CN108256268A - A kind of relay parameter global optimizing method based on K-means radial basis function - Google Patents
A kind of relay parameter global optimizing method based on K-means radial basis function Download PDFInfo
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Abstract
A kind of relay parameter global optimizing method based on K means radial basis function, belongs to relay product design field.The invention aims to solve the problems, such as that current Parameters design can not determine globally optimal solution, can not eliminate factor interactive effects scheme robustness.Method is as follows：First, controllable factor, error component and orthogonal test scheme are determined；2nd, signal-to-noise ratio, sensitivity significance analysis are carried out, determines ballast；3rd, interacting property is analyzed, and determines adjustment factor；4th, the K means radial basis function models and optimization object function of ballast are established, determines ballast optimal solution；5th, adjustment factor multinomial model and offset compensation object function are established, determines adjustment factor optimal solution.The present invention determines adjustment factor, adjustment factor is recycled to compensate the bias of output characteristics, adjusts output characteristics to desired value so as to fulfill in the case where the robustness for not influencing ballast is optimal by being decoupled to parameter.
Description
Technical field
The invention belongs to relay product design fields, and in particular to a kind of based on K-means radial basis function
Relay parameter global optimizing method.
Background technology
Parameter designing is the important link in relay product design process, not only directly determines the output characteristics of product
Design requirement can be met, but also directly affect product design scheme and externally interfere, interior interference, manufacture dispersibility etc. not really
The resistivity of qualitative factor, i.e. robustness.Therefore, using Robust Parameter Design method to the performance of raising relay product
Stability is significant with quality conformance.
The key of Robust Parameter Design is, using the non-linear nature between input parameter and output characteristics, to realize
Do not control uncertainty, i.e., cost it is constant in the case of effectively improve the ability that designing scheme inhibits quality fluctuation.Traditional ginseng
When Calculation of Sensitivity result directly determines the noise that number design method is calculated using Orthogonal Experiment and Design and variance analysis
Go out parameter designing scheme, there are following two shortcomings for this method：It can only be chosen most from the discrete levels value that orthogonal test is chosen
It is excellent to combine scheme as an optimization, and globally optimal solution of the parameter in the range of solution can not be obtained；It can not ensure selected stabilization
The independence of factor and adjustment factor can influence to have determined that the robustness of scheme during output offset amount compensates.
Improvement Robust Parameter Design method based on Monte Carlo can improve the validity of statistical result and optimization knot
The accuracy of fruit.However, this method is improved only for the appearance in experimental design, the level value of interior watch test factor is still
It is so global optimizing that is discrete, therefore can not realizing parameter.
In addition, the traditional parameters design method based on approximate modeling fully enters parameter and output characteristics firstly the need of foundation
Between function model, so that optimal solution be calculated in domain.However there are following two shortcomings for this method：It is building
During vertical approximate model, if the input parameter number of levels chosen is less, it is difficult to ensure that model approaches actual function relationship well,
Influence optimization precision；And when input parameter is more, the number of coefficients to be asked during approximate modeling is more and calculating process is complicated,
Therefore the Parametric optimization problem of multiple input can not be suitable for inclusion in.
Invention content
Can not determine globally optimal solution the purpose of the present invention is to solve current electric equipment products Parameters design, can not
Elimination factor interactive effects scheme robustness, modeling process complexity etc. cause to optimize the problem of precision is low, provide one kind and are based on
The relay parameter global optimizing method of K-means radial basis function.
To achieve the above object, the technical solution that the present invention takes is as follows：
A kind of relay parameter global optimizing method based on K-means radial basis function, the method includes following steps
Suddenly：
Step 1：Input parameter, uncertain factor are determined according to research object and optimization aim, appearance is orthogonal in progress
Experimental design；Wherein, interior table arranges input parameter, and appearance arranges uncertain factor, according to input parameter and uncertain factor
Quantity and number of levels select inside and outside orthogonal arrage respectively and determine testing program；
Step 2：The output characteristics of each testing program is calculated, external watch test result calculates signal-to-noise ratio and sensitivity, and defeated
Enter in interior table, then internal table carries out the variance analysis of signal-to-noise ratio and sensitivity, according to the significance analysis result of each input parameter
Determine its non-linear nature and approximately linear property；
Step 3：The correlation between input parameter is determined by Interaction Analysis, parameter is decoupled, in conjunction with letter
Ratio, sensitivity significance analysis result and Interaction Analysis make an uproar as a result, determining the ballast and adjustment factor in input parameter；
Step 4：The letter between ballast and output characteristics is established using the Radial Basis Function Method based on K-means
Exponential model, meanwhile, to inhibit quality fluctuation as target, Robust Optimization object function is established, then by global optimizing, will solve
The parameter value of output characteristics change rate minimum is made to be determined as the optimal solution of ballast in region；
Step 5：Polynomial function between adjustment factor and output characteristics is established using linear regression method, is counted simultaneously
The difference that output characteristics after ballast optimization deviates desired value is calculated, finally to compensate the offset of output characteristics as target,
Determine the value of adjustment factor.
The present invention is relative to the advantageous effect of the prior art：
(1) present invention can avoid the reciprocation between parameter to designing scheme robustness by the decoupling of input parameter
Influence, while modeling parameters quantity can be effectively reduced and improve modeling accuracy.
(2) it realizes global optimizing in the range of the solution that the method for the present invention can change in continuous parameters, ensures that robustness is set
Meter scheme it is optimal.
(3) the method for the present invention can carry out quantitative compensation in the case where not influencing scheme robustness to output offset amount,
Ensure that output characteristics meets design requirement.
(4) present invention determines adjustment factor, recycles adjustment factor to output characteristics by being decoupled to parameter
Bias compensates, and adjusts output characteristics to mesh so as to fulfill in the case where the robustness for not influencing ballast is optimal
Scale value.
Description of the drawings
Fig. 1 is the flow chart of the method for the invention.
Specific embodiment
Technical scheme of the present invention is further described with reference to embodiment, however, it is not limited to this, every right
Technical solution of the present invention is modified or equivalent replacement, without departing from the scope of technical solution of the present invention, should all cover
Among protection scope of the present invention.
Specific embodiment one：What present embodiment was recorded is a kind of relay ginseng based on K-means radial basis function
Number global optimizing method, the described method comprises the following steps：
Step 1：Input parameter, uncertain factor are determined according to research object and optimization aim, appearance is orthogonal in progress
Experimental design；Wherein, interior table arranges input parameter, and appearance arranges uncertain factor, according to input parameter and uncertain factor
Quantity and number of levels select inside and outside orthogonal arrage respectively and determine testing program；The research object is relay, optimizes mesh
Mark can be armature sucting speed, magnetic retentivity size etc. depending on actual conditions；Input parameter can influence optimization
Each vital part size of relay or the relay coil number of turn of target；Uncertain factor, that is, noise factor, Ke Yishi
The actual size value of input parameter in process of manufacture tolerance fluctuation range, i.e. A '=A ± tolerances, A is input parameter value,
A ' is uncertain factor；
Step 2：The output characteristics of each testing program is calculated, external watch test result calculates signal-to-noise ratio and sensitivity, and defeated
Enter in interior table, then internal table carries out the variance analysis of signal-to-noise ratio and sensitivity, according to the significance analysis result of each input parameter
Determine its non-linear nature and approximately linear property；According to determining controllable input parameter quantity and uncertain factor quantity and water
Flat number selects corresponding orthogonal arrages, determine scheme (for example interior table determines 4 parameters, and each parameter has 3 number of levels, so that it may
To use L9(34) orthogonal arrage, form 9 kinds of schemes；Appearance also determines 4 parameters, and each parameter has 3 number of levels, it is possible to
Using L9(34) orthogonal arrage, form 9 kinds of schemes；Every 1 interior table has 9 kinds of appearance schemes, just has 9 output characteristics as a result, total side
Case is exactly 9 × 9=81 kinds)；Overall numerical procedure number=interior table scheme × appearance scheme.
Output characteristics can be selected according to object (relay), such as armature pickup time, armature sucting speed, magnetic holding
Size of power etc..
Step 3：The correlation between input parameter is determined by Interaction Analysis, parameter is decoupled, in conjunction with letter
Ratio, sensitivity significance analysis result and Interaction Analysis make an uproar as a result, determining the ballast and adjustment factor in input parameter；
Step 4：The letter between ballast and output characteristics is established using the Radial Basis Function Method based on K-means
Exponential model, meanwhile, to inhibit quality fluctuation as target, Robust Optimization object function is established, then by global optimizing, will solve
The parameter value of output characteristics change rate minimum is made to be determined as the optimal solution of ballast in region；
Step 5：Polynomial function between adjustment factor and output characteristics is established using linear regression method, is counted simultaneously
The difference that output characteristics after ballast optimization deviates desired value is calculated, finally to compensate the offset of output characteristics as target,
Determine the value of adjustment factor.
Specific embodiment two：A kind of relay based on K-means radial basis function described in specific embodiment one
Parameter global optimization method, it is described that parameter is decoupled specially in step 3：Arbitrary 2 are chosen from input parameter
Parameter without recombination (X, Y), respectively first calculating parameter X and parameter Y independent changes when correspond to the variation delta x of output characteristics
With Δ y, the variation delta xy that output characteristics is corresponded to when (X, Y) combination changes simultaneously is then calculated, if parameter X and parameter Y are complete
It is complete independent, then it should meet the mathematical relationship of Δ xy=Δ x+ Δs y, it is on the contrary then illustrate between parameter X and parameter Y in the presence of interacting work
With；
Definition interaction factor gamma reflects interactive degree between parameter X and Y, at the same using following formula determine parameter it
Between reciprocation,
| Δ xy- (Δ x+ Δs y) | >=γ × | Δ xy |,
With reference to signal-to-noise ratio, sensitivity significance analysis result and Interaction Analysis as a result, will have approximately linear property and
It is determined as adjustment factor with the mutually independent input parameter of ballast.
Specific embodiment three：A kind of relay based on K-means radial basis function described in specific embodiment one
Parameter global optimization method, it is described to be established between adjustment factor and output characteristics using linear regression method in step 5
Polynomial function is specially：After ballast prioritization scheme is determined, output characteristics can occur partially with the change of parameter value
From calculating the offset Δ F of output characteristics firsts, then Joint regulation is because of prime polynomial Fa, establish offset compensation target H2,
It is shown below,
It, can be right in the case where not influencing scheme robustness due to mutual indepedent between adjustment factor and ballast
Output offset amount carries out quantitative compensation, finally determining adjustment factor XaDesigning scheme.
Embodiment 1：
In step 1, input parameter and uncertain factor are determined according to research object and optimization aim, inside and outside progress
Table Orthogonal Experiment and Design.Wherein, it using input parameter as controllable factor, is arranged into interior table orthogonal arrage.By uncertain factor
As error component, it is arranged into appearance orthogonal arrage.Quantity further according to factor and number of levels select corresponding orthogonal arrage and true
Determine testing program.
In step 2, the corresponding testing program of every appearance (i) is calculated respectively, acquires output characteristics value y, so
Following formula is substituted into afterwards calculates signal-to-noise ratio SiWith sensitivity ηi：
In formula, m is outer watch test number；SmiAverage value for output characteristics fluctuates；VeiEstimated value for error variance；
DB is decibel value；Smi、VeiCalculation formula it is as follows：
In formula,Average value for the mass property under interior table i schemes；J is the corresponding appearance quantity of single interior table scheme；
yijThe corresponding output characteristics of j-th of appearance for table in i-th.
After signal-to-noise ratio and Calculation of Sensitivity result are inserted interior table, determine each input parameter to noise by variance analysis
Than the conspicuousness with sensitivity.Wherein, to SNR influence, significant factor has stronger non-linear nature, is determined as stablizing
Factor.It is not notable on SNR influence and significant factor is influenced on sensitivity there is stronger linear behavio(u)r, and with reference to step
Three Interaction Analysis result is determined as adjustment factor.
In step 3, taken from input parameter arbitrary 2 parameters without recombination (X, Y), respectively first calculating parameter X
The variation delta x of output characteristics and Δ y is corresponded to when changing respectively with parameter Y.Then it calculates when (X, Y) combination changes simultaneously and corresponds to
The variation delta xy of output characteristics.If parameter X is completely independent with parameter Y, the mathematics that should meet Δ xy=Δ x+ Δs y closes
System.It is on the contrary then illustrate that there are reciprocations between parameter X and parameter Y.
Definition interaction factor gamma reflects interactive degree between parameter X and Y, at the same using following formula determine parameter it
Between reciprocation,
|Δxy-(Δx+Δy)|≥γ×|Δxy|。
With reference to signal-to-noise ratio, sensitivity significance analysis result and Interaction Analysis as a result, will have approximately linear property and
It is determined as adjustment factor with the mutually independent input parameter of ballast.
In step 4, established between ballast and output characteristics using the Radial Basis Function Method based on K-means
Function model.To solve the problems, such as to cause interpolation result inaccurate due to radial basis function center is more, by reasonably instructing
Practice required radial basis function center of being chosen from sampled point, reduce the number at radial basis function center, introduce K-means and gather
Class algorithm.It is assumed that there is following relationship between system output response and ballast experimental data point：
Y is the actual value of tested point in formula；Y' is by the obtained value of radial basis function；ε is error term；I is sampling
The serial number of point；N is hits；λiIt is weight coefficient；ΦiIt is radial basis function；ri=| | x-xi| | represent tested point and sampled point
The distance between；X is tested point, xiFor the radial basis function center artificially chosen；C is the width of radial basis function.
Being write formula as matrix form has：Y=Φiλ+ε
In formula, λ is weight coefficient, and Y is the n matrix for exporting response, Y=[y1,y2...yn]T, ynRepresent that each is steady
Determine the corresponding output response of factor sampled point, λ=[λ1,λ2...λm]T,λnFor shared by the radial basis function center of serial number n
Weight coefficient size, ε=[ε1,ε2...εn]T,εnThe error amount between radial basis function response and actual value for serial number n,
λ value is λ=Φ-1*Y。
Since sampled point number n is different from radial basis function center number m at this time, the weights of radial basis function output node
It is solved by pseudoinverse, i.e.,：
λ=(ΦT*Φ)-1ΦT*Y
Since the selection of radial basis function has not significant impact the result of Interpolation Property of Radial Basis Function, application may be selected here
Widest Gaussian function establishes Interpolation Property of Radial Basis Function model, i.e.,R is the Europe of tested point and sampled point
Family name's distance, e are natural Exponents, e ≈ 2.71828；Φ is ΦiThe expression matrix form of (each radial basis function), Φ are centainly reversible.
ΦnmMiddle n refers to the number of sampled point, numbers of the m for radial basis function central point, ΦnmFor radial basis function value in this case.
Radial direction Basis Function Center is screened using K-means clustering algorithms, is divided into following five step：
The first step, arbitrary initial cluster center of choosing is respectively y1(0),y2(0)…ym(0)。
Second step utilizes ri=| | x-xi| | calculate the distance of each sampled point and cluster centre.To each sampled point, according to
Its closest cluster centre is classified, and obtains m sampled point set.
Third walks, and to each sampling point set conjunction average value, which is updated to new cluster centre, i.e. y1(1),y2
(1)…ym(1)。
4th step judges the difference of new cluster centre and former cluster centre, if difference is not in defined error range
Second step is then returned, the 5th step is then carried out in defined error range.
5th step calculates radial basis function width value and node weights coefficient according to radial basis function central value.It calculates public
Formula is λ=(ΦT*Φ)-1ΦT*Y。
6th step using obtained weight coefficient and radial basis function width c, can obtain the prediction at unknown point
Value, you can establish the radial basis function model based on K-means, radial basis function width c be determining cluster centre and from it
The distance between farthest sampled point.
Then, quality fluctuation to be inhibited to establish Robust Optimization object function as target.By ballast multinomial FsPoint
It is other to each ballast XsLocal derviation is sought, obtains slope of the function on respective factor direction.Slope shows that function exists closer to 0
Stability herein is better.Therefore, object function F is established into the progress square summation of more than slope valuesta, so as to which robustness is excellent
Change problem H1It is attributed to and seeks object function FstaMinimum value, be shown below,
In formula, xsiFor i-th of ballast XsPoint, XsFor ballast, value range XsminTo Xsmax, H1It is steady
Strong property optimization object function,
Using the global optimizing method of sequential quadratic programming, determine that ballast makes object function F in domainsta
The optimal case of minimum parameter combination, as ballast.
In step 5, the polynomial function between adjustment factor and output characteristics is established using linear regression method.
After determining ballast prioritization scheme, output characteristics can deviate with the change of parameter value.It is special that output is calculated first
The offset Δ F of propertys, then Joint regulation is because of prime polynomial Fa, establish offset compensation target H2, it is shown below.
In formula, XaIt is factor X in its fluctuation range XsminTo XsmaxAn interior variable, △ XaFor parameter value deviate to
Determine the size of X, H2For offset compensation object function,
It, can be right in the case where not influencing scheme robustness due to mutual indepedent between adjustment factor and ballast
Output offset amount carries out quantitative compensation, finally determining adjustment factor XaDesigning scheme.
Claims (3)
- A kind of 1. relay parameter global optimizing method based on K-means radial basis function, it is characterised in that：The method packet Include following steps：Step 1：Input parameter, uncertain factor are determined according to research object and optimization aim, appearance orthogonal test in progress Design；Wherein, interior table arranges input parameter, and appearance arranges uncertain factor, according to the number of input parameter and uncertain factor Amount and number of levels select inside and outside orthogonal arrage and determine testing program respectively；Step 2：The output characteristics of each testing program is calculated, external watch test result calculates signal-to-noise ratio and sensitivity, and in input In table, then internal table carries out the variance analysis of signal-to-noise ratio and sensitivity, is determined according to the significance analysis result of each input parameter Its non-linear nature and approximately linear property；Step 3：The correlation between input parameter is determined by Interaction Analysis, parameter is decoupled, in conjunction with noise Than, sensitivity significance analysis result and Interaction Analysis as a result, determining the ballast and adjustment factor in input parameter；Step 4：The Function Modules between ballast and output characteristics are established using the Radial Basis Function Method based on K-means Type, meanwhile, to inhibit quality fluctuation as target, Robust Optimization object function is established, then by global optimizing, by domain The parameter value of output characteristics change rate minimum is inside made to be determined as the optimal solution of ballast；Step 5：Polynomial function between adjustment factor and output characteristics is established using linear regression method, is calculated simultaneously Output characteristics deviates the difference of desired value after ballast optimization, finally using the offset for compensating output characteristics as target, determines The value of adjustment factor.
- 2. a kind of relay parameter global optimizing method based on K-means radial basis function according to claim 1, It is characterized in that：It is described that parameter is decoupled specially in step 3：The nothing of arbitrary 2 parameters is chosen from input parameter The variation delta x of output characteristics and Δ y is corresponded to when recombination (X, Y), respectively first calculating parameter X and parameter Y independent changes, so The variation delta xy that output characteristics is corresponded to when (X, Y) combination changes simultaneously is calculated afterwards, if parameter X is completely independent with parameter Y, It should meet the mathematical relationship of Δ xy=Δ x+ Δs y, it is on the contrary then illustrate that there are reciprocations between parameter X and parameter Y；Definition interaction factor gamma reflects interactive degree between parameter X and Y, while is determined between parameter using following formula Reciprocation,| Δ xy- (Δ x+ Δs y) | >=γ × | Δ xy |,With reference to signal-to-noise ratio, sensitivity significance analysis result and Interaction Analysis as a result, will have approximately linear property and with it is steady Determine the mutually independent input parameter of factor and be determined as adjustment factor.
- 3. a kind of relay parameter global optimizing method based on K-means radial basis function according to claim 1, It is characterized in that：In step 5, the multinomial letter established using linear regression method between adjustment factor and output characteristics Number is specially：After ballast prioritization scheme is determined, output characteristics can deviate with the change of parameter value, count first Calculate the offset Δ F of output characteristicss, then Joint regulation is because of prime polynomial Fa, establish offset compensation target H2, such as following formula institute Show,
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