CN104636563A - Reliability design method for upper crossbeam of high-speed pressure machine - Google Patents

Abstract

The invention discloses a reliability design method for an upper crossbeam of a high-speed pressure machine. The method includes the steps: selecting design variables according to reliability requirements in practical upper crossbeam design to establish a reliability design model for the upper crossbeam of the high-speed pressure machine, wherein uncertainty factors are described by intervals; in an experimental design, acquiring sample points required for Kriging fitting by means of LHS (Latin hypercube sampling), acquiring an objective function and a constraint function corresponding to each sample point by means of collaborative simulation to construct a Kriging model; calculating reliability constraint values in the reliability design model on the basis of uniform interval dominance degrees; adopting a double-layer nested genetic algorithm based on interval constraint violation degrees to search an optimal design scheme meeting the reliability requirements. According to the practical reliability requirements of the upper crossbeam of the high-speed pressure machine, reliability index values are calculated according to uniform interval dominance degrees in the reliability design, and the design scheme, meeting the reliability requirements, of the upper crossbeam of the high-speed pressure machine can be acquired conveniently and quickly.

Description

High-speed blanking press entablature reliability design approach

Technical field

The present invention relates to a kind of high-speed blanking press entablature reliability design approach.

Technical background

The performance of high-speed blanking press directly affects the precision of stamping products, usability and production efficiency, and entablature is as the important component part of high-speed blanking press, its Rigidity and strength has direct and important impact to the integral working of pressing machine and machining precision.In order to improve machining precision and the work efficiency of pressing machine, reduce production cost and energy resource consumption, the weight of entablature should be alleviated as much as possible while improving entablature rigidity and intensity, therefore, need the reliability design carrying out turning to high rigidity light weight target to it.

During high-speed blanking press actual design manufactures, there is certain uncertainty fluctuation in the stressing conditions of entablature and material properties, its performance is made to have certain variability, if be still optimized according to certain problem solution throughway, not only final result is not necessarily optimum, even may there is larger deviation, realistic accuracy demand cannot be met.Therefore, in order to ensure the reliability of design result, the uncertainty of these outwardnesies must be taken into full account in design process, reliability design is carried out to high-speed blanking press entablature, real optimization design scheme reliably could be obtained.

Optimal design based on probabilistic reliability is one of probabilistic effective way of process, methods and applications all has and studies comparatively fully.Probability and reliability analysis needs a large amount of sample datas to obtain the exact probability distributed intelligence about Uncertainty, but often can only obtain very limited sample data in engineering, and, probabilistic reliability may be responsive to the distributed intelligence of stray parameter, i.e. the little error of the probability model parameter comparatively big error that structural reliability can be caused to calculate.In actual decision-making, though the probability distribution of Uncertainty not easily accurately obtains, but its boundary be deteriorated then is easy to determine, therefore, the border of interval mathematical theory to Uncertainty can be utilized to be described, in the gamut of Uncertainty, determine reliability of structure, in fact this obtain more reliable structural system.In the Multidisciplinary systems based on interval designs, a variable-value is the uncertainty that interval number reflects this variable-value, thus the size of interval number compares the uncertainty that should be able to reflect variable-value, generally the magnitude relationship of interval number should not thought in absolute terms, and the degree that an interval number is greater than, is equal to or less than another interval number should be provided.Therefore in the entablature reliability design model that interval describes uncertain variables solves, need the reliability index value calculating constraint with a kind of more general, objective, comprehensive interval number comparative approach.

Summary of the invention

For solving the multiple uncertain problem existed in Practical Project high speed press crown high rigidity light-weight design, the object of the present invention is to provide a kind of high-speed blanking press entablature reliability design approach, design variable is selected according to the reliability requirement in fact beam design, set up the high-speed blanking press entablature reliability design model describing uncertain factor with interval, the reliability constraint value in reliability design model is calculated based on uniform interval dominance, adopt double-layer nested genetic algorithm and high-precision Kriging agent model to combine and directly find reliability design model optimum solution.The method can obtain high reliability and high-precision press crown design proposal existing in multiple probabilistic situation.

The present invention is achieved by the following technical solutions: a kind of high-speed blanking press entablature reliability design approach, comprises the following steps:

(1) the high-speed blanking press entablature reliability design model describing uncertain factor with interval is set up: according to actual design demand, determine the uncertain factor that needs in optimization aim in the reliability design of high-speed blanking press entablature and constraint condition, design variable and span thereof, design to consider and waving interval thereof, set up as follows based on the entablature reliability design model of interval variable:

$\underset{x}{\min }f(x,U)$

$s.t.R_{\mathrm{gi}}[g_i(x,U)\≤B_i=[b_i^L,b_i^R\left]\right]\≥R_{\mathrm{si}}$

$h_j(x,U)\≤C_j=[c_j^L,c_j^R]$

$U=(U_1,U_2,...,U_q)\∈I^q;$

Wherein, x is that n ties up design vector, and U is that q ties up interval vector, and f (x, U) is the objective function of entablature reliability design, g _i(x, U) is the mechanical performance index that reliability considered by i-th need, B _i, R _giand R _sibe respectively the permission constant interval of its correspondence, achieved reliability and given reliability constraint value, be respectively B _ilower bound and the upper bound; h _j(x, U) is for jth is without the need to considering the mechanical performance index of reliability, C _jfor the permission constant interval of its correspondence, be respectively C _jlower bound and the upper bound;

(2) adopt Latin Hypercube Sampling method (Latin Hypercube Sampling, LHS) to carry out experimental design in input variable space, obtain matching sample point;

In experimental design, according to the fluctuation range of design vector x and interval vector U, in the input variable space be made up of x and U, adopt LHS to sample, it is [0 that the Latin hypercube experimental design of S input variable, N test run is expressed as span, 1] N × S rank matrix, obtain the sample point group with the uniform property in space and projection homogeneity, then by its renormalization in the input variable space that x and U forms, complete the initial samples to design vector x and interval vector U;

(3) set up parameterized model, obtained the response of mechanical performance index in target corresponding to sample point and constraint function by coordinate imitate technology;

Utilize 3 d modeling software, with design vector x for independent controling parameters, set up high-speed blanking press entablature parametrization three-dimensional model; The real time bidirectional transmission of parameter between modeling software and finite element analysis software is realized by interfacing; By collaborative simulation, call the parametrization three-dimensional model dynamically updated and carry out finite element analysis computation, obtain the response of mechanical performance index in target corresponding to each sample and constraint function;

(4) utilize complete input-output sample points certificate, above beam design variable and uncertain factor are input parameter, with the response of entablature mechanical performance index for output parameter, set up Kriging response surface model;

Kriging model approximate expression is a probability distribution function and a polynomial expression sum, is shown below:

y(x)＝f(x)β+z(x)

In formula, y (x) is unknown Kriging model, and f (x) is the known function about x, provides the overall approximate simulation in design space, and β is regression function undetermined coefficient, and its value is estimated to obtain by known response; Z (x) is a stochastic process, is that the expectation created on the basis of overall situation simulation is 0, variance is σ ²partial deviations, its covariance matrix cov [z (x ⁱ), z (x ^j)] be expressed as

cov[z(x ⁱ),z(x ^j)]＝σ ²R[R(x ⁱ,x ^j)]

In formula, R is correlation matrix; R (x ⁱ, x ^j) represent any two sample point x ⁱ, x ^jrelated function, select Gaussian function as related function, its expression formula is:

$R(x^i,x^j)=\exp [-\underset{k=1}{\overset{n^{\′}}{\mathrm{\Σ}}}{\mathrm{\θ}}_k{|x_k^i-x_k^j|}^2]$

Wherein, n' is the number of sample point, according to condition of unbiasedness and variance minimal condition, in conjunction with method of Lagrange multipliers Sum Maximum Likelihood Estimate method, tries to achieve parameter beta, R and θ _kvalue, and then obtain required Kriging model;

(5) the Calculation of Reliability criterion based on uniform interval dominance is set up;

According to interval mathematical theory, interval A=[a ^l, a ^r] relative to interval B=[b ^l, b ^r] dominance P _(A>B)computing method:

A () works as a ^l>=b ^rtime, P _(A>B)=1;

B () works as b ^l≤ a ^l≤ b ^r≤ a ^rtime, $P_{(A>B)}=\frac{A^R-B^R}{A^R-B^L}+\frac{B^R-B^L}{A^R-B^L}\·\frac{A^L-B^L}{B^R-B^L}+\frac{1}{2}\·\frac{B^R-A^L}{A^R-A^L}\·\frac{B^R-A^L}{B^R-B^L};$

C () works as a ^l≤ b ^l≤ b ^r≤ a ^rtime, $P_{(A>B)}=\frac{A^R-B^R}{A^R-B^L}+\frac{1}{2}\·\frac{B^R-B^L}{A^R-A^L};$

D () works as a ^l≤ b ^l≤ a ^r≤ b ^rtime, $P_{(A>B)}=\frac{1}{2}\·\frac{A^R-B^L}{A^R-A^L}\·\frac{A^R-B^L}{B^R-B^L};$

E () works as b ^l≤ a ^l≤ a ^r≤ b ^rtime, $P_{(A>B)}=\frac{1}{2}\·\frac{A^R-A^L}{B^R-B^L}+\frac{A^L-B^L}{B^R-B^L};$

F () works as a ^l≤ a ^r≤ b ^l≤ b ^rtime, P _(A>B)=0;

Above-mentioned interval dominance computing method are utilized to calculate the section reliability index R of each design constraint performance of high-speed blanking press entablature _gi[g _i(x, U)≤B _i];

(6) double-layer nested genetic algorithm for solving entablature reliability design model is adopted, to outer genetic optimization when all individualities in former generation population, the Kriging model set up in internal layer single objective genetic algorithm and step 4 is utilized to calculate the bound f of mechanical performance index interval value in objective function corresponding to it and constraint function ^r(x), f ^l(x), and obtain mid point and the radius f of wherein objective function and non-reliability constraint function interval value ^c(x), f ^w(x), in integrating step 5, the Calculation of Reliability criterion of uniform interval dominance obtains reliability constraint value R again _gi[g _i(x, U)≤B _i]; Wherein, subscript R, L, C, W represents the interval upper bound, interval lower bound, interval midpoint and interval radius respectively;

To reliability constraint R _gi[g _i(x, U)≤B _i]>=R _si, the account form of its constraint violation degree is:

If (a) R _gi[g _i(x, U)≤B _i]>=R _si, then its constraint violation degree V _i(x)=0;

If (b) R _gi[g _i(x, U)≤B _i] <R _si, then its constraint violation degree is V _i(x)=R _si-R _gi[g _i(x, U)≤B _i];

To non-reliability constraint h _j(x, U)≤C _j, the account form of its constraint violation degree is:

(c) when time, constraint violation degree V _j(x)=<0,0>;

(d) when $h_j^C\left(x\right)=c_j^C$ Time, if $h_j^W\left(x\right)\&le;c_j^W,$ Then V _j(x)=<0,0>, if $h_j^W\left(x\right)>c_j^W,$ Then $V_j\left(x\right)=<0,h_j^W\left(x\right)-c_j^W>;$

(e) when time, constraint violation degree is $V_j\left(x\right)=<h_j^C\left(x\right)-c_j^C,{|h}_j^W\left(x\right)-c_j^W|>;$

The total constraint violation degree when all individualities of former generation population can be calculated thus p is constraint number total in entablature reliability design model, then V _tx the solution of ()=0 is feasible solution, otherwise be infeasible solution;

By f ^c(x), f ^w(x), V _tthe result of calculation of (x) by internal layer optimization be delivered to outer optimize each sample point after, major relation criterion based on Operations of Interva Constraint violation degree carries out trap queuing to all individualities that skin is optimized in population, determine its good and bad tagmeme, thus calculate the fitness obtained when all individualities in former generation population, determine design vector x ₁with x ₂the mode of good and bad relation is:

If (a) x ₁for feasible solution, x ₂for infeasible solution, then there is x all the time ₁be better than x ₂;

If (b) x ₁with x ₂be feasible solution, then the relative superior or inferior both judging with objective function interval value, works as f ^c(x ₁) <f ^c(x ₂) time, or f ^c(x ₁)=f ^c(x ₂) and f ^w(x ₁) <f ^w(x ₂) time, x ₁be better than x ₂;

If (c) x ₁with x ₂be infeasible solution, then judge that it is good and bad, if V according to constraint violation degree _t(x ₁) <V _t(x ₂), then x ₁be better than x ₂, otherwise, x ₂be better than x ₁;

If outer genetic algorithm evolutionary generation reaches given maximal value or reaches convergence requirement, then stop outer genetic algorithm evolutionary process, output has the individuality of maximum adaptation angle value as optimum individual, using vectorial as optimal design for the design vector corresponding to it, be met the high-speed blanking press entablature design proposal of reliability requirement; Otherwise generate population at individual of new generation, evolutionary generation adds 1, continue outer genetic evolution process.

The beneficial effect that the present invention has is:

1) adopt 3 d modeling software and finite element software collaborative simulation, parameterized model can be set up easily for large complicated assembly structure, realize the bi-directional of parameter and dynamically updating of model.

2) uncertain factor that in Practical Project problem, objectivity exists is considered, the form of interval number is adopted to be described, set up more objective and real Multidisciplinary systems Optimized model, uniform interval dominance is applied to the calculating of reliability index, effectively can obtains the constraint reliability index value of each sample point when uncertain variables Probability Distributed Unknown.

3) the Kriging model with good global statistics is built, avoid in reliability design solution procedure, repeatedly calling finite element analysis software and calculate the mechanical performance index value of given entablature design proposal under uncertain factor effect, good computational accuracy and robustness can be ensured while raising solution efficiency.

4) direct solution adopting the double-layer nested genetic algorithm based on constraint violation degree and uniform interval dominance to carry out entablature section reliability to design a model, avoiding the existing reliability design approach based on interval, first need to be converted into the subjectivity of Selecting parameter in the loss of unascertained information when deterministic models solve again and model conversion process random.

Accompanying drawing explanation

Fig. 1 is high-speed blanking press entablature reliability design process flow diagram;

Fig. 2 is high-speed blanking press entablature 1/4 model three-dimensional plot;

Fig. 3 be high-speed blanking press entablature be tied and the schematic diagram of load;

Fig. 4 is high-speed blanking press entablature cross-sectional view and each key dimension planimetric map.

Embodiment

Below in conjunction with drawings and Examples, the invention will be further described.

As shown in Figure 1, a kind of high-speed blanking press entablature of the present invention reliability design approach, comprises the following steps:

(1) the high-speed blanking press entablature reliability design model describing uncertain factor with interval is set up:

Select certain model high-speed blanking press entablature to be research object, be illustrated in figure 2 its 1/4 model, according to actual design demand, with the sectional dimension h of entablature in Fig. 4 ₁, h ₂, l ₁, l ₂and l ₃for size design variable, with external force P shown in Fig. 3 ₁, P ₂, P ₃with the uncertain factor that density p is interval description, take deflection as optimal design target, the maximum permissible stress of entablature is [60,61] MPa, and it is 0.98 that fiduciary level requires, carries out high rigidity lightweight reliability design to entablature.

The maximum equivalent that defined function function δ (x, U) is entablature, then its Reliability Constraint is R _g[δ (x, U)≤[60,61] MPa]>=R _s=0.98, namely

R _g[δ(x,U)＝δ(h ₁,h ₂,l ₁,l ₂,l ₃,P ₁,P ₂,P ₃,ρ)≤[60,61]MPa]≥R _s＝0.98

The weight that defined function w (x, ρ) is entablature, as the constraint function designed a model, namely

w(x,ρ)＝w(h ₁,h ₂,l ₁,l ₂,l ₃,ρ)≤5500kg

Entablature reliability design model then based on interval can be expressed as:

$\underset{U}{\min }d(x,U)=\underset{U}{\min }d(h_1,h_2,l_1,l_2,l_3,P_1,P_2,P_3,\mathrm{\&rho;})$

s.t.R _g[δ(x,U)＝δ(h ₁,h ₂,l ₁,l ₂,l ₃,P ₁,P ₂,P ₃,ρ)≤[60,61]MPa]≥R _s＝0.98；

w(x,ρ)＝w(h ₁,h ₂,l ₁,l ₂,l ₃,ρ)≤5500kg；

200mm≤h ₁≤260mm,250mm≤h ₂≤300mm；

80mm≤l ₁≤120mm,20mm≤l ₂≤60mm,330mm≤l ₃≤400mm；

$P_1=[P_1^L,P_1^R]=[2.44\&times;{10}^5\mathrm{kN},2.56\&times;{10}^5\mathrm{kN}];$

$P_2=[P_2^L,P_2^R]=[4.90\&times;{10}^5\mathrm{kN},5.10\&times;{10}^5\mathrm{kN}];$

$P_3=[P_3^L,P_3^R]=[7.80\&times;{10}^5\mathrm{kN},8.20\&times;{10}^5\mathrm{kN}];$

ρ＝[ρ ^L,ρ ^R]＝[7290kgim ^-2,7310kgim ^-2]。

Wherein, design vector x=(h ₁, h ₂, l ₁, l ₂, l ₃), the interval uncertainty vector U=(P described ₁, P ₂, P ₃, ρ), d (x, U) is the objective function characterizing entablature maximum deformation quantity, R _g[δ (x, U)≤[60,61] MPa], for characterizing the reliability constraint of entablature maximum equivalent, fiduciary level requirement is 0.98, w (x, ρ) is the non-reliability constraint characterizing entablature weight.

(2) LHS is adopted to obtain matching sample point in input variable space.

Under design vector x and the fixed situation of uncertain factor vector U span, in the input variable space be made up of x and U, adopting the Latin Hypercube Sampling method based on minimax Optimality Criteria to generate span is [0,1] matrix, obtain 70 sample points with the uniform property in space, and by its renormalization in input vector space, complete the initial samples to design vector and uncertain interval vector;

(3) set up the parametrization three-dimensional model of high-speed blanking press entablature, obtained the response of each mechanical performance index in target corresponding to sample point and constraint function by coordinate imitate technology;

Utilize 3 d modeling software, with design vector x for independent controling parameters, set up target model high-speed blanking press entablature parameterized model; In finite element software, add uncertain factor vector U is secondary input parameter; The bi-directional of parameter between 3 d modeling software and finite element analysis software is realized by interfacing; By collaborative simulation, call three-dimensional parametric modeling and carry out finite element analysis computation, obtain the response of mechanical performance index in target corresponding to 70 samples and constraint function;

(4) utilize sample points according to the Kriging model setting up each mechanical performance index in target and constraint function;

According to comprising the sample points of complete input-output information according to the Kriging model setting up mechanical performance index in target and constraint function, in fit procedure, selected Gaussian function is basis function, selected second order regression function carries out matching, and fitting result is verified, ensure its fitting precision and generalization ability practical requirement, the Kriging model of foundation is as follows:

$\begin{array}{c}d(x,U)=d(h_1,h_2,l_1,l_2,l_3,P_1,P_2,P_3,\mathrm{\&rho;})\\ =-0.0463+0.5613h_1+0.4187h_2-0.0758l_1+0.0731l_2+0.0426l_3\\ ...+0.0632\mathrm{\&rho;}+0.2254{h_1}^2+0.0159h_1{h}_2+...+0.3701{\mathrm{\&rho;}}^2\\ +0.344\&times;e^{-[8.9{(h_1-245.3)}^2+3.78{(h_2-274.2)}^2+...+5.47{(\mathrm{\&rho;}-7295.7)}^2]}+...\\ -0.152\&times;e^{-[8.9{(h_1-240.5)}^2+3.78{(h_2-285.4)}^2+...+5.47{(\mathrm{\&rho;}-7301.3)}^2]};\end{array}$

$\begin{array}{c}\mathrm{\&delta;}(x,U)=\mathrm{\&delta;}(h_1,h_2,l_1,l_2,l_3,P_1,P_2,P_3,\mathrm{\&rho;})\\ =0.0178-0.5173h_1-0.0287h_2+0.1863l_1-0.0731l_2+\\ ...+0.1371\mathrm{\&rho;}-0.9536{h_1}^2+0.0083h_1{h}_2+...+0.8263{\mathrm{\&rho;}}^2\\ +0.086\&times;e^{-[4.3{(h_1-245.3)}^2+2.11{(h_2-274.2)}^2+...+6.41{(\mathrm{\&rho;}-7295.7)}^2]}+...\\ -0.138\&times;e^{-[4.3{(h_1-240.5)}^2+2.11{(h_2-285.4)}^2+...+6.41{(\mathrm{\&rho;}-7301.3)}^2]};\end{array}$

$\begin{array}{c}w(x,\mathrm{\&rho;})=w(h_1,h_2,l_1,l_2,l_3,\mathrm{\&rho;})\\ =-0.1562-0.0772h_1+0.28h_2-0.4825l_1+0.0561\mathrm{\&rho;}\\ +0.0474{h_1}^2+0.0526h_1{h}_2+...+0.1599{\mathrm{\&rho;}}^2\\ +0.0574\&times;e^{-[2.77{(h_1-240.5)}^2+10.12{(h_2-285.4)}^2+...+8.12{(\mathrm{\&rho;}-7301.3)}^2]}+...\\ -0.0123\&times;e^{-[2.77{(h_1-240.5)}^2+10.12{(h_2-285.4)}^2+...+8.12{(\mathrm{\&rho;}-7301.3)}^2]}.\end{array}$

(5) the Kriging model of reliability design model, full sample point data and matching is updated in double-layer nested genetic algorithm, the maximum evolutionary generation of given ectonexine genetic algorithm is respectively 200 and 400, the population scale of ectonexine genetic algorithm is respectively 100 and 200, the crossover probability of ectonexine genetic algorithm is respectively 0.95 and 0.90, the mutation probability of ectonexine genetic algorithm is respectively 0.01 and 0.05.When outer genetic algorithm reaches end condition, Output rusults scheme is h ₁=229.7mm, h ₂=264.2mm, l ₁=119.6mm, l ₂=55.1mm, l ₃=337.5mm, contrasts its result and initial scheme, its objective function interval midpoint value and reduce weight when meeting reliability requirement, meet high-speed blanking press entablature high rigidity lightweight reliability design requirement.

Claims (3)

1. a high-speed blanking press entablature reliability design approach, is characterized in that, the method comprises the following steps:

(1) the high-speed blanking press entablature reliability design model describing uncertain factor with interval is set up: according to actual design demand, determine the uncertain factor that needs in optimization aim in the reliability design of high-speed blanking press entablature and constraint condition, design variable and span thereof, design to consider and waving interval thereof, set up as follows based on the entablature reliability design model of interval variable:

$\underset{x}{\min }f(x,U)$

$s.t.R_{\mathrm{gi}}[g_i(x,U)\&le;B_i=[b_i^L,b_i^R\left]\right]\&GreaterEqual;R_{\mathrm{si}}$

$h_j(x,U)\&le;C_j=[c_j^L,c_j^R]$

U＝(U ₁,U ₂,…,U _q)∈I ^q；

Wherein, x is that n ties up design vector, and U is that q ties up interval vector, and f (x, U) is the objective function of entablature reliability design, g _i(x, U) is the mechanical performance index that reliability considered by i-th need, B _i, R _giand R _sibe respectively the permission constant interval of its correspondence, achieved reliability and given reliability constraint value, be respectively B _ilower bound and the upper bound; h _j(x, U) is for jth is without the need to considering the mechanical performance index of reliability, C _jfor the permission constant interval of its correspondence, be respectively C _jlower bound and the upper bound;

(2) Latin Hypercube Sampling method (Latin Hypercube Sampling is adopted, LHS) in input variable space, experimental design is carried out, obtain matching sample point: in experimental design, according to the fluctuation range of design vector x and interval vector U, in the input variable space be made up of x and U, adopt LHS to sample, S input variable, it is [0 that the Latin hypercube experimental design of N test run is expressed as span, 1] N × S rank matrix, obtain the sample point group with the uniform property in space and projection homogeneity, again by its renormalization in the input variable space that x and U forms, complete the initial samples to design vector x and interval vector U,

(3) parameterized model is set up, the response of mechanical performance index in target corresponding to sample point and constraint function is obtained: utilize 3 d modeling software by coordinate imitate technology, with design vector x for independent controling parameters, set up high-speed blanking press entablature parametrization three-dimensional model; The real time bidirectional transmission of parameter between modeling software and finite element analysis software is realized by interfacing; By collaborative simulation, call the parametrization three-dimensional model dynamically updated and carry out finite element analysis computation, obtain the response of mechanical performance index in target corresponding to each sample and constraint function;

(4) utilize complete input-output sample points certificate, above beam design variable and uncertain factor are input parameter, with the response of entablature mechanical performance index for output parameter, set up Kriging response surface model;

Kriging model approximate expression is a probability distribution function and a polynomial expression sum, is shown below:

y(x)＝f(x)β+z(x)

In formula, y (x) is unknown Kriging model, and f (x) is the known function about x, provides the overall approximate simulation in design space, and β is regression function undetermined coefficient, and its value is estimated to obtain by known response; Z (x) is a stochastic process, is that the expectation created on the basis of overall situation simulation is 0, variance is σ ²partial deviations, its covariance matrix cov [z (x ⁱ), z (x ^j)] be expressed as

cov[z(x ⁱ),z(x ^j)]＝σ ²R[R(x ⁱ,x ^j)]

In formula, R is correlation matrix; R (x ⁱ, x ^j) represent any two sample point x ⁱ, x ^jrelated function, select Gaussian function as related function, its expression formula is:

$R(x^i,x^j)=\exp [-\underset{k=1}{\overset{n^{\&prime;}}{\mathrm{\&Sigma;}}}{\mathrm{\&theta;}}_k{|x_k^i-x_k^j|}^2]$

Wherein, n' is the number of sample point, according to condition of unbiasedness and variance minimal condition, in conjunction with method of Lagrange multipliers Sum Maximum Likelihood Estimate method, tries to achieve parameter beta, R and θ _kvalue, and then obtain required Kriging model;

(5) the Calculation of Reliability criterion based on uniform interval dominance is set up;

According to interval mathematical theory, interval A=[a ^l, a ^r] relative to interval B=[b ^l, b ^r] dominance P _(A>B)computing method:

A () works as a ^l>=b ^rtime, P _(A>B)=1;

B () works as b ^l≤ a ^l≤ b ^r≤ a ^rtime, $P_{(A>B)}=\frac{A^R-B^R}{A^R-B^L}+\frac{B^R-A^L}{A^R-B^L}\&CenterDot;\frac{A^L-B^L}{B^R-B^L}+\frac{1}{2}\&CenterDot;\frac{B^R-A^L}{A^R-A^L}\&CenterDot;\frac{B^R-A^L}{B^R-B^L};$

C () works as a ^l≤ b ^l≤ b ^r≤ a ^rtime, $P_{(A>B)}=\frac{A^R-B^R}{A^R-B^L}+\frac{1}{2}\&CenterDot;\frac{B^R-B^L}{A^R-A^L};$

D () works as a ^l≤ b ^l≤ a ^r≤ b ^rtime, $P_{(A>B)}=\frac{1}{2}\&CenterDot;\frac{A^R-B^L}{A^R-A^L}\&CenterDot;\frac{A^R-B^L}{B^R-B^L};$

E () works as b ^l≤ a ^l≤ a ^r≤ b ^rtime, $P_{(A>B)}=\frac{1}{2}\&CenterDot;\frac{A^R-A^L}{B^R-B^L}+\frac{A^L-B^L}{B^R-B^L};$

F () works as a ^l≤ a ^r≤ b ^l≤ b ^rtime, P _(A>B)=0;

Above-mentioned interval dominance computing method are utilized to calculate the section reliability index R of each design constraint performance of high-speed blanking press entablature _gi[g _i(x, U)≤B _i];

(6) double-layer nested genetic algorithm for solving entablature reliability design model is adopted, to outer genetic optimization when all individualities in former generation population, the Kriging model set up in internal layer single objective genetic algorithm and step 4 is utilized to calculate the bound f of mechanical performance index interval value in objective function corresponding to it and constraint function ^r(x), f ^l(x), and obtain mid point and the radius f of wherein objective function and non-reliability constraint function interval value ^c(x), f ^w(x), in integrating step 5, the Calculation of Reliability criterion of uniform interval dominance obtains reliability constraint value R again _gi[g _i(x, U)≤B _i]; Wherein, subscript R, L, C, W represents the interval upper bound, interval lower bound, interval midpoint and interval radius respectively;

To reliability constraint R _gi[g _i(x, U)≤B _i]>=R _si, the account form of its constraint violation degree is:

If (a) R _gi[g _i(x, U)≤B _i]>=R _si, then its constraint violation degree V _i(x)=0;

If (b) R _gi[g _i(x, U)≤B _i] <R _si, then its constraint violation degree is V _i(x)=R _si-R _gi[g _i(x, U)≤B _i];

To non-reliability constraint h _j(x, U)≤C _j, the account form of its constraint violation degree is:

(c) when time, constraint violation degree V _j(x)=<0,0>;

(d) when $h_j^C\left(x\right)=c_j^C$ Time, if $h_j^W\left(x\right)\&le;c_j^W,$ Then V _j(x)=<0,0>, if $h_j^W\left(x\right)>c_j^W,$ Then $V_j\left(x\right)=<0,h_j^W\left(x\right)-c_j^W>;$

(e) when $h_j^C\left(x\right)>c_j^C$ Time, constraint violation degree is $V_j\left(x\right)=<h_j^C\left(x\right)-c_j^C,|h_j^W\left(x\right)-c_j^W|>;$

The total constraint violation degree when all individualities of former generation population can be calculated thus p is constraint number total in entablature reliability design model, then V _tx the solution of ()=0 is feasible solution, otherwise be infeasible solution;

By f ^c(x), f ^w(x), V _tthe result of calculation of (x) by internal layer optimization be delivered to outer optimize each sample point after, major relation criterion based on Operations of Interva Constraint violation degree carries out trap queuing to all individualities that skin is optimized in population, determine its good and bad tagmeme, thus calculate the fitness obtained when all individualities in former generation population, determine design vector x ₁with x ₂the mode of good and bad relation is:

If (a) x ₁for feasible solution, x ₂for infeasible solution, then there is x all the time ₁be better than x ₂;

If (b) x ₁with x ₂be feasible solution, then the relative superior or inferior both judging with objective function interval value, works as f ^c(x ₁) <f ^c(x ₂) time, or f ^c(x ₁)=f ^c(x ₂) and f ^w(x ₁) <f ^w(x ₂) time, x ₁be better than x ₂;

If (c) x ₁with x ₂be infeasible solution, then judge that it is good and bad, if V according to constraint violation degree _t(x ₁) <V _t(x ₂), then x ₁be better than x ₂, otherwise, x ₂be better than x ₁;

If outer genetic algorithm evolutionary generation reaches given maximal value or reaches convergence requirement, then stop outer genetic algorithm evolutionary process, output has the individuality of maximum adaptation angle value as optimum individual, using vectorial as optimal design for the design vector corresponding to it, be met the high-speed blanking press entablature design proposal of reliability requirement; Otherwise generate population at individual of new generation, evolutionary generation adds 1, continue outer genetic evolution process.

2. a kind of high-speed blanking press entablature reliability design approach according to claim 1, it is characterized in that: in described step 5, uniform interval dominance is utilized to calculate the reliability index value of entablature organization plan corresponding to each design vector, thus calculate the violation degree of each constraint condition in reliability design model, and calculate total constraint violation degree thus.

3. a kind of high-speed blanking press entablature reliability design approach according to claim 1, it is characterized in that: in described step 6, the double-layer nested genetic algorithm based on constraint violation degree and uniform interval dominance is utilized to achieve the direct solution of press crown reliability design model, wherein, internal layer genetic algorithm utilizes Kriging model to calculate the intrafascicular each entablature mechanical performance index value of reliability design target peace treaty, outer genetic algorithm calculates on the violation degree of each constraint condition and the basis of the total constraint violation degree of design proposal utilizing uniform interval dominance, determine that whether design proposal is feasible, according to its objective function interval response, trap queuing is carried out to feasible program, to infeasible scheme, trap queuing is carried out according to its constraint violation degree.