CN108427832A - A kind of mechanical structure Robust Performance optimum design method violating vector based on Operations of Interva Constraint three-dimensional - Google Patents
A kind of mechanical structure Robust Performance optimum design method violating vector based on Operations of Interva Constraint three-dimensional Download PDFInfo
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Abstract
The invention discloses a kind of mechanical structure performance multiple constraint Robust Optimal Design methods violating vector based on Operations of Interva Constraint three-dimensional.This approach includes the following steps：Uncertain factor is indicated using interval number, establishes mechanical structure performance multiple constraint Robust Optimal Design model, and in double-layer nested genetic algorithm internal layer, be based on Approximate prediction model, the left and right circle of calculating machine structural behaviour index.In double-layer nested genetic algorithm outer layer, vector is violated based on Operations of Interva Constraint three-dimensional, feasibility discrimination is carried out to design vector；Based on normalization overall distance, design vector is ranked up, to realize the solution of mechanical structure performance multiple constraint Robust Optimal Design model, and then obtains mechanical structure Robust Performance optimal solution.This method can ensure that the height of restraint performance is steady horizontal, and the artificial parameter such as need not introduce weighted factor and regularization factors so that optimum results are more objective.
Description
Technical field
The invention belongs to Optimal Design of Mechanical Structure fields, are related to a kind of machinery violating vector based on Operations of Interva Constraint three-dimensional
Structural behaviour Robust Optimal Design method.
Background technology
Currently, domestic and foreign scholars are indicating probabilistic non-probabilistic Robust optimization design of mechanical structure using interval number
In research, constructed section based Robust Design model is mainly solved using indirect method, by introducing the general of section possibility degree
It reads, converts interval model to deterministic models processing.But by siding-to-siding block length and its calculated area of relative position information
Between possibility degree be a concrete numerical value, be unable to fully embody the unascertained information of Operations of Interva Constraint in former Optimized model.Indirectly
Method during model conversion, often utilize weighted factor by the section intermediate value of structural object performance indicator in Optimized model and
Length makees disposed of in its entirety；To prevent the case where number eats decimal greatly from occurring, before being weighted processing to section intermediate value and length,
Also need introducing regularization factors that the two is made to reach the same order of magnitude.Weighted factor, regularization factors value there is larger master
The property seen, and the different values of these model conversion parameters can cause optimum results to there is uncertainty.
In order to improve the defect of indirect method for solving, according to Hu and Wang in 2006《Journal of
Industrial and Management Optimization》On paper " the A novel approach in that deliver
uncertain programing.I:New arithmetic and order relation for interval
Section order relation in numbers ", Cheng and Liu in 2017《Computers and Structures》On the opinion delivered
Text " Robust optimization of uncertain structures based on normalized violation
The concept of Operations of Interva Constraint violation degree is proposed in degree of interval constraint ", proposes to disobey using Operations of Interva Constraint
It is anti-to spend to judge the feasibility of Design of Mechanical Structure vector；By introducing section tagmeme vector, to the direct root of feasible design vector
Trap queuing is carried out according to the section intermediate value and length of target capabilities index, so as to avoid weighting coefficient and regularization factors are introduced
Subjective value is different and causes the uncertainty of optimum results.But the method is better than specified section in restraint performance index section intermediate value
Intermediate value when think to constrain feasible, relatively wide loose constraint feasibility criterion is difficult to ensure that constraint is stringent steady feasible.
Moreover, being ranked up the superiority it is possible that two design vectors to feasible design vector by section tagmeme vector field homoemorphism length
The case where can not comparing.
Invention content
A kind of vector is violated based on Operations of Interva Constraint three-dimensional in view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to provide
Mechanical structure Robust Performance optimum design method.Uncertain factor is indicated using interval number, establishes mechanical structure performance mostly about
Beam Robust Optimal Design model, and in double-layer nested genetic algorithm internal layer, it is based on Approximate prediction model, calculating machine structural behaviour
The left and right circle of index.In double-layer nested genetic algorithm outer layer, vector is violated based on Operations of Interva Constraint three-dimensional, it can to design vector progress
Row differentiates；Based on normalization overall distance, design vector is ranked up, it is steady to realize mechanical structure performance multiple constraint
The solution of strong mathematical optimization models, and then obtain mechanical structure Robust Performance optimal solution.
To achieve the above object, the technical solution adopted by the present invention is：It is a kind of that vector is violated based on Operations of Interva Constraint three-dimensional
Mechanical structure Robust Performance optimum design method, this approach includes the following steps：
1) it is required according to mechanical structure performance multiple constraint Robust Optimal Design, determines taking for uncertain vector sum design vector
It is worth range, using the section intermediate value of the mechanical structure performance indicator with the small characteristic of prestige and length as object function, there will be maximum
The mechanical structure multi-performance index that value limits is described as Operations of Interva Constraint function, establishes mechanical structure performance multiple constraint Robust Optimization
It designs a model；
2) it is sampled, is obtained corresponding to each sample point in the design space determined by design vector and uncertain vector
The mechanical structure performance indicator of design vector builds the Approximate prediction model of structural behaviour index；
3) the mechanical structure performance multiple constraint Robust 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 target and
Restraint performance left and right side dividing value, and calculate whole Operations of Interva Constraint three-dimensional and violate vector v (x), v (x) is that design vector each constrains
Corresponding Operations of Interva Constraint three-dimensional violates vector vi(x) sum, vi(x) it is expressed as：
vi(x)=(v1i(x),v2i(x),v3i(x))
Wherein v1i(x),v2i(x),v3i(x) it is vi(x) three components,WithIt is i-th of constraint respectively
Section of performance indicator or so boundary,WithIt is given section or so boundary respectively；
3.3) in genetic algorithm outer layer, design vector is divided into feasible solution and infeasible solution, | v (x) |=0 design to
Amount is feasible solution, | v (x) |>0 design vector is infeasible solution, and calculates the normalization overall distance D (x) of feasible solution：
Wherein fC(x) and fW(x) be respectively feasible solution in contemporary population structural object performance indicator section intermediate value and length
Degree；WithThe minimum value and maximum value of all feasible solution target capabilities section intermediate value in respectively contemporary population；WithThe minimum value and maximum value of all feasible solution target capabilities siding-to-siding block lengths in respectively contemporary population；
3.4) sorted using D (x) to feasible solution, infeasible solution utilized | v (x) | sequence, feasible solution are better than infeasible solution,
Obtain the trap queuing of all individuals of contemporary population；
3.5) 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 1), the mechanical structure performance multiple constraint robust error estimator model of foundation is specific
It is as follows：
Wherein,
s.t.
Wherein,
X is design vector in formula, and U is uncertain vector, and f (x, U) is structural object performance indicator, fL(x) and fR(x) divide
It is not the section of f (x, U) or so boundary；gi(x, U) is i-th of restraint performance index, BiIt is given section constant, model tool
There is the restraint performance index of l maximum constraint.
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
The mechanical structure performance indicator of design vector is answered, and then utilizes the Approximate prediction mould of Kriging technologies structure structural behaviour index
Type.
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 3.4), D (x) ascending sorts is utilized to feasible solution, infeasible solution is utilized | v (x) |
Ascending sort；Feasible solution and infeasible solution are ranked up, feasible solution is better than infeasible solution；Final each design vector corresponds to one
A sequence serial number R (x), and fitness Fit (x)=1/R (x) is calculated, the maximum design vector of fitness is that contemporary population is optimal
Solution.
The beneficial effects of the invention are as follows：
1) propose that Operations of Interva Constraint three-dimensional violates the feasibility discrimination that vector is designed vector, for the pact of maximum constraint
Beam conditionThe discriminant criterion is with Operations of Interva Constraint performance indicator right margin and the specified section left side
Boundary is according to the high steady level that ensure that restraint performance.The vector can fully reflect the corresponding confining region of infeasible solution simultaneously
Between position with specified section and magnitude relationship, to realize the comparison to infeasible solution.
2) it is based on normalization overall distance D (x) to sort to feasible solution, the mould of vector is violated based on whole Operations of Interva Constraint three-dimensional
It is long | v (x) | sort to infeasible solution, to realize the direct sequence of design vector, the process need not introduce weighted factor and
The parameters such as regularization factors, optimum results are more objective.
Description of the drawings
Fig. 1 is the steady optimized flow chart of mechanical structure performance multiple constraint；
Fig. 2 is upper beam physical model figure；
Fig. 3 is upper beam cross section parameter figure.
Specific implementation mode
Below in conjunction with the drawings and specific embodiments, the invention will be further described.
Steadily and surely optimized using the mechanical structure performance multiple constraint proposed by the present invention for violating vector based on Operations of Interva Constraint three-dimensional
Design method carries out the upper beam of the ultraprecise high-speed blanking press of certain Forming Equipments limited liability company model 300L4 high
Rigidity lightweight robust error estimator, as shown in Figure 1, optimum design method is specific as follows：
1) upper beam threedimensional model as shown in Fig. 2, cross section parameter as shown in figure 3, wherein h1,h2,l1,l2And l3Respectively
For design variable, meanwhile, the uncertainty of the density p and Poisson's ratio υ of its material (HT300) is considered, at uncertain variables
Reason.According to engineering reality and design requirement, determine that the bound of this 7 variables is as shown in table 1.
1 upper beam design variable of table and uncertain variables bound
| h1(mm) | h2(mm) | l1(mm) | l2(mm) | l3(mm) | ρ(kg/mm3) | υ | |
| The upper limit | 250 | 300 | 120 | 55 | 390 | 7200 | 0.27 |
| Lower limit | 210 | 250 | 80 | 25 | 330 | 7400 | 0.33 |
Required according to upper beam Lightweight high-rigidity Robust Optimal Design, with the section intermediate value of upper beam maximum deformation quantity and
Siding-to-siding block length is object function, its weight and the maximum constraint constraints of maximum stress is respectively set, it is more to establish upper beam
Constrain Robust Optimal Design model：
s.t.w(x,U1)=[wL(x),wR(x)]≤[5170,5230]kg
δ (x, U)=[δL(x),δR(x)]≤[40,45]MPa
Wherein
X=(h1,h2,l1,l2,l3), U=(U1,U2)=(ρ, υ)；
210mm≤h1≤250mm,250mm≤h2≤300mm,
80mm≤l1≤120mm,25mm≤l2≤55mm,330mm≤l3≤390mm；
ρ=[7200,7400] kgm-3, υ=[0.27,0.33]
Wherein, x=(h1,h2,l1,l2,l3) it is design vector, U=(U1,U2)=(ρ, υ) it is uncertain vector；d(x,U)
For the maximum distortion of upper beam, dC(x)、dW(x)、dL(x) and dR(x) be respectively d (x, U) section intermediate value, siding-to-siding block length and area
Between or so boundary；w(x,U1) be upper beam weight, wL(x) and wR(x) it is w (x, U1) section or so boundary；δ (x, U) is upper cross
Maximum stress suffered by beam, δL(x) and δR(x) it is the section of δ (x, U) or so boundary.
2) by design variable h1,h2,l1,l2,l3It is super by Latin in the septuple space determined with uncertain variable ρ, υ
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, maximum stress and the weight of the upper beam of corresponding design vector, and then build force application mechanism using Kriging technologies
The Approximate prediction model of performance indicator.
3) the upper beam multiple constraint robust error estimator model that step 1) is established is obtained using double-layer nested genetic algorithm
Optimal solution, 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 upper beam maximum distortion section intermediate value
For 1E-4mm, i.e., when the maximum difference with smallest interval intermediate value is less than 1E-4mm in maximum distortion in contemporary population, it is believed that upper cross
Beam maximum distortion reaches convergence.
2 double-layer nested genetic algorithm initiation parameter of table
| Population Size | Iterations | Crossover probability | Mutation probability | |
| Internal layer | 150 | 100 | 0.99 | 0.05 |
| Outer layer | 200 | 150 | 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
Maximum distortion, maximum stress and weight left and right side dividing value, and the Operations of Interva Constraint for calculating separately weight and maximum stress is three-dimensional
Violate vector v1(x) and v2(x)。
For upper beam weight：
v1(x)=(v11(x),v21(x),v31(x))
For upper beam maximum stress：
v2(x)=(v12(x),v22(x),v32(x))
Vector v is violated by the corresponding Operations of Interva Constraint three-dimensional of design vector weight and maximum stress constraint1(x) and v2(x) structure
Vector v (x)=v is violated at the whole Operations of Interva Constraint three-dimensional corresponding to design vector1(x)+v1(x)。
3.3) in genetic algorithm outer layer, design vector is divided into feasible solution and infeasible solution, | v (x) |=0 design to
Amount is feasible solution, | v (x) |>0 design vector is infeasible solution, and calculates the normalization overall distance D (x) of feasible solution.
WhereinWithAll feasible solutions correspond to the section intermediate value of upper beam maximum distortion in respectively contemporary population
Minimum value and maximum value；WithIn respectively contemporary population all feasible solutions correspond to upper beam maximum distortion section it is long
The minimum value and maximum value of degree.
It is sorted using D (x) to feasible solution, D (x) is smaller, and sequence is more forward；Infeasible solution is utilized | v (x) | sequence, | v
(x) | smaller, sequence is more forward；Feasible solution and infeasible solution are ranked up, feasible solution is better than infeasible solution.Finally each set
The corresponding sequence serial number R (x) of meter vector, and calculate fitness Fit (x)=1/R (x).
3.4) judge whether to reach maximum iteration or the condition of convergence after the completion of iteration every time：Such as reach, executes step
It is rapid 7)；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).
3.5) the maximum design vector of fitness is exported, it is optimal to obtain mechanical structure performance multiple constraint robust error estimator
Solution is (213.74,250.00,80.61,27.90,370.16), the interval number point of corresponding upper beam weight and maximum stress
Not Wei [4999.34,5170.00] kg and [17.93,40.00] MPa, meet constraint level of robustness requirement, the area of maximum distortion
Between number be [0.1170,0.1210].
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. a kind of mechanical structure Robust Performance optimum design method violating vector based on Operations of Interva Constraint three-dimensional, which is characterized in that
This approach includes the following steps：
1) it is required according to mechanical structure performance multiple constraint Robust Optimal Design, determines the value model of uncertain vector sum design vector
It encloses, using the section intermediate value of the mechanical structure performance indicator with the small characteristic of prestige and length as object function, will have maximum value limit
Fixed mechanical structure multi-performance index is described as Operations of Interva Constraint function, establishes mechanical structure performance multiple constraint robust error estimator
Model；
2) it is sampled in the design space determined by design vector and uncertain vector, obtains the corresponding design of each sample point
The mechanical structure performance indicator of vector builds the Approximate prediction model of structural behaviour index；
3) the mechanical structure performance multiple constraint robust error estimator mould that step 1) is established is obtained using double-layer nested genetic algorithm
The maximum design vector of the optimal solution of type, as 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, target and the constraint of current population at individual are calculated according to the Approximate prediction model of structure
Performance left and right side dividing value, and calculate whole Operations of Interva Constraint three-dimensional and violate vector v (x), v (x) be design vector each constrain it is right
The Operations of Interva Constraint three-dimensional answered violates vector vi(x) sum, vi(x) it is expressed as：
vi(x)=(v1i(x),v2i(x),v3i(x))
Wherein v1i(x),v2i(x),v3i(x) it is vi(x) three components,WithIt is that i-th of restraint performance refers to respectively
Target section or so boundary,WithIt is given section or so boundary respectively；
3.3) in genetic algorithm outer layer, design vector is divided into feasible solution and infeasible solution, | v (x) |=0 design vector is
Feasible solution, | v (x) |>0 design vector is infeasible solution, and calculates the normalization overall distance D (x) of feasible solution：
Wherein fC(x) and fW(x) be respectively feasible solution in contemporary population structural object performance indicator section intermediate value and length；WithThe minimum value and maximum value of all feasible solution target capabilities section intermediate value in respectively contemporary population；With
The minimum value and maximum value of all feasible solution target capabilities siding-to-siding block lengths in respectively contemporary population；
3.4) sorted using D (x) to feasible solution, infeasible solution utilized | v (x) | sequence, feasible solution are better than infeasible solution, obtain
The trap queuing of contemporary all individuals of population；
3.5) 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. the mechanical structure Robust Performance optimization design side according to claim 1 for violating vector based on Operations of Interva Constraint three-dimensional
Method, which is characterized in that in the step 1), the mechanical structure performance multiple constraint robust error estimator model of foundation is specifically such as
Under：
Wherein,
s.t.
Wherein,
X is design vector in formula, and U is uncertain vector, and f (x, U) is structural object performance indicator, fL(x) and fR(x) it is respectively f
The section of (x, U) or so boundary；gi(x, U) is i-th of restraint performance index, BiIt is given section constant, which has l
The restraint performance index of maximum constraint.
3. the mechanical structure Robust Performance optimization design side according to claim 1 for violating vector based on Operations of Interva Constraint three-dimensional
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
The mechanical structure performance indicator of vector is counted, and then utilizes the Approximate prediction model of Kriging technologies structure structural behaviour index.
4. the mechanical structure Robust Performance optimization design side according to claim 1 for violating vector based on Operations of Interva Constraint three-dimensional
Method, which is characterized in that in the step 3.1), Initialize installation is specially：The intersection of ectonexine Population Size, ectonexine is set
With mutation probability, maximum iteration, the condition of convergence, setting outer layer genetic algorithm current iteration number is 1.
5. the mechanical structure Robust Performance optimization design side according to claim 1 for violating vector based on Operations of Interva Constraint three-dimensional
Method, which is characterized in that in the step 3.4), D (x) ascending sorts are utilized to feasible solution, infeasible solution is utilized | v (x) | it rises
Sequence sorts；Feasible solution and infeasible solution are ranked up, feasible solution is better than infeasible solution；Final each design vector corresponds to one
Sort serial number R (x), and calculates fitness Fit (x)=1/R (x), and the maximum design vector of fitness is contemporary population optimal solution.
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