CN117313576A - Bayesian optimization method for analyzing importance degree of airfoil physical quantity - Google Patents

Abstract

The embodiment of the present invention discloses a Bayesian optimization method for analysis of the importance of airfoil physical quantities, which involves airfoil digital design technology and can improve design efficiency, improve optimization performance, and reduce the opacity of airfoil design. The present invention uses the airfoil provided by the client to perform dimension sparseness of the airfoil physical characteristics on the server side. The method includes: generating original training samples for simulation calculations, constructing a training data sample library suitable for describing the airfoil physical characteristics, and training The GP agent model is used to predict the target performance of new samples. It designs a Bayesian optimization framework suitable for sparse-dimensional airfoils. It uses the EHVIC acquisition strategy to iterate until the end condition, and finally returns the sparse-dimensional Pareto front design that meets the design requirements to the client. for use. The invention is suitable for aircraft design and optimization that explores the importance of physical parameters.

Description

A Bayesian optimization method for analyzing the importance of airfoil physical quantities

Technical field

The invention relates to airfoil digital design technology, and in particular to a Bayesian optimization method for analyzing the importance of airfoil physical quantities.

Background technique

Airfoil optimization and design mainly uses the existing airfoil as the basis to improve the airfoil to obtain a special airfoil that meets the performance requirements of the aircraft. It is an important and complex research topic. Bayesian optimization method is one of the important methods in the current field of optimization. It is suitable for expensive black-box optimization problems and is a very important means to solve problems such as high-dimensional airfoil design. However, the "black box" nature of the optimization process and the importance of design variables are unknown, which is an issue that needs urgent research. For airfoil designers, the design process under the traditional Bayesian optimization framework is a "black box". It is impossible to learn the corresponding design experience from the optimization process, and it is impossible to explain the impact of changes in design dimensions on the goals. Therefore, when airfoil designers design new airfoils, previously designed airfoils cannot provide a priori information for the current airfoil design. With the continuous development of machine learning algorithms, the complexity of its models has become higher and higher, and more and more researchers have begun to focus on the study of model importance analysis. The purpose of importance analysis research is to review the reliability of the algorithm's decision-making process and prediction results through certain methods, so that the decision-making process and decision-making results can be understood and explained by humans. Research on importance analysis has been extensively studied in the fields of image processing, reinforcement learning and natural language processing.

At present, research work on the importance analysis of traditional Bayesian optimization frameworks is relatively rare. In order to maintain a better aerodynamic performance target, it is often necessary to modify each dimension multiple times and multiple times in order to obtain satisfactory results. This is As a result, the current traditional Bayesian optimization scheme is difficult to deal with airfoil optimization design problems that are difficult to design and have low optimization efficiency in practical applications. Therefore, how to improve the Bayesian optimization framework itself to a certain extent so that it can improve optimization efficiency has become a topic that requires further research and improvement.

Contents of the invention

Embodiments of the present invention provide a Bayesian optimization method for analysis of the importance of airfoil physical quantities. While maintaining the aerodynamic performance target, each performance dimension can be modified as little as possible in a small amount, so that it can be improved. Optimize efficiency.

In order to achieve the above objects, embodiments of the present invention adopt the following technical solutions, as shown in Figure 4:

S1. Accept the airfoil sample data uploaded by the client. The airfoil sample data includes the airfoil sample set generated by the client based on the perturbation of the basic airfoil; wherein the sample set is generated by perturbing the corresponding dimensions based on the basic airfoil. , can be generated through simulation software tools. For example, [0.5,0.5,0.5,0.5] represents a basic airfoil, then [0.6,0.5,0.5,0.5] is another airfoil. It is added to the first number. 0.1, similarly adding different sizes of perturbations in different dimensions will produce different airfoils.

S21. Extract the physical characteristics and performance indicators corresponding to each piece of sample data in the airfoil sample set. The physical characteristics are used to describe the geometric shape of the airfoil. The aerodynamic performance types pointed to by the performance indicators include: airfoil lift and airfoil lift. Airfoil resistance; Different from traditional airfoil optimization that uses CST and HH methods to describe the airfoil, this embodiment extracts the physical characteristics of important parts of the airfoil to describe the airfoil, and can also add additional airfoil physical quantities that require attention.

Among them, the physical characteristics include: leading edge radius, maximum thickness of the upper airfoil and the corresponding x-coordinate, maximum thickness of the lower airfoil and the corresponding x-coordinate, the overall maximum thickness and the corresponding x-coordinate, and the height corresponding to the maximum point of the tail wing curvature. and x coordinate.

S22. Use the extracted physical features to train the GP (Gaussian Process) proxy model, and return the analysis results of the airfoil through the trained GP proxy model. The analysis results include the aerodynamic performance data output by the GP proxy model;; For example: Suppose there are 1,500 pieces of data, each piece of data contains physical features corresponding to the airfoil. This embodiment extracts these physical features for training the GP agent model. Function evaluation is performed through the trained GP agent model. For example: a GP agent model is trained. After training, the physical characteristics of an airfoil are input to the model, and the model outputs the function evaluation corresponding to the airfoil sample. Specifically, it returns the aerodynamics of the airfoil. performance.

S3. According to EHVIC (Expected Hypervolume Improvement with constraint

) point selection strategy, and use the search space to search for candidate airfoils; where the airfoil dimension can be understood as a parameter set composed of multiple parameters related to the airfoil. The search space is used to describe the size of the combination of dimensions. For example: if there are two dimensions, each dimension has two values, 0, 1. Then the size of the search space is 4 (respectively 0, 0; 0, 1 ;1,0;1,1).

S4. Perform a performance evaluation on the obtained candidate airfoil according to the optimization target items; wherein the optimization target items include: using the aerodynamic performance data output by the GP proxy model as the aerodynamic performance target of the airfoil; and, each airfoil corresponds to of dimensions. In S4, while using the corresponding search space to search for candidate airfoils, it also includes searching for airfoil dimensions, which include a combination of physical characteristics and aerodynamic performance data related to the candidate airfoils. S5. Based on the performance evaluation, update the GP agent model in the Bayesian optimization framework;

Among them, the Bayesian optimization framework includes the GP agent model, and updating the GP agent model is essentially equivalent to updating and optimizing the Bayesian optimization framework.

S6. Repeat the optimization cycle consisting of S3 to S5 until the maximum number of optimizations is reached, and output the Pareto front of the airfoil. In each cycle of optimization, the GP agent model in the Bayesian optimization framework is updated. . In practical applications, the Pareto front is constructed from the acquisition points of two targets, which is called the output Pareto front here, which is equivalent to outputting the airfoil Pareto front constructed from aerodynamic performance and sparsity.

Specifically, in each optimization cycle, it includes: using the candidate airfoil and the corresponding lift-to-drag ratio performance as collection points, and importing the sampling points into the GP proxy model of the optimization framework; in the process of updating the GP proxy model of the optimization framework , change the function distribution of the GP agent model, and execute the point selection strategy of S3 to select points again; then execute S4 to S5 in sequence. Use the searched airfoil and the corresponding lift-to-drag ratio aerodynamic performance as a collection point, add it to the proxy model of the optimization framework, update the proxy model, change its function distribution, and use the point selection strategy in step 4 to select the next point. The function is evaluated again and repeated until the maximum number of optimization steps.

Finally, the airfoil optimization design is implemented based on the airfoil sample data given by the client (which can also be called airfoil original data) and the trained function evaluation proxy model (GP proxy model), and then it will meet the client's needs. The airfoil parameters (ie, the Pareto front of the airfoil) are returned to the client.

In this embodiment, the GP agent model is a Gaussian process regression model. In S22, it includes: constructing a Gaussian process regression model according to the physical characteristics and the performance indicators. In practical applications, the wing described by the physical geometric characteristics is used. The Gaussian process regression model is constructed with the corresponding lift-drag aerodynamic performance. The input is the physical geometric characteristics of the airfoil, and the output is the ratio of lift to drag. Among them, the mean function m and covariance function k in the Gaussian process are respectively:

Among them, GP() represents Gaussian process, f(x) represents the function value corresponding to x, 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 represent two different samples in the sample set, v represents the smoothing coefficient, l represents a constant, usually l=1, Γ(v) represents the Gamma function, and K _v represents the Bassel function.

In this embodiment, S3 includes: establishing an EHVIC point selection strategy, and through constrained multi-objective Bayesian optimization, the constraints of each dimension can be flexibly set:

Among them, Δ(s) indicates that the constraint meets expectations, S ⁺ indicates a unit that is not dominated by any member of the Pareto efficient set, P(y) indicates the Pareto efficient point set, and I(·) indicates the next point selection Lift amount, Represents the probability density function of the predicted distribution of the objective function, s represents a point in S ⁺ , y represents the current sampling point, f _x represents the objective function, and y represents the Pareto effective point;

Furthermore, in this embodiment, the basic airfoil is used as the benchmark, positive and negative perturbations are added to each dimension, and the amount of modification to the basic airfoil is determined based on the magnitude and sign of the perturbation. The search target components of the search space include: aerodynamic performance targets and sparse targets, expressed as:

f ₁ =f(x _base +Δx _next )

Different from the general Bayesian optimization of airfoils, this embodiment not only takes the airfoil aerodynamic performance as the optimization goal, but also adds an additional dimension sparse goal, which measures the dimensions with the zero normal form of the positive and negative changes in each dimension. sparsity. The aim is to modify the number and amplitude of each dimension as little as possible while maintaining relatively good aerodynamic performance targets. Among them, f ₁ represents the first goal, the first goal includes the aerodynamic performance of the airfoil, f ₂ represents the second goal, the second goal includes the sparsity of the airfoil disturbance, Represents an intermediate calculation formula,/> Represents the positive and negative perturbations of the i-th dimension relative to the base airfoil, a=10 ^-0.5 , x _base represents the base airfoil, Δx _next represents the positive and negative perturbations relative to the base airfoil, and D is the dimension of Δx _next .

In this embodiment, S4 includes: using the trained Gaussian process regression model to perform function evaluation on the selected airfoil and output the results, including the aerodynamic performance f ₁ of the airfoil and the sparsity degree f ₂ of the airfoil dimension.

The Bayesian optimization method for analysis of the importance of airfoil physical quantities provided by the embodiment of the present invention uses the original data of the airfoil provided by the client as a sample, performs the dimension sparseness of the airfoil physical characteristics on the server side, and generates simulation calculations. Original training samples, construct a training data sample library suitable for describing the physical characteristics of airfoils, train the GP agent model for target performance prediction of new samples, design a Bayesian optimization framework suitable for airfoils with sparse dimensions, and use the EHVIC acquisition strategy to iterate until Ending condition, and finally returns the sparse dimension Pareto front design that meets the design requirements to the client for use. The Bayesian optimization involved is easy to implement and has high optimization efficiency. It does not require the use of computing resources and time-consuming CFD simulation calculations in a huge search space to obtain the aerodynamic performance corresponding to the airfoil, and it can efficiently optimize the wing that meets the target requirements. shape, and the importance of each dimension of the optimized airfoil is known, which can explain the impact of each dimension on the target, and to a certain extent, guide the airfoil designer to optimize the design and shorten the airfoil design cycle. In this way, while maintaining the aerodynamic performance target, each performance dimension can be modified in as small a quantity and amplitude as possible, so as to improve the optimization efficiency.

Description of the drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. Those of ordinary skill in the art can also obtain other drawings based on these drawings without exerting creative efforts.

Figure 1 is a schematic diagram of the system architecture provided by an embodiment of the present invention;

Figure 2 Flow chart of the Bayesian optimization method used for analysis of the importance of airfoil physical quantities;

Figure 3 Framework diagram of the Bayesian optimization method used for analysis of the importance of airfoil physical quantities;

Figure 4 is a schematic flowchart of a method provided by an embodiment of the present invention.

Detailed ways

In order to enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments. Embodiments of the present invention will be described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the drawings are exemplary and are only used to explain the present invention and cannot be construed as limitations of the present invention. Those skilled in the art will understand that, unless expressly stated otherwise, the singular forms "a", "an", "the" and "the" used herein may also include the plural form. It should be further understood that the word "comprising" used in the description of the present invention refers to the presence of stated features, integers, steps, operations, elements and/or components, but does not exclude 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 we refer to an element 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. Additionally, "connected" or "coupled" as used herein may include wireless connections or couplings. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items. It will be understood by one of ordinary skill 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 should also be understood that terms such as those defined in general dictionaries are to be understood to have meanings consistent with their meaning in the context of the prior art, and are not to be taken in an idealized or overly formal sense unless defined as herein. explain.

Figure 1 is a schematic diagram of the system architecture provided by an embodiment of the present invention. Refer to Figure 1. The client provides parameter space boundaries, optimization goals, sparse dimension goals, and constraints. The server trains the model on the original geometric and physical features, and then the team selects points for each iteration. Output its aerodynamic performance until the iteration reaches the maximum number of iteration steps, and return the Pareto front airfoil to the client for importance analysis.

Figure 2 is a flow chart of the Bayesian optimization method for analysis of the importance of airfoil physical quantities. Refer to Figure 2 and follow the flow diagram to complete the design of the Bayesian optimization method for analysis of the importance of airfoil physical quantities:

The original information of the airfoil sample in step 101 is provided by the client. In the calculation of airfoil lift and drag aerodynamic performance, grid generation and simulation calculation are completed by the server. After the calculation is completed, the lift and drag aerodynamic performance data of the corresponding airfoil are output and saved.

Physical characteristics serve as variables in subsequent calculations and can also be called "physical characteristic variables." In step 102, based on the original airfoil sample, the physical characteristic variables related to the airfoil are extracted to obtain relevant design parameters describing the airfoil. Specifically, they refer to:

Physical features are actually used to describe the physical shape of the airfoil. According to the physical shape of the airfoil, geometric features used to describe the shape of the airfoil are extracted as the physical features. Among them, the geometric features include: the leading edge radius, the maximum thickness of the upper wing surface and the corresponding x coordinate, the maximum thickness of the lower wing surface and the corresponding x coordinate, the overall maximum thickness and the corresponding x coordinate, the height and x corresponding to the maximum point of the tail wing curvature coordinates, and the performance indicators include: airfoil lift and airfoil drag.

The step 103 uses the relevant design parameter data describing the airfoil to train the GP agent model, and returns the objective function evaluation through the trained GP agent model, specifically referring to:

The Gaussian process regression model is constructed using the airfoil described by physical geometric characteristics and the corresponding lift-drag aerodynamic performance. The input is the physical geometric characteristics of the airfoil, and the output is the ratio of lift to drag. Among them, the Gaussian process is determined by its mean function m and covariance function k:

in,

The covariance function (also called kernel function) used is the Matern kernel, and the kernel function formula is:

The step 104 uses the EHVIC point selection strategy to search for candidate airfoils and airfoil dimensions in the corresponding search space, specifically referring to:

Among them, Δ(s) is the constraint satisfying the expectation, S ⁺ refers to the unit that is not dominated by any member of the Pareto efficient set, P(y) is the Pareto efficient point set, and I(·) is the next point selection Lift amount, is the probability density function of the predicted distribution of the objective function.

The search target of the search space consists of two parts, namely the aerodynamic performance target and the sparse target, and their functional forms are as follows:

f ₁ = f (x _next )

The step 105 of performing airfoil performance evaluation on the airfoil selected according to the optimization target item specifically refers to:

Use the Gaussian process regression surrogate model trained in step S3 to evaluate the function of the selected airfoil and output it. The function expression is:

f ₁ =-GPR (x _next )

The step 106 uses the evaluated candidate airfoil and the corresponding performance evaluation to update the proxy model of the optimization framework, and repeats S4, S5, and S6 until the maximum number of optimizations is reached, specifically referring to: updating the searched airfoil and the corresponding lift. The drag ratio aerodynamic performance is used as a collection point and added to the surrogate model of the optimization framework. The surrogate model is updated and its function distribution is changed. The point selection strategy in step S4 is used to select the next point. Then the function is evaluated and repeated until the maximum optimization step. number.

The step 107 will output the Pareto front of the airfoil that meets the airfoil design requirements and has sparse dimensions, specifically referring to:

The airfoil optimization design is carried out based on the original airfoil data given by the client and the trained function evaluation agent model, and then the airfoil parameters that meet the client's needs are returned to the client.

Each embodiment in this specification is described in a progressive manner. The same and similar parts between the various embodiments can be referred to each other. Each embodiment focuses on its differences from other embodiments. In particular, for the equipment embodiment, since it is basically similar to the method embodiment, the description is relatively simple. For relevant details, please refer to the partial description of the method embodiment. The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present invention. All are covered by the protection scope of 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 analysis of the importance of airfoil physical quantities, which is characterized by including: S1. Accept the airfoil sample data uploaded by the client. The airfoil sample data includes the airfoil sample set generated by the client based on the basic airfoil perturbation; S2. Use the airfoil sample set to train the GP (Gaussian Process) proxy model, analyze the airfoil through the trained GP proxy model, and set optimization target items based on the analysis results; S3. Search for candidate airfoils according to the EHVIC point selection strategy and use the search space; S4. Evaluate the performance of the obtained candidate airfoil according to the optimization target items; S5. Based on the performance evaluation, update the GP agent model in the Bayesian optimization framework; S6. Repeat the optimization cycle consisting of S3 to S5 until the maximum number of optimizations is reached, and the Pareto frontier of the airfoil is output. 2. The method according to claim 1, characterized in that, S2 includes: S21. Extract the physical characteristics and performance indicators corresponding to each piece of sample data in the airfoil sample set. The physical characteristics are used to describe the geometric shape of the airfoil. The aerodynamic performance types pointed to by the performance indicators include: airfoil lift and airfoil lift. type resistance; S22. Use the extracted physical features to train a GP (Gaussian Process) proxy model, and return the analysis results of the airfoil through the trained GP proxy model. The analysis results include the aerodynamic performance data output by the GP proxy model. 3. The method according to claim 1 or 2, characterized in that the physical characteristics include: leading edge radius, upper airfoil maximum thickness and corresponding x-coordinate, lower airfoil maximum thickness and corresponding x-coordinate, overall The maximum thickness and corresponding x-coordinate and the height and x-coordinate corresponding to the maximum point of tail wing curvature. 4. The method according to claim 2, wherein the optimization target item includes: using the aerodynamic performance data output by the GP agent model in S22 as the aerodynamic performance target of the airfoil; and, the corresponding dimensions of each airfoil. 5. The method according to claim 4, characterized in that, in S4, it further includes: While searching for candidate airfoils in the corresponding search space, it also includes searching for airfoil dimensions, which include a combination of physical characteristics and aerodynamic performance data related to the candidate airfoils. 6. The method according to claim 1, wherein the GP agent model is a Gaussian process regression model. In S22, it further includes: constructing a Gaussian process regression model according to the physical characteristics and the performance index; Among them, the mean function m and covariance function k in the Gaussian process are respectively: Among them, GP() represents Gaussian process, f(x) represents the function value corresponding to x, x and x’ represent two different data points in the sample; The kernel function used in the Gaussian process is: x _i , x _j represent two different samples in the sample set, v represents the smoothing coefficient, l represents the forward parameter, usually l=1, Γ(v) represents the Gamma function, and K _v represents the Bassel function. 7. The method according to claim 1, characterized in that, in S3, it includes: Establish an EHVIC site selection strategy: Among them, Δ(s) indicates that the constraint satisfies expectations, and S ⁺ indicates a unit that is not dominated by any member of the Pareto efficient set, represents the Pareto effective point set, I(·) represents the improvement amount of the next point selection,/> Represents the probability density function of the objective function's predicted distribution, s represents a point in S ⁺ , y represents the current sampling point, f _x represents the objective function,/> Represents the Pareto efficient point. 8. The method according to claim 7, characterized in that 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 ) Among them, f ₁ represents the first goal, the first goal includes the aerodynamic performance of the airfoil, f ₂ represents the second goal, the second goal includes the sparsity of the airfoil disturbance, Represents an intermediate calculation formula,/> Represents the positive and negative perturbations of the i-th dimension relative to the base airfoil, a=10 ^-0.5 , x _base represents the base airfoil, Δx _next represents the positive and negative perturbations relative to the base airfoil, and D is the dimension of Δx _next . 9. The method according to claim 1, characterized in that, in S4, it includes: Using the trained Gaussian process regression model, function evaluation is performed on the selected airfoil and the results are output, including the aerodynamic performance f ₁ of the airfoil and the sparsity f ₂ of the airfoil dimension. 10. The method according to claim 1, characterized in that the GP agent model in the Bayesian optimization framework is updated in each cycle of optimization; In each optimization cycle, it includes: Use the candidate airfoil and corresponding lift-to-drag ratio performance as collection points, and import the sampling points into the GP proxy model of the optimization framework; In the process of updating the GP agent model of the optimization framework, the function distribution of the GP agent model is changed, and the point selection strategy of S3 is executed to select points again; Then S4~S5 are executed in sequence.