CN105631093B - A kind of Design of Mechanical Structure method based on M-BSWA multiple-objection optimizations - Google Patents
A kind of Design of Mechanical Structure method based on M-BSWA multiple-objection optimizations Download PDFInfo
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Abstract
A kind of Design of Mechanical Structure method category technical field of mechanical design based on M BSWA multiple-objection optimizations, the present invention include the following steps：1. establishing the mathematical model of mechanical structure multi-objective optimization design of power；2. being sampled using orthogonal experiment design；3. constructing radial basis function agent model；4. determining evaluation agent model accuracy；5. the multi-objective optimization algorithm M BSWA designed for solving-optimizing problem；6. verifying the validity of optimum results.The present invention is suitable for the multi-objective optimization design of power of mechanical structure, the mechanical configuration parameter distribution of acquisition is more reasonable, to keep the mechanical structure performance of design more preferable, the present invention uses numerical computation method, calculating speed is fast, it is substantially shorter the design cycle, and is ensured under the premise of not increasing mechanical structure total quality, realizes the target for improving mechanical structure comprehensive performance.
Description
Technical field
The invention belongs to Optimal Design of Mechanical Structure technical fields, and in particular to a kind of machine based on M-BSWA multiple-objection optimizations
Tool construction design method.
Background technology
Optimal Design of Mechanical Structure refer on the basis of existing design scheme, by optimization process, make design parameter to
More preferably direction adjusts, until finding most rational design scheme within the scope of constraints.With traditional optimization design phase
Than modern optimization design is guidance with numerical value basic theory, and optimizing is carried out in entire design domain, can quickly be set
Meter scheme, and judge that gained scheme is good and bad, the finally optimum scheme comparison in numerous schemes.Method because using numerical computations,
Design time is saved, cost is reduced.
Optimization problem is often multi-objective optimization question in produce reality, more in multi-objective optimization question under normal circumstances
It is conflicting between a sub-goal, the improvement of a target is possible to cause the drop of another or multiple sub-goal performances
It is low, that is to say, that multiple optimization aims cannot be optimal simultaneously, how balance the relationship between each performance indicator, obtain most
Rational optimizing design scheme is the main task of multiple-objection optimization." optimization " is the eternal topic in engineering design how
Quickly and effectively multi-objective optimization algorithm is designed, the optimization method to build mechanical structure is to solve the problems, such as Practical Project
Basis.
Invention content
The present invention considers the multinomial performance index of mechanical structure, for example, the structure in lightweight problem weight, volume；
Maximum energy absorption, maximum deformation quantity, peak value crushing force in collision problem etc..The present invention, which proposes one kind and can take into account simultaneously, to be examined
Consider the Design of Mechanical Structure method based on multiple-objection optimization of multiple structural behaviour indexs.
A kind of Design of Mechanical Structure method based on M-BSWA multiple-objection optimizations of the present invention includes the following steps：
1. establishing the mathematical model of mechanical structure multi-objective optimization design of power, include the following steps：
1.1 establish the initial CAD model of mechanical structure；
1.2 selected design variables, optimization object function and constraints；
1.3 establish the mathematical model of mechanical structure, and mathematic(al) representation is：
In formula：f1(x),f2(x),...,fn(x) object function related with mechanical structure performance is indicated；N is object function
Number；(x1,x2,...,xl) indicate design variable；Indicate Design of Mechanical Structure range；L becomes for Design of Mechanical Structure
Measure number；hj(x)≤0,hj(x)=0 the inequality constraints condition that should meet in specific mechanical structure optimization and equation are indicated respectively
Constraints；
2. being sampled using orthogonal (DOE) method, including choose empirical factor, orthogonal arrage level；
3. constructing radial basis function agent model；
4. determining evaluation agent model accuracy, the mathematic(al) representation of used test point evaluation index is：
In formula：R is factor of determination；RadjTo adjust factor of determination；M is number of samples；K is the number of design variable；It is illustrated respectively in the measured value, average value and predicted value of Simulation Calculation at test point；When factor of determination and adjustment
Factor of determination closer to 1 when, Response Face Function, that is, agent model precision of construction is higher.Work as R2>=99.8%, Radj>=99.5%
When, the agent model of structure meets design requirement；
5. designed for the multi-objective optimization algorithm M-BSWA of solving-optimizing problem, include the following steps：
5.1 convert multi-objective optimization question to single-object problem with quadratic sum weighting method, and mathematic(al) representation is：
5.2 [are seen with Lagrangian multiplier methods：The Beijing the Hunan Yuan Ya nonlinear optimization computational methods [M] Science Press,
2008] it converts the constrained optimization problem in step 1.5.1 to unconstrained optimization problem, builds following Lagrangian letters
Number：
In formula：λj,αi,βiFor Lagrangian multipliers；
5.3 after step 5.2 and step 5.3 processing, establish the mathematical model of unconstrained optimization problem, mathematic(al) representation
For：
In formula：X is the vector of design variable composition；It is constructed by Lagrangian multiplier methods
Lagrangian functions；
5.4 [are seen with M-BFGS Quasi-Newton algorithms：Comparison [J] mathematics of the Huanghai Sea, several modified Rodrigues parameters of woods fringe China is ground
Study carefully, 2011] the iterative estimate value of design variable is calculated, the Iteration of M-BFGS Quasi-Newton algorithms is：
xk+1=xk+αkdk
In formula：αkSearch is step-length, is determined by Armijo inexact linear searchings；
dkFor the direction of search, i.e.,：
In formula：For the approximation of the Hessian matrixes of j-th of object function,For j-th object function
Derivative,For weighted factor；
5.5 multiple-objection optimizations for solving-optimizing problem that step 5.1,5.2 and 5.3 are formed using matlab tools
Algorithm M-BSWA carries out coding programming, the iterative estimate value for calculating design variable, realizes Optimization Solution, determines prioritization scheme；
6. verifying the validity of optimum results.
Multi-objective optimization algorithm M-BSWA described in step 5 for solving-optimizing problem is converted multi-objective optimization question
During for single-object problem, a part is determined using tolerance method in every group of weighting coefficient, and another part is based onPrinciple determine, then according to specific Design of Mechanical Structure problem, 50- is provided by adjusting the tolerance of object function
150 groups of weighting coefficient wi, i=1,2 ..., n.
The M-BSWA that the present invention designs in theory with all have that calculating speed is fast, meets convergence in practical engineering application
Numerical computation method.
Mathematical model between multiple performance indicators and design variable of the present invention by building specific mechanical structure, in order to add
Fast calculating speed, reduces the complexity of problem, and constructs agent model, fully considers between each performance indicator of mechanical structure
Correlation regard a variety of evaluation indexes as object function simultaneously, designs a kind of numerical algorithm solving multi-objective optimization question,
The algorithm being capable of rapid solving Constrained multi-objective optimization question.Finally propose a kind of machine based on M-BSWA multiple-objection optimizations
The design method of tool structure.
The present invention is suitable for the multi-objective optimization design of power of mechanical structure, and the mechanical configuration parameter distribution of acquisition is more reasonable,
To keep the mechanical structure performance of design more preferable, the present invention uses numerical computation method, and calculating speed is fast, is substantially shorter design
Period, and ensure under the premise of not increasing mechanical structure total quality, realize the target for improving mechanical structure comprehensive performance.
Description of the drawings
Fig. 1 is the flow chart of the Design of Mechanical Structure method based on M-BSWA multiple-objection optimizations
Fig. 2 is the design flow diagram of the M-BSWA algorithms of the Design of Mechanical Structure based on M-BSWA multiple-objection optimizations
Fig. 3 is the structural schematic diagram of coachbuilt body front portion structure energy absorbing component
Fig. 4 is the structural schematic diagram of front part of saloon car energy-absorption box
Specific implementation mode
Below in conjunction with front part of saloon car energy-absorption box structure design, the detailed description present invention.
As depicted in figs. 1 and 2, a kind of front part of saloon car energy-absorption box structure based on M-BSWA multiple-objection optimizations of the invention is set
Meter method, includes the following steps：
1. establish the mathematical model of car energy-absorption box structure multi-objective optimization design of power, including to establish energy-absorption box structure initial
CAD model selectes design variable, optimization object function and constraints；
2. the sampling of orthogonal (DOE) method of selection, constructs radial basis function agent model, determines evaluation agent mould
Type precision；
3. designed for the multi-objective optimization algorithm M-BSWA of solving-optimizing problem, according to flow is solved, coding volume is carried out
Journey realizes Optimization Solution；
4. verifying the validity of optimum results.
In step 1, the mathematical model for establishing car energy-absorption box structure multi-objective optimization design of power, includes the following steps：
1.1 to establish the initial CAD model of energy-absorption box structure as shown in Figure 4；
1.3 choose conquassation force efficiency (CFE) energy-absorbing ratio (SEA) as two optimization aims, and build associated target
Function f1(x),f2(x)；
1.4 setting constraintss：E (x) ＞ Ec,M(x)≤Mc；
In step 2, in choice experiment design (DOE) method sampling, radial basis function agent model is constructed, determines evaluation generation
It is mainly included the following steps that during reason model accuracy：
2.1 experimental design methods sample, and sample to obtain sample point and test point using orthogonal experiment design, and calculate
Go out sample point and the target function value of test point；
The precision of 2.2 evaluation agent models sets agent model precision evaluation index, calculates agent model at test point
Response and its precision, if not reaching accuracy criteria, more new sample point rebuilds agent model, used survey
Pilot evaluation index is as follows：
In formula：R is factor of determination；RadjTo adjust factor of determination；M is number of samples；K is the number of design variable；It is illustrated respectively in the measured value, average value and predicted value of Simulation Calculation at test point；
Work as R2>=99.8%, RadjWhen >=99.5%, the agent model of structure can meet design requirement；
In step 3, it is designed for the multi-objective optimization algorithm M-BSWA of solving-optimizing problem, for solving energy-absorption box knot
Structure optimization design problem includes the following steps：
3.1 convert multi-objective problem to single-object problem using quadratic sum weighting methods, specific method can retouch for：
In formula：fi *(x) it is the optimal solution of each object function, wiFor weighting coefficient.
One determines that another is based on using tolerance method in every group of weighting coefficientPrinciple determine.
Then according to specific Design of Mechanical Structure problem, 100 groups of weighting coefficients are provided by adjusting the tolerance of object function
wi, i=1,2.Tolerance method defines：If αi≤fi(x)≤βi, i=1,2 ..., L then claimFor
The tolerance of the object function.
The weighting coefficient mathematic(al) representation determined by tolerance method is：
In conclusion the mathematical model of the front part of saloon car energy-absorption box structure multiple-objection optimization based on quadratic sum weighting method can table
State for：
3.2 convert constrained optimization problem to unconstrained optimization problem using Lagrangian multiplier methods, can specifically retouch
State for：
In formula：lj(j=1,2), αi,βi(i=1,2,3) it is Lagrange multiplier.
In conjunction with (3) formula, (2) formula can be rewritten as：
Quasi-Newton algorithm is the prefered method for solving unconstrained optimization problem, and efficient calculating speed and convergence are allowed to
Good performance is shown in terms of solving unconstrained optimization problem.
The present invention has selected a kind of M-BFGS algorithms to solve the unconstrained optimization problem that (4) formula describes.
3.3 solve above-mentioned unconstrained optimization problem using a kind of improved BFGS (M-BFGS) algorithm.
M-BFGS algorithms the specific steps are：
A. initial point x is chosen0∈Rn, initial symmetric positive definite matrix B0∈Rn×n, parameter ε, ρ ∈ (0,1), δ ∈ (0,0.5)
Enable k:=1；
If b. | | gk| |≤ε stops iteration；Otherwise solution system of linear equations Bkdk+gk=0, obtain direction of search dk；
In formula：It is object function fj(x) Hessian matrixes.
C. step factor α is determined by Armijo non-linear search rulesk；
D. Iteration xk+1:=xk+αkdk；
It corrects BFGS updating formulas and calculates Bk+1：
rk=2 (fk+1-fk-gk Tsk)/||sk||2；
sk=fk+1-fk；
t∈[0,1]。
E. k is enabled:=k+1, goes to step b.
According to the algorithm that step 3.1,3.2 and 3.3 describe, to the mathematical model established for energy-absorption box optimization particular problem
It is programmed, realizes Optimization Solution.
Front part of saloon car energy-absorption box structure is optimized according to obtained Optimal Parameters value.
The validity of optimum results is verified finally by simulation software.
Claims (2)
1. a kind of Design of Mechanical Structure method based on M-BSWA multiple-objection optimizations, it is characterised in that include the following steps：
1.1 establish the mathematical model of mechanical structure multi-objective optimization design of power, include the following steps：
1.1.1 the initial CAD model of mechanical structure is established；
1.1.2 design variable, optimization object function and constraints are selected；
1.1.3 the mathematical model of mechanical structure is established, mathematic(al) representation is：
In formula：f1(x),f2(x),...,fn(x) object function related with mechanical structure performance is indicated；N is object function
Number；(x1,x2,...,xl) indicate design variable；Indicate Design of Mechanical Structure range；L becomes for Design of Mechanical Structure
Measure number；hj(x)≤0,hj(x)=0 indicate respectively the inequality constraints condition that should meet in specific mechanical structure optimization problem and
Equality constraint, wherein：J=1,2 ..., m0..., m indicates j-th of constraints in specific optimization problem, m0For differ
The number of formula constraints, m are the total number of constraints；
1.2 are sampled using orthogonal (DOE) method, including choose empirical factor, and it is horizontal to choose orthogonal arrage；
1.3 construction radial basis function agent models；
1.4 determine that evaluation agent model accuracy, the mathematic(al) representation of used test point evaluation index are：
In formula：R is factor of determination；RadjTo adjust factor of determination；M is number of samples；K is the number of design variable；yi,
It is illustrated respectively in the measured value, average value and predicted value of Simulation Calculation at test point；
1.5 are designed for the multi-objective optimization algorithm M-BSWA of solving-optimizing problem, include the following steps：
1.5.1 multi-objective optimization question is converted to single-object problem with quadratic sum weighting method, mathematic(al) representation is：
In formula：fi(x) object function is indicated；N is the number of object function；fi *For the optimal solution of each object function；wiFor weighting
Coefficient；
1.5.2 the constrained optimization problem in step 1.5.1 is converted to unconstrained optimization problem with Lagrangian multiplier methods,
Build following Lagrangian functions：
In formula：λj,αi,βiFor Lagrangian multipliers；
1.5.3 after step 1.5.2 and step 1.5.3 processing, the mathematical model of unconstrained optimization problem, mathematical expression are established
Formula is：
In formula：X is the vector of design variable composition；It is constructed by Lagrangian multiplier methods
Lagrangian functions；
1.5.4 M-BFGS Quasi-Newton algorithms is used to calculate the iterative estimate value of design variable, the iteration lattice of M-BFGS Quasi-Newton algorithms
Formula is：
xk+1=xk+αkdk
In formula：αkFor step-size in search, determined by Armijo inexact linear searchings；dkFor the direction of search, i.e.,：
In formula：For the approximation of the Hessian matrixes of j-th of object function,For leading for j-th object function
Number,For weighted factor,
1.5.5 the multiple target for solving-optimizing problem for using matlab tools to form step 1.5.1,1.5.2 and 1.5.3
Optimization algorithm M-BSWA carries out coding programming, the iterative estimate value for calculating design variable, realizes Optimization Solution, determines optimization side
Case；
The validity of 1.6 verification optimum results.
2. the Design of Mechanical Structure method as described in claim 1 based on M-BSWA multiple-objection optimizations, it is characterised in that step
The 1.5 multi-objective optimization algorithm M-BSWA for solving-optimizing problem are that multi-objective optimization question is converted into single goal is excellent
During change problem, a part is determined using tolerance method in every group of weighting coefficient, and another part is based onPrinciple it is true
It is fixed, then according to specific Design of Mechanical Structure problem, 50-150 group weighting coefficients w is provided by adjusting the tolerance of object functioni,
I=1,2 ..., n.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101887478A (en) * | 2010-07-19 | 2010-11-17 | 北京理工大学 | Sequence radial basis function agent model-based high-efficiency global optimization method |
| CN104091028A (en) * | 2014-07-18 | 2014-10-08 | 湖大海捷(湖南)工程技术研究有限公司 | Multi-objective optimization design method of spiral oil wedge bearing |
| CN104866692A (en) * | 2015-06-18 | 2015-08-26 | 北京理工大学 | Aircraft multi-objective optimization method based on self-adaptive agent model |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101887478A (en) * | 2010-07-19 | 2010-11-17 | 北京理工大学 | Sequence radial basis function agent model-based high-efficiency global optimization method |
| CN104091028A (en) * | 2014-07-18 | 2014-10-08 | 湖大海捷(湖南)工程技术研究有限公司 | Multi-objective optimization design method of spiral oil wedge bearing |
| CN104866692A (en) * | 2015-06-18 | 2015-08-26 | 北京理工大学 | Aircraft multi-objective optimization method based on self-adaptive agent model |
Non-Patent Citations (2)
| Title |
|---|
| Nonlinear Lagrangian for Multiobjective Optimization and Applications to Duality and Exact Penalization;X. X. Huang 等;《2002 Society for Industrial and Applied Mathematics》;20020131;第13卷(第3期);第675–692页 * |
| 基于近似模型的高速磨床零部件结构优化设计研究;文桂林 等;《中国机械工程》;20090430;第20卷(第8期);第906–910页 * |
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