An adaptive sampling method for aerodynamic characteristic modeling

Abstract

The application discloses an adaptive sampling method for aerodynamic characteristic modeling, and belongs to the field of aerodynamics. The application solves the sample waste problem caused by the lack of targeted sampling ability of the existing traditional sampling method in the aerodynamic characteristic modeling; the application is directed to the aerodynamic characteristic modeling, the parameter interval where the complex function is located is determined by comprehensively weighting the uncertainty of the Gaussian process regression and the parameter sensitivity analysis result, the non-uniform sampling is carried out according to the complexity of the parameter interval, and the targeted sampling of the complex function region is realized; the sensitivity analysis adopts a joint data mining method, and contains two methods of Sobol algorithm and decision tree; and the application effectively improves the sample utilization efficiency of small sample aerodynamic characteristic modeling.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerodynamics, in particular to an adaptive sampling method for aerodynamic characteristic modeling. BACKGROUND

[0002] In recent years, with the development of machine learning technology, some researches have applied machine learning technology to the field of aerodynamic characteristic modeling and aerodynamic prediction, and have achieved effective engineering application. When modeling aerodynamic characteristics, the parameter space of the input variables needs to be sampled first. The representativeness of the sample points directly affects the fitting of the model to the aerodynamic characteristics. Traditional modeling sampling methods such as Latin hypercube, uniform design, and orthogonal design divide and process the input variable parameter space, so that the selected sample points are as "uniformly full" as possible. Such traditional sampling methods only focus on the input variable space, and do not focus on the spatial form of the target function value.

[0003] The aerodynamic characteristic data of an aircraft often has complex situations such as inflection points and jump points. Compared with smooth and linear segments, more data points need to be invested in this type of region to ensure modeling accuracy. Since the core of traditional sampling methods is to ensure that the sample points are "uniformly full" in the parameter space, the number of samples in each interval is relatively close, and there is a lack of targeted sampling ability for complex function regions. Therefore, if traditional sampling methods are used for sampling, when the number of samples in the inflection point, jump point and other regions meets the modeling accuracy requirement, the sample points in the smooth and linear segments have already exceeded the required number of samples, causing sample waste and increasing the data set preparation cost of aerodynamic characteristic modeling. The current mainstream non-uniform sampling method is mostly aimed at the field of signal images, and needs to be adjusted and verified for the relatively small aerodynamic characteristic modeling problem.

[0004] In summary, a targeted adaptive sampling method for aerodynamic characteristic modeling is needed to reduce sample waste in the aerodynamic characteristic modeling process and improve the modeling accuracy of complex function regions. SUMMARY

[0005] The present application provides an adaptive sampling method for aerodynamic characteristic modeling to solve the problem of sample waste caused by the lack of targeted sampling ability for complex function regions in the existing traditional sampling method in aerodynamic characteristic modeling. The method includes the following steps:

[0006] S1. Apply the optimal Latin hypercube sampling method to sample the input variable parameter space to obtain original sample data, and the number of samples is 50% of the total number of modeling samples. Apply wind tunnel test or computational fluid dynamics method to obtain the aerodynamic characteristic values corresponding to each sample state;

[0007] S2. Model the sample data by using a Gaussian process regression model to obtain an aerodynamic characteristic model; calculate the uncertainty of each input dimension in the aerodynamic characteristic model to obtain an uncertainty result; perform parameter sensitivity analysis on each dimension of the aerodynamic characteristic model by using a Sobol algorithm and a decision tree method to obtain a parameter sensitivity analysis result;

[0008] S3. Based on the uncertainty result and the parameter sensitivity analysis result in S2, comprehensively obtain the function complexity of each parameter interval by weighting; perform non-uniform incremental sampling on the overall parameter space based on the function complexity of each parameter interval to obtain incremental sampling sample data, and the number of non-uniform incremental sampling is 10% of the total number of modeling samples;

[0009] S4. Repeat S2 and S3 until the number of samples reaches 100% of the total number of modeling samples or reaches a preset convergence condition.

[0010] Further, in S1, the optimal Latin hypercube sampling method is implemented by:

[0011] :

[0012] Sampling the input variable parameter space, wherein, is a target function optimized by sample points, is a sampling design matrix, is the number of distances between sample points, represents the first distance value, represents the number of point pairs with a distance of , and is the number of point pairs with a distance of is an optimization weight parameter.

[0013] Further, in S2, the modeling of sample data by using a Gaussian process regression model is implemented by:

[0014] ;

[0015] ;

[0016] ;

[0017] , wherein, is a Gaussian function, is a mean function, is a covariance function, is a predicted target mean, is a covariance vector between the predicted target and the training points, is the transpose of the covariance vector between the predicted target and the training points, is a training output value vector, is a kernel function, is a first spatial sample point, is a second spatial sample point, is a first spatial sample point and a second spatial sample point between them, is a length scale parameter, is a smoothness parameter, is a gamma function, is a second kind modified Bessel function.

[0018] Further, the calculation of the uncertainty of each input dimension in the aerodynamic characteristics model in S3 is performed by:

[0019] ;

[0020] ;

[0021] obtained, wherein, is the prediction variance of the regression prediction point, is the test point itself variance, the standard deviation mean characterizes the interval uncertainty, is the number of test points of the interval regression prediction, is the prediction standard deviation of the th test point.

[0022] Further, in S3, the Sobol algorithm is performed by:

[0023] ;

[0024] ;

[0025] ;

[0026] a parameter sensitivity analysis is implemented, wherein, is the total variance, is the one-factor variance contribution of , is the interaction variance contribution of and , is the high-order interaction of all variables, is the one-factor sensitivity result of , is the sensitivity analysis result of and interaction.

[0027] Furthermore, in S3, the decision tree method adopts a regression tree model based on the CART algorithm, using the mean squared error as the impurity evaluation index of the regression tree. The overall splitting of the decision tree is controlled by setting the minimum impurity parameter and the minimum number of split samples for node splitting. The branching direction of the decision tree is read to determine the direction of the correlation of the parameters and the turning point of the local correlation. If the mean value of the function of the child node increases after the branching, the range of the node is positively correlated; otherwise, the range of the node is negatively correlated.

[0028] Furthermore, in S3, the number of non-uniform incremental samples is determined by:

[0029] ;

[0030] Obtain, among which, For the current dimension Interval non-uniform incremental sampling number For the first Interval complexity score This represents the total number of intervals in the current dimension. This represents the total number of non-uniform incremental samples in the current incremental phase.

[0031] Compared with the prior art, the present invention has the following beneficial effects: The present invention addresses the problem of aerodynamic characteristic modeling. It addresses the problem that traditional sampling methods lack the ability to add points to complex function regions, resulting in wasted sample points in simple function regions and insufficient sample points in complex function regions. The present invention divides the parameter space and uses uncertainty analysis and parameter sensitivity analysis 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 aerodynamic characteristic modeling process, and specifically improve the modeling accuracy in complex function regions. Attached Figure Description

[0032] Figure 1 This is a flowchart of an adaptive sampling method for aerodynamic characteristic modeling. Detailed Implementation

[0033] Example: Combining Figure 1 This embodiment describes an adaptive sampling method for aerodynamic characteristic modeling, the method comprising the following steps:

[0034] S1. The optimal Latin hypercube sampling method is applied to sample the input variable parameter space to obtain the original sample data. The number of samples is 50% of the total number of modeling samples. The aerodynamic characteristic values ​​corresponding to each sample state are obtained by applying wind tunnel tests or computational fluid dynamics methods.

[0035] S2. modeling the sample data by 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 by using a Sobol algorithm and a decision tree method to obtain a parameter sensitivity analysis result;

[0036] S3. obtaining the function complexity of each parameter interval by comprehensive weighting based on the uncertainty result and the parameter sensitivity analysis result in S2; performing non-uniform incremental sampling on the overall parameter space based on the function complexity of each parameter interval to obtain incremental sampling sample data, and the number of non-uniform incremental sampling is 10% of the total number of modeling samples;

[0037] S4. repeating S2 and S3 until the number of samples reaches 100% of the total number of modeling samples or reaches a preset convergence condition.

[0038] Specifically, the sample data in S2 before incremental sampling is the original sample data in S1; and the sample data in S2 after incremental sampling includes the original sample data in S1 and the incremental sampling sample data in S3.

[0039] In S3, the modeling complexity of each interval is obtained by comprehensive weighting according to the uncertainty analysis result and the parameter sensitivity analysis result after adjusting to the same amplitude range, and the weight distribution of different stages is known through Table 1:

[0040] Table 1 Weight distribution of each stage of incremental sampling

[0041]

[0042] In S4, if the adaptive sampling target is to reduce sample waste and improve modeling accuracy, the entire incremental sampling process is completed; if the adaptive sampling target is to reduce the total number of samples, a convergence standard is set, and the proportion of each incremental sampling to the total sampling is reduced, and the incremental sampling is stopped when the convergence standard is met.

[0043] In S1, the optimal Latin hypercube sampling method is performed by:

[0044] :

[0045] sampling the input variable parameter space, wherein, is a target function of sample point optimization, is a sampling design matrix, is the number of distances between sample points, denotes the th distance value, denotes the number of point pairs with a distance of , To optimize the weight parameters.

[0046] Specifically, the optimal Latin hypercube sampling method (OLHS) used is a further improvement of the ordinary Latin hypercube sampling (LHS).

[0047] In S2, the Gaussian process regression model is used to model the sample data by:

[0048] ;

[0049] ;

[0050] ;

[0051] is achieved, wherein, is a Gaussian function, is a mean function, is a covariance function, is a predicted target mean, is a covariance vector between the predicted target and the training points, is the transpose of the covariance vector between the predicted target and the training points, is a training output value vector, is a kernel function, is a first spatial sample point, is a second spatial sample point, is the Euclidean distance between the first spatial sample point and the second spatial sample point . is a length scale parameter, is a smoothness parameter, is a gamma function, is a second kind of modified Bessel function.

[0052] In S3, the uncertainty of each input dimension in the aerodynamic characteristic model is calculated by:

[0053] ;

[0054] ;

[0055] is obtained, wherein, is the predicted variance of the regression prediction point, is the test point itself variance, the standard deviation mean characterizes the interval uncertainty, is the number of test points of the interval regression prediction, is the predicted standard deviation of the th test point.

[0056] Specifically, based on the aerodynamic characteristic model, points are evenly taken in each parameter interval and interval uncertainty is calculated. To avoid "dimension disaster" in calculation when there are many parameters, in the calculation process, interval division is performed on only one parameter dimension at the same time, and the division step of the parameter interval is 10%.

[0057] In S3, the Sobol algorithm is used by:

[0058] ;

[0059] ;

[0060] ;

[0061] The parameter sensitivity analysis is implemented, wherein, is the total variance, is the single factor variance contribution, is the and interaction variance contribution, is the high-order interaction of all variables, is the single factor sensitivity result, is the and interaction sensitivity analysis result.

[0062] Specifically, the numerical value of the final sensitivity analysis result is provided by the Sobol algorithm.

[0063] In S3, the decision tree method uses 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 and the minimum number of split samples of node splitting; the correlation direction and the turning relationship of local correlation of the decision tree branch direction judgment parameter are read, if the function mean of the child node after branching increases, the node range is positively correlated, otherwise, the node range is negatively correlated.

[0064] Specifically, the correlation direction and the turning relationship of local correlation are provided by the decision tree method.

[0065] In S3, the non-uniform incremental sampling number is obtained by:

[0066] ;

[0067] wherein, is the non-uniform incremental sampling number of the current dimension, and is the interval. is the first interval complexity score, is the total number of intervals for the current dimension, is the total number of non-uniform incremental samples for the current incremental phase.

[0068] While the present application has been described in terms of several embodiments, those skilled in the art will appreciate that other embodiments can be devised without departing from the scope and spirit of the application. Accordingly, the scope of the application should be determined not with reference to the above description, but instead with reference to the appended claims along with their full scope of equivalents.

Claims

1. An adaptive sampling method for aerodynamic property modeling, the method comprising: The method comprises the following steps: S1. Apply the optimal Latin hypercube sampling method to sample the variable parameter space to obtain original sample data, the sampling number being 50% of the total number of modeling samples, and the aerodynamic characteristic values corresponding to each sample state being obtained by wind tunnel test or computational fluid dynamics method; S2. Model the sample data by using a Gaussian process regression model to obtain an aerodynamic characteristic model, calculate the uncertainty of each input dimension in the aerodynamic characteristic model to obtain an uncertainty result, and perform parameter sensitivity analysis on each dimension of the aerodynamic characteristic model by using a Sobol algorithm and a decision tree method to obtain a parameter sensitivity analysis result; S3. Based on the uncertainty result and the parameter sensitivity analysis result in S2, the function complexity of each parameter interval is obtained by comprehensive weighting, and the overall parameter space is non-uniformly incrementally sampled based on the function complexity of each parameter interval to obtain incrementally sampled sample data, the non-uniformly incrementally sampled number being 10% of the total number of modeling samples; S4. Repeat S2 and S3 until the sampling number reaches 100% of the total number of modeling samples or a preset convergence condition is reached; In S2, the modeling of the sample data by using the Gaussian process regression model is performed by: ； ； ； Implementation, wherein, is a Gaussian function, is a mean function, is a covariance function, is a predicted target mean, is a covariance vector between the predicted target and the training points, is the transpose of the covariance vector between the predicted target and the training points, is a training output value vector, is a kernel function, is a first spatial sample point, is a second spatial sample point, is a first spatial sample point and a second spatial sample point between the first and second spatial sample points, is a length scale parameter, is a smoothness parameter, is a gamma function, is a second kind modified Bessel function; In S3, the calculation of the uncertainty of each input dimension in the aerodynamic characteristic model is performed by: ； ； obtained, wherein is the prediction variance of the regression prediction point, is the test point itself variance, standard deviation mean characterizes the interval uncertainty, is the number of test points of the interval regression prediction, is the prediction standard deviation for the test point. In S3, the Sobol algorithm is performed by: ； ； ； Implementing parameter sensitivity analysis, wherein, is the total variance, is is the single factor variance contribution of is and is the interaction variance contribution of is the high order interaction of all variables, is is the single factor sensitivity result of is and is the sensitivity analysis result of interaction.

2. The adaptive sampling method for aerodynamic characteristics modeling according to claim 1, wherein, In S1, the optimal Latin hypercube sampling method is performed by: ； The input variable parameter space is sampled, wherein, The objective function to be optimized for the sample points. Design matrix for sampling, This represents the number of distances between sample point pairs. Indicates the first A distance value, Indicates distance as Number of point pairs To optimize the weight parameters.

3. The adaptive sampling method for aerodynamic characteristics modeling according to claim 1, wherein, In S3, the decision tree method adopts a regression tree model based on a CART algorithm, takes mean square error as a regression tree impurity evaluation index, and controls the overall splitting of the decision tree by setting a minimum impurity parameter and a minimum split sample number for node splitting; The branching direction of the decision tree is read to determine the correlation direction and the turning relationship of the local correlation of the parameters, if the function mean of the child nodes after branching increases, the node range is positively correlated, otherwise, the node range is negatively correlated.

4. The adaptive sampling method for aerodynamic characteristics modeling of claim 1, wherein, In S3, the non-uniformly incrementally sampled number is determined by: ； obtained, wherein, is the current dimension total interval number, is the interval non-uniform increment sampling number, is the current dimension total interval number, is the interval complexity score, is the current dimension total interval number, is the current increment stage total non-uniform increment sampling number.

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