CN104504462A - Automobile form evolution trend prediction method based on improved gray BPNN (BP Neural Network) and Markov chain - Google Patents

Abstract

The invention relates to an automobile form evolution trend prediction method based on an improved gray BPNN (BP Neural Network) and a Markov chain. Taking a certain brand of automobile as an example, the side contour lines of all generations of an automobile appearing in the evolutionary process are extracted, and software is input to obtain the coordinates and coordinate data of feature points of BEZIER curves of the side contour lines. The automobile form evolution trend prediction method specifically comprises the following steps of adopting an improved gray model to complete the rough matching of evolutionary curves of the automobile form feature points; using a match value as an input value and a measured value as a target value, and training the BP neural network (BPNN), wherein the trained network can carry out quantitative prediction on the evolutionary trend of the feature points; on this basis, dividing a system state in virtue of the Markov chain, and correcting the predicted result to improve the precision. The combination method has higher precision and reliability, and thus has potential application value.

Description

Based on the automobile form trend of evolution Forecasting Methodology improveing grey BPNN and markov chain

Technical field

The present invention relates to a kind of Forecasting Methodology, be specifically related to the automobile form trend of evolution Forecasting Methodology based on improvement grey BPNN and markov chain.

Background technology

The prediction of automobile form trend of evolution is the study hotspot of Automobile Design always.Ripe automobile brand can retain certain Morphological continuity in its model change process, promotes brand recognition with this, therefore studies automobile form trend of evolution and not only can provide design information for brand itself, can also provide design reference for other brands.Quantitative test based on evolution algorithm.Qualitative analysis is as used shape grammar research product and automobile form design, or the mapping relations established between product feature change and consumer's image carry out qualitative forecasting.But compared with qualitative analysis, quantitative test can provide clearer and more definite design information for designer, as set up generative approach method by genetic algorithm research automobile style, but use the fitness evaluation of subjective assessment setting evolution algorithm can affect the objectivity of result, for strengthening the confidence level predicted the outcome, measured data is carried out numerical prediction in conjunction with combined method and is more of practical significance.

The difficult point of automobile form trend of evolution quantitative forecast uses single model to need great amount of samples, as linear regression etc.And automobile form evolutionary generation is very few, its unique point Evolution Forecasting belongs to the prediction of typical small sample, therefore how to obtain by the data of small sample the difficult point that automobile form trend of evolution is prediction.

Summary of the invention

For solving the difficult problem of Wave type Small Sample Database prediction, this invention takes following steps:

The present invention includes following steps:

(1) data are extracted

Suppose that certain vehicle experienced by c update.In ALIAS software, automobile digital-to-analogue with front-wheel core wheel for co-ordinate zero point, be after standard carries out convergent-divergent with uniform length, obtain broadside lines, every bar line comprises front car light, front bonnet, front windshield, roof, rear seat windscreen, trunk and rear vehicle lamp seven part.With Bezier curve form, it is described, every bar Bezier curve comprises two end points, front car light, front windshield, rear seat windscreen have 1 reference mark, and front bonnet, roof, trunk, rear vehicle lamp have 2 reference mark, and adjacent curve shares same end points.In two-dimensional coordinate system, obtain some X-axis and Y-axis coordinate, obtain 19 point coordinate, point coordinate is generation change ordered series of numbers from 1st generation to c.Because automobile form change algebraically is less, its ordered series of numbers belongs to typical small sample ordered series of numbers,

(2) gray model is improved, make it be more suitable for Wave type data prediction

A, suppose to have unique point X-coordinate data sequence be: x={x ₁, x ₂..., x _n.Set up new data sequence x '=x ' ₁, x ' ₂..., x ' _n, and replace sequence x;

Work as j=1, when 2, x ' _j=x _j;

Work as j=3,4 ..., during n, as x ₁> x ₂, x _j-1>=x _jtime, u _j=0, otherwise, u _j=-2 [x _j-x _j-1]; As x ₁< x ₂, x _j-1≤ x _jtime, u _j=0, otherwise, u _j=2 [x _j-x _j-1];

B, to x ' ⁽⁰⁾=x ' ₁ ⁽⁰⁾, x ' ₂ ⁽⁰⁾..., x ' _n ⁽⁰⁾carry out single order add up, generation module x ' ⁽¹⁾=x ' ₁ ⁽¹⁾, x ' ₂ ⁽¹⁾..., x ' _n ⁽¹⁾;

By single order gray model x ' ⁽¹⁾the differential equation formed is:

$\frac{{\mathrm{dx}}^{\&prime;\left(1\right)}}{\mathrm{dt}}+a{x\&prime;}^{\left(1\right)}=b---\left(1\right)$

In formula, a is System Development coefficient, and b is interior raw control variable;

After discrete for (1) formula, obtain Y=XB, Y is sequence variables matrix, and X is single order sum function matrix, and B is estimator matrix.It is obtained by least square method:

$B={\left(X^{T}X\right)}^{-1}\left(X^{T}Y\right)=\left|\begin{array}{c}a\\ b\end{array}\right|$

Wherein: $X=\left[\begin{array}{cc}-\frac{1}{2}[{{x^{\&prime;}}_1}^{\left(1\right)}+{{x^{\&prime;}}_2}^{\left(1\right)}]& 1\\ -\frac{1}{2}[{{x^{\&prime;}}_2}^{\left(1\right)}+{{x^{\&prime;}}_3}^{\left(1\right)}]& 1\\ .& .\\ .& .\\ .& .\\ -\frac{1}{2}[{{x^{\&prime;}}_{n-1}}^{\left(1\right)}+{{x^{\&prime;}}_n}^{\left(1\right)}]& 1\end{array}\right],Y=\left[\begin{array}{c}{{x^{\&prime;}}_2}^{\left(0\right)}\\ {{x^{\&prime;}}_3}^{\left(0\right)}\\ .\\ .\\ .\\ {{x^{\&prime;}}_n}^{\left(0\right)}\end{array}\right];$

Solutions of Ordinary Differential Equations is:

${{{\hat{x}}^{\&prime;}}_{k+1}}^{\left(1\right)}=({{x^{\&prime;}}_1}^{\left(0\right)}-\frac{b}{a})e^{-\mathrm{ak}}+\frac{b}{a},k=\mathrm{1,2,3},...---\left(2\right)$

match value be:

${{{\hat{x}}^{\&prime;}}_{k+1}}^{\left(0\right)}={{{\hat{x}}^{\&prime;}}_{k+1}}^{\left(1\right)}-{{{\hat{x}}^{\&prime;}}_k}^{\left(1\right)}---\left(3\right)$

C, from u={u ₃, u ₄..., u _nin get nonzero value, if not null value number is more than or equal to 4, then set up sequence v ⁽⁰⁾, and repeat step 2, by the analogue value sequence obtained replace nonzero value corresponding in former sequence u, and in u, null value remains unchanged, thus obtain new sequence if not null value number is less than 4, then

D, acquisition improvement gray model match value

Work as j=1, when 2, ${{\hat{x}}_j}^{\left(0\right)}{={{\hat{x}}^{\&prime;}}_j}^{\left(0\right)};$

Work as j=3,4 ..., during n, ${{\hat{x}}_j}^{\left(0\right)}={{{\hat{x}}^{\&prime;}}_j}^{\left(0\right)}+\underset{i=3}{\overset{j}{\mathrm{\&Sigma;}}}{u^{\&prime;}}_i,j=\mathrm{3,4},...,n,$ As x ₁> x ₂, $u^{\&prime;}=\hat{u},$ As x ₁< x ₂, $u^{\&prime;}=-\hat{u};$

(3) curve that grey BPNN evolves to unique point is improved

Using gray model match value as input value, using actual value as output valve, and the feature of the self study that few and neural network has in conjunction with grey forecasting model desired data and adaptive ability, neural network is trained, when the actual output of network and desired output closely time, show that the mapping relations between constrained input are grasped in web results study preferably, neural network can be eliminated like this and do not consider the negative effect that data precedence relationship is brought;

Improvement grey BPNN model comprises three layers: input layer, hidden layer, output layer.The analogue value of improvement gray model for input vector, original measurement value x is output valve.Get front 75% be training set, rear 25% is inspection set.Output layer nodes is 1, and node in hidden layer is 3, and predicted data sequence is designated as R;

(4) markov chain is to the correction that predicts the outcome of improvement Grey BP Neural Network

Markov chain (Markov Chain) referred to as, improvement grey BPNN predicts young mobile modelling feature point position, the random fluctuation within the specific limits usually of its result, Markov chain effectively can be predicted and eliminate the predicated error produced by system randomness;

A, utilize golden section ratio principle calculate data state area between

Forecasting sequence R and actual value sequence x according to improveing grey BPNN obtain relative error value sequence q, after its normalized, obtain average golden section ratio is Ω=0.618, is calculated as follows cut-point λ, realizes the division in w interval:

${\mathrm{\&lambda;}}_h={\mathrm{\&Omega;}}^s\stackrel{\&OverBar;}{q},h<w,h=\mathrm{1,2},...---\left(4\right)$

Getting s value is 1 and-1, obtains 3 state space [0, a ₁], [a ₁, a ₂], [a ₂, 1].Reverted in sequence q, obtained r between three state areas ₁[r _1-, r ₁₊], r ₂[r _2-, r ₂₊], r ₃[r _3-, r ₃₊], wherein r _1-=e _min, r ₁₊=r _2-=e _min+ a ₁(e _max-e _min), r ₂₊=r _3-=e _min+ a ₂(e _max-e _min), r ₃₊=e _max.E _max, e _minrepresent the minimum and maximum value in relative error value sequence q respectively;

B, calculating transition probability matrix

Markov chain forecast model is expressed as:

P _t+1＝P ₀[P ⁽¹⁾] ^t+1(5)

In formula, P _t+1for the probability distribution in t+1 moment, P ₀for the unconditional probability of initial time distributes, P ⁽¹⁾be a step transition probability matrix, its expression formula is:

$P^{\left(1\right)}=\begin{array}{cccc}{p}^{11}& p^{12}& ...& p^{1m}\\ p^{21}& p^{22}& ...& p^{2m}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ p^{1m}& p^{2m}& ...& p^{\mathrm{mm}}\end{array}---\left(6\right)$

P in formula _ij(haveing nothing to do with initial time) is a step transition probability, represents that process is from t _nmoment state a _it is transferred to through a step _n+1moment state a _jprobability, p _ij=P (X _n+1=a _j| X _n=a _i). $0\&le;p_{\mathrm{ij}}\&le;1,\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{p}_{\mathrm{ij}}=1,(i,j=\mathrm{1,2},...,n;n\&Element;Z).$

C, the probability interval in t+1 moment can be calculated according to formula (5), r [r between the relative error state area obtaining this moment _-, r ₊], finally predict the outcome into:

Beneficial effect of the present invention

The invention provides a kind of automobile form trend of evolution Forecasting Methodology based on improveing grey BPNN and markov chain, solving a prediction difficult problem for Wave type Small Sample Database.Tradition gray model, due to defect itself, is only applicable to the occasion that data exponentially change, and during data irregular and fluctuation change, fitting effect is not ideal enough.Usage data replacement method is improved it, can weaken the randomness between raw data and improve fitting precision; The combination of gray model and neural network, has drawn the feature of self study that the few and neural network of grey forecasting model desired data has and adaptive ability; Utilize markov chain to predict the outcome to grey BPNN to revise, factor data undulatory property can be made up greatly on the impact that it produces.

Accompanying drawing explanation

Fig. 1: the extracting method representing automobile side outline line; A, B, C, D, E, F, G represent the front car light of automobile side outline line, front bonnet, front windshield, roof, rear seat windscreen, trunk and rear vehicle lamp each several part successively; 1-19 represents 19 points obtained after use Bezier curve form is described;

Fig. 2: representation feature point coordinate extracting method; ALIAS software is used in two-dimensional coordinate system, to obtain point coordinate, X ₁and Y ₁represent X and the Y-axis coordinate of first point, by that analogy;

Fig. 3: represent Grey BP Neural Network structural drawing; The analogue value x of improvement gray model for input vector, original measurement value x is output valve, and output layer nodes is 1, and node in hidden layer is 3;

Fig. 4: expression the 9th generation broadside lines compared with the first eight generation; In figure, 1-9 represents the broadside lines from the first generation to the 9th generation respectively.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described with implementing example:

(1) see in Fig. 1, certain vehicle experienced by 8 updates.In ALIAS software, automobile digital-to-analogue with front-wheel core wheel for co-ordinate zero point, be after standard carries out convergent-divergent with uniform length, obtain broadside lines, every bar line comprises front car light, front bonnet, front windshield, roof, rear seat windscreen, trunk and rear vehicle lamp seven part.With Bezier curve form, it is described, every bar Bezier curve comprises two end points, front car light, front windshield, rear seat windscreen have 1 reference mark, and front bonnet, roof, trunk, rear vehicle lamp have 2 reference mark, and adjacent curve shares same end points.In two-dimensional coordinate system, obtain some X-axis and Y-axis coordinate (as Fig. 2), obtain 19 point coordinate, point coordinate is as shown in table 1 to the 8th generation change ordered series of numbers from 1st generation;

Table 1 unique point changes in coordinates ordered series of numbers

With X ₆for example, this point is the intersection point of front bonnet and front windshield, and coordinate sequence represents the change of this some X-axis coordinate from the first to the eight generation evolutionary process, X ₆={ 303.55,29.075,278.0,2297.43,207.33,205.23,212.19,304.05};

(2) gray model is improved, make it be more suitable for Wave type data prediction

2.1 set up new data sequence X ' ₆={ 303.55,29.075,278.0,2258.61,168.52,166.42,15.946,67.60}, with X ' ₆replace X ₆;

2.2 couples of X ' ₆ ⁽⁰⁾=X ' _6,1 ⁽⁰⁾, X ' _6,2 ⁽⁰⁾..., X ' _{6, n} ⁽⁰⁾carry out single order add up, generation module X ' ₆ ⁽¹⁾=X ' _6,1 ⁽¹⁾, X ' _6,2 ⁽¹⁾..., X ' _{6, n} ⁽¹⁾, and calculate a=0.0279, b=290.7239;

This unique point evolution grey forecasting model is:

${{{\hat{x}}^{\&prime;}}_{6,k+1}}^{\left(1\right)}=-10100.6e^{-0.0279k}+10404.2,k=\mathrm{1,2,3},...---\left(8\right)$

Obtain ${{{\hat{X}}^{\&prime;}}_6}^{\left(0\right)}=\left\{\mathrm{303.55,31393,264.64,223.09,188.06,158,54,133,65,112.66}\right\},$ In u, nonzero value number is less than 4, gets $\hat{u}=u;$ Obtain improvement gray model result, ${{\hat{X}}_6}^{\left(0\right)}=\{\mathrm{303.55,31393},\mathrm{264.64,261.90,226.88,197.35,186.38},$ $\mathrm{349.11,33142}\},$ Namely unique point is from the first generation to the match value in the 9th generation;

(3) curve that grey BPNN evolves to unique point is improved

Using gray model match value as input value, using actual value as output valve, and the feature of the self study that few and neural network has in conjunction with grey forecasting model desired data and adaptive ability, neural network is trained, when the actual output of network and desired output closely time, show that the mapping relations between constrained input are grasped in web results study preferably, neural network can be eliminated like this and do not consider the negative effect that data precedence relationship is brought;

Improvement grey BPNN comprises three layers: input layer, hidden layer, output layer.The analogue value of improvement gray model for input vector, original measurement value x is output valve.Get front 75% be training set, rear 25% is inspection set.Output layer nodes is 1, and node in hidden layer is 3, and predicted data sequence is designated as R;

With match value is the input of BP neural network, X ₆actual value is for exporting; arrive for training set, arrive for inspection set.Improvement Grey BP Neural Network model predication value R is obtained after having trained ₆={ 296.40,293.07,277.24,27.009,207.2,7204.35,203.19,288.34,288.95};

(4) markov chain combines the correction predicted the outcome to improvement grey BPNN

4.1 calculate between the state area of data

By R ₆sequence and X ₆everyly in sequence obtain relative error value sequence q, by R _6,1to R _6,7relative error change be divided between three state areas:

r ₁[-0.00797,0.01084]；r ₂[0.01084,10.04129]；r ₃[0.04129,0.09190]；

4.2 calculate transition probability matrix

Calculate R _6,1to R _6,7fall into r ₁, r ₂, r ₃the number of state is divided into 4,1,2, and generates a step transition probability matrix:

$P^{\left(1\right)}=\left[\begin{array}{ccc}1/2& 0& 1/2\\ 1& 0& 1\\ 1/2& 0& 1/2\end{array}\right]---\left(9\right)$

4.3 checking correction effects

R _6,8state transition probability is in r ₂interval.Improvement Grey BP Neural Network predicted value is 349.11, and after Markov correction, result is 295.85, and this actual value is 304.05, and relative error drops to 2.70% from 14.81%, and precision of prediction is improved, and proves the validity of the method;

(5) result and data convert

X-axis when all 19 points of above-mentioned embodiment application being evolved to the 9th generation and the prediction of Y-axis coordinate figure, result is as shown in table 2;

In table 2 broadside lines 19 points the 9th generation, predicts the outcome

	1	2	3	4	5	6	7	8	9	10
											X-axis	-645.32	-636.20	-565.69	-445.69	-326.13	296.48	583.46	773.22	1075.60	1950.16
Y-axis	157.69	262.13	321.24	428.95	494.31	445.8	674.42	779.68	848.76	855.34
												11	12	13	14	15	16	17	18	19
X-axis	2028.16	2144.65	2335.55	2493.07	2659.00	2687.41	2695.56	2719.33	2701.13
											Y-axis	825.61	774.37	607.15	596.99	588.76	501.03	471.23	404.22	311.26

Predict the outcome table 2 input ALIAS software, obtains this brand automobile the 9th generation broadside lines, and compare with the first eight generation, as shown in Figure 4.

By automobile form characteristic point data and result of making prediction is that to obtain automobile form trend of evolution be the most also most effective method.The sample of raw data is little and change irregular to be the difficult point of quantitative prediction, to use improvement gray model to be combined with BPNN, and utilize markov chain to carry out modified result, can solve this problem, the validity of the method by Example Verification.Overcome sequence data after the improvement of GM (1,1) model to fluctuate the impact brought gray prediction, data fitting precision is improved.Improvement gray model and the combination of BPNN, utilize the advantage of the few and Neural Network Self-learning of gray model desired data, making to predict the outcome has better adaptivity.The correction of Markov chain to improvement grey BPNN result can improve model prediction accuracy further, and along with the increase of sequence data sample size, correction effect will be more desirable.This model, except can applying to other car body characteristic curve Study on Evolution, also extends to other product design fields, also can be applicable to other small sample forecasting problems.

Claims (1)

1., based on the automobile form trend of evolution Forecasting Methodology improveing grey BPNN and markov chain, it is characterized in that:

(1) data are extracted

Suppose that certain vehicle experienced by c update, in ALIAS software, automobile digital-to-analogue with front-wheel core wheel for co-ordinate zero point, be after standard carries out convergent-divergent with uniform length, obtain broadside lines, every bar line comprises front car light, front bonnet, front windshield, roof, rear seat windscreen, trunk and rear vehicle lamp seven part, with Bezier curve form, it is described, every bar Bezier curve comprises two end points, front car light, front windshield, rear seat windscreen has 1 reference mark, front bonnet, roof, trunk, rear vehicle lamp has 2 reference mark, and adjacent curve shares same end points.In two-dimensional coordinate system, obtain some X-axis and Y-axis coordinate, obtain 19 point coordinate, point coordinate is generation change ordered series of numbers from 1st generation to c, and because automobile form change algebraically is less, its ordered series of numbers belongs to typical small sample ordered series of numbers,

(2) gray model is improved, make it be more suitable for Wave type data prediction

A, suppose to have unique point X-coordinate data sequence be: x={x ₁, x ₂..., x _n.Set up new data sequence x'={x' ₁, x' ₂..., x' _n, and replace sequence x;

Work as j=1, when 2, x' _j=x _j;

Work as j=3,4 ..., during n, as x ₁> x ₂, x _j-1>=x _jtime, u _j=0, otherwise, u _j=-2 [x _j-x _j-1]; As x ₁< x ₂, x _j-1≤ x _jtime, u _j=0, otherwise, u _j=2 [x _j-x _j-1];

B, to x' ⁽⁰⁾={ x' ₁ ⁽⁰⁾, x' ₂ ⁽⁰⁾..., x' _n ⁽⁰⁾carry out single order add up, generation module x' ⁽¹⁾={ x' ₁ ⁽¹⁾, x' ₂ ⁽¹⁾..., x' _n ⁽¹⁾;

By single order gray model x' ⁽¹⁾the differential equation formed is:

In formula, a is System Development coefficient, and b is interior raw control variable;

After discrete for (1) formula, obtain Y=XB, Y is sequence variables matrix, and X is single order sum function matrix, and B is estimator matrix.It is obtained by least square method:

Wherein:

Solutions of Ordinary Differential Equations is:

match value be:

C, from u={u ₃, u ₄..., u _nin get nonzero value, if not null value number is more than or equal to 4, then set up sequence v ⁽⁰⁾, and repeat step 2, by the analogue value sequence obtained replace nonzero value corresponding in former sequence u, and in u, null value remains unchanged, thus obtain new sequence if not null value number is less than 4, then

D, acquisition improvement gray model match value

Work as j=1, when 2,

Work as j=3,4 ..., during n, as x ₁> x ₂, as x ₁> x ₂,

(3) curve that grey BPNN evolves to unique point is improved

Using gray model match value as input value, using actual value as output valve, and the feature of the self study that few and neural network has in conjunction with grey forecasting model desired data and adaptive ability, neural network is trained, when the actual output of network and desired output closely time, show that the mapping relations between constrained input are grasped in web results study preferably, neural network can be eliminated like this and do not consider the negative effect that data precedence relationship is brought;

Improvement grey BPNN model comprises three layers: input layer, hidden layer, output layer.The analogue value of improvement gray model for input vector, original measurement value x is output valve.Get front 75% be training set, rear 25% is inspection set, and output layer nodes is 1, and node in hidden layer is 3, and predicted data sequence is designated as R;

(4) markov chain is to the correction that predicts the outcome of improvement Grey BP Neural Network

Markov chain (Markov Chain) referred to as, improvement grey BPNN predicts young mobile modelling feature point position, the random fluctuation within the specific limits usually of its result, Markov chain effectively can be predicted and eliminate the predicated error produced by system randomness;

A, utilize golden section ratio principle calculate data state area between

Forecasting sequence R and actual value sequence x according to improveing grey BPNN obtain relative error value sequence q, after its normalized, obtain average , golden section ratio is Ω=0.618, is calculated as follows cut-point λ, realizes the division in w interval:

Getting s value is 1 and-1, obtains 3 state space [0, a ₁], [a ₁, a ₂], [a ₂, 1].Reverted in sequence q, obtained r between three state areas ₁[r _1-, r ₁₊], r ₂[r _2-, r ₂₊], r ₃[r _3-, r ₃₊], wherein r _1-=e _min, r ₁₊=r _2-=e _min+ a ₁(e _max-e _min), r ₂₊=r _3-=e _min+ a ₂(e _max-e _min), r ₃₊=e _max.E _max, e _minrepresent the minimum and maximum value in relative error value sequence q respectively;

B, calculating transition probability matrix

Markov chain forecast model is expressed as:

P _t+1＝P ₀[P ⁽¹⁾] ^t+1(5)

In formula, P _t+1for the probability distribution in t+1 moment, P ₀for the unconditional probability of initial time distributes, P ⁽¹⁾be a step transition probability matrix, its expression formula is:

P in formula _ij(haveing nothing to do with initial time) is a step transition probability, represents that process is from t _nmoment state a _it is transferred to through a step _n+1moment state a _jprobability, p _ij=P (X _n+1=a _j| X _n=a _i).0≤p _ij≤1，

C, the probability interval in t+1 moment can be calculated according to formula (5), r [r between the relative error state area obtaining this moment _-, r ₊], finally predict the outcome into: