CN108256268B - Relay parameter global optimization method based on K-means radial basis function - Google Patents
Relay parameter global optimization method based on K-means radial basis function Download PDFInfo
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Abstract
A global optimization method for relay parameters based on K-means radial basis functions belongs to the technical field of relay product design. The invention aims to solve the problems that the existing parameter design method cannot determine the global optimal solution and cannot eliminate the robustness of the interactive influence scheme of the factors. The method comprises the following steps: firstly, determining controllable factors, error factors and an orthogonal test scheme; secondly, analyzing the signal-to-noise ratio and the sensitivity significance to determine a stability factor; performing interactive analysis to determine an adjusting factor; establishing a K-means radial basis function model of the stability factor and an optimization objective function, and determining an optimal solution of the stability factor; and fifthly, establishing an adjustment factor polynomial model and an offset compensation objective function, and determining an optimal solution of the adjustment factor. According to the invention, the parameters are decoupled, the adjusting factors are determined, and the deviation of the output characteristics is compensated by using the adjusting factors, so that the output characteristics are adjusted to the target value under the condition of optimal robustness without influencing the stability factors.
Description
Technical Field
The invention belongs to the technical field of relay product design, and particularly relates to a relay parameter global optimization method based on a K-means radial basis function.
Background
The parameter design is an important link in the design process of a relay product, not only directly determines whether the output characteristics of the product meet the design requirements, but also directly influences the resistance of the product design scheme to external interference, internal interference, manufacturing dispersion and other uncertain factors, namely robustness. Therefore, the design method of the robustness parameters has great significance for improving the performance stability and quality consistency of the relay product.
The key of the design of the robustness parameters is that the nonlinear property between the input parameters and the output characteristics is utilized to effectively improve the capability of the design scheme for inhibiting quality fluctuation under the condition of not controlling uncertainty, namely, not changing cost. The traditional parameter design method directly determines a parameter design scheme by utilizing a signal-to-noise ratio and sensitivity calculation result obtained by orthogonal experimental design and variance analysis calculation, and has the following two defects: only the optimal combination can be selected from discrete horizontal values selected by the orthogonal test as an optimization scheme, and the global optimal solution of the parameters in the solving range cannot be obtained; the independence of the selected stability factor and the adjustment factor cannot be guaranteed, and the robustness of the determined scheme is influenced in the process of output offset compensation.
The improved robustness parameter design method based on the Monte Carlo can improve the effectiveness of statistical results and the accuracy of optimized results. However, this method only improves on the appearance in the experimental design, and the level values of the internal appearance experimental factors are still discrete, so that global optimization of the parameters cannot be achieved.
In addition, the conventional parameter design method based on approximate modeling needs to establish a function model between all input parameters and output characteristics first, so that an optimal solution is calculated in a solving area. However, this method has two disadvantages: when an approximate model is established, if the selected input parameter level number is less, the model is difficult to be ensured to be well approximated to the actual function relation, and the optimization precision is influenced; when the input parameters are more, the number of coefficients to be solved in the approximate modeling process is more and the calculation process is complex, so that the method cannot be applied to the parameter optimization problem containing multiple inputs.
Disclosure of Invention
The invention aims to solve the problems that the existing electric appliance product parameter design method cannot determine a global optimal solution, cannot eliminate factor interaction influence scheme robustness, is complex in modeling process and the like, and accordingly is low in optimization precision, and provides a relay parameter global optimization method based on a K-means radial basis function.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a global optimization method for relay parameters based on K-means radial basis functions comprises the following steps:
the method comprises the following steps: determining input parameters and uncertainty factors according to a research object and an optimization target, and carrying out orthogonal test design on an internal and external surface; the method comprises the following steps that input parameters are arranged in an inner table, uncertainty factors are arranged in an outer table, an inner and outer orthogonal table is respectively selected according to the number and the horizontal number of the input parameters and the uncertainty factors, and a test scheme is determined;
step two: calculating the output characteristics of each test scheme, calculating the signal-to-noise ratio and the sensitivity of the test result of the external table, inputting the test result into the internal table, performing variance analysis on the signal-to-noise ratio and the sensitivity of the internal table, and determining the nonlinear property and the approximate linear property of the internal table according to the significance analysis result of each input parameter;
step three: determining the correlation among input parameters through interactive analysis, decoupling the parameters, and determining the stability factor and the adjustment factor in the input parameters by combining the signal-to-noise ratio, the sensitivity significance analysis result and the interactive analysis result;
step four: establishing a function model between a stability factor and an output characteristic by adopting a radial basis function method based on K-means, establishing a stability optimization objective function by taking the suppression of quality fluctuation as a target, and determining a parameter value which enables the output characteristic change rate to be minimum in a solving area as an optimal solution of the stability factor through global optimization;
step five: and establishing a polynomial function between the adjusting factor and the output characteristic by adopting a linear regression method, calculating a difference value of the output characteristic deviating from a target value after the stability factor is optimized, and finally determining the value of the adjusting factor by taking the offset of the compensated output characteristic as a target.
Compared with the prior art, the invention has the beneficial effects that:
(1) according to the invention, through decoupling of the input parameters, the influence of interaction among the parameters on the robustness of the design scheme can be avoided, and meanwhile, the number of modeling parameters can be effectively reduced and the modeling precision can be improved.
(2) The method can realize global optimization in the solving range of continuous parameter change and ensure the optimization of the robust design scheme.
(3) The method can carry out quantitative compensation on the output offset under the condition of not influencing the robustness of the scheme, and ensures that the output characteristic meets the design requirement.
(4) According to the invention, the parameters are decoupled, the adjusting factors are determined, and the deviation of the output characteristics is compensated by using the adjusting factors, so that the output characteristics are adjusted to the target value under the condition of optimal robustness without influencing the stability factors.
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FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The technical solutions of the present invention are further described below with reference to the following examples, but the present invention is not limited thereto, and modifications and equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit of the technical solutions of the present invention, and the technical solutions of the present invention are covered by the protection scope of the present invention.
The first embodiment is as follows: the embodiment describes a global optimization method for relay parameters based on a K-means radial basis function, and the method comprises the following steps:
the method comprises the following steps: determining input parameters and uncertainty factors according to a research object and an optimization target, and carrying out orthogonal test design on an internal and external surface; the method comprises the following steps that input parameters are arranged in an inner table, uncertainty factors are arranged in an outer table, an inner orthogonal table and an outer orthogonal table are respectively selected according to the number and the horizontal number of the input parameters and the uncertainty factors, and a test scheme is determined; the research object is a relay, and the optimization target is determined according to the actual situation and can be the attraction speed of the armature, the magnitude of the magnetic holding force and the like; the input parameter can be the size of each key part of the relay influencing the optimization target, and can also be the number of turns of a coil of the relay; the uncertain factor, namely the noise factor, can be an actual size value of an input parameter in a tolerance fluctuation range in the production and processing process, namely A '═ A +/-tolerance value, A is an input parameter value, and A' is the uncertain factor;
step two: calculating the output characteristics of each test scheme, calculating the signal-to-noise ratio and sensitivity of the test results of the external table, inputting the signal-to-noise ratio and sensitivity into the internal table, and performing variance division of the signal-to-noise ratio and sensitivity on the internal tableAnalyzing, namely determining the nonlinear property and the approximate linear property of each input parameter according to the significance analysis result of each input parameter; selecting corresponding orthogonal table according to the determined controllable input parameter number, uncertain factor number and level number, determining scheme (such as the inner table determines 4 parameters, each parameter has 3 levels, L can be adopted9(34) Orthogonal tables, forming 9 schemes; the appearance also determines 4 parameters, each of which has 3 levels, so that L can be adopted9(34) Orthogonal tables, forming 9 schemes; there are 9 appearance schemes for every 1 inner surface, there are 9 output characteristic results, the total scheme is 9 × 9 ═ 81); the total number of calculation schemes is equal to the inner table scheme x the outer table scheme.
The output characteristics can be selected according to the object (relay), such as the armature attracting time, the armature attracting speed, the magnitude of the magnetic holding force and the like.
Step three: determining the correlation among input parameters through interactive analysis, decoupling the parameters, and determining the stability factor and the adjustment factor in the input parameters by combining the signal-to-noise ratio, the sensitivity significance analysis result and the interactive analysis result;
step four: establishing a function model between a stability factor and an output characteristic by adopting a radial basis function method based on K-means, establishing a stability optimization objective function by taking the suppression of quality fluctuation as a target, and determining a parameter value which enables the output characteristic change rate to be minimum in a solving area as an optimal solution of the stability factor through global optimization;
step five: and establishing a polynomial function between the adjusting factor and the output characteristic by adopting a linear regression method, calculating a difference value of the output characteristic deviating from a target value after the stability factor is optimized, and finally determining the value of the adjusting factor by taking the offset of the compensated output characteristic as a target.
The second embodiment is as follows: in a specific embodiment, the method for global optimization of relay parameters based on a K-means radial basis function specifically includes, in step three, decoupling parameters: selecting non-recombination (X, Y) of any 2 parameters from input parameters, firstly respectively calculating variation delta X and delta Y corresponding to output characteristics when the parameter X and the parameter Y are independently changed, then calculating variation delta xy corresponding to the output characteristics when the (X, Y) combination is simultaneously changed, if the parameter X and the parameter Y are completely independent, the mathematical relationship of delta xy being delta X + delta Y is satisfied, otherwise, the interaction exists between the parameter X and the parameter Y;
the interaction factor Y is defined to reflect the degree of interaction between the parameters X and Y, while the interaction between the parameters is determined using the following formula,
|Δxy-(Δx+Δy)|≥γ×|Δxy|，
and determining input parameters which have approximate linear properties and are independent of the stability factors as adjusting factors by combining the signal-to-noise ratio, the sensitivity significance analysis result and the interactivity analysis result.
The third concrete implementation mode: in a specific embodiment, the method for global optimization of relay parameters based on the K-means radial basis function, in the fifth step, the method for establishing a polynomial function between the adjustment factor and the output characteristic by using a linear regression method specifically includes: after determining the stability factor optimization scheme, the output characteristic deviates along with the change of the parameter value, and firstly, the offset delta F of the output characteristic is calculatedsAnd then jointly adjust the factor polynomial FaEstablishing an offset compensation target H2As shown in the following formula,
because the adjusting factors and the stabilizing factors are independent, the output offset can be quantitatively compensated under the condition of not influencing the robustness of the scheme, and the adjusting factor X is finally determinedaThe design of (1).
Example 1:
in the first step, input parameters and uncertainty factors are determined according to a research object and an optimization target, and orthogonal test design of an internal and external table is carried out. Wherein the input parameters are used as controllable factors and are arranged in an internal table orthogonal table. And arranging uncertainty factors serving as error factors into the appearance orthogonal table. And selecting a corresponding orthogonal table according to the number and the horizontal number of the factors and determining a test scheme.
In the second step, the test scheme corresponding to each appearance (i) is calculated respectively to obtain an output characteristic value y, and then the output characteristic value y is substituted into the following formula to calculate the signal-to-noise ratio SiAnd sensitivity ηi：
In the formula, m is the number of appearance tests; smiFluctuation as an average value of the output characteristic; veiIs an estimate of the error variance; dB is a decibel value; smi、VeiThe calculation formula of (a) is as follows:
in the formula (I), the compound is shown in the specification,
is the average value of the quality characteristics under the scheme of the inner table i; j is the number of the corresponding outer surfaces of the single inner surface scheme; y isijAn output characteristic corresponding to a jth outer table of the ith inner table.
And filling the signal-to-noise ratio and sensitivity calculation results into an inner table, and determining the significance of each input parameter on the signal-to-noise ratio and the sensitivity through variance analysis. Wherein, the factor which has obvious influence on the signal-to-noise ratio has stronger nonlinear property and is determined as a stable factor. And factors which have no significant influence on the signal to noise ratio and have significant influence on the sensitivity have stronger linear property, and are determined as adjustment factors by combining the interactive analysis result of the step three.
In step three, non-recombination (X, Y) of arbitrary 2 parameters is taken from the input parameters, and first, the variation Δ X and Δ Y corresponding to the output characteristics when the parameter X and the parameter Y are respectively changed are calculated. Then, the variation Δ xy of the corresponding output characteristic when the combination of (X, Y) is varied simultaneously is calculated. If the parameter X is completely independent of the parameter Y, then the mathematical relationship Δ xy ═ Δ X + Δ Y should be satisfied. Otherwise, the interaction between the parameter X and the parameter Y is indicated.
The interaction factor Y is defined to reflect the degree of interaction between the parameters X and Y, while the interaction between the parameters is determined using the following formula,
|Δxy-(Δx+Δy)|≥γ×|Δxy|。
and determining input parameters which have approximate linear properties and are independent of the stability factors as adjusting factors by combining the signal-to-noise ratio, the sensitivity significance analysis result and the interactivity analysis result.
In the fourth step, a function model between the stability factor and the output characteristic is established by adopting a radial basis function method based on K-means. In order to solve the problem that interpolation results are inaccurate due to the fact that the number of radial basis function centers is large, the required radial basis function centers are selected from sampling points through reasonable training, the number of the radial basis function centers is reduced, and a K-means clustering algorithm is introduced. The following relationship between the system output response value and the stability factor experiment data point is assumed:
wherein y is the actual value of the point to be measured; y' is a value obtained by a radial basis function; ε is the error term; i is the serial number of the sampling point; n is the number of samples; lambda [ alpha ]iIs a weight coefficient; phiiIs a radial basis function; r isi＝||x-xiThe | | l represents the distance between the point to be measured and the sampling point; x is the point to be measured, xiIs a manually selected radial basis function center; c is the width of the radial basis function.
Writing the formula in matrix form: y is phiiλ+ε
Where λ is a weight coefficient, Y is a matrix of n output response values, and Y ═ Y1,y2...yn]T，ynRepresenting the output response value corresponding to each stability factor sampling point, λ ═ λ1,λ2...λm]T,λnThe weight coefficient occupied by the center of the radial basis function with the sequence number n is epsilon ═ epsilon1,ε2...εn]T,εnIn the order ofThe error between the response of the radial basis function of n and the actual value, λ being λ Φ-1*Y。
At this time, because the number n of sampling points is different from the number m of the centers of the radial basis functions, the weight of the output nodes of the radial basis functions is solved through a pseudo-inverse method, namely:
λ＝(ΦT*Φ)-1ΦT*Y
as the selection of the radial basis function has no obvious influence on the interpolation result of the radial basis function, the Gaussian function with the most extensive application can be selected to establish a radial basis function interpolation model, namely
r is the Euclidean distance between the point to be measured and the sampling point, e is a natural index, and e is approximately equal to 2.71828; phi is phiiThe matrix representation of (each radial basis function), Φ must be invertible. PhinmWhere n denotes the number of sampling points, m is the number of radial basis function center points, ΦnmThe radial basis function value in this case.
Adopting a K-means clustering algorithm to screen the radial basis function center, and comprising the following five steps:
first, randomly selecting initial clustering centers as y1(0),y2(0)…ym(0)。
Second, using ri＝||x-xiAnd | | l, calculating the distance between each sampling point and the clustering center. And classifying each sampling point according to the nearest clustering center to obtain m sampling point sets.
Thirdly, taking the average value of each sampling point set, and updating the value to a new clustering center, namely y1(1),y2(1)…ym(1)。
And fourthly, judging the difference value between the new clustering center and the original clustering center, returning to the second step if the difference value is not within the specified error range, and performing the fifth step within the specified error range.
And fifthly, calculating a radial basis function width value and a node weight coefficient according to the radial basis function center value. The formula is λ ═ (Φ)T*Φ)-1ΦT*Y。
And sixthly, obtaining a predicted value at an unknown point by using the obtained weight coefficient and the radial basis function width c, namely establishing a radial basis function model based on K-means, wherein the radial basis function width c is the distance between the determined clustering center and a sampling point farthest from the determined clustering center.
Subsequently, a robustness optimization objective function is established with the aim of suppressing the quality fluctuation. Stability factor polynomial FsFor each stability factor X separatelysAnd (4) solving the partial derivatives to obtain the slopes of the functions in the directions of the respective factors. The closer the slope is to 0, indicating the better stability of the function at this point. Therefore, summing the squares of the above slope values establishes the objective function FstaTo optimize robustness to problem H1Reduced to the objective function FstaThe minimum value of (a) is shown by the following formula,
in the formula, xsiIs the ith stabilizing factor XsDot, XsFor stability reasons, the value range is XsminTo Xsmax，H1The objective function is optimized for robustness,
determining a stability factor to enable an objective function F in a solution area by adopting a global optimization method of sequential quadratic programmingstaThe minimum parameter combination is the optimal scheme of the stability factor.
In step five, a linear regression method is adopted to establish a polynomial function between the adjusting factors and the output characteristics. After determining the stability factor optimization scheme, the output characteristics may deviate as the parameter values change. First, the offset amount Δ F of the output characteristic is calculatedsAnd then jointly adjust the factor polynomial FaEstablishing an offset compensation target H2The following formula is shown below.
In the formula, XaFor the factor X in its fluctuation range XsminTo XsmaxA variable within, Δ XaOffset by a given value of X, H2The objective function is compensated for the offset,
because the adjusting factors and the stabilizing factors are independent, the output offset can be quantitatively compensated under the condition of not influencing the robustness of the scheme, and the adjusting factor X is finally determinedaThe design of (1).
Claims (1)
1. A relay parameter global optimization method based on a K-means radial basis function is characterized in that: the method comprises the following steps:
the method comprises the following steps: determining input parameters and uncertainty factors according to a research object and an optimization target, and carrying out orthogonal test design on an internal and external surface; the method comprises the following steps that input parameters are arranged in an inner table, uncertainty factors are arranged in an outer table, an inner orthogonal table and an outer orthogonal table are respectively selected according to the number and the horizontal number of the input parameters and the uncertainty factors, and a test scheme is determined;
step two: calculating the output characteristics of each test scheme, calculating the signal-to-noise ratio and the sensitivity of the test result of the external table, inputting the test result into the internal table, performing variance analysis on the signal-to-noise ratio and the sensitivity of the internal table, and determining the nonlinear property and the approximate linear property of the internal table according to the significance analysis result of each input parameter;
step three: determining the correlation among input parameters through interactive analysis, decoupling the parameters, and determining the stability factor and the adjustment factor in the input parameters by combining the signal-to-noise ratio, the sensitivity significance analysis result and the interactive analysis result; the decoupling of the parameters specifically comprises: selecting non-recombination (X, Y) of any 2 parameters from input parameters, firstly respectively calculating variation delta X and delta Y corresponding to output characteristics when the parameter X and the parameter Y are independently changed, then calculating variation delta xy corresponding to the output characteristics when the (X, Y) combination is simultaneously changed, if the parameter X and the parameter Y are completely independent, the mathematical relationship of delta xy being delta X + delta Y is satisfied, otherwise, the interaction exists between the parameter X and the parameter Y;
the interaction factor Y is defined to reflect the degree of interaction between the parameters X and Y, while the interaction between the parameters is determined using the following formula,
|Δxy-(Δx+Δy)|≥γ×|Δxy|，
determining input parameters which have approximate linear properties and are independent of stability factors as adjusting factors by combining the signal-to-noise ratio, the sensitivity significance analysis result and the interactivity analysis result;
step four: establishing a function model between a stability factor and an output characteristic by adopting a radial basis function method based on K-means, establishing a stability optimization objective function by taking the suppression of quality fluctuation as a target, and determining a parameter value which enables the output characteristic change rate to be minimum in a solving area as an optimal solution of the stability factor through global optimization;
step five: establishing a polynomial function between the adjusting factor and the output characteristic by adopting a linear regression method, calculating a difference value of the output characteristic deviating from a target value after optimizing the stability factor, and finally determining the value of the adjusting factor by taking the offset of the compensated output characteristic as a target; the method for establishing the polynomial function between the adjusting factor and the output characteristic by adopting the linear regression method specifically comprises the following steps: after determining the stability factor optimization scheme, the output characteristic deviates along with the change of the parameter value, and firstly, the offset delta F of the output characteristic is calculatedsAnd then jointly adjust the factor polynomial FaEstablishing an offset compensation target H2As shown in the following formula,
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