CN104008248A - Gaussian process based injection molding forming process robust design and tolerance design method - Google Patents

Abstract

The invention relates to a Gaussian process based injection molding forming process robust design and tolerance design method. The Gaussian process based injection molding forming process robust design and tolerance design method comprises obtaining the correlation of process parameters and quality objectives by a Gaussian process based self-adaptive canonical correlation analysis method and classify the parameters into main parameters and secondary parameters according to the sizes of degrees of the correlation; establishing a robust optimization model of the main parameters, adding the fluctuation quantity into an objective function and constraint conditions and obtaining a robust process parameter combination through simultaneous optimization of the two targets of the mean and variance to reduce the complexity of calculation of a multi-parameter model reasonably; performing analysis on the relation of the process parameter fluctuation tolerance range and the cost, establishing a mathematical expectation model of a quality overall loss and setting a reasonable tolerance range for every process parameter. According to the Gaussian process based injection molding forming process robust design and tolerance design method, the influence of human experience and trial and error experiment is greatly reduced in the design process, the design cycle is short, the qualified rate of products is high, the system cost is low, an intelligent control project is implemented conveniently, and the Gaussian process based injection molding forming process robust design and tolerance design method can be widely applied to the forming process of various materials.

Description

The injection forming process based Robust Design and Tolerance Design Method based on Gaussian process

Technical field

The present invention relates to a kind of based Robust Design and Tolerance Design Method of the injection forming process, especially the injection forming process that relates to a kind of Gaussian process canonical correlation analysis models coupling optimized algorithm is controlled based Robust Design and Tolerance Design Method, belongs to injection molding technology engineering field.

Background technology

Along with continuous progress and the development of social science and technology, market also more and more trends towards high precision, high qualification rate, low cost to the requirement of product, and production technology also progressively makes the transition to intellectuality.In injection molding technology engineering field, the obtaining of a large amount of prediction that is applied to forming quality of computer simulation technique and optimal procedure parameters combination.Yet in the middle of actual production manufacture process, the quality of goods is also subject to the impact of a lot of noise factor, as the fluctuation of technological parameter and personnel's operation etc.Thereby by the impact that based Robust Design reduces these factors, improve product percent of pass and also just seem more and more important.On the other hand, the required key factor of considering of the cost Ye Shi enterprise of product, the tolerance of technological parameter not only has vital effect to product quality, and directly affects system cost.In existing based Robust Design and Tolerance Design Method, have following several:

(1) aspect sane process parameter optimizing, as Huang exists: ' Research on Robust Design of Craft Parameters in Plastic Injection Based on Relation Degree ' (the Shooting Technique parameter Robust Optimal Design research based on the degree of association) (China Academic Journal Electronic Publishing House.1004-132X (2009) 21-2627-05) (academic magazine electronic publishing society, 2009, while 2627-2631 page) being optimized, utilize degree of association screening design variable and noise factor, and take warpage and injection moulding process is analyzed as quality index, but the noise factor causing for technological parameter fluctuation lacks certain computing method.

(2) aspect the cost control of sane technique, Wei exists: ' Robust Optimization and Tolerance Analysis of Autobody Panel Stamping ' (sane optimization and the tolerance analysis of automobile coverage forming technique) (Department of Plasticity Technology Shanghai Jiao Tong University, 2009) (Shanghai Communications University's plastic forming engineering department, 2009) by brief response surface model of joining a little, analyzed the impact of tolerance on product quality, verified by the tolerance of appropriate design technological parameter and can improve the quality of products, reduce manufacturing cost, for providing certain method, the sane Allowance Design of optimizing instructs, but do not accomplish to distribute tolerance into technological parameter.

In sum, in existing based Robust Design and Tolerance Design Method, deficiency is mainly reflected in following three aspects: 1,, because the application to agent model is less, its computing time is often long; 2, because each technological parameter in Practical Project exists complicated relevance to aimed quality index, traditional optimal design is all generally for all technological parameters, has so just brought a large amount of workloads, and design cycle cost increases greatly; 3, the research of the practical application of Allowance Design being done is less, especially, on the basis based on based Robust Design, is guaranteeing how further systematically to reduce cost on the satisfactory basis of qualification rate.

Summary of the invention

The object of the invention is to propose a kind of Gaussian process and control based Robust Design and Tolerance Design Method in conjunction with the injection forming process of optimized algorithm, rely on Gauss's canonical correlation analysis to filter out major parameter, and further design on this basis, solve traditional optimization long computing time, the problem of design cycle and high cost.

The present invention realizes the technical scheme that above-mentioned purpose takes: a kind of the injection forming process based on Gaussian process is controlled based Robust Design and Tolerance Design Method, comprise experimental design method sampling, correlation analysis based on Gaussian process, based Robust Design and Allowance Design, specifically according to following steps, carry out:

Step 1, according to the given starting condition of user, propagates the Latin hypercube ETPHLD methods of sampling by enhancement mode translation and carries out experimental design, obtains design variable combination X=[x ₁, x ₂..., x _n] ^t, and design variable combination is carried out respectively to high accuracy analysis solve, obtain corresponding response Y=[y ₁, y ₂..., y _n] ^t, combine the training dataset (X, y) of composition model in the lump with design variable;

Step 2, with the resulting training dataset of step 1, the canonical correlation analysis model of foundation based on Gaussian process, determine the covariance function in the canonical correlation analysis model based on Gaussian process, obtain the relevance between technological parameter and quality index, the following formula of computing formula (1) of this covariance function:

${\mathrm{\Σ}}_{\mathrm{kj}}^i={\mathrm{\σ}}_{\mathrm{iy}}^2\exp (-({\left|\right|x_{1k}-x_{1j}\left|\right|}^2+{\left|\right|x_{2k}-x_{2j}\left|\right|}^2)/2l_i^2+{\mathrm{\σ}}_{\mathrm{in}}^2{I}_N,---\left(1\right)$

K=1 in formula, 2 ... N, j=1,2 ... N, i=1,2; N is the number of sample set; x _1jj sample point in first data stream; x _2jj sample point in second data stream; l _i, σ _iyand σ _infor the super parameter of Gaussian process, σ _infor sample noise, I _nfor N rank unit matrix;

Step 3, obtains the relevance between technological parameter and quality index according to step 2, is divided into major parameter and minor parameter, and sets up based Robust Design model for major parameter according to the large young pathbreaker's technological parameter of the degree of association;

Step 4, the based Robust Design model that the particle cluster algorithm that adopts gradient to strengthen is set up step 3 is optimized and solves;

Step 5, for the resulting sane solution of step 4, the relation of analysis process parameter tolerances scope and mass loss, manufacturing cost and substandard product cost, set up the following formula of Mathematical Expectation Model (2) of quality overall loss:

E[C _T]＝E[L(y)]+E[C _M]+E[C _R] (2)

Minimum for various loss summations are dropped to, adopt Optimized model below, following formula (3):

L in formula (y) represents the quality loss function of influence factor y; C _t, C _r, C _mrepresent respectively oeverall quality loss, manufacturing cost and substandard product cost, y ₀be the desired value of certain technological parameter, its average and variance are respectively μ and σ ², K is mass loss coefficient, δ is the depart from objectives modified value of average size of controlling factor, a ₀be one with the irrelevant constant of range of tolerable variance, its value is decided by manufacturing equipment, a ₁be a constant relevant to margin tolerance, and range of tolerable variance is less, its value is just larger;

Step 6, the optimization problem of mentioning for step 5, as shown in formula (3), solves by Lambert function, and the optimal value that obtains δ is as formula (4):

${\mathrm{\δ}}^{*}=\sqrt{-2\mathrm{LambertW}\left\{\frac{\sqrt{2\mathrm{\π}}{a}_1\mathrm{\σ}\·e^{\frac{-[{(\mathrm{\μ}-y_0)}^2+{\mathrm{\σ}}^2-1-\frac{C_R}{K}]}{2}}}{2K}\right\}+2[{(\mathrm{\μ}-y_0)}^2+{\mathrm{\σ}}^2-1-\frac{C_R}{K}]}---\left(4\right)$

Finally obtain the rational range of tolerable variance of each technological parameter as formula (5):

USL ^*＝μ+δ ^*σ

(5)

LSL ^*＝μ-δ ^*σ

USL in formula ^*and LSL ^*be respectively the upper and lower bound of the range of tolerable variance after process parameter optimizing.

The resulting technological parameter of canonical correlation analysis model based on Gaussian process described in step 2 and the Computing Principle of the relevance between quality index are: first by transforming canonical correlation main shaft, try to achieve canonical correlation variable, finally utilize the canonical correlation variable of trying to achieve to calculate the related coefficient between parameter, and related coefficient is exactly the large Small Indicators of the degree of association between variable.

The influence of fluctuations that simultaneously adds constraint function and objective function in major parameter based Robust Design model described in step 3, the process of establishing step of its model is:

Steps A adds undulate quantity to consider in constraint condition, as formula (6):

$g_i(x,p)={{\mathrm{\μ}}_g}_i(x,p)+{\mathrm{k\σ}}_{g_i}(x,p)\≤0,i=\mathrm{1,2},...,l---\left(6\right)$

μ in formula _gi(x, p) represents the average of constraint function, σ _gi(x, p) represent the standard deviation of constraint function, k represents that Sigma level allows the degree of probability flux, when retraining the fluctuation Normal Distribution of response amount, k=3 represents that the probability that optimal value meets constraint condition is the number that 99.87%, i represents constraint function;

Step B adds undulate quantity to consider in objective function, as formula (7):

$\begin{array}{cc}\min & \mathrm{\α}\frac{{\mathrm{\μ}}_f(x,p)}{{{\mathrm{\μ}}^{*}}_f(x,p)}+(1-\mathrm{\α})\frac{{\mathrm{\δ}}_f(x,p)}{{{\mathrm{\δ}}^{*}}_f(x,p)},0\≤\mathrm{\α}\≤1\end{array}---\left(7\right)$

μ in formula _f(x, p) and δ _f(x, p) is respectively average and the variance of objective function f (x, p) in deterministic optimization model, μ ^* _fand δ ^* _fbe respectively the optimal value of objective function while only considering average and variance, α is weight coefficient, when the importance of average and variance is the same, and α=0.5;

Then simultaneously optimization aim function and constraint condition, obtain major parameter based Robust Design model as formula (8):

$\begin{array}{cc}\min & \mathrm{\α}\frac{{\mathrm{\μ}}_f(x,p)}{{{\mathrm{\μ}}^{*}}_f(x,p)}+(1-\mathrm{\α})\frac{{\mathrm{\δ}}_f(x,p)}{{{\mathrm{\δ}}^{*}}_f(x,p)},0\≤\mathrm{\α}\≤1\\ s.t.& g_i(x,p)={{\mathrm{\μ}}_g}_i(x,p)+{{\mathrm{k\σ}}_g}_i(x,p)\≤0,i=\mathrm{1,2},...,l\\ & X^L+{\mathrm{k\σ}}_x\≤{\mathrm{\μ}}_x\≤X^U-{\mathrm{k\σ}}_x\end{array}---\left(8\right)$

X in formula ^uand X ^lbe respectively the upper and lower bound of influence factor x.

The foundation of the technological parameter range of tolerable variance described in step 5 and the Mathematical Expectation Model of cost is specifically divided into three parts:

The relation of technological parameter and mass loss is as formula (9):

$E\left[L\left(y\right)\right]=\underset{\mathrm{LSL}}{\overset{\mathrm{USL}}{\∫}}L\left(y\right)f\left(y\right)\mathrm{dy}---\left(9\right)$

Relation between technological parameter and manufacturing cost is as formula (10):

E[C _M]＝a ₀+2δσa ₁ (10)

Relation between technological parameter and substandard product is as formula (11).

Compared with prior art, the beneficial effect that the present invention possesses is: propose a kind of simple and practical the injection forming process based on Gaussian process and control based Robust Design and Tolerance Design Method, with the key concept of standard Gaussian process regression model and the formula of model, be embodied as basis, utilize canonical correlation analysis to obtain the degree of association relation between technological parameter and quality qualitative change; And then carry out based Robust Design for the major parameter filtering out, not only can reduce design cycle and calculated amount, and insensitive to noise factor of the system that guaranteed; Finally on sane basis of separating, by analyzing the relation between tolerance and cost, for each technological parameter arranges rational range of tolerable variance, guaranteeing on the basis of qualification rate, can effectively reduce cost, be convenient to Intelligent Control Engineering and realize, can be widely used in various types of materials forming process, there is good production application prospect.

Accompanying drawing explanation

Fig. 1 is the sane optimum results isogram in the embodiment of the present invention 1.

Fig. 2 is (one) two-dimentional three-view diagram of part in the embodiment of the present invention 2.

Fig. 3 is (two) two-dimentional three-view diagram of part in the embodiment of the present invention 2.

Fig. 4 is (three) two-dimentional three-view diagram of part in the embodiment of the present invention 2.

Fig. 5 is (one) positive two side views of part in the embodiment of the present invention 2.

Fig. 6 is (two) positive two side views of part in the embodiment of the present invention 2.

Fig. 7 is the Optimizing Flow figure in the embodiment of the present invention 2.

Fig. 8 is cost comparison diagram before and after the Allowance Design in the embodiment of the present invention 2.

Embodiment

Below in conjunction with embodiment and accompanying drawing detailed description thereof, the injection forming process based on Gaussian process is controlled the technical scheme of based Robust Design and Tolerance Design Method, but the specific embodiment of the present invention is not limited to following embodiment.

In embodiment 1, the based Robust Design based on Gaussian process proposed by the invention and validity and the feasibility of Tolerance Design Method will be proved by a numerical example.In order to reach comparison object, the present invention will contrast with traditional deterministic optimization.

Embodiment 1

Seek sane the numerical example of separating

Based Robust Design based on Gaussian process and a Tolerance Design Method, comprise experimental design method sampling, the correlation analysis based on Gaussian process, and based Robust Design and Allowance Design, specifically comprise the following steps:

Step 1, seeks problem according to the numerical value that user is given, and its mathematical description is as formula (12), by Latin hypercube sampling method, get 10 initial training samples, and bring in formula (12) analytic expression, the value of meeting with a response, and form in the lump training dataset with its sample set;

$\begin{array}{c}f\left(x\right)={(x_2-\frac{5.1}{{4\mathrm{\π}}^2}{x}_1^2+\frac{5}{\mathrm{\π}}{x}_1-6)}^2+10(1-\frac{1}{8\mathrm{\π}})\cos \left(x_1\right)+10\\ -5\≤x_1\≤\mathrm{5,5}\≤x_2\≤15\end{array}---\left(12\right)$

The standard deviation of supposing variable in formula is [0.5,0.5], and Normal Distribution.

Step 2, for the numerical example of step 1, after its objective function and constraint condition have been added to undulate quantity, the Optimized model obtaining is as formula (13):

$\begin{array}{cc}\min & \mathrm{\σ}(x_1,x_2)\\ s.t.& \mathrm{\μ}(x_1,x_2)\≤10\\ & -5+{{3\mathrm{\σ}}_x}_1\≤x_1\≤5-{{\mathrm{\σ}}_x}_1\\ & 5+{{\mathrm{\σ}}_x}_2\≤x_2\≤15-{{\mathrm{\σ}}_x}_2\end{array}---\left(13\right)$

Step 3, the optimization problem that adopts genetic algorithm to propose step 2 solves, algorithm parameter arranges as follows: Population Size is 50, iterations is 200, crossover probability is 0.8, genetic probability is 0.1, and as Fig. 1 is and the comparison diagram of traditional deterministic optimization, the sane solution of function is that the asterisk in the figure lower right corner indicates point.The result obtaining is represented in table 1:

Table 1 optimum solution and sane comparison of separating

Optimal value	x 1	x 2	σ
				Optimum solution	π	2.275	1.20
Sane solution	1.131	2.223	1.17

From table, can find, the optimum results of sane solution and optimum solution is difference slightly, many but variance fluctuation has but reduced.

Embodiment 2

The injection forming process based on Gaussian process is controlled based Robust Design and the application of Tolerance Design Method in injection mo(u)lding

Based Robust Design and the Tolerance Design Method of employing based on Gaussian process optimized certain automobile glass guide slot part, and its two-dimentional moulding figure and cut-open view are as shown in Fig. 2-Fig. 6, and the based Robust Design of Shooting Technique parameter and the flow process of Allowance Design as shown in Figure 7, comprise the steps:

Step 1, the technical papers of formulating according to client, selected molding technique parameter to be optimized, and determine its span: melt temperature T _w=190 ℃～230 ℃; Mold temperature T _m=40 ℃～75 ℃; Inject time t _i=2s～4s; Dwell time t _p=5s～25s; Injection pressure P _i=60Mpa～190Mpa; Dwell pressure P _p=60Mpa～160Mpa.By enhancement mode translation, propagate Latin Hypercube Sampling method and carry out experimental design, obtain 10 groups of combination of process parameters, and utilize Computer Aided Engineering for Injection Molding software to set up respectively finite element model according to the corresponding combination of process parameters of each group sample and carry out numerical simulation, according to the response obtaining and combination of process parameters, become in the lump training dataset, in Table 2:

Table 2 sampling sample set and response thereof

Step 2, the training dataset obtaining with step 1, sets up Gaussian process model, and in the process of modeling, utilize the degree of association of canonical correlation analysis technological parameter and quality index, comprising the correlation parameter of its covariance function is estimated and optimized, as shown in formula (14)

Cov(Y ₁,Y ₂)＝E[(Y ₁-E(Y ₁))(Y ₂-E(Y ₂)]＝E((Y ₁-μ ₁)(Y ₂-μ ₂)) (14)

Y in formula ₁and Y ₂be respectively tables of data X ₁and X ₂canonical correlation variable, they are the linear combination of parameter, are so: make Y for Gaussian process defines these two parameter data sets _i(x _i)=b _ix _i+ c _i, i=1,2, b wherein _i, c _ifor procedure parameter, and b _ican be regarded as canonical correlation main shaft.Solve canonical correlation main shaft and obtain each technological parameter degree of association, as shown in formula (15) (16):

Y ₁＝0.069T _w+0.297T _m-0.631t _i-0.049P _i+0.211P _p+0.074t _p+0.190 (15)

Y ₂＝V-0.180 (16)

Relatively the correlation degree of each technological parameter and quality index is known, exists the parameter of positive incidence to have: T with volume filling rate V _m, T _w,, P _pand t _p, there is having of negative incidence: t with it _pand P _i.From degree of association numerical values recited, can find the larger technological parameter of volume filling rate V impact to have: T _m, t _iand p _p.Based on this analysis result, the adjustment process of technological parameter just can be paid the utmost attention to the adjustment to these 3 major parameters, thereby more improves to efficiency the quality of product.

Step 3,3 major parameters that obtain according to step 2, further carry out based Robust Design, are optimized model as shown in formula (17):

$\begin{array}{cc}\min & \mathrm{\α}\frac{{\mathrm{\μ}}_f}{{{\mathrm{\μ}}_f}^{*}}+(1-\mathrm{\α})\frac{{\mathrm{\δ}}_f}{{{\mathrm{\δ}}_f}^{*}},\\ \mathrm{find}& X=[T_m,t_i,p_p]\\ s.t& .\left\{\begin{array}{c}40\≤T_m\≤75\\ 2\≤t_i\≤4\\ 60\≤p_p\≤160\end{array}\right.\end{array}---\left(17\right)$

For described optimization problem, utilize the sane optimization problem of this example of PSO Algorithm of gradient reinforcement, iterations is 200.Because melt temperature, injection pressure and dwell pressure are not fairly obvious to the impact effect of volume filling rate, therefore the average of simulation before adopting reduces calculated amount, the sane solution obtaining is as shown in table 3:

The sane solution of table 3 based on Gaussian process regression model

Technological parameter	T w/℃	T m/℃	T i/s	P i/Mp	P p/Mp	T p/s
							Sane solution	220.00	70.36	2.21	75.00	72.45	15.00

Validity for the sane solution that further checking the method is tried to achieve, utilize Computer Aided Engineering for Injection Molding software to verify, the injection mo(u)lding figure obtaining shows that phenomenon does not appear shorting in injection moulding process, filling effect is good, then resulting technological parameter is carried out to actual processing, produce continuously 10,000 nothings and short phenomenon, qualification rate reaches 100%.

Step 4, the sane solution obtaining according to step 3, in conjunction with actual production process, further carries out Allowance Design to each technological parameter.According to formula (9), in present case, injection machine is sea day HTF58T type, and rated power is 11Kw, 360 products of this part/hour, if only consider the electrical loss of injection machine, a ₀value can be defined as 0.003 (unit), a ₁value may be defined as 1, if there is waste product, the formula for loss (10) that causes so represents, considers material cost and cost of labor hypothesis C _rvalue be 0.5 (unit).

Suppose 3 sane distribution situation Normal Distribution of separating of major parameter in this case, and variance is σ ², the average of establishing inject time is μ ₁, the average of mold temperature is μ ₂, the average of dwell pressure is μ ₃, its corresponding desired value is respectively the sane solution of trying to achieve, i.e. y ₁=2.21, y ₂=70.36, y ₃=72.45, variance is σ ₁ ², σ ₂ ², σ ₃ ², get respectively 10 groups of random samples as shown in table 4.

Table 4 is chosen major parameter sample

Sequence number	Inject time/s	Mold temperature/℃	Dwell pressure/Mp
				1	1.20	67.00	63.00
2	1.40	68.00	65.00
				3	1.60	69.00	67.00
4	1.80	70.00	69.00
				5	2.00	71.00	71.00
6	2.20	72.00	73.00
				7	2.40	73.00	75.00
8	2.60	74.00	77.00
				9	2.80	75.00	79.00
10	3.00	76.00	81.00

By statistical computation, obtain corresponding average and variance is respectively: μ ₁=2.10, μ ₂=71.50, μ ₃=72.00, σ ₁ ²=0.33, σ ₂ ²=8.25, σ ₃ ²=33.00, the result obtaining is brought in formula (4), utilize Lambert W function to solve and can obtain: δ ₁ ^*=0.97, δ ₂ ^*=0.81, δ ₃ ^*=1.06.

Then utilize the range of tolerable variance of the technological parameter that formula (5) just can be optimized to be respectively respectively: inject time [1.54,2.66], mold temperature [69.18,73.82], dwell pressure [65.92,78.08], after rounding in conjunction with the condition of production, be the tolerance that actual process parameter is controlled.

The result of gained is brought in formula (2) and calculated, and with the comparison of deterministic optimization technique, the cost result respectively each major parameter fluctuation being produced counts in Fig. 8.

The present invention is on the basis of standard Gaussian process regression model, a kind of based Robust Design and Tolerance Design Method of simple and practical injection molding process have been proposed, first by Gauss's canonical correlation analysis, filter out major parameter and minor parameter, then for major parameter, carry out based Robust Design, design cycle and calculated amount had so both been reduced, make again optimum results insensitive to noise factor, finally on sane basis of separating, further carry out Allowance Design, for each technological parameter arranges rational tolerance, guaranteeing, under the prerequisite of qualification rate, to reduce system cost.By 2 embodiment, prove that based Robust Design and the Tolerance Design Method based on Gaussian process has obvious advantage in raising product percent of pass and aspect controlling cost.

Above-described specific descriptions; object, technical scheme and beneficial effect to invention further describe; institute is understood that; the foregoing is only specific embodiments of the invention; and the protection domain being not intended to limit the present invention; within the spirit and principles in the present invention all, any modification of making, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (4)

1. the injection forming process based on Gaussian process is controlled based Robust Design and a Tolerance Design Method, comprises experimental design method sampling, and the correlation analysis based on Gaussian process and based Robust Design and Allowance Design, is characterized in that, specifically carries out in accordance with the following steps:

Step 1, according to the given starting condition of user, propagates the Latin hypercube ETPHLD methods of sampling by enhancement mode translation and carries out experimental design, obtains design variable combination X=[x ₁, x ₂..., x _n] ^t, and design variable combination is carried out respectively to high accuracy analysis solve, obtain corresponding response Y=[y ₁, y ₂..., y _n] ^t, combine the training dataset (X, y) of composition model in the lump with design variable;

Step 2, with the resulting training dataset of step 1, the canonical correlation analysis model of foundation based on Gaussian process, determine the covariance function in the canonical correlation analysis model based on Gaussian process, obtain the relevance between technological parameter and quality index, the following formula of computing formula (1) of this covariance function:

${\mathrm{\Σ}}_{\mathrm{kj}}^i={\mathrm{\σ}}_{\mathrm{iy}}^2\exp (-({\left|\right|x_{1k}-x_{1j}\left|\right|}^2+{\left|\right|x_{2k}-x_{2j}\left|\right|}^2)/2l_i^2+{\mathrm{\σ}}_{\mathrm{in}}^2{I}_N,---\left(1\right)$

K=1 in formula, 2 ... N, j=1,2 ... N, i=1,2; N is the number of sample set; x _1jj sample point in first data stream; x _2jj sample point in second data stream; l _i, σ _iyand σ _infor the super parameter of Gaussian process, σ _infor sample noise, I _nfor N rank unit matrix;

Step 3, obtains the relevance between technological parameter and quality index according to step 2, is divided into major parameter and minor parameter, and sets up based Robust Design model for major parameter according to the large young pathbreaker's technological parameter of the degree of association;

Step 4, the based Robust Design model that the particle cluster algorithm that adopts gradient to strengthen is set up step 3 is optimized and solves;

Step 5, for the resulting sane solution of step 4, the relation of analysis process parameter tolerances scope and mass loss, manufacturing cost and substandard product cost, set up the following formula of Mathematical Expectation Model (2) of quality overall loss:

E[C _T]＝E[L(y)]+E[C _M]+E[C _R] (2)

Minimum for various loss summations are dropped to, adopt Optimized model below, following formula (3):

L in formula (y) represents the quality loss function of influence factor y; C _t, C _r, C _mrepresent respectively oeverall quality loss, manufacturing cost and substandard product cost, y ₀be the desired value of certain technological parameter, its average and variance are respectively μ and σ ², K is mass loss coefficient, δ is the depart from objectives modified value of average size of controlling factor, a ₀be one with the irrelevant constant of range of tolerable variance, its value is decided by manufacturing equipment, a ₁be a constant relevant to margin tolerance, and range of tolerable variance is less, its value is just larger;

Step 6, the optimization problem of mentioning for step 5, as shown in formula (3), solves by Lambert function, and the optimal value that obtains δ is as formula (4):

${\mathrm{\δ}}^{*}=\sqrt{-2\mathrm{LambertW}\left\{\frac{\sqrt{2\mathrm{\π}}{a}_1\mathrm{\σ}\·e^{\frac{-[{(\mathrm{\μ}-y_0)}^2+{\mathrm{\σ}}^2-1-\frac{C_R}{K}]}{2}}}{2K}\right\}+2[{(\mathrm{\μ}-y_0)}^2+{\mathrm{\σ}}^2-1-\frac{C_R}{K}]}---\left(4\right)$

Finally obtain the rational range of tolerable variance of each technological parameter as formula (5):

USL ^*＝μ+δ ^*σ

(5)

LSL ^*＝μ-δ ^*σ

USL in formula ^*and LSL ^*be respectively the upper and lower bound of the range of tolerable variance after process parameter optimizing.

2. the injection forming process based on Gaussian process according to claim 1 is controlled based Robust Design and Tolerance Design Method, it is characterized in that, the resulting technological parameter of canonical correlation analysis model based on Gaussian process described in step 2 and the computing method of the relevance between quality index are: first by transforming canonical correlation main shaft, try to achieve canonical correlation variable, finally utilize the canonical correlation variable of trying to achieve to calculate the related coefficient between parameter, related coefficient is exactly the large Small Indicators of the degree of association between variable.

3. the injection forming process based on Gaussian process according to claim 1 is controlled based Robust Design and Tolerance Design Method, it is characterized in that, the influence of fluctuations that simultaneously adds constraint function and objective function in major parameter based Robust Design model described in step 3, the process of establishing step of its model is:

Steps A adds undulate quantity to consider in constraint condition, as formula (6):

$g_i(x,p)={{\mathrm{\μ}}_g}_i(x,p)+{\mathrm{k\σ}}_{g_i}(x,p)\≤0,i=\mathrm{1,2},...,l---\left(6\right)$

μ in formula _gi(x, p) represents the average of constraint function, σ _gi(x, p) represent the standard deviation of constraint function, k represents that Sigma level allows the degree of probability flux, when retraining the fluctuation Normal Distribution of response amount, k=3 represents that the probability that optimal value meets constraint condition is the number that 99.87%, i represents constraint function;

Step B adds undulate quantity to consider in objective function, as formula (7):

$\begin{array}{cc}\min & \mathrm{\α}\frac{{\mathrm{\μ}}_f(x,p)}{{{\mathrm{\μ}}^{*}}_f(x,p)}+(1-\mathrm{\α})\frac{{\mathrm{\δ}}_f(x,p)}{{{\mathrm{\δ}}^{*}}_f(x,p)},0\≤\mathrm{\α}\≤1\end{array}---\left(7\right)$

μ in formula _f(x, p) and δ _f(x, p) is respectively average and the variance of objective function f (x, p) in deterministic optimization model, μ ^* _fand δ ^* _fbe respectively the optimal value of objective function while only considering average and variance, α is weight coefficient, when the importance of average and variance is the same, and α=0.5;

Then simultaneously optimization aim function and constraint condition, obtain major parameter based Robust Design model as formula (8):

$\begin{array}{cc}\min & \mathrm{\α}\frac{{\mathrm{\μ}}_f(x,p)}{{{\mathrm{\μ}}^{*}}_f(x,p)}+(1-\mathrm{\α})\frac{{\mathrm{\δ}}_f(x,p)}{{{\mathrm{\δ}}^{*}}_f(x,p)},0\≤\mathrm{\α}\≤1\\ s.t.& g_i(x,p)={{\mathrm{\μ}}_g}_i(x,p)+{{\mathrm{k\σ}}_g}_i(x,p)\≤0,i=\mathrm{1,2},...,l\\ & X^L+{\mathrm{k\σ}}_x\≤{\mathrm{\μ}}_x\≤X^U-{\mathrm{k\σ}}_x\end{array}---\left(8\right)$

X in formula ^uand X ^lbe respectively the upper and lower bound of influence factor x.

4. the injection forming process based on Gaussian process according to claim 1 is controlled based Robust Design and Tolerance Design Method, it is characterized in that, the foundation of the technological parameter range of tolerable variance described in step 5 and the Mathematical Expectation Model of cost is specifically divided into three parts:

The relation of technological parameter and mass loss is as formula (9):

$E\left[L\left(y\right)\right]=\underset{\mathrm{LSL}}{\overset{\mathrm{USL}}{\∫}}L\left(y\right)f\left(y\right)\mathrm{dy}---\left(9\right)$

Relation between technological parameter and manufacturing cost is as formula (10):

E[C _M]＝a ₀+2δσa ₁ (10)

Relation between technological parameter and substandard product is as formula (11).