CN108319794A - A kind of electromagnetic relay quality conformance design method based on Orthogonal Least Squares - Google Patents
A kind of electromagnetic relay quality conformance design method based on Orthogonal Least Squares Download PDFInfo
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Abstract
A kind of electromagnetic relay quality conformance design method based on Orthogonal Least Squares, belongs to relay product design field.Cause the invention aims to solving the problems, such as that current relay product output quality conformance is poor, can not determine globally optimal solution in product parameters design process, can not eliminate factor interactive effects scheme robustness, modeling process complexity etc. to optimize precision low.Method is as follows：One, controllable factor, error component and orthogonal test scheme are determined；Two, signal-to-noise ratio, sensitivity significance analysis are carried out, determines ballast；Three, interacting property is analyzed, and determines adjustment factor；Four, the Orthogonal Least Square function model and Robust Optimization object function for establishing ballast, determine ballast optimal solution；Five, adjustment factor multinomial model and offset compensation object function are established, determines adjustment factor optimal solution.The present invention is suitable for relay product design field.
Description
Technical field
The invention belongs to relay product design fields, and in particular to it is a kind of based on the electromagnetism of Orthogonal Least Squares after
Electric apparatus quality consistency design method.
Background technology
Parameter designing is the important link in electromagnetic relay product design process, not only directly determines the output of product
Can characteristic meet design requirement, but also directly affect product design scheme externally interfere, interior interference, manufacture dispersibility etc.
The resistivity of uncertain factor, i.e. robustness.Therefore, had to parameter using rational quality conformance design method
It is significant with consistency for the performance stabilization for improving electromagnetic relay product to imitate control design case.
The key of design parameter is that, using the non-linear nature between input parameter and output characteristics, realization is not controlling
The ability that design scheme inhibits quality fluctuation is effectively improved in the case that uncertainty, i.e. cost are constant.Traditional consistency is set
The noise that meter method is calculated using Orthogonal Experiment and Design and variance analysis when directly determine to join by Calculation of Sensitivity result
Number design scheme, there are following two disadvantages for this method：Optimal set can only be chosen from the discrete levels value that orthogonal test is chosen
Cooperation is prioritization scheme, and is unable to get parameter and is solving the globally optimal solution in range；It can not ensure selected ballast
With the independence of adjustment factor, the robustness for having determined that scheme can be influenced during output offset amount compensates.
Improvement Robust Parameter Design method based on Monte Carlo can improve the validity and optimization knot of statistical result
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 cannot achieve 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 disadvantages for this method：It is building
When 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
The purpose of the present invention is to solve current electric equipment products Parameters designs can not determine globally optimal solution, can not
Elimination factor interactive effects scheme robustness, modeling process complexity etc. cause to optimize the low problem of precision, provide one kind and are based on
The electromagnetic relay quality conformance design method of Orthogonal Least Squares.
To achieve the above object, the technical solution adopted by the present invention is as follows：
A kind of electromagnetic relay quality conformance design method based on Orthogonal Least Squares, the method includes following steps
Suddenly：
Step 1：Input parameter, uncertain factor are determined according to research object and optimization aim, and it is orthogonal to carry out interior appearance
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：Function model between ballast and output characteristics is established using Orthogonal Least Square, meanwhile, with
Inhibition quality fluctuation is target, establishes Robust Optimization object function, then by global optimizing, will make output special in domain
The parameter value of property change rate minimum is determined as the optimal solution of ballast；
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 advantageous effect of the present invention compared with the existing technology is：
(1) present invention can avoid the reciprocation between parameter to design scheme robustness by the decoupling of input parameter
Influence, while modeling parameters quantity can be effectively reduced and improve modeling accuracy.
(2) the method for the present invention can realize global optimizing within the scope of the solution that continuous parameters change, and ensure 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 in the case where the robustness for not influencing ballast is optimal to realize
Scale value.
Description of the drawings
Fig. 1 is the flow chart of the method for the invention.
Specific implementation mode
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 spirit of the technical scheme of the invention range, should all cover
Among protection scope of the present invention.
Specific implementation mode one：What present embodiment was recorded is a kind of electromagnetic relay quality based on Orthogonal Least Squares
Consistency design method, the described method comprises the following steps：
Step 1：Input parameter, uncertain factor are determined according to research object and optimization aim, and it is orthogonal to carry out interior appearance
Experimental design；Wherein, interior table arranges input parameter, and appearance arranges uncertain factor, according to input characteristics 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 of target, can also be relay coil the number of turns；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；
Corresponding orthogonal arrage is selected according to determining controllable input parameter quantity and uncertain factor quantity and number of levels, really
Determining scheme, (table determines that 4 parameters, each parameter have 3 number of levels in such as, so that it may to use L9(34) orthogonal arrage, form 9
Kind scheme；Appearance also determines 4 parameters, and each parameter has 3 number of levels, so that it may to use L9(34) orthogonal arrage, form 9 kinds
Scheme；Every 1 interior table has 9 kinds of appearance schemes, just has 9 output characteristics as a result, total scheme is exactly 9 × 9=81 kinds)；It is 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：Function model between ballast and output characteristics is established using Orthogonal Least Square, meanwhile, with
Inhibition quality fluctuation is target, establishes Robust Optimization object function, then by global optimizing, will make output special in domain
The parameter value of property change rate minimum is determined as the optimal solution of ballast；
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 implementation mode two：A kind of electromagnetic relay matter based on Orthogonal Least Squares described in specific implementation mode one
Consistency design method is measured, it is described that parameter is decoupled specially in step 3：Arbitrary 2 are chosen from input parameter
Parameter without recombination (X, Y), the variation delta x of output characteristics is corresponded to when calculating separately parameter X and parameter Y independent changes first
With Δ y, then calculates (X, Y) combination while corresponding to the variation delta xy of output characteristics when changing, 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 |,
In conjunction with 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 implementation mode three：A kind of electromagnetic relay matter based on Orthogonal Least Squares described in specific implementation mode one
Consistency design method is measured, it is described to be established between adjustment factor and output characteristics using linear regression method in step 5
Polynomial function is specially：After determining ballast prioritization scheme, 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, final to determine adjustment factor XaDesign 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：
M is outer watch test number in formula；SmiIt is fluctuated for the average value of output characteristics；VeiFor the estimated value of error variance；dB
For decibel value.Smi、VeiCalculation formula it is as follows：
In formula,For the average value of the mass property under interior table i schemes；J is the corresponding appearance quantity of table scheme in single；
yijFor the corresponding output characteristics of j-th of appearance of table in i-th.
After table in signal-to-noise ratio and Calculation of Sensitivity result filling, determine each input parameter to noise by variance analysis
Than the conspicuousness with sensitivity.Wherein, there is stronger non-linear nature to the significant factor of SNR influence, 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 combine step
Three Interaction Analysis result is determined as adjustment factor.
In step 3, taken from input parameter arbitrary 2 parameters without recombination (X, Y), calculate separately parameter X first
The variation delta x and Δ y of output characteristics are corresponded to when changing respectively with parameter Y.Then it calculates (X, Y) combination while being corresponded to when changing
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|。
In conjunction with 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, the function model between ballast and output characteristics is established using Orthogonal Least Square.For
It solves to cause interpolation result inaccurate and to choose randomness larger at radial basis function center because radial basis function center is more
Problem introduces OLS algorithms.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| | indicate 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 matrix of n output response, Y=[y1,y2...yn]T, ynIndicate that each is steady
Determine the corresponding output response of factor sampled point, λ=[λ1,λ2...λm]T, λnRadial basis function response for serial number n and reality
Error term between value, ε=[ε1,ε2...εn]T, εnFor the error between the radial basis function response of serial number n and actual value
, λ value is λ=Φ-1*Y
In formula, ΦnmMiddle n refers to the number of sampled point, and m is the number of radial basis function central point, ΦnmFor in this case
Radial basis function value.It is optional here since the selection of radial basis function has not significant impact the result of Interpolation Property of Radial Basis Function
It selects most widely used Gaussian function and establishes Interpolation Property of Radial Basis Function model, i.e.,R is tested point and sampling
The Euclidean distance of point, e is natural Exponents, e ≈ 2.71828；Φ is ΦiThe expression matrix form of (each radial basis function), Φ mono-
It is fixed reversible.
It is respectively vector P to enable n vector therein first1To Pn.Orthogonal-triangle decomposition is carried out to matrix Φ, is obtained
Φ=QA
A is the upper triangular matrix of m × m, Q=[q in formula1,q2…qm] be n × m matrix, qmRefer to carrying out orthogonal-triangle
The m column vectors of matrix Q after decomposition, and each row of matrix Q are orthogonal, and formula is substituted into Y=Φ λ+ε, can obtain equation Y=QA λ+ε
G=A λ are enabled, g is a multiplication of vectors as a result, substitution above formula, obtains Y=Qg+ ε without physical significance here.And because
For g=(ΦT*Φ)-1ΦT* Y, i.e.,
In formula, Y is output response matrix value, qiIt refer to the i-th column vector for carrying out the matrix Q after orthogonal-triangle decomposition；gi
It is the i-th column vector of matrix g, 1≤i≤m；
It substitutes into Y=Qg+ ε modifications and abbreviation obtains
ε in formulaTε is whole square error term, enables sampled point error contribution rate calculation formulaIt is maximum, you can to ensure
εTε is minimum.To vectorial P1To PnError contribution rate is sought, and using the corresponding sampled point of the highest column vector of error contribution rate as diameter
To Basis Function Center.
Then pass through pseudoinverse technique λ=(ΦT*Φ)-1ΦT* Y seeks the weights of output node, establishes Radial Basis Function neural
Network model, and error of the sample data under the approximate model is calculated, stop operation if error is met the requirements, if not
Meet, remaining n-1 column vector is subjected to Gram-Schmidt orthogonalizations, is reselected according to error contribution rate calculation formula
Approximate model is established at radial basis function center, and circulate operation is until meet model error requirement.
Then, to inhibit quality fluctuation to establish Robust Optimization object function as target.By ballast multinomial FsPoint
It is other to each ballast XsLocal derviation is sought, slope of the function on respective factor direction is obtained.Slope shows that function exists closer to 0
Stability herein is better.Therefore, object function F is established into the progress square summation of the above slope valuesta, 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
Minimum parameter combination, the as optimal case of 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 XaminTo XamaxAn 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, final to determine adjustment factor XaDesign scheme.
Claims (3)
1. a kind of electromagnetic relay quality conformance design method based on Orthogonal Least Squares, it is characterised in that：The method
Include the following steps：
Step 1：Input parameter, uncertain factor are determined according to research object and optimization aim, carry out interior appearance orthogonal test
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：Function model between ballast and output characteristics is established using Orthogonal Least Square, meanwhile, to inhibit
Quality fluctuation is target, establishes Robust Optimization object function, then by global optimizing, output characteristics will be made to become in domain
The parameter value of rate minimum is 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 electromagnetic relay quality conformance design method based on Orthogonal Least Squares according to claim 1,
It is characterized in that：It is described that parameter is decoupled specially in step 3：Arbitrary 2 parameters are chosen from input parameter
Without recombination (X, Y), the variation delta x and Δ y of output characteristics are corresponded to when calculating separately parameter X and parameter Y independent changes first,
Then it calculates (X, Y) combination while corresponding to the variation delta xy of output characteristics when changing, if parameter X is completely independent with parameter Y,
It should then 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 being determined between parameter using following formula
Reciprocation,
| Δ xy- (Δ x+ Δs y) | >=γ × | Δ xy |,
In conjunction with 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 is determined as adjustment factor.
3. a kind of electromagnetic relay quality conformance design method based on Orthogonal Least Squares according to claim 1,
It is characterized in that：In step 5, the multinomial established using linear regression method between adjustment factor and output characteristics
Function is specially：After determining ballast prioritization scheme, output characteristics can deviate with the change of parameter value, 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
It is shown：
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| CN106777581A (en) * | 2016-12-01 | 2017-05-31 | 哈尔滨理工大学 | A kind of composite bone plate Optimization Design based on threetimes design method |
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