CN108108583A - A kind of adaptive SVM approximate models parameter optimization method - Google Patents
A kind of adaptive SVM approximate models parameter optimization method Download PDFInfo
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Abstract
The invention discloses a kind of adaptive SVM approximate models parameter optimization methods, and for improving the precision of SVM approximate models, step is as follows：The analysis to physical model is combined using optimal Latin hypercube experimental design method, obtains training sample set and test sample collection；Using the relative error of test sample collection as fitness value, using genetic algorithm, optimize the parameter of SVM approximate models, obtain optimized parameter SVM approximate models；Using the relative error of test sample collection as criterion, using greedy algorithm, update training and test sample；New SVM approximate models are constructed on the basis of new samples, iteration is repeatedly until SVM approximate models meet required precision.The present invention solve thes problems, such as that SVM approximate model parameters are difficult to select to be difficult to be promoted with precision, increases substantially the efficiency of complicated physical model analysis in engineering, and engineering significance is notable.
Description
Technical Field
The invention relates to the technical field of approximate models of complex physical models, in particular to a parameter optimization method of an adaptive SVM approximate model.
Background
The approximate model is a technology for optimizing service, and the optimization method based on the approximate model is one of the optimal hopes for solving the large-scale nonlinear problem, and is widely applied to the field of engineering optimization in view of high efficiency and time saving. The approximate model technique is mainly composed of two parts: the test design method and the approximate model construction directly influence the prediction precision of the approximate model to construct efficiency.
The test design actually selects a reasonable most representative test sample point combination in a design space, directly determines the number and the spatial distribution condition of sample points required for constructing an approximate model, and influences the fitting precision of the approximate model to a real physical model. Common test design methods include: full factor test design, orthogonal design, uniform design, center composite design, latin hypercube test design and the like. The Latin hypercube test design is a test design method based on random sampling, and has the advantages of strong nonlinear response fitting capacity, freely selectable number of test sample points, uniform application of each factor on each level and the like. The invention can avoid the defects by adding a maximum and minimum distance criterion, so that the response condition of the real physical model can be reflected to the maximum extent by the sample set.
The construction principle of the approximate model is that when the actual values of a certain number of points around a certain point in a design space are known, a hypersurface is established in a certain mode and replaces an original responsible physical model with the hypersurface to carry out efficient calculation. Common approximate model construction methods include a Response Surface Method (RSM), a Kriging function method (Kriging), an Artificial Neural Network (ANN), a Support Vector Machine (SVM), and the like. The RSM has a simple structure and high transparency, but is not suitable for establishing a nonlinear and high-complexity model; the BP model has a simple structure, but easily falls into an over-learning state to cause great reduction of prediction precision; kriging is significantly affected by data noise and modeling time is long. The SVM algorithm is firstly proposed by Vapnik, and can well solve the problem of small sample learning. The basic idea is as follows: the input vector x is mapped to a high-dimensional feature space Z by some pre-selected non-linear mapping, i.e. kernel function, in which the optimal classification hyperplane is constructed. The SVM algorithm has many specific advantages in solving the problems of small samples, nonlinearity and high-dimensional pattern recognition, and can effectively avoid the problems of over-learning, obvious influence of data noise and the like due to the fact that the SVM algorithm is based on the principle of minimizing structural risk. However, in the process of constructing the SVM approximate model, parameters influencing the precision and generalization capability of the SVM approximate model are more, and the adaptive SVM approximate model parameter optimization method provided by the invention can effectively solve the problem and improve the precision of the SVM approximate model.
Disclosure of Invention
The invention aims to provide a self-adaptive SVM approximate model parameter optimization method, which effectively solves the problems of complexity and time consumption in SVM approximate model parameter selection and improves the model precision and generalization capability.
The technical solution for realizing the purpose of the invention is as follows: a method for optimizing parameters of an adaptive SVM approximate model comprises the following steps:
step 1, obtaining a training sample set S = { (x (i), f) by using an optimal Latin hypercube test design method and combining with analysis of a physical model f x (i)),i＝1,2,…,n s }。
Step 2, obtaining a test sample set T = { (y (i), f), by using an improved optimal Latin hypercube test design method and combining with analysis of a physical model f y (i)),i＝1,2,…,n t Are such that n is s A training sample point to n t The distance between the test sample points is the largest.
Step 3, determining coefficient R by testing sample set 2 Optimizing 3 weights of SVM approximation model by genetic algorithm as fitness valueAnd obtaining an optimal parameter SVM approximate model by using parameters, namely approximation precision epsilon, penalty parameter C and kernel parameter sigma.
Step 4, using the decision coefficient of the final iteration step in step 3As a greedy criterion, a greedy algorithm is adopted to update the training sample set and the test sample set, and the greedy criterion is updated until n is reached t And =0, obtaining the SVM approximate model after final optimization.
Compared with the prior art, the invention has the remarkable advantages that:
(1) The optimal Latin hypercube test design method introducing the maximum and minimum distance criterion simultaneously meets the spatial uniformity of training sample points and the projection uniformity on each variable.
(2) The improved optimal Latin hypercube test design method meets the requirement that the distance between a training sample point and a test sample point is the largest, and enables the whole training sample point and the whole test sample point to continuously keep the space uniformity and the projection uniformity on each variable.
(3) The SVM approximate model is optimized based on genetic algorithm optimization, and the accuracy of the SVM approximate model is greatly improved compared with the accuracy of an SVM approximate model established based on empirical parameters.
(4) Based on a greedy algorithm, the SVM approximate model sample space is optimized, and compared with the method that a training sample set is directly used for establishing a model, the information of the test sample set can be considered to the maximum extent.
Drawings
FIG. 1 is a flow chart of the adaptive SVM approximation model parameter optimization method of the present invention.
FIG. 2 is a flow chart of an optimal Latin hypercube test design method incorporating a maximum and minimum distance criterion.
FIG. 3 is a flow chart of 3 important parameters for optimizing SVM approximate model based on genetic algorithm.
FIG. 4 is a flow chart of a sample space for optimizing an SVM approximation model based on a greedy algorithm.
Fig. 5 is a sample distribution diagram of the projections of training sample points on two factors obtained by the method for designing the pull Ding Chao cubic test in embodiment 1 of the present invention.
Fig. 6 is a sample distribution diagram of the projections of training sample points on two factors obtained by the optimal latin hypercube test design method in embodiment 1 of the present invention.
Fig. 7 is a sample distribution diagram of the projections of the test sample points and the training sample points on two factors obtained by the design method of the pull Ding Chao cubic test in embodiment 1 of the present invention.
Fig. 8 is a sample distribution diagram of the projections of the test sample points and the training sample points on two factors obtained by the optimal latin hypercube design method introducing the improved maximum-minimum distance criterion in embodiment 1 of the present invention.
FIG. 9 is a graph showing the change of the determination coefficient depending on the number of iterations of the genetic algorithm in example 1 of the present invention.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
With reference to fig. 1 to 4, a method for optimizing parameters of an adaptive SVM approximate model includes the following steps:
step 1, obtaining a training sample set S = { (x (i), f) by using an optimal Latin hypercube test design method and combining with analysis of a physical model f x (i)),i＝1,2,…,n s }; the method comprises the following specific steps:
step 1-1, dividing each dimension variable of a training sample into n in the value range thereof s Intervals, in each interval a sampling point is randomly generated, and randomly combined to form an n s And (3) the training sample matrix X of X m is the training sample point, and the step 1-2 is carried out.
Step 1-2, let OUT =1,IN =1, optimally training sample matrix X best = X; and (5) transferring to the step 1-3.
Step 1-3, exchanging any two elements IN the IN column of the training sample matrix X for A times to constructA new set of training sample matrices X 1 ,X 2 ,…,X A Selecting the best design X from the maximum and minimum distance criteria try ，
The maximum minimum distance criterion is: in a training sample matrix X, d (X) i ,x j ) Represents the distance between two training sample points:the parameter t =1 or 2,k is an independent variable, and the judgment standardI.e. in a new set of training sample matrices X 1 ,X 2 ,…,X A In (1), selecting X try Satisfies the condition F (X) try )＝max{F(X 1 ),F(X 2 ),…,F(X A ) }; and (5) transferring to the step 1-4.
Step 1-4, judging F (X) best ) And F (X) try ) If F (X) best )≤F(X try ) Then X best ＝X try IN = IN +1; if F (X) best )>F(X try ) IN = IN +1; and (5) transferring to the step 1-5.
Step 1-5, comparing m with the updated IN IN step 1-4, and if IN is larger than m, turning to step 1-6; otherwise, returning to the step 1-3.
Step 1-6, let OUT = OUT +1, if OUT&G, B, outputting an optimal training sample matrix X best And (4) switching to the step 1-7, wherein B is the number of external cycles; otherwise, IN =1, return to step 1-3.
1-7, obtaining an optimal training sample matrix X best And obtaining a training sample set S = { (x (i), f) in combination with analysis of the physical model f x (i)),i＝1,2,…,n s }。
Step 2, obtaining a test sample by combining the improved optimal Latin hypercube test design method with the analysis of the physical model fThis set T = { (y (i), f) y (i)),i＝1,2,…,n t Are such that n is s Training sample point to n t The distance between the test sample points is the largest; the method comprises the following specific steps:
the dimension of the test sample points y (i) is m, and the number of the test sample points is n t The value range of y (i) is [ y min ,y max ]The improved optimal Latin hypercube test design method comprises the following algorithm steps:
step 2-1, dividing each dimension variable of the test sample into n within the value range t Intervals, in each interval a sampling point is randomly generated, and randomly combined to form an n t And (3) the testing sample matrix Y of x m is the testing sample point, and the step 2-2 is carried out.
Step 2-2, let OUT =1, IN =1, and optimally testing the sample matrix Y bret And = Y, the step 2-3 is carried out.
Step 2-3, exchanging any two elements IN the IN row of the input test sample matrix Y for P times, and constructing a batch of new test sample matrix Y 1 ,Y 2 ,…,Y P Selecting the best design Y from the improved maximum and minimum distance criteria try ，
The improved maximum-minimum distance criterion is: according to the test sample matrix Y and the optimal training sample matrix X in the step 1 best To obtain a (n) s +n t ) New sample matrix of x m, Z, d (Z) i ,z j ) Represents the distance between two sample points in the new sample matrix Z:t =1 or 2,k as an independent variable, and a criterionI.e. in a new set of sample matrices Y 1 ,Y 2 ,…,Y P In (1), selecting Y try When Y is try And X best Combination ofTo form a new matrix Z try Then, the condition is satisfied: f (Z) try )＝max{F(Z 1 ),F(Z 2 ),…,F(Z P ) And fifthly, turning to the step 2-4.
Step 2-4, judging F (Z) best ) And F (Z) try ) If F (Z) is best )≤F(Z try ) Then Y is best ＝Y try IN = IN +1, if F (Z) best )>F(Z try ) IN = IN +1; and (5) transferring to the step 2-5.
Step 2-5, comparing m with the updated IN IN step 2-4, and if IN is larger than m, turning to step 2-6; otherwise, returning to the step 2-3.
Step 2-6, making OUT = OUT +1, if OUT>, B, outputting the optimal input test sample matrix Y best And (4) transferring to the step 2-7, wherein B is the number of external circulation; otherwise, IN =1, return to step 2-3.
Step 2-7, inputting a sample matrix Y according to the obtained optimal test best And obtaining a test sample set T = { (y (i), f) in combination with analysis on the physical model f y (i)),i＝1,2,…,n t }。
Step 3, determining coefficient R by testing sample set 2 As fitness values, optimizing 3 important parameters of the SVM approximate model, namely approximation precision epsilon, penalty parameter C and kernel parameter sigma, through a genetic algorithm to obtain an optimal parameter SVM approximate model; the method comprises the following specific steps:
step 3-1, assigning an initial range to each of the three variables ε, C, and σ, i.e. AndwhereinAndare all coefficients. Creating an initial population with the number of n r And (4) turning to the step 3-2.
Step 3-2, training a sample set S = { (x (i), f) in step 1 by SVM parameters corresponding to each individual in the initial population x (i)),i＝1,2,…,n s Establishing an SVM approximate model; using the test sample set T = { (y (i), f) in the step 2 y (i)),i＝1,2,…,n t Coefficient of determination R 2 As fitness value, the quality of each individual in the initial population is evaluated, and the coefficient R is determined 2 Is of the formula
Wherein f is y (i) Is the true response of the physical model f,is f y (i) Is determined by the average value of (a) of (b),is the SVM approximate model response, n t Is the number of test sample points; and (4) transferring to the step 3-3.
And 3-3, the iteration times are s, convergence is achieved through selection, crossing and variation, the optimal individual is obtained, and the step 3-4 is carried out.
Step 3-4, reducing the ranges of the variables epsilon, C and sigma according to the optimal individual, returning to the step 3-1 until the variables epsilon, C and sigma are correspondingly converged in the ranges (0, epsilon (1+k) for at least 3 times ε )]、(0,C(1+k C )]And (0, σ (1+k) σ )]In k ε 、k C And k σ Are all coefficients, at which time the optimum parameter ε is obtained best 、C best 、σ best Current coefficient of determinationAnd an optimal parametric SVM approximation model.
Step 4, using the decision coefficient of the final iteration step in step 3As a greedy criterion, a greedy algorithm is adopted to update the training sample set and the test sample set, and the greedy criterion is updated until n is reached t =0, obtaining the final optimized SVM approximation model; the method comprises the following specific steps:
step 4-1, calculating the relative error RE of each test point in the test sample set according to the optimal parameter SVM approximate model in the step 3 i ，i＝1,2,…,n t (ii) a And (4) transferring to a step 4-2.
Step 4-2, selecting a test sample point maxRE with the largest relative error i The test sample point is taken out of the test sample set and put into the training sample set, i.e. n s ＝n s +1，n t ＝n t -1; and (4) transferring to a step 4-3.
Step 4-3, based on epsilon obtained in step 3 best 、C best And σ best And 4-2, establishing a new SVM approximate model and predicting to obtain a new decision coefficientAnd (5) turning to a step 4-4.
Step 4-4, executing greedy criterion:
if it is notThenTurning to the step 4-5; otherwise, the test sample point is removed from the training sample set and the test sample set, namely n s ＝n s -1, going to step 4-5;
and 4-5, judging whether all the test sample points are subjected to greedy algorithm test:
if n is t &0, returning to the step 4-1; if n is t And =0, terminating the iteration and outputting the final optimized SVM approximate model.
Part2 example
The physical model f of the object researched by the embodiment is a nonlinear finite element dynamic model optimization problem of the gun upper-mounted part. Firstly, establishing a finite element dynamic model of a certain artillery upper-loading part, selecting design variables by taking muzzle disturbance as an optimization target, and selecting indexes for measuring the muzzle disturbance. The method comprises the following specific steps:
(1) And establishing a finite element dynamic model of the upper part of a certain artillery. The nonlinear finite element model of the artillery built by the embodiment has 253121 units and 279134 nodes. And (3) coordinate system: the x-axis direction is directed axially along the barrel toward the muzzle, the y-axis direction is perpendicular to the x-axis, and the z-axis follows the right-hand rule. The model consists of a barrel recoil part, a cradle part, an upper frame part and a seat ring part. The structure of the barrel recoil part, the gear arcs of the high-low machine, the seat ring and the like adopts a hexahedral unit; most structures of the cradle and the upper frame adopt plate shell units; the balancing machine is simulated with a rod unit.
The connection relationship among the components of the artillery is as follows: simulating the connection between the cradle trunnion and the upper cradle trunnion seat by using degree-of-freedom coupling, and only releasing the degree of freedom of rotation around the trunnion axis; the contact between the gear of the high-low machine and the tooth arc is defined; defining a face-to-face contact at a surface area of contact between the barrel and the bushing to simulate a contact collision relationship therebetween; and setting a reference point at the central point of the muzzle, and connecting the reference point and the unit node at the muzzle by adopting coupling constraint so as to output muzzle disturbance data.
Artillery loading and boundary conditions: applying bore pressure changing along with time on the breech surface to simulate the acting force of gunpowder gas; the braking force, the re-advancing force and the balancing force are simulated by a nonlinear spring; the gravity is directly loaded in the model as a constant force; a fully constrained boundary condition is imposed at the race bottom surface.
(2) And selecting a design variable. Aiming at the characteristics of artillery structure and combining the sensitivity of the artillery in the early stageAnalyzing the result, and selecting the rigidity s of the cradle 1 Stiffness of upper frame s 2 The clearance c between the front lining tile and the rear lining tile and the barrel, the mass eccentricity e of the recoil part in the y-axis direction, the mass m of the muzzle brake as 5 design variables, and the horizontal transverse angular displacement theta of the muzzle position at the moment that the projectile exits the muzzle y High and low angular displacement theta z Horizontal transverse angular velocity ω y High and low angular velocity omega z As an index to measure muzzle disturbances. The initial values and the value ranges of the design variables are shown in table 1.
TABLE 1 initial values and value ranges of design variables
(3) And selecting an index for measuring the disturbance of the blast hole. Selecting horizontal transverse angular displacement theta of muzzle position at the moment when the projectile exits the muzzle y High and low angular displacement theta z Horizontal transverse angular velocity ω y High and low angular velocity omega z As an index to measure muzzle disturbances.
Establishing an adaptive SVM approximate model oriented to the nonlinear finite element dynamic optimization of the large-caliber artillery, wherein the parameter optimization method of the adaptive SVM approximate model comprises the following steps:
step 1, extracting 50 training sample points by using an optimal Latin hypercube test design method introducing a maximum and minimum distance criterion and combining with analysis of the nonlinear finite element dynamic model of the large-caliber artillery to obtain a training sample set S = { (x (i), f) x (i) I =1,2, …,50}; the method comprises the following specific steps:
step 1-1, dividing each dimensional variable of a training sample into 50 intervals in a value range shown in table 1, randomly generating a sampling point in each interval, randomly combining to form a 50X 5 training sample matrix X, namely a training sample point, and turning to step 1-2;
step 1-2, let OUT =1, IN =1, optimally training sample matrix X best = X; turning to the step 1-3;
step 1-3, training sample matrixAny two elements IN the Xth IN column are exchanged 1225 times to construct a new training sample matrix X 1 ,X 2 ,…,X 1225 Selecting the best design X from the maximum and minimum distance criteria try ；
The maximum minimum distance criterion is: in a training sample matrix X, d (X) i ,x j ) Represents the distance between two training sample points:k is independent variable, and the criterion is judgedI.e. in a new set of training sample matrices X 1 ,X 2 ,…,X 1225 In (1), selecting X try Satisfies the condition F (X) try )＝max{F(X 1 ),F(X 2 ),…,F(X 1225 ) }; turning to the step 1-4;
step 1-4, judging F (X) best ) And F (X) try ) If F (X) best )≤F(X try ) Then X best ＝X try IN = IN +1; if F (X) best )>F(X try ) IN = IN +1; turning to the step 1-5;
step 1-5, comparing the dimension 5 with the updated IN IN the step 1-4, and if the IN is more than 5, turning to the step 1-6; otherwise, returning to the step 1-3;
step 1-6, let OUT = OUT +1, if OUT>, 200, outputting an optimal training sample matrix X best And (4) transferring to the step 1-7, wherein 200 is the number of external cycles; otherwise, IN =1, returning to step 1-3;
1-7, obtaining an optimal training sample matrix X best Combining with analysis of the nonlinear finite element kinetic model of the large-caliber artillery, obtaining a training sample set S = { (x (i), f) x (i)),i＝1,2,…,50}。
FIG. 5 is a sample distribution diagram of the projection of training sample points on two of the factors obtained by the design method of the pull Ding Chao cubic test without introducing the maximum and minimum distance criterion; FIG. 6 is a sample distribution diagram of the projection of training sample points on two factors obtained by the optimal Latin hypercube test design method with the maximum and minimum distance criterion introduced; it can be seen from fig. 5 and 6 that the maximum-minimum distance criterion effectively improves the spatial uniformity of the training sample points and the projection uniformity on each variable.
Step 2, extracting 50 test sample points at 50 training sample points by using an optimal Latin hypercube test design method introducing an improved maximum and minimum distance criterion and combining with the analysis of the nonlinear finite element dynamic model of the large-caliber artillery to obtain a test sample set T = { (y (i), f y (i) I =1,2, …,50}, such that the distance between 50 training sample points to 50 test sample points is maximized; the method comprises the following specific steps:
step 2-1, dividing each dimension variable of a test sample into 50 intervals in a value range shown in table 1, randomly generating a sampling point in each interval, randomly combining to form a test sample matrix Y of 50 x 5, namely a test sample point, and turning to step 2-2;
step 2-2, let OUT =1, IN =1, and optimally testing the sample matrix Y bret = Y, go to step 2-3;
step 2-3, exchanging 1225 times any two elements IN the IN column of the input test sample matrix Y, and constructing a batch of new test sample matrices Y 1 ,Y 2 ,…,Y 1225 Selecting the best design Y from the modified maximum and minimum distance criteria try ；
The improved maximum-minimum distance criterion is: according to the test sample matrix Y and the optimal training sample matrix X in the step 1 best To obtain a new sample matrix Z, d (Z) of 100 × 5 i ,z j ) Represents the distance between two sample points in the new sample matrix Z:k is independent variable, and the criterion is judgedI.e. in a new set of sample matrices Y 1 ,Y 2 ,…,Y 1225 In (1), selecting Y try When Y is try And X best Combined into a new matrix Z try Then, the condition is satisfied: f (Z) try )＝max{F(Z 1 ),F(Z 2 ),…,F(Z 1225 ) Fourthly, turning to the step 2-4;
step 2-4, judging F (Z) best ) And F (Z) try ) If F (Z) is best )≤F(Z try ) Then Y is best ＝Y try IN = IN +1, if F (Z) best )>F(Z try ) Then IN = IN +1; turning to the step 2-5;
step 2-5, comparing the dimension 5 with the updated IN IN the step 2-4, and if the IN is larger than 5, turning to the step 2-6; otherwise, returning to the step 2-3;
step 2-6, let OUT = OUT +1, if OUT>, 200, outputting an optimal input test sample matrix Y best And (4) transferring to the step 2-7, wherein 200 is the number of external circulation; otherwise, IN =1, returning to the step 2-3;
2-7, inputting a sample matrix Y according to the obtained optimal test best And obtaining a test sample set T = { (y (i), f) by combining analysis of the nonlinear finite element dynamic model of the large-caliber artillery y (i)),i＝1,2,…,50}。
FIG. 7 is a sample distribution diagram of the projections of the test sample points and the training sample points on two factors obtained by the Latin hypercube test design method; FIG. 8 is a sample distribution graph showing the projection of test sample points and training sample points on two of these factors, obtained by the optimal Latin hypercube design method incorporating the improved maximum-minimum distance criterion; it is seen from the figure that the improved maximum-minimum criterion significantly increases the distance between the training sample points and the test sample points and allows the spatial uniformity and the projection uniformity on each variable to be maintained throughout the training sample points and the test sample points.
Step 3, considering that the approximation model of the single mapping is easier to achieve high prediction accuracy, and for 4 indexes of measuring the muzzle disturbance, the rotation angle displacement theta is calculated y High and low angle positionsShift theta z Angular velocity of revolution omega y High and low angular velocity omega z Respectively establishing SVM approximate models, and respectively optimizing three important parameter approximation precision epsilon, punishment parameter C and kernel parameter sigma of the four approximate models based on a genetic algorithm to obtain an optimal parameter SVM approximate model; the method comprises the following specific steps:
step 3-1, respectively endowing three variables of epsilon, C and sigma with an initial range, namely (0,1 ], (0,10 ] and (0,1 ]. Creating an initial population, wherein the population number is 500, and then, turning to step 3-2;
step 3-2, training a sample set S = { (x (i), f) in step 1 by SVM parameters corresponding to each individual in the initial population x (i) I =1,2, …,50}, and establishing an SVM approximate model; using the test sample set T = { (y (i), f) in the step 2 y (i) I =1,2, …,50}, and 2 as a fitness value, evaluating the quality of each individual in the initial population and determining a coefficient R 2 Is of the formula
Wherein f is y (i) Is the true response of the physical model f,is f y (i) Is determined by the average value of (a) of (b),is the SVM approximate model response; turning to the step 3-3;
3-3, the iteration times are 200, convergence is achieved through selection, crossing and variation, the optimal individual is obtained, and the step 3-4 is carried out;
step 3-4, reducing the ranges of the variables epsilon, C and sigma according to the optimal individual, and returning to the step 3-1 until the variables epsilon, C and sigma are correspondingly converged in the ranges (0, epsilon (1+k) for at least 3 times ε )]、(0,C(1+k C )]And (0, σ (1+k) σ )]In k ε 、k C And k σ Are coefficients, depending on the different approximation models. This is achieved byTime-obtaining optimum parameter epsilon best 、C best 、σ best Current coefficient of determinationAnd an optimal parametric SVM approximation model. The optimization results are shown in table 2. With the output being theta y For example, the accuracy of the model is shown in fig. 9 as the number of iterations of the genetic algorithm changes.
TABLE 2 SVM approximation model parameter optimization results
And 4, updating 50 samples for testing into a sample space by combining a greedy algorithm, and further improving the precision of the approximate model, wherein the method specifically comprises the following steps:
step 4-1, calculating the relative error RE of each test point in the test sample set according to the optimal parameter SVM approximate model in the step 3 i ，i =1,2, …,50; turning to the step 4-2;
step 4-2, selecting a test sample point maxRE with the largest relative error i The test sample point is taken out of the test sample set and put into the training sample set, i.e. n s ＝n s +1，n t ＝n t -1; turning to the step 4-3;
step 4-3, based on epsilon obtained in step 3 best 、C best And σ best And 4-2, establishing a new SVM approximate model and predicting to obtain a new decision coefficientTurning to step 4-4;
step 4-4, executing greedy criterion:
if it is notThenTurning to the step 4-5; otherwise, the test sample point is removed from the training sample set and the test sample set, namely n s ＝n s -1, go to step 4-5;
and 4-5, judging whether all the test sample points are subjected to greedy algorithm test:
if n is t &0, returning to the step 4-1; if n is t And =0, terminating the iteration and outputting the final optimized SVM approximate model.
Finally, four outputs are obtained, namely the rotation angular displacement theta y High and low angular displacement theta z Angular velocity of revolution omega y High and low angular velocity omega z Compared with an approximate model established according to empirical parameters and an original sample space, the model accuracy of the SVM approximate model is greatly improved, as shown in Table 3.
TABLE 3 comparison of the present invention with model accuracy based on empirical parameters
In conclusion, the adaptive SVM approximate model parameter optimization method provided by the invention meets the projection uniformity and the space uniformity of the training samples and the test samples in the sample interval, simultaneously meets the maximum distance between the test samples and the training samples, optimizes the algorithm parameters based on the genetic algorithm, optimizes the sample space based on the greedy algorithm and effectively improves the precision of the approximate model.
Claims (5)
1. A method for optimizing parameters of an adaptive SVM approximate model is characterized by comprising the following steps:
step 1, obtaining a training sample by combining an optimal Latin hypercube test design method with analysis of a physical model fSet S = { (x (i), f) x (i)),i＝1,2,…,n s }；
Step 2, obtaining a test sample set T = { (y (i), f) by using an improved optimal Latin hypercube test design method and combining analysis of a physical model f y (i)),i＝1,2,…,n t Are such that n is s Training sample point to n t The distance between the test sample points is maximum;
step 3, determining coefficient R by testing sample set 2 As fitness values, optimizing 3 important parameters of the SVM approximate model, namely approximation precision epsilon, penalty parameter C and kernel parameter sigma, through a genetic algorithm to obtain an optimal parameter SVM approximate model;
step 4, using the decision coefficient of the final iteration step in step 3As a greedy criterion, a greedy algorithm is adopted to update the training sample set and the test sample set, and the greedy criterion is updated until n is reached t And =0, obtaining the SVM approximate model after final optimization.
2. The adaptive SVM approximation model parameter optimization method according to claim 1, wherein: step 1, combining the optimal Latin hypercube test design method with the analysis of the physical model f to obtain a training sample set S = { (x (i), f) x (i)),i＝1,2,…,n s The method concretely comprises the following steps:
the dimension of the training sample point x (i) is m, and the number of the sample points is n s And x (i) has a value range of [ x min ,x max ]The algorithm steps of the optimal Latin hypercube test design method are as follows:
step 1-1, dividing each dimension variable of a training sample into n in the value range thereof s Intervals, in each interval a sampling point is randomly generated, and randomly combined to form an n s The training sample matrix X of X m is the training sample point, and the step 1-2 is carried out;
step 1-2, let OUT =1, IN =1, optimally training sample matrix X best = X; turning to the step 1-3;
step 1-3, exchanging any two elements IN the IN column of the training sample matrix X for A times, and constructing a batch of new training sample matrix X 1 ,X 2 ,…,X A Selecting the best design X from the maximum and minimum distance criteria try ，
The maximum minimum distance criterion is: in a training sample matrix X, d (X) i ,x j ) Represents the distance between two training sample points:the parameter t =1 or 2,k is an independent variable, and the criterion is judgedI.e. in a new set of training sample matrices X 1 ,X 2 ,…,X A In (1), selecting X try Satisfies the condition F (X) try )＝max{F(X 1 ),F(X 2 ),…,F(X A ) }; turning to the step 1-4;
step 1-4, judging F (X) best ) And F (X) try ) If F (X) best )≤F(X try ) Then X best ＝X try IN = IN +1; if F (X) best )>F(X try ) IN = IN +1; turning to the step 1-5;
step 1-5, comparing m with the updated IN IN step 1-4, and if IN is larger than m, turning to step 1-6; otherwise, returning to the step 1-3;
step 1-6, let OUT = OUT +1, if OUT&G, B, outputting an optimal training sample matrix X best And (4) transferring to the step 1-7, wherein B is the number of external circulation; otherwise, IN =1, returning to step 1-3;
1-7, obtaining an optimal training sample matrix X best And obtaining a training sample set S = { (x (i), f) in combination with analysis of the physical model f x (i)),i＝1,2,…,n s }。
3. The adaptive SVM approximation model parameter optimization method according to claim 1, wherein: step 2, combining the improved optimal Latin hypercube test design method with the analysis of the physical model f to obtain a test sample set T = { (y (i), f) y (i)),i＝1,2,…,n t Are such that n is s Training sample point to n t The distance between the individual test sample points is the largest, as follows:
the dimension of the test sample points y (i) is m, and the number of the test sample points is n t The value range of y (i) is [ y min ,y max ]The improved optimal Latin hypercube test design method comprises the following algorithm steps:
step 2-1, dividing each dimension variable of the test sample into n within the value range thereof t Intervals, in each interval a sampling point is randomly generated, and randomly combined to form an n t The testing sample matrix Y of x m is the testing sample point, and the step 2-2 is carried out;
step 2-2, let OUT =1, IN =1, and optimally testing the sample matrix Y bret = Y, go to step 2-3;
step 2-3, exchanging any two elements IN the IN row of the input test sample matrix Y for P times, and constructing a batch of new test sample matrix Y 1 ,Y 2 ,…,Y P Selecting the best design Y from the modified maximum and minimum distance criteria try ，
The improved maximum-minimum distance criterion is: according to the test sample matrix Y and the optimal training sample matrix X in the step 1 best To obtain a (n) s +n t ) New sample matrix of x m, Z, d (Z) i ,z j ) Represents the distance between two sample points in the new sample matrix Z:t =1 or 2,k as the independent variable, andcriteria of judgmentI.e. in a new set of sample matrices Y 1 ,Y 2 ,…,Y P In (1), selecting Y try When Y is try And X best Combined into a new matrix Z try After that, the condition is satisfied: f (Z) try )＝max{F(Z 1 ),F(Z 2 ),…,F(Z P ) Fourthly, turning to the step 2-4;
step 2-4, judging F (Z) best ) And F (Z) try ) If F (Z) is best )≤F(Z try ) Then Y is best ＝Y try IN = IN +1, if F (Z) best )>F(Z try ) Then IN = IN +1; turning to the step 2-5;
step 2-5, comparing m with the updated IN IN step 2-4, and if IN is larger than m, turning to step 2-6; otherwise, returning to the step 2-3;
step 2-6, let OUT = OUT +1, if OUT>, B, outputting the optimal input test sample matrix Y best And (4) transferring to the step 2-7, wherein B is the number of external circulation; otherwise, IN =1, returning to step 2-3;
step 2-7, inputting a sample matrix Y according to the obtained optimal test best And obtaining a test sample set T = { (y (i), f) in combination with analysis of the physical model f y (i)),i＝1,2,…,n t }。
4. The adaptive SVM approximation model parameter optimization method of claim 1, characterized in that: step 3 of determining the coefficient R by the test sample point 2 As a fitness value, 3 important parameters of the SVM approximation model, namely, approximation accuracy epsilon, penalty parameter C and kernel parameter sigma, are optimized through a genetic algorithm to obtain an optimal parameter SVM approximation model, which is specifically as follows:
step 3-1, assigning an initial range to each of the three variables ε, C and σ, i.e. AndwhereinAndare all coefficients; creating an initial population with the number n r And turning to the step 3-2;
step 3-2, SVM parameters corresponding to each individual in the initial population and the training sample set S = { (x (i), f) in step 1 x (i)),i＝1,2,…,n s Establishing an SVM approximate model; using the test sample set T = { (y (i), f) in the step 2 y (i)),i＝1,2,…,n t Coefficient of determination R 2 As fitness value, the quality of each individual in the initial population is evaluated, and the coefficient R is determined 2 Is of the formula
Wherein f is y (i) Is the true response of the physical model f,is f y (i) Is determined by the average value of (a) of (b),is the SVM approximate model response, n t Is the number of test sample points; turning to the step 3-3;
3-3, the iteration times are s, convergence is achieved through selection, crossing and variation, the optimal individual is obtained, and the step 3-4 is carried out;
step 3-4, reducing the range of the epsilon, C and sigma variables according to the optimal individual, and returning to the step 3-1 until the optimal individual reaches the range of the epsilon, C and sigma variablesThe three variables of epsilon, C and sigma are converged in the range (0, epsilon (1+k) for at least 3 times ε )]、(0,C(1+k C )]And (0, σ (1+k) σ )]In k ε 、k C And k σ Are all coefficients, at which time the optimum parameter epsilon is obtained best 、C best 、σ best Current coefficient of determinationAnd an optimal parametric SVM approximation model.
5. The adaptive SVM approximation model parameter optimization method according to claim 1, wherein: step 4, determining coefficients of the final iteration step in step 3As a greedy criterion, a greedy algorithm is adopted to update the training sample set and the test sample set, and the greedy criterion is updated until n is reached t =0, obtaining a final optimized SVM approximate model, specifically as follows:
step 4-1, calculating the relative error RE of each test point in the test sample set according to the optimal parameter SVM approximate model in the step 3 i ，i＝1,2,…,n t (ii) a Turning to the step 4-2;
step 4-2, selecting a test sample point maxRE with the largest relative error i The test sample point is taken out of the test sample set and put into the training sample set, i.e. n s ＝n s +1，n t ＝n t -1; turning to the step 4-3;
step 4-3, based on epsilon obtained in step 3 best 、C best And σ best And 4-2, establishing a new SVM approximate model and predicting to obtain a new decision coefficientTurning to the step 4-4;
step 4-4, executing greedy criterion:
if it is notThen theTurning to the step 4-5; otherwise, the test sample point is removed from the training sample set and the test sample set, namely n s ＝n s -1, going to step 4-5;
and 4-5, judging whether all the test sample points are subjected to greedy algorithm test:
if n is t &0, returning to the step 4-1; if n is t And =0, terminating the iteration and outputting the final optimized SVM approximate model.
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