CN113886947B - Aircraft static aeroelastic system output state quantity interval determination method based on iteration strategy - Google Patents

Aircraft static aeroelastic system output state quantity interval determination method based on iteration strategy Download PDF

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CN113886947B
CN113886947B CN202111066107.2A CN202111066107A CN113886947B CN 113886947 B CN113886947 B CN 113886947B CN 202111066107 A CN202111066107 A CN 202111066107A CN 113886947 B CN113886947 B CN 113886947B
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CN113886947A (en
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邱志平
祝博
李云龙
姜南
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Beihang University
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Abstract

The invention discloses an iterative strategy-based aircraft static aeroelastic system output state quantity interval determination method, which considers uncertainty factors objectively existing in an aircraft static aeroelastic system in actual engineering, firstly describes uncertainty input quantity as interval parameters, and expresses the uncertainty static aeroelastic system as an interval nonlinear equation set; secondly, establishing an iteration strategy of an output state quantity interval based on the Taylor series of the input interval variable and the output state quantity; solving the interval increment of the output state quantity by using an interval mathematical method and updating the interval; and finally, repeating iteration until a termination condition is met, and obtaining an output state quantity value range influenced by uncertainty, thereby being beneficial to further realizing the static aeroelastic system structure and pneumatic comprehensive performance evaluation under the influence of uncertainty. The method ensures the calculation precision through an iteration technology, reduces the solving difficulty by utilizing a Taylor series expansion technology, and provides a new idea for predicting the output state quantity interval of the static aeroelastic system containing interval parameters.

Description

Aircraft static aeroelastic system output state quantity interval determination method based on iteration strategy
Technical Field
The invention relates to the technical field of uncertainty system numerical analysis, in particular to an iterative strategy-based aircraft static aeroelastic system output state quantity interval determination method, which is used for determining the upper bound and the lower bound of a static aeroelastic system output state quantity interval influenced by uncertainty of structure and pneumatic related physical quantities, and provides a feasible calculation method for guiding engineering technicians to realize high-efficiency and high-precision prediction of an interval static aeroelastic system output state quantity value interval.
Background
In the field of aeronautics, multidisciplinary systems involving the interaction of many disciplines (e.g., structural, aerodynamic, etc.) are often involved. The aeroelastic static problem is also called as the aeroelastic problem, the deformation of the aircraft under the action of aerodynamic load and the stability of static deformation generated by aerodynamic force are researched, the deformation of the aeroelastic is used for determining the lift force and the structural safety under the constant flight condition, and the aeroelastic static problem has important significance on the flight quality of modern high-performance aircraft. In the static aeroelastic problem, the state quantities which are most concerned by designers, namely the attack angle and the moment, determine the aerodynamic lift, and determine the structural bearing working condition, so that the optimization of the comprehensive performance of the aircraft can be pursued only by considering the performance requirements of two subjects. In processing the static gas bomb problem, time variable is not usually considered, so the static gas bomb system can be described as a nonlinear state equation system in mathematics, and the nonlinear state equation system is respectively composed of related equations of a structure and a pneumatic subject, and the equation system can be solved through a numerical calculation technology, so that an attack angle and a moment are determined, and the attack angle and the moment are used for evaluating pneumatic and structural performances.
In actual engineering, uncertainty widely exists in a static gas bomb system due to reasons of material property dispersity, geometric dimension measurement errors, external loads, environmental disturbance and the like, the uncertainty factors cause uncertainty of performance state quantities of subjects such as an attack angle, a moment and the like along with state quantity transmission between pneumatic subjects and structural subjects, and the uncertainty factors must be fully considered in design, so that static gas bomb calculation under an uncertainty condition is particularly important for reliability design of an engineering system. In the uncertainty system response calculation, the research of probability model-based methods is mainly focused at present, namely uncertainty parameters are random variables obeying a certain distribution, however, the acquisition of probability information must be supported by a large amount of experimental data. For an actual engineering system which is difficult to carry out physical tests for multiple times, a small-sample-based non-probability interval model is higher in applicability, namely, an uncertainty parameter is valued in a certain interval, and an interval upper bound and an interval lower bound are taken as numerical characteristics, so that a system response is valued in the certain interval, and the uncertainty response is calculated by determining the upper bound and the lower bound of a response interval, so that the influence of uncertainty of input parameters of the system on output response dispersity is evaluated; however, the current research on section uncertainty propagation analysis mainly targets a single discipline system, and cannot process the coupling effect in a multidiscipline system, so that the method cannot be directly applied to the calculation of the output state quantity section of the uncertain aeroelastic system with structural/pneumatic discipline intersection.
In conclusion, the problem of the static air bomb relates to the coupling effect between the structural and aerodynamic subjects, and the deformation of the static air bomb has important significance for the optimal design of the comprehensive performance of the aircraft; the existence of uncertainty causes certain difficulty in accurately predicting the output state quantity of the static gas bomb system, and if the influence of uncertainty on the comprehensive performance of the system cannot be effectively evaluated, the safety of a design scheme is possibly insufficient. Therefore, a method for quantifying uncertainty of the output state quantity of the static aeroelastic system must be developed, the static aeroelastic system is regarded as a whole, and coupling between disciplines and transfer of uncertainty between disciplines are fully considered; further considering the situation that the number of uncertain samples is insufficient in the actual engineering, it is necessary to develop a calculation method of the output state quantity interval of the static aeroelastic system based on a non-probability interval model. However, in the technical field of uncertainty response calculation for multidisciplinary systems, the correlation techniques related to the non-probability interval model are relatively few, and the foundation is weak.
In summary, existing uncertainty analysis techniques for multidisciplinary systems mainly focus on probabilistic uncertainty, and are deficient in relevant technical research on uncertainty of non-probabilistic intervals; in addition, the current interval uncertainty propagation analysis technology can not be directly applied to an uncertainty static aeroelastic system, otherwise, the problems of calculation precision and calculation efficiency exist.
Disclosure of Invention
The invention solves the problems: in order to effectively predict the upper and lower bounds of the output state quantity interval of the static aeroelastic system containing interval uncertainty parameters, an aircraft static aeroelastic system output state quantity interval determination method based on an iteration strategy is provided, mathematical modeling is carried out on the calculation problem of the uncertain aircraft static aeroelastic system, linearization and simplification of the problem are completed through a Taylor series expansion technology, the calculation precision problem caused by simplification processing is avoided by utilizing the iteration calculation technology, and therefore the output state quantity interval of the static aeroelastic system with higher precision can be obtained efficiently.
The technical scheme of the invention is as follows: in consideration of the coupling propagation effect of the small sample-based non-probability interval uncertainty between the structure and the pneumatic subject in the static aeroelastic system in the actual engineering, the static aeroelastic system with interval input variables is modeled into an interval non-linear state equation set, the interval mathematical theory is used as the basis, taylor series expansion and iterative solution strategies are utilized, the interval iterative calculation method for calculating the uncertainty static aeroelastic system is established, the linear approximation of the original non-linear equation is obtained through the Taylor series expansion technology in the mathematics, the interval iterative solution strategy for the output state quantity of the interval static aeroelastic system is established by combining the basic idea of iterative calculation, the interval increment is solved by utilizing the interval analysis technology to determine the equation, the upper bound and the lower bound of the output state quantity of each step of iteration are updated, and the gradual approximation of the interval limit of the output state quantity of the interval static aeroelastic system is realized. The method gradually linearizes the nonlinear problem related to the original static aeroelastic problem, reduces the solving difficulty and the calculated amount, has higher analysis precision, and can provide effective and convenient technical means for research and designers in related fields.
The technical scheme of the invention is as follows: an aircraft static aeroelastic system output state quantity interval determining method based on an iteration strategy comprises the following implementation steps:
the first step is as follows: the static aeroelastic system in the aircraft (the static aeroelastic system is a multidisciplinary system coupled by pneumatic and structural disciplines, particularly the static aeroelastic system in the airfoil structure of the aircraft subjected to pneumatic load in the invention is expressed by the following equation of state group:
F structure of the product (x 1 ,x 2 ,Y)＝0
A Pneumatic power (x 1 ,x 2 ,Y)＝0
Wherein x is 1 Representing a structurally-related physical quantity vector comprising: the material properties,Structural rigidity, etc.; x is the number of 2 Represents a pneumatic-related physical quantity vector comprising: incoming flow attributes, appearance parameters, aerodynamic coefficients and the like; y represents the output state quantity of the system under the condition input, and the output state quantity comprises the following components: angle of attack, structural moment; equation F Structure of the device (x 1 ,x 2 Y) =0 represents the static equilibrium relationship of the structure under the action of pneumatic force, equation A Pneumatic drive (x 1 ,x 2 Y) =0 represents an aerodynamic relation under structural deformation;
physical quantity x in a static gas bomb system 1 ,x 2 When the measurement and processing steps have uncertainty due to errors and the values are taken within a known interval, that is to say
Figure BDA0003258450820000031
And &>
Figure BDA0003258450820000032
It is described as an interval parameter, and input interval physical quantities of the system are defined as:
Figure BDA0003258450820000033
wherein the content of the first and second substances,x 1 ,
Figure BDA0003258450820000034
respectively represent structure-related physical quantities x 1 Lower and upper bounds, and limits of the value range of (1)x 2 ,/>
Figure BDA0003258450820000035
Corresponds to the pneumatically relevant physical quantity x 2 (ii) a Furthermore, a median ≥ value is defined for an interval>
Figure BDA0003258450820000036
And the section radius->
Figure BDA0003258450820000037
Respectively represent the lower value interval of the input physical quantity X of the static gas bomb systemA bound and an upper bound; based on the median value X of the interval c And defining interval radius delta X, and equivalently representing physical quantity of input interval as X I ＝X c +δX I Wherein δ X I ＝[-△X,△X]And represents the value variation range of the input physical quantity around the median value in the interval.
Using physical quantity X of input interval I The static aeroelastic system containing interval parameters is expressed as an interval nonlinear equation system, namely:
Figure BDA0003258450820000038
wherein, phi (X) I Y) represents the system of equations of state of the aeroelastic system of the aircraft, i.e. the uniform and simple expression of formula (1), the right side of the first equal sign represents the function F Structure of the device (X I Y) and A Pneumatic power (X I Y) and the right side of the second equation is the zero vector, the dimension of which is equal to phi (X) I And Y) are the same.
The second step is that: based on the interval nonlinear equation set established in the first step, the quantitative problem of the interval of the output state quantity (attack angle and structural moment) of the static aeroelastic system containing the interval parameters is mathematically modeled into a solving problem of the interval nonlinear equation set, namely:
Figure BDA0003258450820000041
Figure BDA0003258450820000042
i＝1,2,…,N
wherein the content of the first and second substances,
Figure BDA0003258450820000043
andY i respectively represents an upper bound and a lower bound of the output state quantity (attack angle and structure moment), and the output state quantity interval is expressed as->
Figure BDA0003258450820000044
Defining a median value in an interval>
Figure BDA0003258450820000045
And the section radius->
Figure BDA0003258450820000046
Solving an interval nonlinear equation set by adopting an iteration method, and based on a deterministic iteration strategy of the nonlinear equation set:
Y k+1 ＝Y k +△Y k
because physical quantities such as material attribute, structural rigidity, inflow attribute, appearance parameter, aerodynamic coefficient and the like in the static aeroelastic system are interval variables, the calculated delta Y in each iteration step k Is also an interval variable, and based on the interval mathematical theory, the iterative solution Y of the next iteration step k And also is an interval variable, and then an interval iteration strategy is obtained by using interval four arithmetic operations:
Figure BDA0003258450820000047
Figure BDA0003258450820000048
the third step: let the iteration step number k =1, since the calculation of the iteration strategy formula (5) requires a set of iteration initial values of the output state quantities, the iteration initial values need to be set
Figure BDA0003258450820000049
AndY 1 and a convergence tolerance ε; the selection method of the iteration initial value of the output state quantity comprises the following steps: considering the deterministic case, the input physical quantity of the system is made to take the value at the median of the interval, namely X = X c Solving a nonlinear equation system representing the deterministic static aeroelastic system in the step (1) by using a Newton iteration method:
Figure BDA00032584508200000410
obtaining the output state quantity Y of the deterministic static aeroelastic system after solving c Initial value of interval iteration
Figure BDA00032584508200000411
The fourth step: in the kth iteration step, a Taylor series expansion method is utilized to set the interval nonlinear equation at (X) c ,Y k ) The linear expansion is:
Figure BDA00032584508200000412
newton's iteration method based on determinism, let phi (X) I ,Y k+1 ) =0, establishing an output state quantity interval increment determination equation, namely:
Figure BDA00032584508200000413
by solving the equation, the upper and lower increment boundaries in the iteration strategy of the upper and lower boundaries of the interval static aeroelastic system output state quantity interval in the second step are obtained
Figure BDA00032584508200000414
And ΔY k The specific solving method is as follows:
in the kth iteration step, the output state quantity interval increment determination equation is written as:
G Y △Y k ＝-Φ(X c ,Y k )-G X δX I
wherein the content of the first and second substances,
Figure BDA0003258450820000051
and &>
Figure BDA0003258450820000052
Gradient matrices representing the function Φ with respect to the variables X and Y, respectively; thus, there are:
△Y k ＝-(G Y ) -1 Φ(X c ,Y k )-(G Y ) -1 G X δX I
based on interval mathematic four-rule operation, interval static gas bomb system output state quantity interval increment delta Y is determined through the following formula k Upper and lower bounds
Figure BDA0003258450820000053
Figure BDA0003258450820000054
Wherein, (.) -1 And | · | represent matrix inversion and absolute value operation, respectively. The upper and lower bounds of the calculation result of the last iteration step are defined
Figure BDA0003258450820000055
AndY k substituting the interval increment equation to obtain:
Figure BDA0003258450820000056
Figure BDA0003258450820000057
respectively used for iterative calculation of an upper bound and a lower bound of an interval static gas bomb system output state quantity interval increment; in the formula, the first step is that,
Figure BDA0003258450820000058
the iteration increment of the upper bound of the output state quantity interval corresponds to the first line of the iteration strategy formula in the second step; />
Figure BDA0003258450820000059
Is the lower bound iteration increment of the output state quantity interval, corresponding to the second line of the iteration strategy formula in the second step。
After the four arithmetic methods of interval mathematics are respectively used for solving, the output state quantity interval upper bound iteration increment in the iteration strategy formula in the second step is made
Figure BDA00032584508200000510
Lower bound iteration increment/greater than or equal to the output state variable interval>
Figure BDA00032584508200000511
Wherein->
Figure BDA00032584508200000512
And
Figure BDA00032584508200000513
respectively is the solved upper bound iteration increment ^ of the output state quantity interval>
Figure BDA00032584508200000514
Upper bound of and lower bound of the output state quantity interval ∑ is iteratively incremented>
Figure BDA00032584508200000515
Lower bound of (4), upper and lower bounds on the increment of the completion output status amount interval->
Figure BDA00032584508200000516
And ΔY k And (4) obtaining.
The fifth step: the upper and lower limits of the interval increment obtained in the fourth step
Figure BDA00032584508200000517
And ΔY k Substituting into interval iteration strategy to obtain the iteration solution of the (k + 1) th iteration step>
Figure BDA00032584508200000518
AndY k+1 ；/>
and a sixth step: entering the next iteration step, updating the iteration step number k, and repeating the fourth step to the fifth step until the following termination conditions are met:
Figure BDA00032584508200000519
wherein epsilon is the convergence tolerance set in step (3), and | | · | | | represents the euclidean norm; will finally obtain
Figure BDA00032584508200000520
AndY k+1 as the upper and lower bounds of the output state quantity (attack angle, moment) of the static gas bomb system.
Through the 6 steps, the upper bound and the lower bound of the unknown interval can be determined, high-precision prediction of the value range of the output state quantity of the static aeroelastic system under the influence of uncertainty factors is achieved, and the relative error can be controlled within 5%.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a new method for output uncertainty quantification aiming at a static aeroelastic system containing interval parameters, under the condition that input parameters are interval variables, the method can be used for determining the value interval of system output state quantities (attack angle and moment), the deficiency of the existing non-probability interval uncertainty calculation method in the aspect of the static aeroelastic system is made up to a certain extent, the obtained value interval can be used for evaluating the influence degree of uncertainty on the structure and the aerodynamic performance of the static aeroelastic system, and the method is favorable for guiding designers to evaluate and improve the comprehensive performance of the static aeroelastic system of an aircraft. The method for determining the upper and lower bounds of the interval static gas bomb system output state quantity interval based on the iteration strategy utilizes Taylor series expansion to linearize the nonlinear problem corresponding to the original static gas bomb system, reduces the complexity and solving difficulty of the problem, further combines the interval mathematical theory and the iterative calculation technology, establishes the interval iteration strategy for solving the interval static gas bomb system, can gradually approach the upper and lower bounds of the output state quantity in an iteration mode, ensures the accuracy of the calculation result, and lays a certain technical foundation for realizing the efficient calculation of the static gas bomb system output state quantity under the uncertain condition.
Drawings
FIG. 1 is a flow chart of an implementation of the method of the present invention;
FIG. 2 is a schematic diagram of a binary airfoil static aeroelastic model according to an embodiment of the present invention;
FIG. 3 is an iterative convergence history of the upper and lower bounds of the angle of attack computed by the method of the present invention in an embodiment of the present invention;
FIG. 4 is an iterative convergence process diagram of the upper and lower bounds of the moment computed by the method of the present invention in an embodiment of the present invention.
Detailed Description
The following description of the present invention will be provided for clarity and completeness with reference to the accompanying drawings and examples.
As shown in fig. 1, the embodiment of the present invention comprises the following steps:
(1) The binary wing static aeroelastic model shown in fig. 2 is taken as an object, the length of the wing chord is b, the rigid center is E, and a rigidity K is fixed at the rigid center θ The pneumatic center a to the rigid center distance of the torsion spring of (2) is 0.5b. Wing area S, incoming flow velocity v, incoming flow density ρ, and lift line slope
Figure BDA0003258450820000061
The torsional distortion in the structural discipline of the binary airfoil is represented by the twist angle θ, which is also the angle of attack in the aerodynamic discipline; assuming an initial angle of attack of the wing theta 0 Given the incoming flow conditions, the wing will reach equilibrium at the new angle of attack under the effect of the aerodynamic moment M and the torsional stiffness. In the embodiment, the torsional rigidity and the incoming flow speed are assumed as uncertainty interval parameters, and the interval upper bound and the interval lower bound of the aerodynamic moment and the attack angle of the binary wing under the balance condition are calculated by using the method. The static gas bomb system is first expressed as a nonlinear system of equations: />
Figure BDA0003258450820000071
The input physical quantity is torsional rigidity and incoming flow speed, and the output state quantity of the static aeroelastic system is aerodynamic moment and attack angle; to simply showDefining the input physical quantity vector X = (K) of the static aeroelastic system θ V), an aerostatic bomb system output state quantity vector Y = (M, θ) is defined.
In addition to the input physical quantity and the output state quantity, values of other parameters in the static aeroelastic system are shown in table 1.
TABLE 1
Figure BDA0003258450820000072
The parameter intervals of the physical quantities of the input intervals are listed in Table 2.
TABLE 2
Figure BDA0003258450820000073
By using X I The static aeroelastic system containing interval parameters is expressed as an interval nonlinear equation system, namely:
Figure BDA0003258450820000074
(2) Based on the interval nonlinear equation set established in the first step, the physical quantity X in the static aeroelastic system is in the interval
Figure BDA0003258450820000075
The internal value is taken, and according to the interval expansion theory, the output state quantity Y of the system is also taken as a value in a certain interval, so that the quantitative problem of the output state quantity (aerodynamic moment M and attack angle theta) interval of the static aeroelastic system containing the interval parameters is mathematically modeled into a solving problem of an interval nonlinear equation set, namely:
Figure BDA0003258450820000076
Figure BDA0003258450820000077
i＝1,2
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003258450820000078
andY i representing the upper and lower bounds of the output state quantities (aerodynamic moment M and angle of attack θ), respectively, the intervals being expressed as: />
Figure BDA0003258450820000081
Defining a median value in an interval>
Figure BDA0003258450820000082
And a section radius>
Figure BDA0003258450820000083
An iterative method is adopted to solve an interval nonlinear equation set, and the interval iterative strategy is as follows:
Figure BDA0003258450820000084
Figure BDA0003258450820000085
/>
where k represents the number of iteration steps.
(3) Setting iteration initial value by enabling iteration step number k =1
Figure BDA0003258450820000086
AndY 1 let the input physical quantity take the value at the median of its interval, i.e. K θ The output state quantity is obtained by substituting the equation set which is expressed as a nonlinear equation by a gas/static system and is equivalent to =0.5 × (166.32 + 169.68) N · m/deg =168N · m/deg, and v =0.5 × (49.5, 50.5) m/s =50m/s, and the output state quantity is ^ 0.5 × (166.32 + 169.68) N · m/deg>
Figure BDA0003258450820000087
Figure BDA0003258450820000088
Initial iteration of intervalValue->
Figure BDA0003258450820000089
The convergence tolerance e =0.0001 is set.
(4) In the kth iteration step, an interval nonlinear equation for describing an interval static gas bomb system is set to be (X) by using a Taylor series expansion method c ,Y k ) The linear expansion is:
Figure BDA00032584508200000810
let phi (X) be based on the basic idea of Newton iteration I ,Y k+1 ) =0, an interval increment determination equation is established, namely:
Figure BDA00032584508200000811
solving an interval increment determination equation of the output state quantity by using an interval mathematical method to obtain upper and lower boundaries of the interval increment in the interval iteration strategy in the second step
Figure BDA00032584508200000812
And ΔY k The specific solving method is as follows:
in the kth iteration, the interval increment determination equation is written as:
G Y △Y k ＝-Φ(X c ,Y k )-G X δX I
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00032584508200000813
and &>
Figure BDA00032584508200000814
Gradient matrices representing the function Φ with respect to the variables X and Y, respectively; thus, there are:
△Y k ＝-(G Y ) -1 Φ(X c ,Y k )-(G Y ) -1 G X δX I
based on interval mathematic four-rule operation, interval static gas bomb system output state quantity interval increment delta Y is determined through the following formula k Upper and lower bounds:
Figure BDA00032584508200000815
Figure BDA00032584508200000816
wherein, (. Cndot.) -1 And | · | represent matrix inversion and absolute value operation, respectively. The upper and lower bounds of the calculation result of the last iteration step are divided into
Figure BDA0003258450820000091
AndY k substituting the interval increment equation to obtain:
Figure BDA0003258450820000092
Figure BDA0003258450820000093
respectively used for iterative calculation of an upper bound and a lower bound of interval state quantity increment output by an interval static gas bomb system; after the four arithmetic methods of interval mathematics are respectively used for solving, the order is given
Figure BDA0003258450820000094
Completing interval increment upper and lower bounds>
Figure BDA0003258450820000095
And ΔY k And (4) obtaining.
(5) The interval increment obtained in the fourth step is bounded by the upper and the lower bounds
Figure BDA0003258450820000096
And ΔY k Substituting into the interval iteration strategy in the second step to obtain the iteration solution/judgment of the (k + 1) th iteration step>
Figure BDA0003258450820000097
AndY k+1 ；
(6) Entering the next iteration step, setting k as a new iteration step, and repeating the fourth step to the fifth step until the following termination conditions are met:
Figure BDA0003258450820000098
will finally obtain
Figure BDA0003258450820000099
AndY k+1 as upper and lower bounds of the output state quantity of the silent bomb system, i.e.>
Figure BDA00032584508200000910
Y＝Y k+1
The calculation results of the specific component form are:
Figure BDA00032584508200000911
M＝Y 1 k+1 ＝301.886N·m
Figure BDA00032584508200000912
θ＝Y 2 k+1 ＝3.779deg
the above processes are embodiments of the present invention in combination with examples.
Fig. 3 and 4 show the iterative calculation process of the upper and lower bounds of the output state quantity M and θ in the present invention, and it can be seen that the present invention has good convergence properties. Further explaining the calculation accuracy of the invention, a high-accuracy reference solution for the output state quantity interval of the binary wing aeroelastic system in the embodiment is calculated by a Monte Carlo method (a calculation technology for acquiring the response interval of an uncertain system through large-scale sampling, the accuracy is extremely high but the efficiency is extremely low), the comparison of the calculation results of the two methods is listed in Table 3, and the comparison result shows that the calculation result of the invention can reach the calculation accuracy equivalent to that of the Monte Carlo method, and the maximum relative error does not exceed 1%.
TABLE 3
Figure BDA00032584508200000913
Figure BDA0003258450820000101
In summary, the method of the invention first describes the uncertain physical quantity as an interval parameter as an input variable of the static gas bomb system, so as to express the uncertain static gas bomb system as an interval nonlinear equation set; secondly, expanding an interval nonlinear equation set into a first-order Taylor series about input interval variables and output state quantities, and establishing an iterative solution strategy of upper and lower boundaries of an output state quantity interval of the static aeroelastic system based on a Newton iteration method; then, solving an output state quantity interval increment determination equation by using an interval mathematical method, calculating an interval iteration step length of the output state quantity of the static gas bomb system, and realizing iteration updating of an output state quantity interval boundary by using an iteration strategy; and finally, repeating the iteration process until an iteration termination condition is met, and determining the upper and lower limits of the output state quantity interval of the static aeroelastic system containing interval parameters, namely determining the output state quantity measuring range of the static aeroelastic system influenced by uncertainty factors, so that the method can be used for quantitative evaluation of the comprehensive performance of the structure and the pneumatics in the static aeroelastic system under the influence of uncertainty.
The invention has not been described in detail and is part of the common general knowledge of a person skilled in the art.
The above are only specific steps of the present invention, and do not limit the scope of the present invention; all the technical solutions formed by equivalent transformation or equivalent replacement fall within the protection scope of the present invention.

Claims (3)

1. An aircraft static aeroelastic system output state quantity interval determining method based on an iteration strategy is characterized by comprising the following steps: the method is applied to an aircraft static aeroelastic system containing interval parameters, and comprises the following implementation steps:
step 1: constructing an aircraft static aeroelastic system state equation set:
Figure FDA0003258450810000011
F structure of the product (x 1 ,x 2 Y) =0 represents a static balance relation of the aircraft airfoil structure under the action of aerodynamic force;
A pneumatic power (x 1 ,x 2 Y) =0 denotes the aerodynamic relation under deformation of the aircraft airfoil structure;
wherein x is 1 Representing a vector of related physical quantities of an aircraft airfoil structure, comprising: material properties and structural stiffness; x is the number of 2 Represents a pneumatic-related physical quantity vector comprising: inflow properties, profile parameters and aerodynamic coefficients;
y represents the physical quantity x of the aeroelastic system of the aircraft in the structural and aerodynamic disciplines 1 And x 2 The output state quantity to be predicted under the condition input of (1), the output state quantity comprising: angle of attack and structural moment;
physical quantity x in a static gas bomb system 1 ,x 2 With uncertainty, but when the value is within a known interval, i.e.
Figure FDA0003258450810000012
And &>
Figure FDA0003258450810000013
The physical quantity of the input interval of the static gas bomb system is as follows:
Figure FDA0003258450810000014
wherein x is 1 ,
Figure FDA0003258450810000015
Respectively representing the relevant physical quantity x of the aircraft airfoil structure 1 Lower and upper bounds of the value range of (1), and the bound x 2 ,
Figure FDA0003258450810000016
Corresponds to the pneumatically relevant physical quantity x 2 (ii) a Median interval->
Figure FDA0003258450810000017
And a section radius>
Figure FDA0003258450810000018
X,/>
Figure FDA0003258450810000019
Respectively representing the lower bound and the upper bound of the value interval of the input physical quantity X of the static gas bomb system; based on the median value X of the interval c And defining interval radius delta X, and equivalently representing physical quantity of input interval as X I ＝X c +δX I Wherein δ X I ＝[-△X,△X]；
Using physical quantities X in input intervals I The static aeroelastic system containing interval parameters is expressed as an interval nonlinear equation system, namely:
Figure FDA00032584508100000110
wherein, phi (X) I Y) represents the state equation set of the static aeroelastic system of the aircraft, namely the uniform and simple expression of the formula (1), and the right side of the first equal sign represents the state equation set represented by a function F Structure of the device (X I Y) and A Pneumatic power (X I Y) and the right side of the second equation is the zero vector, the dimension of which is equal to phi (X) I Y) are consistent;
and 2, step: based on the interval nonlinear equation set established in the step 1, the output state quantity of the static aeroelastic system containing interval parameters, namely the quantization problem of the attack angle and the structural moment interval is mathematically modeled into an interval nonlinear equation set, namely:
Figure FDA0003258450810000021
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003258450810000022
andY i respectively represent an upper bound and a lower bound of an output state quantity, the output state quantity interval being represented as->
Figure FDA0003258450810000023
Median interval->
Figure FDA0003258450810000024
And a section radius>
Figure FDA0003258450810000025
Solving the interval nonlinear equation set by adopting an iteration method, establishing the following relation
Figure FDA0003258450810000026
AndY k+1 and the interval iteration strategy formula (5) is respectively used for estimating the values of the aerodynamic profile attack angle in the static aeroelastic system and the values of the bearing moment of the wing surface structure of the aircraft, namely an upper bound and a lower bound:
Figure FDA0003258450810000027
and step 3: let the iteration step number k =1, the calculation of the iteration strategy formula (5) needs a group of iteration initial values of the output state quantity, and the iteration initial values of the output state quantity are set
Figure FDA0003258450810000028
AndY 1 and a convergence tolerance ε;
and 4, step 4: in the k iteration step, an interval increment determination equation of the output state quantity is solved by using an interval mathematical method:
Figure FDA0003258450810000029
obtaining the interval increment upper and lower bounds of the output state quantity of the static gas bomb system in the interval iteration strategy in the step 2
Figure FDA00032584508100000210
And ΔY k ；
And 5: the upper and lower bounds of the interval increment obtained in the step 4
Figure FDA00032584508100000211
And ΔY k Substituting into the interval iteration strategy formula (5) to obtain the iteration solution/judgment of the (k + 1) th iteration step>
Figure FDA00032584508100000212
AndY k+1 ；
step 6: entering the next iteration step, updating the iteration step number k, and repeating the steps 4 to 5 until the following termination conditions are met:
Figure FDA00032584508100000213
wherein epsilon is a set convergence tolerance, and | | · | |, represents a euclidean norm; will finally obtain
Figure FDA00032584508100000214
AndY k+1 the upper and lower limits are used as the output state quantity of the static gas bomb system;
when the input physical quantity X in the static aeroelastic system shown in the formula (2) has interval uncertainty, the state quantity Y to be predicted of the static aeroelastic system in the static equilibrium state is influenced by the input physical quantity X and is also taken in an unknown interval.
2. The iterative strategy-based aircraft aeroelastic system output state quantity interval determination method according to claim 1, characterized in that: in the step (3), the selection of the iteration initial value of the output state quantity follows the following method: initial value of interval iteration
Figure FDA00032584508100000215
Wherein Y is c By letting X = X c And solving equation (3) to obtain phi (X) c ,Y)＝0。
3. The iterative strategy-based aircraft aeroelastic system output state quantity interval determination method according to claim 1, characterized in that: in the step (4), the upper and lower bounds of interval increment of the output state quantity
Figure FDA0003258450810000031
And ΔY k The specific solving method comprises the following steps: in the kth iteration, the output state quantity interval increment is determined by the equation:
G Y △Y k ＝-Φ(X c ,Y k )-G X δX I
wherein the content of the first and second substances,
Figure FDA0003258450810000032
and &>
Figure FDA0003258450810000033
Gradient matrices respectively representing functions phi with respect to the input physical quantity X and the output state quantity Y; thus, there are:
△Y k ＝-(G Y ) -1 Φ(X c ,Y k )-(G Y ) -1 G X δX I
based on interval mathematic four-rule operation, interval increment delta Y of output state quantity of interval static gas bomb system is determined by the following formula k Upper and lower bounds:
Figure FDA0003258450810000034
△Y k ＝-(G Y ) -1 Φ(X c ,Y k )-|(G Y ) -1 G X |△X
wherein, (.) -1 And |. Represents matrix inversion and absolute value operation respectively, and the upper and lower bounds of the calculation result of the kth iteration are defined
Figure FDA0003258450810000035
AndY k substituting the interval increment equation into the formula (6) to obtain: />
Figure FDA0003258450810000036
Figure FDA0003258450810000037
Respectively used for iterative calculation of an upper bound and a lower bound of an interval static gas bomb system output state quantity interval increment; in the formula, the content of the active carbon is shown in the specification,
Figure FDA0003258450810000038
is an output state quantity interval upper bound iteration increment, corresponding to the first line of equation (5) in said step (2); />
Figure FDA0003258450810000039
Is the lower bound iteration increment of the output state quantity interval, corresponding to the second line of formula (5) in step (2);
respectively solving by using the interval mathematics four fundamental operations, and then obtaining the result in the step (2)Output state quantity interval upper bound iteration increment in equation (5)
Figure FDA00032584508100000310
Iteration increment on the lower bound of an output state variable interval>
Figure FDA00032584508100000311
Wherein +>
Figure FDA00032584508100000312
And &>
Figure FDA00032584508100000313
Respectively, solved output state quantity interval upper bound iteration increment>
Figure FDA00032584508100000314
Upper bound and lower bound iteration increments of an output state quantity interval->
Figure FDA00032584508100000315
Lower bound of (d), upper and lower bounds on state quantity interval increment in completion interval iteration>
Figure FDA00032584508100000316
And ΔY k And (4) obtaining. />
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Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105843073A (en) * 2016-03-23 2016-08-10 北京航空航天大学 Method for analyzing wing structure aero-elasticity stability based on aerodynamic force uncertain order reduction
WO2017005052A1 (en) * 2015-07-09 2017-01-12 北京航空航天大学 Optimization and design method for gradient segmentation of intervals of spacecraft pulse rendezvous trajectory
CN106529093A (en) * 2016-12-15 2017-03-22 北京航空航天大学 Pneumatic/structure/static aeroelasticity coupling optimizing method for high-aspect-ratio wing
CN106874561A (en) * 2017-01-17 2017-06-20 北京航空航天大学 Multidisciplinary uncertainty propagation analysis method based on Newton iteration
CN107247831A (en) * 2017-05-26 2017-10-13 北京航空航天大学 It is a kind of based on iteration by dimension method multidisciplinary bounded-but-unknown uncertainty analysis method
CN107958310A (en) * 2017-12-07 2018-04-24 北京航空航天大学 A kind of optimal Maintenance Design method of the existing structure based on interval model time-varying reliability for considering quiet dynamic uncertainty
CN108121865A (en) * 2017-12-15 2018-06-05 北京航空航天大学 Analysis method is propagated in a kind of response of the structure section containing more uncertain parameters based on adjoint variable method
CN110908364A (en) * 2019-12-06 2020-03-24 南京航空航天大学 Fault detection method based on robust interval estimation
WO2020228310A1 (en) * 2019-10-17 2020-11-19 浙江大学 Interval and bounded probability mixed uncertainty-based mechanical arm robustness optimization design method

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2017005052A1 (en) * 2015-07-09 2017-01-12 北京航空航天大学 Optimization and design method for gradient segmentation of intervals of spacecraft pulse rendezvous trajectory
CN105843073A (en) * 2016-03-23 2016-08-10 北京航空航天大学 Method for analyzing wing structure aero-elasticity stability based on aerodynamic force uncertain order reduction
CN106529093A (en) * 2016-12-15 2017-03-22 北京航空航天大学 Pneumatic/structure/static aeroelasticity coupling optimizing method for high-aspect-ratio wing
CN106874561A (en) * 2017-01-17 2017-06-20 北京航空航天大学 Multidisciplinary uncertainty propagation analysis method based on Newton iteration
CN107247831A (en) * 2017-05-26 2017-10-13 北京航空航天大学 It is a kind of based on iteration by dimension method multidisciplinary bounded-but-unknown uncertainty analysis method
CN107958310A (en) * 2017-12-07 2018-04-24 北京航空航天大学 A kind of optimal Maintenance Design method of the existing structure based on interval model time-varying reliability for considering quiet dynamic uncertainty
CN108121865A (en) * 2017-12-15 2018-06-05 北京航空航天大学 Analysis method is propagated in a kind of response of the structure section containing more uncertain parameters based on adjoint variable method
WO2020228310A1 (en) * 2019-10-17 2020-11-19 浙江大学 Interval and bounded probability mixed uncertainty-based mechanical arm robustness optimization design method
CN110908364A (en) * 2019-12-06 2020-03-24 南京航空航天大学 Fault detection method based on robust interval estimation

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
梁佳骅 ; 白俊强 ; 李国俊 ; .基于Peters-ONERA模型的失速颤振特性研究.西北工业大学学报.2018,(第05期),全文. *
聂雪媛 ; 黄程德 ; 杨国伟 ; .基于CFD/CSD耦合的结构几何非线性静气动弹性数值方法研究.振动与冲击.2016,(第08期),全文. *

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