CN112989497A - Tight branch radial basis function data transfer method based on geometric space main feature extraction - Google Patents
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Abstract
The invention discloses a tight branch radial basis function data transfer method based on geometric space main feature extraction, which comprises the following steps: extracting original grid node coordinates of a structural calculation grid for calculating aerodynamic heat generated by the overall shape or the local member shape of the aircraft and a non-structural calculation grid for calculating a temperature field to form an original coordinate matrix; secondly, performing principal component analysis on the original coordinate matrix formed in the first step to obtain a feature vector matrix; thirdly, performing coordinate transformation on the original coordinate matrix by using the characteristic vector matrix; step four, carrying out geometric dimension normalization on the node coordinates subjected to coordinate conversion in the step three; fifthly, interpolating the normalized node coordinates based on the tight radial basis function and the like; the invention realizes more precise prediction of the temperature of the aerodynamic thermal environment and the structural field of the aircraft and realizes higher-precision data transmission; the interpolation efficiency at the grid interface is improved, and the data transmission efficiency is further improved.
Description
Technical Field
The invention relates to the field of data transfer methods, in particular to a tight branch radial basis function data transfer method based on geometric space main feature extraction.
Background
The loose coupling method is a main method for solving the aerodynamic force/heat/structure multi-physics coupling problem of the current aircraft, and the basic idea is to solve a fluid control equation and a structure control equation in respective solvers according to a set sequence, and fully utilize the existing CFD and CSD solving methods and program modules. Because the solvers of the flow field and the structure which are developed and matured respectively have different characteristics, grids adopted in calculation are greatly different, so that the two sets of grids are not matched on an interface, and the problem of interpolation calculation processing of data transmission of the grid interface in multi-field coupling analysis is caused. In recent years, an interpolation processing method using Radial Basis Function (RBF) has been gradually developed, and has been successfully applied to multi-field coupling numerical value transfer. The method is simple in form and does not depend on discrete format of a solver and a grid topological structure. More commonly used radial basis functions include splines such as thin-plate splines (TPS), multiple-quadratic-surface bi-harmonic (MQ) surface fitting, and tight-support C2 basis functions.
The traditional tight radial basis function is isotropic, and the distribution of physical quantities of the hypersonic flight vehicle with a complex shape is highly related to local flow characteristics and has severe gradient change, such as the large distribution difference of the physical quantities of the head, the front edge, a wing rudder interference area, a large-area fuselage area, pressure, heat flow and the like of the flight vehicle is considered; in addition to the above factors, since the division of the complex-shape grid can perform encryption processing in the region with severe shape curvature or physical quantity change, the distribution of the grid points is also anisotropic, and the anisotropic factors of different grid point distributions are artificially introduced, so that there is a defect when the isotropic basis function is adopted to perform highly anisotropic physical quantity space calculation processing, and a bottleneck in improving precision and conservation is caused.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a tight branch radial basis function data transfer method based on geometric space main feature extraction, realizes more precise prediction on the temperature of the pneumatic thermal environment and the structural field of an aircraft, and realizes higher-precision data transfer; the calculation processing efficiency of the grid interface is improved, and the transmission efficiency of the data generated by the overall shape of the aircraft or the shape of the local component is improved.
The purpose of the invention is realized by the following scheme:
the tight branch radial basis function data transfer method based on the geometric space main feature extraction comprises the following steps:
step one, generating a structural computational grid C1 for calculating the aerodynamic heat and a non-structural computational grid C2 for calculating the temperature field for the overall shape or the local member shape of the aircraft respectively, extracting the original grid node coordinates of the computational grid C1, forming an original coordinate matrix A1 of the computational grid of the aerodynamic heat flow field of the aircraft, and storing the original coordinate matrix A1 in a computer memory; extracting original grid node coordinates of a computational grid C2, forming an original coordinate matrix A2 of an aircraft temperature field, and storing the original coordinate matrix A2 in a computer memory;
secondly, performing principal component analysis processing on the original coordinate matrix A1 of the computational grid of the aerodynamic heat flow field of the aircraft formed in the first step in a computer processor to obtain a characteristic vector matrix D, and storing the characteristic vector matrix D in a computer memory;
thirdly, carrying out coordinate transformation processing on an aircraft aerodynamic heat flow field calculation grid original coordinate matrix A1 and an aircraft temperature field original coordinate matrix A2 by using the eigenvector matrix D, respectively obtaining an aerodynamic heat node coordinate E1 and a temperature field node coordinate E2, and then storing the obtained coordinates in a computer memory;
fourthly, performing geometric scale normalization on the aerodynamic thermal node coordinate E1 and the temperature field node coordinate E2 obtained after coordinate conversion in the third step to obtain a normalized aerodynamic thermal node coordinate F1 and a normalized temperature field node coordinate F2, and storing the normalized aerodynamic thermal node coordinate F1 and the normalized temperature field node coordinate F2 in a computer memory;
and fifthly, calculating and processing the heat flow of the aircraft under the fixed Mach number and the attack angle in a computer processor on the basis of the tight support radial basis function on the normalized aerodynamic heat node coordinate F1 and the temperature field node coordinate F2, so that the overall shape or local component shape data transmission of the aircraft is completed.
Further, in the step one, the method comprises the steps of:
extracting original grid node coordinates of the structural calculation grid C1 of the computational aerodynamic heat to form an original coordinate matrix
Wherein
Coordinate vectors respectively representing the three directions of X, Y and Z of A1; extracting original grid node coordinates of the non-structural calculation grid C2 of the calculated temperature field to form an original coordinate matrix
Wherein
And respectively represent coordinate vectors of the x direction, the y direction and the z direction of the original coordinate matrix A2 of the temperature field of the aircraft.
Further, in the second step, the method comprises the following steps:
firstly, respectively constructing a covariance matrix B of an aircraft aerodynamic heat flow field calculation grid original coordinate matrix A1 according to the following formula (1):
wherein
For unknown characteristic root, I represents identity matrix, solving expression
To obtain a solution of the equation
Matrix of
Calculating a diagonal matrix formed by eigenvalues of a covariance matrix of a grid coordinate matrix for the aircraft aerodynamic heat flow field, and calculating an eigenvector matrix D corresponding to the covariance matrix B by using the following expression:
further, in the third step, according to the following formula (2), coordinate transformation is performed on the original grid coordinate matrix a1 of the aircraft aerodynamic heat field calculation grid by using the eigenvector matrix D to obtain an aerodynamic heat node coordinate E1, and meanwhile, coordinate transformation is performed on the original aircraft temperature field coordinate matrix a2 by using the eigenvector matrix D to obtain a temperature field node coordinate E2:
further, in step four, the aerodynamic-thermal node coordinate E1 and the temperature field node coordinate E2 after coordinate conversion in step three are geometrically normalized according to the following equation (3):
wherein,
respectively calculating a coordinate vector formed by each coordinate point after the grid transformation of the aerodynamic heat flow field calculation grid and the temperature field calculation grid of the aircraft;
is a vector formed by the maximum values of coordinates of the aerodynamic thermal node coordinate E1 and the temperature field node coordinate E2 in the x direction, the y direction and the z direction respectively,
is a vector formed by minimum values of coordinates of the aerodynamic thermal node coordinate E1 and the temperature field node coordinate E2 in three directions of x, y and z respectively,
and respectively calculating the number of all data points of the aircraft aerodynamic heat flow field calculation grid and the temperature field calculation grid.
Further, in step five, for the heat flow Q calculated by the computation grid of the aerodynamic heat flow field in the given mach number and attack angle state, the computation processing of the heat flow is completed by adopting a tight-support radial basis function from the aerodynamic heat node coordinate F1 to the temperature field node coordinate F2.
The invention has the beneficial effects that:
the invention realizes more precise prediction of the temperature of the aerodynamic thermal environment and the structural field of the aircraft and realizes higher-precision data transmission; the interpolation efficiency at the grid interface is improved, and the data transmission efficiency generated by the overall shape or the local member shape of the aircraft is further improved; specifically, the method comprises the following steps:
(1) in the embodiment of the invention, in order to solve the problems mentioned in the background, the characteristic that the grid distribution rule is basically consistent with the physical quantity distribution in the actual calculation of the aircraft is considered, namely the grid distribution is denser in the place with larger physical quantity gradient, and the grid distribution is sparser in the place with more gentle physical quantity distribution. According to the characteristic of grid distribution, the grid nodes formed by the overall shape or local component shape generation data of the aircraft are mapped by adopting principal component analysis, so that the distribution change of the physical quantity in the direction of the first main shaft is small, and the distribution change of the physical quantity in the direction of the second main shaft is large. On the basis, a shape data interpolation method of a radial basis function based on scale normalization is further utilized for processing, and the influence of physical quantity change in each direction is comprehensively considered in the basis function for processing the shape data, so that the interpolation precision of the shape data of the whole shape or local components of the aircraft is improved, the shape data transmission is more efficient, and the calculation processing time is saved; by using the data transmission method of the embodiment, the lower redundancy quality design of the thermal protection system of the aircraft can be realized, and the more precise and efficient prediction of the temperature change of the aerodynamic thermal environment and the structural field of the aircraft can be realized.
(2) In the embodiment of the invention, the principal component analysis is introduced into the problem of profile data transmission, the data of the overall profile or the local component profile of the aircraft is transformed in the interpolation calculation processing process, the distribution of physical quantity change is fully considered, and on the basis, the control is performed based on the scale of the geometric model, so that more points with similar physical quantities are selected to be processed in the same tight support radius range, and the points calculated by using the method have representativeness and aggregation, so that the calculation result can represent the physical actual distribution characteristics, the calculation error is reduced, and the calculation accuracy is improved. Verification tests prove that the method can realize the effect of reducing the error by 3 orders of magnitude, and obtains an obvious error improvement effect. The accuracy greatly improves the prediction of the temperature change of the thermal environment and the structural field of the aircraft, can effectively reduce the redundancy of the thermal protection system of the aircraft, and is favorable for obtaining the design of the thermal protection system of the aircraft which is safer and lighter.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic diagram of principal axis selection using principal component analysis;
FIG. 2 is a schematic diagram of a grid after projection using principal component analysis;
FIG. 3 is a cloud of heat flow error distributions before and after improvement using the method of an embodiment of the present invention; wherein, (a) is a heat flow error distribution cloud picture before improvement, and (b) is a heat flow error distribution cloud picture after improvement;
FIG. 4 is a flowchart illustrating steps of a method according to an embodiment of the present invention.
Detailed Description
All features disclosed in all embodiments in this specification, or all methods or process steps implicitly disclosed, may be combined and/or expanded, or substituted, in any way, except for mutually exclusive features and/or steps.
As shown in fig. 1 to 4, a tight branch radial basis function data transfer method based on geometric space main feature extraction includes:
step one, generating a structural computational grid C1 for calculating the aerodynamic heat and a non-structural computational grid C2 for calculating the temperature field for the overall shape or the local member shape of the aircraft respectively, extracting the original grid node coordinates of the computational grid C1, forming an original coordinate matrix A1 of the computational grid of the aerodynamic heat flow field of the aircraft, and storing the original coordinate matrix A1 in a computer memory; extracting original grid node coordinates of a computational grid C2, forming an original coordinate matrix A2 of an aircraft temperature field, and storing the original coordinate matrix A2 in a computer memory;
secondly, performing principal component analysis processing on the original coordinate matrix A1 of the computational grid of the aerodynamic heat flow field of the aircraft formed in the first step in a computer processor to obtain a characteristic vector matrix D, and storing the characteristic vector matrix D in a computer memory;
thirdly, carrying out coordinate transformation processing on an aircraft aerodynamic heat flow field calculation grid original coordinate matrix A1 and an aircraft temperature field original coordinate matrix A2 by using the eigenvector matrix D, respectively obtaining an aerodynamic heat node coordinate E1 and a temperature field node coordinate E2, and then storing the obtained coordinates in a computer memory;
fourthly, performing geometric scale normalization on the aerodynamic thermal node coordinate E1 and the temperature field node coordinate E2 obtained after coordinate conversion in the third step to obtain a normalized aerodynamic thermal node coordinate F1 and a normalized temperature field node coordinate F2, and storing the normalized aerodynamic thermal node coordinate F1 and the normalized temperature field node coordinate F2 in a computer memory;
and fifthly, calculating and processing the heat flow of the aircraft under the fixed Mach number and the attack angle in a computer processor on the basis of the tight support radial basis function on the normalized aerodynamic heat node coordinate F1 and the temperature field node coordinate F2, so that the overall shape or local component shape data transmission of the aircraft is completed.
Further, in the step one, the method comprises the steps of:
extracting original grid node coordinates of the structural calculation grid C1 of the computational aerodynamic heat to form an original coordinate matrix
Wherein
Coordinate vectors respectively representing the three directions of X, Y and Z of A1; extracting original grid node coordinates of the non-structural calculation grid C2 of the calculated temperature field to form an original coordinate matrix
Wherein
And respectively represent coordinate vectors of the x direction, the y direction and the z direction of the original coordinate matrix A2 of the temperature field of the aircraft.
Further, in the second step, the method comprises the following steps:
firstly, respectively constructing a covariance matrix B of an aircraft aerodynamic heat flow field calculation grid original coordinate matrix A1 according to the following formula (1):
wherein
For unknown characteristic root, I represents identity matrix, solving expression
To obtain a solution of the equation
Matrix of
Calculating a diagonal matrix formed by eigenvalues of a covariance matrix of a grid coordinate matrix for the aircraft aerodynamic heat flow field, and calculating an eigenvector matrix D corresponding to the covariance matrix B by using the following expression:
further, in the third step, according to the following formula (2), coordinate transformation is performed on the original grid coordinate matrix a1 of the aircraft aerodynamic heat field calculation grid by using the eigenvector matrix D to obtain an aerodynamic heat node coordinate E1, and meanwhile, coordinate transformation is performed on the original aircraft temperature field coordinate matrix a2 by using the eigenvector matrix D to obtain a temperature field node coordinate E2:
further, in step four, the aerodynamic-thermal node coordinate E1 and the temperature field node coordinate E2 after coordinate conversion in step three are geometrically normalized according to the following equation (3):
wherein,
respectively calculating a coordinate vector formed by each coordinate point after the grid transformation of the aerodynamic heat flow field calculation grid and the temperature field calculation grid of the aircraft;
is a vector formed by the maximum values of coordinates of the aerodynamic thermal node coordinate E1 and the temperature field node coordinate E2 in the x direction, the y direction and the z direction respectively,
is a vector formed by minimum values of coordinates of the aerodynamic thermal node coordinate E1 and the temperature field node coordinate E2 in three directions of x, y and z respectively,
and respectively calculating the number of all data points of the aircraft aerodynamic heat flow field calculation grid and the temperature field calculation grid.
Further, in step five, for the heat flow Q calculated by the computation grid of the aerodynamic heat flow field in the given mach number and attack angle state, the computation processing of the heat flow is completed by adopting a tight-support radial basis function from the aerodynamic heat node coordinate F1 to the temperature field node coordinate F2.
The idea of the invention is mainly to map n-dimensional features onto k-dimensions, the k-dimensions of the completely new orthogonal features are called principal components, and if k is equal to n, the original data is only converted. From finding a set of mutually orthogonal axes sequentially in the original space, the new axis selection is closely related to the data itself. In the idea of the invention, principal component analysis is innovatively introduced into the multi-field coupled data transfer problem, in the interpolation process, the original grid node data of the overall shape of the aircraft or the shape of a local component is transformed, so that the distribution of physical quantity change is fully considered in the direction of a new coordinate axis, on the basis, the coefficient scaling control is carried out on the xyz three directions in the radial basis calculation based on the scale of the geometric model, so as to select more points with similar physical quantities for calculation processing in the same tight-branch radius range, therefore, the points used for calculation and processing can be more representative and aggregative, so that the interpolation result can represent the physical actual distribution characteristics more, the calculation and processing precision is improved, the specific application of the idea can provide a feasible data transmission method with higher precision for the aerodynamic force/heat/structure multi-field coupling calculation of the aircraft.
For example, in other embodiments of the invention, the calculation processing of the heat flow data of the aircraft is carried out on a certain airfoil of the overall shape or the local component shape of the aircraft, and the number of grid nodes on the surface of the airfoil flow field is
4073 units, 4016 units; number of lattice nodes on the surface of the structure
The number of the cells is 5317, the number of the cells is 10520, and the heat flow value of each point on the grid points of the known flow field structure is known.
Constructing a coordinate matrix of the original grid nodes of the airfoil according to the step one
And constructing a covariance matrix B of the original node through the second step, and performing characteristic decomposition on the covariance matrix B by adopting a matlab system to obtain a characteristic vector matrix D:
and converting through the third step to obtain new coordinate values E1 and E2. Knowing this profile:
and (4) calculating according to the formula (3) in the step four to obtain the scaling factor of each point in different directions. The value of the scaled radial basis is calculated according to the scaling factor. And (3) replacing the radial basis in the standard tight branch radial basis function with the value of the scaled radial basis to finish the transfer calculation processing of data, wherein the actual error improvement effect of the method is shown in figure 3.
Other embodiments than the above examples may be devised by those skilled in the art based on the foregoing disclosure, or by adapting and using knowledge or techniques of the relevant art, and features of various embodiments may be interchanged or substituted and such modifications and variations that may be made by those skilled in the art without departing from the spirit and scope of the present invention are intended to be within the scope of the following claims.
The functionality of the present invention, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium, and all or part of the steps of the method according to the embodiments of the present invention are executed in a computer device (which may be a personal computer, a server, or a network device) and corresponding software. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, or an optical disk, exist in a read-only Memory (RAM), a Random Access Memory (RAM), and the like, for performing a test or actual data in a program implementation.
Claims (6)
1. The tight branch radial basis function data transfer method based on the geometric space main feature extraction is characterized by comprising the following steps:
step one, generating a structural computational grid C1 for calculating the aerodynamic heat and a non-structural computational grid C2 for calculating the temperature field for the overall shape or the local member shape of the aircraft respectively, extracting the original grid node coordinates of the computational grid C1, forming an original coordinate matrix A1 of the computational grid of the aerodynamic heat flow field of the aircraft, and storing the original coordinate matrix A1 in a computer memory; extracting original grid node coordinates of a computational grid C2, forming an original coordinate matrix A2 of an aircraft temperature field, and storing the original coordinate matrix A2 in a computer memory;
secondly, performing principal component analysis processing on the original coordinate matrix A1 of the computational grid of the aerodynamic heat flow field of the aircraft formed in the first step in a computer processor to obtain a characteristic vector matrix D, and storing the characteristic vector matrix D in a computer memory;
thirdly, carrying out coordinate transformation processing on an aircraft aerodynamic heat flow field calculation grid original coordinate matrix A1 and an aircraft temperature field original coordinate matrix A2 by using the eigenvector matrix D, respectively obtaining an aerodynamic heat node coordinate E1 and a temperature field node coordinate E2, and then storing the obtained coordinates in a computer memory;
fourthly, performing geometric scale normalization on the aerodynamic thermal node coordinate E1 and the temperature field node coordinate E2 obtained after coordinate conversion in the third step to obtain a normalized aerodynamic thermal node coordinate F1 and a normalized temperature field node coordinate F2, and storing the normalized aerodynamic thermal node coordinate F1 and the normalized temperature field node coordinate F2 in a computer memory;
and fifthly, calculating and processing the heat flow of the aircraft under the fixed Mach number and the attack angle in a computer processor on the basis of the tight support radial basis function on the normalized aerodynamic heat node coordinate F1 and the temperature field node coordinate F2, so that the overall shape or local component shape data transmission of the aircraft is completed.
2. The tight branch radial basis function data transfer method based on geometric space main feature extraction according to claim 1, characterized in that in step one, the method comprises the steps of:
extracting original grid node coordinates of the structural calculation grid C1 of the computational aerodynamic heat to form an original coordinate matrix
Wherein
Coordinate vectors respectively representing the three directions of X, Y and Z of A1; extracting original grid node coordinates of the non-structural calculation grid C2 of the calculated temperature field to form an original coordinate matrix
Wherein
And respectively represent coordinate vectors of the x direction, the y direction and the z direction of the original coordinate matrix A2 of the temperature field of the aircraft.
3. The method for transferring data of tight-branch radial basis function based on geometric space main feature extraction according to claim 2, wherein in the second step, the method comprises the following steps:
firstly, respectively constructing a covariance matrix B of an aircraft aerodynamic heat flow field calculation grid original coordinate matrix A1 according to the following formula (1):
wherein
For unknown characteristic root, I represents identity matrix, solving expression
To obtain a solution of the equation
Matrix of
Calculating a diagonal matrix formed by eigenvalues of a covariance matrix of a grid coordinate matrix for the aircraft aerodynamic heat flow field, and calculating an eigenvector matrix D corresponding to the covariance matrix B by using the following expression:
4. the method for transferring data of tight radial basis function based on principal feature extraction in geometric space according to claim 3, wherein in step three, the original coordinate matrix A1 of the computational grid of the aircraft aerodynamic heat field is subjected to coordinate transformation by using the eigenvector matrix D to obtain an aerodynamic heat node coordinate E1, and the original coordinate matrix A2 of the aircraft temperature field is subjected to coordinate transformation by using the eigenvector matrix D to obtain a temperature field node coordinate E2 according to the following formula (2):
5. the method for transferring data of tight radial basis function based on geometric space principal feature extraction according to claim 4, characterized in that in step four, the aerodynamic-thermal node coordinate E1 and the temperature field node coordinate E2 after coordinate transformation in step three are subjected to geometric dimension normalization according to the following equation (3):
wherein,
respectively calculating a coordinate vector formed by each coordinate point after the grid transformation of the aerodynamic heat flow field calculation grid and the temperature field calculation grid of the aircraft;
is a vector formed by the maximum values of coordinates of the aerodynamic thermal node coordinate E1 and the temperature field node coordinate E2 in the x direction, the y direction and the z direction respectively,
is a vector formed by minimum values of coordinates of the aerodynamic thermal node coordinate E1 and the temperature field node coordinate E2 in three directions of x, y and z respectively,
and respectively calculating the number of all data points of the aircraft aerodynamic heat flow field calculation grid and the temperature field calculation grid.
6. The method for transferring data of tight branch radial basis function based on principal feature extraction in geometric space as claimed in claim 5, wherein in step five, for the heat flow Q calculated by the computational grid of the aerodynamic heat flow field under the given Mach number and attack angle state, the calculation process of the heat flow is completed by using the tight branch radial basis function from the aerodynamic heat node coordinate F1 to the temperature field node coordinate F2.
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