CN108520087A - A kind of the robustness measurement and balance optimizing design method of mechanical structure foreign peoples multiple target performance - Google Patents
A kind of the robustness measurement and balance optimizing design method of mechanical structure foreign peoples multiple target performance Download PDFInfo
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Abstract
The invention discloses a kind of robustness of mechanical structure foreign peoples multiple target performance measurements and balance optimizing design method.This approach includes the following steps：Consider section uncertain factor, establishes and calculate the left and right circle of each structural behaviour index in double-layer nested genetic algorithm internal layer comprising cost type, the mechanical structure Robust Performance mathematical optimization models of fixed, income type and deviation type heterogeneous destinations performance.In genetic algorithm outer layer, feasibility discrimination is carried out to design vector；The steady equalizing coefficient of steady balanced property coefficient and section heterogeneous destinations performance based on Operations of Interva Constraint performance, robustness equilibrium classification is carried out to feasible solution, based on heterogeneous destinations Robust Performance overall distance, it sorts to design vector, to realize the steady balance optimizing of mechanical structure foreign peoples's multiple target performance.The method achieve the unified Modeling of foreign peoples's multiple target Robust Performance optimization problem, it ensure that the height of restraint performance is steady horizontal, optimum results are objective, and each heterogeneous structure performance is whole steady balanced.
Description
Technical field
The invention belongs to Optimal Design of Mechanical Structure fields, are related to a kind of robustness of mechanical structure foreign peoples multiple target performance
Measurement and balance optimizing design method.
Background technology
With the continuous improvement of complex equipment performance requirement, designer needs when being optimized to key part structure
Consider more and more performance indicators.Influence due to uncertain factor and based Robust Design demand need simultaneously in optimization process
Mean value and the fluctuation for considering structural behaviour index, further increase target to be optimized and the number of constraint, and these targets and constraint
Between often conflict with each other, mutually restrict.However domestic and foreign scholars are in the mechanical structure for indicating uncertain factor using interval number
In more Robust Performance optimization design researchs, usually only considers the robustness of single goal multiple constraint performance, do not consider multiple Objectives
The balanced Robust Optimization problem of energy, can not ensure the whole robustness of mechanical structure performance.
Existing numerous studies show for mechanical structure performance multi-objective optimization design of power, and processing mode is often by taking
Regularization factors and weighted factor convert multi-objective optimization question to single-object problem, regularization factors and weighted factor
Selection need a large amount of experiences, different values that will lead to Different Optimization as a result, with greatly uncertain.Meanwhile it is existing
There is the multi-objective Optimization optimization form that predominantly " minimum ", " maximization " or two kinds combine, and leads in Practical Project
It is commonly present four kinds of heterogeneous destinations performances, including cost type, fixed, income type and deviation type, existing research lacks to this four class
The unified modeling method of target capabilities and derivation algorithm to corresponding foreign peoples's multi-objective Model.
Invention content
In view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to provide a kind of the steady of mechanical structure foreign peoples multiple target performance
Strong property measurement and balance optimizing design method.Consider bounded-but-unknown uncertainty factor influence, establish comprising cost type, fixed,
The mechanical structure section Robust Optimal Design model of income type and deviation type heterogeneous destinations performance, and in double-layer nested genetic algorithm
Internal layer is based on Approximate prediction model, the left and right circle of calculating machine structure foreign peoples's performance indicator.Outside double-layer nested genetic algorithm
Layer carries out feasibility discrimination to design vector；Steady balanced property coefficient based on Operations of Interva Constraint performance and section heterogeneous destinations
The steady equalizing coefficient of energy carries out robustness equilibrium classification to feasible solution, is based on heterogeneous destinations Robust Performance overall distance, right
Design vector is ranked up, and to realize the steady balance optimizing of mechanical structure foreign peoples's multiple target performance, and then obtains machinery
Structure foreign peoples's Robust Performance equilibrium optimal solution.
To achieve the above object, the technical solution adopted by the present invention is：A kind of mechanical structure foreign peoples multiple target performance it is steady
Strong property measurement and balance optimizing design method, this approach includes the following steps：
1) it is required according to mechanical structure foreign peoples's performance Robust Optimal Design, determines the value of uncertain vector sum design vector
Range, while considering that the section intermediate value and length of cost type, fixed, income type and deviation type target capabilities are object function,
And the mechanical structure performance indicator with maximum constraint is described as Operations of Interva Constraint function, establish mechanical structure foreign peoples's multiple target
The robust error estimator model of performance：
s.t.
Wherein,
X is design vector in formula, and U is uncertain vector, fji(x, U) is i-th of target capabilities under jth kind target type
Index,WithWithIt is f respectivelyjiThe section of (x, U) or so boundary, section intermediate value and length, j
=1 is cost type, and j=2 is fixed, and j=3 is income type, and j=4 is deviation type,WithRespectively j-th of target type
Under i-th of people be specified target capabilities section intermediate value and length, which is respectively provided with n_fc cost type, and n_fg is a
Fixed, n_fs income type and n_fp deviation type target capabilities index；gk(x, U) is k-th of restraint performance index,WithRespectively gkThe section of (x, U) or so boundary, BkIt is given k-th of section constant,WithRespectively Bk
Section or so boundary, which has the restraint performance index of n_g maximum constraint；
2) it is sampled, is obtained corresponding to each sample point in the design space determined by design vector and uncertain vector
Mechanical structure foreign peoples's performance indicator of design vector builds the Approximate prediction model of structure foreign peoples's performance indicator；
3) mechanical structure foreign peoples's multiple target Robust Performance that step 1) foundation is obtained using double-layer nested genetic algorithm is excellent
Change the optimal solution to design a model, the as maximum design vector of fitness；Specifically include following sub-step：
3.1) double-layer nested genetic algorithm Initialize installation generates initial population；
3.2) in genetic algorithm internal layer, foreign peoples's mesh of current population at individual is calculated according to the Approximate prediction model of structure
Mark and restraint performance left and right side dividing value；Calculate steady harmony coefficient B _ g of the Operations of Interva Constraint performance corresponding to design vectork
(x), the steady equalizing coefficient B_f of section heterogeneous destinations performanceji(x), Operations of Interva Constraint system balanced with heterogeneous destinations Robust Performance
Number B_gfk(x)；
WhereinWithThe area of k-th of structural constraint performance indicator of design vector in respectively current population
Between intermediate value and length,WithThe section intermediate value and length in respectively k-th specified section；
For cost type and income type target capabilities, j=1,3：
For fixed and deviation type target capabilities, j=2,4：
WhereinWithIn respectively current population under all j-th of target types of the design vector that need to be compared
The average value of i-th target capabilities section intermediate value and siding-to-siding block length；
3.3) in genetic algorithm outer layer, design vector is divided into feasible solution and infeasible solution；
Steady harmony coefficient B _ g based on Operations of Interva Constraint performancek(x) and the steady equilibrium of section heterogeneous destinations performance is
Number B_fji(x), classify to feasible solution, if all B_gj(x) and B_fji(x) it is all higher than 0, then feasible solution x overall performances are equal
Weighing apparatus, is classified as A classes；If all B_gj(x) it is more than 0 and there are B_fji(x) it is less than 0, then feasible solution x restraint performances are balanced, are classified as B
Class；If there are B_gj(x) it is less than 0 and all B_fji(x) it is more than 0, then feasible solution x heterogeneous destinations balancing performance, is classified as C classes；If
There are B_gj(x) and B_fji(x) it is respectively less than 0, then feasible solution x overall performances lack of balance, is classified as D classes；
3.4) A, B, C are calculated separately, the heterogeneous destinations Robust Performance overall distance D (x) of tetra- class feasible solutions of D is specific to walk
It is rapid as follows：
3.4.1 the section heterogeneous destinations for i-th of target capabilities index that feasible solution corresponds under j-th of target type) are calculated
Robust Performance distance Dji(x)；
For cost type target capabilities, i.e. j=1, i=1,2 ..., n_fc：
For fixed target capabilities, i.e. j=2, i=1,2 ..., n_fg：
For income type target capabilities, i.e. j=3, i=1,2 ..., n_fs：
For deviation type target capabilities, i.e. j=4, i=1,2 ..., n_fp：
3.4.2) to n_fc cost type of design vector, n_fg fixed, n_fs income type and n_fp deviation
Type section space aim performance is utilized respectively Dji(x) ascending sort is carried out, each feasible solution has n_fc+n_fg+n_fs+n_ by corresponding
Fp sequence serial number rji(x), it is to calculate heterogeneous destinations Robust Performance overall distance D (x)：
3.5) tetra- class feasible solution of A, B, C, D is utilized respectively D (x) and carries out class internal sort, is ranked up to infeasible solution, feasible
Solution is better than infeasible solution, and feasible solution A classes obtain the trap queuing of all individuals of contemporary population better than C classes better than B classes better than D classes；
3.6) judge whether to reach maximum iteration or the condition of convergence after the completion of iteration every time：Such as reach, output is most
Excellent solution；Otherwise, 1 processing is added to current iteration number, and intersect with mutation operation to generate outer layer genetic algorithm novel species
The new individual of group, return to step 3.2).
Further, in the step 2), pass through drawing in the design space determined by design vector and uncertain vector
Fourth hypercube method is sampled, and right using each sample point institute of the collaborative simulation technical limit spacing of Pro/E and Ansys Workbench
Mechanical structure foreign peoples's performance indicator of design vector is answered, and then utilizes the close of Kriging technologies structure structure foreign peoples's performance indicator
Like prediction model.
Further, in the step 3.1), Initialize installation is specially：Ectonexine Population Size, ectonexine are set
Intersect and mutation probability, maximum iteration, the condition of convergence, setting outer layer genetic algorithm current iteration number are 1.
Further, in the step 3.3), the Operations of Interva Constraint satisfaction P corresponding to design vector is utilizedj(x) it distinguishes and sets
Count the feasibility of vector.
If all Pk(x) it is equal to 1, then design vector x is feasible solution, if there are Pk(x) it is less than 1, then design vector x is
Infeasible solution；
Further, in the step 3.5), to A, B, C, tetra- class feasible solutions of D are utilized respectively D (x) and carry out ascending order row in class
Sequence utilizes n_g P to infeasible solutionk(x) and carry out descending sort；Feasible solution and infeasible solution are ranked up, feasible solution
Better than infeasible solution；To A, B, C, the sequence of tetra- class feasible solutions of D, A classes are better than D classes better than B classes better than C classes；It is final each design to
The corresponding sequence serial number R (x) of amount, and fitness Fit (x)=1/R (x) is calculated, the maximum design vector of fitness is the present age
Population optimal solution.
The beneficial effects of the invention are as follows：
1) while considering four kinds of cost type, fixed, income type and deviation type mechanical structure target capabilities indexs, establish different
The unified model of class multiple target Robust Performance optimization so that the model has more versatility.
2) the robustness measurement and balanced way for proposing mechanical structure foreign peoples's multiple target performance, based on Operations of Interva Constraint performance
Steady equalizing coefficient B_gji(x) and the steady equalizing coefficient B_f of section heterogeneous destinations performanceji(x), it is steady to be carried out to feasible solution
Property equilibrium classification, ensure the portfolio effect of robustness between mechanical structure foreign peoples's performance, to reach the whole steady of structural behaviour
Strong property.
3) feasibility discrimination of vector is designed using Operations of Interva Constraint satisfaction, for the constraint item of maximum constraint
Part, this method ensure that the height of restraint performance is steady using Operations of Interva Constraint performance indicator right margin and specified section left margin as foundation
Strong level.This method can fully reflect that the corresponding constraint section of infeasible solution is closed with the position in specified section and size simultaneously
System, to realize the comparison to infeasible solution.
4) heterogeneous destinations Robust Performance overall distance D (x) is based on to sort to the identical feasible solution of steady harmony classification,
To realize that the direct sequence of design vector, the process need not introduce the parameters such as weighted factor and regularization factors, optimization knot
Fruit is more objective.
Description of the drawings
Fig. 1 is mechanical structure foreign peoples's multiple target Robust Performance balance optimizing flow chart；
Fig. 2 is that high-speed blanking press force application mechanism 1/2 simplifies symmetrical junction composition；
Fig. 3 is high-speed blanking press force application mechanism sliding block cross section parameter figure.
Specific implementation mode
Below in conjunction with the drawings and specific embodiments, the invention will be further described.
Using mechanical structure foreign peoples multiple target performance proposed by the present invention robustness measurement with balance optimizing design method,
It is steady that high efficiency high rigidity lightweight is carried out to the ultraprecise high-speed blanking press of certain Forming Equipments limited liability company model 300L4
Strong property optimization design, as shown in Figure 1, optimum design method is specific as follows：
1) high-speed blanking press threedimensional model as shown in Fig. 2, sliding block cross section parameter as shown in figure 3, wherein b1,b2,
b3, h and speed of mainshaft n are design variable, meanwhile, consider that sliding block (material HT300) density p and Poisson's ratio υ's is uncertain
Property, describe it as interval variable.According to engineering reality and design requirement, determine that the bound of this 7 variables is as shown in table 1.
1 design variable of table and uncertain variables bound
| b1(mm) | b2(mm) | b3(mm) | h(mm) | n(r/min) | ρ(kg/mm3) | υ | |
| The upper limit | 50 | 20 | 15 | 880 | 250 | 7200 | 0.27 |
| Lower limit | 120 | 40 | 50 | 1120 | 750 | 7400 | 0.33 |
Consider that the Wen Sheng in punching course causes influence of the thermal deformation to force application mechanism overall performance, by sliding block maximum heat
The section intermediate value and siding-to-siding block length of deformation target as an optimization.Sliding block punching press number per minute (punching press frequency) directly affects
Ram efficiency and forcing press internal temperature rise, therefore the also target as an optimization by punching press frequency.Since maximum distortion is cost type target
Performance, so j=1, because only that a cost type target, so n_fc=1；Since punching press frequency is income type Objective
Can, so corresponding j=3, because only that an income type target, so n_fs=1.Meanwhile in order to ensure sliding block in length
The maximum thermal stress of sliding block and the maximum value of weight is respectively set in reliability in time press work and lightweight requirements
Constraints is limited, to establish foreign peoples's multiple target Robust Performance mathematical optimization models of high-speed blanking press force application mechanism：
s.t.w(x,U1)=[wL(x),wR(x)]≤[1400,1500]kg
δ (x, U)=[δL(x),δR(x)]≤[100,110]MPa
DC (x)=(dL (x)+dR(x))/2,dW(x)=dR(x)-dL(x)；
X=(b1,b2,b3, h, n), U=(U1,U2)=(ρ, υ)
50mm≤b1≤120mm,20mm≤b2≤40mm,15mm≤b3≤50mm,
880mm≤h≤11200mm,250r/min≤n≤750r/min；
ρ=[7200,7400] kgm-3, υ=[0.27,0.33]
Wherein, x=(b1,b2,b1, h, n) and it is design vector；U=(U1,U2)=(ρ, υ) it is uncertain vector；D (x, U) is
The maximum thermal deformation of sliding block, dC(x), dW(x), dL(x) and dR(x) it is respectively the section intermediate value of d (x, U), length and left and right
Boundary；Spm (n) is sliding block punching press frequency, and only related with design variable n, spm (n)=n is real number；w(x,U1) it is sliding block
Weight, wL(x) and wR(x) it is w (x, U1) section or so boundary；δ (x, U) is the maximum thermal stress of sliding block, δL(x) and δ R
(x) it is the section of δ (x, U) or so boundary.Simultaneously as j=1,3,
2) by design variable b1,b2,b3, h, n and uncertain variable ρ, the septuple space that υ is determined are interior super by Latin
Cube method of sampling obtains sample point, utilizes each sample point institute of the collaborative simulation technical limit spacing of Pro/E and Ansys Workbench
Maximum distortion, the maximum stress of the sliding block of corresponding design vector, weight and punching press frequency, and then utilize Kriging technology structures
Build the Approximate prediction model of force application mechanism performance indicator.
3) high-speed blanking press force application mechanism foreign peoples's multiple target that step 1) is established is obtained using double-layer nested genetic algorithm
The optimal solution of energy Robust Optimal Design model, the as maximum design vector of fitness；Specifically include following sub-step：
3.1) setting genetic algorithm parameter is as shown in table 2, and determines the convergence threshold of sliding block maximum distortion section intermediate value
Convergence threshold for 1E-4mm, punching press frequency is 1r/min, i.e., maximum and smallest region in the maximum distortion both in contemporary population
Between intermediate value difference be less than 1E-4mm, and the difference of the maxima and minima of sliding block punching press frequency be less than 1r/min when, recognize
Reach convergence for optimization aim performance.
2 double-layer nested genetic algorithm initiation parameter of table
| Population Size | Iterations | Crossover probability | Mutation probability | |
| Internal layer | 150 | 80 | 0.99 | 0.05 |
| Outer layer | 150 | 100 | 0.99 | 0.05 |
3.2) in genetic algorithm internal layer, current population at individual is calculated according to the Kriging Approximate prediction models of structure
The maximum distortion of sliding block, maximum stress and weight left and right dividing value and punching press frequency.
The steady balanced property coefficient for calculating the section heterogeneous destinations performance of sliding block maximum distortion, since sliding block maximum becomes
Shape is cost type target capabilities, j=1 and i=1, therefore B_f11(x) it is：
WhereinWithThe corresponding sliding block maximum distortion of all design vectors compared in respectively current population
The average value of section intermediate value and siding-to-siding block length.
The steady balanced property coefficient for calculating the section heterogeneous destinations performance of sliding block punching press frequency, due to sliding block punching press frequency
Rate is income type target capabilities, and j=3, i=1 and spm (n) are real number, i.e. spmC(n)=spm (n), spmW(n)=0, thus B_
f31(x) it is：
WhereinWithSliding block punching press frequency zones are corresponded to for all design vectors compared in current population
Between intermediate value and length average value, due to punching press frequency be real number, thereforeEqual to all designs compared in current population
The average value of the corresponding sliding block punching press frequency of vectorIt follows that the section space aim performance of any real number
Steady balanced property coefficient be 0.
Calculate the Operations of Interva Constraint satisfaction P of sliding block weight1(x), steady harmony coefficient B _ g of Operations of Interva Constraint performance1
(x) and Operations of Interva Constraint and target capabilities robustness equalizing coefficient B_gf1(x)：
wC(x) and wW(x) it is the section intermediate value and siding-to-siding block length of sliding block weight.
Calculate the Operations of Interva Constraint satisfaction P of sliding block maximum stress2(x), the steady balanced property coefficient of Operations of Interva Constraint performance
B_g2(x) and Operations of Interva Constraint and target capabilities robustness equalizing coefficient B_gf2(x)：
Wherein δC(x) and δW(x) it is the section intermediate value and length of sliding block maximum stress.
3.3) in genetic algorithm outer layer, it is based on Operations of Interva Constraint satisfaction, design vector is divided into feasible solution and infeasible
Solution, P1(x) and P2(x) be 1 design vector be feasible solution, there are P1(x) or P2(x) design vector for being less than 1 is infeasible
Solution；
The steady equalizing coefficient of steady balanced property coefficient and section heterogeneous destinations performance based on Operations of Interva Constraint performance, pair can
Row solution is classified, if B_g1(x), B_g2(x), B_f11(x) and B_f31(x) it is all higher than equal to 0, then feasible solution x overall performances
Equilibrium is classified as A classes；If B_g1(x) and B_g2(x) it is all higher than equal to 0 and there are B_f11(x) or B_f31(x) less than 0, then feasible
It is balanced to solve x restraint performances, is classified as B classes；If there are B_g1(x) or B_g2(x) it is less than 0 and B_f11(x) and B_f31(x) it is all higher than
In 0, then feasible solution x heterogeneous destinations balancing performance, is classified as C classes；If there are B_g1(x) or B_g2(x) it is less than 0 and there are B_f11
(x) or B_f31(x) it is less than 0, then feasible solution x overall performances lack of balance, is classified as D classes.
3.4) the section heterogeneous destinations Robust Performance distance that design vector corresponds to sliding block maximum distortion is calculated, due under
Sliding block maximum distortion is cost type target capabilities, j=1 and i=1, therefore D11(x) it is expressed as：
D11(x)==(1-B_f11(x))×dC(x)
The section heterogeneous destinations Robust Performance distance that design vector corresponds to sliding block punching press frequency is calculated, due to sliding block
Maximum distortion is income type target capabilities, j=3, i=1 and be real number, therefore D31(x) it is expressed as：
D31(x)=- (1+B_f3i(x))×spmC(n)=- spm (n)
Based on section heterogeneous destinations Robust Performance distance, to the corresponding sliding block maximum distortion of design vector and punching press
Frequency is ranked up respectively, D11(x) it is smaller to correspond to serial number for smaller then sliding block maximum distortion；D31(x) smaller then sliding block punching press
It is smaller that frequency corresponds to serial number.Then, design vector has sequence serial number r by corresponding11(x) and r31(x), to calculate foreign peoples's mesh
Marking Robust Performance overall distance D (x) is
3.5) it is sorted using D (x) to steady harmonious generic feasible solution, D (x) is smaller, and sequence is more forward；To can not
Row solution utilizes P1(x)+P2(x) it sorts, the value is bigger, and sequence is more forward；Feasible solution and infeasible solution are ranked up, feasible solution
Better than infeasible solution；Steady harmonious different classes of feasible solution is ranked up, A classes are better than D classes better than B classes better than C classes.Most
Each design vector corresponds to a sequence serial number R (x) eventually, and calculates fitness Fit (x)=1/R (x).
3.6) judge whether to reach maximum iteration or the condition of convergence after the completion of iteration every time：Such as reach, output is most
Excellent solution；Otherwise, 1 processing is added to current iteration number, and intersect with mutation operation to generate outer layer genetic algorithm novel species
The new individual of group, return to step 4).
3.7) the maximum design vector of fitness is exported, mechanical structure foreign peoples's multiple target Robust Performance balance optimizing is obtained and sets
It is (74.3,49.7,16.0,1080.5,366.7) to count optimal solution, the interval number of corresponding glide fast weight and maximum stress
Respectively [1323.2,1357.8] kg and [84.0,91.4] MPa, meets constraint level of robustness requirement, and the maximum of sliding block becomes
Shape and punching press frequency are [0.2899,0.2957] mm and 367.
Above-described embodiment is only the present invention preferably feasible embodiment, for illustrating technical scheme of the present invention, not office
Limit protection scope of the present invention.It although the present invention is described in detail referring to the foregoing embodiments, but still can be
Without departing substantially under the spirit and scope of claim and its equivalent, modify to the technical solution recorded in previous embodiment,
Or equivalent replacement of some of the technical features, therefore these modifications or substitutions this technical solution protection domain it
It is interior.
Claims (5)
1. robustness measurement and the balance optimizing design method of a kind of mechanical structure foreign peoples multiple target performance, which is characterized in that should
Method includes the following steps：
1) it is required according to mechanical structure foreign peoples's performance Robust Optimal Design, determines the value model of uncertain vector sum design vector
It encloses, while considering that the section intermediate value and length of cost type, fixed, income type and deviation type target capabilities are object function, and
Mechanical structure performance indicator with maximum constraint is described as Operations of Interva Constraint function, establishes mechanical structure foreign peoples's multiple target
The robust error estimator model of energy：
s.t.
Wherein,
X is design vector in formula, and U is uncertain vector, fji(x, U) is that i-th of target capabilities under jth kind target type refer to
Mark,WithWithIt is f respectivelyjiThe section of (x, U) or so boundary, section intermediate value and length, j=
1 is cost type, and j=2 is fixed, and j=3 is income type, and j=4 is deviation type,WithUnder respectively j-th of target type
I-th of people be specified target capabilities section intermediate value and length, which is respectively provided with n_fc cost type, and n_fg are consolidated
Sizing, n_fs income type and n_fp deviation type target capabilities index；gk(x, U) is k-th of restraint performance index,
WithRespectively gkThe section of (x, U) or so boundary, BkIt is given k-th of section constant,WithRespectively BkSection
Left and right circle, the model have the restraint performance index of n_g maximum constraint；
2) it is sampled in the design space determined by design vector and uncertain vector, obtains the corresponding design of each sample point
Mechanical structure foreign peoples's performance indicator of vector builds the Approximate prediction model of structure foreign peoples's performance indicator；
3) mechanical structure foreign peoples's multiple target Robust Performance optimization that step 1) is established is obtained using double-layer nested genetic algorithm to set
Count the optimal solution of model, the as maximum design vector of fitness；Specifically include following sub-step：
3.1) double-layer nested genetic algorithm Initialize installation generates initial population；
3.2) in genetic algorithm internal layer, according to the Approximate prediction model of structure be calculated current population at individual heterogeneous destinations and
Restraint performance left and right side dividing value；Calculate steady harmony coefficient B _ g of the Operations of Interva Constraint performance corresponding to design vectork(x), area
Between heterogeneous destinations performance steady equalizing coefficient B_fji(x), Operations of Interva Constraint and heterogeneous destinations Robust Performance equalizing coefficient B_gfk
(x)；
WhereinWithIn respectively current population in the section of k-th of structural constraint performance indicator of design vector
Value and length,WithThe section intermediate value and length in respectively k-th specified section；
For cost type and income type target capabilities, j=1,3：
For fixed and deviation type target capabilities, j=2,4：
WhereinWithI-th in respectively current population under all j-th of target types of the design vector that need to be compared
The average value of target capabilities section intermediate value and siding-to-siding block length；
3.3) in genetic algorithm outer layer, design vector is divided into feasible solution and infeasible solution；
Steady harmony coefficient B _ g based on Operations of Interva Constraint performancek(x) and the steady equalizing coefficient B_ of section heterogeneous destinations performance
fji(x), classify to feasible solution, if all B_gj(x) and B_fji(x) it is all higher than 0, then feasible solution x overall performances are balanced, return
For A classes；If all B_gj(x) it is more than 0 and there are B_fji(x) it is less than 0, then feasible solution x restraint performances are balanced, are classified as B classes；If depositing
In B_gj(x) it is less than 0 and all B_fji(x) it is more than 0, then feasible solution x heterogeneous destinations balancing performance, is classified as C classes；If there are B_gj
(x) and B_fji(x) it is respectively less than 0, then feasible solution x overall performances lack of balance, is classified as D classes；
3.4) A, B, C are calculated separately, the heterogeneous destinations Robust Performance overall distance D (x) of tetra- class feasible solutions of D, specific steps are such as
Under：
3.4.1 the section heterogeneous destinations performance for i-th of target capabilities index that feasible solution corresponds under j-th of target type) is calculated
Robustness distance Dji(x)；
For cost type target capabilities, i.e. j=1, i=1,2 ..., n_fc：
For fixed target capabilities, i.e. j=2, i=1,2 ..., n_fg：
For income type target capabilities, i.e. j=3, i=1,2 ..., n_fs：
For deviation type target capabilities, i.e. j=4, i=1,2 ..., n_fp：
3.4.2) to n_fc cost type of design vector, n_fg fixed, n_fs income type and n_fp inclined separating type areas
Between target capabilities be utilized respectively Dji(x) ascending sort is carried out, each feasible solution has n_fc+n_fg+n_fs+n_fp by corresponding
The serial number that sorts rji(x), it is to calculate heterogeneous destinations Robust Performance overall distance D (x)：
3.5) tetra- class feasible solution of A, B, C, D is utilized respectively D (x) and carries out class internal sort, is ranked up to infeasible solution, feasible solution is excellent
In infeasible solution, feasible solution A classes are better than D classes better than C classes better than B classes, obtain the trap queuing of all individuals of contemporary population；
3.6) judge whether to reach maximum iteration or the condition of convergence after the completion of iteration every time：Such as reach, output is optimal
Solution；Otherwise, 1 processing is added to current iteration number, and intersect with mutation operation to generate outer layer genetic algorithm new population
New individual, return to step 3.2).
2. robustness measurement and the balance optimizing design side of mechanical structure foreign peoples multiple target performance according to claim 1
Method, which is characterized in that in the step 2), surpassed by Latin in the design space determined by design vector and uncertain vector
Cube method is sampled, and is set corresponding to each sample point of collaborative simulation technical limit spacing using Pro/E and Ansys Workbench
Mechanical structure foreign peoples's performance indicator of vector is counted, and then pre- using the approximation of Kriging technologies structure structure foreign peoples's performance indicator
Survey model.
3. the mechanical structure Robust Optimal Design method according to claim 1 for considering multiple target multiple constraint balancing performance,
It is characterized in that, in the step 3.1), Initialize installation is specially：Be arranged ectonexine Population Size, ectonexine intersection and
Mutation probability, maximum iteration, the condition of convergence, setting outer layer genetic algorithm current iteration number are 1.
4. the mechanical structure Robust Optimal Design method according to claim 1 for considering multiple target multiple constraint balancing performance,
It is characterized in that, in the step 3.3), the Operations of Interva Constraint satisfaction P corresponding to design vector is utilizedj(x) design vector is distinguished
Feasibility；
If all Pk(x) it is equal to 1, then design vector x is feasible solution, if there are Pk(x) be less than 1, then design vector x be can not
Row solution；
5. robustness measurement and the balance optimizing design side of mechanical structure foreign peoples multiple target performance according to claim 4
Method, which is characterized in that in the step 3.5), to A, B, C, tetra- class feasible solutions of D are utilized respectively D (x) and carry out ascending sort in class,
N_g P is utilized to infeasible solutionk(x) and carry out descending sort；Feasible solution and infeasible solution are ranked up, feasible solution is excellent
In infeasible solution；To A, B, C, the sequence of tetra- class feasible solutions of D, A classes are better than D classes better than B classes better than C classes；Final each design vector
A corresponding sequence serial number R (x), and fitness Fit (x)=1/R (x) is calculated, the maximum design vector of fitness is the present age kind
Group's optimal solution.
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