CN102999672B - Based on the parallel support vector machines approximate model optimization method of vehicle collision resistant - Google Patents

Abstract

Based on a parallel support vector machines approximate model optimization method for vehicle collision resistant, the steps include: that (1) sets up network; (2) generate initial sample and automatically transfer to grid node; (3) initial sample is assigned to each computing node; (4) stochastic generation sample point; (5) approximate model based on SVM is set up; (6) obtain the error criterion of SVM approximate model, judge whether to reach convergence level; If so, then the node of all generations is adopted to build the SVM model of the overall situation; (7) judge whether the SVM model of the overall situation restrains; If convergence, then process terminates, anyway, then jump procedure (8); (8) maximum error district is found; (9) error district information is sued for peace, stochastic generation sample in the region after summation, and be evenly distributed to each computing node, and jump to step (4), until process terminates.The present invention adopt to SVM carry out the pattern of parallelization process, the speed that significantly can promote modeling and optimization efficiency, improve precision.

Description

Based on the parallel support vector machines approximate model optimization method of vehicle collision resistant

Technical field

The present invention is mainly concerned with the safety-optimized design field in Car design manufacture, refers in particular to a kind of parallel support vector machines approximate model optimization method based on vehicle collision resistant.

Background technology

Crash-worthiness is the main problem considered in automotive safety optimal design; and affect in the design process often of vehicle safety and be supplied to automobile for being out of shape the parts of energy-absorbing; as front longitudinal, crashworthiness box etc.; the characteristic of the energy absorbing component of these keys and deformation pattern just determine the power of automobile in collision process or acceleration; vital effect is played to passenger protection, so thin-walled energy absorbing members is all an emphasis of automobile optimal design all the time.

Optimization in early days for crash-worthiness problem is based on gradient classic optimisation algorithm, has practitioner to combine emulation technology and traditional optimization for the optimization of crash-worthiness problem, and designs for car crass in conjunction with multidisciplinary business software iSight.Along with proposition and the development of Approximate Model Method, based on optimization method widespread use in Automobile Design of approximate model technology, replace the traditional optimization based on gradient gradually and become the mainstream technology in the design of current vehicle safety.

Practitioner is separately had to adopt SuccessiveRSM method to be studied simple energy-absorbing beam and front crash-worthiness of hitting problem, and adopt the safe design of the method to ChevroletC2500 to be optimized, and this method also adopt by business software LS-OPT.6Sigma method of quality control in conjunction with approximate model technology, is established the Optimization Design of the robustness for automobile side crash by Koch etc., and the robustness of its optimum results is improved to some extent.In addition, a lot of scholar have employed StepwiseRegression (SR), the main stream approach such as MLS, Mutiquadric (MQ), Kriging and AdaptiveandInteractiveModelingSystem (AIMS) are tested the problem of touching before automobile respectively.Result shows: existing a kind of not method can meet the modeling requirement of collision problem completely, needs to set up a kind of brand-new numerical method and studies this kind of problem.

Whether the approximate model that these methods construct above can reflect the inner characteristic of optimization aim, and how evaluating the approximate model constructed by these methods, these problems become the obstruction that approximate model technology is applied in engineering practice.At present, substantially be based upon on the basis that regretional analysis, variance analysis and unbiased esti-mator etc. take statistical theory as foundation for the evaluation of approximate model quality, the standard of this kind of judgment models quality can be summed up as in fact so-called empirical risk minimization criterion.But empirical risk minimization might not mean that expected risk is minimum, for approximate model, its reason mainly attempts the sample going matching limited with very complicated model, causes losing Generalization Ability.In recent years, along with interdisciplinary continuous intersection, fusion, a kind of technology of the Corpus--based Method theories of learning: SupportVectorMachine (SVM, support vector machine) theory receives extensive concern.SVM and neural network similar, be all learning-oriented mechanism, but use mathematical method and optimisation technique with neural network unlike SVM, the gordian technique of SVM is kernel function.Lower dimensional space vector set is difficult to divide usually, and the method for solution is that they are mapped to higher dimensional space.But the consequence that this way is brought is exactly the increase of computation complexity, and kernel function just in time solves this problem dexterously.That is, as long as select suitable kernel function, the classification function of higher dimensional space can just be obtained.In SVM theory, different kernel functions is adopted to cause different SVM algorithms.At present, in the world the discussion of this theory and research are strengthened gradually, and Preliminary Applications is in the matching of complex nonlinear problem.

The major defect of above-mentioned SVM method is its optimization efficiency, and owing to needing great amount of samples to build sane approximate model, therefore for the vehicle collision resistant problem of complexity, the calculating sample required for SVM method is huge, is difficult to be applied to engineering reality.

Summary of the invention

The technical problem to be solved in the present invention is just: the technical matters existed for prior art, the invention provides a kind of employing to SVM carry out the pattern of parallelization process, the speed that significantly can promote modeling and optimization efficiency, carry the high-precision parallel support vector machines approximate model optimization method based on vehicle collision resistant.

For solving the problems of the technologies described above, the present invention by the following technical solutions:

Based on a parallel support vector machines approximate model optimization method for vehicle collision resistant, the steps include:

(1) set up sparse network according to design space, initial sample point is positioned at network node;

(2) generate initial sample by super Latin square experimental design method, sample transfers to grid node automatically;

(3) the initial sample generated is assigned to each computing node;

(4) on each computing node, monte carlo method stochastic generation sample point is used;

(5) according to the sample generated in current computing node, each computing node is set up approximate model based on SVM respectively;

(6) obtain the error criterion of the SVM approximate model that each computing node builds respectively, judge whether to reach convergence level; If reach convergence level at this computing node, the then sample interval in this region of initial setting, store, step (4) sample for constructing approximate model in each computing node is reached host process, adopt the node of all generations to build the SVM model of the overall situation;

(7) judge whether the SVM model of the overall situation restrains; If convergence, then process terminates, otherwise, then jump to step (8);

(8) for the SVM model of not restraining for each region, then according to by mistake extent, preliminary and find maximum error district; Relatively convergence SVM model region, search its non-coincidence region, determine maximum error region;

(9) each interval error district information obtained be dealt into host process and sue for peace, stochastic generation sample in the region after summation, and being evenly distributed to each computing node, and jumping to step (4), until process terminates.

As a further improvement on the present invention:

The interpretational criteria of following three approximate models is have employed, if X in step (6) and (7) _i(i=1,2 ... m) be m of stochastic generation in design domain and obey equally distributed test sample book point:

（1）R ²；

$R^2=1-\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(f\left(X_i\right)-\hat{f}\left(X_i\right))}^2}{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(f\left(X_i\right)-\stackrel{\_}{f}\left(X_i\right))}^2}$

Wherein, the mean value of output function at m test sample book point, for the approximating function value of test sample book, this refers to the precision reflecting an approximate model on the whole, R ²value more close to 1, then approximate model is more accurate;

(2)RAAE；

$\mathrm{RAAE}=\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}|f\left(X_i\right)-\hat{f}\left(X_i\right)|}{m*\mathrm{STD}}$

Here, STD represents standard deviation, with R ²the same, this index reflects the precision of approximate model on the whole, and the value of RAAF is more close to 0, then model is more accurate;

(3)RMAE；

$\mathrm{RMAE}=\frac{\max \left(\right|f\left(X_1\right)-\hat{f}\left(X_1\right)|,...,|f\left(X_m\right)-\hat{f}\left(X_m\right)\left|\right)}{\mathrm{STD}}$

This is a local indexes, and RMAE describes the error of certain local field of design space, and therefore the value of RMAE is the smaller the better.

In described step (1) by the density domination of grid at 1/10 of sample space, i.e. the density p m=10 of grid.

Compared with prior art, the invention has the advantages that: optimization method of the present invention is the SVM optimization system based on parallel mechanism, owing to adopting parallel architecture, the number of initial sample point and the mesh-density of design space can suitably increase, and therefore can obtain the characteristic studied a question to greatest extent; Meanwhile, owing to adopting parallel architecture, the sample information in each iteration step is far longer than serial algorithm, and namely algorithm have employed more sample architecture approximate model.Compare with serial algorithm, the precision of approximate model is higher, also more easily restrains.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of the inventive method.

Fig. 2 is that the present invention's certain micro-car in embody rule example is just hitting front and back energy-absorbing contrast schematic diagram.

Fig. 3 is impact force contrast schematic diagram before and after the present invention optimizes in embody rule example.

Embodiment

Below with reference to Figure of description and specific embodiment, the present invention is described in further details.

As shown in Figure 1, the parallel support vector machines approximate model optimization method based on vehicle collision resistant of the present invention, its idiographic flow is as follows:

1, set up sparse network according to design space, initial sample point is positioned at network node; In order to control the density of follow-up generation sample in design space, need to carry out sparse grid distribution to design space, all follow-up generation samples all must move on nearest grid node.Wherein, the density of grid determines the density of sample, and density is overstocked, and the expense of layouting is excessive, even can cause over-fitting problem; Otherwise, then can drop-out.According to the fitting result to trial function, can by the density domination of grid at 1/10 of sample space, i.e. the density p m=10 of grid.When the interval of design parameter is [-5,5], so grid be spaced apart 1.

2, generate initial sample by super Latin square experimental design method, sample transfers to grid node automatically;

3, the initial sample generated is assigned to each CPU(and computing node);

4, on each CPU, monte carlo method stochastic generation sample point is used;

5, according to current C PU(computing node) in the sample (comprising the historical sample generated) that generates, at each CPU(computing node) on set up approximate model based on SVM respectively;

6, obtain each CPU(computing node) on the error criterion of SVM approximate model that builds respectively, be respectively R2, RAAE, RMAE, consider the bottleneck of three's error, i.e. the mean value of error criterion, judges whether three all reaches convergence level; If at this CPU(computing node) reach convergence level, the then sample interval in this region of initial setting, store, by step (4) at each CPU(computing node) in reach host process for the sample constructing approximate model, adopt all generations node build the overall situation SVM model;

7, judge whether the SVM model of the overall situation restrains, and the mode of judgement is close with step (6); If convergence, then process terminates, otherwise, then jump to step (8);

8, for the SVM model of not restraining for each region, then according to by mistake extent, preliminary and find maximum error district; Relatively convergence SVM model region, search its non-coincidence region, determine its maximum error region;

9, each interval error district information obtained be dealt into host process and sue for peace, stochastic generation sample in the region after summation, and being evenly distributed to each CPU(computing node), and jump to step (4), until process terminates.

In steps of 5, if return sample set S be

$S=\left\{(x_i,y_i)\right|i\∈I\}\⋐R^n\×R,---\left(1\right)$

R in formula ⁿfor the set of real numbers of n-dimensional space, R set of real numbers, I={1,2 ..., n}, x _i, y _irepresent design driver respectively and export response.

Utilize Nonlinear Mapping by sample from input space R ⁿbe mapped to high-dimensional feature space:

ψ(x)＝(φ(x ₁),φ(x ₂),…,φ(x _i))，i＝1，2,…,n,(2)

Linear fit problem in high-dimensional feature space is become to make the nonlinear fitting problem in the input space.Wherein, ψ (x) is mapping function collection, φ (x _i) be mapping function.

At the linear regression model (LRM) of high-dimensional feature space structure be:

In formula, w and b is respectively coefficient to be asked, and φ (x) is mapping function, and f (x) is regression model function.According to SVR principle, consider function complexity and error of fitting, linear regression problem can be expressed as constrained optimization problem:

$\underset{w,b,\mathrm{\ϵ}}{\mathrm{Min}}(w,b,\mathrm{\ϵ})=\frac{1}{2}{\left|\right|w\left|\right|}^2+\frac{1}{2}\mathrm{\γ}{\left|\right|\mathrm{\ϵ}\left|\right|}^2---\left(4\right)$

Wherein J (w, b, ε) is objective function, and γ is penalty coefficient, and ε is error of fitting, and penalty coefficient is γ > 0.In formula, error of fitting ε meets:

ε _i＝y _i-f(x _i),i＝1，2,…,n(5)

Y in formula _iwith f (x _i) be respectively match value and the actual function value of i-th sample.

Solve above-mentioned optimization problem, introducing Lagrange function l (w, b, ε, a) be converted into unconstrained optimization problem constrained optimization problem:

$l(w,b,\mathrm{\ϵ},a)=J(w,b,\mathrm{\ϵ})-\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i\{w^T\mathrm{\φ}\left(x_i\right)+b+{\mathrm{\ϵ}}_i-y_i\}---\left(6\right)$

In formula, N is training sample number, a _i∈ R is Lagrange multiplier, and w is weight function, and T is transposition symbol.

By Lagrange optimal conditions, ask respectively and l (w, b, ε, partial differential a) are asked to variable (w, b, ε) and Lagrange multiplier

, except a _i=γ ε _ioutside condition, formula (7) is consistent with classical SVM method, and meets simultaneously:

$\left\{\begin{array}{c}w=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i{x}_i\\ y_i=f\left(x_i\right)+{\mathrm{\ϵ}}_i\\ a_i={\mathrm{\γ\ϵ}}_i\end{array}\right.---\left(8\right)$

F (x in formula _i) be the approximating function after matching, cancellation variable ε _i, after w, above-mentioned optimization problem is finally converted into separates following system of linear equations:

$\left[\begin{array}{cc}0& I^T\\ I& \mathrm{\Ψ}+\frac{1}{\mathrm{\γ}}I\end{array}\right]\left[\begin{array}{c}b\\ a\end{array}\right]=\left[\begin{array}{c}0\\ y\end{array}\right]---\left(9\right)$

In formula

y＝[y ₁,y ₂,…y _N],(10)

I＝[1,1,…1],(11)

a＝[a ₁,a ₂,…a _N],(12)

In formula, φ (x) is Nonlinear Mapping, Ψ _{i, j}for kernel function, subscript T represents transposition.

According to Mercer condition, if existed about Nonlinear Mapping kernel function:

If there is any g (x), and ∫ g (x) ²dx bounded, then have

∫K(x _i,x _j)g(x _i)g(x _j)dx _idx _j≥0(15)

Can prove:

Solve this system of equations, finally obtaining regression model can be expressed as:

$y\left(x\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_{l}K(x,x_i)+b---\left(17\right)$

The kernel function of usual employing is:

$K(x_i,x_j)=e^{(-{\left|\right|x_i-x_j\left|\right|}^2/{\mathrm{\σ}}^2)}---\left(18\right)$

Wherein σ is bandwidth, determines according to probability distribution.

In the present embodiment, in step (6) and (7), have employed the interpretational criteria of following three approximate models:

If X _i(i=1,2 ... m) be m of stochastic generation in design domain and obey equally distributed test sample book point:

（1）R ²；

$R^2=1-\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(f\left(X_i\right)-\hat{f}\left(X_i\right))}^2}{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(f\left(X_i\right)-\stackrel{\_}{f}\left(X_i\right))}^2}$

Wherein, the mean value of output function at m test sample book point, for the approximating function value of test sample book, this refers to the precision reflecting an approximate model on the whole, R ²value more close to 1, then approximate model is more accurate.

(2)RAAE；

$\mathrm{RAAE}=\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}|f\left(X_i\right)-\hat{f}\left(X_i\right)|}{m*\mathrm{STD}}$

Here, STD represents standard deviation, with R ²the same, this index reflects the precision of approximate model on the whole, and the value of RAAE is more close to 0, then model is more accurate.

(3)RMAE

$\mathrm{RMAE}=\frac{\max \left(\right|f\left(X_1\right)-\hat{f}\left(X_1\right)|,...,|f\left(X_m\right)-\hat{f}\left(X_m\right)\left|\right)}{\mathrm{STD}}$

This is a local indexes, and RMAE describes the error of certain local field of design space, and therefore the value of RMAE is the smaller the better.

Method of the present invention and traditional SVM method are compared.First, get 3 higher-dimension trial functions (see table 1), adopt one group of identical training sample point (computational costs is identical) to adopt SVM and parallel SVM two kinds of methods to carry out modeling respectively for same function and compare their precision, result of calculation is as table 2 (in order to reflect the performance of this algorithm more objectively, the data in table are the mean value of calculating 100 times).From data analysis in table, for the parallel SVM model of 3 trial functions, R ²value is (more close to 1, model is more accurate) close to 1, RAAE value is (more close to 0, model is more accurate) all between 0 and 0.12, RMAE value (the smaller the better) is all below 0.15, parallel SVM model can reflect the characteristic of true model preferably as can be seen here, and fitting precision is higher; And for 3 SVM models, R ²be worth all very low (less than 0.3, even occur negative value), and RMAE value all higher (being greater than 3), fitting result is undesirable.Above analytic explanation, for higher-dimension problem, based on same one group of training sample, adopt the approximate model that SVM Method Modeling obtains, precision is poor, can not as the approximate model of true model, but, but to obtain degree of approximation higher for SVM method to adopt the present invention to walk abreast, and can be used for the approximate model of Optimization analyses.

Table 1

Table 2

For an embody rule example of the present invention, the present invention will be further described.

Select car load head-on crash finite element model to be the physical model of optimization problem, simplify the complex nonlinear problems such as geometrical non-linearity, physical nonlinearity and the material nonlinearity brought by car load head-on crash by the approximate model building finite element model.This model is made up of 17554 unit and 19217 nodes, comprises 208 parts and 20 kinds of materials.In whole finite element head-on crash simulation process, vehicle fixes rigid wall according to head-on crash laws and regulations requirement with the speed impacts of 50km/h, the collision simulation process of whole system completes in 150ms, the sheet thickness choosing car load front part energy absorbing component is design variable, in the research process to this car load crash-worthiness problem, paper examines to as if the acceleration of car load B post measurement point in design space, the collision safety performance of this car is improved.For this reason, the thickness of slab that have chosen front part of vehicle 10 parts is that design variable comes just to hit Optimization analyses, main energy absorbing component (as: the front longitudinal inner and outer plates in complete vehicle structure is included in these 10 parts, bumper bar etc.) and crew module is had to the parts (as fire wall etc.) of material impact, using the maximal impact of car load B post test point as this optimization design problem objective function, design variable and related constraint as shown in table 3, last optimum results is as shown in table 4.By the contrast to emulation and experimental result, demonstrate the accuracy of final design result; Optimize the energy absorption performance collision performance of the collision result of front and back respectively as shown in Figures 2 and 3, and then it is reasonable to describe the collision result after optimization.

Table 3 design variable and related constraint

Table 4 design variable optimal value and response

Below be only the preferred embodiment of the present invention, protection scope of the present invention be not only confined to above-described embodiment, all technical schemes belonged under thinking of the present invention all belong to protection scope of the present invention.It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principles of the present invention, should be considered as protection scope of the present invention.

Claims (3)

1., based on a parallel support vector machines approximate model optimization method for vehicle collision resistant, it is characterized in that, step is:

(1) set up sparse network according to design space, initial sample point is positioned at grid node;

(2) generate initial sample by super Latin square experimental design method, sample transfers to grid node automatically;

(3) the initial sample generated is assigned to each computing node;

(4) on each computing node, monte carlo method stochastic generation sample point is used;

(5) according to the sample point generated in current computing node, each computing node is set up approximate model based on support vector machines respectively;

(6) obtain the error criterion of the support vector machines approximate model that each computing node builds respectively, judge whether to reach convergence level; If reach convergence level at this computing node, the then sample interval in initial setting region, store, step (4) sample for constructing approximate model in each computing node is reached host process, adopt the node of all generations to build the support vector machines model of the overall situation;

(7) judge whether the SVM model of the overall situation restrains; If convergence, then process terminates, otherwise, then jump to step (8);

(8) for each support vector machines model of not restraining region, then according to by mistake extent, preliminary and find maximum error region; Relatively convergence support vector machines model region, search its non-coincidence region, determine maximum error region;

(9) each interval error band information obtained be dealt into host process and sue for peace, stochastic generation sample in the region after summation, and being evenly distributed to each computing node, and jumping to step (4), until process terminates.

2. the parallel support vector machines approximate model optimization method based on vehicle collision resistant according to claim 1, is characterized in that, have employed the interpretational criteria of following three approximate models, if X in step (6) and (7) _im the equally distributed test sample book point of obedience of stochastic generation in design domain, wherein i=1,2 ... m;

(1)R ²；

$R^2=1-\frac{\underset{i=1}{\overset{m}{\Σ}}{\left(f\right(X_i)-\hat{f}(X_i\left)\right)}^2}{\underset{i=1}{\overset{m}{\Σ}}{\left(f\right(X_i)-\stackrel{\‾}{f}(X_i\left)\right)}^2}$

Wherein, f (X _i) be respectively the actual function value of i-th sample, the mean value of output function at m test sample book point, for the approximating function value of test sample book, reflect the precision of an approximate model on the whole, R ²value more close to 1, then approximate model is more accurate;

(2)RAAE；

$RAAE=\frac{\underset{i=1}{\overset{m}{\Σ}}|f\left(X_i\right)-\hat{f}\left(X_i\right)|}{m*STD}$

Here, STD represents standard deviation, with R ²the same, this index reflects the precision of approximate model on the whole, and the value of RAAE is more close to 0, then model is more accurate;

(3)RMAE；

$RMAE=\frac{max\left(\right|f\left(X_1\right)-\hat{f}\left(X_1\right)|,...,|f\left(X_m\right)-\hat{f}\left(X_m\right)\left|\right)}{STD}$

This is a local indexes, and RMAE describes the error of certain local field of design space, and therefore the value of RMAE is the smaller the better.

3. the parallel support vector machines approximate model optimization method based on vehicle collision resistant according to claim 1, is characterized in that, in described step (1) by the density domination of grid at 1/10 of sample space, i.e. the density p m=10 of grid.