CN117634020A - Hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion - Google Patents
Hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion Download PDFInfo
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Abstract
The invention discloses a hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion, which is used for converting a least square problem equation of eigen orthogonal decomposition into a regression process by introducing a Bayesian regression technology, so as to fuse aerodynamic data with high reliability and low reliability of an aircraft, and improve the aerodynamic characteristic overall model precision in the aircraft design process; on the basis, the overall design method well realizes the balance of aerodynamic stability design and control design, has the capability of solving the problem of optimizing the design of multiple state points in the flight envelope, and provides a quick and reliable design tool for hypersonic aircrafts.
Description
Technical Field
The invention relates to the technical field of aircraft design, in particular to a hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion.
Background
The design method of the traditional aircraft generally adopts a distributed design thought to decompose the design task of the aircraft into a plurality of design disciplines, and the disciplines are relatively independent. This design concept is efficient and feasible when the coupling relationship between the disciplines is weak or the interactions between disciplines are linear.
For hypersonic aircraft, there is typically a strong nonlinear coupling relationship between the aircraft subsystems and high sensitivity to design variables. The results obtained with conventional distributed design methods are not satisfactory and often do not meet the performance and stability requirements. Therefore, the design of modern aircrafts must be from the multi-disciplinary point of view to obtain an aircraft design scheme with excellent performance, and the performance potential of the aircrafts is truly exploited.
During development of an aircraft, it is necessary to provide a large amount of aerodynamic data for different flight conditions throughout the flight envelope. The aerodynamic data of the aircraft are usually derived from three modes of numerical calculation, wind tunnel test and flight test, wherein various numerical calculation methods belong to a low-reliability aerodynamic data acquisition mode, and the acquisition is more convenient, but the conditions of lower precision and difficult convergence exist; high-reliability pneumatic data generally have higher precision and cost, generally come from wind tunnel tests and flight tests, and the data volume is insufficient to meet the design requirements of the aircraft.
Therefore, in order to try to solve the above problems, it is necessary to develop a multidisciplinary collaborative design research based on improving the accuracy of the aerodynamic characteristics model of the aircraft, so as to enhance the reliability of the aircraft design and the engineering application value.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion, which carries out data fusion modeling on high-low reliability data sets under the condition of limited high-reliability sample number, expands the pneumatic data fusion range and improves the data fusion precision, and the data fusion method is applied to the hypersonic aircraft pneumatic and control collaborative design field, so that the aircraft design reliability and engineering application value are enhanced.
In order to solve the technical problems, the invention provides a hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion, which comprises the following steps:
step 1, initializing geometrical design variables and constraint ranges of an aircraft;
step 2, determining a hypersonic aircraft reference aerodynamic layout, and parameterizing and describing the aircraft geometric configuration by adopting a state type function method;
step 3, based on the parameterized geometric shape, respectively obtaining high-low fidelity data sets by adopting an engineering estimation method and a CFD fluid calculation method, and carrying out multi-fidelity data fusion on the high-low fidelity data sets by adopting an intrinsic orthogonal decomposition method based on Bayesian expansion to obtain an aircraft aerodynamic characteristic prediction proxy model;
step 4, establishing an aerospace vehicle dynamics characteristic model, and judging whether the aerodynamic stability requirements of the aerospace vehicle in the transverse and lateral directions are met under the multi-state point of the aerospace vehicle by combining a flight envelope according to a collaborative design method of aerodynamic stability and control of the aerospace vehicle based on a space criterion diagram;
and 5, introducing a control system to combine with control law design on the premise of meeting the stability requirement, and finally outputting an aircraft pneumatic layout design result meeting the pneumatic stability and control collaborative design requirement by adjusting the parameters of the controller to meet the closed-loop control pneumatic stability criterion and the non-minimum phase requirement.
Preferably, in step 1, the design variables are geometrical parameters of hypersonic aircraft wing sweep angle and fuselage height.
Preferably, in the step 2, the hypersonic aircraft adopts a hypersonic aircraft with large sweepback double-delta wing and no horizontal tail type pneumatic layout, the section of the aircraft body is in a sharp side edge back configuration, two sides of the aircraft body are double-sweepback delta wings, a pair of elevator surfaces on two sides control a pitching channel, and a single vertical tail type design controls a flying transverse channel.
Preferably, in step 3, the intrinsic orthogonal decomposition data fusion method based on bayesian expansion specifically includes the following steps:
step 31, initializing design variables of a multi-credibility pneumatic model, and respectively carrying out experimental design on different credibility models to obtain corresponding model responses and obtain a high-low credibility data set;
step 32, obtaining an intrinsic orthogonal decomposition modal matrix through singular value decomposition calculation based on a low-reliability data model;
step 33, searching and determining the data point coordinates of the low fidelity data closest to the high reliability data, and obtaining the intrinsic orthogonal decomposition base coefficient based on a least square method and combining the intrinsic orthogonal decomposition modal matrix;
step 34, converting the least square problem of the intrinsic orthogonal decomposition into a regression problem based on the Bayesian theory, and constructing a corresponding Gaussian process regression model aiming at the intrinsic orthogonal decomposition modal matrix and the corresponding high-fidelity data set;
and 35, outputting the mean value and variance information of the data fusion solutions under different input conditions by evaluating the prediction distribution of all rows of the intrinsic orthogonal decomposition modal matrix.
Preferably, in step 31, initializing design variables of the multi-credibility pneumatic model, respectively performing experimental design on different credibility models, and obtaining corresponding model responses, thereby obtaining a high-low credibility data set, which specifically includes the following steps:
step 31a, the design variable is x= [ x ] 1 ,x 2 ,...,x d ]E D, where D is the design space and D is the design space dimension, and satisfiesR is a real number set;
step 32b, experimental design refers to sampling different credibility models in a design space D to obtain a high-reliability data set and a low-reliability data set Y = [ Y ] 1 ,...,y n ]＝[y(ξ 1 ),...,y(ξ n )]Low confidence data design variable ζ i E D, i=1,..n, n is the number of low confidence datasets; high confidence data set t= [ t ] 1 ,...,t s ]＝[y′(e 1 ),...,y′(e s )]High confidence data design variable e i E, D, i=1, s; s is the number of high-reliability data sets. The sampling method is one of optimal Latin hypercube sampling, full factor design and orthogonal experiment design methods or the assumed sample point is given.
Preferably, in step 32, the eigenvalue decomposition mode matrix obtained by singular value decomposition calculation based on the low-reliability data model is specifically:
for the low fidelity data set Y E R N×n Singular value decomposition is carried out to obtain:
Y＝U∑V T
wherein U= [ U ] 1 ,...,u N ]∈R N×N Sum v= [ V 1 ,...,v n ]∈R n×n As standard orthogonal matrix, i.e. U T U＝UU T ＝I N And V T V＝VV T ＝I n Wherein Σ=diag (σ) 1 ,...,σ n )∈R N×n Comprising singular values sigma arranged in descending order 1 ≥...≥σ n ≥0；
Assuming that the rank of matrix Y is r=rank (Y), then only the first r singular values are non-zero. The corresponding r left singular vectors, the first r columns of the matrix U, form a data set y 1 ,...,y n Standard orthonormal basis { u } of the composed space 1 ,...,u r "i.e. eigen-orthogonal basis of decomposition U r 。
Preferably, in step 33, the searching determines the data point coordinates of the low fidelity data closest to the high reliability data, and the eigenvalue orthogonal decomposition base coefficient can be obtained based on the least square method and combined with the eigenvalue orthogonal decomposition modal matrix, which is specifically:
a given vector t epsilon R of high confidence data s Can be defined as at y' ∈R N Of only componentsA known vector, where s < N is the number of sampling points, j 1 ,...,j s ∈{1,...,N}：
For a matrixWherein->Represents the j th i Standard basis vectors. Characterizing the component of the vector t with the component of the vector y' by nearest neighbor search of s sample point coordinates in the computational grid;
the vector y' is approximated in the eigen-orthogonal decomposition subspace, and the eigen-orthogonal decomposition base coefficients can be foundSo that
In U r ＝[u 1 ,...,u r ]∈R N×r The basis vector matrix, the first r columns of U, is decomposed for eigen-orthogonality. Base coefficient vectorGenerating L that is the smallest observation for vector y 2 Error, defined by least squares problem
Typically, x=p T U r ∈R s×r With full rank, the above solution is therefore unique:
vector the base coefficientSubstituting the approximation equation, the estimated value +.>
Preferably, in step 34, based on bayesian theory, the least squares problem of the intrinsic orthogonal decomposition is converted into a regression problem, and the construction of the corresponding gaussian process regression model is specifically performed for the intrinsic orthogonal decomposition modal matrix and the corresponding high-fidelity data set:
based on the Bayesian expansion idea, defining a least square problem equation of the intrinsic orthogonal decomposition as a regression process, and constructing a mapping f:directly matrix U r The rows mapped to vector y'
Obtaining a set of data pairs at a given sampling location:
{(x i ,t i )|i＝1,...,s}
wherein the method comprises the steps ofModal matrix U representing eigen-orthogonal decomposition r Is the j of (2) i The number of rows of the device is,responding to the corresponding sample;
and adopting a Gaussian process regression agent for the input-output relation of the data pair set:
assuming a gaussian process with zero mean for f (x), for any two inputs x, x' ∈r r Its covariance Cov [ f (x), f (x')]Given by covariance function k (x, x'), a widely used class of covariance is employedThe difference function is as follows:
k(x,x′)＝θ 0 ·exp(-θ 1 ||x-x′|| 2 )+θ 2 x T x′
in θ 0 ，θ 1 ，θ 2 For superparameters, the superparameters are typically not defined in advance, but rather are determined from the data by maximizing the log-boundary likelihood function:
then, for a new input variable x * ∈R r ，f * :＝f(x * ) The predictive distribution of (2) is as follows
E[f * ]＝k(x * )(K+σ 2 I) -1 t
Var[f * ]＝k(x * ,x * )-k(x * ) T (K+σ 2 I) -1 k(x * )
Wherein k (x) * ):＝(k(x * ,x i )) i＝1,..,s ∈R s And k= (K (x) i ,x j )) i,j＝1,..,s ∈R s×s 。
Preferably, in step 35, by evaluating the prediction distribution of all rows of the eigen-orthogonal decomposition mode matrix, the mean value and variance information of the data fusion solution under different input conditions are specifically: by evaluating all rows x of the modal matrix * ＝(U r ) i I=1, & gt, and N, obtaining a data fusion prediction result of an intrinsic orthogonal decomposition method based on Bayesian expansion
The fusion evaluation criterion comprises Root Mean Square Error (RMSE) and a determination coefficient R 2 And an interval evaluation criterion PIC:
wherein N is V To verify the number of samples, y i In order to verify the true value of the sample point,to verify sample point predictions, +.>Is y i Q is any quantile between (0, 1), taking q=0.025 and q=0.975.
Preferably, in step 4, an aerospace vehicle dynamics characteristic model is established, and the aerospace vehicle aerodynamic stability and control collaborative design method based on a space criterion diagram is combined with a flight envelope to judge whether the aircraft meets the requirements of lateral aerodynamic stability under multiple state points, specifically:
the hypersonic aircraft attitude dynamics model is constructed as follows:
wherein, (alpha, beta, mu) is the attack angle, sideslip angle and roll angle of the aircraft; (p, q, r) roll, pitch and yaw angular velocities, L, Y being the lift and side forces, respectively, experienced by the aircraft; l, M, N are the roll moment, pitch moment and yaw moment experienced by the aircraft, respectively; m and V are the mass and speed of the aircraft respectively; i x 、I z 、I y The rotational inertia of each shaft is respectively; i zx For each axis rotation product.
And selecting state points according to the flight envelope, and linearizing the model under each state point. According to the principle of small disturbance, the attitude kinetic equation can be decoupled into longitudinal motion and transverse lateral motion after being linearized by utilizing the horizontal sideslip-free flight condition. Decoupling the above equations into longitudinal and lateral equations with neglecting gravity, lift and lateral forces, stability analysis and control system design is based on the following equations:
wherein L' α 、L′ β 、L′ p 、L r ′、L q ′、Respectively rolling moment derivatives of all channels; n' α 、N′ β 、N′ p 、N r ′、N q ′、Respectively yaw moment derivatives of all channels; m's' α 、M′ β 、/>M q ' each channel pitch moment derivative; delta e The deflection angle of the elevator; delta a Is the aileron yaw angle.
Each operator in the equation is defined as follows:
for hypersonic aircraft, the lateral-lateral channel is usually unstable, and the selection of lateral-lateral stability parameters and lateral-lateral control laws is particularly important;
by solving the characteristic equation |λI-A|, the lateral stability criterion can be written as the following equation:
wherein C is nβ 、C lβ Are two classical stability parameters.
Based on a space criterion graph method, the x-axis and the y-axis are respectively corresponding to the transverse and lateral stability parameters C lβ And C nβ The above equation can be written as:
the transverse and lateral open-loop stability space criterion diagram can be drawn, whether the transverse and lateral stability requirements are met at a plurality of state points in the flight envelope of the aircraft under the configuration is judged, if not, new geometric shape parameters are selected again, and the step 2 is returned; if so, proceed to step 5.
Preferably, in step 5, on the premise of meeting the stability requirement, a control system is introduced to combine with control law design, and the closed-loop control pneumatic stability criterion and the non-minimum phase requirement are met by adjusting the parameters of the controller, so that the final output of the pneumatic layout design result of the aircraft under the pneumatic stability and control collaborative design requirement is specifically as follows:
since the lateral path of the aircraft is unstable, it is necessary to stabilize with a control law. Therefore, the design of a control system is introduced, and the closed-loop control pneumatic stability criterion is as follows:
where H, F represents different closed loop stability characteristic regions.
Similarly, the spatial criteria map corresponds to:
furthermore, according to the transversal non-minimum phase criterion, there is a straight line through the origin:
in the method, in the process of the invention,is an aileron induced aerodynamic stability parameter.
When the stability parameter (C lβ ,C nβ ) When the corresponding point is positioned above the straight line, the transverse system of the aircraft is a non-minimum phase system, and the transverse system is controlled by a conventional control method.
The beneficial effects of the invention are as follows: according to the method, a Bayesian regression technology is introduced to convert the least square problem equation of the intrinsic orthogonal decomposition into a regression process, so that aerodynamic data with high reliability and low reliability of the aircraft are fused, and the overall model precision of aerodynamic characteristics in the aircraft design process is improved; on the basis, the overall design method well realizes the balance of aerodynamic stability design and control design, has the capability of solving the problem of optimizing the design of multiple state points in the flight envelope, and provides a quick and reliable design tool for hypersonic aircrafts.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention.
FIG. 2 is a flow chart of a pneumatic data fusion method according to the present invention.
FIG. 3 is a schematic illustration of a flow chart of the aerodynamic stability and control co-design of an aircraft of the present invention.
Detailed Description
As shown in fig. 1, a hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion comprises the following steps:
step 1, initializing geometrical design variables and constraint ranges of an aircraft;
the design variables and the constraint ranges are defined according to practical problems, and the design variables can be set as geometrical parameters of the wing sweepback angle and the body height of the hypersonic aircraft by way of example;
step 2, determining a hypersonic aircraft reference aerodynamic layout, and parameterizing and describing the aircraft geometric configuration by adopting a state type function method;
the hypersonic aircraft reference aerodynamic layout takes SR-72 as a reference model, and adopts a hypersonic aircraft with large sweepback double-delta wing horizontal-tail-free aerodynamic layout. The section of the fuselage is in a sharp side edge back configuration, double-sweepback triangle wings are arranged on two sides of the fuselage, a pair of elevator surfaces on two sides control a pitching channel, and a single vertical tail type design controls a flying transverse channel.
Step 3, based on the parameterized geometric shape, respectively obtaining high-low fidelity data sets by adopting an engineering estimation method and a CFD fluid calculation method, and carrying out multi-fidelity data fusion on the high-low fidelity data sets by adopting an intrinsic orthogonal decomposition method based on Bayesian expansion to obtain an aerodynamic characteristic prediction proxy model of the aircraft, as shown in fig. 2;
step 31, initializing design variables of a multi-credibility pneumatic model, and respectively carrying out experimental design on different credibility models to obtain corresponding model responses and obtain a high-low credibility data set;
let the design variable be x= [ x ] 1 ,x 2 ,...,x d ]E D, where D is the design space and D is the design space dimension, and satisfiesR is a real number set;
and sampling different reliability models in the design space D to obtain a high-reliability data set and a low-reliability data set Y = [ Y ] 1 ,...,y n ]＝[y(ξ 1 ),...,y(ξ n )]Low confidence data design variable ζ i E D, i=1,..n, n is the number of low confidence datasets; high confidence data set t= [ t ] 1 ,...,t s ]＝[y′(e 1 ),...,y′(e s )]High confidence data design variable e i E, D, i=1, s; s is a high-credibility data setNumber of the pieces. The sampling method is one of optimal Latin hypercube sampling, full factor design and orthogonal experiment design methods or the assumed sample point is given.
Step 32, obtaining an intrinsic orthogonal decomposition modal matrix through singular value decomposition calculation based on a low-reliability data model; for the low fidelity data set Y E R N×n Singular value decomposition is carried out to obtain:
Y＝U∑V T
wherein: u= [ U ] 1 ,...,u N ]∈R N×N Sum v= [ V 1 ,...,v n ]∈R n×n As standard orthogonal matrix, i.e. U T U＝UU T ＝I N And V T V＝VV T ＝I n Wherein Σ=diag (σ) 1 ,...,σ n )∈R N×n Comprising singular values sigma arranged in descending order 1 ≥...≥σ n ≥0；
Assuming that the rank of matrix Y is r=rank (Y), then only the first r singular values are non-zero. The corresponding r left singular vectors, the first r columns of the matrix U, form a data set y 1 ,...,y n Standard orthonormal basis { u } of the composed space 1 ,...,u r "i.e. eigen-orthogonal basis of decomposition U r 。
Step 33, searching and determining the data point coordinates of the low fidelity data closest to the high reliability data, and obtaining the intrinsic orthogonal decomposition base coefficient based on a least square method and combining the intrinsic orthogonal decomposition modal matrix;
a given vector t epsilon R of high confidence data s Can be defined as at y' ∈R N Of only componentsA known vector, where s < N is the number of sampling points, j 1 ,...,j s ∈{1,...,N}：
For a matrixWherein->Represents the j th i Standard basis vectors. Characterizing the component of the vector t with the component of the vector y' by nearest neighbor search of s sample point coordinates in the computational grid;
the vector y' is approximated in the eigen-orthogonal decomposition subspace, and the eigen-orthogonal decomposition base coefficients can be foundSo that
In U r ＝[u 1 ,...,u r ]∈R N×r The basis vector matrix, the first r columns of U, is decomposed for eigen-orthogonality. Base coefficient vectorGenerating L that is the smallest observation for vector y 2 Error, defined by least squares problem
Typically, x=p T U r ∈R s×r With full rank, the above solution is therefore unique:
vector the base coefficientSubstituting the approximation equation, the estimated value +.>
Step 34, converting the least square problem of the intrinsic orthogonal decomposition into a regression problem based on the Bayesian theory, and constructing a corresponding Gaussian process regression model aiming at the intrinsic orthogonal decomposition modal matrix and the corresponding high-fidelity data set;
based on the Bayesian expansion idea, defining a least square problem equation of the intrinsic orthogonal decomposition as a regression process, and constructing a mapping f:directly matrix U r The rows mapped to vector y'
Obtaining a set of data pairs at a given sampling location:
{(x i ,t i )|i＝1,...,s}
wherein the method comprises the steps ofModal matrix U representing eigen-orthogonal decomposition r Is the j of (2) i The number of rows of the device is,responding to the corresponding sample;
and adopting a Gaussian process regression agent for the input-output relation of the data pair set:
assuming a gaussian process with zero mean for f (x), for any two inputs x, x' ∈r r Its covariance Cov [ f (x), f (x')]Given by covariance function k (x, x'), a widely used class of covariance functions is employed as follows:
k(x,x′)＝θ 0 ·exp(-θ 1 ||x-x′|| 2 )+θ 2 x T x′
in θ 0 ，θ 1 ，θ 2 For superparameters, the superparameters are typically not defined in advance, but rather are determined from the data by maximizing the log-boundary likelihood function:
then, for a new input variable x * ∈R r ，f * :＝f(x * ) The predictive distribution of (2) is as follows
E[f * ]＝k(x * )(K+σ 2 I) -1 t
Var[f * ]＝k(x * ,x * )-k(x * ) T (K+σ 2 I) -1 k(x * )
Wherein k (x) * ):＝(k(x * ,x i )) i＝1,..,s ∈R s And k= (K (x) i ,x j )) i,j＝1,..,s ∈R s×s 。
Step 35, outputting mean value and variance information of data fusion solutions under different input conditions by evaluating prediction distribution of all rows of the intrinsic orthogonal decomposition modal matrix;
by evaluating all rows x of the modal matrix * ＝(U r ) i I=1, & gt, and N, obtaining a data fusion prediction result of an intrinsic orthogonal decomposition method based on Bayesian expansion
The fusion evaluation criterion comprises Root Mean Square Error (RMSE) and a determination coefficient R 2 And an interval evaluation criterion PIC:
wherein N is V To verify the number of samples, y i To verify that the sample point is authenticThe value of the sum of the values,to verify sample point predictions, +.>Is y i Q is any quantile between (0, 1), typically taking q=0.025 and q=0.975.
Step 4, establishing an aerospace vehicle dynamics characteristic model, and judging whether the aerodynamic stability requirements of the aerospace vehicle in the transverse and lateral directions are met under the multi-state point of the aerospace vehicle by combining a flight envelope according to a collaborative design method of aerodynamic stability and control of the aerospace vehicle based on a space criterion diagram;
the hypersonic aircraft attitude dynamics model is constructed as follows:
wherein, (alpha, beta, mu) is the attack angle, sideslip angle and roll angle of the aircraft; (p, q, r) roll, pitch and yaw angular velocities, L, Y being the lift and side forces, respectively, experienced by the aircraft; l, M, N are the roll moment, pitch moment and yaw moment experienced by the aircraft, respectively; m and V are the mass and speed of the aircraft respectively; i x 、I z 、I y The rotational inertia of each shaft is respectively; i zx For each axis rotation product.
And selecting state points according to the flight envelope, and linearizing the model under each state point. According to the principle of small disturbance, the attitude kinetic equation can be decoupled into longitudinal motion and transverse lateral motion after being linearized by utilizing the horizontal sideslip-free flight condition. Decoupling the above equations into longitudinal and lateral equations with neglecting gravity, lift and lateral forces, stability analysis and control system design is based on the following equations:
wherein L' α 、L′ β 、L′ p 、L r ′、L q ′、Respectively rolling moment derivatives of all channels; n' α 、N′ β 、N′ p 、N r ′、N q ′、Respectively yaw moment derivatives of all channels; m's' α 、M′ β 、/>M q ' each channel pitch moment derivative; delta e The deflection angle of the elevator; delta a Is the aileron yaw angle.
The operators in the equation are defined as follows:
for hypersonic aircraft, the lateral-to-lateral channel is often unstable, and the choice of lateral-to-lateral stability parameters and lateral-to-lateral control laws is particularly important.
By solving the characteristic equation |λI-A|, the lateral stability criterion can be written as the following equation:
wherein C is nβ 、C lβ Are two classical stability parameters.
Based on a space criterion graph method, the x-axis and the y-axis are respectively corresponding to the transverse and lateral stability parameters C lβ And C nβ The above equation can be written as:
the transverse and lateral open-loop stability space criterion diagram can be drawn, whether the transverse and lateral stability requirements are met at a plurality of state points in the flight envelope of the aircraft under the configuration is judged, if not, new geometric shape parameters are selected again, and the step 2 is returned; if yes, continuing to step 5;
step 5, on the premise of meeting the stability requirement, introducing a control system to combine with control law design, and finally outputting an aircraft pneumatic layout design result meeting the pneumatic stability and control collaborative design requirement by adjusting controller parameters to meet a closed-loop control pneumatic stability criterion and a non-minimum phase requirement;
since the lateral path of the aircraft is unstable, it is necessary to stabilize with a control law. Therefore, the design of a control system is introduced, and the closed-loop control pneumatic stability criterion is as follows:
where H, F represents different closed loop stability characteristic regions.
Similarly, the spatial criteria map corresponds to:
furthermore, according to the transversal non-minimum phase criterion, there is a straight line through the origin:
in the method, in the process of the invention,caused by aileronsPneumatic stability parameters.
When the stability parameter (C lβ ,C nβ ) When the corresponding point is positioned above the straight line, the transverse system of the aircraft is a non-minimum phase system, and the transverse system can be controlled by a conventional control method. In conclusion, the aircraft pneumatic layout design result meeting the pneumatic stability and control collaborative design requirements is finally output.
Claims (10)
1. The hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion is characterized by comprising the following steps of:
step 1, initializing geometrical design variables and constraint ranges of an aircraft;
step 2, determining a hypersonic aircraft reference aerodynamic layout, and parameterizing and describing the aircraft geometric configuration by adopting a state type function method;
step 3, based on the parameterized geometric shape, respectively obtaining high-low fidelity data sets by adopting an engineering estimation method and a CFD fluid calculation method, and carrying out multi-fidelity data fusion on the high-low fidelity data sets by adopting an intrinsic orthogonal decomposition method based on Bayesian expansion to obtain an aircraft aerodynamic characteristic prediction proxy model;
step 4, establishing an aerospace vehicle dynamics characteristic model, and judging whether the aerodynamic stability requirements of the aerospace vehicle in the transverse and lateral directions are met under the multi-state point of the aerospace vehicle by combining a flight envelope according to a collaborative design method of aerodynamic stability and control of the aerospace vehicle based on a space criterion diagram;
and 5, introducing a control system to combine with control law design on the premise of meeting the stability requirement, and finally outputting an aircraft pneumatic layout design result meeting the pneumatic stability and control collaborative design requirement by adjusting the parameters of the controller to meet the closed-loop control pneumatic stability criterion and the non-minimum phase requirement.
2. The hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion according to claim 1, wherein in step 2, the hypersonic aircraft adopts a hypersonic aircraft with large sweepback and double-delta wing free-tail aerodynamic layout, the section of the aircraft body is in a sharp side edge back configuration, the two sides of the aircraft body are double-sweepback and delta wings, a pair of elevator surfaces on the two sides control pitching channels, and a single vertical tail type design controls a flying transverse channel.
3. The hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion according to claim 1, wherein in step 3, the eigen orthogonal decomposition data fusion method based on bayesian expansion specifically comprises the following steps:
step 31, initializing design variables of a multi-credibility pneumatic model, and respectively carrying out experimental design on different credibility models to obtain corresponding model responses and obtain a high-low credibility data set;
step 32, obtaining an intrinsic orthogonal decomposition modal matrix through singular value decomposition calculation based on a low-reliability data model;
step 33, searching and determining the data point coordinates of the low fidelity data closest to the high reliability data, and obtaining an intrinsic orthogonal decomposition base coefficient based on a least square method and combining the intrinsic orthogonal decomposition modal matrix;
step 34, converting the least square problem of the intrinsic orthogonal decomposition into a regression problem based on the Bayesian theory, and constructing a corresponding Gaussian process regression model aiming at the intrinsic orthogonal decomposition modal matrix and the corresponding high-fidelity data set;
and 35, outputting the mean value and variance information of the data fusion solutions under different input conditions by evaluating the prediction distribution of all rows of the intrinsic orthogonal decomposition modal matrix.
4. The hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion according to claim 3, wherein in step 31, initializing design variables of a multi-credibility pneumatic model, respectively performing experimental design on different credibility models, and obtaining corresponding model responses, and obtaining a high-low credibility data set specifically comprises the following steps:
step 31a,The design variable is x= [ x ] 1 ,x 2 ,...,x d ]E D, where D is the design space and D is the design space dimension, and satisfiesR is a real number set;
step 32b, experimental design refers to sampling different credibility models in a design space D to obtain a high-reliability data set and a low-reliability data set Y = [ Y ] 1 ,...,y n ]＝[y(ξ 1 ),...,y(ξ n )]Low confidence data design variable ζ i E D, i=1,..n, n is the number of low confidence datasets; high confidence data set t= [ t ] 1 ,...,t s ]＝[y′(e 1 ),...,y′(e s )]High confidence data design variable e i E, D, i=1, s; s is the number of high-reliability data sets, and the sampling method is one of optimal Latin hypercube sampling, full factor design and orthogonal experiment design methods or is assumed that a sample point is given.
5. The hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion according to claim 3, wherein in step 32, based on a low-reliability data model, the eigenvalue decomposition modal matrix obtained by singular value decomposition calculation is specifically:
for the low fidelity data set Y E R N×n Singular value decomposition is carried out to obtain:
Y＝U∑V T
wherein U= [ U ] 1 ,...,u N ]∈R N×N Sum v= [ V 1 ,...,v n ]∈R n×n As standard orthogonal matrix, i.e. U T U＝UU T ＝I N And V T V＝VV T ＝I n Wherein Σ=diag (σ 1 ,...,σ n )∈R N×n Comprising singular values sigma arranged in descending order 1 ≥...≥σ n ≥0；
Assuming that the matrix Y has rank r=rank (Y), then only the first r singular values are non-Zero, corresponding r left singular vectors, the first r columns of matrix U, form a data set y 1 ,...,y n Standard orthonormal basis { u } of the composed space 1 ,...,u r "i.e. eigen-orthogonal basis of decomposition U r 。
6. The hypersonic vehicle overall control collaborative design method based on multi-fidelity data fusion according to claim 3, wherein in step 33, searching and determining low-fidelity data point coordinates closest to high-reliability data, and obtaining intrinsic orthogonal decomposition base coefficients based on a least square method and combining the intrinsic orthogonal decomposition modal matrix is specifically as follows:
a given vector t epsilon R of high confidence data s Can be defined as at y' ∈R N Of only componentsA known vector, where s < N is the number of sampling points, j 1 ,...,j s ∈{1,...,N}：
For a matrixWherein->Represents the j th i The components of the vector y' are used for representing the components of the vector t by searching nearest neighbors of coordinates of s sampling points in a calculation grid;
the vector y' is approximated in the eigen-orthogonal decomposition subspace, and the eigen-orthogonal decomposition base coefficients can be foundSo that
In U r ＝[u 1 ,...,u r ]∈R N×r For eigenvector matrix, i.e. the first r columns of U, the base coefficient vector is decomposed eigenvectorGenerating L that is the smallest observation for vector y 2 Error, defined by least squares problem
Typically, x=p T U r ∈R s×r With full rank, the above solution is therefore unique:
vector the base coefficientSubstituting the approximation equation to obtain the estimated value +.>
7. The hypersonic vehicle overall control collaborative design method based on multi-fidelity data fusion according to claim 3, wherein in step 34, based on bayesian theory, the least square problem of eigen-orthogonal decomposition is converted into a regression problem, and the construction of a corresponding gaussian process regression model is specifically as follows:
based on Bayesian expansion idea, defining the least square problem equation of the intrinsic orthogonal decomposition as a regression process to construct a mappingDirectly matrix U r The rows mapped to vector y'
Obtaining a set of data pairs at a given sampling location:
{(x i ,t i )|i＝1,...,s}
wherein the method comprises the steps ofModal matrix U representing eigen-orthogonal decomposition r Is the j of (2) i The number of rows of the device is,responding to the corresponding sample;
and adopting a Gaussian process regression agent for the input-output relation of the data pair set:
assuming a gaussian process with zero mean for f (x), for any two inputs x, x' ∈r r Its covariance Cov [ f (x), f (x')]Given by covariance function k (x, x'), a widely used class of covariance functions is employed as follows:
k(x,x′)＝θ 0 ·exp(-θ 1 ||x-x′|| 2 )+θ 2 x T x′
in θ 0 ，θ 1 ，θ 2 For superparameters, the superparameters are typically not defined in advance, but rather are determined from the data by maximizing the log-boundary likelihood function:
then, for a new input variable x * ∈R r ，f * :＝f(x * ) The predictive distribution of (2) is as follows
E[f * ]＝k(x * )(K+σ 2 I) -1 t
Var[f * ]＝k(x * ,x * )-k(x * ) T (K+σ 2 I) -1 k(x * )
Wherein k (x) * ):＝(k(x * ,x i )) i＝1,..,s ∈R s And k= (K (x) i ,x j )) i,j＝1,..,s ∈R s×s 。
8. The hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion according to claim 3, wherein in step 35, by evaluating the prediction distribution of all rows of the eigenvalue orthogonal decomposition modal matrix, the mean and variance information of the data fusion solution under different input conditions is output specifically as follows: by evaluating all rows x of the modal matrix * ＝(U r ) i I=1, & gt, and N, obtaining a data fusion prediction result of an intrinsic orthogonal decomposition method based on Bayesian expansion
The fusion evaluation criterion comprises Root Mean Square Error (RMSE) and a determination coefficient R 2 And an interval evaluation criterion PIC:
wherein N is V To verify the number of samples, y i In order to verify the true value of the sample point,to verify sample point predictions, +.>Is y i Q is any quantile between (0, 1), taking q=0.025 and q=0.975.
9. The hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion according to claim 1, wherein in step 4, an aerospace aircraft dynamics characteristic model is established, and the aerospace aircraft aerodynamic stability and control collaborative design method based on a space criterion diagram is combined with a flight envelope to judge whether the requirements of lateral aerodynamic stability are met under the multi-state points of the aircraft, which is specifically as follows:
the hypersonic aircraft attitude dynamics model is constructed as follows:
wherein, (alpha, beta, mu) is the attack angle, sideslip angle and roll angle of the aircraft; (p, q, r) is the roll angle speed, pitch angle speed and yaw angle speed, L, Y is the lift and side forces experienced by the aircraft, respectively; l, M, N are the roll moment, pitch moment and yaw moment experienced by the aircraft, respectively; m and V are the mass and speed of the aircraft respectively; i x 、I z 、I y The rotational inertia of each shaft is respectively; i zx For each axis rotation product;
selecting state points according to the flight envelope, and carrying out linearization treatment on the model under each state point; according to the principle of small disturbance, the attitude kinetic equation is linearized by utilizing the horizontal sideslip-free flight condition and then decoupled into longitudinal motion and transverse lateral motion; decoupling the above equations into longitudinal and lateral equations with neglecting gravity, lift and lateral forces, stability analysis and control system design is based on the following equations:
wherein L' α 、L′ β 、L′ p 、L′ r 、L′ q 、Respectively rolling moment derivatives of all channels; n' α 、N′ β 、N′ p 、N′ r 、N′ q 、/>Respectively yaw moment derivatives of all channels; m's' α 、M′ β 、/>M′ q The pitch moment derivatives of the channels are respectively; delta e The deflection angle of the elevator; delta a Is the aileron deflection angle;
the operators in the equation are defined as follows:
for hypersonic aircrafts, the lateral and lateral channels are unstable, and the selection of lateral and lateral stability parameters and lateral control laws is particularly important;
by solving the characteristic equation |λI-A|, the lateral stability criterion is written as the following equation:
wherein C is nβ 、C lβ Is two classical stability parameters;
based on a space criterion graph method, the x-axis and the y-axis are respectively corresponding to the transverse and lateral stability parameters C lβ And C nβ The above equation can be written as:
drawing a transverse and lateral open-loop stability space criterion diagram, judging whether the transverse and lateral stability requirements are met at a plurality of state points in the flight envelope of the aircraft under the configuration, if not, reselecting new geometric shape parameters, and returning to the step 2; if so, proceed to step 5.
10. The hypersonic aircraft overall control collaborative design method based on multi-fidelity data fusion according to claim 1, wherein in step 5, on the premise of meeting the stability requirement, a control system is introduced to combine with control law design, the closed-loop control pneumatic stability criterion and the non-minimum phase requirement are met by adjusting the controller parameters, and the aircraft pneumatic layout design result under the pneumatic stability and control collaborative design requirement is finally output:
because the transverse direction channel of the aircraft is unstable and needs to be stabilized by adopting a control law, the design of a control system is introduced, and the closed-loop control pneumatic stability criterion is as follows:
wherein H, F represents distinct closed loop stability characteristic regions;
similarly, the spatial criteria map corresponds to:
furthermore, according to the transversal non-minimum phase criterion, there is a straight line through the origin:
in the method, in the process of the invention,aerodynamic stability parameters for ailerons;
when the stability parameter (C lβ ,C nβ ) When the corresponding point is positioned above the straight line, the transverse system of the aircraft is a non-minimum phase system, and the transverse system is controlled by a conventional control method.
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