CN109325284B - Honeycomb structure control surface equivalent parameter strong robustness identification method considering uncertainty - Google Patents

Honeycomb structure control surface equivalent parameter strong robustness identification method considering uncertainty Download PDF

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CN109325284B
CN109325284B CN201811071742.8A CN201811071742A CN109325284B CN 109325284 B CN109325284 B CN 109325284B CN 201811071742 A CN201811071742 A CN 201811071742A CN 109325284 B CN109325284 B CN 109325284B
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王磊
莫江
刘东亮
夏海军
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Abstract

The invention discloses a honeycomb structure control surface equivalent parameter strong robustness identification method considering uncertainty. And then, combining a static force-based model equivalent method with a genetic algorithm, and further equating the honeycomb equivalent model into a plate structure. Through the equivalent process, the response of the plate structure model under the load is very close to that of the original model of the control surface. The method considers the influence of uncertainty of the elastic parameters of the structure on simplification of the control surface model, provides a robustness index based on a non-probability interference model, and obtains the robustness identification result of the elastic modulus of the structure under the action of a plurality of working conditions.

Description

Honeycomb structure control surface equivalent parameter strong robustness identification method considering uncertainty
Technical Field
The invention relates to the technical field of uncertainty structure model equivalence, in particular to a strong robustness identification method of honeycomb structure control surface equivalent parameters considering uncertainty. The method can provide a theoretical method for equivalently simplifying the model of the honeycomb structure of the control surface containing uncertain parameters into a plate structure.
Background
The structure dynamic load identification belongs to the inverse problem of structure dynamics, and the dynamic load borne by the structure is inversely calculated according to the dynamic characteristics of a known structure system and the actually measured dynamic response, so that the limitation of objective engineering conditions that external excitation is difficult to directly measure or can not be measured under a complex service environment is overcome. The determination of the dynamic load is one of the keys for realizing the design of the structural load, which is particularly important for realizing the lightweight design of the air-breathing hypersonic aircraft structure. The inverse problem is generally an ill-posed problem and a nonlinear problem, and dynamic load identification is no exception. Due to the unsuitability and nonlinearity of the vibration inversion problem, it is difficult to develop an efficient and practical inversion method. Nevertheless, because the exact dynamic load can provide reliable basis for problems such as power design, power optimization, shock absorption and vibration isolation, the method is an important guarantee for the reliability and safety of engineering structures.
The importance of the dynamic load identification problem is widely recognized, however, most of the current researches on the dynamic load identification of the air-breathing hypersonic aircraft are still in theoretical research and verification stages, and the success of research results in the practical application of engineering is rarely reported. The method is used for solving the problems that the universality of a rigidity high-precision equivalent model under the multiple working conditions of a complex model and the dynamic distribution load of a nonlinear structure system under a low signal-to-noise ratio is difficult to recognize robust and the like in the current mainstream load recognition method under the application environment of cross influence of the complex load working condition and the multiple source uncertainty in the full flight envelope of the air-breathing hypersonic aircraft. To simplify the problem, the model needs to be simplified. Because both the material parameters and the load values of the model have certain uncertainty, a structural parameter equivalent strong robustness identification model needs to be constructed aiming at the uncertainty so as to realize reasonable equivalence of the uncertainty model.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, and provides the honeycomb structure control surface equivalent parameter strong robustness identification method considering uncertainty. In the invention, the uncertainty of the honeycomb structure of the actual control surface is considered, the equivalent entity elastic modulus of the honeycomb structure is calculated by adopting an equivalent formula, and then aiming at the characteristics of the actual structure of the control surface, a shell unit and an entity unit are used for dividing grids to obtain a honeycomb equivalent control surface model; and then combining a model equivalent method based on static force with a genetic algorithm to further equate the honeycomb equivalent model into a plate structure. The response of the plate structure model obtained by the method under the action of load is very close to that of the original model of the control surface, and a reasonable simplified model of the control surface can be provided.
The technical scheme adopted by the invention is as follows: a strong robustness identification method for honeycomb structure control surface equivalent parameters considering uncertainty can provide a theoretical method for equivalently simplifying a model of a honeycomb structure of a control surface containing uncertainty parameters into a plate structure, and the method comprises the following implementation steps:
the method comprises the following steps: simplifying the honeycomb of the model into a solid structure through a mechanical property equivalent form, constructing a control surface honeycomb equivalent structure, and obtaining an equivalent mechanical parameter formula of the control surface honeycomb sandwich structure:
Figure BDA0001799649780000021
wherein, E s And G s The elastic modulus and the shear modulus of the sandwich material are respectively, t is the thickness of the thin honeycomb wall, nt is the thickness of the thick honeycomb wall, l is the length of a regular hexagon forming the honeycomb, and the thickness of the honeycomb sandwich is h c =b,ρ s Is the density of the cell; e cx ,E cy ,E cz Respectively, the modulus of elasticity, mu, in the plane of the honeycomb structure along the x, y, z-axis directions xyyzxz Poisson's ratio, G, along the x, y, z axes of the honeycomb structure, respectively cxy ,G cyz ,G czx Transverse shear modulus in xoy, yoz, zox plane, respectively;
step two: the honeycomb equivalent finite element model of the control surface is equivalent into a plate structure through a model identification method according to the principle of rigidity equivalence, the control surface structure is divided into subareas according to the difference of different subarea control surface thicknesses, and the elasticity modulus is respectively endowed to different subareas:
E 1 ,E 2 ,…,E n
wherein n represents the number of control surface partitions;
step three: setting the elastic parameter of the honeycomb equivalent structure as the number of intervals by considering the dispersibility of the structural material;
step four: considering the dispersibility of aircraft structural materials, simplifying displacement interval vectors of a model under a plurality of load working conditions
Figure BDA0001799649780000031
Displacement interval vector corresponding to position of accurate model
Figure BDA0001799649780000032
Establishing a robustness index by a non-probability interference model:
Figure BDA0001799649780000033
wherein, the first and the second end of the pipe are connected with each other,u i,r and
Figure BDA0001799649780000034
the lower bound and the upper bound of the node displacement of the ith degree of freedom of the simplified structure respectively,u i,a and
Figure BDA0001799649780000035
lower and upper bounds, K, of the displacement of the node of the ith degree of freedom of the precise structure j To simplify the stiffness of the jth region of the model, Δ K j Is the amount of change in stiffness; subscripts i, r and a represent the ith load condition, simplified model and accurate model, respectively;
step five: aiming at the kth working condition, calculating to obtain displacement values corresponding to the upper and lower bounds of the material parameters of the accurate model by adopting a sensitivity analysis method according to the upper and lower bounds of the elastic parameters of the original structure, and obtaining the elastic modulus central value K of the equivalent model through iteration j,k And a variation Δ K j,k
Step six: and calculating to obtain the optimal solution of the robustness index by adopting a genetic algorithm on the basis of the elastic modulus central value and the variable quantity obtained by calculating under a plurality of working conditions, and obtaining the elastic modulus identification result of which the structure has robustness under the action of the plurality of working conditions.
In the first step, the honeycomb of the model is simplified into a solid structure in a mechanical property equivalent mode, and a control surface honeycomb equivalent structure is constructed.
And in the second step, for the control surface equivalent plate structure, the control surface structure is divided into regions according to the different thicknesses of the control surface and is respectively endowed with the elastic modulus.
And in the third step, the dispersibility of the structural material is considered, and the elastic parameter of the honeycomb equivalent structure is set as the interval number.
Step four, simplifying displacement interval vectors of the model under a plurality of load working conditions
Figure BDA0001799649780000036
Displacement interval vector corresponding to position of accurate model
Figure BDA0001799649780000037
And establishing a robustness index by the non-probability interference model.
Obtaining the elastic modulus central value K of the equivalent model through iteration in the fifth step j,k And a variation Δ K j,k
And sixthly, calculating by adopting a genetic algorithm to obtain an optimal solution of the robustness index based on the elastic modulus central value and the variable quantity obtained under multiple working conditions, and obtaining an elastic modulus identification result of which the structure has robustness under the action of multiple working conditions.
Compared with the prior art, the invention has the advantages that:
the invention provides a honeycomb structure control surface equivalent parameter strong robustness identification method considering uncertainty. On the basis of considering the uncertainty of the actual control surface honeycomb structure, an equivalent entity of the honeycomb structure is obtained through mechanical property equivalence, and then the honeycomb equivalent model is further equivalent to a plate structure based on a static model equivalent method and a genetic algorithm. The method overcomes the problem of complex structure of the original control surface, greatly reduces the calculated amount in the process of load identification, also simplifies unnecessary structural features for load identification, and has important significance for rapid identification of dynamic loads.
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FIG. 1 is a flow chart of the invention for equivalent simplification of a control surface model;
FIG. 2 is a model schematic diagram of an equivalent simplified embodiment of the control surface model of the invention;
FIG. 3 is a diagram of the horizontal unidirectional force of a cellular cell and its equivalent, wherein FIG. 3 (a) is a diagram of unit cell stress analysis, and FIG. 3 (b) is a diagram of unit cell equivalent force and moment;
FIG. 4 is a schematic diagram of a honeycomb equivalent model of a control surface in an embodiment of the invention;
FIG. 5 is a schematic diagram of a simplified equivalent plate finite element model according to an embodiment of the present invention;
FIG. 6 is a graph comparing z-displacement (upper modulus bound) of equivalent and original structures at an angle of attack of 2 ° for an embodiment of the present invention;
FIG. 7 is a graph comparing z-displacement (lower modulus bound) of an equivalent structure and an original structure at an angle of attack of 2 ° for an embodiment of the present invention;
FIG. 8 is a graph of z-displacement comparison (upper modulus) of an equivalent structure and an original structure at an angle of attack of 5 ° in an embodiment of the present invention;
fig. 9 is a z-displacement comparison (lower modulus) of the equivalent structure and the original structure at an angle of attack of 5 ° in the example of the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
As shown in fig. 1, the invention provides a honeycomb structure control surface equivalent parameter strong robustness identification method considering uncertainty, which comprises the following steps:
(1) Simplifying the honeycomb of the model into a solid structure in a mechanical property equivalent mode, and constructing a control surface honeycomb equivalent structure to obtain an equivalent mechanical parameter formula of the control surface honeycomb sandwich structure.
The derivation method of the equivalent mechanical parameter formula is explained by taking the elastic modulus in the x-axis direction and the poisson ratio formula as examples. The honeycomb is composed of a series of regular hexagons. The top view of the honeycomb is shown in the following figures. And a rectangular coordinate system is established, wherein the horizontal right direction is an x axis, the horizontal upward direction is a y axis, and the vertical plane is a z axis. Due to process limitations, the thickness of the honeycomb core in the y direction is different from that in other places, and the thickness in the y direction is set to be n times of that in other directions. Let E s The elastic modulus of the sandwich material is shown, t is the thickness of a thin honeycomb wall, nt is the thickness of a thick honeycomb wall, l is the length of a regular hexagon forming the honeycomb, and the thickness of the honeycomb sandwich is h c = b. For ease of analysis and derivation, the cellular structure is divided into individual cells, as shown by the dashed boxes in fig. 2.
To derive the modulus of elasticity E in the plane of the honeycomb structure along the x-axis cx Now, uniform unidirectional stress σ is applied to the left and right sides of the cell 1 As shown in fig. 3 (a). The stress is equivalent to two points A and C, and a concentrated force P and a moment M are obtained, as shown in FIG. 3 (b).
From the total force equalisation it can be derived:
P=σ 1 b(l+l sinθ) (1)
since the rotation angle at point A is 0, there is θ MP =0, further, it is possible to obtain:
Figure BDA0001799649780000051
the thin wall AB can be regarded as a cantilever beam, and the cross section of the cantilever beam is rectangular. The deflection of the thin wall AB perpendicular to its axial direction caused by the force P and the moment M is:
Figure BDA0001799649780000052
the axial elongation of the thin wall AB is:
Figure BDA0001799649780000053
due to the symmetry, the deformation of the thin wall BC is the same as the deformation of the thin wall AB. Then the equal effect of the cell in the x direction can be obtained as:
Figure BDA0001799649780000054
the equal effects of the cell in the y-direction become:
Figure BDA0001799649780000055
the equivalent elastic modulus in the x-direction is then:
Figure BDA0001799649780000056
the equivalent poisson's ratio in the x-direction is:
Figure BDA0001799649780000057
since θ = π/6, substituting equations (8) and (9), we can simplify:
Figure BDA0001799649780000061
Figure BDA0001799649780000062
the formulas of other elastic parameters can be derived by a method completely similar to the method to obtain the equivalent mechanical parameter formula of the honeycomb sandwich structure of the control surface:
Figure BDA0001799649780000063
wherein E is s And G s The elastic modulus and the shear modulus of the sandwich material are respectively, t is the thickness of the thin honeycomb wall, nt is the thickness of the thick honeycomb wall, l is the length of a regular hexagon forming the honeycomb, and the thickness of the honeycomb sandwich is h c =b,ρ s Is the density of the cell; e cx ,E cy ,E cz Respectively, the modulus of elasticity, mu, in the plane of the honeycomb structure along the x, y, z-axis directions xyyzxz Poisson's ratio, G, along the x, y, z axes of the honeycomb structure, respectively cxy ,G cyz ,G czx Transverse shear modulus in the xoy, yoz, zox plane, respectively.
(2) The honeycomb equivalent finite element model of the control surface is equivalent into a plate structure through a model identification method according to the principle of rigidity equivalence, the control surface structure is divided into subareas according to the difference of different subarea control surface thicknesses, and the elasticity modulus is respectively endowed to different subareas:
E 1 ,E 2 ,…,E n
wherein n represents the number of control surface divisions.
(3) The elastic parameter of the honeycomb equivalent structure is set to the number of sections in consideration of the dispersibility of the structural material. Such as setting the elasticity parameter E i The upper and lower limits of (c) are:
Figure BDA0001799649780000071
(4) Considering the dispersibility of aircraft structural materials, simplifying displacement interval vectors of a model under a plurality of load working conditions
Figure BDA0001799649780000072
Displacement interval vector corresponding to position of accurate model
Figure BDA0001799649780000073
Establishing a robustness index by a non-probability interference model:
Figure BDA0001799649780000074
wherein the content of the first and second substances,u i,r and
Figure BDA0001799649780000075
respectively a lower bound and an upper bound of node displacement of the ith degree of freedom of the simplified structure,u i,a and
Figure BDA0001799649780000076
lower and upper bounds, K, of node displacement for the ith degree of freedom of the precise structure, respectively j To simplify the stiffness of the jth region of the model, Δ K j Is the amount of change in stiffness; the indices i, r and a represent the ith load condition, the simplified model and the exact model, respectively.
(5) Aiming at the kth working condition, calculating to obtain displacement values corresponding to the upper and lower bounds of the material parameters of the accurate model by adopting a sensitivity analysis method according to the upper and lower bounds of the elastic parameters of the original structure, and obtaining the elastic modulus central value K of the equivalent model through iteration j,k And a variation Δ K j,k
Firstly, calculating to obtain the displacement of the honeycomb equivalent finite element model under the action of aerodynamic load, and then extracting the coordinates (x) of surface nodes in the honeycomb equivalent finite element model j ,y j ,z j ) And z-direction displacement value u z,j Wherein the subscript j represents the number of the surface nodes in the complete finite element model, and the number of the surface nodes in the model is set as n m J =1,2, \ 8230;, n m
Extract the plate model node coordinate (x) i ,y i ,z i ) I =1,2, \ 8230;, n, based on the coordinates of the nodes of the panel model and the coordinates (x) of the surface nodes in the honeycomb equivalent model obtained previously j ,y j ,z j ) And z-direction displacement value u z,j Obtaining the reference displacement u of the plate model by adopting a radial basis function interpolation method i0
For the plate model structure in the present embodiment, the initial elastic modulus E of three divisions is given 1,0 、E 2,0 And E 3,0 Then the displacement value u of the node of the plate model can be calculated n×1 . The error function is defined as:
e=u 0 -u (14)
where e is a column vector of n × 1, u 0 The column vector is displaced for the determined reference. Let p = [ E ] 1 ,E 2 ,E 3 ] T Then e and u are both functions of p, i.e.:
e(p)=u 0 -u(p) (15)
into Ku 0 = F, may obtain:
e(p)=K -1 F-u(p) (16)
and K and F are respectively a total rigidity matrix and a load vector.
A first order taylor expansion is performed on equation (17) to obtain:
Figure BDA0001799649780000081
let the sensitivity matrix be:
Figure BDA0001799649780000082
wherein:
Figure BDA0001799649780000083
the error function defining the scalar is:
J(p)=e(p+Δp) T e(p+Δp) (20)
order to
Figure BDA0001799649780000084
The following can be obtained:
S T SΔp=-S T e(p) (21)
from equation (22), the least squares solution can be found as:
Δp=-(S T S) -1 S T e(p) (22)
according to the iterative solving process, the elastic modulus under the condition of upper bound displacement or lower bound displacement under one working condition can be calculatedE 1 、E 2 And E 3 And the displacement difference of the plate model obtained by further equivalence and the complete finite element model under the static action is minimized.
(6) And calculating to obtain the optimal solution of the robustness index by adopting a genetic algorithm on the basis of the elastic modulus central value and the variable quantity obtained by calculating under a plurality of working conditions, and obtaining the elastic modulus identification result of which the structure has robustness under the action of the plurality of working conditions.
Example (b):
in order to more fully understand the characteristics of the invention and the applicability thereof to engineering practice, the invention aims at carrying out model equivalent simplification on the aircraft control surface structure shown in FIG. 2, and the simplified flow is shown in FIG. 1. The control surface load working condition is that the flying speed is 3Ma, the flying height is 20000m, and the attack angles are 2 degrees and 5 degrees respectively. The elasticity parameter of the honeycomb equivalent structure is set with an error of 2% (as shown in table 1) due to μ xy And the deviation is close to 1, the deviation is considered to be only 2% downwards, and the model identification index considering the uncertainty is constructed to meet the requirement of the robustness of the identification result.
TABLE 1 distribution intervals of elasticity parameters
Figure BDA0001799649780000085
Figure BDA0001799649780000091
For the plate model structure, the initial elastic modulus E of three sections is given 1,0 、E 2,0 And E 3,0 . Based on a deterministic process, taking the interval solution of two working conditions of an attack angle of 2 degrees and an attack angle of 5 degrees as an initial value, adopting a genetic algorithm in MATLAB to solve, and calculating to obtain the robustness identification results of three elastic moduli of the plate model as shown in the table, wherein the comparison results of the displacement of the plate model corresponding to the upper and lower boundaries of the elastic moduli and the displacement of the original model are shown in figures 6-9 (the comparison graphs of the upper and lower boundaries of the equivalent structure and the z-direction displacement of the original structure under the conditions of the attack angles of 2 degrees and 5 degrees, see the description of the attached figures).As can be seen from FIGS. 6-9, the identification result obtained by the above calculation has better robustness, and for different loading conditions, the structural response of the identification result is basically consistent with that of the original structure, and the displacements are basically superposed.
TABLE 2 Steady identification results of three elastic moduli of the plate model
Figure BDA0001799649780000092
The above are only the specific steps of the present invention, and the protection scope of the present invention is not limited in any way; the method can be expanded and applied to the fields of equivalent and simplified uncertain complex control surface structures, and all technical schemes formed by equivalent transformation or equivalent replacement fall within the protection scope of the invention.
The invention has not been described in detail and is part of the common general knowledge of a person skilled in the art.

Claims (1)

1. A honeycomb structure control surface equivalent parameter strong robustness identification method considering uncertainty can provide a way for model simplification of honeycomb structure control surfaces containing uncertainty factors, and is characterized by comprising the following implementation steps:
the method comprises the following steps: simplifying the honeycomb of the model into a solid structure in a mechanical property equivalent mode, constructing a control surface honeycomb equivalent structure, and obtaining an equivalent mechanical parameter formula of the control surface honeycomb sandwich structure:
Figure FDA0003744477830000011
wherein E is s And G s Respectively the elastic modulus and the shear modulus of the sandwich material, t is the thickness of the thin wall of the honeycomb, n is the thickness of the thick wall of the honeycomb, l is the length of a regular hexagon forming the honeycomb, and rho s Is the density of the cell; e cx ,E cy ,E cz Respectively, the modulus of elasticity, mu, in the plane of the honeycomb structure along the x, y, z-axis directions xyyzxz Are respectivelyPoisson's ratio, G, of honeycomb structure along x, y, z-axis direction cxy ,G cyz ,G cxz The transverse shear modulus in xoy, yoz and zox planes respectively;
step two: the honeycomb equivalent finite element model of the control surface is equivalent into a plate structure through a model identification method according to the principle of rigidity equivalence, the control surface structure is divided into subareas according to the difference of the thicknesses of the control surfaces of different subareas, and the elastic modulus is respectively given to the different subareas:
E 1 ,E 2 ,…,E m
wherein m represents the number of control surface partitions;
step three: setting the elastic parameter of the honeycomb equivalent structure as the number of intervals by considering the dispersibility of the structural material;
step four: considering the dispersibility of aircraft structural materials, and simplifying the displacement interval vector of the model under multiple load working conditions
Figure FDA0003744477830000021
Displacement interval vector corresponding to position of accurate model
Figure FDA0003744477830000022
Establishing a robustness index by a non-probability interference model:
Figure FDA0003744477830000023
wherein, the first and the second end of the pipe are connected with each other,u i,r and
Figure FDA0003744477830000024
the lower bound and the upper bound of the node displacement of the ith degree of freedom of the simplified structure respectively,u i,a and
Figure FDA0003744477830000025
lower and upper bounds, K, of the displacement of the node of the ith degree of freedom of the precise structure j To simplify the stiffness of the jth region of the model,. DELTA.K j Is the amount of change in stiffness; lower partThe marks i, r and a respectively represent the ith load working condition, a simplified model and an accurate model;
step five: aiming at the kth working condition, calculating to obtain displacement values corresponding to the upper and lower bounds of the material parameters of the accurate model by adopting a sensitivity analysis method according to the upper and lower bounds of the elastic parameters of the original structure, and obtaining the elastic modulus central value K of the equivalent model through iteration j,k And amount of change Δ K j,k
Step six: and calculating to obtain the optimal solution of the robustness index by adopting a genetic algorithm on the basis of the elastic modulus central value and the variable quantity obtained by calculating under a plurality of working conditions, and obtaining the elastic modulus identification result of which the structure has robustness under the action of the plurality of working conditions.
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