CN102999672A - Parallel support vector machine approximate model optimization method based on automobile crashworthiness - Google Patents

Abstract

The invention relates to a parallel support vector machine approximate model optimization method based on automobile crashworthiness. The parallel support vector machine approximate model optimization method comprises the steps of (1) establishing a network; (2) generating initial samples, and automatically transferring the initial samples to a grid node; (3) distributing the initial samples to calculating nodes; (4) generating sample points at random; (5) establishing an approximate model based on SVM (Support Vector Machine); (6) obtaining an error standard of an SVM approximate model, and judging whether the error standard reaches the convergence level or not; if so, constructing an entire SVM model by adopting all the generated nodes; (7) judging whether the entire SVM model converges or not; if so, finishing the process, otherwise, skipping to the step (8); (8) finding out the maximum error region; and (9) calculating the sum of the information of the error region, generating samples at random in the region after the summation, uniformly distributing the samples to the calculation nodes, and skipping to the step (4) till the process is finished. According to the parallel support vector machine approximate model optimization method, the mode that the SVM (support vector machine) is subjected to parallel processing is adopted, so that the modeling speed is greatly increased and the optimization efficiency and the precision are improved.

Description

Parallel support vector machines approximate model optimization method based on vehicle collision resistant

Technical field

The present invention is mainly concerned with the safety-optimized design field of vehicle in manufacturing and designing, and 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 of considering in the automotive safety optimal design; offer the parts that automobile is used for the distortion energy-absorbing in the often design process of vehicle safety and affect; such as front longitudinal, crashworthiness box etc.; the characteristic of the energy absorbing component that these are crucial and deformation pattern have just determined power or the acceleration of automobile in collision process; passenger protection is played vital effect, so thin-walled energy-absorbing member all is an emphasis of automobile optimal design all the time.

The in early days optimization for the crash-worthiness problem is based on gradient classic optimisation algorithm, has the practitioner that emulation technology and traditional optimization are combined for the optimization of crash-worthiness problem, and is used for the car crass design 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 gradually the mainstream technology that becomes based on the traditional optimization of gradient in the present vehicle safety design.

Other has the practitioner to adopt Successive RSM method that simple energy-absorbing beam and the crash-worthiness of before hitting problem are studied, and adopt the method that the safe design of Chevrolet C2500 is optimized, and this method is also adopted by business software LS-OPT.Koch etc. in conjunction with the approximate model technology, have set up the Optimization Design for the robustness of automobile side crash with the 6Sigma method of quality control, and the robustness of its optimum results is improved to some extent.In addition, a lot of scholars have adopted Stepwise Regression (SR), MLS, the main stream approach such as Mutiquadric (MQ), Kriging and Adaptive and Interactive Modeling System (AIMS) are tested the problem of bumping before the automobile respectively.The result shows: existing do not have the modeling demand that a kind of method can satisfy collision problem fully, need to set up a kind of brand-new numerical method this class problem is studied.

More than these methods approximate model of constructing whether can reflect the inner characteristic of optimization aim, how the constructed approximate model of these methods is estimated, these problems become the obstruction that the approximate model technology is used in engineering practice.At present, evaluation for the approximate model quality is based upon on the bases take statistical theory as foundation such as regretional analysis, variance analysis and the inclined to one side estimation of nothing basically, and the standard of this class judgment models quality can be summed up as in fact so-called empirical risk minimization criterion.But it is minimum that empirical risk minimization might not mean expected risk, and for approximate model, its reason mainly is to attempt to remove the limited sample of match with very complicated model, causes having lost Generalization Ability.In recent years, along with interdisciplinary continuous intersection, fusion, a kind of technology based on Statistical Learning Theory: Support Vector Machine (SVM, support vector machine) theory has been subject to extensive concern.SVM and neural network are similar, all are learning-oriented mechanism, but different from neural network what be that SVM uses is mathematical method and optimisation technique, and the gordian technique of SVM is kernel function.The lower dimensional space vector set is difficult to divide usually, and 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 has just in time solved this problem dexterously.That is to say, as long as select suitable kernel function, just can obtain the classification function of higher dimensional space.In the SVM theory, adopt different kernel functions will cause different SVM algorithms.At present, in the world discussion and the research of this theory are strengthened gradually, and Preliminary Applications is in the match of complex nonlinear problem.

The major defect of above-mentioned SVM method is its optimization efficiency, owing to need great amount of samples to make up sane approximate model, therefore for the vehicle collision resistant problem of complexity, the needed calculating sample of 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 just is: for the technical matters that prior art exists, the invention provides a kind of employing to SVM carry out pattern, the speed that can significantly promote modeling and optimization that parallelization processes efficient, carry 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:

A kind of parallel support vector machines approximate model optimization method based on vehicle collision resistant the steps include:

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

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

The initial sample that (3) will generate is assigned to each computing node;

(4) on each computing node, generate at random sample point with monte carlo method;

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

(6) obtain on each computing node the error criterion of the SVM approximate model that makes up respectively, judge whether to reach the convergence level; If reach the convergence level at this computing node, the sample interval that then initial setting should the zone, store, the sample that step (4) is used for the structure approximate model in each computing node reaches host process, adopts the node of all generations to make up overall SVM model;

Whether the SVM model of (7) judging the overall situation restrains; If convergence, then process finishes, otherwise, then jump to step (8);

(8) for the SVM model of not restraining for each the zone, then according to the size of error, preliminary and find the maximum error district; Relatively restrain the SVM model the zone, search its non-coincidence zone, determine maximum error zone;

(9) the error district information of each interval being obtained is dealt into host process and summation, generates at random sample in the zone after summation, and mean allocation is to each computing node, and jumps to step (4), until process finishes.

As a further improvement on the present invention:

In step (6) and (7), adopt the interpretational criteria of following three approximate models, established X _i(i=1,2 ... m) be m the equally distributed test sample book point of obedience that in design domain, generates at random:

（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,

Be output function at the mean value of m test sample book point, Be the approximating function value of test sample book, this has referred to reflect on the whole the precision of an approximate model, R ²Value more near 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 has reflected the precision of approximate model on the whole, and the value of RAAF is more near 0, and 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 has described the error of certain local field of design space, so the value of RMAE is the smaller the better.

Density with grid in described step (1) is controlled 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 based on the SVM optimization system of parallel mechanism, because adopt parallel framework, the number of initial sample point and the mesh-density of design space can suitably increase, therefore can obtain to greatest extent the characteristic that studies a question; Simultaneously, owing to adopt parallel framework, the sample information in each iteration step is far longer than serial algorithm, and namely algorithm has adopted more sample architecture approximate model.Compare with serial algorithm, the precision of approximate model is higher, also easier convergence.

Description of drawings

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

Fig. 2 is that the present invention's certain little car in concrete application example is just hitting front and back energy-absorbing contrast synoptic diagram.

Fig. 3 is impact force contrast synoptic diagram before and after the present invention optimizes in concrete application 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 the design space, initial sample point is positioned at network node; In order to control the density of follow-up generation sample in the design space, need to carry out the sparse grid distribution to the design space, all follow-up generation samples all must move on the nearest grid node.Wherein, the density of grid has determined the density of sample, and density is overstocked, and the expense of layouting is excessive, even can cause the over-fitting problem; Otherwise, then can drop-out.According to the fitting result to trial function, the density of grid can be controlled at 1/10 of sample space, i.e. the density p m=10 of grid.When the interval of design parameter is [5,5], grid is spaced apart 1 so.

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

It is computing node that the initial sample that 3, will generate is assigned to each CPU();

4, on each CPU, generate at random sample point with monte carlo method;

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

6, obtain each CPU(computing node) on the error criterion of the SVM approximate model that makes up respectively, be respectively R2, RAAE, RMAE, consider the bottleneck of three's error, namely the mean value of error criterion judges whether the three all reaches the convergence level; If at this CPU(computing node) reach the convergence level, the sample interval that then initial setting should the zone, store, with step (4) at each CPU(computing node) in be used for the structure approximate model sample reach host process, adopt the node of all generations to make up the SVM model of the overall situation;

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

8, for the SVM model of not restraining for each the zone, then according to the size of error, preliminary and find the maximum error district; Relatively restrain the SVM model the zone, search its non-coincidence zone, determine its maximum error zone;

9, the error district information of each interval being obtained is dealt into host process and summation, generates at random sample in the zone after summation, and mean allocation is to each CPU(computing node), and jump to step (4), until process finishes.

In step 5, establish and return sample set S and be

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

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

Utilize Nonlinear Mapping With 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)

So that the nonlinear fitting problem in the input space becomes the linear fit problem in the high-dimensional feature space.Wherein, ψ (x) is the mapping function collection, φ (x _i) be mapping function.

Linear regression model (LRM) at the high-dimensional feature space structure is:

W and b are respectively coefficient to be asked in the formula, and φ (x) is mapping function, and f (x) is the regression model function.According to the SVR principle, consider function complexity and error of fitting, the linear regression problem can be expressed as the 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.Error of fitting ε satisfies in the formula:

ε _i＝y _i-f(x _i),i＝1，2,…,n (5)

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

Find the solution above-mentioned optimization problem, introducing Lagrange function l (ε a) is converted into unconstrained optimization problem to the constrained optimization problem for w, b:

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

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

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

, except a _i=γ ε _iOutside the condition, formula (7) is consistent with classical SVM method, and satisfies 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 the formula _i) be the approximating function after the match, cancellation variable ε _i, behind the w, above-mentioned optimization problem finally is 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 the formula

y＝[y ₁,y ₂,…y _N], (10)

I＝[1,1,…1], (11)

a＝[a ₁,a ₂,…a _N], (12)

φ in the formula (x) is Nonlinear Mapping, Ψ _{I, j}Be kernel function, subscript T represents transposition.

According to the Mercer condition, if exist about Nonlinear Mapping

Kernel function:

If there is any g (x), and ∫ g (x) ²Dx bounded then has

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

Can prove:

Find the solution this system of equations, finally obtaining regression model can be expressed as:

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

Usually the kernel function that adopts 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), adopted the interpretational criteria of following three approximate models:

If X _i(i=1,2 ... m) be m the equally distributed test sample book point of obedience that in design domain, generates at random:

（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,

Be output function at the mean value of m test sample book point,

Be the approximating function value of test sample book, this has referred to reflect on the whole the precision of an approximate model, R ²Value more near 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 has reflected the precision of approximate model on the whole, and the value of RAAE is more near 0, and 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 has described the error of certain local field of design space, so the value of RMAE is the smaller the better.

Method of the present invention and traditional SVM method are compared.At first, get 3 higher-dimension trial functions (seeing Table 1), adopt identical one group of training sample point (computational costs is identical) to adopt respectively SVM and two kinds of methods of parallel SVM to carry out modeling for same function and also compare their precision, result of calculation such as table 2 (in order to reflect more objectively this Algorithm Performance, the data in the table are to calculate 100 times mean value).By data analysis in the table as can be known, for the parallel SVM model of 3 trial functions, R ²Value (more near 1, model is more accurate) near 1, RAAE value (more near 0, model is more accurate) all between 0 and 0.12, RMAE value (the smaller the better) this shows that all below 0.15 parallel SVM model can reflect the characteristic of true model preferably, and fitting precision is higher; And for 3 SVM models, R ²Value all very low (below 0.3, even negative value occurring), and RMAE value all higher (greater than 3), fitting result is undesirable.Above analytic explanation, for the higher-dimension problem, based on one group of same training sample, the approximate model that adopts the SVM Method Modeling to obtain, precision is relatively poor, can not be as the approximate model of true model, yet, it is higher to adopt the parallel SVM method of the present invention but can obtain degree of approximation, can be used for optimizing the approximate model of analysis.

Table 1

Table 2

Take a concrete application example of the present invention as example, the present invention will be further described.

Selecting car load head-on crash finite element model is the physical model of optimization problem, simplifies the complex nonlinear problems such as geometrical non-linearity, physical nonlinearity and material nonlinearity of being brought by the car load head-on crash by the approximate model that makes up finite element model.This model is comprised of 17554 unit and 19217 nodes, comprises 208 parts and 20 kinds of materials.In whole finite element head-on crash simulation process, vehicle clashes into fixedly rigid wall according to the head-on crash laws and regulations requirement with the speed of 50km/h, the collision simulation process of whole system is finished in 150ms, the sheet thickness of choosing car load front part energy absorbing component is design variable, in the research process to this car load crash-worthiness problem, main investigate to as if the acceleration of car load B post measurement point in the design space, the collision safety performance of this car is improved.For this reason, the thickness of slab of having chosen 10 parts of front part of vehicle is that design variable is just hitting the optimization analysis, comprised main energy absorbing component (as: the front longitudinal inner and outer plates in the complete vehicle structure in these 10 parts, bumper bar etc.) and the parts (such as fire wall etc.) that the crew module had material impact, with the maximal impact of car load B post test point as this optimization design problem objective function, design variable and related constraint are as shown in table 3, and last optimum results is as shown in table 4.By the contrast to emulation and experimental result, verified final design result's accuracy; The energy absorption performance collision performance of collision result before and after optimizing is distinguished as shown in Figures 2 and 3, and then has illustrated that the collision result after optimizing is reasonable.

Table 3 design variable and related constraint

Table 4 design variable optimal value and response

Below only be preferred implementation of the present invention, protection scope of the present invention also not only is confined to above-described embodiment, and all technical schemes that belongs under the thinking of the present invention all belong to protection scope of the present invention.Should be pointed out that for those skilled in the art the some improvements and modifications not breaking away under the principle of the invention prerequisite should be considered as protection scope of the present invention.

Claims (3)

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

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

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

The initial sample that (3) will generate is assigned to each computing node;

(4) on each computing node, generate at random sample point with monte carlo method;

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

(6) obtain on each computing node the error criterion of the SVM approximate model that makes up respectively, judge whether to reach the convergence level; If reach the convergence level at this computing node, the sample interval that then initial setting should the zone, store, the sample that step (4) is used for the structure approximate model in each computing node reaches host process, adopts the node of all generations to make up overall SVM model;

Whether the SVM model of (7) judging the overall situation restrains; If convergence, then process finishes, otherwise, then jump to step (8);

(8) for the SVM model of not restraining for each the zone, then according to the size of error, preliminary and find the maximum error district; Relatively restrain the SVM model the zone, search its non-coincidence zone, determine maximum error zone;

(9) the error district information of each interval being obtained is dealt into host process and summation, generates at random sample in the zone after summation, and mean allocation is to each computing node, and jumps to step (4), until process finishes.

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

（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,

Be output function at the mean value of m test sample book point,

Be the approximating function value of test sample book, this has referred to reflect on the whole the precision of an approximate model, R ²Value more near 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 has reflected the precision of approximate model on the whole, and the value of RAAE is more near 0, and 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 has described the error of certain local field of design space, so the value of RMAF 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 the density with grid in described step (1) is controlled at 1/10 of sample space, i.e. the density p m=10 of grid.

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