of the electromagnetic force of the discrete operating points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) Wherein
Figure BDA0002977664630000081
In the formula F (i)n,xm) Representing dispersionOperating point (i)n,xm) Corresponding electromagnetic force, f represents the number of equally divided working strokes;
3.2 applying least squares or partial least squares to the sample points (i)n,F(in)a) Linear regression is carried out to obtain a linear regression equation of current-electromagnetic force
Figure BDA0002977664630000082
Wherein
Figure BDA0002977664630000083
Is inCorresponding regression average electromagnetic force predicted values, wherein k and b are regression coefficients;
3.3 calculating the average value of the electromagnetic force under different working strokes of the same current
Figure BDA0002977664630000084
The expression is
Figure BDA0002977664630000085
Wherein F (i)n)aThe average value of the electromagnetic force of different discrete working condition points of the working stroke under the same working current is, and e represents the number of equally divided working currents;
3.4 calculate the sum of the squares of the total deviations SST, expressed as
Figure BDA0002977664630000086
Wherein F (i)t)aThe average value of the electromagnetic force of discrete working condition points with different working strokes for equal working current;
3.5 calculating the regression Square sum SSR, the expression is
Figure BDA0002977664630000087
Wherein
Figure BDA0002977664630000088
The regression average electromagnetic force predicted value corresponding to the discrete operating point with the same working current and different working strokes;
3.6 calculating to obtain an integral complex correlation coefficient R2The expression is
Figure BDA0002977664630000091
Step four, according to the integral complex correlation coefficient R between the current and the electromagnetic force2The linear characteristic of the electromagnetic force of the proportional electromagnet is judged
Integral complex correlation coefficient R between current and electromagnetic force2The closer to 1, the better the linear characteristic of the electromagnetic force of the proportional electromagnet is; integral complex correlation coefficient R between current and electromagnetic force2The closer to 0, the worse the linear characteristic of the proportional electromagnet electromagnetic force.
The second embodiment is as follows:
referring to fig. 4, the difference between the present embodiment and the first embodiment is that the overall complex correlation coefficient R between the current and the electromagnetic force is calculated in the third step2The method specifically comprises the following steps: 3.1 calculating the average value F (i) of the electromagnetic force of the discrete operating points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) Wherein
Figure BDA0002977664630000092
In the formula F (i)n,xm) Representing discrete operating points (i)n,xm) Corresponding electromagnetic force, xm∈[xa,xd]F represents the number of equally divided working strokes;
3.2 defining the working area of primary and secondary current, the interval [ ia,ib)、(ic,id]For the current minor operating region, interval [ ib,ic]Is an electric currentA main working area wherein ia、ib、ic、id∈[ia,id]And i isa<ib<ic<id；
3.3 sample points (i) for each current operating region by using least squares or partial least squaresn,F(in)a) Performing linear regression to obtain three groups of current-electromagnetic force linear regression equations:
Figure BDA0002977664630000093
Figure BDA0002977664630000094
Figure BDA0002977664630000095
wherein
Figure BDA0002977664630000096
Respectively i in different current working regionsp、iq、ijCorresponding regression mean electromagnetic force prediction value, kp、bp、kq、bq、kj、bjIs a regression coefficient;
3.4 calculating the average value of the average electromagnetic force in the same current working area under the same current working condition
Figure BDA0002977664630000097
Figure BDA0002977664630000098
Wherein
Figure BDA0002977664630000099
ip∈[ia,ib) And g represents that the operating point falls on the operating lineRange region [ i ]a,ib) The number of (2);
Figure BDA00029776646300000910
iq∈[ib,ic]and h represents that the operating point falls within the operating stroke region [ i ]b,ic) The number of (2);
Figure BDA0002977664630000101
ij∈(ic,id]and t represents that the operating point falls within the operating stroke region (i)c,id]The number of (2);
3.5 calculating the sum of squared deviations SST of each current working area respectivelyab、SSTbc、SSTcdWherein
Figure BDA0002977664630000102
ip∈[ia,ib)；
Figure BDA0002977664630000103
iq∈[ib,ic]；
Figure BDA0002977664630000104
ij∈(ic,id]；
Wherein F (i)p)a、F(iq)a、F(ij)aThe average value of the electromagnetic force of discrete working condition points with equal working current and different working strokes in each current working area;
3.6 calculating the regression Square sum SST of each current working areaab、SSTbc、SSTcdWherein
Figure BDA0002977664630000105
ip∈[ia,ib)；
Figure BDA0002977664630000106
iq∈[ib,ic]；
Figure BDA0002977664630000107
ij∈(ic,id]；
Wherein
Figure BDA0002977664630000108
Respectively obtaining regression average electromagnetic force predicted values corresponding to any current working condition point in the current working area;
3.7 respectively calculating the complex correlation coefficient R of each current working area2 ab、R2 bc、R2 cdWherein
Figure BDA0002977664630000109
Figure BDA00029776646300001010
Figure BDA00029776646300001011
3.8 setting weighting coefficients for each current working region, current working region [ ia,ib)、[ib,ic]、(ic,id]Weighting factor K of the corresponding complex correlation coefficient1、K2、K3As shown in fig. 5;
3.9 weighting the complex correlation coefficient of the electromagnetic force in each working current region according to the current region to obtain the overall complex correlation coefficient R between the current and the electromagnetic force2The expression is R2＝K1·R2 ab+K2·R2 bc+K3·R2 cd。
The third concrete implementation mode:
referring to fig. 6, the difference between the present embodiment and the first embodiment is that the overall complex correlation coefficient R between the current and the electromagnetic force is calculated in the third step2The method specifically comprises the following steps:
3.1 defining the working area of the primary and secondary strokes, the interval [ xa,xb)、(xc,xd]For the secondary working area of the journey, interval [ xb,xc]Is the main working area of the stroke, wherein xa、xb、xc、xd∈[xa,xd]And x isa<xb<xc<xd；
3.2 setting weighting coefficients of each travel working area, travel working area [ xa,xb)、[xb,xc]、(xc,xd]Weighting coefficient S of corresponding complex correlation coefficient1、S2、S3As shown in fig. 7;
3.3 calculating the weighted average F (i) of the electromagnetic force at the discrete operating points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) Wherein
Figure BDA0002977664630000111
In the formula F (i)n,xm) Representing discrete operating points (i)n,xm) Corresponding electromagnetic force, xp∈[xa,xb)，xq∈[xb,xc]，xj∈(xc,xd]U, v and w each represents F (i)n,xm) Falling in the current working region [ x ]a,xb)、[xb,xc]、(xc,xd]The number of (2);
3.4 use of least squaresOr partial least squares to sample points (i)n,F(in)a) Linear regression is carried out to obtain a linear regression equation of current-electromagnetic force
Figure BDA0002977664630000112
Wherein
Figure BDA0002977664630000113
Is inCorresponding regression average electromagnetic force predicted values, wherein k and b are regression coefficients;
3.5 calculating the average value of the weighted average values of the electromagnetic forces under different working strokes of the same current
Figure BDA0002977664630000114
The expression is
Figure BDA0002977664630000115
Wherein F (i)n)aThe average value of the electromagnetic force of different discrete working condition points of the working stroke under the same working current is, and e represents the number of equally divided working currents;
3.6 calculate the sum of the squares of the total deviations SST, expressed as
Figure BDA0002977664630000116
Wherein F (i)t)aThe average value of the electromagnetic force of discrete working condition points with different working strokes for equal working current;
3.7 calculating the regression Square sum SSR, the expression is
Figure BDA0002977664630000117
Wherein
Figure BDA0002977664630000118
For each operating currentThe regression average electromagnetic force predicted values corresponding to the same discrete operating point with different working strokes;
3.8 calculating to obtain an integral complex correlation coefficient R2The expression is
Figure BDA0002977664630000119
The fourth concrete implementation mode:
referring to fig. 8, the difference between the present embodiment and the first embodiment is that the overall complex correlation coefficient R between the current and the electromagnetic force is calculated in the third step2The method specifically comprises the following steps:
3.1 defining the working area of the primary and secondary strokes, the interval [ xa,xb)、(xc,xd]For the secondary working area of the journey, interval [ xb,xc]Is the main working area of the stroke, wherein xa、xb、xc、xd∈[xa,xd]And x isa<xb<xc<xd；
3.2 setting the weighting coefficient of each stroke working area, and falling into the stroke secondary working area [ x ] for the working pointa,xb)、(xc,xd]According to a weighting coefficient S1、S3Performing weighted calculation to the working point falling in the travel main working area [ x ]b,xc]By a weighting factor S2Performing a weighting calculation, as shown in fig. 7;
3.3 calculating the weighted average F (i) of the electromagnetic force at the discrete operating points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) Wherein
Figure BDA0002977664630000121
In the formula F (i)n,xm) Representing discrete operating points (i)n,xm) Corresponding electromagnetic force, xp∈[xa,xb)，xq∈[xb,xc]，xj∈(xc,xd]U, v and w each represents F (i)n,xm) Falling in the current working region [ x ]a,xb)、[xb,xc]、(xc,xd]The number of (2);
3.4 define the working area of primary and secondary current, interval [ ia,ib)、(ic,id]For the current minor operating region, interval [ ib,ic]Is a current main working area, wherein ia、ib、ic、id∈[ia,id]And i isa<ib<ic<id；
3.5 sample points (i) of each current working area by using least square method or partial least square methodn,F(in)a) Performing linear regression to obtain three groups of current-electromagnetic force linear regression equations:
Figure BDA0002977664630000122
Figure BDA0002977664630000123
Figure BDA0002977664630000124
wherein
Figure BDA0002977664630000125
Respectively i in different current working regionsp、iq、ijCorresponding regression mean electromagnetic force prediction value, kp、bp、kq、bq、kj、bjIs a regression coefficient;
3.6 calculating the average value of the weighted average electromagnetic force in the same current working area under the same current working condition
Figure BDA0002977664630000126
Figure BDA0002977664630000127
Wherein
Figure BDA0002977664630000128
ip∈[ia,ib) And g represents that the operating point falls within the operating stroke region [ i ]a,ib) The number of (2);
Figure BDA0002977664630000129
iq∈[ib,ic]and h represents that the operating point falls within the operating stroke region [ i ]b,ic) The number of (2);
Figure BDA00029776646300001210
ij∈(ic,id]and t represents that the operating point falls within the operating stroke region (i)c,id]The number of (2);
3.7 calculating the sum of squared deviations SST of each current working area respectivelyab、SSTbc、SSTcdWherein
Figure BDA00029776646300001211
ip∈[ia,ib)；
Figure BDA00029776646300001212
iq∈[ib,ic]；
Figure BDA00029776646300001213
ij∈(ic,id]；
Wherein F (i)p)a、F(iq)a、F(ij)aThe average value of the electromagnetic force of discrete working condition points with equal working current and different working strokes in each current working area;
3.8 calculating the regression Square sum SST of each current working areaab、SSTbc、SSTcdWherein
Figure BDA0002977664630000131
ip∈[ia,ib)；
Figure BDA0002977664630000132
iq∈[ib,ic]；
Figure BDA0002977664630000133
ij∈(ic,id]；
Wherein
Figure BDA0002977664630000134
Respectively obtaining regression average electromagnetic force predicted values corresponding to any current working condition point in the current working area;
3.9 respectively calculating the complex correlation coefficient R of each current working area2 ab、R2 bc、R2 cdWherein
Figure BDA0002977664630000135
Figure BDA0002977664630000136
Figure BDA0002977664630000137
3.10, settingWeighting factor of each current working region, current working region [ ia,ib)、[ib,ic]、(ic,id]The weighting coefficients of the corresponding complex correlation coefficients are respectively K1、K2、K3As shown in fig. 5;
3.11 weighting the complex correlation coefficient of the electromagnetic force in each working current region according to the current region to obtain the overall complex correlation coefficient R between the current and the electromagnetic force2The expression is R2＝K1·R2 ab+K2·R2 bc+K3·R2 cd。
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 (8)

1. A method for evaluating the linear characteristic of electromagnetic force of a proportional electromagnet based on multiple correlation coefficients is characterized by comprising the following steps:
step 1, dividing a full-working-condition plane;
step 2, obtaining the electromagnetic force of the discrete working condition points;
step 3, calculating the overall complex correlation coefficient R between the current and the electromagnetic force2；
Step 4, according to the integral complex correlation coefficient R between the current and the electromagnetic force2The linear characteristic of the electromagnetic force of the proportional electromagnet is judged according to the numerical value of the proportional electromagnet.
2. The method for evaluating the electromagnetic force linear characteristic of the proportional electromagnet based on the complex correlation coefficient as claimed in claim 1, wherein the dividing method of the full-working-condition plane in the step 1 is as follows:
1.1, 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 marked as [ ia,id]The working stroke of the armature is denoted as [ x ]a,xd]；
1.2, equally dividing and dispersing the full working condition plane formed by the working current and the working stroke, and further obtaining 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]Is equally divided into corresponding arbitrary working strokes.
3. The method for evaluating the linear characteristic of the electromagnetic force of the proportional electromagnet based on the complex correlation coefficient as claimed in claim 1, wherein the method for obtaining the electromagnetic force of the discrete working point by means of simulation or experiment in the step 2 comprises the following steps:
2.1, adjusting the working stroke to a certain discrete working condition point value and then keeping the working stroke unchanged;
2.2, sequentially adjusting the working current to different discrete working condition point values, and respectively measuring corresponding electromagnetic force;
and 2.3, adjusting the working stroke to another discrete working condition point value, keeping the working stroke unchanged, and repeating the process to obtain the electromagnetic force of all the discrete working condition points.
4. The method for evaluating the electromagnetic force linearity characteristics of proportional electromagnets based on complex correlation coefficient as claimed in claim 1, wherein the overall complex correlation coefficient R between the current and the electromagnetic force in step 3 is2The calculation method comprises the following steps:
3.1, respectively calculating the average value F (i) of the electromagnetic force of the discrete working points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) Wherein
Figure FDA0002977664620000011
In the formula F (i)n,xm) Representing discrete operating points (i)n,xm) Corresponding electromagnetic force, f represents the number of equally divided working strokes;
3.2 sample point (i) by least squares or partial least squaresn,F(in)a) Linear regression is carried out to obtain a linear regression equation of current-electromagnetic force
Figure FDA0002977664620000012
Wherein
Figure FDA0002977664620000013
Is inCorresponding regression average electromagnetic force predicted values, wherein k and b are regression coefficients;
3.3, calculating the average value of the electromagnetic force under different working strokes of the same current
Figure FDA0002977664620000014
The expression is
Figure FDA0002977664620000015
Figure FDA0002977664620000021
Wherein F (i)n)aThe average value of the electromagnetic force of different discrete working condition points of the working stroke under the same working current is, and e represents the number of equally divided working currents;
3.4 calculating the sum of the squares of the total deviations SST, which is expressed as
Figure FDA0002977664620000022
Wherein F (i)t)aThe average value of the electromagnetic force of discrete working condition points with different working strokes for equal working current;
3.5, calculating the regression square sum SSR, wherein the expression is
Figure FDA0002977664620000023
Wherein
Figure FDA0002977664620000024
For each working current phaseThe regression average electromagnetic force predicted values corresponding to the discrete operating point with different working strokes are obtained;
3.6, calculating to obtain an integral complex correlation coefficient R2The expression is
Figure FDA0002977664620000025
5. The method for evaluating the electromagnetic force linearity characteristics of proportional electromagnets based on complex correlation coefficient as claimed in claim 1, wherein the overall complex correlation coefficient R between the current and the electromagnetic force in step 3 is2The calculation method comprises the following steps:
3.1, respectively calculating the average value F (i) of the electromagnetic force of the discrete working points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) Wherein
Figure FDA0002977664620000026
In the formula F (i)n,xm) Representing discrete operating points (i)n,xm) Corresponding electromagnetic force, xm∈[xa,xd]F represents the number of equally divided working strokes;
3.2, defining the working area of primary and secondary current, and the interval [ ia,ib)、(ic,id]For the current minor operating region, interval [ ib,ic]Is a current main working area, wherein ia、ib、ic、id∈[ia,id]And i isa<ib<ic<id；
3.3 sample points (i) of each current working area by using least square method or partial least square methodn,F(in)a) Performing linear regression to obtain three groups of current-electromagnetic force linear regression equations:
Figure FDA0002977664620000027
Figure FDA0002977664620000028
Figure FDA0002977664620000029
wherein
Figure FDA00029776646200000210
Respectively i in different current working regionsp、iq、ijCorresponding regression mean electromagnetic force prediction value, kp、bp、kq、bq、kj、bjIs a regression coefficient;
3.4, respectively calculating the average value of the average electromagnetic force in the same current working area under the same current working condition
Figure FDA00029776646200000211
Figure FDA00029776646200000212
Wherein
Figure FDA00029776646200000213
ip∈[ia,ib) And g represents that the operating point falls within the operating stroke region [ i ]a,ib) The number of (2);
Figure FDA0002977664620000031
iq∈[ib,ic]and h represents that the operating point falls within the operating stroke region [ i ]b,ic) The number of (2);
Figure FDA0002977664620000032
ij∈(ic,id]and t represents that the operating point falls within the operating stroke region (i)c,id]The number of (2);
3.5, respectively calculating the sum of squared deviations SST of each current working areaab、SSTbc、SSTcdWherein
Figure FDA0002977664620000033
Figure FDA0002977664620000034
Figure FDA0002977664620000035
Wherein F (i)p)a、F(iq)a、F(ij)aThe average value of the electromagnetic force of discrete working condition points with equal working current and different working strokes in each current working area;
3.6, calculating the regression square sum SST of each current working area respectivelyab、SSTbc、SSTcdWherein
Figure FDA0002977664620000036
Figure FDA0002977664620000037
Figure FDA0002977664620000038
Wherein
Figure FDA0002977664620000039
Respectively obtaining regression average electromagnetic force predicted values corresponding to any current working condition point in the current working area;
3.7 respectively calculating the complex correlation coefficient R of each current working area2 ab、R2 bc、R2 cdWherein
Figure FDA00029776646200000310
Figure FDA00029776646200000311
Figure FDA00029776646200000312
3.8 setting weighting coefficients of each current working area, ia,ib)、[ib,ic]、(ic,id]The weighting coefficients of the corresponding complex correlation coefficients are respectively K1、K2、K3；
3.9, carrying out weighted calculation on the complex correlation coefficient of each working current region according to the current region to obtain the integral complex correlation coefficient R2The expression is R2＝K1·R2 ab+K2·R2 bc+K3·R2 cd。
6. The method for evaluating the electromagnetic force linearity characteristics of proportional electromagnets based on complex correlation coefficient as claimed in claim 1, wherein the overall complex correlation coefficient R between the current and the electromagnetic force in step 3 is2The calculation method comprises the following steps:
3.1, define the working area of the primary and secondary travel, the interval [ xa,xb)、(xc,xd]For the secondary working area of the journey, interval [ xb,xc]Is the main working area of the stroke, wherein xa、xb、xc、xd∈[xa,xd]And x isa<xb<xc<xd；
3.2 setting the weighting coefficient of each stroke working area, the stroke secondary working area [ xa,xb)、[xb,xc]、(xc,xd]The weighting coefficients of the corresponding complex correlation coefficients are S1、S2、S3；
3.3, respectively calculating the electromagnetic force weighted average value F (i) of the discrete operating points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) Wherein
Figure FDA0002977664620000041
Figure FDA0002977664620000042
In the formula F (i)n,xm) Representing discrete operating points (i)n,xm) Corresponding electromagnetic force, xp∈[xa,xb)，xq∈[xb,xc]，xj∈(xc,xd]U, v and w each represents F (i)n,xm) Falling in the current working region [ x ]a,xb)、[xb,xc]、(xc,xd]The number of (2);
3.4 sample point (i) by least squares or partial least squaresn,F(in)a) Linear regression is carried out to obtain a linear regression equation of current-electromagnetic force
Figure FDA0002977664620000043
Wherein
Figure FDA0002977664620000044
Is inCorresponding regression average electromagnetic force predicted values, wherein k and b are regression coefficients;
3.5, calculating the average value of the weighted average values of the electromagnetic forces under different working strokes of the same current
Figure FDA0002977664620000045
The expression is
Figure FDA0002977664620000046
F(in)aThe average value of the electromagnetic force of different discrete working condition points of the working stroke under the same working current is, and e represents the number of equally divided working currents;
3.6 calculating the sum of squared deviations SST, which is expressed as
Figure FDA0002977664620000047
Wherein F (i)t)aThe average value of the electromagnetic force of discrete working condition points with different working strokes for equal working current;
3.7 calculating regression Square sum SSR with the expression of
Figure FDA0002977664620000048
Wherein
Figure FDA0002977664620000049
The regression average electromagnetic force predicted value corresponding to the discrete operating point with the same working current and different working strokes;
3.8, calculating to obtain an integral complex correlation coefficient R2The expression is
Figure FDA00029776646200000410
7. The method for evaluating the electromagnetic force linearity characteristic of the proportional electromagnet based on the complex correlation coefficient as claimed in claim 1, wherein: integration between the current and the electromagnetic force in the step 3Multiple correlation coefficient R2The calculation method comprises the following steps:
3.1, define the working area of the primary and secondary travel, the interval [ xa,xb)、(xc,xd]For the secondary working area of the journey, interval [ xb,xc]Is the main working area of the stroke, wherein xa、xb、xc、xd∈[xa,xd]And x isa<xb<xc<xd；
3.2 setting the weighting coefficient of each stroke working area, the stroke secondary working area [ xa,xb)、[xb,xc]、(xc,xd]The weighting coefficients of the corresponding complex correlation coefficients are S1、S2、S3；
3.3, respectively calculating the electromagnetic force weighted average value F (i) of the discrete operating points with the same working current and different working strokesn)aObtaining a series of current and electromagnetic force linear regression sample points (i)n,F(in)a) Wherein
Figure FDA00029776646200000411
Figure FDA0002977664620000051
In the formula F (i)n,xm) Representing discrete operating points (i)n,xm) Corresponding electromagnetic force, xp∈[xa,xb)，xq∈[xb,xc]，xj∈(xc,xd]U, v and w each represents F (i)n,xm) Falling in the current working region [ x ]a,xb)、[xb,xc]、(xc,xd]The number of (2);
3.4, defining the working area of primary and secondary current, and the interval [ ia,ib)、(ic,id]For the current minor operating region, interval [ ib,ic]Is a current main working area, wherein ia、ib、ic、id∈[ia,id]And i isa<ib<ic<id；
3.5 sample points (i) of each current working area by using least square method or partial least square methodn,F(in)a) Performing linear regression to obtain three groups of current-electromagnetic force linear regression equations:
Figure FDA0002977664620000052
Figure FDA0002977664620000053
Figure FDA0002977664620000054
wherein
Figure FDA0002977664620000055
Respectively i in different current working regionsp、iq、ijCorresponding regression mean electromagnetic force prediction value, kp、bp、kq、bq、kj、bjIs a regression coefficient;
3.6, respectively calculating the average value of the weighted average electromagnetic force in the same current working area under the same current working condition
Figure FDA0002977664620000056
Figure FDA0002977664620000057
Wherein
Figure FDA0002977664620000058
ip∈[ia,ib) G indicates that the operating point falls onWorking stroke area [ i ]a,ib) The number of (2);
Figure FDA0002977664620000059
iq∈[ib,ic]and h represents that the operating point falls within the operating stroke region [ i ]b,ic) The number of (2);
Figure FDA00029776646200000510
ij∈(ic,id]and t represents that the operating point falls within the operating stroke region (i)c,id]The number of (2);
3.7, respectively calculating the sum of squared deviations SST of each current working areaab、SSTbc、SSTcdWherein
Figure FDA00029776646200000511
Figure FDA00029776646200000512
Figure FDA00029776646200000513
Wherein F (i)p)a、F(iq)a、F(ij)aThe average value of the electromagnetic force of discrete working condition points with equal working current and different working strokes in each current working area;
3.8, respectively calculating the regression square sum SST of each current working areaab、SSTbc、SSTcdWherein
Figure FDA00029776646200000514
Figure FDA0002977664620000061
Figure FDA0002977664620000062
Wherein
Figure FDA0002977664620000063
Respectively obtaining regression average electromagnetic force predicted values corresponding to any current working condition point in the current working area;
3.9 respectively calculating the complex correlation coefficient R of each current working area2 ab、R2 bc、R2 cdWherein
Figure FDA0002977664620000064
Figure FDA0002977664620000065
Figure FDA0002977664620000066
3.10 setting weighting coefficients of each current working area, current working area [ ia,ib)、[ib,ic]、(ic,id]The weighting coefficients of the corresponding complex correlation coefficients are respectively K1、K2、K3；
3.11, carrying out weighting calculation on the complex correlation coefficient under each working current according to the current region to obtain an integral complex correlation coefficient R2The expression is R2＝K1·R2 ab+K2·R2 bc+K3·R2 cd。
8. The method for evaluating the electromagnetic force linearity characteristic of the proportional electromagnet based on the complex correlation coefficient as claimed in claim 1, wherein: in the step 4, the overall complex correlation coefficient R between the current and the electromagnetic force is used2The method for judging the linear characteristic of the electromagnetic force of the proportional electromagnet comprises the following steps: integral complex correlation coefficient R between current and electromagnetic force2The closer to 1, the better the linear characteristic of the electromagnetic force of the proportional electromagnet is; integral complex correlation coefficient R between current and electromagnetic force2The closer to 0, the worse the linear characteristic of the proportional electromagnet electromagnetic force.
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