CN114218686A - Multi-precision data smooth scale approximate modeling method for aircraft - Google Patents

Multi-precision data smooth scale approximate modeling method for aircraft Download PDF

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CN114218686A
CN114218686A CN202210154400.2A CN202210154400A CN114218686A CN 114218686 A CN114218686 A CN 114218686A CN 202210154400 A CN202210154400 A CN 202210154400A CN 114218686 A CN114218686 A CN 114218686A
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CN114218686B (en
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武泽平
彭博
王志祥
雷勇军
张为华
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National University of Defense Technology
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Abstract

The invention discloses a smooth scale approximate modeling method for multi-precision data of an aircraft. In the process of establishing the scale function, the relevance of the high-precision model and the low-precision model is considered, the scale function is enabled to be as smooth as possible, namely the linear term of the low-precision model, the shape parameter of the scale function and the smooth factor of the scale function are subjected to parameter training by taking the minimum average curvature of the scale function as a target, and finally the prediction precision of the multi-precision proxy model is obviously improved, so that the high-efficiency and accurate construction of the multi-precision model of the aircraft is realized, the number of high-precision sample points required by modeling is reduced, the modeling efficiency is obviously improved, and the subsequent optimization is guided.

Description

Multi-precision data smooth scale approximate modeling method for aircraft
Technical Field
The invention relates to the technical field of optimization design of aircrafts, in particular to a smooth scale approximate modeling method for multi-precision data of an aircraft.
Background
With the rapid development of computer technology, an optimization method based on a proxy model becomes one of the methods widely applied in the design process of an aircraft. However, in the process of optimization design, multiple times of calling of a high-precision simulation model cannot be avoided, and the calculation time is consumed, so that the requirements of high speed and high efficiency of aircraft design cannot be met. The multi-precision model fusion order-reduction characterization method is used for establishing the multi-precision agent model by introducing low-precision numerical simulation analysis, so that the calculation consumption can be obviously reduced while the accuracy of the model is ensured, and the subsequent optimization design is guided.
The commonly used multi-precision agent model establishing method at present comprises the following steps:
1. the multi-precision proxy model modeling method based on the scale function comprises the following steps: establishing a low-precision proxy model by using a large number of low-precision sample points, establishing a scale function between the high-precision model and the low-precision model by taking the error between the high-precision real output of the sample points and the prediction output of the low-precision model as output, and fusing the scale function and the low-precision proxy model by adopting an additive scale or multiplication scale method to establish a multi-precision proxy model;
2. the multi-precision agent model modeling method based on the space mapping comprises the following steps: and searching a proper transfer function, mapping the design variable space of the high-precision analysis model to the design variable space of the low-precision analysis model, or mapping the low-precision output space to the output space of the high-precision analysis model to construct a multi-precision proxy model. Converting the high-precision model optimization problem into a low-precision model optimization problem through a transfer function;
3. the Co-Kriging multi-precision agent model modeling method comprises the following steps: based on the Bayesian theory, a trend is provided by a low-precision analysis model, and a multi-precision agent model is constructed by interpolating high-precision sample points.
The conventional multi-precision agent model modeling method has the following defects:
1. the relevance research of high-precision and low-precision analysis models is insufficient based on a scale function and a Co-Kriging multi-precision agent model modeling method, high-precision numerical simulation and low-precision numerical simulation are still regarded as two independent modeling problems, the strong relevance of the high-precision numerical simulation and the low-precision numerical simulation in engineering problems is not searched, and the further improvement of the model precision is limited;
2. the multi-precision agent model modeling method based on space mapping mainly enables the optimal solution of a low-precision simulation function to approach the optimal solution of a high-precision simulation function through the design space of a low-precision simulation function, the core of the process lies in finding a proper mapping relation to convert the high-precision simulation function and the low-precision simulation function, however, the form of a conversion function is complicated and difficult to judge the accuracy of the mapping relation, continuous trial is needed, and meanwhile, the capability of quantifying errors is lacked, so that the method is poor in applicability.
Disclosure of Invention
Aiming at the problems that in the prior art, when a multi-precision agent model is constructed in the process of aircraft optimization design, the model precision is poor, and the follow-up optimization design cannot be effectively guided, the invention provides a multi-precision data smooth scale approximate modeling method for an aircraft, which can effectively improve the performance and realize the accurate construction of the multi-precision agent model in the aircraft optimization design.
To achieve the above object, the present invention provides a smooth scale approximate modeling method for multi-precision data of an aircraft, comprising the steps of:
step 1, obtaining design variables and a design domain, and initially sampling to obtain high-precision sample points and low-precision sample points;
step 2, establishing a low-precision proxy model based on the low-precision sample points;
step 3, taking the difference between the high-precision sample point and the low-precision proxy model predicted value as a scale function sample point to obtain a scale function sample point set;
step 4, constructing a scale function based on the scale function sample point set to obtain the average curvature of the scale function in the design domain, and performing smoothness training on the scale function by taking the minimum average curvature of the scale function in the design domain as a target;
and 5, obtaining a multi-precision agent model.
In another embodiment, in step 1, the initial sampling obtains a high-precision sample point and a low-precision sample point, specifically:
respectively selecting by adopting a Latin hypercube sampling method
Figure 894207DEST_PATH_IMAGE001
A low precision sampling point and
Figure 14610DEST_PATH_IMAGE002
each high-precision sampling point is obtained by running a simulation model with corresponding precision at each sampling point respectively
Figure 325506DEST_PATH_IMAGE003
A low precision sample point and
Figure 127239DEST_PATH_IMAGE002
the high-precision sample points of each sample are respectively as follows:
Figure 472770DEST_PATH_IMAGE004
in the formula (I), the compound is shown in the specification,X iLis shown asiThe input value of one of the low-precision sample points,Y iLis shown asiThe response value of the sample point of low precision,X iHis shown asiThe input value of each sample point with high precision,Y iHis shown asiAnd (5) high-precision sample point response values.
In another embodiment, in step 2, the low-precision proxy model is:
Figure 29653DEST_PATH_IMAGE005
in the formula (I), the compound is shown in the specification,f L(x) In order to be a low-precision proxy model,
Figure 703211DEST_PATH_IMAGE007
for any point in the design domain
Figure 433270DEST_PATH_IMAGE008
And a first
Figure 272788DEST_PATH_IMAGE010
A low precision sample point
Figure 797310DEST_PATH_IMAGE011
Is a distance therebetween, i.e.
Figure 286060DEST_PATH_IMAGE012
；
Figure 429597DEST_PATH_IMAGE013
Is as follows
Figure 484140DEST_PATH_IMAGE014
The basis function coefficients of the low precision sample points,
Figure 320509DEST_PATH_IMAGE015
is as follows
Figure 93293DEST_PATH_IMAGE016
The basis functions of the low precision sample points.
In another embodiment, a Gauss function is selected as a basis function of the low-precision sample points, which is:
Figure 774941DEST_PATH_IMAGE017
in the formula (I), the compound is shown in the specification,
Figure 215150DEST_PATH_IMAGE018
is as follows
Figure 455376DEST_PATH_IMAGE019
The shape parameters of the basis functions are:
Figure 918719DEST_PATH_IMAGE020
in the formula (I), the compound is shown in the specification,
Figure 528692DEST_PATH_IMAGE021
is as follows
Figure 229931DEST_PATH_IMAGE022
The distance between the one low precision sample point to the farthest sample point,
Figure 735999DEST_PATH_IMAGE024
to design spatial dimensions;
will be provided with
Figure 93162DEST_PATH_IMAGE026
Substituting the input value and the response value of each low-precision sample point into the low-precision proxy model to obtain the basis function coefficient of the low-precision sample point
Figure 772405DEST_PATH_IMAGE027
And solving the equation set to obtain a basis function coefficient to obtain the low-precision proxy model.
In another embodiment, step 3 specifically includes:
calculating the difference between the response value of the high-precision sample point and the predicted value of the low-precision proxy model as a scaling function sample point, wherein the difference is as follows:
Figure 531414DEST_PATH_IMAGE028
in the formula (I), the compound is shown in the specification,
Figure 208383DEST_PATH_IMAGE029
is as follows
Figure 443055DEST_PATH_IMAGE031
The difference between the individual high-precision sample point response values and the low-precision proxy model prediction values,
Figure 768732DEST_PATH_IMAGE033
、
Figure 975722DEST_PATH_IMAGE034
respectively linear correction constants for the low-precision proxy model,
Figure 620330DEST_PATH_IMAGE035
is as follows
Figure 217665DEST_PATH_IMAGE036
The predicted value of the low-precision agent model at each high-precision sample point;
obtaining a set of scale function sample points:
Figure 176394DEST_PATH_IMAGE037
in the formula (I), the compound is shown in the specification,X iDis shown asiThe sample point input values of the individual scaling functions,Y iLis shown asiThe point response values of the sample points of the individual scaling functions,n Dthe number of sample points is a scaling function.
In another embodiment, in step 4, the constructing a scale function based on the scale function sample point set specifically includes:
Figure 769049DEST_PATH_IMAGE038
in the formula (I), the compound is shown in the specification,
Figure 725504DEST_PATH_IMAGE039
for any point in the design domain
Figure 872451DEST_PATH_IMAGE040
And a first
Figure 431608DEST_PATH_IMAGE041
Sample points of a scaling function
Figure 285295DEST_PATH_IMAGE042
The distance between the two or more of the two or more,
Figure 6126DEST_PATH_IMAGE043
；
Figure 640370DEST_PATH_IMAGE044
is as follows
Figure 377120DEST_PATH_IMAGE045
The basis function coefficients of the individual scale function sample points;
Figure 209946DEST_PATH_IMAGE046
is as follows
Figure 977045DEST_PATH_IMAGE047
The basis functions of the sample points of the individual scaling functions.
In another embodiment, the Gauss function is chosen as the basis function for the scaling function sample points as:
Figure 98585DEST_PATH_IMAGE048
in the formula (I), the compound is shown in the specification,
Figure 265124DEST_PATH_IMAGE049
a shape parameter correction factor;
Figure 562244DEST_PATH_IMAGE050
is as follows
Figure 93720DEST_PATH_IMAGE051
The shape parameters of the basis functions are:
Figure 233714DEST_PATH_IMAGE052
in the formula (I), the compound is shown in the specification,
Figure 79310DEST_PATH_IMAGE053
is as follows
Figure 621150DEST_PATH_IMAGE054
The distance between the sample point of the individual scaling functions to the farthest sample point;
will be provided with
Figure 323527DEST_PATH_IMAGE055
Substituting the input value and the response value of the sample point of the scaling function into the scaling function to obtain the coefficient of the sample point of the scaling function
Figure 324719DEST_PATH_IMAGE056
The system of linear equations of (1) is:
Figure 833061DEST_PATH_IMAGE057
in the formula (I), the compound is shown in the specification,
Figure 432669DEST_PATH_IMAGE058
and solving the equation set to obtain a basic function coefficient for a scale function smoothing factor to obtain a scale function.
In another embodiment, the average curvature of the scaling function in the design domain is:
Figure 978051DEST_PATH_IMAGE059
in the formula:
Figure 358217DEST_PATH_IMAGE061
is the average curvature of the scaling function in the design domain,
Figure 14457DEST_PATH_IMAGE062
as a function of scale in
Figure 734152DEST_PATH_IMAGE063
Local curvature of the surface.
In another embodiment, in step 4, the smoothness training of the scale function is performed with the goal of minimizing the average curvature of the scale function in the design domain, specifically:
Figure 575069DEST_PATH_IMAGE064
in the formula (I), the compound is shown in the specification,
Figure 317897DEST_PATH_IMAGE065
for the maximum error between the multi-precision proxy model prediction value and the high-precision sample point response value,
Figure 902462DEST_PATH_IMAGE066
constraining an upper bound for errors
In another embodiment, in step 5, the multi-precision proxy model is:
Figure 476663DEST_PATH_IMAGE067
in the formula (I), the compound is shown in the specification,f(x) Representing a multi-precision proxy model.
Compared with the prior art, the smooth scale approximate modeling method for the multi-precision data of the aircraft has the following beneficial technical effects:
1. aiming at the problems that the multi-precision agent model is inaccurate and the relevance between high-precision data and low-precision data is neglected in the optimization design process of the aircraft, the high-efficiency and accurate multi-precision agent model modeling method is provided. The hyper-parameters in the multi-precision proxy model are trained, the average curvature of the scaling function in the proxy model is optimized, the prediction precision of the multi-precision proxy model is effectively improved, the number of high-precision sample points required by modeling is reduced, the modeling efficiency is remarkably improved, and the subsequent optimization is guided;
2. according to the method, a low-precision proxy model is constructed by using low-precision simulation data, linear term parameters are added to correct the low-precision proxy model, and a scale function is constructed through a difference value between a high-precision sample point and a low-precision predicted value of a corresponding position of the high-precision sample point. In the process of establishing the scale function, the relevance of the high-precision model and the low-precision model is considered, the scale function is made to be as smooth as possible, namely, the linear term of the low-precision model, the shape parameter of the scale function and the smooth factor of the scale function are subjected to parameter training by taking the minimum average curvature of the scale function as a target, and finally, the prediction precision of the multi-precision proxy model is obviously improved, so that the high-efficiency and accurate construction of the multi-precision model of the aircraft is realized.
Drawings
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, 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 the structures shown in the drawings without creative efforts.
FIG. 1 is a flow chart of a smooth scale approximation modeling method for multi-precision data in an embodiment of the invention;
FIG. 2 is a schematic structural representation of an exemplary heavy launch vehicle concentration force dispersion cabin segment in an embodiment of the invention;
FIG. 3 is a schematic diagram illustrating an exemplary multi-zone skin partitioning method according to an embodiment of the present disclosure;
FIG. 4 is a schematic view of an exemplary variable cross-section main beam in an embodiment of the invention;
FIG. 5 is a schematic illustration of an exemplary non-uniform secondary beam/stringer layout in an embodiment of the present invention;
fig. 6 is a schematic diagram of an exemplary layout format of middle boxes and end boxes in the embodiment of the present invention.
The implementation, functional features and advantages of the objects of the present invention will be further explained with reference to the accompanying drawings.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that all the directional indicators (such as up, down, left, right, front, and rear … …) in the embodiment of the present invention are only used to explain the relative position relationship between the components, the movement situation, etc. in a specific posture (as shown in the drawing), and if the specific posture is changed, the directional indicator is changed accordingly.
In addition, the descriptions related to "first", "second", etc. in the present invention are only for descriptive purposes and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "connected," "secured," and the like are to be construed broadly, and for example, "secured" may be a fixed connection, a removable connection, or an integral part; the connection can be mechanical connection, electrical connection, physical connection or wireless communication connection; they may be directly connected or indirectly connected through intervening media, or they may be connected internally or in any other suitable relationship, unless expressly stated otherwise. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In addition, the technical solutions in the embodiments of the present invention may be combined with each other, but it must be based on the realization of those skilled in the art, and when the technical solutions are contradictory or cannot be realized, such a combination of technical solutions should not be considered to exist, and is not within the protection scope of the present invention.
The embodiment provides an efficient and accurate multi-precision agent model modeling method, and particularly provides a smooth scale approximate modeling method for multi-precision data of an aircraft, aiming at the problems that a multi-precision agent model is inaccurate and ignores the correlation between high-precision data and low-precision data in the optimization design process of the aircraft. The method comprises the steps of firstly constructing a low-precision proxy model by using low-precision simulation data, adding linear term parameters to correct the low-precision proxy model, constructing a scale function through a difference value between a high-precision sample point and a low-precision predicted value of a corresponding position of the high-precision sample point, and in the process of establishing the scale function, considering the relevance of the high-precision model and the low-precision model, enabling the scale function to be as smooth as possible, namely performing parameter training on the linear term of the low-precision model, the shape parameters of the scale function and the smooth factors of the scale function by taking the minimum average curvature of the scale function as a target, and finally obviously improving the prediction precision of the multi-precision proxy model, so that the high-efficiency and accurate construction of the multi-precision model of the aircraft is realized.
Referring to FIG. 1, in an implementation, a method for smooth scale approximate modeling of multi-precision data for an aircraft includes the following steps 1-5.
Step 1, obtaining design variables and a design domain of a given aircraft optimization design, and initially sampling to obtain high-precision sample points and low-precision sample points. The initial application process of the high-precision sample points and the low-precision sample points is specifically as follows:
respectively selecting by adopting a Latin hypercube sampling method
Figure 127962DEST_PATH_IMAGE069
A low precision sampling point and
Figure 951561DEST_PATH_IMAGE071
each high-precision sampling point is obtained by running a simulation model with corresponding precision at each sampling point respectively
Figure 543079DEST_PATH_IMAGE072
A low precision sample point and
Figure 909470DEST_PATH_IMAGE073
the high-precision sample points of each sample are respectively as follows:
Figure 92189DEST_PATH_IMAGE074
in the formula (I), the compound is shown in the specification,X iLis shown asiThe input value of one of the low-precision sample points,Y iLis shown asiThe response value of the sample point of low precision,X iHis shown asiThe input value of each sample point with high precision,Y iHis shown asiAnd (5) high-precision sample point response values.
Step 2, establishing a low-precision proxy model based on the low-precision sample points, which comprises the following steps:
Figure 871927DEST_PATH_IMAGE075
in the formula (I), the compound is shown in the specification,f L(x) In order to be a low-precision proxy model,
Figure 673661DEST_PATH_IMAGE077
for any point in the design domain
Figure 19191DEST_PATH_IMAGE078
And a first
Figure 513758DEST_PATH_IMAGE079
A low precision sample point
Figure 515212DEST_PATH_IMAGE080
Is a distance therebetween, i.e.
Figure 245270DEST_PATH_IMAGE081
；
Figure 553630DEST_PATH_IMAGE083
Is as follows
Figure 609310DEST_PATH_IMAGE084
The basis function coefficients of the low precision sample points,
Figure 98060DEST_PATH_IMAGE085
is as follows
Figure 241597DEST_PATH_IMAGE086
The basis functions of the low precision sample points. Selecting a Gauss function as a basic function of the low-precision sample point, wherein the basic function comprises the following steps:
Figure 561720DEST_PATH_IMAGE087
in the formula (I), the compound is shown in the specification,
Figure 725985DEST_PATH_IMAGE089
is as follows
Figure 374135DEST_PATH_IMAGE090
The shape parameter of each basis function adopts a direct determination method, and comprises the following steps:
Figure 445996DEST_PATH_IMAGE091
in the formula (I), the compound is shown in the specification,
Figure 823888DEST_PATH_IMAGE092
is as follows
Figure 565579DEST_PATH_IMAGE093
The distance between the one low precision sample point to the farthest sample point,
Figure 825659DEST_PATH_IMAGE094
to design spatial dimensions;
will be provided with
Figure 75113DEST_PATH_IMAGE096
Substituting the input value and the response value of each low-precision sample point into the low-precision proxy model to obtain the basis function coefficient of the low-precision sample point
Figure 307511DEST_PATH_IMAGE097
The system of linear equations of (1) is:
Figure 344737DEST_PATH_IMAGE098
and solving the equation set to obtain a basis function coefficient to obtain the low-precision proxy model.
And 3, taking the difference between the high-precision sample point and the low-precision proxy model predicted value as a scale function sample point to obtain a scale function sample point set. In the specific implementation process:
calculating the difference between the response value of the high-precision sample point and the predicted value of the low-precision proxy model as a scaling function sample point, wherein the difference is as follows:
Figure 233059DEST_PATH_IMAGE099
in the formula (I), the compound is shown in the specification,
Figure 646722DEST_PATH_IMAGE100
is as follows
Figure 405731DEST_PATH_IMAGE102
The difference between the individual high-precision sample point response values and the low-precision proxy model prediction values,
Figure 82700DEST_PATH_IMAGE103
、
Figure 51793DEST_PATH_IMAGE104
respectively linear correction constants for the low-precision proxy model,
Figure 144514DEST_PATH_IMAGE105
is as follows
Figure 351504DEST_PATH_IMAGE106
The predicted value of the low-precision agent model at each high-precision sample point;
obtaining a set of scale function sample points:
Figure 730533DEST_PATH_IMAGE107
in the formula (I), the compound is shown in the specification,X iDis shown asiThe sample point input values of the individual scaling functions,Y iLis shown asiThe point response values of the sample points of the individual scaling functions,n Dthe number of sample points is a scaling function.
And 4, constructing a scale function based on the scale function sample point set to obtain the average curvature of the scale function in the design domain, and performing smoothness training on the scale function by taking the minimum average curvature of the scale function in the design domain as a target. Wherein the scaling function is specifically:
Figure 826403DEST_PATH_IMAGE108
in the formula (I), the compound is shown in the specification,
Figure 581869DEST_PATH_IMAGE109
for any point in the design domain
Figure 643366DEST_PATH_IMAGE110
And a first
Figure 334242DEST_PATH_IMAGE111
Sample points of a scaling function
Figure 543506DEST_PATH_IMAGE112
The distance between the two or more of the two or more,
Figure 40346DEST_PATH_IMAGE113
；
Figure 628454DEST_PATH_IMAGE114
is as follows
Figure 880443DEST_PATH_IMAGE116
The basis function coefficients of the individual scale function sample points;
Figure 186791DEST_PATH_IMAGE117
is as follows
Figure 487322DEST_PATH_IMAGE118
The basis functions of the sample points of the individual scaling functions. Selecting a Gauss function as a basic function of a scale function sample point, wherein the shape parameter adopts a direct determination method and comprises the following steps:
Figure 320149DEST_PATH_IMAGE119
in the formula (I), the compound is shown in the specification,
Figure 851362DEST_PATH_IMAGE121
a shape parameter correction factor;
Figure 972902DEST_PATH_IMAGE122
is as follows
Figure 608283DEST_PATH_IMAGE123
The shape parameters of the basis functions are:
Figure 436562DEST_PATH_IMAGE124
in the formula (I), the compound is shown in the specification,
Figure 764775DEST_PATH_IMAGE125
is as follows
Figure 108031DEST_PATH_IMAGE127
The distance between the sample point of the individual scaling functions to the farthest sample point;
will be provided with
Figure 688048DEST_PATH_IMAGE129
Substituting the input value and the response value of the sample point of the scaling function into the scaling function to obtain the coefficient of the sample point of the scaling function
Figure 495467DEST_PATH_IMAGE130
The system of linear equations of (1) is:
Figure 869948DEST_PATH_IMAGE131
in the formula (I), the compound is shown in the specification,
Figure 700501DEST_PATH_IMAGE132
and solving the equation set to obtain a basic function coefficient for a scale function smoothing factor to obtain a scale function.
The average curvature of the scaling function in the design domain is found from its local curvature at each low precision sample point location, i.e.:
Figure 943263DEST_PATH_IMAGE133
in the formula:
Figure 979090DEST_PATH_IMAGE134
is the average curvature of the scaling function in the design domain,
Figure 649106DEST_PATH_IMAGE135
as a function of scale in
Figure 966955DEST_PATH_IMAGE136
Local curvature of the surface.
Since the mean curvature of the scale function in the design domain is a multi-dimensional problem, the hessian matrix is used
Figure 623195DEST_PATH_IMAGE137
Solving (Hessian Matrix), wherein the specific implementation process comprises the following steps:
Figure 405206DEST_PATH_IMAGE138
in the formula:
Figure 121490DEST_PATH_IMAGE139
is composed of
Figure 926635DEST_PATH_IMAGE141
To (1) a
Figure 511200DEST_PATH_IMAGE142
A characteristic value;
the hessian matrix is of the form:
Figure 23084DEST_PATH_IMAGE143
the form of the scaling function can be written as:
Figure 34902DEST_PATH_IMAGE144
in the formula (I), the compound is shown in the specification,
Figure 61764DEST_PATH_IMAGE145
as a gaussian function, can be written as:
Figure 89500DEST_PATH_IMAGE146
Figure 314945DEST_PATH_IMAGE147
is composed of
Figure 700927DEST_PATH_IMAGE148
And a first
Figure 418348DEST_PATH_IMAGE149
The distance between sample points of the individual scaling functions can be written as:
Figure 344715DEST_PATH_IMAGE150
in the formula: subscript
Figure 627929DEST_PATH_IMAGE151
Is shown as
Figure 122496DEST_PATH_IMAGE152
And (4) each dimension.
Figure 186266DEST_PATH_IMAGE153
In that
Figure 854008DEST_PATH_IMAGE154
Is to be treated as
Figure 929412DEST_PATH_IMAGE155
The first order partial derivatives of the dimensions are:
Figure 719513DEST_PATH_IMAGE156
Figure 402340DEST_PATH_IMAGE157
in that
Figure 936089DEST_PATH_IMAGE159
Is to be treated as
Figure 865999DEST_PATH_IMAGE160
The first order partial derivatives of the dimensions are:
Figure 764685DEST_PATH_IMAGE161
then scaling function
Figure 803048DEST_PATH_IMAGE162
In that
Figure 750276DEST_PATH_IMAGE163
Is to be treated as
Figure 800271DEST_PATH_IMAGE164
The first order partial derivatives of the dimensions are:
Figure 197755DEST_PATH_IMAGE165
scaling function
Figure 395518DEST_PATH_IMAGE166
In that
Figure 910550DEST_PATH_IMAGE168
Is to be treated as
Figure 939686DEST_PATH_IMAGE169
The second order partial derivative of the dimension is:
when in use
Figure 852279DEST_PATH_IMAGE170
The method comprises the following steps:
Figure 802917DEST_PATH_IMAGE171
when in use
Figure 216581DEST_PATH_IMAGE172
The method comprises the following steps:
Figure 241169DEST_PATH_IMAGE173
according to the above process, the product is obtained
Figure 449296DEST_PATH_IMAGE175
At any low precision sample point
Figure 621651DEST_PATH_IMAGE176
Hessian matrix of
Figure 714372DEST_PATH_IMAGE177
And then solving the local curvature of the calibration function at the position to finally obtain the average curvature of the calibration function in the design domain.
In the above steps 1 to 4, there are
Figure 718100DEST_PATH_IMAGE178
Four hyper-parameters, by training four parameters, such that the scaling function
Figure 565971DEST_PATH_IMAGE179
With minimal mean curvature and due to the introduction of a smoothing factor
Figure 396261DEST_PATH_IMAGE180
If the multi-precision agent model cannot accurately pass through each high-precision sample point, the maximum error between the predicted value of the multi-precision agent model and the response value of the high-precision sample point is taken as a constraint, and then the mathematical description of parameter training is as follows:
Figure 151728DEST_PATH_IMAGE181
in the formula (I), the compound is shown in the specification,
Figure 150908DEST_PATH_IMAGE182
the maximum error between the multi-precision agent model predicted value and the high-precision sample point response value is obtained;
Figure 169679DEST_PATH_IMAGE183
an upper bound is constrained for error.
And 5, finally obtaining a multi-precision proxy model, which is as follows:
Figure 847785DEST_PATH_IMAGE184
in the formula (I), the compound is shown in the specification,f(x) Representing a multi-precision proxy model.
The modeling method in this embodiment is further explained below by taking the structural performance prediction of the launch vehicle cabin segment as an example.
The concentrated force diffusion cabin section is used as a main connecting cabin section of the main binding device and plays a role in transferring and diffusing the thrust of the booster to a core stage, and the axial pressure bearing capacity is a main performance index for designing the structure. For the problem of structural optimization of the concentrated force diffusion cabin, static analysis is used as a low-precision analysis model, implicit kinetic analysis is used as a high-precision analysis model, and the problem is used for calculating the bearing capacity of the axle load. Fig. 2 is a schematic diagram, in which a portion in fig. 2 is a schematic diagram of a structure of a concentrated force diffusion cabin of a conventional single bundled booster, and b portion is a schematic diagram of a structure of a concentrated force diffusion cabin of a double-layer bundled booster.
The implementation process of the modeling method in the embodiment is as follows:
1. an optimization target and design variables are given, a proxy model is established by taking the bearing load bearing capacity as a response value, and 50 parameters such as the skin thickness of different regions of the concentrated force diffusion cabin section and the design parameters of a main beam, an auxiliary beam, a stringer and a middle frame are taken as design variables, wherein the design variables are as follows:
skin multi-zone variable thickness design:
according to the bearing characteristics, skins with different thicknesses are designed at different force bearing parts, the region division form is shown in fig. 3, and the value range is shown in table 1.
TABLE 1 initial design and value range of different areas of skin thickness
Figure 547888DEST_PATH_IMAGE186
The variable cross section design of the main beam:
as a main bearing part of the concentrated force diffusion cabin section, a main beam adopts a variable cross-section design, and the structural parameters are shown in fig. 4, wherein part a in fig. 4 is the top dimension, part b is the bottom dimension, and the value range is shown in table 2.
TABLE 2 initial design and value range of relevant parameters of variable section girder
Figure 260629DEST_PATH_IMAGE188
And (3) proportional layout design of secondary beams and stringers:
the distances between the auxiliary beams and the stringers are distributed according to an equal ratio number series to realize the non-uniform layout, and three equal ratio coefficients are introduced
Figure 450302DEST_PATH_IMAGE189
The spatial positions of the secondary beam and the stringer are respectively characterized, the mathematical description is as follows, the layout diagram is shown in fig. 5, and the design range is shown in table 3.
Figure 756650DEST_PATH_IMAGE190
Wherein the content of the first and second substances,
Figure 119498DEST_PATH_IMAGE191
the central angle representing the corresponding position of the adjacent ribs (secondary beams or stringers).
Figure 890008DEST_PATH_IMAGE192
Representing the number of secondary beams arranged in the main diffusion B region;
Figure 686800DEST_PATH_IMAGE193
representing the number of secondary beams arranged in the main diffusion C region;
Figure 339498DEST_PATH_IMAGE195
representing the number of stringers placed in the non-main diffusion D region.
Figure 443721DEST_PATH_IMAGE196
Represents rounding up;
Figure 271999DEST_PATH_IMAGE197
indicating a rounding down.
TABLE 3 initial design and value range of parameters related to secondary beams and stringers
Figure 600212DEST_PATH_IMAGE198
Layout design of a middle frame and an end frame:
the layout of the middle frame and the end frame is shown in FIG. 6, and the design range is shown in Table 4.
TABLE 4 initial design and value range of related parameters of middle frame and end frame
Figure 943469DEST_PATH_IMAGE199
2. Design of experimentsRespectively selecting by adopting a Latin hypercube method
Figure 257907DEST_PATH_IMAGE201
One low precision sample point and 50 high precision sample points.
3. Performing calculation by using the static analysis model as a low-precision simulation model
Figure 65326DEST_PATH_IMAGE201
A low precision sample point response value. 4. And calculating 50 high-precision sample point response values by using an implicit kinetic analysis model as a high-precision simulation model.
5. By using
Figure 439807DEST_PATH_IMAGE203
And establishing a low-precision proxy model by using the low-precision sample points.
6. The difference between the high-precision response value and the low-precision proxy model prediction value is calculated at the 50 high-precision sample point positions.
7. And establishing a proxy model by using the difference values of the 50 high-precision sample points and the corresponding positions.
8. And reducing the mean curvature of the scale function model by using a parameter training method.
9. And combining the low-precision proxy model with the scaling function to obtain the final multi-precision proxy model.
And (3) reselecting 50 high-precision sample points by using a Latin hypercube method, calculating the response value by using an implicit dynamics simulation model, comparing the result with the constructed multi-precision proxy model, and calculating to obtain the relative Root Mean Square Error (RMSE). Number of low precision sample points
Figure 270359DEST_PATH_IMAGE205
The results are shown in the following table 5 when taken together:
TABLE 5 comparison of modeling accuracy between the method and the conventional method
Figure 778701DEST_PATH_IMAGE206
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all modifications and equivalents of the present invention, which are made by the contents of the present specification and the accompanying drawings, or directly/indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (10)

1. A smooth scale approximate modeling method for multi-precision data of an aircraft is characterized by comprising the following steps:
step 1, obtaining design variables and a design domain, and initially sampling to obtain high-precision sample points and low-precision sample points;
step 2, establishing a low-precision proxy model based on the low-precision sample points;
step 3, taking the difference between the high-precision sample point and the low-precision proxy model predicted value as a scale function sample point to obtain a scale function sample point set;
step 4, constructing a scale function based on the scale function sample point set to obtain the average curvature of the scale function in the design domain, and performing smoothness training on the scale function by taking the minimum average curvature of the scale function in the design domain as a target;
and 5, obtaining a multi-precision agent model.
2. The method for modeling an aircraft according to claim 1, wherein in step 1, the initial sampling is performed to obtain high-precision sample points and low-precision sample points, specifically:
respectively selecting by adopting a Latin hypercube sampling method
Figure 575726DEST_PATH_IMAGE001
A low precision sampling point and
Figure 24025DEST_PATH_IMAGE002
each high-precision sampling point is provided with a simulation model with corresponding precisionForm (a) to obtain
Figure 69341DEST_PATH_IMAGE003
A low precision sample point and
Figure 244976DEST_PATH_IMAGE004
the high-precision sample points of each sample are respectively as follows:
Figure 324928DEST_PATH_IMAGE005
in the formula (I), the compound is shown in the specification,X iLis shown asiThe input value of one of the low-precision sample points,Y iLis shown asiThe response value of the sample point of low precision,X iHis shown asiThe input value of each sample point with high precision,Y iHis shown asiAnd (5) high-precision sample point response values.
3. The method according to claim 2, wherein in step 2, the low-precision proxy model is:
Figure 678549DEST_PATH_IMAGE006
in the formula (I), the compound is shown in the specification,f L(x) In order to be a low-precision proxy model,
Figure 211161DEST_PATH_IMAGE007
for any point in the design domain
Figure 941220DEST_PATH_IMAGE008
And a first
Figure 626410DEST_PATH_IMAGE009
A low precision sample point
Figure 150932DEST_PATH_IMAGE010
Is a distance therebetween, i.e.
Figure 436420DEST_PATH_IMAGE011
；
Figure 704591DEST_PATH_IMAGE012
Is as follows
Figure 493555DEST_PATH_IMAGE013
The basis function coefficients of the low precision sample points,
Figure 703825DEST_PATH_IMAGE014
is as follows
Figure 211030DEST_PATH_IMAGE015
The basis functions of the low precision sample points.
4. The method according to claim 3, wherein the Gauss function is selected as the basis function of the low-precision sample points as follows:
Figure 751733DEST_PATH_IMAGE016
in the formula (I), the compound is shown in the specification,
Figure 926362DEST_PATH_IMAGE017
is as follows
Figure 527108DEST_PATH_IMAGE018
The shape parameters of the basis functions are:
Figure 537920DEST_PATH_IMAGE019
in the formula (I), the compound is shown in the specification,
Figure 882314DEST_PATH_IMAGE020
is as follows
Figure 911450DEST_PATH_IMAGE021
The distance between the one low precision sample point to the farthest sample point,
Figure 948676DEST_PATH_IMAGE022
to design spatial dimensions;
will be provided with
Figure 430473DEST_PATH_IMAGE023
Substituting the input value and the response value of each low-precision sample point into the low-precision proxy model to obtain the basis function coefficient of the low-precision sample point
Figure 578557DEST_PATH_IMAGE024
And solving the equation set to obtain a basis function coefficient to obtain the low-precision proxy model.
5. The method for smooth-scale approximate modeling of multi-precision data for an aircraft according to claim 3 or 4, wherein step 3 specifically comprises:
calculating the difference between the response value of the high-precision sample point and the predicted value of the low-precision proxy model as a scaling function sample point, wherein the difference is as follows:
Figure 711467DEST_PATH_IMAGE025
in the formula (I), the compound is shown in the specification,
Figure 919595DEST_PATH_IMAGE026
is as follows
Figure 888688DEST_PATH_IMAGE027
The difference between the individual high-precision sample point response values and the low-precision proxy model prediction values,
Figure 574884DEST_PATH_IMAGE028
、
Figure 578612DEST_PATH_IMAGE029
respectively linear correction constants for the low-precision proxy model,
Figure 708373DEST_PATH_IMAGE030
is as follows
Figure 899183DEST_PATH_IMAGE031
The predicted value of the low-precision agent model at each high-precision sample point;
obtaining a set of scale function sample points:
Figure 654650DEST_PATH_IMAGE032
in the formula (I), the compound is shown in the specification,X iDis shown asiThe sample point input values of the individual scaling functions,Y iLis shown asiThe point response values of the sample points of the individual scaling functions,n Dthe number of sample points is a scaling function.
6. The method according to claim 5, wherein in step 4, the step of constructing the scale function based on the scale function sample point set comprises:
Figure 981726DEST_PATH_IMAGE033
in the formula (I), the compound is shown in the specification,
Figure 797235DEST_PATH_IMAGE034
for any point in the design domain
Figure 475341DEST_PATH_IMAGE035
And a first
Figure 283766DEST_PATH_IMAGE036
Sample points of a scaling function
Figure 730928DEST_PATH_IMAGE037
The distance between the two or more of the two or more,
Figure 186180DEST_PATH_IMAGE038
；
Figure 617161DEST_PATH_IMAGE039
is as follows
Figure 448851DEST_PATH_IMAGE040
The basis function coefficients of the individual scale function sample points;
Figure 32410DEST_PATH_IMAGE041
is as follows
Figure 658564DEST_PATH_IMAGE042
The basis functions of the sample points of the individual scaling functions.
7. The method according to claim 6, wherein the Gauss function is selected as the basis function of the scale function sample points as follows:
Figure 576841DEST_PATH_IMAGE043
in the formula (I), the compound is shown in the specification,
Figure 212222DEST_PATH_IMAGE044
a shape parameter correction factor;
Figure 633976DEST_PATH_IMAGE045
is as follows
Figure 696610DEST_PATH_IMAGE046
The shape parameters of the basis functions are:
Figure 85872DEST_PATH_IMAGE047
in the formula (I), the compound is shown in the specification,
Figure 524943DEST_PATH_IMAGE048
is as follows
Figure 66783DEST_PATH_IMAGE049
The distance between the sample point of the individual scaling functions to the farthest sample point;
will be provided with
Figure 565898DEST_PATH_IMAGE050
Substituting the input value and the response value of the sample point of the scaling function into the scaling function to obtain the coefficient of the sample point of the scaling function
Figure 927609DEST_PATH_IMAGE051
The system of linear equations of (1) is:
Figure 655524DEST_PATH_IMAGE052
in the formula (I), the compound is shown in the specification,
Figure 51871DEST_PATH_IMAGE053
and solving the equation set to obtain a basic function coefficient for a scale function smoothing factor to obtain a scale function.
8. The method of claim 7, wherein the average curvature of the scaling function in the design domain is:
Figure 721887DEST_PATH_IMAGE054
in the formula:
Figure 570894DEST_PATH_IMAGE055
is the average curvature of the scaling function in the design domain,
Figure 86189DEST_PATH_IMAGE056
as a function of scale in
Figure 337042DEST_PATH_IMAGE057
Local curvature of the surface.
9. The method according to claim 8, wherein in step 4, the smooth scale approximation modeling of the multi-precision data for the aircraft is performed by performing smoothness training on the scale function with the goal of minimizing the average curvature of the scale function in the design domain, specifically:
Figure 427226DEST_PATH_IMAGE058
in the formula (I), the compound is shown in the specification,
Figure 763530DEST_PATH_IMAGE059
for the maximum error between the multi-precision proxy model prediction value and the high-precision sample point response value,
Figure 348095DEST_PATH_IMAGE060
an upper bound is constrained for error.
10. The method according to claim 9, wherein in step 5, the multi-precision proxy model is:
Figure 719033DEST_PATH_IMAGE061
in the formula (I), the compound is shown in the specification,f(x) Representing a multi-precision proxy model.
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