CN110020466A - Negative poisson's ratio structure energy-absorption box optimization design method based on agent model - Google Patents
Negative poisson's ratio structure energy-absorption box optimization design method based on agent model Download PDFInfo
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Abstract
The invention discloses a kind of the negative poisson's ratio structure energy-absorption box optimization design method based on agent model, specific steps are as follows: the mathematical model of multiple target Cooperative Optimization is established according to the architectural characteristic of negative poisson's ratio structure energy-absorption box；Establish collision simulation parameterized model；It is sampled in design domain using Taguchi orthogonal strategy；Precision test is carried out based on the agent model of Least square support vector regression building objective function, and to agent model；It designs a kind of improvement population multi-objective optimization algorithm and Cooperative Optimization mathematical model is solved；It determines optimization design scheme and verifies.The present invention solves the problems, such as the high dimension and strong nonlinearity in the design of energy-absorption box collision energy-absorbing characteristic optimizing, proceeds from the situation as a whole to realize Cooperative Optimization of the negative poisson's ratio structure energy-absorption box under not syn-collision operating condition.
Description
Technical field
The present invention relates to vehicle structure crash-worthiness design fields, and in particular to a kind of negative poisson's ratio knot based on agent model
Structure energy-absorption box optimization design method.
Background technique
Energy-absorption box is the important energy absorbing component of automobile front beam system, it be located at bumper beam and automobile front longitudinal beam it
Between.When crashing, is deformed by conquassation and absorb collision energy, while part distortion being controlled in smaller area as far as possible
It is interior to protect remaining important spare part, reduce subsequent maintenance cost.Negative poisson's ratio structural material can when being acted on by load
Steady and controllable compressive deformation occurs, while rigidity is presented under the action of negative poisson's ratio characteristic to enhance characteristic, by negative Poisson
It is designed than structural material applications in energy-absorption box, protection need when different speeds are collided to pedestrian, vehicle and occupant can be met simultaneously
It asks.
Research shows that the geometric dimension of negative poisson's ratio structure inner core has significant shadow for the shock dynamics performance of structure
It rings, this certainly will also affect the collision safety characteristic of negative poisson's ratio structure energy-absorption box.Meanwhile the phase interaction of box body structure and inner core
With the important factor in order for being also energy-absorption box collision safety performance.Therefore, more parameter of structure design, more performance objectives and the two
Between Complex Response relationship, this makes the design of negative poisson's ratio structure energy-absorption box need the Cooperative Optimization using multiple target
Method.
Patent CN103577618B discloses a kind of vehicle energy absorption box design method, comprising the following steps: goal-selling is inhaled
The length and conquassation rate of energy box, calculate the conquassation distance for obtaining energy-absorption box；Obtain the theoretical energy of energy-absorption box impact absorption；It will inhale
Can the theoretical energy of box impact absorption divided by it be crushed distance and obtain the theory of energy-absorption box and be averaged crushing force；According to average crushing force
Formula calculates the actual average crushing force of the energy-absorption box of various alternative specifications；It is greater than according to energy-absorption box actual average crushing force
Theory equal to energy-absorption box is averaged the principle of crushing force, chooses appropriate size from alternative specification and designs target energy-absorption box.But
This method still relies on the theoretical formula and design experiences of traditional energy-absorption box, not can be used directly in negative poisson's ratio structure energy-absorption box
Design, and do not have to describe the relationship between design parameter and performance response in its design method, lead to the optimization of energy-absorption box
Design is difficult to realize.
Summary of the invention
The purpose of the present invention is to provide a kind of negative poisson's ratio structure energy-absorption box Cooperative Optimization based on agent model
Method.
Realize the technical solution of the object of the invention are as follows: a kind of negative poisson's ratio structure energy-absorption box collaboration based on agent model is excellent
Change design method, comprising the following steps:
Step 1, the mathematical modulo of multiple target Cooperative Optimization is established according to the architectural characteristic of negative poisson's ratio structure energy-absorption box
Type；
Step 2, collision simulation parameterized model is established；
Step 3, it is sampled in design domain using Taguchi orthogonal strategy；
Step 4, the agent model based on Least square support vector regression building objective function, and agent model is carried out
Precision test；
Step 5, Cooperative Optimization mathematical model is solved using improvement population multi-objective optimization algorithm；
Step 6, it determines optimization design scheme and verifies.
Compared with prior art, remarkable result of the invention are as follows: the present invention is constructed by way of establishing agent model
Multiple performance indicators of the negative poisson's ratio structure energy-absorption box under not syn-collision operating condition and the display mathematical model between design parameter, fill
Divide and consider the coupled relation between design parameter and the associate feature between performance indicator, solves energy-absorption box collision energy-absorbing
High dimension and strong nonlinearity problem in characteristic optimizing design；Meanwhile it is a kind of suitable for multiple target by designing to proceed from the situation as a whole
The intelligent algorithm of optimization problem realizes Cooperative Optimization of the negative poisson's ratio structure energy-absorption box under not syn-collision operating condition.
Detailed description of the invention
Fig. 1 is that the present invention is based on the signals of the negative poisson's ratio structure energy-absorption box optimization design method process of agent model
Figure.
Fig. 2 is the structural schematic diagram of negative poisson's ratio structure energy-absorption box of the present invention.
Fig. 3 is the flow diagram of parametric modeling of the present invention and analysis.
Fig. 4 is Modified particle swarm optimization algorithm flow schematic diagram of the present invention.
Fig. 5 is the forward position the Pareto schematic diagram that multiple target of the present invention cooperates with optimization problem optimizing to obtain.
Specific embodiment
As shown in Figure 1, a kind of negative poisson's ratio structure energy-absorption box optimization design method based on agent model, specific to walk
Suddenly are as follows:
Step 1, the mathematical modulo of multiple target Cooperative Optimization is established according to the architectural characteristic of negative poisson's ratio structure energy-absorption box
Type:
According to the structure feature of negative poisson's ratio structure energy-absorption box, the independent geometry variable that will characterize structure feature is tentatively fixed
Justice is optimal design parameter and determines parameter variation range；The state of negative poisson's ratio structure energy-absorption box collision energy-absorbing characteristic will be characterized
Variable-definition is objective function；Selected part state variable defines constraint condition；Establish negative poisson's ratio structure energy-absorption box multiple target
The mathematical model of Cooperative Optimization, expression formula are as follows:
Wherein,
(1) design vector x={ x1,x1,…xm}；
(2) .V-min indicates vector minimization, i.e. object vector f (x)=[f1(x),f2(x),…fp(x),]TIn institute
Having specific item scalar functions all must reach minimum as far as possible；
(3).giIt (x)≤0 is inequality constraints condition.
Step 2, it establishes collision simulation parameterized model: negative poisson's ratio structure being inhaled using design parameter as adjustable structure variable
Energy box establishes parametric modeling, including finite element modeling and 100% head-on crash operating condition simulation analysis.
Step 3, it is sampled in design domain using Taguchi orthogonal strategy:
Based on Taguchi orthogonal strategy, determines the test level of design parameter, formulates experimental design table and is true
Determine sample point in optimization problem design domain, call parameters model calculates the state variable response of sample point.
Step 4, the agent model based on Least square support vector regression building objective function, and agent model is carried out
Precision test:
All sample points and its corresponding response in experimental design table are extracted, Least square support vector regression is based on
The agent model of state variable is constructed, the citation form of agent model may be expressed as:
Wherein, αiThe corresponding sample that is not zero is supporting vector, αiFor fitting coefficient, b is constant vector, xiFor training
Sample input vector, x are then sample input vector to be predicted；In conjunction with the random sample point in design domain, by predicted value
Error analysis is to verify the precision of agent model.
Step 5, Cooperative Optimization mathematical model is solved using improvement population multi-objective optimization algorithm, is obtained
The Pareto optimal solution set of design domain, comprising:
Multi-objective optimization is carried out to objective function using particle swarm algorithm, the solution of each optimization problem is considered as D dimension search
A bird in space, referred to as " particle ".By the position and speed of more new particles, them are made to follow individual history optimal
Value Phest and global optimum's particle Gbest is searched in solution space until seeking optimal solution.Position and speed of the particle in search
More new formula may be expressed as:
Wherein,WithIt is position of the i particle in kth and k+1 iteration step respectively；WithIt is i respectively
Speed of the son in kth and k+1 iteration step, ωk+1It is to maintain the coefficient of previous step iteration speed, referred to as inertia weight, c1It is
The Studying factors of Particle tracking oneself history optimal value, c2It is the Studying factors of Particle tracking globally optimal solution, r1And r2It is two
Random function, value range [0,1], to increase search randomness.
Step 6, it determines optimization design scheme and verifies
Define extent function, calculating side after the response of solutions all in Pareto optimal solution set is normalized
Case satisfaction determines optimization design scheme by sorting, compares verifying to optimal design.
Further, being when solution agent model nonlinear regression problem in step 4 will be former empty by introducing kernel function
Between nonlinear function approximation problem successful conversion be higher dimensional space linear function fit problem, then be supported in higher dimensional space
SYSTEM OF LINEAR VECTOR Regressive Solution.The method chooses kernel function of the Gaussian radial basis function as support vector regression:
Wherein, nuclear parameter σ usually can refer toD is the independent variable quantity of training sample point.
Further, in order to improve the Searching efficiency of particle swarm optimization algorithm described in step 5, in standard multi-target particle
Using two kinds of strategies of adaptive inertia weight and time-varying Studying factors come excellent to multi-objective particle swarm on the basis of colony optimization algorithm
Change algorithm to improve, inertia weight may be expressed as:
Wherein, t is current iteration number, tmaxIt is greatest iteration total degree.Likewise, the expression formula of Studying factors is changed
Into for when deformation type:
Wherein, c1maxAnd c1miIt is Studying factors c respectively1Maximum value and minimum value, c2maxAnd c2minRespectively be study because
Sub- c2Maximum value and minimum value.
Further, the extent function in step 6 may be defined as:
Wherein fi min、fi maxIt is objective function f in the forward position Pareto respectivelyi(x) minimum, maximum value.P is summation number,
That is f (x) subfunction number.
It elaborates below with reference to embodiment and attached drawing to the present invention.
Embodiment
As shown in Figure 1, a kind of negative poisson's ratio structure energy-absorption box optimization design method based on agent model, including with
Lower step:
Step 1: as shown in Fig. 2, the only of structure feature will be characterized according to the structure feature of negative poisson's ratio structure energy-absorption box
Vertical geometry variable preliminary definition is optimal design parameter and determines parameter variation range are as follows: the bending of indent hexagon Cellular structure
Born of the same parents arm lengths L, the wall thickness T of born of the same parents' arm section factor α, born of the same parents' arm lengths factor beta, cell element angle theta and thin wall box structure, wherein
θ is the angle for being bent born of the same parents' arm 101 and supporting born of the same parents' arm 102, and born of the same parents arm section factor α is born of the same parents' arm sectional area and suffered stress axis, is used
With bending resistance or the torsional property etc. for evaluating born of the same parents' arm.It is optimal design parameter and parameter variation range shown in table 1, and corresponding
The initial value of optimal design parameter；
1 negative poisson's ratio structure energy-absorption box optimal design parameter table of table
The state variable for characterizing negative poisson's ratio structure energy-absorption box collision energy-absorbing characteristic is defined as objective function；For negative pool
Collision safety performance of the pine than structure energy-absorption box under two kinds of operating conditions of low-speed head-on collision and middling speed head-on crash, to realize two kinds
Collaboration optimization under operating condition, chooses the peak value impact force F under speed operation respectivelymaxWith average impact Fave, under middling speed operating condition
Than energy-absorbing EiAs objective function, it is desirable that FmaxIt is minimized, FaveAnd EiIt is maximized, has both met RCAR low speed collision mark
Standard, and improve the energy-absorbing effect under middling speed collision；Selected part state variable defines constraint condition；Constraint condition is mainly wrapped
Include: one, design parameter own dimensions constrain, and the cell element of negative poisson's ratio structure inner core has indent characteristic；Two, lightweight is current
The important indicator of body structure design, the mass M of energy-absorption box is not above former designing quality M after optimization0；Establish negative poisson's ratio knot
The mathematical model of structure energy-absorption box multiple target Cooperative Optimization, expression formula are as follows:
Step 2: being illustrated in figure 3 the flow diagram of parametric modeling and analysis, become by adjustable structure of design parameter
Amount establishes parametric modeling, including finite element modeling and the emulation point of 100% head-on crash operating condition to negative poisson's ratio structure energy-absorption box
Analysis.The parametric modeling for carrying out negative poisson's ratio structure energy-absorption box for main program carrier with Matlab is specifically included, input is passed through
Parameter of structure design calculates the node coordinate and unit information of grid model, and material is assigned based on the grid model of foundation
Attribute, load constraint and load-up condition, setting contact, definition solves control card and output requires, finally by simulation model
All information are write according to the format of .rad file to be solved file and Radioss solver is called to carry out numerical solution, final to obtain
To finite element result be then individually stored for follow-up study and extract analysis.
Step 3: being based on Taguchi orthogonal strategy, determine the test level of design parameter, table 2 is this implementation
The experimental design factor level table of example, it is horizontal comprising five factor four shown in table 1；
2 experimental design factor level table of table
After determining factor and level, selecting orthogonal arrage is the committed step of Orthogonal Experiment and Design, this experimental design includes altogether
Five four horizontal factors, select L between not Consideration on the basis of reciprocation16(45) orthogonal arrage arranges to test.It will
Experimental factor and objectives of examination are arranged into orthogonal arrage respectively, that is, give the L comprising 16 sampled points16(45) orthogonal experiment plan
Meter scheme, is shown in Table 3.In table other than 16 sample points of experimental design, 6 random sample points are separately attached with, are built for verifying
The precision of vertical agent model.Four are classified as the state variable obtained by corresponding parameterized model progress collision simulation after in table 3
Response.
3 L of table16(45) Orthogonal Experiment and Design
Step 4: extract experimental design table in all sample points and its corresponding response, based on least square support to
Amount returns the agent model of (Least Squares Support Vector Regression LS-SVR) building state variable,
The citation form of agent model may be expressed as:
Wherein, αiThe corresponding sample that is not zero is supporting vector, αiFor fitting coefficient, xiFor training sample input vector,
X is then sample input vector to be predicted.Choose kernel function of the Gaussian radial basis function as support vector regression:
σ is taken in above formula nuclear parameter2=40, penalty coefficient c=100000.Kernel function is substituted into regression model, can must be acted on behalf of
The form of model is as follows:
According to the training sample in table 3, using the above-mentioned agent model construction method based on LS-SVR to state variable into
Row fitting, the parameter alpha for the agent model being fittediIt is as described in Table 4 with b:
4 Least square support vector regression agent model of table
After agent model based on LS-SVR establishes, error analysis is carried out using random sample point, chooses and determines coefficient
R2, the precision evaluation index of root-mean-square error RMSE, maximum value error MAE as agent model, list this implementation in table 5
The error of fitting of the LS-SVR agent model of example.
5 LS-SVR agent model error of fitting of table
By, it is found that the agent model overall fit degree based on LS-SVR is good, confidence level is high in table, it can be used for subsequent optimization and set
Meter.
Step 5: designing a kind of improvement population multi-objective optimization algorithm (Multi-objective Particle Swarm
Optimization MOPSO) and Cooperative Optimization mathematical model is solved, obtain the Pareto optimal solution of design domain
Collection, Fig. 4 are the Modified particle swarm optimization algorithm flow schematic diagram of the present embodiment, are specifically included:
Multi-objective optimization is carried out to objective function using particle swarm algorithm, the solution of each optimization problem is considered as D dimension search
A bird in space, referred to as " particle ".By the position and speed of more new particles, them are made to follow individual history optimal
Value Pbest and global optimum's particle Gbest is searched in solution space until seeking optimal solution.Position and speed of the particle in search
More new formula may be expressed as:
Wherein,WithIt is position of the i particle in kth and k+1 iteration step respectively；WithIt is i respectively
Speed of the son in kth and k+1 iteration step, ωk+1It is to maintain the coefficient of previous step iteration speed, referred to as inertia weight, c1It is
The Studying factors of Particle tracking oneself history optimal value, c2It is the Studying factors of Particle tracking globally optimal solution, r1And r2It is two
Random function, value range [0,1], to increase search randomness.
In order to improve the Searching efficiency of particle swarm optimization algorithm described in step 5, in standard multi-objective particle
On the basis of using two kinds of strategies of adaptive inertia weight and time-varying Studying factors come to multi-objective particle carry out
It improves, inertia weight may be expressed as:
Wherein, t is current iteration number, tmaxIt is greatest iteration total degree.Likewise, the expression formula of Studying factors is changed
Into for when deformation type:
Wherein, c1maxAnd c1minIt is Studying factors c respectively1Maximum value and minimum value, c2maxAnd c2minRespectively be study because
Sub- c2Maximum value and minimum value.
In summary improvement strategy has been write improvement multi-objective particle by Matlab and has been applied to
The collaboration of novel energy-absorption box optimizes, and the basic parameter setting of algorithm is as shown in table 6.
Table 6 improves the setting of MOPSO basic parameter
Fig. 5 gives the Pareto optimal solution set by obtaining after improvement multi-objective particle optimizing, the disaggregation
It is made of 100 noninferior solutions.As can be seen from Figure, modified particle swarm optiziation can successfully realize that the collaboration of multiple objective function is sought
It is excellent, and the convergence of Pareto disaggregation and distributivity are also preferable, finally the number of iterations is 46 when convergence, calculates time-consuming about 1.5h.
Step 6: in order to be compared with original design, according to minimum peak impact force, maximum average impact and most in table 7
Have chosen three optimal compromise solutions from the forward position Pareto than the design requirement of energy-absorbing greatly.Compared with original design, minimum peak
F in impact force schememax55.9% is reduced, F in maximum average impact schemeave71.1% is improved, high specific energy-absorbing side
E in caseiThen improve 145%.
7 negative poisson's ratio structure energy-absorption box Cooperative Optimization scheme of table
Extent function is defined, such as following formula:
Wherein fi min、fi maxIt is objective function f in the forward position Pareto respectivelyi(x) minimum value, maximum value.
Rear numerical procedure satisfaction is normalized in three target capabilities parameters, then is more respectively satisfied with angle value,
Final scheme satisfaction sequence from excellent to bad are as follows: high specific energy-absorbing, maximum average impact, minimum peak impact force, former design.
In conclusion the resistance to of energy-absorption box can be significantly improved based on support vector regression and the energy-absorption box collaboration optimization for improving particle swarm algorithm
Hitting property index, and optimization process and final result be it is believable, this for novel negative poisson's ratio structure energy-absorption box crash-worthiness design
Provide effective approach.
Claims (9)
1. a kind of negative poisson's ratio structure energy-absorption box optimization design method based on agent model, which is characterized in that including with
Lower step:
Step 1, the mathematical model of multiple target Cooperative Optimization is established according to the architectural characteristic of negative poisson's ratio structure energy-absorption box；
Step 2, collision simulation parameterized model is established；
Step 3, it is sampled in design domain using Taguchi orthogonal strategy；
Step 4, the agent model based on Least square support vector regression building objective function, and precision is carried out to agent model
Verifying；
Step 5, Cooperative Optimization mathematical model is solved using improvement population multi-objective optimization algorithm；
Step 6, it determines optimization design scheme and verifies.
2. the negative poisson's ratio structure energy-absorption box optimization design method according to claim 1 based on agent model,
It is characterized in that, step 1 specifically:
According to the structure feature of negative poisson's ratio structure energy-absorption box, the independent geometry variable preliminary definition that will characterize structure feature is
Optimal design parameter simultaneously determines parameter variation range；
The state variable for characterizing negative poisson's ratio structure energy-absorption box collision energy-absorbing characteristic is defined as objective function；
It chooses state variable and defines constraint condition；
Establish the mathematical model of negative poisson's ratio structure energy-absorption box multiple target Cooperative Optimization.
3. the negative poisson's ratio structure energy-absorption box optimization design method according to claim 2 based on agent model,
It is characterized in that, the mathematical model expression formula of multiple target Cooperative Optimization are as follows:
Wherein,
(1) design vector x={ x1,x1,…xm}；
(2) V-min indicates vector minimization, i.e. object vector f (x)=[f1(x),f2(x),…fp(x)]TIn all sub-goals
Function must all reach minimum as far as possible；
(3)giIt (x)≤0 is inequality constraints condition.
4. the negative poisson's ratio structure energy-absorption box optimization design method according to claim 1 based on agent model,
It is characterized in that, in step 2, parametric modeling is carried out to negative poisson's ratio structure energy-absorption box using design parameter as adjustable structure variable,
Including finite element modeling and 100% head-on crash operating condition simulation analysis.
5. the negative poisson's ratio structure energy-absorption box optimization design method according to claim 1 based on agent model,
It is characterized in that, step 3 specifically:
Based on Taguchi orthogonal strategy, determines the test level of design parameter, formulates experimental design table and determination is excellent
Sample point in change problem design domain, call parameters model calculate the state variable response of sample point.
6. the negative poisson's ratio structure energy-absorption box optimization design method according to claim 1 based on agent model,
It is characterized in that, step 4 specifically:
All sample points and its corresponding response in experimental design table are extracted, is constructed based on Least square support vector regression
The citation form of the agent model of state variable, agent model indicates are as follows:
Wherein, αiThe corresponding sample that is not zero is supporting vector, αiFor fitting coefficient, xiFor training sample input vector, x is then
For sample input vector to be predicted；In conjunction with the random sample point in design domain, verified by the error analysis to predicted value
The precision of agent model；
Higher dimensional space linear function fit problem is converted by former Space Nonlinear Function Fitting problem by introducing kernel function, then
SYSTEM OF LINEAR VECTOR Regressive Solution is supported in higher dimensional space；Choose core letter of the Gaussian radial basis function as support vector regression
Number:
Wherein, nuclear parameterD is the independent variable quantity of training sample point.
7. the negative poisson's ratio structure energy-absorption box optimization design method according to claim 1 based on agent model,
It is characterized in that, step 5 specifically:
Cooperative Optimization mathematical model is solved using population multi-objective optimization algorithm is improved, obtains design domain
Pareto optimal solution set, comprising:
It is right using adaptive inertia weight and two kinds of strategies of time-varying Studying factors on the basis of multi-objective particle
Multi-objective particle improves, and inertia weight indicates are as follows:
Wherein, t is current iteration number, tmaxIt is greatest iteration total degree；Likewise, the expression formula of Studying factors is improved to
When deformation type:
Wherein, c1maxAnd c1minIt is Studying factors c respectively1Maximum value and minimum value, c2maxAnd c2minIt is Studying factors c respectively2
Maximum value and minimum value.
8. the negative poisson's ratio structure energy-absorption box optimization design method according to claim 1 based on agent model,
It is characterized in that, step 6 specifically:
Extent function is defined, rear numerical procedure, which is normalized, in the response of solutions all in Pareto optimal solution set expires
Meaning degree determines optimization design scheme by sorting, compares verifying to optimal design.
9. the negative poisson's ratio structure energy-absorption box optimization design method according to claim 8 based on agent model,
It is characterized in that, the extent function in step 6 is defined as:
Wherein fi min、fi maxIt is objective function f in the forward position Pareto respectivelyi(x) minimum value, maximum value.
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