CN117313576A - Bayesian optimization method for analyzing importance degree of airfoil physical quantity - Google Patents
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Abstract
The embodiment of the invention discloses a Bayesian optimization method for analyzing the importance of physical quantity of an airfoil, which relates to the digital design technology of the airfoil, and can improve the design efficiency, improve the optimization performance and reduce the opacity of the airfoil design. The invention uses the wing profile provided by the client side to carry out the dimension sparseness of the wing profile physical characteristics at the server side, and the method comprises the following steps: generating an original training sample of simulation calculation, constructing a training data sample base suitable for describing wing-shaped physical characteristics, training a GP proxy model for predicting new sample target performance, designing a wing-shaped Bayesian optimization framework suitable for dimension sparseness, iterating by adopting an EHVIC acquisition strategy until the end condition, and finally returning the sparse dimension Pareto front design meeting design requirements to a client for use. The invention is suitable for the design and optimization of the aircraft for exploring the importance of the physical parameters.
Description
Technical Field
The invention relates to an airfoil digital design technology, in particular to a Bayesian optimization method for analyzing the importance degree of airfoil physical quantity.
Background
The airfoil optimization and design are mainly improved by taking the existing airfoil as a reference airfoil, and the special airfoil meeting the performance requirement of the aircraft is obtained. The Bayesian optimization method is one of the important methods in the current optimization field, is suitable for the problem of black box optimization with high cost, and is a very important means for solving the problem of high-dimensional airfoil design. However, the "black box" nature and the importance of the design variables in the optimization process are unknown and are a problem to be studied urgently. For airfoil designers, the design process under the traditional Bayesian optimization framework is a black box, the corresponding design experience cannot be learned from the optimization process, and the influence degree of the change of the design dimension on the target cannot be explained. Thus, airfoil designers have not been able to provide prior information to current airfoil designs when designing new airfoils. With the continuous development of machine learning algorithms, the complexity of models is also higher and higher, and more researchers are focusing on the research of model importance analysis. The goal of importance analysis research is to look at the reliability of the decision process and the predicted outcome of an algorithm by a method that allows the decision process and the decision outcome to be understood and interpreted by humans. The research of importance analysis has been widely studied in the fields of image processing, reinforcement learning, and natural language processing.
At present, research work on importance analysis of a traditional Bayesian optimization framework is less, and under the condition of keeping a better aerodynamic performance target, a satisfactory result can be obtained only by modifying each dimension for a plurality of times and a plurality of amplitudes, so that the problem that the conventional Bayesian optimization scheme is difficult to cope with airfoil optimization design with large design difficulty and low optimization efficiency in actual application is caused. Therefore, how to improve the bayesian optimization framework itself to a certain extent, so that the optimization efficiency can be improved, and the problem of further research and improvement is needed.
Disclosure of Invention
The embodiment of the invention provides a Bayesian optimization method for analyzing the importance degree of airfoil physical quantity, which can modify each performance dimension as little as possible and with small amplitude under the condition of maintaining aerodynamic performance targets, so that the optimization efficiency can be improved.
In order to achieve the above objective, the following technical solution is adopted in the embodiment of the present invention, as shown in fig. 4:
s1, receiving airfoil sample data uploaded by a client, wherein the airfoil sample data comprises an airfoil sample set generated by the client based on basic airfoil disturbance; wherein the sample set is generated by perturbing the corresponding dimensions based on the base airfoil, and may be generated by a simulation software tool, for example, one base airfoil is represented by [0.5,0.5,0.5,0.5], then [0.6,0.5,0.5,0.5] is another airfoil, and the first number is added with 0.1, and similarly, perturbing of different dimensions with different magnitudes may generate different airfoils.
S21, extracting physical characteristics and performance indexes corresponding to each sample data in the airfoil sample set, wherein the physical characteristics are used for describing the geometrical shape of the airfoil, and the pneumatic performance types pointed by the performance indexes comprise: airfoil lift and airfoil drag; unlike the conventional airfoil optimization in which CST and HH methods are used to describe the airfoil, the present embodiment extracts physical features of important portions of the airfoil to describe the airfoil, and may add additional airfoil physical quantities that require attention.
Wherein the physical features include: the radius of the front edge, the maximum thickness of the upper airfoil surface and the corresponding x coordinate, the maximum thickness of the lower airfoil surface and the corresponding x coordinate, the total maximum thickness and the corresponding x coordinate and the height and x coordinate corresponding to the maximum point of the tail wing camber.
S22, training a GP (Gaussian Process) proxy model by using the extracted physical characteristics, and returning an analysis result of the airfoil profile through the trained GP proxy model, wherein the analysis result comprises pneumatic performance data output by the GP proxy model; the method comprises the steps of carrying out a first treatment on the surface of the For example: assuming 1500 pieces of data, each piece of data contains physical features corresponding to the wing profile, the embodiment extracts the physical features for training the GP proxy model. Functional evaluation by trained GP proxy model is for example: a GP proxy model is trained, physical characteristics of an airfoil are input into the model after training, and the model outputs function evaluation corresponding to the airfoil sample, specifically, aerodynamic performance of the airfoil is returned.
S3 according to EHVIC (Expected Hypervolume Improvement with constraint)
) Selecting a point strategy, and searching candidate wing profiles by using a search space; the airfoil dimension may be understood as a set of parameters consisting of a plurality of parameters associated with the airfoil. The search space is used to describe the combined case size of the dimensions, for example: there are two dimensions, each having two values of 0,1, respectively, that search space size is 4 (0, 0;0,1;1,0;1, respectively).
S4, performing performance evaluation on the obtained candidate wing profile according to the optimization target item; wherein, the optimization target item comprises: taking the aerodynamic performance data output by the GP proxy model as an aerodynamic performance target of the airfoil; and, a dimension corresponding to each airfoil. In S4, searching for the candidate airfoil using the corresponding search space includes searching for an airfoil dimension that includes a combination of physical characteristics and aerodynamic performance data associated with the candidate airfoil. S5, updating a GP proxy model in the Bayesian optimization framework according to the performance evaluation;
the Bayesian optimization framework comprises a GP proxy model, and updating the GP proxy model is essentially equivalent to updating and optimizing the Bayesian optimization framework.
And S6, repeating the optimization period formed by S3 to S5 until the maximum optimization times are reached, and outputting the pareto front edge of the airfoil, wherein the GP proxy model in the Bayesian optimization framework is updated in the optimization of each period. In practical application, the pareto front is constructed by the acquisition points of two targets, which is called as outputting the pareto front herein, namely, outputting the airfoil-shaped pareto front constructed by the aerodynamic performance and the sparseness.
Specifically, in each optimization cycle, it includes: taking the candidate wing profile and the corresponding lift-drag ratio performance as sampling points, and importing the sampling points into a GP proxy model of an optimization framework; in the process of updating the GP proxy model of the optimization framework, changing the function distribution of the GP proxy model, and executing the point selection strategy of S3 so as to perform point selection again; and then sequentially executing S4 to S5. And (3) taking the searched wing profile and the corresponding lift-drag ratio aerodynamic performance as acquisition points, adding the acquisition points into a proxy model of the optimization framework, updating the proxy model, changing the function distribution of the proxy model, performing next point selection by using the point selection strategy of the step (4), and performing function evaluation and repeating until the maximum optimization step number is reached.
Finally, the wing profile optimization design is realized according to wing profile sample data (also called wing profile raw data) given by the client and a trained function evaluation proxy model (GP proxy model), and then wing profile parameters (namely the pareto front edge of the wing profile) meeting the requirements of the client are returned to the client.
In this embodiment, the GP proxy model is a gaussian process regression model, and in S22, the method includes: according to the physical characteristics and the performance indexes, a Gaussian process regression model is constructed, and in practical application, an airfoil described by the physical geometrical characteristics and corresponding lift force resistance aerodynamic performance are utilized to construct the Gaussian process regression model, wherein the input is the airfoil physical geometrical characteristics, and the output is the ratio of lift force to resistance. The mean function m and the covariance function k in the Gaussian process are respectively:
wherein GP () represents a gaussian process, f (x) represents a function value corresponding to x, and x' represent two different data points in the sample;
the covariance function (also called kernel function, matern kernel) used in the gaussian process is:
x i ，x j representing differences in a sample setV represents a smoothing coefficient, l represents a constant, typically l=1, Γ (v) represents a Gamma function, K v Representing the Bassel function.
In this embodiment, in S3, it includes: establishing an EHVIC point selection strategy, and flexibly setting constraint conditions of each dimension through multi-objective Bayesian optimization with constraint:
wherein Δ (S) represents that the constraint satisfies the expectations, S + Represents a unit that is not dominated by any member of the pareto active set, P (y) represents the set of pareto active points, I (·) represents the lift of the next selection point,probability density function representing the predicted distribution of the objective function, S representing S + Y represents the current sampling point, f x Representing an objective function, y representing a pareto effective point;
further, in this embodiment, the basic airfoil profile is used as a reference, positive and negative disturbances are added to each dimension, and the modification amount of the reference airfoil profile is determined according to the magnitude and positive and negative of the disturbances. The components of the search target of the search space include: aerodynamic performance targets and sparse targets, expressed as:
f 1 ＝f(x base +Δx next )
in contrast to the general airfoil bayesian optimization, in this embodiment, in addition to taking the airfoil aerodynamic performance as an optimization target, a dimension sparse target is additionally added, where the target uses the positive and negative of each dimensionThe zero-norm of the variation measures the sparsity of the dimension. The number and magnitude of dimensions are modified in as small a number and magnitude as possible while maintaining a relatively good aerodynamic performance objective. Wherein f 1 Representing a target I comprising airfoil aerodynamic performance, f 2 Representing a second object, wherein the second object comprises sparsity of airfoil disturbance,representing an intermediate calculation formula,/->Representing positive and negative disturbances of the ith dimension relative to the base airfoil, a=10 -0.5 ，x base Representing the base airfoil, deltax next Representing positive and negative disturbances relative to the base airfoil, D is Δx next Is a dimension of (c).
In this embodiment, in S4, it includes: performing function evaluation on the selected airfoil by using a trained Gaussian process regression model and outputting a result including the aerodynamic performance f of the airfoil 1 And airfoil dimension sparsity f 2 。
According to the Bayesian optimization method for analyzing the importance degree of the wing-shaped physical quantity, wing-shaped raw data provided by a client side are used as samples, the wing-shaped physical characteristics are sparse in dimension at a server side, an original training sample for simulating calculation is generated, a training data sample base suitable for describing the wing-shaped physical characteristics is constructed, a GP proxy model is trained for predicting the target performance of a new sample, a wing-shaped Bayesian optimization framework suitable for sparse in dimension is designed, EHVIC acquisition strategy iteration is adopted until the end condition is reached, and finally the sparse dimension Pareto front design meeting the design requirement is returned to the client side for use. The Bayesian optimization is easy to realize, the optimization efficiency is high, the aerodynamics corresponding to the wing profile can be efficiently optimized without using calculation resources and time CFD simulation calculation in a huge search space, the importance degree of each dimension of the optimized wing profile is known, the influence degree of each dimension on the target can be explained, the optimization design of a wing profile designer is guided to a certain extent, and the wing profile design period is shortened. Therefore, under the condition of maintaining the pneumatic performance target, each performance dimension can be modified as little as possible, and the optimization efficiency can be improved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments 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 other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a system architecture according to an embodiment of the present invention;
FIG. 2 is a flow chart of a Bayesian optimization method for airfoil physical quantity importance analysis;
FIG. 3 is a frame diagram of a Bayesian optimization method for airfoil physical quantity importance analysis;
fig. 4 is a schematic flow chart of a method according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail below with reference to the drawings and detailed description for the purpose of better understanding of the technical solution of the present invention to those skilled in the art. Embodiments of the present invention will hereinafter be described in detail, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary only for explaining the present invention and are not to be construed as limiting the present invention. As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless expressly stated otherwise, as understood by those skilled in the art. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. The term "and/or" as used herein includes any and all combinations of one or more of the associated listed items. It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
Fig. 1 is a schematic diagram of a system architecture provided by an embodiment of the present invention, and referring to fig. 1, a client provides a parameter space boundary, an optimization target, a sparse dimension target, and a constraint condition, a server trains a model for original geometric physical characteristics, and then a whole team outputs aerodynamic performance of the model at each iteration point selection until iteration reaches a maximum iteration step number, and returns the model to a pareto front wing profile for importance analysis of the client.
Fig. 2 is a flowchart of a bayesian optimization method for analyzing importance of physical quantities of an airfoil, and referring to fig. 2, according to a schematic flow diagram, a bayesian optimization method design for analyzing importance of physical quantities of an airfoil is completed:
the raw information of the airfoil sample of step 101 is provided by the client. In the calculation of the aerofoil lift resistance aerodynamic performance, grid generation and simulation calculation are completed by a server, and lift force and resistance aerodynamic performance data of the corresponding aerofoil are output and stored after calculation is completed.
The physical characteristics are used as variables in subsequent calculation, and may also be referred to as "physical characteristic variables" in step 102, and the relevant physical characteristic variables of the airfoil are extracted according to the original airfoil sample, so as to obtain relevant design parameters describing the airfoil specifically refer to:
the physical features are actually used to describe the physical shape of the airfoil, from which the geometric features used to describe the airfoil shape are extracted as the physical features. Wherein the geometric features include: the performance indexes comprise: airfoil lift and airfoil drag.
And step 103, training a GP proxy model by utilizing relevant design parameter data describing the wing profile, and returning an objective function to evaluate through the trained GP proxy model, wherein the specific steps are as follows:
the wing profile described by the physical geometrical characteristics and the corresponding lift force resistance aerodynamic performance are utilized to construct a Gaussian process regression model, wherein the input is the wing profile physical geometrical characteristics, and the output is the ratio of lift force to resistance. Wherein the gaussian process is determined by its mean function m and covariance function k:
wherein,
the covariance function (also called kernel function) used is a Matern kernel, whose formula is:
the searching of the candidate airfoil and the airfoil dimension in the corresponding search space by using EHVIC point selection strategy in step 104 specifically refers to:
where Δ (S) is that the constraint satisfies the expectations, S + Refers to a unit that is not dominated by any member of the pareto active set, P (y) is the set of pareto active points, I (·) is the lift of the next selection point,is a probability density function of the predicted distribution of the objective function.
The search target of the search space consists of two parts, a aerodynamic performance target and a sparse target, respectively, whose functional form is as follows:
f 1 ＝f(x next )
the step 105 of evaluating the performance of the airfoil according to the airfoil selection target item specifically refers to:
and (3) using the Gaussian process regression proxy model trained in the step (S3) to perform function evaluation on the selected airfoil and output, wherein the function expression is as follows:
f 1 ＝-GPR(x next )
the step 106 updates the agent model of the optimization framework by using the evaluated candidate airfoil and the corresponding performance evaluation, and repeats S4, S5, and S6 until the maximum optimization times are reached, specifically referring to: and (3) taking the searched wing profile and the corresponding lift-drag ratio aerodynamic performance as acquisition points, adding the acquisition points into a proxy model of the optimization framework, updating the proxy model, changing the function distribution of the proxy model, performing next point selection by utilizing the point selection strategy of the step S4, and performing function evaluation and repeating until the maximum optimization step number is reached.
Step 107 is to output an airfoil pareto front edge which meets the airfoil design requirement and has sparse dimensions, and specifically refers to:
and carrying out airfoil optimization design according to airfoil original data given by the client and the trained function evaluation proxy model, and then returning airfoil parameters meeting the requirements of the client to the client.
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for the apparatus embodiments, since they are substantially similar to the method embodiments, the description is relatively simple, and reference is made to the description of the method embodiments for relevant points. The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be included in the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (10)
1. A bayesian optimization method for airfoil physical quantity importance analysis, comprising:
s1, receiving airfoil sample data uploaded by a client, wherein the airfoil sample data comprises an airfoil sample set generated by the client based on basic airfoil disturbance;
s2, training a GP (Gaussian Process) proxy model by using the wing profile sample set, analyzing the wing profile by using the trained GP proxy model, and setting an optimization target item according to an analysis result;
s3, searching candidate wing profiles according to the EHVIC point selection strategy and by utilizing a search space;
s4, performing performance evaluation on the obtained candidate wing profile according to the optimization target item;
s5, updating a GP proxy model in the Bayesian optimization framework according to the performance evaluation;
and S6, repeating the optimization period formed by the steps S3 to S5 until the maximum optimization times are reached, and outputting the pareto front edge of the airfoil.
2. The method according to claim 1, characterized in that at S2 comprises:
s21, extracting physical characteristics and performance indexes corresponding to each sample data in the airfoil sample set, wherein the physical characteristics are used for describing the geometrical shape of the airfoil, and the pneumatic performance types pointed by the performance indexes comprise: airfoil lift and airfoil drag;
s22, training GP (Gaussian Process) an agent model by using the extracted physical characteristics, and returning an analysis result of the wing profile through the trained GP agent model, wherein the analysis result comprises aerodynamic performance data output by the GP agent model.
3. The method of claim 1 or 2, wherein the physical features comprise: the radius of the front edge, the maximum thickness of the upper airfoil surface and the corresponding x coordinate, the maximum thickness of the lower airfoil surface and the corresponding x coordinate, the total maximum thickness and the corresponding x coordinate and the height and x coordinate corresponding to the maximum point of the tail wing camber.
4. The method of claim 2, wherein optimizing the target item comprises: taking the aerodynamic performance data output by the GP proxy model in the S22 as an aerodynamic performance target of the airfoil;
and, a dimension corresponding to each airfoil.
5. The method of claim 4, wherein in S4, further comprising:
searching for candidate airfoils in a corresponding search space includes searching for airfoil dimensions that include a combination of physical characteristics and aerodynamic performance data associated with the candidate airfoils.
6. The method of claim 1, wherein the GP proxy model is a gaussian process regression model, and in S22, further comprising: constructing a Gaussian process regression model according to the physical characteristics and the performance indexes;
the mean function m and the covariance function k in the Gaussian process are respectively:
wherein GP () represents a gaussian process, f (x) represents a function value corresponding to x, and x' represent two different data points in the sample;
the kernel function used in the gaussian process is:
x i ，x j representing two different samples in a sample set, v representing the smoothing coefficient, l representing the forward parameter, typically l=1, Γ (v) representing the Gamma function, K v Representing the Bassel function.
7. The method according to claim 1, characterized in that in S3 it comprises:
establishing an EHVIC point selection strategy:
wherein Δ (S) represents that the constraint satisfies the expectations, S + Represents a unit that is not dominated by any member of the pareto active set,representing the set of pareto active points, I (·) representing the lift of the next selection point, +.>Probability density function representing the predicted distribution of the objective function, S representing S + Y represents the current sampling point, f x Representing an objective function +.>Indicating pareto effective points.
8. The method of claim 7, wherein the component parts of the search target of the search space comprise: aerodynamic performance targets and sparse targets, expressed as:
f 1 ＝f(x base +Δx next )
wherein f 1 Representing a target I comprising airfoil aerodynamic performance, f 2 Representing a second object, wherein the second object comprises sparsity of airfoil disturbance,representing an intermediate calculation formula,/->Representing positive and negative disturbances of the ith dimension relative to the base airfoil, a=10 -0.5 ，x base Representing the base airfoil, deltax next Representing positive and negative disturbances relative to the base airfoil, D is Δx next Is a dimension of (c).
9. The method according to claim 1, characterized in that in S4 it comprises:
performing a function on the selected airfoil using a trained Gaussian process regression modelEvaluating and outputting results, including aerodynamic properties f of airfoils 1 And airfoil dimension sparsity f 2 。
10. The method of claim 1, wherein the GP proxy model in the bayesian optimization framework is updated during each cycle of optimization;
in each optimization cycle, it includes:
taking the candidate wing profile and the corresponding lift-drag ratio performance as sampling points, and importing the sampling points into a GP proxy model of an optimization framework;
in the process of updating the GP proxy model of the optimization framework, changing the function distribution of the GP proxy model, and executing the point selection strategy of S3 so as to perform point selection again;
and then sequentially executing S4 to S5.
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| CN114564787B (en) * | 2022-01-24 | 2024-09-20 | 南京航空航天大学 | Bayesian optimization method, device and storage medium for target related airfoil design |
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