CN105046079B - A kind of field mouthful test design method based on the optimal interior table designs of D- - Google Patents
A kind of field mouthful test design method based on the optimal interior table designs of D- Download PDFInfo
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Abstract
The present invention provides a kind of field mouthful test design method based on the optimal interior table designs of D, and this method comprises the concrete steps that：1. according to test objective, condition and engineering experience, the fundamental test information such as constraint between test response, the factor, the factor is provided；2. according to the number of noise factor and intending the horizontal number used, suitable uniform designs table is selected；3. determine the relational model between response and the factor and interior watch test number；4. in design section, the interior table designing scheme of given test number (TN) is provided using D optimal-design methods, table designs in completion；5. using based on quantile methods such as empirical distribution functions, appearance design is completed；6. being tested according to testing program, performance Index Calculation mass property signal-to-noise ratio is obtained according to experiment, being calculated makes the maximized controllable factor optimum level of signal-to-noise ratio；7. stable factor optimum level is determined based on Sensitivity Analysis Method；8. changing Dynamic gene, optimum factor horizontal combination is determined.
Description
Technical field
The present invention relates to one kind based on the optimal interior table designs of D- (i.e. most to change testing site determinant (Determinant) greatly
For the design method of criterion) field mouthful test design method, not only can effectively solve that traditional field mouthful design is reluctant to be set
The irregular situation in region is counted, and can effectively alleviate field mouthful design to cause what experimental design number increased severely using direct product sheet form
Problem, suitable for correlative technology fields such as product design, the manufacturing, quality control and process optimizations.
Background technology
One rational experimental design scheme can fully disclose each under the resources supplIes such as limited time, cost
Influence of the factor of influence to target response, obtains optimal target response as a result, to improve product under limited test number (TN)
Quality seeks optimal combination of process parameters etc..
For the stability enhanced product performance, the profound doctor in field mouthful proposes field mouthful design method, using interior table, appearance
The form of direct product, arranges each level of controllable factor in interior table, arranges noise factor to be tested in appearance, and so-called
Direct product method, refers to each collocation of controllable factor in internal table, simulates various interference using the error factor of appearance, calculates this and take
The antijamming capability matched somebody with somebody, i.e. signal-to-noise ratio (SN ratios), so that the comparison of various schemes is designed by internal table, using SN than finding most
Good controllable factor collocation.
Inventionbroadly, all experimental designs are all resource-constrained design in itself, and the purpose of experimental design is exactly to the greatest extent
In the case that amount economizes on resources, the information of as far as possible more systems or process, optimization design and technique are obtained.In traditional field mouthful
In design, interior table, appearance are carried out using orthogonal design, carry out data analysis by variance analysis, the requirement of its design section is
The hypercube of rule, generally causes the irregular situation of design section without considering there is constraint between the factor.In actual work
Cheng Zhong, due between factor of influence be often it is not independent, there are certain interaction so that it is irregular to produce design section
Situation, at this moment, using orthogonal design carry out in table design, need to cut or fill up test area and carry out compromise repeatedly, contrast,
Not only design process is complicated, but also since dimensionality reduction is excessive, causes design efficiency relatively low.Meanwhile the direct product sheet form of field mouthful design,
So that in the case where noise factor is more, test number (TN) increases severely, and the scope often allowed beyond experiment resource, causes enterprise difficult
To bear；Further, since appearance design is carried out using orthogonal design in traditional field mouthful, and orthogonal design is based on design table
Design, causes field mouthful design experiment number to be adjusted flexibly according to the actual requirements, be easy to cause resource cannot make full use of or
The situation of inadequate resource.Therefore, study in the case where factor of influence has constraint, reasonably Selection experiment point, so that science
Ground collects and analyzes data, and obtains more preferably parameter combination, optimization design and technique, with important theory significance and urgently
Current demand.
For this reason, The present invention gives a kind of field mouthful test design method based on the optimal interior table designs of D-.
The content of the invention
(1) purpose of the present invention：The present invention is for traditional field mouthful design in limited test number (TN), it is difficult to flexibly high
Effect solves the problems, such as experimental design when test area is irregular, there is provided a kind of field mouthful experimental design based on the optimal interior table designs of D-
Method, to filter out more representational testing site, so as to carry out accurate, efficient, flexible plan design.
D- optimal designs are a kind of design methods based on mathematical model, can be according to model parameter number, what is given
In design section, the optimal design for meeting any test number (TN) in the range of certain condition is provided；Frame of the present invention in field mouthful design
Under frame, designed using table in the progress of D- optimal designs, in the case of there can be constraint between the factor, provide more flexible, height
The experimental design scheme of effect, establishes more close to Product processing or the mathematical model of production process reality, is more accurately counted
According to analysis and prediction, so that it is determined that optimal factor level combination.
(2) technical solution：
The present invention gives a kind of field mouthful test design method based on the optimal interior table designs of D-.
The method that field mouthful design is combined with Nei Biao and appearance carries out based Robust Design, and uses signal-to-noise ratio (SN) to be used as matter
Evaluation index is measured, to seek most stable of parameter combination.
Traditional field mouthful design, interior table arrange the experiment of controllable factor using orthogonal design, and appearance is pacified using orthogonal design
The experiment of noise factor is arranged, the size fluctuated using signal-to-noise ratio (SN) Measure Indexes.Due to the limitation of orthogonal design, work as design
When region is irregular, traditional field mouthful design method can not provide efficient designing scheme.In addition, orthogonal test number is by setting
Meter method determines, rather than test accuracy, and under the action of field mouthful design direct product table, the property of orthogonal design " neat comparable " makes
Obtain test number (TN) to increase severely, and adjust very inflexible.However, during signal-to-noise ratio computation, it is not required that in testing program
Each error component " neat comparable ", therefore, can loosen the requirement of " neat comparable ", explore more efficiently experimental design side
Method.
The present invention is using table design in the progress of D- optimal designs, using uniformly setting based on quantiles such as empirical distribution functions
Meter carries out appearance design.By general equivalence theorem, for there is the linear model of p parameter, exist by n*(p≤n*≤p(p+
1)/2) the D- optimal designs ξ of a testing site composition*.I.e. D- optimal designs can use within the specific limits, provide arbitrarily devised area
Domain, the interior watch test designing scheme of any test number (TN), and as the increase of test factor number, D- optimal designs are required
Minimum test number (TN) will be far smaller than other designs.On the premise of test accuracy is met, table in the progress of D- optimal designs is used
Design, and combine uniform design and carry out appearance design, not only can effectively solve traditional field mouthful and design between the reluctant factor
There is a situation where constraint, and efficient experimental design scheme can be provided under less test number (TN).
Based on above-mentioned theory and thinking, a kind of field mouthful test design method based on the optimal interior table designs of D- of the present invention, tool
Body implementation steps are as follows：
Step 1：According to test objective, condition and engineering experience, experiment fundamental test information is provided, including experiment is rung
Answer (mass property i.e. of interest), factor of influence (including controllable factor and noise factor) and its value range, each factor it
Between restriction relation and experiment resource allow experiment total degree ntotal。
Step 2：According to the number of noise factor and intend the horizontal number m used, select suitable uniform designs table,
And appearance test number (TN) n is determined with thisouter.System of selection is described as follows：
Assuming that there is noise factor l, plan uses number of levels m, then uniform table is selected from uniform design Table storehouseAppearance test number (TN) is determined as n at the same timeouter=ω.
Step 3：Determine the relational model between response and the factor and interior watch test frequency ninner。
Relational model in the step between response and the factor specifically determines that method is as follows：
Based on the experiment essential information in step 1, the pass between response and the factor is given expression in the form of mathematical model
It is model, is denoted as y=X β+ε.Wherein,For known ninner× p ties up parameter model matrix；f
(xi) it is on xiKnown function, react whole controllable factors and its between restriction relation；β=(β0,β1,β2,...,βp)T
For p parameters to be estimated, the influence relation between each factor and response is reacted.
Interior watch test frequency ninnerDefinite method it is as follows：
By general equivalence theorem, for there is the linear model of p parameter, exist by n*(p≤n*≤ p (p+1)/2) a examination
Test a D- optimal designs ξ for composition*.So according to overall test frequency ntotalWith appearance test number (TN) nouter, it is not difficult to provide D- most
Excellent interior watch test numbers range [p, min (p (p+1)/2, ntotal/nouter)]。
Therefore, according to actual test conditions, any n is selectedinner∈[p,min(p(p+1)/2,ntotal/nouter)].
Step 4：In design section, given test number (TN) n is provided using D- optimal-design methodsinnerInterior table design
Scheme, table design, its specific design method are as follows in completion：
First, by each factor value range specification to [- 1,1] interval range, according to the restriction relation between the actual factor,
Determine design section；Then, in the design section, selection meets the design ξ of given number so that information matrixDeterminant is maximum, so far completes the optimal interior table designs of D-.Further, using G- optimum efficiencies
Weigh the Optimality of the design.The definition of G- optimum efficiencies is：
Here, G- optimum efficiencies value GeffCloser to 1, represent that design ξ is better.
Step 5：Using based on the quantile method such as empirical distribution function, for each appearance testing site in interior table, determine
Noise factor is horizontal, completes appearance design.
The definite method of noise factor level is as follows in the step：
Remember x[i]It is variable x based on the grade quantile of empirical distribution function i-th, it is defined as follows：
Wherein, F (x) is the distribution function of stochastic variable x, and m is noise factor number of levels；ArgF () representative function F
The inverse function of ().In other words, above formula represents, whenWhen, the value of corresponding stochastic variable x is denoted as x[i], x[i]As because
I-th of level value of sub- x.
Step 6：Specifically tested according to testing program, it is special that the product performance index obtained according to experiment calculates quality
Property signal-to-noise ratio, fitting obtain the regression function η (x between signal-to-noise ratio and the factori), being calculated makes signal-to-noise ratio maximumlly controllable
Factor optimum level.
Step 7:Stable factor and its optimum level are determined based on Sensitivity Analysis Method.
Signal-to-noise ratio is to factor of influence xi, i=1,2 ..., the sensitivity definition of n is as follows：
SijNumerical value representTo variable xiSensitivity, SijSymbolic indicationTo variable xiMonotonicity.
The larger S of numerical valueijThe corresponding factor is stable factor, takes the combination of its optimal level to make system defeated to reach the stability of system
The fluctuation gone out is reduced to a minimum.Its cofactor is Dynamic gene, and the output valve for adjusting system makes up to or close to mesh
Scale value, so that in the case where reducing fluctuation to the greatest extent, obtains so that the optimal parameter of mass property closest to its desired value combines.
Step 8:Regression fit tries to achieve unknown parameter in relational model y, and Dynamic gene is adjusted according to this, determines
Optimum factor horizontal combination so that mass property estimate is closest to desired value under the testing program.
(3) advantage and effect：
The present invention provides a kind of field mouthful test design method based on the optimal interior table designs of D-, its advantage is：
1. this hair is designed using table in the progress of D- optimal designs, can be given between test factor under Existence restraint condition
Go out efficient and rational field oral examination and test designing scheme.
2. test number (TN) sharp increase problem of the invention caused by effectively alleviating field mouthful design direct product sheet form, and Nei Biao can
To provide the experiment for meeting arbitrary number of times under certain condition so that testing program number can be adjusted flexibly.
Brief description of the drawings
Fig. 1 is the method for the present invention flow chart.
Embodiment
Below by taking bead nitridation process as an example, with reference to attached drawing, the present invention is described in further details.
Feedback spring is the critical component of electrohydraulic servo valve, at the feedback groove requirement on bead and spool on its feedback rod
In zero clearance mated condition.During the use of feedback spring, if bead hardness surface is inadequate, easily trigger wear phenomenon,
Cause no load discharge curve to be mutated, so as to cause mistake servosignal, electrohydraulic servo valve is produced critical fault.In order to improve
Bead surface hardness to bead, it is necessary to carry out ion soft-nitriding processing.Nitride layer depth is deeper, then the wearability of bead is better,
But nitride layer depth is restricted be subject to the small ball's diameter change at the same time.While in order to ensure that the diameter of bead is in allowed band,
Bead surface hardness is improved, sets nitride layer depth desired value as 0.05mm.See Fig. 1, based on specific implementation step of the present invention such as
Under：
Step 1：Determine test response (mass property i.e. of interest), factor of influence (including controllable factor and noise because
Son) and its value range, the experiment total degree n that restriction relation and experiment resource between each factor allowtotal.Here, examine
Consider experiment resource and schedule requirement, the requirement of overall test number is no more than 150 times.
By the depth of nitration case in response, during ion soft-nitriding, a sputtering stage is undergone every time
With two nitridation stages, table 1 summarizes each factor of influence and its value range：
1 factor of influence of table and its value range
It is theoretical according to ion soft-nitriding, to ensure nitriding result, set constraints：x5-x2>=20 DEG C, x9-x5≥10
℃.In addition, Ar, H2,N2Throughput (L/min) is difficult to accurately control, and there is fluctuation, is noise factor, its tolerance is respectively
Step 2：According to the number of noise factor and intend the horizontal number m used, select suitable uniform designs table,
And appearance test number (TN) n is determined with thisouter.System of selection is described as follows：
Assuming that there is noise factor l, plan uses number of levels m, then from uniform design Table storehouse, uniform table is selected according to deviationOrAnd appearance test number (TN) is determined as nouter=ω.
Assuming that there is noise factor l, plan uses number of levels m, then uniform table U is selected from uniform design Table storehouseω(ml), and
Appearance test number (TN) is determined as nouter=ω.
In this example, 3 noise factors are shared, to reduce test number (TN) on the premise of precision is ensured, to each factor
Choose 6 levels to be tested, select uniform designs tableCarry out appearance design, appearance test number (TN) nouter=6.
Step 3：Determine the relational model between response and the factor and interior watch test frequency ninner。
Relational model in the step between response and the factor specifically determines that method is as follows：
Based on the experiment essential information in step 1, the pass between response and the factor is given expression in the form of mathematical model
It is model, is denoted as y=X β+ε.Wherein,For known ninner× p ties up parameter model matrix；f
(xi) it is on xiKnown function, react whole controllable factors and its between restriction relation；β=(β0,β1,β2,...,βp)T
For p parameters to be estimated, the influence relation between each factor and response is reacted.
Interior watch test frequency ninnerDefinite method it is as follows：
By general equivalence theorem, for there is the linear model of p parameter, exist by n*(p≤n*≤ p (p+1)/2) a examination
Test a D- optimal designs ξ for composition*.So according to overall test frequency ntotalWith appearance test number (TN) nouter, it is not difficult to provide D- most
Excellent interior watch test numbers range [p, min (p (p+1)/2, ntotal/nouter)].Therefore, it is any according to actual test conditions, selection
ninner∈[p,min(p(p+1)/2,ntotal/nouter)].
In the present embodiment, according to engineering experience, such as drag is chosen：
Y=β0+x1β1+x2β2+xβ3+x4β4+x5β5+x6β6+x7β7+x8β8+x9β9+x2x3β23+
x2x5β25+x2x8β28+x3x5β35+x3x6β36+x3x7β37+x3x8β38+x3x9β39+x6x9β69+e
Wherein, error e~N (0, σ2)。
19 unknown parameters, i.e. p=19 are shared in the model.The number with reference to needed for interior table, it may be determined that appearance test number (TN)
19≤n of value rangeinner≤min(19(19+1)/2,ntotal/6).Consider overall test resource, watch test number in selection
ninner=19.
Step 4：In design section, given test number (TN) n is provided using D- optimal-design methodsinnerInterior table design
Scheme, table design in completion.Specific design method is as follows：
First, by each factor value range specification to [- 1,1] interval range, according to the restriction relation between the actual factor,
Determine design section；Then, in the design section, selection meets the design ξ of given number so that information matrixDeterminant is maximum, wherein, f (xi) it is on xiKnown function, so far complete D- it is optimal in
Table designs.Further, the Optimality of the design is weighed using G- optimum efficiencies.The definition of G- optimum efficiencies is：
Wherein, d (x, ξ)=fT(x)M-1(ξ)f(x).G- optimum efficiency values GeffCloser to 1, then it represents that design ξ is better.
In the present embodiment, the optimal interior table design tables of D- are as follows：
Interior watch test scheme (coding) of the table 2 based on D- optimal designs
| Sequence number | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 |
| 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | -0.38418 | 1 |
| 2 | -1 | -0.12675 | 1 | -1 | 0.66667 | 1 | 1 | -1 | 1 |
| 3 | 0.02211 | -0.19135 | 0.001343 | 0.021786 | -0.1083 | -0.01131 | 0.050151 | -0.03109 | 1 |
| 4 | 1 | 1 | 0.022368 | 1 | 0.66667 | -0.00126 | 1 | -0.01406 | 1 |
| 5 | -1 | 1 | 1 | -1 | -0.33333 | -1 | -1 | 1 | 1 |
| 6 | 1 | 0.31204 | 0.036341 | -1 | -1 | 1 | 1 | -1 | -0.66667 |
| 7 | -1 | 1 | 0.073784 | 1 | 0.66667 | 1 | -1 | 1 | 1 |
| 8 | 1 | -1 | -1 | -0.15154 | -1 | 1 | 1 | 0.025892 | 1 |
| 9 | 0.072806 | -1 | -1 | 1 | -1 | -0.03687 | -1 | -1 | -0.66667 |
| 10 | 1 | 0.18165 | 1 | 1 | -1 | -1 | 1 | -1 | -0.66667 |
| 11 | -1 | 1 | -1 | -1 | 0.66667 | -1 | -0.10588 | -0.045 | 1 |
| 12 | -1 | -1 | 0.020447 | 1 | -0.09342 | -1 | -1 | -1 | 0.23992 |
| 13 | -1 | -0.03265 | 1 | 1 | -1 | 1 | 1 | 1 | 1 |
| 14 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | -0.00697 | 0.27705 |
| 15 | 1 | -1 | -0.26793 | -1 | -1 | -1 | -1 | -1 | 1 |
| 16 | -1 | -1 | 1 | 1 | 0.66667 | -1 | -1 | 1 | 1 |
| 17 | 1 | 0.020626 | 0.074386 | 1 | -1 | -1 | -1 | 0.055004 | 1 |
| 18 | -1 | 0.33333 | 1 | -0.04891 | -1 | 1 | 1 | 1 | -0.66667 |
| 19 | -0.08383 | 1 | 1 | 0.048094 | 0.66667 | -1 | -1 | -1 | 1 |
The G efficiency of the designIt can be seen that its design efficiency is higher.
Step 5：Using based on the quantile method such as empirical distribution function, for each appearance testing site in interior table, determine
Noise factor is horizontal, completes appearance design.
The definite method of noise factor level is as follows in the step：
Remember x[i]It is variable x based on the grade quantile of empirical distribution function i-th, it is defined as follows：
Wherein, F (x) is the distribution function of stochastic variable x, and m is noise factor number of levels；ArgF () representative function F
The inverse function of ().In other words, above formula represents, whenWhen, the value of corresponding stochastic variable x is denoted as x[i], x[i]As because
I-th of level value of sub- x.
In this example, it is assumed that the equal Normal Distribution N (0, σ of noise factor2), there are relation between tolerance Δ and standard deviation sigma
The σ of Δ=3, the variance that can obtain three noise factors are respectively：
Mean μ is then determined according to corresponding interior table.By taking table in table 2 No. 2 as an example, three definite noise factor number of levels under the conditions of being somebody's turn to do
It is shown in Table 3.
Table corresponds to the setting of noise factor number of levels in table 32
Then corresponding appearance is designed as：
The corresponding appearance design of table in table 42
Step 6：Specifically tested according to testing program, it is special that the product performance index obtained according to experiment calculates quality
Property signal-to-noise ratio, fitting obtain the regression function η (x between signal-to-noise ratio and the factori), being calculated makes signal-to-noise ratio maximumlly controllable
Factor optimum level.
In the example, Definite purpose is presented in response nitride layer depth of interest, according to gained test data, calculates each
Signal-to-noise ratio under part is shown in Table 5
5 experimental design scheme (decoding) of table and signal-to-noise ratio
Using above-mentioned data, model parameter estimation is carried out to signal-to-noise ratio η and each factor, use method of gradual regression can obtain with
Drag
η=3465.311+0.033862x1-1.34615x2+16.60486x3-0.1968x4-6.99205x5-384.59x6
+84.20613x7+0.3755x8-5.12495x9+0.148254x1x3+0.002458x2x5+0.328684x4x6
+0.255114x4x7+2.575394x6x8+0.88726x7x8+0.010374x5x9
Using non-linear solving method, obtain in the case where meeting experiment constraint so that the factor level group of signal-to-noise ratio maximum
It is combined into：
x*=[30,500,0.6,120,520,0.07,0.475,150,530]
Step 7:Stable factor and its optimum level are determined based on Sensitivity Analysis Method.
Signal-to-noise ratio is to factor of influence xi, i=1,2 ..., the sensitivity definition of n is as follows：
SijNumerical value representTo variable xiSensitivity, SijSymbolic indicationTo variable xiMonotonicity.
The larger S of numerical valueijThe corresponding factor is stable factor, takes the combination of its optimal level to make system defeated to reach the stability of system
The fluctuation gone out is reduced to a minimum.Its cofactor is Dynamic gene, and the output valve for adjusting system makes up to or close to mesh
Scale value, so that in the case where reducing fluctuation to the greatest extent, obtains so that the optimal parameter of mass property closest to its desired value combines.
In the present embodiment, object function η is as follows to the Calculation of Sensitivity of each factor of influence：
Sensitivity of the object function η to all factors of influence is arrogant to small collect for：
6 η of table is to each factor of influence sensitivity summary sheet
Obviously, object function η is to N2Throughput is most sensitive, secondly H2Throughput and Ar throughputs.Accordingly, it is determined that N2、
H2Three kinds of factors of Ar throughputs are stable factor, choose its optimum level to signal-to-noise ratio；Determine three phases duration of ventilation and
Ventilation air is Dynamic gene, and the mass property of designing scheme is adjusted to desired value using Dynamic gene.
Step 8:Regression fit tries to achieve unknown parameter in relational model y, and Dynamic gene is adjusted according to this, determines
Optimum factor horizontal combination so that mass property estimate is closest to desired value under the testing program.
In the present embodiment, using least square method, trying to achieve unknown parameters ' value in relational model y is：
β=(β0,β1,...,β69)
=(1.9666,0.0003, -0.086, -0.7368, -0.0002, -0.001, -0.0019,0.1384,0.78,
-0.0083,0,0572,-0.0006,0.0028,-0.0006,0.0011,-0.1771,0.001,0.003,
0.231)
According to relational model, Dynamic gene is transferred, determines that final optimal case is：
x*=[30,440,0.6,120,350,0.07,0.475,120,500]
Under the parameter combination, bead nitride layer depth predicted value is 5.01mm, reaches desired value requirement, satisfactorily completes small
Ball surface nitrogenizes the target of experimental design.
Claims (1)
- A kind of 1. field mouthful test design method based on the optimal interior table designs of D-, it is characterised in that：This method comprises the following steps that：Step 1：According to test objective, condition and engineering experience, experiment fundamental test information is provided, including test response is Mass property of interest, factor of influence include controllable factor and noise factor and its value range, the constraint between each factor The experiment total degree n that relation and experiment resource allowtotal；Step 2：According to the number of noise factor and intend the horizontal number m used, select suitable uniform designs table, and with This determines appearance test number (TN) nouter, system of selection is described as follows：Assuming that there is noise factor l, plan uses number of levels m, then uniform table is selected from uniform design Table storehouse Appearance test number (TN) is determined as n at the same timeouter=ω；Step 3：Determine the relational model between response and the factor and interior watch test frequency ninner；Relational model in the step between response and the factor specifically determines that method is as follows：Based on the experiment essential information in step 1, the relation mould between response and the factor is given expression in the form of mathematical model Type, is denoted as y=X β+ε；Wherein,For known ninner× p ties up parameter model matrix；f(xi) For on xiKnown function, reflect whole controllable factors and its between restriction relation；β=(β0,β1,β2,...,βp)TFor p+ 1 parameter to be estimated, reflects the influence relation between each factor and response；Interior watch test frequency ninnerDefinite method it is as follows：By general equivalence theorem, for there is the linear model of p parameter, exist by n*The D- optimal designs of a testing site composition ξ*, wherein, p≤n*≤p(p+1)/2；So according to overall test frequency ntotalWith appearance test number (TN) nouter, it is not difficult to provide D- Optimal interior watch test numbers range [p, min (p (p+1)/2, ntotal/nouter)]；Therefore, according to actual test conditions, any n is selectedinner∈[p,min(p(p+1)/2,ntotal/nouter)]；Step 4：In design section, given test number (TN) n is provided using D- optimal-design methodsinnerInterior table designing scheme, Table designs in completion, its specific design method is as follows：First, by each factor value range specification to [- 1,1] interval range, according to the restriction relation between the actual factor, determine Design section；Then, in the design section, selection meets the design ξ of given number so that information matrixDeterminant is maximum, so far completes the optimal interior table designs of D-；Further, using G- optimum efficiencies The Optimality of the design is weighed, the definition of G- optimum efficiencies is：<mrow> <msub> <mi>G</mi> <mrow> <mi>e</mi> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mi>p</mi> <mrow> <munder> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <mrow> <mi>x</mi> <mo>&Element;</mo> <mi>X</mi> </mrow> </munder> <mi>d</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>&xi;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>Wherein, d (x, ξ)=fT(x)M-1(ξ) f (x), G- optimum efficiency values GeffCloser to 1, then it represents that design ξ is better；Step 5：Using based on the quantile method such as empirical distribution function, for each appearance testing site in interior table, noise is determined Factor level, completes appearance design；The definite method of noise factor level is as follows in the step：Remember x[i]It is variable x based on the grade quantile of empirical distribution function i-th, it is defined as follows：<mrow> <msub> <mi>x</mi> <mrow> <mo>&lsqb;</mo> <mi>i</mi> <mo>&rsqb;</mo> </mrow> </msub> <mo>=</mo> <mi>arg</mi> <mi> </mi> <mi>F</mi> <mrow> <mo>(</mo> <mfrac> <mi>i</mi> <mi>m</mi> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>m</mi> </mrow>Wherein, F (x) is the distribution function of stochastic variable x, and m is noise factor number of levels；ArgF () representative function F's () Inverse function；In other words, above formula represents, whenWhen, the value of corresponding stochastic variable x is denoted as x[i], x[i]As factor x's I-th of level value；Step 6：Specifically tested according to testing program, the product performance index obtained according to experiment calculates mass property letter Make an uproar and compare, fitting obtains the regression function η (x between signal-to-noise ratio and the factori), being calculated makes the maximized controllable factor of signal-to-noise ratio Optimum level；Step 7:Stable factor and its optimum level are determined based on Sensitivity Analysis Method；Signal-to-noise ratio is to factor of influence xi, i=1,2 ..., the sensitivity definition of n is as follows：SijNumerical value representTo variable xiSensitivity, SijSymbolic indicationTo variable xiMonotonicity, numerical value Larger SijThe corresponding factor is stable factor, takes the combination of its optimal level to reach the stability of system, makes what system exported Fluctuation is reduced to a minimum；Its cofactor is Dynamic gene, and the output valve for adjusting system makes up to or close to desired value, So as in the case where reducing fluctuation to the greatest extent, obtain so that the optimal parameter of mass property closest to its desired value combines；Step 8:Regression fit tries to achieve unknown parameter in relational model y, and Dynamic gene is adjusted according to this, determines optimal Factor level combines so that mass property estimate is closest to desired value under the testing program.
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