CN108733864A - A kind of aircraft wing structure Global sensitivity analysis method based on support vector machines - Google Patents
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Abstract
The present invention proposes that a kind of aircraft wing structure Global sensitivity analysis method based on support vector machines, specific link are：1. using based on barycenter " voronoi " structure (centroidal voronoi tessellation, abbreviation CVT) experimental design method sampled point is obtained, obtain aircraft wing finite element model each corresponding points output valve.2. pair input variable is normalized with output response.3. according to the distribution of the stochastic inputs variable of wing structure and its numerical characteristic, two groups of input samples of sampling are denoted as matrix A, B；4, structural matrix Ci, the matrix by B matrixes i-th row by A matrixes i-th row replace after matrix；5. the aircraft wing agent model built using support vector machines calculates A, B, CiMatrix corresponds to wing structure output response, and y is denoted as respectively after renormalizationA, yB,；6. according to MC methods are simplified, the importance measure index s of each input variable are calculatediWith；7. the importance degree of pair input variable is ranked up, to provide guidance to the fail-safe analysis of wing structure, prediction and optimization.
Description
Technical field：
The present invention relates to security reliability technical fields, and in particular to Reliability Sensitivity Method, more particularly to one
Kind is based on support vector machines aircraft wing structure Global sensitivity analysis method.
Background technology：
With the development of science and technology, modern structure is also gradually increasing crucial and somewhat complex design demand, and each row is each
The machine and equipment of industry becomes increasingly complex, wherein flower of the aircraft as modern industry, complexity is self-evident, same with this
When, the integrity problem of aircraft is also increasingly taken seriously, because its reliability is not only related to the economy profit of country and enterprise
Benefit and reputation, it is also closely bound up with life security.
In security analysis of structure, be primarily upon two aspect the problem of：Fail-safe analysis and sensitivity analysis.Reliably
Property analysis be intended to calculate failure probability and reliability, sensitivity analysis is intended to the uncertainty or distributed constant of research input variable
Influence to output performance statistical property.One of core technology of reliability design is exactly reliability sensitivity analysis, 19th century
Since the sixties, the variable sensitivity index of domestic and international numerous studies structural response, characteristic or index to input variable partial derivative.
This kind of method is sensitivity of partial derivative when taking nominal value using each input variable as the variable, thus substantially office
Portion's sensitivity.Relative to local sensitivity, the importance measure of input variable can be defined as input variable in model not really
Qualitative to respond probabilistic percentage contribution to model output, the importance measure of input variable is also known as global sensitivity.It
The relative importance that there emerged a input variable can be given, to provide guidance to Analysis of structural reliability, prediction and optimization.
Due to some uncontrollable enchancement factors, uncertainty is generally existing, and therefore, understanding and processing are uncertain
The problem of it is most important to the practicability of fail-safe analysis result.In aircraft wing structure, input variable frequently includes very much,
Such as structure size (length, thickness etc.), material parameter (elasticity modulus, Poisson's ratio etc.), external applied load (power, torque etc.),
The uncertainty of temperature etc., these input variables can be transmitted to output (stress, strain, displacement, service life etc. by wing model
Deng), when engineer for aircraft wing structure carry out further research (fail-safe analysis, performance design, risk assessment,
Optimization design) when, a lot of stochastic inputs variable of quantity can increase the fussy degree of problem so that further analysis, which calculates, to be become
It obtains complex.Global sensitivity analysis is carried out to aircraft wing structure, can obtain influencing the defeated of output performance value rule
Enter the importance measure of variable, can then determine successively they experiment or research priority level, that is, determine input variable
Significance sequence, and then provide foundation for follow-up study.For example, some stochastic inputs for influencing very little on output performance become
Amount, can be handled as certainty variable, when optimizing, can be paid the utmost attention to more important random defeated
Enter variable etc..
Traditional global sensitivity method generally use Monte Carlo method is calculated, for this large size of aircraft wing
Complicated limit element artificial module when, Monte Carlo method need it is a large amount of call finite element models, calculation amount is larger, takes
It is long, cause this method to can hardly be applied to engineering in practice.
It is excessive for such calculation amount, long problem is taken, researcher proposes to be replaced emulating using approximate model
The method that model carries out sensitivity analysis.Approximate model, also referred to as agent model are obtained by calling the simulation model of limited number of time
Sampled point is obtained, to build the agent model of engineering challenge, to replace simulation model into line sensitivity with the approximate model
Analysis.Common approximate model has kriging models, radial basic mode type, neural network and support vector machines etc..
There are matrixes to calculate complexity for Kriging models, and model construction difficulty is big.Radial basic mode type needs a large amount of calculating,
Cost is higher.Then there is over-fitting in another aspect neural network.And support vector machines is based on Statistical Learning Theory
A kind of machine learning method, the advantage protruded is that have stronger small-sample learning ability and generalization ability, is asked non-linear
Precision is higher in topic.
Invention content：
What the present invention was implemented is designed to provide a kind of aircraft wing structure global sensitivity based on support vector machines point
Analysis method proposes the performance of computer and calculating cost when conventional digital analog approach method can be avoided to carry out double stratified sample
Huge challenge, can be that the numerous stochastic inputs variables of aircraft wing structure carry out importance rankings, and then to subsequent
Prediction and optimization provide guidance, and a feasible new way is provided targetedly to improve structural model.
Technical solution of the invention：A kind of aircraft wing structure Global sensitivity analysis side based on support vector machines
Method.Its analytic process includes mainly：Build the support vector machines agent model of wing structure；According to the stochastic inputs of wing structure
The distribution of variable and its numerical characteristic, two groups of input samples (every group of sample number is N) of sampling, are denoted as matrix .., B；According to
Matrix A, B, construction sample matrix Ci；According to the support vector machines agent model of wing structure, sample matrix A, B, C are calculatediIt is corresponding
OutputByCalculate stochastic inputs variable xiTwo importance measure indexs：Main measurement index SiWith
Total measurement indexAccording to gained importance measure index, variable importance sequence is carried out；It is sorted by gained variable importance,
Subsequent analysis is instructed.
It further, can be by direct Monte Carlo or Latin hypercube directly according to stochastic variable for matrix A, B
Distribution characteristics is sampled：
Wherein, n indicates that the number of stochastic variable, N indicate that number of samples, A, B are the identical sample matrix of two dimensions.
Then, according to sample matrix A, B, structural matrix C obtained by previous stepi, which is the i-th row of B matrixes by A matrixes
I-th row replace after matrix；
Wherein, n indicates that the number of stochastic variable, N indicate number of samples, and the value range of i is 1~n, i.e. CiMatrix is specific
For C1, C2..., CN；
According to the support vector machines agent model of aircraft wing structure, by existing sample matrix A, B, CiIt substitutes into respectively,
Its corresponding output response is obtained, and carries out renormalization and obtains true output
yA=f (A)
yB=f (B)
Wherein, f (x) indicate input output between mapping relations, herein for input sample matrix substitute into support to
Amount machine agent model obtains output predicted value, obtains really exporting predicted value by renormalization.
Further, stochastic variable is calculated according to the simplification MC methods based on variance
The calculating of wherein importance measure index be applied to total probability formula E (E (and Y | Xi))=E (Y),Respectively by sample matrix A, B, CiMake
The vector that interested output response quautity to input obtained wing structure forms, g0It is matrix yAThe mean value of middle all elements,
That is the desired value of Y,Oeprator " .* " indicates the identical row element sum of products of two column matrix divided by element
Number.
Further, using the importance measure index of the stochastic inputs variable of gained, as needed, to wing structure
The importance degree of input variable is ranked up, to provide guidance to the fail-safe analysis of wing structure, prediction and optimization.
The Global sensitivity analysis method of a kind of aircraft wing structure of the invention, compared to traditional Local sensitivity analysis
Method can feel engineering design kind from the entire range of indeterminacy of input variable to weigh the uncertainty of input variable
Probabilistic percentage contribution of the output performance of interest.
Description of the drawings：
Fig. 1 Global sensitivity analysis method flow diagrams；
The rough schematic of Fig. 2 aircraft wing structures；
Fig. 3 aircraft wing ANSYS model vertical views；
Fig. 4 aircraft wing ANSYS model schematics；
Fig. 5 aircraft wing structure stochastic inputs variable importances estimate result；
Fig. 6 swept-back wing structure node coordinates
Fig. 7 swept-back wing structure truss element numbers are grouped with stochastic variable
Fig. 8 sweepback wing structure tension plate units are numbered to be grouped with stochastic variable
Fig. 9 sweepback wing structure is grouped by shear number with stochastic variable
Specific implementation mode：
With two examples, the present invention is described further below, is carried first with a numerical value Example Verification present invention
The precision of method, then institute's extracting method of the present invention is applied to a swept-back wing wing.
Example 1：Ishigami function examples
Wherein, XiIndependently of each other, it and obeying and is uniformly distributed on section (- π, π), i=1,2,3, a, b are constant, this
In example, a=5, b=0.1 are taken.
This is a Nonlinear Monotone function, is used usually as the test function of sensitivity analysis.
Its each sensitivity index, which can parse, to be acquired, and table 1 lists pair that institute's extracting method of the present invention acquires result and analytic solutions
Than.
1 Ishigami function sensitivity analysis result tables of table
In this example, function model used is nonlinearity, as seen from the above table, the method and parsing that the present invention is carried
Solution is compared, error very little, therefore the present invention has certain practicability and accuracy.
Example 2：Bentwing wing structure
In conjunction with attached drawing and example, the invention will be further described.With the attached sweepback wing structures shown in Fig. 4 of an attached drawing 1-
For.Total is flat full symmetrical about X-Y, i.e., symmetrical about the median plane of structure.The upper half of sweepback wing structure is taken below
Make structure explanation in part.The node coordinate of sweepback wing structure is as shown in Fig. 6.The sweepback wing structure is by 60 tension plate units.
70 by shear unit and 20 truss bar unit compositions.Total is constituted using aluminum alloy materials, and the density of material is
0.0961bs/in3, Poisson's ratio 0.3.Truss rod element number is as shown in Fig. 7, and tension plate unit number is as shown in Fig. 8,
It is as shown in Fig. 9 by shear element number.The load working condition of sweepback wing structure is for example as shown in table 2, wherein X and the equal no-load of Y-direction
Lotus acts on.Elasticity modulus by pulling plate and cross-sectional area and material by shear and rod piece is stochastic inputs variable, a total of
15 variables.Using the displacement at node 44 as output response quautity, Global sensitivity analysis is carried out.Assuming that each stochastic inputs become
Between amount independently of each other, all equal Normal Distributions of parameter, their distributed constant is shown in Table 3：
2 swept-back wing load working condition of table
The distributed constant of 3 sweepback wing structure stochastic variable of table
In this example, all calculating process are calculated by matlab written in code with desktop computer.Complexity is tied
Structure, such as aircraft wing structure then need to use finite element model or agent model without explicit expression formula between input and output
To determine its Implicitly function relationship.Support vector machines used herein establishes agent model.The result of calculation of this example such as attached drawing 5
It is shown：
Variable importance is ordered as it can be seen from the above result of calculation：X1> X15> X3> X10> X6> X12> X13>
X8> X2> X14> X9> X7> X4> X11> X5。
Claims (6)
1. a kind of aircraft wing structure Global sensitivity analysis method based on variance, it is characterised in that following steps：
Step 1：After the distribution and the numerical characteristic that determine the stochastic inputs variable of sampled point number and wing structure, using base
It is obtained in barycenter " voronoi " structure (centroidal voronoi tessellation, abbreviation CVT) experimental design method
Sampled point, by matlab call aircraft wing finite element model, obtain the finite element model each corresponding points output valve.
Step 2：Normalizing is carried out respectively to the input variable trainX output valve trainYs corresponding with sampled point at sampled point
Change, normalizes to [- 1,1], avoid the value effect training result that numerical value is larger.Training Support Vector Machines obtain aircraft wing
SVM agent models.And random sampling obtains test sample testX and testY, test agent model accuracy.
Wherein xiFor the data before normalization,For the data after normalization, xmaxAnd xminFor data before normalization maximum value and
Minimum value.
Step 3：According to the distribution of the stochastic inputs variable of wing structure and its numerical characteristic, two groups of (every group of input samples of sampling
Sample number be N), be denoted as matrix A, B；
Step 4：By sample matrix A, B obtained by step 1, structural matrix Ci, which is the i-th row of B matrixes by A matrixes
I-th arranges the matrix after replacing；
Step 5：Using aircraft wing support vector machines agent model, the sample matrix A obtained by step 3 and step 4 is calculated,
B, Ci, the interested output of corresponding wing structure, and carry out renormalization and obtain true output, it is denoted as y respectivelyA,
yB,
yA=f (A)
Wherein f (x) indicates that input sample matrix obtains output predicted value for people's support vector machines agent model, and carries out anti-normalizing
Change obtains really exporting predicted value
Step 6：By first three step the data obtained, according to MC methods are simplified, the importance measure for calculating each input variable refers to
Mark SiWith
WhereinRespectively by sample matrix
A, B, Ci, as the vector for the interested output response quautity composition for inputting obtained wing structure, g0It is matrix yAIn all members
The mean value of element, the i.e. desired value of Y.Oeprator " .* " indicates of the identical row element sum of products of two column matrix divided by element
Number.
Step 7：The importance measure obtained by step 6 is as a result, carry out the importance degree of the input variable of wing structure
Sequence, to provide guidance to the fail-safe analysis of wing structure, prediction and optimization.The method is sensitive compared to traditional part
Analysis method is spent, the uncertainty of input variable can be weighed to engineering design from the entire range of indeterminacy of input variable
In interested output performance probabilistic percentage contribution.
2. a kind of aircraft wing structure Global sensitivity analysis method based on support vector machines according to claim 1,
It is characterized in that, according to the Joint Distribution of known stochastic inputs variable, sample drawn matrix A, B, further according to the two matrixes,
Structural matrix Ci。
3. a kind of aircraft wing structure Global sensitivity analysis method based on support vector machines according to claim 1,
It is characterized in that, the solution structure output response quautity described in step 5, selects support vector machines agent model method, agent model
Method can effectively approximate Practical Project problem, reduce expensive finite element call number.
4. a kind of aircraft wing structure Global sensitivity analysis method based on variance according to claim 1, feature
It is, the method for the construction sample matrix described in step 3 and step 4 is avoided when conventional digital analogy method solves and needed
The huge calculation amount for carrying out double stratified sample and then bringing.
5. a kind of aircraft wing structure Global sensitivity analysis method based on variance according to claim 1, feature
It is, by the calculating of step 6, two measurement indexs of stochastic variable can be obtained, be main importance measure index S respectivelyiWith it is total
Importance measure index
6. one kind according to claim 1 is based on support vector machines aircraft wing structure Global sensitivity analysis method,
It is characterized in that, it can be by step 6 obtained two kinds of importance surveys office Sensitivity Analysis Method, which is characterized in that can be by step 6
Obtained two kinds of importance degree of determination index carries out the importance ranking of variable, to becoming at random as needed in step 7
The importance of amount carries out comprehensive consideration, and practicability is more preferably.
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