CN106202623A - Weapon station multi-state structural optimization method based on Kriging algorithm - Google Patents

Abstract

The invention provides a kind of weapon station multi-state structural optimization method based on Kriging algorithm, comprise the steps: step one, given bracing frame elastic modelling quantity, cartridge box quality, the scope of buffer rigidity；Step 2, employing Latin hypercube EXPERIMENTAL DESIGN choose acquisition N group sample point；Step 3, the calculating vibration integrated parameter of gun muzzle；Step 4, associating N group sample point and the vibration integrated parameter of N number of gun muzzle constitute initial training sample point set；Step 5, use genetic algorithm carry out optimizing to kriging agent model, find out optimum point and greatest hope improves point；Step 6, based on dual kriging Model sequence iteration optimization algorithms structure parameter optimizing problem carried out optimizing until convergence.Step 7, the different firing angle structure optimization parameter of acquisition, and the optimum structure parameter of each firing angle is updated in the weapon station kinetic model of other operating mode, find the average structural parameters final structure parameters optimization the most optimizing amplitude maximum.

Description

Weapon station multi-state structural optimization method based on Kriging algorithm

Technical field

The invention belongs to weapon station technical field, tie particularly to a kind of weapon station multi-state based on Kriging algorithm Structure optimization method.

Background technology

During Canon launching, the TRANSIENT HIGH TEMPERATURE of powder burning generation, pushed at high pressure bullet high-speed motion in thorax, cannon in addition Effect of inertia, make cannon produce high vibration, cause gun muzzle point to change, have a strong impact on fire accuracy.Research cannon The gun muzzle disturbance launched and Changing Pattern thereof, for evaluating and examine cannon performance, identifying that the cannon quality of production, raising cannon are penetrated Hit precision and there is important theory significance.Make gun muzzle disturbance minimum by overhead weapon station structural parameters are optimized.

Summary of the invention

The present invention has designed and developed a kind of weapon station multi-state structural optimization method based on Kriging algorithm, by right The optimization of structural parameters, it is thus achieved that optimize, under different firing angles, the parameter that amplitude is maximum, draws the structure ginseng that average optimization amplitude is maximum Number final structure parameters optimization the most, solves the big problem affecting fire accuracy of gun muzzle disturbance amount.

The technical scheme that the present invention provides is:

A kind of weapon station multi-state structural optimization method based on Kriging algorithm, comprises the steps:

Step one, the scope E ∈ [E of given overhead weapon station bracing frame elastic modulus E_a,E_b], scope m of cartridge box quality m ∈[m_a,m_b], the scope K ∈ [K of buffer stiffness K_a,K_b]；

Step 2, employing Latin hypercube EXPERIMENTAL DESIGN choose the value of E, m, K, obtain N group sample point (E_i,m_i,K_i), i= 1,2,...,N；

Step 3, overhead weapon station bracing frame elastic modelling quantity, cartridge box quality, buffer rigidity are respectively set as E_i、m_i、 K_i, overhead weapon station is carried out gun muzzle disturbance test, obtains height to linear velocity mean-square value D_i(v_z), level mean square to linear velocity Value D_i(v_y), height to angular displacement mean-square value D_i(θ_z) and level to angular displacement mean-square value D_i(θ_y), calculate gun muzzle vibration integrated Parameter F_i

F_i=w₁D(v_z)+w₂D(θ_z)+w₃D(v_y)+w₄D(θ_y)

Wherein, w₁、w₂、w₃、w₄For weight coefficient；

Step 4, associating N group sample point (E_i,m_i,K_i) and vibration integrated parameter F of N number of gun muzzle_iConstitute initial training sample Point set, builds kriging agent model；

Step 5, use genetic algorithm carry out optimizing to kriging agent model, find out optimum point and greatest hope improves Point；

Step 6, the optimum point obtained in step 5 and greatest hope are improved two variance smallest point of point as to be added Sampled point, re-start kriging agent model optimizing, until optimum point restrain；The weapon station bracing frame bullet now obtained Property modulus E₀, cartridge box quality m₀, buffer K₀It is overhead weapon station structure optimization parameter；

Step 7, repeat the above steps three to step 5, obtain firing angle be respectively-5 °, 0 °, 15 °, 30 °, 45 °, 60 ° time Overhead weapon station structure optimization parameter, and the optimum structure parameter of each firing angle is updated to the weapon station kinetic simulation of other operating mode In type, find the average structural parameters final structure parameters optimization the most optimizing amplitude maximum.

Preferably, in step 3, w₁=w₃=1, w₂=w₄=10.

Preferably, in step 6, convergence criterion is:

$\frac{{\hat{y}}_{\min }^{k+1}-{\hat{y}}_{\min }^k}{{\hat{y}}_{\min }^k}\≤1\%$

Wherein,It is respectively kth generation, the optimal value of kth+1 generation kriging model.

Preferably, in step 2, Latin hypercube test is used to extract 35 groups of sample points.

Preferably, in step 5, Population in Genetic Algorithms quantity is 44, and crossover probability is 0.7, and mutation probability is 0.05, receives Holding back threshold values is 0.001.

Preferably, the scope E ∈ [1.5,2.5] of bracing frame elastic modulus E.

Preferably, the scope m ∈ [50,130] of cartridge box quality m.

Preferably, the scope K ∈ [500,750] of buffer stiffness K.

The invention has the beneficial effects as follows: the invention provides a kind of weapon station multi-state structure based on Kriging algorithm Optimization method, by designing the optimization of bracing frame elastic modelling quantity, cartridge box quality, buffer rigidity, makes gun muzzle disturbance amount minimum.

Accompanying drawing explanation

Fig. 1 is weapon station multi-state structural optimization method flow chart based on Kriging algorithm of the present invention.

Detailed description of the invention

The present invention is described in further detail below in conjunction with the accompanying drawings, to make those skilled in the art with reference to description literary composition Word can be implemented according to this.

As it is shown in figure 1, the invention provides a kind of weapon station multi-state structural optimization method based on Kriging algorithm, Comprise the following steps:

Step one: select bracing frame elastic modulus E, cartridge box quality m, buffer stiffness K these three structural parameters as excellent The design variable of change problem, shown in the span chart 1 of these three parameter:

Table 1

Step 2: use Latin hypercube EXPERIMENTAL DESIGN to choose the value of E, m, K, obtain 35 groups of sample point (E_i,m_i,K_i), i =1,2 ..., 35.

Step 3, overhead weapon station bracing frame elastic modelling quantity, cartridge box quality, buffer rigidity are respectively set as E_i、m_i、 K_i, overhead weapon station is carried out gun muzzle disturbance test, obtains height to linear velocity mean-square value D_i(v_z), level mean square to linear velocity Value D_i(v_y), height to angular displacement mean-square value D_i(θ_z) and level to angular displacement mean-square value D_i(θ_y), calculate gun muzzle vibration integrated Function

MinF=min (w₁D(v_z)+w₂D(θ_z)+w₃D(v_y)+w₄D(θ_y))

Wherein, w₁、w₂、w₃、w₄For weight coefficient, effect is that the dimension to Vibration Parameter is unified, and value is: w₁=w₃= 1, w₂=w₄=10.

Step 4: generate initial training sample space.By 35 groups of sample point (E_i,m_i,K_i), i=1,2 ..., 35 together with big gun The vibration integrated parameter of mouth generates initial training sample space, and part sample space is as shown in table 2

Table 2

Step 5: on the basis of initial training sample space, utilizes " DACE " Toolbox structure first in Matlab For kriging model, regression function selects binary quadratic polynomial, and correlation function selects Gaussian function, and considers anisotropy Effect, individually gives θ value to each design variable, and scope takes [0.1,20], and initial value is unified is set to 10.Select genetic algorithm As optimized algorithm, arranging population quantity is 44, and crossover probability is 0.7, and mutation probability is 0.05, and convergence threshold values is 0.001.

Kriging agent model is substantially a kind of approximate model [139] based on theory of statistics, its effectiveness and accurately Property is affected little by random error.Kriging agent model, when being predicted unknown point, needs by the most known sampling The information of point, estimates unknown point by this information is weighted combination, and method of weighting is then according to minimizing estimated value error Variance determine, it is therefore contemplated that kriging model is optimum linear unbiased estimate.

Kriging, as the approximate model of a kind of half parametric, is made up of linear regression part and nonparametric part:

In formula, F (β, x) for returning part, multinomial and regression coefficient β by a series of x together decide on:

$\begin{array}{c}F(\mathrm{\β},x)={\mathrm{\β}}_1{f}_1\left(x\right)+{\mathrm{\β}}_2{f}_2\left(x\right)+...+{\mathrm{\β}}_p{f}_p\left(x\right)\\ ==\left[\begin{array}{cccc}{\mathrm{\β}}_1& {\mathrm{\β}}_2& ...& {\mathrm{\β}}_n\end{array}\right]\left[\begin{array}{c}{f}_1\left(x\right)\\ f_2\left(x\right)\\ .\\ .\\ .\\ f_n\left(x\right)\end{array}\right]\\ ==f{\left(x\right)}^T\mathrm{\β}\end{array}$

In Interpolation Process, (β, x) provides overall situation approximation to F, and the polynomial form of x can be chosen as 0 rank, 1 rank or 2 rank.

Z (x) is nonparametric part, provides the approximation of partial deviations in Interpolation Process, has a following statistical property:

$\left\{\begin{array}{c}E\left(z_i\right(x\left)\right)=0\\ Var\left(z_i\right(x\left)\right)={\mathrm{\δ}}_i^2\\ Cov\[z\left(x^i\right),z\left(x^j\right)\]={\mathrm{\δ}}^{2}R\[x^i,x^j,\mathrm{\θ}\]\end{array}\right.$

In formula, E is expectation, and Var is variance, and Cov is covariance, and R is correlation function, and θ is associated vector.

Assume that the sample point set comprising n design variable number known to a group is X=[x¹,x²,…,xⁿ]^T, it is corresponding Functional value be Y=[y¹,y²,…,yⁿ]^T, then after using kriging to carry out interpolation, to any one unknown point response value It is estimated as:

In formula, c is interpolation coefficient.The estimation difference of agent model is:

In formula, F=[f₁,f₂,…,f_n]^T, Z=[z₁,z₂,…,z_n]^T。

In order to ensure the unbiasedness of estimated result, need to make above-mentioned estimation difference is desired for 0:

I.e. have:

F^TC-f (x)=0

Now, the mean square deviation of estimated value is:

In formula,

$\left\{\begin{array}{c}R=R(\mathrm{\θ},x^i,x^j),(i,j=1,2,...,n)\\ r\left(x\right)={\[R\left(\mathrm{\θ},s,x^1\right),R(\mathrm{\θ},s,x^2),...,R(\mathrm{\θ},s,x^n)\]}^T\end{array}\right.$

Kriging model needsMinimum, therefore coefficient c can minimize mean square deviation Optimized model by foundation and solves Draw:

Introducing Lagrange multiplier obtains:

L (c, λ)=σ²(1+c^TRc-2c^Tr)-λ^T(F^Tc-f(x))

Above formula about the gradient of c is:

$\frac{\∂\left(L\right(c,\mathrm{\λ}))}{\∂c}=2{\mathrm{\σ}}^2(Rc-r)-F\mathrm{\λ}$

Can obtain system equation in conjunction with constraints is:

$\left[\begin{array}{cc}R& F\\ F^T& 0\end{array}\right]\left[\begin{array}{c}c\\ \widetilde{\mathrm{\λ}}\end{array}\right]=\left[\begin{array}{c}r\\ f\end{array}\right]$

Can derive further:

$\left\{\begin{array}{c}c=R^{-1}(r-F\widetilde{\mathrm{\λ}})\\ \widetilde{\mathrm{\λ}}=-\frac{\mathrm{\λ}}{2{\mathrm{\σ}}^2}={\left(F^T{R}^{-1}F\right)}^{-1}(F^T{R}^{-1}r-f)\end{array}\right.$

Above formula is substituted into:

The parameter estimation maximum likelihood function of logarithmic form is:

$Ln(\mathrm{\β},{\mathrm{\σ}}^2,\mathrm{\θ})=-\frac{1}{2}\[nln\left(2\mathrm{\π}\right)+{\mathrm{nln\σ}}^2+ln\left|R\right|+\frac{1}{{\mathrm{\σ}}^2}{(y-F\mathrm{\β})}^T{R}^{-1}(y-F\mathrm{\β})\]$

After θ initial value is given, by maximum likelihood function respectively to β and σ²Differentiate, and make it be equal to 0, then can obtain Maximum-likelihood estimation to two parameters is:

Now, kriging is minimum dispersion linear unbiased estimator to the estimation of unknown point:

Step 6: according to above-mentioned initial condition, based on dual kriging Model sequence iteration optimization algorithms, weapon station is tied Structure Parametric optimization problem carries out optimizing, and convergence criterion is:

$\frac{{\hat{y}}_{\min }^{k+1}-{\hat{y}}_{\min }^k}{{\hat{y}}_{\min }^k}\≤1\%$

In formula,It is respectively kth generation, the optimal value of kth+1 generation kriging model.

Result as shown in table 3, table 4, wherein x₁、x₂、x₃The most corresponding bracing frame elastic modelling quantity, cartridge box quality and buffering Device rigidity.

Table 3

Table 4

From characteristic point history, in the searching process of weapon station gun muzzle vibration optimization problem, optimal value is not one Diminish taste, but fluctuate back and forth between-40 to 40, cause the kriging agent model that the reason of this phenomenon is to simulate There is several close minimum points, when the pattern search of epicycle kriging to optimum point through add some points raising accuracy after, separately One close minimum point highlights, and becomes the optimum point of next round kriging model, optimizing the most repeatedly, adds some points, and one Until these several minimum points " are filled and led up ", globe optimum is retained.

Knowable to table 3, table 4, whole optimization process experienced by 26 renewals taking turns kriging model, altogether adds some points 26, The global optimum of convergence is 1.965 eventually, has compared initial value, and objective function optimization amplitude is 24.7%, corresponding structure ginseng Number optimal solution is: bracing frame elastic modelling quantity is 1.913GPa, cartridge box quality is 122.506kg, buffer rigidity 615.69N/mm.

Step 7, employing-5 °, 0 °, 15 °, 30 °, 45 °, 60 ° of these six kinds of firing angles test, and use dual kriging It is solved by Model sequence iteration optimization algorithms respectively, and optimum results is as shown in table 5.

Table 5

As shown in Table 5, the optimal solution that under different firing angles, overhead weapon station structure parameter optimizing model is corresponding is different, and reason exists Change in firing angle makes load direction of transfer change, and the power suffered by parts such as barrel, gudgeon, reel cage, bracket and moment have Changed, so that weapon station integral power characteristic changes, ultimately resulted in the inconsistent of optimal solution.Indicated above, by The optimal solution that single operating mode optimizing obtains, does not illustrate the optimality for other operating mode.

Therefore, for the feature of weapon station difference shooting operating mode correspondence Different structural parameters optimal solution, for showing that one group is fitted With structural parameters widest in area, on the basis of each shooting operation optimization model optimizing result, by the optimum structure of each firing angle Parameter is updated in the weapon station kinetic model of other operating mode；Contrast the optimization that all operating mode gun muzzles are vibrated by each structural parameters Effect, selects the most averagely to optimize one group of maximum structural parameters of amplitude as multi-state optimal solution.Gun muzzle vibration before and after optimization The contrast of comprehensive amount is as shown in table 6, and different optimal solutions are as shown in table 7 to the optimization amplitude of different firing angle kinetic models.

Table 6

Table 7

From result above, having compared the vibration integrated amount of gun muzzle of initial solution, different firing angle optimal solutions are to respective firing angle Gun muzzle vibration degree of optimization of weapon station kinetic model differs, and wherein, seeks the weapon station kinetic model that firing angle is 60 ° The excellent optimal solution obtained is the highest to the degree of optimization of himself kinetic model, gun muzzle vibration suppressioning effect best, optimizes amplitude Being 36.7%, remaining degree of optimization is followed successively by-5 ° of firing angles, 30 ° of firing angles, 0 ° of firing angle, 45 ° of firing angles and 15 ° of firing angles from high to low The optimal solution that kinetic model is corresponding；For overall firing angle operating mode, different firing angle optimal solutions are to all operating mode weapon station kinetics Gun muzzle vibration optimization amplitude of model differs, and even indivedual optimal solutions are vibrated also for gun muzzle of other firing angle kinetic model Deterioration effect (being the situation of negative corresponding to amplitude of variation) can be played, wherein, seek the weapon station kinetic model that firing angle is 60 ° The excellent structural parameters optimal solution obtained, best to the global optimization effect of different operating mode weapon station kinetic model gun muzzle vibrations, Average optimization amplitude is 16.2%, and remaining optimization amplitude is followed successively by-5 ° of firing angles, 30 ° of firing angles, 45 ° of firing angles, 0 ° of firing angle from high to low And the optimal solution that 15 ° of firing angle kinetic models are corresponding.It is seen that, the structure that more the firing angle optimizing of edge, the more limit obtains Parametric optimal solution, its suitability relaxes the good of firing angle than centre, and this illustrates to a certain extent by limiting condition optimizing The optimum structure parameter obtained has to the compatibility relaxing operating mode.

To sum up, the weapon station kinetic model optimizing that firing angle is 60 ° the structural parameters optimal solution obtained is to all operating modes Global optimization effect is ideal, the suitability best, the most also explanation overhead weapon station structural parameters are adjusted to After this prioritization scheme, the adaptability to different operating modes is the strongest.

Although embodiment of the present invention are disclosed as above, but it is not restricted in description and embodiment listed Using, it can be applied to various applicable the field of the invention completely, for those skilled in the art, and can be easily Realizing other amendment, therefore under the general concept limited without departing substantially from claim and equivalency range, the present invention does not limit In specific details with shown here as the legend with description.

Claims (8)

1. a weapon station multi-state structural optimization method based on Kriging algorithm, it is characterised in that comprise the steps:

Step one, the scope E ∈ [E of given overhead weapon station bracing frame elastic modulus E_a,E_b], the scope m ∈ of cartridge box quality m [m_a,m_b], the scope K ∈ [K of buffer stiffness K_a,K_b]；

Step 2, employing Latin hypercube EXPERIMENTAL DESIGN choose the value of E, m, K, obtain N group sample point (E_i,m_i,K_i), i=1, 2,...,N；

Step 3, overhead weapon station bracing frame elastic modelling quantity, cartridge box quality, buffer rigidity are respectively set as E_i、m_i、K_i, right Overhead weapon station carries out gun muzzle disturbance test, obtains height to linear velocity mean-square value D_i(v_z), level is to linear velocity mean-square value D_i (v_y), height to angular displacement mean-square value D_i(θ_z) and level to angular displacement mean-square value D_i(θ_y), calculate the vibration integrated parameter of gun muzzle F_i

F_i=w₁D(v_z)+w₂D(θ_z)+w₃D(v_y)+w₄D(θ_y)

Wherein, w₁、w₂、w₃、w₄For weight coefficient；

Step 4, associating N group sample point (E_i,m_i,K_i) and vibration integrated parameter F of N number of gun muzzle_iConstitute initial training sample point set, Build kriging agent model；

Step 5, use genetic algorithm carry out optimizing to kriging agent model, find out optimum point and greatest hope improves point；

Step 6, the optimum point obtained and greatest hope are improved two variance smallest point of point adopt as to be added in step 5 Sampling point, re-starts kriging agent model optimizing, until optimum point restrains；The weapon station bracing frame springform now obtained Amount E₀, cartridge box quality m₀, buffer K₀It is overhead weapon station structure optimization parameter；

Step 7, repeat the above steps three to step 5, obtain firing angle be respectively-5 °, 0 °, 15 °, 30 °, 45 °, 60 ° time overhead Weapon station structure optimization parameter, and the optimum structure parameter of each firing angle being applied in weapon station, show that average optimization amplitude is Big structural parameters final structure parameters optimization the most.

Weapon station multi-state structural optimization method based on Kriging algorithm the most according to claim 1, its feature exists In, in step 3, w₁=w₃=1, w₂=w₄=10.

Weapon station multi-state structural optimization method based on Kriging algorithm the most according to claim 2, its feature exists In, in step 6, convergence criterion is:

$\frac{{\hat{y}}_{\min }^{k+1}-{\hat{y}}_{\min }^k}{{\hat{y}}_{\min }^k}\≤1\%$

Wherein,It is respectively kth generation, the optimal value of kth+1 generation kriging model.

Weapon station multi-state structural optimization method based on Kriging algorithm the most according to claim 3, its feature exists In, in step 2, use Latin hypercube test to extract 35 groups of sample points.

Weapon station multi-state structural optimization method based on Kriging algorithm the most according to claim 4, its feature exists In, in step 5, Population in Genetic Algorithms quantity is 44, and crossover probability is 0.7, and mutation probability is 0.05, and convergence threshold values is 0.001.

Weapon station multi-state structural optimization method based on Kriging algorithm the most according to claim 5, its feature exists In, the scope E ∈ [1.5,2.5] of bracing frame elastic modulus E.

Weapon station multi-state structural optimization method based on Kriging algorithm the most according to claim 5, its feature exists In, the scope m ∈ [50,130] of cartridge box quality m.

Weapon station multi-state structural optimization method based on Kriging algorithm the most according to claim 5, its feature exists In, the scope K ∈ [500,750] of buffer stiffness K.