Adaptive sampling method for aerodynamic characteristic modeling

Abstract

The invention discloses a self-adaptive sampling method for aerodynamic characteristic modeling, and belongs to the field of aerodynamics. The problem that in aerodynamic characteristic modeling, an existing traditional sampling method lacks the targeted sampling capacity for a complex function area, and consequently samples are wasted is solved. According to the method, modeling is carried out for aerodynamic characteristics, a parameter interval where a complex function is located is determined through comprehensive weighting of uncertainty of Gaussian process regression and a parameter sensitivity analysis result, non-uniform sampling is carried out according to the complexity condition of the parameter interval, and targeted sampling of a complex function area is achieved; sensitivity analysis adopts a joint data mining method, and comprises two methods of a Sobol algorithm and a decision tree; according to the method, the sample utilization efficiency of small sample aerodynamic characteristic modeling is effectively improved.

Description

Technical Field

[0001] The invention relates to the field of aerodynamics, and in particular to an adaptive sampling method for aerodynamic characteristic modeling. Background Art

[0002] In recent years, with the development of machine learning technology, some studies have applied machine learning technology to the field of aerodynamic modeling and aerodynamic prediction, and have achieved effective engineering applications. When modeling aerodynamic characteristics, it is first necessary to sample the parameter space of the input variables. The representativeness of the sample points directly affects the model's fitting of the aerodynamic characteristics. Traditional modeling sampling methods such as Latin hypercube, uniform design, orthogonal design divide and process the input variable parameter space to make the selected sample points as "uniformly fill" the variable parameter space as possible. Such traditional sampling methods only focus on the input variable space, but not the spatial form of the objective function value.

[0003] The aerodynamic characteristics data of aircraft often have complex situations such as inflection points and jump points. Compared with smooth segments and linear segments, more data points are needed to ensure the modeling accuracy in such areas during modeling. Since the core of the traditional sampling method is to ensure that the sample points "evenly fill" the parameter space, the number of samples in each interval is relatively close, and there is a lack of the ability to add points in a targeted manner to complex function areas. Therefore, if the traditional sampling method is used, when the number of samples in the inflection points, jump points and other areas meets the modeling accuracy requirements, the sample points in the smooth segments and linear segments have already exceeded the required number of samples, resulting in sample waste and increasing the data set preparation cost for aerodynamic characteristics modeling. The current mainstream non-uniform sampling methods are mostly oriented to the field of signal images, and the aerodynamic characteristics modeling problems with relatively small sample sizes still need to be adjusted and verified.

[0004] In summary, an adaptive sampling method specifically for aerodynamic characteristic modeling is needed to reduce sample waste in the aerodynamic characteristic modeling process and improve the modeling accuracy of complex function areas. Summary of the invention

[0005] In order to solve the problem of sample waste caused by the lack of targeted sampling capability of complex function areas in the existing traditional sampling method in aerodynamic characteristic modeling, the present invention provides an adaptive sampling method for aerodynamic characteristic modeling, the method comprising the following steps: S1. Apply the optimal Latin hypercube sampling method to sample the input variable parameter space to obtain the original sample data. The sampling number is 50% of the total modeling sample number. Apply wind tunnel test or computational fluid dynamics method to obtain the aerodynamic characteristic value corresponding to each sample state; S2. Modeling the sample data using a Gaussian process regression model to obtain an aerodynamic characteristic model; calculating the uncertainty of each input dimension in the aerodynamic characteristic model to obtain an uncertainty result; performing parameter sensitivity analysis on each dimension of the aerodynamic characteristic model using a Sobol algorithm and a decision tree method to obtain a parameter sensitivity analysis result; S3. Based on the uncertainty results and parameter sensitivity analysis results described in S2, the function complexity of each parameter interval is obtained by comprehensive weighting; based on the function complexity of each parameter interval, the overall parameter space is subjected to non-uniform incremental sampling to obtain incremental sampling sample data, and the number of non-uniform incremental sampling is 10% of the total number of modeling samples; S4. Repeat S2 and S3 until the number of samples reaches 100% of the total modeling samples or the preset convergence condition is reached.

[0006] Further, in S1, the optimal Latin hypercube sampling method is: : The input variable parameter space is sampled, where is the objective function optimized for the sample points, is the sampling design matrix, is the number of distances between pairs of sample points, Indicates distance values, Indicates the distance The number of point pairs, To optimize the weight parameters.

[0007] Further, in S2, the Gaussian process regression model is used to model the sample data by: ; ; ; To achieve, is a Gaussian function, is the mean function, is the covariance function, is the predicted target mean, is the covariance vector between the predicted target and the training point, is the transpose of the covariance vector between the predicted target and the training point, is the training output value vector, for Kernel function, is the first spatial sample point, is the second space sample point, is the first spatial sample point With the second space sample point The Euclidean distance between is the length scale parameter, is the smoothness parameter, is the gamma function, is the modified Bessel function of the second kind.

[0008] Further, the uncertainty of each input dimension in the aerodynamic characteristic model is calculated in S3 by: ; ; Obtain, among which, is the prediction variance of the regression prediction point, is the variance of the test point itself, standard deviation mean Characterize the interval uncertainty, is the number of test points for interval regression prediction, For the The predicted standard deviation of the test points.

[0009] Further, in S3, the Sobol algorithm is: ; ; ; Implement parameter sensitivity analysis, where is the total variance, for The single factor variance contribution of for and The interactive variance contribution of are the higher-order interactions of all variables, for The single factor sensitivity results, for and Results of sensitivity analysis of interaction effects.

[0010] Furthermore, in S3, the decision tree method adopts a regression tree model based on the CART algorithm, takes the mean square error as the regression tree impurity evaluation index, and controls the overall splitting of the decision tree by setting the minimum impurity parameter of the node splitting and the minimum number of split samples; reads the branch direction of the decision tree to determine the correlation direction of the parameter and the turning relationship of the local correlation. If the function mean of the child node increases after the branch, the node range is positively correlated; otherwise, the node range is negatively correlated.

[0011] Furthermore, in S3, the number of non-uniform incremental samples is obtained by: ; Obtain, among which, The current dimension The number of interval non-uniform incremental sampling, For the Interval complexity score, is the total number of intervals in the current dimension, It is the total number of non-uniform incremental samples in the current incremental stage.

[0012] Compared with the prior art, the present invention has the following beneficial effects: the present invention is aimed at the problem of aerodynamic characteristic modeling. In view of the problem that traditional sampling methods lack the ability to add points in a targeted manner to complex function areas, which leads to waste of sample points in simple function areas and insufficient sample points in complex function areas, the parameter space is divided, and uncertainty analysis and parameter sensitivity analysis methods are used to quantitatively analyze the function modeling complexity in each interval. Based on the function complexity results, non-uniform incremental sampling is performed to achieve adaptive sampling for aerodynamic characteristic modeling, reduce sample waste in the process of aerodynamic characteristic modeling, and improve the modeling accuracy of complex function areas in a targeted manner. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Flowchart of an adaptive sampling method for aerodynamic modeling. DETAILED DESCRIPTION

[0014] Example: Combination Figure 1 This embodiment describes an adaptive sampling method for aerodynamic characteristics modeling, the method comprising the following steps: S1. Apply the optimal Latin hypercube sampling method to sample the input variable parameter space to obtain the original sample data. The sampling number is 50% of the total modeling sample number. Apply wind tunnel test or computational fluid dynamics method to obtain the aerodynamic characteristic value corresponding to each sample state; S2. Modeling the sample data using a Gaussian process regression model to obtain an aerodynamic characteristic model; calculating the uncertainty of each input dimension in the aerodynamic characteristic model to obtain an uncertainty result; performing parameter sensitivity analysis on each dimension of the aerodynamic characteristic model using a Sobol algorithm and a decision tree method to obtain a parameter sensitivity analysis result; S3. Based on the uncertainty results and parameter sensitivity analysis results described in S2, the function complexity of each parameter interval is obtained by comprehensive weighting; based on the function complexity of each parameter interval, the overall parameter space is subjected to non-uniform incremental sampling to obtain incremental sampling sample data, and the number of non-uniform incremental sampling is 10% of the total number of modeling samples; S4. Repeat S2 and S3 until the number of samples reaches 100% of the total modeling samples or the preset convergence condition is reached.

[0015] Specifically, the sample data in S2 is the original sample data in S1 before incremental sampling; the sample data in S2 includes the original sample data in S1 and the incrementally sampled sample data in S3 after incremental sampling.

[0016] In S3, the uncertainty analysis results and parameter sensitivity analysis results are adjusted to the same amplitude range and then weighted, and the comprehensive weighted score is used as the modeling complexity of each interval. The weight distribution of different stages can be seen from Table 1: Table 1 Weight distribution of each stage of incremental sampling

[0017] In S4, if the adaptive sampling goal is to reduce sample waste and improve modeling accuracy, the entire incremental sampling process is completed; if the adaptive sampling goal is to reduce the total number of samples, the convergence standard is set, and the proportion of each incremental sampling to the total sampling is reduced, and the incremental sampling is stopped after the convergence standard is met.

[0018] In S1, the optimal Latin hypercube sampling method is achieved by: : The input variable parameter space is sampled, where is the objective function optimized for the sample points, is the sampling design matrix, is the number of distances between pairs of sample points, Indicates distance values, Indicates the distance The number of point pairs, To optimize the weight parameters.

[0019] Specifically, the optimal Latin hypercube sampling method (OLHS) adopted is a further improvement of the ordinary Latin hypercube sampling (LHS).

[0020] In S2, the Gaussian process regression model is used to model the sample data by: ; ; ; To achieve, is a Gaussian function, is the mean function, is the covariance function, is the predicted target mean, is the covariance vector between the predicted target and the training point, is the transpose of the covariance vector between the predicted target and the training point, is the training output value vector, for Kernel function, is the first spatial sample point, is the second space sample point, is the first spatial sample point With the second space sample point The Euclidean distance between is the length scale parameter, is the smoothness parameter, is the gamma function, is the modified Bessel function of the second kind.

[0021] The uncertainty of each input dimension in the aerodynamic characteristic model is calculated in S3 by: ; ; Obtain, among which, is the prediction variance of the regression prediction point, is the variance of the test point itself, standard deviation mean Characterize the interval uncertainty, is the number of test points for interval regression prediction, For the The predicted standard deviation of the test points.

[0022] Specifically, based on the aerodynamic characteristic model, points are evenly selected in each parameter interval and the interval uncertainty is calculated. In order to avoid the "dimensional disaster" when there are many parameters, only one parameter dimension is divided into intervals at the same time during the calculation process, and the step size of the parameter interval is 10%.

[0023] In S3, the Sobol algorithm is implemented by: ; ; ; Implement parameter sensitivity analysis, where is the total variance, for The single factor variance contribution of for and The interactive variance contribution of are the higher-order interactions of all variables, for The single factor sensitivity results, for and Results of sensitivity analysis of interaction effects.

[0024] Specifically, the numerical value of the final sensitivity analysis result is provided by the Sobol algorithm.

[0025] In S3, the decision tree method adopts a regression tree model based on the CART algorithm, takes the mean square error as the regression tree impurity evaluation index, and controls the overall splitting of the decision tree by setting the minimum impurity parameter of the node splitting and the minimum number of split samples; reads the branch direction of the decision tree to determine the correlation direction of the parameter and the turning relationship of the local correlation. If the function mean of the child node increases after the branch, the node range is positively correlated; otherwise, the node range is negatively correlated.

[0026] Specifically, the correlation action direction and the turning relationship of the local correlation are provided by the decision tree method.

[0027] In S3, the non-uniform incremental sampling quantity is obtained by: ; Obtain, among which, The current dimension The number of interval non-uniform incremental sampling, For the Interval complexity score, is the total number of intervals in the current dimension, It is the total number of non-uniform incremental samples in the current incremental stage.

[0028] Although the present invention has been described according to a limited number of embodiments, it will be apparent to those skilled in the art, with the benefit of the above description, that other embodiments may be envisioned within the scope of the invention thus described. In addition, it should be noted that the language used in this specification is selected primarily for readability and teaching purposes, rather than for explaining or defining the subject matter of the present invention. Therefore, many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the appended claims. The disclosure of the present invention is illustrative, not restrictive, with respect to the scope of the present invention, which is defined by the appended claims.

Claims

1. An adaptive sampling method for aerodynamic characteristics modeling, characterized in that: The method comprises the following steps: S1. Apply the optimal Latin hypercube sampling method to sample the input variable parameter space to obtain the original sample data. The sampling number is 50% of the total modeling sample number. Apply wind tunnel test or computational fluid dynamics method to obtain the aerodynamic characteristic value corresponding to each sample state; S2. Modeling the sample data using a Gaussian process regression model to obtain an aerodynamic characteristic model; calculating the uncertainty of each input dimension in the aerodynamic characteristic model to obtain an uncertainty result; performing parameter sensitivity analysis on each dimension of the aerodynamic characteristic model using a Sobol algorithm and a decision tree method to obtain a parameter sensitivity analysis result; S3. Based on the uncertainty results and parameter sensitivity analysis results described in S2, the function complexity of each parameter interval is obtained by comprehensive weighting; based on the function complexity of each parameter interval, the overall parameter space is subjected to non-uniform incremental sampling to obtain incremental sampling sample data, and the number of non-uniform incremental sampling is 10% of the total number of modeling samples; S4. Repeat S2 and S3 until the number of samples reaches 100% of the total modeling samples or the preset convergence condition is reached.

2. The adaptive sampling method for aerodynamic characteristics modeling according to claim 1, characterized in that: In S1, the optimal Latin hypercube sampling method is achieved by: ： The input variable parameter space is sampled, where is the objective function optimized for the sample points, is the sampling design matrix, is the number of distances between pairs of sample points, Indicates distance values, Indicates the distance The number of point pairs, To optimize the weight parameters.

3. The adaptive sampling method for aerodynamic characteristics modeling according to claim 1, characterized in that: In S2, the Gaussian process regression model is used to model the sample data by: ； ； ； To achieve, is a Gaussian function, is the mean function, is the covariance function, is the predicted target mean, is the covariance vector between the predicted target and the training point, is the transpose of the covariance vector between the predicted target and the training point, is the training output value vector, for Kernel function, is the first spatial sample point, is the second space sample point, is the first spatial sample point With the second space sample point The Euclidean distance between is the length scale parameter, is the smoothness parameter, is the gamma function, is the modified Bessel function of the second kind.

4. The adaptive sampling method for aerodynamic characteristics modeling according to claim 1, characterized in that: The uncertainty of each input dimension in the aerodynamic characteristic model is calculated in S3 by: ； ； Obtain, among which, is the prediction variance of the regression prediction point, is the variance of the test point itself, standard deviation mean Characterize the interval uncertainty, is the number of test points for interval regression prediction, For the The predicted standard deviation of the test points.

5. The adaptive sampling method for aerodynamic characteristic modeling according to claim 1, characterized in that: In S3, the Sobol algorithm is implemented by: ； ； ； Implement parameter sensitivity analysis, where is the total variance, for The single factor variance contribution of for and The interactive variance contribution of are the higher-order interactions of all variables, for The single factor sensitivity results, for and Results of sensitivity analysis of interaction effects.

6. The adaptive sampling method for aerodynamic characteristic modeling according to claim 1, characterized in that: In S3, the decision tree method adopts a regression tree model based on the CART algorithm, takes the mean square error as the regression tree impurity evaluation index, and controls the overall splitting of the decision tree by setting the minimum impurity parameter of node splitting and the minimum number of split samples; Read the branch direction of the decision tree to determine the correlation direction of the parameters and the turning relationship of the local correlation. If the function mean of the child node increases after the branch, the node range is positively correlated; otherwise, the node range is negatively correlated.

7. The adaptive sampling method for aerodynamic characteristic modeling according to claim 1, characterized in that: In S3, the non-uniform incremental sampling quantity is obtained by: ； Obtain, among which, The current dimension The number of interval non-uniform incremental sampling, For the Interval complexity score, is the total number of intervals in the current dimension, It is the total number of non-uniform incremental samples in the current incremental stage.

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