CN102495932A - Finite element model updating method based on response surface modeling and improved particle swarm algorithm - Google Patents

Abstract

The invention relates to a finite element model updating method based on response surface modeling and improved particle swarm algorithm, which solves problems of low efficiency and limited precision of an existing finite element model updating method. The finite element model updating method includes grouping structural parameters, selecting initial iteration points, calculating response values, obtaining a response surface model function by the aid of the least square method, calculating modal frequency values if valid, constructing a fitness function, dividing the structural parameters into an optimal solution group and an inferior solution group according to fitness, carrying out Logistic mapping and inverse mapping for particles of the optimal solution group to obtain the original structural parameters, obtaining current new speeds and positions by means of updating again, calculating fitness function values again, varying particles of the inferior solution group, and calculating fitness of the particles after variation; and determining the new-generation optimal individual and the optimal group, outputting the optimal solution if termination conditions are met, otherwise, continuing iteration. The response surface modeling and the particle swarm algorithm are combined to update a finite element model, and updating efficiency and precision are effectively improved.

Description

A kind of based on response surface modeling and the correction method for finite element model that improves particle cluster algorithm

Technical field

The present invention relates to a kind of based on response surface modeling and the correction method for finite element model that improves particle cluster algorithm.

Background technology

Modern spacecraft adopts hardware and software platform, modular design mostly, and novel spacecraft often adopts just can accomplish design to the improvement of ripe platform, shortens the lead time as far as possible, practices thrift reasearch funds, to adapt to the fast development in market, space.Along with the continuous research and development of finite element analysis software and perfect, result of finite element substitute structure test to a certain extent obtains having the analysis data of certain precision, thus to the structural strength of spacecraft and in orbit state carry out express-analysis.

Finite Element Model Updating is widely used in Aerospace Engineering, and high-precision finite element model is accurately to carry out the basis that structural mechanics characteristic is analyzed.Because factor affecting such as modeling error; Always exist the difference that is difficult to eliminate between result of finite element and the measured result; Utilize the response of structure actual measurement responsive corrections FEM calculation, make that revising the back finite element model calculated response value process consistent with test measurements is the finite element model correction.The finite element model correction utilizes practical structures field measurement response data correction finite element theory Model Calculation data, thereby dwindles the error between theoretical model and the practical structures, makes response and the trial value of revising the back Model Calculation reach unanimity.The performance model correction technique can save some large-sized structure experiments, only makes the parts level as required and verifies and revise, so that revised finite element model can be represented real structural model.Makeover process makes full use of structural test and finite element analysis advantage, with a spot of test figure finite element model is revised, and revises the back model and can replace practical structures to carry out multiple analysis, practices thrift test funds and time.

Summary of the invention

The objective of the invention is in order to solve the existing problem that correction method for finite element model efficient is low, precision is limited, the invention provides a kind of based on response surface modeling and the correction method for finite element model that improves particle cluster algorithm.

Correction method for finite element model based on response surface modeling and improvement particle cluster algorithm of the present invention is realized through following steps:

One, adopts the orthogonal experiment design method design experiment, with structural parameters x=[x ₁, x ₂... x _n] be divided into the k group by varying level, then the structural parameters of k group are expressed as

The k round numbers;

Two, the selected structural parameters x=[x that is used for the tectonic response face ₁, x ₂... x _n] the primary iteration point, be designated as

The primary iteration point is got the mean value of k group place structural parameters;

Three, calculate j group place's response of structure value

as follows with formula (1):

${\hat{y}}_j=a_0+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{a}_i{x}_i+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{b}_i\exp (-\frac{{\left|\right|x_i-\stackrel{\‾}{x_i}\left|\right|}^2}{2{\mathrm{\σ}}^2})---\left(1\right)$

Wherein, x _iBe i structural parameters of corresponding j group,

Be structural parameters x in k the group _iMean value;

It is j group structural parameters corresponding response surface model calculated value; 1≤j≤k, the j round numbers; σ representes the controlled variable in the response surface model;

Four, find the solution the undetermined coefficient a in the formula (1) with the least square rule ₀, a _iAnd b _iThereby, supported vector machine response surface model function;

Five, calculate check point place response surface model calculated value

Judge response surface model function validity, effectively then calculate the model frequency value, Wherein, f _iIt is the corresponding model frequency value of structural parameters of j group; The invalid step 1 of then returning carries out again that parameter is divided into groups and the structure of response surface model function;

Six, according to formula (2) computation structure parameter x=[x ₁, x ₂... x _n] fitness min fit (x),

$\min \mathrm{fit}\left(x\right)=\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{ER}({\hat{f}}_i,f_i)=\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left|\frac{{\hat{f}}_i-f_i}{f_i}\right|---\left(2\right)$

In the formula (2), x=[x ₁, x ₂... x _n] be structural parameters, f _iThe benchmark model frequency values that records for test,

Be the model frequency value that obtains in the step 5;

Seven, the structural parameters x of fitness min fit (x) meanfit (x) that step 6 is obtained is the excellent crowd of separating, and the structural parameters x of fitness min fit (x) meanfit (x) is the inferior solution crowd, and wherein meanfit (x) is a structural parameters fitness mean value;

Eight, according to Logistic mapping formula (3), (4) and (5), the structural parameters x (being particle position) among the excellent crowd of separating that step 7 is obtained maps to chaotic space and carries out Chaos Search, and the gained Chaos Variable reflects that penetrating go back to former design space obtains former design variable x _i(being structural parameters) is again with former design variable x _iCalculate the fitness function value by formula (2);

cx _i+1＝μcx _i(1-cx _i) (3)

cx _i＝(x _i-x _i?min)/(x _i?max-x _i?min) (4)

x _i＝x _i?min+cx _i(x _i?max-x _i?min) (5)

μ is a control variable, (3.5699456,4] between value; Cx _iBe former design variable x _iCorresponding Chaos Variable and cx _i∈ (0,1), x _{I max}, x _{I min}Be x _iMaximal value and minimum value; Former design space is that structural parameters in the step 1 constitute;

Nine, the Chaos Variable cx that step 8 is obtained _iCarry out the renewal of particle colony (being structural parameters) speed and position as the point of the primary iteration in the particle cluster algorithm; Particle among the wherein excellent crowd of separating (being structural parameters among the excellent crowd of separating) upgrades by speed and evolution formula and obtains current new speed and position and calculate the fitness function value by formula (2) again; The more new formula of speed and position is formula (6), as follows:

$\left\{\begin{array}{c}{v_{\mathrm{id}}}^{t+1}=\mathrm{\ω}{v_{\mathrm{id}}}^t{+c}_1{r}_1(p_{\mathrm{id}}-{x_{\mathrm{id}}}^t)+c_2{r}_2(p_{\mathrm{gd}}-{x_{\mathrm{gd}}}^t)\\ {x_{\mathrm{id}}}^{t+1}=x_{\mathrm{id}}^t+{v_{\mathrm{id}}}^{t+1}\end{array}\right.---\left(6\right)$

In the formula (6),

The speed of i particle (structural parameters) d dimension when being the t+1 time iteration,

The position of i particle (structural parameters) d dimension when being the t+1 time iteration,

Be the d dimension optimal location of i particle (structural parameters) when the t time iteration stops,

Be the d dimension optimal location of whole particle colony when the t time iteration stops, c ₁The memory capability and the c of the historical optimal location that the expression particle lives through oneself ₁＞0, c ₂The expression particle is to the memory capability and the c of colony's optimal location of being experienced in the whole colony flight course ₂＞0, r ₁And r ₂Be equally distributed random number between [0,1], inertial factor ω>=0;

Ten, the structural parameters (being particle) among the inferior solution crowd who step 7 is obtained make a variation and calculate variation back particle position and speed by formula (7), and variation formula (7) is:

$\left\{\begin{array}{c}{v_{\mathrm{id}}}^{t+1}=\mathrm{\ω}{v_{\mathrm{id}}}^t{+c}_1{r}_1(p_{\mathrm{id}}-{x_{\mathrm{id}}}^t)+c_2{r}_2(p_{\mathrm{gd}}-{x_{\mathrm{gd}}}^t)\\ {x_{\mathrm{id}}}^{t+1}=x_{\mathrm{id}}^t+\mathrm{\ηN}\left(\mathrm{0,1}\right){v_{\mathrm{id}}}^{t+1}\end{array}\right.---\left(7\right)$

Each parameter meaning cotype (6) is the same in the formula (7); Wherein, η is constant or self-regulating variable; Be used for controlling the disturbance step-length; Computing formula is generally set η ∈ (0.1 0.5) for

, and N (0,1) is for obeying Gaussian (0; 1) distributed random variable,

is variation back particle;

11, step 9 and step 10 are searched for gained particle (being structural parameters) calculates particle (being structural parameters) respectively according to formula (2) ideal adaptation degree value min fit (x), select the colony optimal particle of the minimum particle of ideal adaptation degree value as a new generation;

12, whether the Search Results in the determining step 11 satisfies the algorithm end condition that sets,, satisfied then export optimum solution, otherwise the continuation iteration, wherein, min fit (x)≤0.01 is an end condition.

Structural parameters x=[x among the present invention ₁, x ₂... x _n] in the value of n be those skilled in the art's common practise; Select different number of parameters according to different model; Generally to be first analytical model the inside analyze this Several Parameters the inside then to the high Several Parameters of result of calculation influence degree, and which is arranged is uncertain; Or need revise, confirm the structural parameters number, i.e. the value of n.

Select suitable orthogonal array according to structural parameters number and actual conditions when in the step 1 of the present invention structural parameters being divided into groups; Orthogonal array commonly used all can be found on the existing relevant books of orthogonal design; General as long as number of parameters is identical, selected packet mode is the same.The span of k can be confirmed according to prior art for those skilled in the art in the step 1.

In the formula of step 3 of the present invention (1), σ representes the controlled variable in the response surface model, confirms parameter value according to practical problems, general structural parameters scope radius.Adopt method such as finite element to calculate in the step 3.

(Rootmean Squared Error is RMSE) with coefficient of determination R to adopt relative root-mean-square error RMSE in the step 5 of the present invention ²Judge response surface model validity; Computing formula is respectively suc as formula shown in (8) and the formula (9): effective then can the response surface of being constructed be used for the structure (compute mode frequency values) of fitness function, the invalid step 1 of then returning carries out again that parameter is divided into groups and the response surface structure.

$\mathrm{RMSE}=\frac{1}{k\stackrel{\‾}{y}}\sqrt{\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{(y_j-{\hat{y}}_j)}^2}---\left(8\right)$

$R^2=\frac{\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{({\hat{y}}_j-\stackrel{\‾}{y})}^2}{\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{(y_j-\stackrel{\‾}{y})}^2}---\left(9\right)$

Wherein, in formula (8) and the formula (9), k is the parameter packet count of being confirmed by test design, y _jBe the corresponding actual measurement responses of j group structural parameters,

Be j group structural parameters corresponding response surface model function calculation value,

Mean value for all k group structural parameters actual measurement responses.RMSE → 0 (generally getting RMSE ∈ (0 0.1)) and R ²→ 1 (generally gets R ²∈ (0.9 1)) expression response surface error is little, and fitting precision is high.

μ in the step 8 of the present invention=4 o'clock are complete chaos state, this moment cx _iTraversal in (0,1) scope.Can prove that Logistic is mapped with three fixed points (0.25,0.5,0.75), in the structural parameters assignment procedure of step 5 to step 7, should avoid the use of these fixed points.

Adopting particle cluster algorithm in the step 9 of the present invention, is particle colony thus, and the parameter that corresponds to response surface model the inside is exactly structural parameters.

The present invention introduces particle cluster algorithm with the grouping control strategy, at first particle colony is divided into excellent separating and two big types of inferior solutions by fitness, excellent separating is introduced Chaos Search mechanism, to reduce the probability that it is absorbed in local optimum; Inferior solution is made a variation, to improve himself quality and search efficiency.Secondly the present invention proposes linearity-Gauss and makes up nuclear SVMs response surface (being the response surface modeling); This response surface combines the linear fit ability of linear kernel and the nonlinear fitting function of gaussian kernel, can carry out the high precision match to linear system and NLS.Response surface modeling and particle cluster algorithm combined finite element model is revised, can effectively improve the efficient and the precision of correction.

Be applied to the common used material cellular board of aerospace field is revised based on response surface modeling and the correction method for finite element model that improves particle cluster algorithm with of the present invention; And then revise certain model dummy satellite; Confirmed that this correction algorithm can obviously improve finite element model correction efficient; Practice thrift design of satellites reasearch funds and manufacturing cost, shortened the satellite lead time, helped advancing hardware and software platform, the modular design of modern spacecraft.The present invention can be widely used in and the finite element model correction of each model aerospace vehicle, also can use this technology to the model correction of Other Engineering structure.

Of the present invention is to be that calculate on the basis with finite element software MSC/PATRAN/NASTRAN and software for mathematical computing MATLAB based on response surface modeling and the correction method for finite element model that improves particle cluster algorithm; Wherein MATLAB is used for divide into groups control particle cluster algorithm and linearity-Gauss made up and examines the calculating of programming of SVMs response surface, can adopt MSC/PATRAN/NASTRAN to be used for realistic model is set up finite element model.

Embodiment

Technical scheme of the present invention is not limited to following cited embodiment, also comprises the combination in any between each embodiment.

Embodiment one: the correction method for finite element model based on response surface modeling and improvement particle cluster algorithm of this embodiment is realized through following steps:

One, adopts the orthogonal experiment design method design experiment, with structural parameters x=[x ₁, x ₂... x _n] be divided into the k group by varying level, then the structural parameters of k group are expressed as

The k round numbers;

Two, the selected structural parameters x=[x that is used for the tectonic response face ₁, x ₂... x _n] the primary iteration point, be designated as

The primary iteration point is got the mean value of k group place structural parameters;

Three, calculate j group place's response of structure value as follows with formula (1):

${\hat{y}}_j=a_0+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{a}_i{x}_i+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{b}_i\exp (-\frac{{\left|\right|x_i-\stackrel{\‾}{x_i}\left|\right|}^2}{2{\mathrm{\σ}}^2})---\left(1\right)$

Wherein, x _iBe i structural parameters of corresponding j group, Be structural parameters x in k the group _iMean value;

It is j group structural parameters corresponding response surface model calculated value; 1≤j≤k, the j round numbers; σ representes the controlled variable in the response surface model;

Four, find the solution the undetermined coefficient a in the formula (1) with the least square rule ₀, a _iAnd b _iThereby, supported vector machine response surface model function;

Five, calculate check point place response surface model calculated value

Judge response surface model function validity, effectively then calculate the model frequency value, Wherein, f _iIt is the corresponding model frequency value of structural parameters of j group; The invalid step 1 of then returning carries out again that parameter is divided into groups and the structure of response surface model function;

Six, according to formula (2) computation structure parameter x=[x ₁, x ₂... x _n] fitness min fit (x),

$\min \mathrm{fit}\left(x\right)=\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{ER}({\hat{f}}_i,f_i)=\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left|\frac{{\hat{f}}_i-f_i}{f_i}\right|---\left(2\right)$

In the formula (2), x=[x ₁, x ₂... x _n] be structural parameters, f _iThe benchmark model frequency values that records for test,

Be the model frequency value that obtains in the step 5;

Seven, the structural parameters x of fitness min fit (x) meanfit (x) that step 6 is obtained is the excellent crowd of separating, and the structural parameters x of fitness min fit (x) meanfit (x) is the inferior solution crowd, and wherein meanfit (x) is a structural parameters fitness mean value;

Eight, according to Logistic mapping formula (3), (4) and (5), the structural parameters x (being particle position) among the excellent crowd of separating that step 7 is obtained maps to chaotic space and carries out Chaos Search, and the gained Chaos Variable reflects that penetrating go back to former design space obtains former design variable x _i(being structural parameters) is again with former design variable x _iCalculate the fitness function value by formula (2);

cx _i+1＝μcx _i(1-cx _i) (3)

cx _i＝(x _i-x _i?min)/(x _i?max-x _i?min) (4)

x _i＝x _i?min+cx _i(x _i?max-x _i?min) (5)

μ is a control variable, (3.5699456,4] between value; Cx _iBe former design variable x _iCorresponding Chaos Variable and cx _i∈ (0,1), x _{I max}, x _{I min}Be x _iMaximal value and minimum value; Former design space is that structural parameters in the step 1 constitute;

Nine, the Chaos Variable cx that step 8 is obtained _iCarry out the renewal of particle colony (being structural parameters) speed and position as the point of the primary iteration in the particle cluster algorithm; Particle among the wherein excellent crowd of separating (being structural parameters among the excellent crowd of separating) upgrades by speed and evolution formula and obtains current new speed and position and calculate the fitness function value by formula (2) again; The more new formula of speed and position is formula (6), as follows:

$\left\{\begin{array}{c}{v_{\mathrm{id}}}^{t+1}=\mathrm{\ω}{v_{\mathrm{id}}}^t{+c}_1{r}_1(p_{\mathrm{id}}-{x_{\mathrm{id}}}^t)+c_2{r}_2(p_{\mathrm{gd}}-{x_{\mathrm{gd}}}^t)\\ {x_{\mathrm{id}}}^{t+1}=x_{\mathrm{id}}^t+{v_{\mathrm{id}}}^{t+1}\end{array}\right.---\left(6\right)$

In the formula (6),

The speed of i particle (structural parameters) d dimension when being the t+1 time iteration,

The position of i particle (structural parameters) d dimension when being the t+1 time iteration,

Be the d dimension optimal location of i particle (structural parameters) when the t time iteration stops,

Be the d dimension optimal location of whole particle colony when the t time iteration stops, c ₁The memory capability and the c of the historical optimal location that the expression particle lives through oneself ₁＞0, c ₂The expression particle is to the memory capability and the c of colony's optimal location of being experienced in the whole colony flight course ₂＞0, r ₁And r ₂Be equally distributed random number between [0,1], inertial factor ω>=0;

Ten, the structural parameters (being particle) among the inferior solution crowd who step 7 is obtained make a variation and calculate variation back particle position and speed by formula (7), and variation formula (7) is:

$\left\{\begin{array}{c}{v_{\mathrm{id}}}^{t+1}=\mathrm{\ω}{v_{\mathrm{id}}}^t{+c}_1{r}_1(p_{\mathrm{id}}-{x_{\mathrm{id}}}^t)+c_2{r}_2(p_{\mathrm{gd}}-{x_{\mathrm{gd}}}^t)\\ {x_{\mathrm{id}}}^{t+1}=x_{\mathrm{id}}^t+\mathrm{\ηN}\left(\mathrm{0,1}\right){v_{\mathrm{id}}}^{t+1}\end{array}\right.---\left(7\right)$

Each parameter meaning cotype (6) is the same in the formula (7); Wherein, η is constant or self-regulating variable; Be used for controlling the disturbance step-length; Computing formula is generally set η ∈ (0.1 0.5) for

, and N (0,1) is for obeying Gaussian (0; 1) distributed random variable,

is variation back particle;

11, step 9 and step 10 are searched for gained particle (being structural parameters) calculates particle (being structural parameters) respectively according to formula (2) ideal adaptation degree value min fit (x), select the colony optimal particle of the minimum particle of ideal adaptation degree value as a new generation;

12, whether the Search Results in the determining step 11 satisfies the algorithm end condition that sets,, satisfied then export optimum solution, otherwise the continuation iteration, wherein, min fit (x)≤0.01 is an end condition.

The response surface modeling method that adopts in this embodiment (being that linearity-Gauss makes up nuclear SVMs response surface method) comprises the steps (being that step 1 is to step 5) briefly:

(1) selected primary iteration point is generally got the average point;

(2) select the test design method design experiment, select kernel function, stochastic variable is pressed varying level divide into groups;

(3) with each horizontal parameter group place structural response of numerical calculations such as finite element;

(4) find the solution weighting matrix, find the solution undetermined coefficient with the least square rule then, thereby confirm SVMs response surface function;

Calculate check point place response surface model calculated value, judge response surface model validity, effectively then can be used for further calculating, otherwise continue iteration.

The process of the particle cluster algorithm of grouping control strategy in this embodiment comprises the steps: to brief overview

(1) random initializtion population parameter (being structural parameters selected in the step 1) is divided into groups to particle according to each particle fitness in the colony, and the high person of fitness is the excellent crowd that separates, and the low person of fitness is the inferior solution crowd;

(2) according to the Logistic mapping, particle position among the excellent crowd of separating is mapped to chaotic space carry out Chaos Search, the reflection of gained Chaos Variable is penetrated go back to former design space and is obtained former design variable, and calculates its fitness function value;

(3) particle obtains current new speed and position and recomputates the fitness function value by speed and the renewal of evolution formula among the excellent crowd of separating;

(4) particle makes a variation and calculates variation back particle fitness among the inferior solution crowd;

(5) compare ideal adaptation degree and colony's optimal-adaptive degree, determine individual optimum and colony's optimum of a new generation;

(6) judge whether Search Results satisfies the algorithm end condition, satisfied then export optimum solution, otherwise continue iteration.

This embodiment is introduced particle cluster algorithm with the grouping control strategy, at first particle colony is divided into excellent separating and two big types of inferior solutions by fitness, excellent separating is introduced Chaos Search mechanism, to reduce the probability that it is absorbed in local optimum; Inferior solution is made a variation, to improve himself quality and search efficiency.Secondly the present invention proposes linearity-Gauss and makes up nuclear SVMs response surface (being the response surface modeling); This response surface combines the linear fit ability of linear kernel and the nonlinear fitting function of gaussian kernel, can carry out the high precision match to linear system and NLS.Response surface modeling and particle cluster algorithm combined finite element model is revised, can effectively improve the efficient and the precision of correction.

The correction method for finite element model based on response surface modeling and improvement particle cluster algorithm of this embodiment is applied to the common used material cellular board of aerospace field is revised; And then revise certain model dummy satellite; Confirmed that this correction algorithm can obviously improve finite element model correction efficient; Practice thrift design of satellites reasearch funds and manufacturing cost, shortened the satellite lead time, helped advancing hardware and software platform, the modular design of modern spacecraft.

Present embodiment can be widely used in and the FEM model correction of each model aerospace vehicle, also can use this technology to the model correction of Other Engineering structure.

Embodiment two: this embodiment and embodiment one are different is that σ representes structural parameters x=[x in the formula (1) of step 3 ₁, x ₂... x _n] radius of scope.Other step and parameter are identical with embodiment one.

Embodiment three: what this embodiment was different with embodiment one or two is that (Rootmean Squared Error is RMSE) with coefficient of determination R for the relative root-mean-square error RMSE of employing in the step 5 ²Judge response surface model validity, computing formula is respectively suc as formula shown in (8) and the formula (9): effective then can the response surface of being constructed be used for the structure of fitness function, invalidly return then that step 1 is carried out the parameter grouping again and response surface is constructed.

$\mathrm{RMSE}=\frac{1}{k\stackrel{\‾}{y}}\sqrt{\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{(y_j-{\hat{y}}_j)}^2}---\left(8\right)$

$R^2=\frac{\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{({\hat{y}}_j-\stackrel{\‾}{y})}^2}{\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{(y_j-\stackrel{\‾}{y})}^2}---\left(9\right)$

Wherein, in formula (8) and the formula (9), k is the parameter packet count of being confirmed by test design, y _jBe the corresponding actual measurement responses of j group structural parameters,

Be j group structural parameters corresponding response surface model function calculation value, Mean value for all k group structural parameters actual measurement responses.RMSE → 0 and R ²→ 1 expression response surface error is little, and fitting precision is high.

Other step and parameter are identical with embodiment one or two.

Embodiment four: this embodiment and embodiment one, two or three are different is that μ in the step 8=4 o'clock are complete chaos state, this moment cx _iTraversal in (0,1) scope.

Employing is revised cellular board and dummy satellite based on response surface modeling and the correction method for finite element model that improves particle cluster algorithm, and its step is consistent with embodiment one described content, and wherein, σ is structural parameters x=[x in the formula of step 3 (1) ₁, x ₂... x _n] radius of scope, in the step 5 by embodiment relative root-mean-square error RMSE of three described employings and coefficient of determination R ²Judge response surface model validity.And combine with sandwich battenboard Theoretical Calculation cellular board and satellite equivalent structure parameter; Use the design that makes an experiment of test design method based on orthogonal design; Thereby the influence of frequency response is confirmed to be used to construct the corrected parameter of treating that linearity-Gauss makes up nuclear SVMs response surface through each structural parameters of F value check judgement; And confirm the weighting matrix of response surface kernel function and then the structural parameters in definite embodiment one described step 1 according to the parameter influence degree.

With the optimum solution substitution finite element model of output, then cellular board and dummy satellite calculated mass improve, and carry out multiple analytical calculation.Effectively improve efficient and the precision of revising.

Claims (4)

1. one kind based on response surface modeling and the correction method for finite element model that improves particle cluster algorithm, it is characterized in that realizing through following steps based on response surface modeling and the correction method for finite element model that improves particle cluster algorithm:

One, adopts the orthogonal experiment design method design experiment, with structural parameters x=[x ₁, x ₂... x _n] be divided into the k group by varying level, then the structural parameters of k group are expressed as

The k round numbers;

Two, the selected structural parameters x=[x that is used for the tectonic response face ₁, x ₂... x _n] the primary iteration point, be designated as

The primary iteration point is got the mean value of k group place structural parameters;

Three, calculate j group place's response of structure value

as follows with formula (1):

${\hat{y}}_j=a_0+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{a}_i{x}_i+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{b}_i\exp (-\frac{{\left|\right|x_i-\stackrel{\‾}{x_i}\left|\right|}^2}{2{\mathrm{\σ}}^2})---\left(1\right)$

Wherein, x _iBe i structural parameters of corresponding j group,

Be structural parameters x in k the group _iMean value; It is j group structural parameters corresponding response surface model calculated value; 1≤j≤k, the j round numbers; σ representes the controlled variable in the response surface model;

Four, find the solution the undetermined coefficient a in the formula (1) with the least square rule ₀, a _iAnd b _iThereby, supported vector machine response surface model function;

Five, calculate check point place response surface model calculated value

Judge response surface model function validity, effectively then calculate the model frequency value,

Wherein, f _iIt is the corresponding model frequency value of structural parameters of j group; The invalid step 1 of then returning carries out again that parameter is divided into groups and the structure of response surface model function;

Six, according to formula (2) computation structure parameter x=[x ₁, x ₂... x _n] fitness min fit (x),

$\min \mathrm{fit}\left(x\right)=\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{ER}({\hat{f}}_i,f_i)=\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left|\frac{{\hat{f}}_i-f_i}{f_i}\right|---\left(2\right)$

In the formula (2), x=[x ₁, x ₂... x _n] be structural parameters, f _iThe benchmark model frequency values that records for test,

Be the model frequency value that obtains in the step 5;

Seven, the structural parameters x of the fitness min fit (x) that step 6 is obtained≤meanfit (x) is the excellent crowd of separating, and the structural parameters x of fitness min fit (x)>=meanfit (x) is the inferior solution crowd, and wherein meanfit (x) is a structural parameters fitness mean value;

Eight, according to Logistic mapping formula (3), (4) and (5), the structural parameters x among the excellent crowd of separating that step 7 is obtained maps to chaotic space and carries out Chaos Search, and the gained Chaos Variable reflects that penetrating go back to former design space obtains former design variable x _i, again with former design variable x _iCalculate the fitness function value by formula (2);

cx _i+1＝μcx _i(1-cx _i) (3)

cx _i＝(x _i-x _i?min)/(x _i?max-x _i?min) (4)

x _i＝x _i?min+cx _i(x _i?max-x _i?min) (5)

μ is a control variable, (3.5699456,4] between value; Cx _iBe former design variable x _iCorresponding Chaos Variable and cx _i∈ (0,1), x _{I max}, x _{I min}Be x _iMaximal value and minimum value; Former design space is that structural parameters in the step 1 constitute;

Nine, the Chaos Variable cx that step 8 is obtained _iCarry out the renewal of particle colony (being structural parameters) speed and position as the point of the primary iteration in the particle cluster algorithm; Particle upgrades by speed and evolution formula and obtains current new speed and position and calculate the fitness function value by formula (2) again among the wherein excellent crowd of separating; The more new formula of speed and position is formula (6), as follows:

$\left\{\begin{array}{c}{v_{\mathrm{id}}}^{t+1}=\mathrm{\ω}{v_{\mathrm{id}}}^t{+c}_1{r}_1(p_{\mathrm{id}}-{x_{\mathrm{id}}}^t)+c_2{r}_2(p_{\mathrm{gd}}-{x_{\mathrm{gd}}}^t)\\ {x_{\mathrm{id}}}^{t+1}=x_{\mathrm{id}}^t+{v_{\mathrm{id}}}^{t+1}\end{array}\right.---\left(6\right)$

In the formula (6),

The speed of i particle d dimension when being the t+1 time iteration, The position of i particle d dimension when being the t+1 time iteration,

Be the d dimension optimal location of i particle when the t time iteration stops,

Be the d dimension optimal location of whole particle colony when the t time iteration stops, c ₁The memory capability and the c of the historical optimal location that the expression particle lives through oneself ₁＞0, c ₂The expression particle is to the memory capability and the c of colony's optimal location of being experienced in the whole colony flight course ₂＞0, r ₁And r ₂Be equally distributed random number between [0,1], inertial factor ω>=0;

Ten, the structural parameters among the inferior solution crowd who step 7 is obtained make a variation and calculate variation back particle position and speed by formula (7), and variation formula (7) is:

$\left\{\begin{array}{c}{v_{\mathrm{id}}}^{t+1}=\mathrm{\ω}{v_{\mathrm{id}}}^t{+c}_1{r}_1(p_{\mathrm{id}}-{x_{\mathrm{id}}}^t)+c_2{r}_2(p_{\mathrm{gd}}-{x_{\mathrm{gd}}}^t)\\ {x_{\mathrm{id}}}^{t+1}=x_{\mathrm{id}}^t+\mathrm{\ηN}\left(\mathrm{0,1}\right){v_{\mathrm{id}}}^{t+1}\end{array}\right.---\left(7\right)$

Each parameter meaning cotype (6) is the same in the formula (7); Wherein, η is constant or self-regulating variable; Be used for controlling the disturbance step-length; Computing formula is

sets η ∈ (0.1 0.5), and N (0,1) is for obeying Gaussian (0; 1) distributed random variable,

is variation back particle;

11, step 9 and step 10 are searched for the gained particle calculates particle respectively according to formula (2) ideal adaptation degree value min fit (x), select the colony optimal particle of the minimum particle of ideal adaptation degree value as a new generation;

12, whether the Search Results in the determining step 11 satisfies the algorithm end condition that sets, satisfied then export optimum solution, otherwise the continuation iteration, wherein, min fit (x)≤0.01 is an end condition.

2. according to claim 1 a kind of based on response surface modeling and the correction method for finite element model that improves particle cluster algorithm, it is characterized in that the middle σ of formula (1) of step 3 representes structural parameters x=[x ₁, x ₂... x _n] radius of scope.

3. according to claim 1 and 2 a kind of based on response surface modeling and the correction method for finite element model that improves particle cluster algorithm, it is characterized in that adopting in the step 5 relative root-mean-square error RMSE and coefficient of determination R ²Judge response surface model validity, computing formula is respectively suc as formula shown in (8) and the formula (9): effective then can the response surface of being constructed be used for the structure of fitness function, invalidly return then that step 1 is carried out the parameter grouping again and response surface is constructed.

$\mathrm{RMSE}=\frac{1}{k\stackrel{\‾}{y}}\sqrt{\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{(y_j-{\hat{y}}_j)}^2}---\left(8\right)$

$R^2=\frac{\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{({\hat{y}}_j-\stackrel{\‾}{y})}^2}{\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{(y_j-\stackrel{\‾}{y})}^2}---\left(9\right)$

Wherein, in formula (8) and the formula (9), k is the parameter packet count of being confirmed by test design, y _jBe the corresponding actual measurement responses of j group structural parameters,

Be j group structural parameters corresponding response surface model function calculation value,

Mean value for all k group structural parameters actual measurement responses.RMSE → 0 and R ²→ 1 expression response surface error is little, and fitting precision is high.

4. according to claim 1 and 2 a kind of based on response surface modeling and the correction method for finite element model that improves particle cluster algorithm, it is characterized in that μ in the step 8=4 o'clock are complete chaos state, this moment cx _iTraversal in (0,1) scope.