A multi-objective optimization method for the aerodynamic shape of the second-segment wing of a hypersonic winged reentry vehicle

Abstract

The present invention discloses a multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle. Based on multi-fidelity data fusion using a deep learning neural network, the method fits the linear and nonlinear relationships between high-fidelity and low-fidelity aerodynamic data, thereby improving the accuracy and reliability of aerodynamic parameters at various flight state points during the design of the second-segment wing shape of the vehicle. On this basis, a proxy model constructed using a radial basis function neural network algorithm is combined with a simulated annealing optimization method, which has better applicability for complex nonlinear fitting problems in the field of aerodynamic shape design, while improving the globality and robustness of the optimization results of the geometric shape design variables, thereby providing a new, efficient and accurate design tool for hypersonic winged reentry vehicles.

Description

Technical Field

[0001] The present invention relates to the technical field of hypersonic winged reentry vehicle design, in particular to a multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle. Background Art

[0002] Traditional aerodynamic shape optimization approaches typically combine numerical simulation and optimization algorithms, with the Kriging surrogate model being a common surrogate model. However, the Kriging surrogate model performs poorly when dealing with highly nonlinear, multimodal, and high-dimensional problems, lacks global fitting capabilities, and struggles to capture complex vehicle aerodynamic characteristics.

[0003] Deep learning neural network algorithms and radial basis function neural network surrogate models possess excellent nonlinear fitting capabilities and generalization performance, effectively capturing the complex nonlinear relationships in aircraft aerodynamic characteristics, thereby improving the efficiency and accuracy of design optimization. Simulated annealing, as a global optimization method, can escape local optimal solutions within the design space, helping to discover more optimal aircraft aerodynamic shapes. Combining neural network surrogate models with simulated annealing allows for a more comprehensive and in-depth search of the design variable space.

[0004] Aircraft shape design requires extensive aerodynamic data from multiple flight states. Low-fidelity aerodynamic data is obtained through numerical simulations, such as engineering software estimation methods, providing rich, less accurate data at a low cost. High-fidelity aerodynamic data is obtained through wind tunnel testing and actual flight tests, providing reliable and authentic aerodynamic data, but at high time and labor costs. Multi-fidelity data fusion methods based on deep learning neural networks can fit the nonlinear relationship between high- and low-fidelity data, improving the efficiency of aerodynamic shape optimization and the credibility of the optimization results.

[0005] Based on the above problems, combining the neural network proxy model with the simulated annealing algorithm can improve the accuracy of aerodynamic data and provide a new optimization method for the aerodynamic shape design of hypersonic aircraft. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a multi-objective optimization method for the aerodynamic shape of the second-section wing of a hypersonic winged reentry vehicle, which enhances the credibility of the aircraft shape optimization results and has higher optimization efficiency in engineering applications.

[0007] To solve the above technical problems, the present invention provides a multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle, comprising the following steps:

[0008] Step 1: Initialize the geometric design variables and constraint range of the second-segment wing of the winged reentry vehicle;

[0009] Step 2: Use the Latin hypercube sampling method to sample all design variables in the design space to obtain geometric design variable samples;

[0010] Step 3: Design a baseline aerodynamic layout for a winged reentry vehicle, parametrically describe the vehicle geometry based on the class shape function transformation method, and construct a parametric geometric shape of the second-segment wing of the winged reentry vehicle;

[0011] Step 4: Based on the aforementioned winged reentry vehicle geometry samples, computational fluid dynamics (CFD) and engineering estimation methods are used on the geometry samples at different flight states to obtain high-confidence and low-confidence datasets.

[0012] Step 5: Based on the deep learning neural network, the high-fidelity and low-fidelity data sets are fused to construct a multi-fidelity data fusion proxy model for high-fidelity aerodynamic parameter prediction of design variables;

[0013] Step 6: Based on the linear weighted method, the aerodynamic data predicted by the multi-fidelity data fusion proxy model at multiple flight state points are integrated to obtain the comprehensive aerodynamic indicators for the two-section wing shape optimization; an aerodynamic optimization proxy model is constructed based on the comprehensive aerodynamic indicators, and the proxy model generation method is a radial basis function neural network;

[0014] Step 7: Based on the aerodynamic optimization agent model constructed by deep learning neural network, the simulated annealing algorithm is used to optimize the agent model, and the optimal comprehensive optimization index and the optimal design variable corresponding to the index are obtained within the range of the design variables.

[0015] Preferably, in step 2, the Latin hypercube sampling method is used to sample all design variables in the design space to obtain the design variable samples of the geometric shape: the design variables are Among them, V is the design space, the design space dimension is 2, and it satisfies R is the set of real numbers;

[0016] Determine the sample sizes N1 and N2 of the design variables in the high and low confidence data sets respectively; and divide the subinterval width of the i-th design variable:

[0017]

[0018] is the maximum value of the i-th design variable; is the minimum value of the i-th design variable;

[0019] Construct the initial sample matrix X:

[0020]

[0021] In the formula i=1,...,N t ;j=1,2;t=1,2;r ij is a random number in the range [0,1);

[0022] Generate a permutation matrix:

[0023]

[0024] For each column t=1,2;j=1,2,which includes 1 to N t The unique integers are randomly arranged and satisfy p i1 ≠p i2 ,i=1,...,N t ; t=1,2; achieves the uniqueness of sample points in each parameter dimension and the uniform distribution of sample points in multi-dimensional parameters;

[0025] Perform element-level crossover operation on the initial sample matrix X according to the permutation matrix P to obtain the sorted sample matrix:

[0026]

[0027] Finally, we get the following sample of design variables for the geometric shape:

[0028]

[0029] When t=1, S1 represents the high-fidelity design variable sample; when t=2, S2 represents the low-fidelity design variable sample.

[0030] Preferably, in step 3, the baseline aerodynamic layout of the hypersonic winged reentry vehicle is a twin vertical tail (TVT) winged reentry vehicle; wherein the fuselage cross-section is D-shaped, and two sections of triangular wings with sweep angles of 10° and 45° are on both sides of the fuselage, a pair of elevator surfaces on both sides control the pitch channel, and the twin vertical tail design controls the lateral flight channel.

[0031] Preferably, in step 4, based on the geometric shape samples of the winged reentry vehicle, computational fluid dynamics (CFD) methods and engineering estimation methods are used on the geometric shape samples at different flight state points to obtain two data sets, one with high confidence and the other with low confidence. Specifically, the flight state points are defined according to actual conditions, B flight state points are required for aerodynamic shape optimization, and aerodynamic analysis is performed at all flight state points.

[0032] Get the aerodynamic data of each flight state point, namely C i =[C Li C Di C Mi ],i=1,...,B,C Li is the lift coefficient of state point i; C Di is the resistance coefficient of state point i; C Mi is the pitching moment coefficient at state point i, select the key aerodynamic data, and assume the number is K;

[0033] Based on the design variable sample, aerodynamic simulation is performed at each flight state point i, i = 1, ..., B, using the CFD fluid calculation method to obtain a high-confidence data set:

[0034]

[0035] Where Y H Represents high-fidelity aerodynamic data; represents the jth key aerodynamic coefficient calculated by CFD simulation for the i-th high-fidelity design variable sample;

[0036] Based on the design variable samples, a quick estimation is performed at each flight state point i using the engineering estimation method, where i = 1, ..., B, to obtain a low-confidence data set:

[0037]

[0038] Where Y L Represents low-fidelity aerodynamic data; represents the jth key aerodynamic coefficient calculated using the engineering estimation method for the i-th low-fidelity design variable sample.

[0039] Preferably, in step 5, based on a deep learning neural network, high-fidelity and low-fidelity data sets are fused to construct a multi-fidelity data fusion proxy model for high-fidelity aerodynamic parameter prediction of design variables, specifically comprising the following steps:

[0040] Step 51: Based on the low-fidelity data set, a deep learning neural network is used to construct a low-fidelity proxy model for predicting low-fidelity aerodynamic parameters;

[0041] Step 52: Input the high-fidelity dataset into the low-fidelity proxy model to obtain a low-fidelity prediction value. The low-fidelity prediction value and the high-fidelity dataset are used to train a deep learning neural network to construct a prediction value correction proxy model.

[0042] Step 53: Based on the low-fidelity proxy model and the predicted value modified proxy model, the low-fidelity data set design variables are used as initial input variables, and the two models are connected in series to form a multi-fidelity data fusion proxy model;

[0043] Step 54: Based on the Latin hypercube sampling method and the CFD simulation method, a validation data set is obtained, and the goodness of fit is used as an indicator to test the iterative optimization and evaluate the accuracy of the surrogate model.

[0044] Preferably, in step 51, the deep learning neural network structure is an input layer, three hidden layers and an output layer; the number of neuron nodes in the input layer is 2; the number of neuron nodes in each hidden layer is 4; the number of neuron nodes in the output layer is K;

[0045] Based on design variables and aerodynamic parameter variables C L 、C D 、C M , let S2 be the input value, Y L is the true label, forward propagation step:

[0046] Excluding the input layer, the neural network is a 4-layer neural network, where the sum of the inputs to the i-th neuron in the k-th layer is:

[0047]

[0048] Where w ij is the connection weight between the jth neuron in the k-1th layer and the i-th neuron in the kth layer, is the output of the jth neuron in the k-1th layer, is the threshold of the i-th neuron in the k-th layer, i.e., the bias term;

[0049] The output of the i-th neuron in the k-th layer is:

[0050]

[0051] f is the mapping relationship of the activation function. The activation function is one of the hyperbolic tangent function and the rectified linear unit (ReLU) function, or it is assumed that the activation function is given;

[0052] The resulting low-fidelity neural network proxy model can be summarized as follows:

[0053]

[0054] In the formula is the value predicted by the neural network, where represents the predicted value of the kth sample of the low-fidelity neural network proxy model; represents the predicted value of the jth key aerodynamic parameter in sample k;

[0055] Backward propagation step:

[0056] In order to minimize the error between the true value and the neural network prediction value, the objective function is set as the variance function:

[0057]

[0058] For this network, w ij 、 For the network parameters that need to be determined, the gradient descent method is used to optimize the parameters based on the objective function J;

[0059] Let the weight matrix connecting the k-1th layer and the kth layer be W (k) , the bias vector of the kth layer is B (k) , the input vector of the kth layer is U (k) , the output vector of the kth layer is V (k) ;

[0060]

[0061] Where V (0) =S2, is the output layer activation function V (k) =f(U (k) ), the activation function f is one of the hyperbolic tangent function, the linear rectifier (Rectified Linear Unit, ReLU) function, or the activation function is assumed to be given; where U (k) =V (k-1) W (k) +B (k) ;

[0062] Use Adam optimizer to optimize hyperparameters and update the weight W of each layer (k) and bias B (k) :

[0063]

[0064]

[0065] initialization and is 0.9; and is 0.999; and is 0; ε is any minimal matrix; μ is the learning rate hyperparameter; through continuous iteration step 51 until the following termination condition is met: the number of neural network training times M ≥ M max , where Mmax is the maximum number of training times.

[0066] Preferably, in step 52, the design variable sample S1 in the high-fidelity data set is used as an independent variable to input the low-fidelity proxy model Obtain low-fidelity predictions of high-fidelity design variables

[0067] The deep learning neural network structure consists of an input layer, three hidden layers, and an output layer. The number of neuron nodes in the input layer is K+2; the number of neuron nodes in each hidden layer is 4; and the number of neuron nodes in the output layer is K.

[0068] Then S1, is the input value, Y H is the true label;

[0069] The neural network parameter optimization method is the gradient descent method, and the hyperparameter optimization method is the Adam optimizer;

[0070] The obtained predicted value correction proxy model can be summarized as follows:

[0071]

[0072] The surrogate model can fit the low-fidelity surrogate model prediction value and the high-fidelity true value Y H The deviation relationship between them.

[0073] Preferably, in step 53, the design variable sample S2 in the low-fidelity data set is input as an independent variable into the low-fidelity proxy model Get low-fidelity predicted response values ​​for low-fidelity design variables The predicted response value output by the low-fidelity surrogate model As the input value of the predicted value correction proxy model, the predicted value correction proxy model finally outputs a high-fidelity predicted response value;

[0074] The comprehensive multi-fidelity data fusion agent model can be summarized as follows:

[0075]

[0076] Predict response values ​​for high-fidelity aerodynamic data of design variables.

[0077] Preferably, in step 54, a verification data set design variable sample S3 is obtained based on the Latin hypercube sampling method, the number of samples is N3, and a CFD simulation method is used to perform fluid calculations at various flight state points to obtain a verification data set:

[0078] M V={S3,Y V},Y V =f(S3)

[0079] Where Y V Represents high-fidelity aerodynamic data of the validation dataset samples;

[0080] Input the design variable sample S3 into the multi-fidelity data fusion agent model to obtain a high-fidelity prediction value:

[0081]

[0082] Construct a goodness-of-fit test based on the validation dataset:

[0083]

[0084] Where Y V,i represents the aerodynamic coefficient vector of the i-th design variable sample in the validation data set; represents the predicted value of the multi-fidelity data fusion agent model for the i-th sample; is the mean vector of predicted values; is the goodness of fit judgment value;

[0085] If the surrogate model does not meet the goodness-of-fit criteria, then the high-fidelity dataset for the CFD simulation is expanded and the process returns to step 4. If the surrogate model meets the goodness-of-fit criteria, then the process proceeds to step 6.

[0086] Preferably, in step 6, based on a linear weighted method, the aerodynamic data predicted by the multi-fidelity data fusion proxy model at multiple flight state points are integrated to obtain comprehensive aerodynamic indicators for the optimization of the two-section wing shape; and an aerodynamic optimization proxy model is constructed based on the comprehensive aerodynamic indicators. The proxy model generation method is a radial basis function neural network, specifically including the following steps:

[0087] Step 61: Generate the objective function and the constraint range of the design variables at each flight state point. Based on the optimization objectives of all flight state points, generate a comprehensive aerodynamic index through a linear weighting method;

[0088] Step 62: construct an aerodynamic optimization proxy model based on the comprehensive aerodynamic index. The proxy model is generated using a radial basis function neural network to construct a mapping relationship between the design variables and the comprehensive aerodynamic index.

[0089] Step 63: Based on the Latin hypercube sampling method and the CFD simulation method, an interpolated data set and an extrapolated data set are obtained, and accuracy verification and generalization testing are performed respectively to evaluate the accuracy and generalization ability of the aerodynamic optimization proxy model.

[0090] Preferably, in step 61, the optimization target is to integrate key aerodynamic parameters of multiple flight state points:

[0091]

[0092] F i The objective function established for the aerodynamic data of the i-th flight state point; f i is the mapping relationship between the aerodynamic data of the i-th flight state point and the objective function;

[0093] The objective functions at different state points are normalized and weighted to generate comprehensive aerodynamic indicators for the two-section wing shape optimization:

[0094]

[0095] Among them (F i )0 represents the normalization process of the i-th objective function, and the normalization method is one of the maximum and minimum normalization, z-score normalization, L2 norm normalization, or it is assumed that the normalization method is given; k i represents the weighted coefficient of the i-th objective function;

[0096] High-fidelity aerodynamic parameter predictions based on a multi-fidelity data fusion surrogate model Generate comprehensive aerodynamic indicators:

[0097]

[0098] F S is the comprehensive aerodynamic index function of each flight state point; f S It is the mapping relationship between high-fidelity aerodynamic parameter prediction values ​​and comprehensive aerodynamic indicators.

[0099] Preferably, in step 62, the input layer, hidden layer, and output layer of the radial basis function neural network are defined according to actual conditions. In this example, the deep learning neural network structure is: input layer, hidden layer, and output layer. The number of neuron nodes in the input layer is 2; the number of neuron nodes in each hidden layer is M; the number of neuron nodes in the output layer is 1;

[0100] Take S2 ​​as input value, F S is the true label;

[0101] Initialize the training data points and the expected output vector:

[0102] i=1,...,N2

[0103]

[0104] Where X i represents the i-th design variable sample; d j represents the expected output value of the jth sample;

[0105] The radial basis function neural network agent model is:

[0106]

[0107] In the formula is the interpolation matrix, where:

[0108] i=1,...,N2;p=1,...,N2

[0109] Radial Basis Function is one of the Gauss function, inverse S-function, inverse multiquadratic function, or the radial basis function is assumed to be given;

[0110] For each sample data X j ,get j=1,2,...,N2

[0111] Self-organizing learning selects the radial basis function center:

[0112] Select M samples from the training data X and initialize the cluster center t i , i=1,...,M; continue to assign M samples in X to cluster center t according to the nearest neighbor rule i , forming a sample cluster set θ i , and the following relations are satisfied:

[0113]

[0114] Among them L i represents the minimum Euclidean distance;

[0115] Calculate the set θ i The average value of the samples in is used as the new cluster center:

[0116]

[0117] Among them, P i is θ i The number of input samples;

[0118] According to regularization theory:

[0119]

[0120] Where D is the linear differential operator, which represents the F (X) prior knowledge; λ is the regularization parameter, and λ∈R + , represents the relative importance of the regularization term; represents the standard error term; represents the regularization term;

[0121] The weight vector of the regularization problem is solved:

[0122] W=G + d

[0123] In the formula is the Green matrix; G + represents the pseudo-inverse matrix of G; where:

[0124] g ip =G(X i -X p ),i=1,...,N2;p=1,...,M

[0125] Defining Green's function with Gaussian function:

[0126]

[0127] Where σ j is the model hyperparameter; here d m is the maximum distance between cluster centers;

[0128] The obtained aerodynamic optimization agent model can be summarized as follows:

[0129]

[0130] Preferably, in step 63, the interpolation test sample S obtained based on the Latin hypercube sampling method is I , the number of samples is N4; and the extrapolation test sample S O , the number of samples is N5; CFD simulation method is used to perform fluid calculation at each flight state point to obtain interpolated data set and extrapolated data set:

[0131]

[0132] Where Y I represents the high-fidelity aerodynamic data of the interpolated dataset samples; Y O represents high-fidelity aerodynamic data of the extrapolated dataset samples;

[0133] Constructing comprehensive aerodynamic indicators of real aerodynamic data of interpolated and extrapolated datasets:

[0134] F S (I) =f S (Y I )

[0135] F S (O) =f S (Y O )

[0136] The design variable sample S I and S O Input the aerodynamic optimization agent model to obtain the predicted value of comprehensive aerodynamic indicators:

[0137]

[0138]

[0139] In the formula represents the predicted value of comprehensive aerodynamic index of interpolated samples; represents the predicted value of comprehensive aerodynamic index of extrapolated samples;

[0140] Construct a goodness-of-fit based on the interpolated and extrapolated datasets:

[0141]

[0142] Among them F S,i (I) and F S,i (O) are the true values ​​of the i-th comprehensive aerodynamic index of the interpolated data set and the extrapolated data set, respectively; and are the predicted values ​​of the i-th comprehensive aerodynamic index of the interpolated data set and the extrapolated data set, respectively; is the mean of the interpolated sample prediction values; is the mean of the extrapolated sample prediction values; and is the goodness of fit judgment value;

[0143] If the surrogate model does not meet the goodness-of-fit criteria, expand the design variable sample and return to step 2; if it meets the criteria, proceed to step 7.

[0144] Preferably, in step 7, the aerodynamic optimization proxy model constructed based on the deep learning neural network is optimized using a simulated annealing algorithm to find the optimal value within the acceptable range of the design variables to obtain the optimal comprehensive optimization index and the optimal design variables corresponding to the index. Specifically, the simulated annealing method parameters are initialized as follows:

[0145] T0 represents the initial temperature for annealing; x0 is the randomly generated initial solution; E(x0) is the internal energy corresponding to x0, that is, the objective function value;

[0146] For the current solution x k Apply random perturbations to generate a new solution x in its domain k+1 :

[0147] Calculate the difference in internal energy between the new solution and the current solution:

[0148] ΔE=E(xk+1 )-E(x k )

[0149] Based on the Metropolis criterion, the acceptance probability is:

[0150]

[0151] If we accept the new solution, then x′ k =x k+1 ; Otherwise, x′ k =x k ;

[0152] Repeat the perturbation process and acceptance process L times, where L is the length of the Markov chain;

[0153] Update the simulated annealing temperature: T′ = αT; where α is the temperature drop rate and α∈[0,1];

[0154] Repeat step 7 for iterative optimization until the following termination conditions are met:

[0155] ΔT=TT f <0

[0156] Where T f is the termination temperature.

[0157] The beneficial effects of the present invention are as follows: the present invention uses multi-fidelity data fusion based on deep learning neural networks to fit the linear and nonlinear relationships between high-fidelity and low-fidelity aerodynamic data, thereby improving the accuracy and reliability of aerodynamic parameters at various flight state points during the design of the aircraft's two-section wing shape; on this basis, the proxy model constructed by the radial basis function neural network algorithm is combined with the simulated annealing optimization method, which has better applicability for complex nonlinear fitting problems in the field of aerodynamic shape design, while improving the globality and robustness of the optimization results of the geometric shape design variables, providing a new type of efficient and accurate design tool for hypersonic winged reentry vehicles. BRIEF DESCRIPTION OF THE DRAWINGS

[0158] Figure 1 Schematic diagram of the method of the present invention.

[0159] Figure 2 This is a flow chart of the aerodynamic data fusion method of the present invention.

[0160] Figure 3 This is a flowchart of the deep learning neural network of the present invention.

[0161] Figure 4 This is a flow chart of the radial basis function neural network of the present invention.

[0162] Figure 5This is a structural diagram of the deep neural network of the present invention.

[0163] Figure 6 This is a structural diagram of the radial basis function neural network of the present invention.

[0164] Figure 7 This is a flow chart of the simulated annealing method of the present invention. DETAILED DESCRIPTION

[0165] like Figure 1 As shown, a multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle comprises the following steps:

[0166] Step 1: Initialize the geometric design variables and constraint range of the second-segment wing of the winged reentry vehicle;

[0167] The design variables and constraint ranges are defined according to the actual situation. For example, the design variables can be set as geometric parameters such as the two wing sweep angles of the second wing of the winged reentry vehicle; and the value ranges of the two wing sweep angles of the second wing are determined to be and

[0168] Step 2: Use the Latin hypercube sampling method to sample all design variables in the design space to obtain geometric design variable samples;

[0169] The design variables are Among them, V is the design space, the design space dimension is 2, and it satisfies R is the set of real numbers.

[0170] Determine the sample sizes N1 and N2 of the design variables in the high and low confidence data sets respectively; and divide the subinterval width of the i-th design variable:

[0171]

[0172] is the maximum value of the i-th design variable; is the minimum value of the i-th design variable;

[0173] Construct the initial sample matrix X:

[0174]

[0175] In the formula i=1,...,N t ;j=1,2;t=1,2;r ij is a random number in the range [0,1).

[0176] Generate a permutation matrix:

[0177]

[0178] For each column t=1,2;j=1,2,which includes 1 to N t The unique integers are randomly arranged and satisfy p i1 ≠p i2 ,i=1,...,N t ; t = 1, 2. The uniqueness of the sample points in each parameter dimension and the uniform distribution of the sample points in the multi-dimensional parameters are achieved.

[0179] Perform element-level crossover operation on the initial sample matrix X according to the permutation matrix P to obtain the sorted sample matrix:

[0180]

[0181] Finally, we get the following sample of design variables for the geometric shape:

[0182]

[0183] When t=1, S1 represents the high-fidelity design variable sample; when t=2, S2 represents the low-fidelity design variable sample.

[0184] Step 3: Design a baseline aerodynamic layout for a winged reentry vehicle, parametrically describe the vehicle geometry based on the class shape function transformation method, and construct a parametric geometric shape of the second-segment wing of the winged reentry vehicle;

[0185] The baseline aerodynamic layout for a winged reentry vehicle is a Twin Vertical Tail (TVT) winged reentry vehicle. The fuselage has a D-shaped cross-section, flanked by two triangular wings with sweep angles of 10° and 45°, respectively. A pair of elevator surfaces control pitch, while a twin vertical tail design controls lateral flight.

[0186] Step 4: Based on the aforementioned winged reentry vehicle geometry samples, computational fluid dynamics (CFD) and engineering estimation methods are used on the geometry samples at different flight states to obtain high-confidence and low-confidence datasets.

[0187] The flight state points are defined according to the actual situation. For example, there are B flight state points required for aerodynamic shape optimization, and aerodynamic analysis is performed at all flight state points.

[0188] Get the aerodynamic data of each flight state point, namely C i =[C Li C Di CMi ],i=1,...,B. C Li is the lift coefficient of state point i; C Di is the resistance coefficient of state point i; C Mi is the pitching moment coefficient at state point i. Select the key aerodynamic data and assume that the number is K.

[0189] Based on the design variable sample, aerodynamic simulation is performed at each flight state point i, i = 1, ..., B, using the CFD fluid calculation method to obtain a high-confidence data set:

[0190]

[0191] Where Y H Represents high-fidelity aerodynamic data; represents the jth key aerodynamic coefficient calculated by CFD simulation for the i-th high-fidelity design variable sample.

[0192] Based on the design variable samples, a quick estimation is performed at each flight state point i using the engineering estimation method, where i = 1, ..., B, to obtain a low-confidence data set:

[0193]

[0194] Where Y L Represents low-fidelity aerodynamic data; represents the jth key aerodynamic coefficient calculated using the engineering estimation method for the i-th low-fidelity design variable sample.

[0195] Step 5: Based on the deep learning neural network, the high-fidelity and low-fidelity data sets are fused to build a multi-fidelity data fusion agent model for high-fidelity aerodynamic parameter prediction of design variables, such as Figure 2 、 3 and 5;

[0196] Step 51: Based on the low-fidelity data set, a deep learning neural network is used to construct a low-fidelity proxy model for predicting low-fidelity aerodynamic parameters;

[0197] The input, hidden, and output layers of a deep learning neural network are defined based on real-world scenarios. In this example, the deep learning neural network structure consists of an input layer, three hidden layers, and an output layer. The input layer has two neurons; each hidden layer has four neurons; and the output layer has K neurons.

[0198] Based on design variables and aerodynamic parameter variables C L 、C D 、C M . Let S2 be the input value, YL is the true label. The following are the steps of forward propagation and back propagation of deep learning neural network.

[0199] Forward propagation step:

[0200] Excluding the input layer, the neural network is a 4-layer neural network, where the sum of the inputs to the i-th neuron in the k-th layer is:

[0201]

[0202] Where w ij is the connection weight between the jth neuron in the k-1th layer and the i-th neuron in the kth layer, is the output of the jth neuron in the k-1th layer, is the threshold of the i-th neuron in the k-th layer, that is, the bias term.

[0203] The output of the i-th neuron in the k-th layer is:

[0204] k=1,2,3,4

[0205] f is the mapping relationship of the activation function. The activation function is one of the hyperbolic tangent function and the rectified linear unit (ReLU) function, or it is assumed that the activation function is given.

[0206] The resulting low-fidelity neural network proxy model can be summarized as follows:

[0207]

[0208] In the formula is the value predicted by the neural network. represents the predicted value of the kth sample of the low-fidelity neural network proxy model; represents the predicted value of the jth key aerodynamic parameter in sample k.

[0209] Backward propagation step:

[0210] In order to make the error between the true value and the neural network prediction value as small as possible, the objective function is set as the variance function:

[0211]

[0212] For this network, w ij 、 are the network parameters that need to be determined. Based on the objective function J, the gradient descent method is used to optimize the parameters.

[0213] Let the weight matrix connecting the k-1th layer and the kth layer be W (k), the bias vector of the kth layer is B (k) , the input vector of the kth layer is U (k) , the output vector of the kth layer is V (k) .

[0214]

[0215] Where V (0) =S2, is the output layer activation function V (k) =f(U (k) ), the activation function f is one of the hyperbolic tangent function, the linear rectifier (Rectified Linear Unit, ReLU) function, or the activation function is assumed to be given; where U (k) =V (k-1) W (k) +B (k) .

[0216] Use Adam optimizer to optimize hyperparameters and update the weight W of each layer (k) and bias B (k) :

[0217]

[0218]

[0219] initialization and is 0.9; and is 0.999; and is 0; ε is an arbitrary minimal matrix; μ is the learning rate hyperparameter.

[0220] Step 51 is iterated continuously until the following termination condition is met:

[0221] The number of neural network training times M≥M max , where M max is the maximum number of training times.

[0222] Step 52: Input the high-fidelity dataset into the low-fidelity proxy model to obtain a low-fidelity prediction value. The low-fidelity prediction value and the high-fidelity dataset are used to train a deep learning neural network to construct a prediction value correction proxy model.

[0223] Based on the design variable sample S1 in the high-fidelity data set, it is input as an independent variable into the low-fidelity surrogate model Obtain low-fidelity predictions of high-fidelity design variables

[0224] The input, hidden, and output layers of a deep learning neural network are defined based on real-world scenarios. In this example, the deep learning neural network structure consists of an input layer, three hidden layers, and an output layer. The input layer has K+2 neuron nodes; each hidden layer has 4 neuron nodes; and the output layer has K neuron nodes.

[0225] Then S1, is the input value, Y H is the true label.

[0226] The neural network structure is similar to step 51, the neural network parameter optimization method is the gradient descent method, and the hyperparameter optimization method is the Adam optimizer.

[0227] The obtained predicted value correction proxy model can be summarized as follows:

[0228]

[0229] The surrogate model can fit the low-fidelity surrogate model prediction value and the high-fidelity true value Y H The deviation relationship between them.

[0230] Step 53: Based on the low-fidelity proxy model and the predicted value modified proxy model, the low-fidelity data set design variables are used as initial input variables, and the two models are connected in series to form a multi-fidelity data fusion proxy model;

[0231] The design variable sample S2 in the low-fidelity data set is input as an independent variable into the low-fidelity surrogate model Get low-fidelity predicted response values ​​for low-fidelity design variables The predicted response value output by the low-fidelity surrogate model It serves as the input value of the predicted value correction proxy model, and finally the predicted value correction proxy model outputs a high-fidelity predicted response value.

[0232] The comprehensive multi-fidelity data fusion agent model can be summarized as follows:

[0233]

[0234] Predict response values ​​for high-fidelity aerodynamic data of design variables.

[0235] Step 54: Based on the Latin hypercube sampling method and CFD simulation method, a validation data set is obtained. The goodness of fit is used as an indicator to test the iterative optimization and evaluate the accuracy of the surrogate model.

[0236] The validation data set obtained based on the Latin hypercube sampling method is designed with variable sample S3 and sample number N3. The CFD simulation method is used to perform fluid calculations at various flight state points to obtain the validation data set:

[0237] M V ={S3,Y V},Y V =f(S3)

[0238] Where Y V Represents high-fidelity aerodynamic data for the validation dataset samples.

[0239] Input the design variable sample S3 into the multi-fidelity data fusion agent model to obtain a high-fidelity prediction value:

[0240]

[0241] Construct a goodness-of-fit test based on the validation dataset:

[0242]

[0243] Where Y V,i represents the aerodynamic coefficient vector of the i-th design variable sample in the validation data set; represents the predicted value of the multi-fidelity data fusion agent model for the i-th sample; is the mean vector of predicted values; is the goodness of fit judgment value.

[0244] If the surrogate model does not meet the goodness-of-fit criteria, then the high-fidelity dataset for the CFD simulation is expanded and the process returns to step 4. If the surrogate model meets the goodness-of-fit criteria, then the process proceeds to step 6.

[0245] Step 6: Based on the linear weighted method, the aerodynamic data predicted by the multi-fidelity data fusion agent model at multiple flight state points are integrated to obtain the comprehensive aerodynamic index of the two-section wing shape optimization. The aerodynamic optimization agent model is constructed based on the comprehensive aerodynamic index. The agent model generation method is the radial basis function neural network, such as Figure 4 and Figure 6 shown

[0246] Step 61: Generate the objective function and the constraint range of the design variables at each flight state point. Based on the optimization objectives of all flight state points, generate a comprehensive aerodynamic index through a linear weighting method;

[0247] The optimization goal is to integrate the key aerodynamic parameters of multiple flight state points:

[0248]

[0249] F iThe objective function established for the aerodynamic data of the i-th flight state point; f i is the mapping relationship between the aerodynamic data of the i-th flight state point and the objective function.

[0250] The objective functions at different state points are normalized and weighted to generate comprehensive aerodynamic indicators for the two-section wing shape optimization:

[0251]

[0252] Among them (F i )0 represents the normalization process of the i-th objective function, and the normalization method is one of the maximum and minimum normalization, z-score normalization, L2 norm normalization, or it is assumed that the normalization method is given; k i Represents the weighting coefficient of the i-th objective function.

[0253] High-fidelity aerodynamic parameter predictions based on a multi-fidelity data fusion surrogate model Generate comprehensive aerodynamic indicators:

[0254]

[0255] F S is the comprehensive aerodynamic index function of each flight state point; f S It is the mapping relationship between high-fidelity aerodynamic parameter prediction values ​​and comprehensive aerodynamic indicators.

[0256] Step 62: construct an aerodynamic optimization proxy model based on the comprehensive aerodynamic index. The proxy model is generated using a radial basis function neural network to construct a mapping relationship between the design variables and the comprehensive aerodynamic index.

[0257] The input, hidden, and output layers of a radial basis function neural network are defined based on real-world scenarios. In this example, the deep learning neural network structure consists of: input, hidden, and output layers. The input layer has two neuron nodes; each hidden layer has M neuron nodes; and the output layer has one neuron node.

[0258] Take S2 ​​as input value, F S is the true label.

[0259] Initialize the training data points and the expected output vector:

[0260]

[0261]

[0262] Where X i represents the i-th design variable sample; d jrepresents the expected output value of the jth sample.

[0263] The radial basis function neural network agent model is:

[0264]

[0265] In the formula is the interpolation matrix, where:

[0266]

[0267] Radial Basis Function It is one of the Gauss function, inverse S-function, inverse multi-quadratic function, or the radial basis function is assumed to be given.

[0268] For each sample data X j ,get

[0269] Self-organizing learning selects the radial basis function center:

[0270] Select M samples from the training data X and initialize the cluster center t i , i=1,...,M. Continue to assign M samples in X to cluster center t according to the nearest neighbor rule i , forming a sample cluster set θ i , and the following relations are satisfied:

[0271]

[0272] Among them L i Represents the minimum Euclidean distance.

[0273] Calculate the set θ i The average value of the samples in is used as the new cluster center:

[0274]

[0275] Among them, P i is θ i The number of input samples.

[0276] According to regularization theory:

[0277]

[0278] Where D is the linear differential operator, which represents the F (X) prior knowledge; λ is the regularization parameter, and λ∈R + , represents the relative importance of the regularization term; represents the standard error term; represents the regularization term.

[0279] The weight vector of the regularization problem is solved:

[0280] W=G + d

[0281] In the formula is the Green matrix; G + represents the pseudo-inverse matrix of G; where:

[0282] g ip =G(X i -X p ),i=1,...,N2;p=1,...,M

[0283] Defining Green's function with Gaussian function:

[0284]

[0285] Where σ j is the model hyperparameter. d m is the maximum distance between cluster centers.

[0286] The obtained aerodynamic optimization agent model can be summarized as follows:

[0287]

[0288] Step 63: Based on the Latin hypercube sampling method and the CFD simulation method, an interpolated data set and an extrapolated data set are obtained, and accuracy verification and generalization test are performed respectively to evaluate the accuracy and generalization ability of the aerodynamic optimization proxy model;

[0289] Interpolation test sample S obtained based on Latin hypercube sampling method I , the number of samples is N4; and the extrapolation test sample S O , the number of samples is N5; CFD simulation method is used to perform fluid calculation at each flight state point to obtain interpolated data set and extrapolated data set:

[0290]

[0291] Where Y I represents the high-fidelity aerodynamic data of the interpolated dataset samples; Y O Represents high-fidelity aerodynamic data of the extrapolated dataset samples.

[0292] Constructing comprehensive aerodynamic indicators of real aerodynamic data of interpolated and extrapolated datasets:

[0293] F S (I) =f S (Y I)

[0294] F S (O) =f S (Y O )

[0295] The design variable sample S I and S O Input the aerodynamic optimization agent model to obtain the predicted value of comprehensive aerodynamic indicators:

[0296]

[0297] In the formula represents the predicted value of comprehensive aerodynamic index of interpolated samples; Represents the predicted value of the comprehensive aerodynamic index of the extrapolated sample.

[0298] Construct a goodness-of-fit based on the interpolated and extrapolated datasets:

[0299]

[0300] Among them F S,i (I) and F S,i (O) are the true values ​​of the i-th comprehensive aerodynamic index of the interpolated data set and the extrapolated data set, respectively; and are the predicted values ​​of the i-th comprehensive aerodynamic index of the interpolated data set and the extrapolated data set, respectively; is the mean of the interpolated sample prediction values; is the mean of the extrapolated sample prediction values; and is the goodness of fit judgment value.

[0301] If the surrogate model does not meet the goodness-of-fit criteria, expand the design variable sample and return to step 2; if it meets the criteria, proceed to step 7.

[0302] Step 7: Based on the aerodynamic optimization agent model constructed by deep learning neural network, the simulated annealing algorithm is used to optimize the agent model, and the optimal comprehensive optimization index and the optimal design variable corresponding to the index are obtained within the range of the design variables. Figure 7 As shown;

[0303] Initialize simulated annealing parameters:

[0304] T0 represents the initial temperature for starting annealing; x0 is the randomly generated initial solution; E(x0) is the internal energy corresponding to x0, that is, the objective function value.

[0305] For the current solution x kApply random perturbations to generate a new solution x in its domain k+1 :

[0306] Calculate the difference in internal energy between the new solution and the current solution:

[0307] ΔE=E(x k+1 )-E(x k )

[0308] Based on the Metropolis criterion, the acceptance probability is:

[0309]

[0310] If we accept the new solution, then x′ k =x k+1 ; Otherwise, x′ k =x k .

[0311] Repeat the perturbation process and acceptance process L times, where L is the length of the Markov chain.

[0312] Update the simulated annealing temperature: T′=αT; where α is the temperature drop rate and α∈[0,1].

[0313] Repeat step 7 for iterative optimization until the following termination conditions are met:

[0314] ΔT=TT f <0

[0315] Where T f is the termination temperature.

[0316] In summary, the final output is the aerodynamic shape design results of the two-section wing with coordinated optimization of aerodynamic parameters under various aerodynamic conditions.

Claims

1. A multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle, characterized by: include: Step 1: Initialize the geometric design variables and constraint range of the second-segment wing of the winged reentry vehicle; Step 2: Use the Latin hypercube sampling method to sample all design variables in the design space to obtain geometric design variable samples; Step 3: Design a baseline aerodynamic layout for a winged reentry vehicle, parametrically describe the vehicle geometry based on the class shape function transformation method, and construct a parametric geometric shape of the second-segment wing of the winged reentry vehicle; Step 4: Based on the geometric shape samples of the winged reentry vehicle, the computational fluid dynamics (CFD) method and engineering estimation method are used on the geometric shape samples at different flight state points to obtain two datasets: high-confidence and low-confidence. Step 5: Based on the deep learning neural network, the high-fidelity and low-fidelity data sets are fused to construct a multi-fidelity data fusion proxy model for high-fidelity aerodynamic parameter prediction of design variables; Step 6: Based on the linear weighted method, the aerodynamic data predicted by the multi-fidelity data fusion proxy model at multiple flight state points are integrated to obtain the comprehensive aerodynamic indicators for the two-section wing shape optimization; an aerodynamic optimization proxy model is constructed based on the comprehensive aerodynamic indicators, and the proxy model generation method is a radial basis function neural network; Step 7: Based on the aerodynamic optimization agent model constructed by deep learning neural network, the simulated annealing algorithm is used to optimize the agent model, and the optimal comprehensive optimization index and the optimal design variable corresponding to the index are obtained within the range of the design variables.

2. The multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle according to claim 1, characterized in that: In step 2, the Latin hypercube sampling method is used to sample all design variables in the design space to obtain the design variable samples of the geometric shape: the design variables are Among them, V is the design space, the design space dimension is 2, and it satisfies R is the set of real numbers; Determine the sample sizes N1 and N2 of the design variables in the high and low confidence data sets respectively; and divide the subinterval width of the i-th design variable: is the maximum value of the i-th design variable; is the minimum value of the i-th design variable; Construct the initial sample matrix X: In the formula r ij is a random number in the range [0,1); Generate a permutation matrix: For each column It contains 1 to N t The unique integers are randomly arranged and satisfy p i1 ≠p i2 ,i=1,...,N t ; t=1,2; achieves the uniqueness of sample points in each parameter dimension and the uniform distribution of sample points in multi-dimensional parameters; Perform element-level crossover operation on the initial sample matrix X according to the permutation matrix P to obtain the sorted sample matrix: Finally, we get the following sample of design variables for the geometric shape: When t=1, S1 represents the high-fidelity design variable sample; when t=2, S2 represents the low-fidelity design variable sample.

3. The multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle according to claim 1, characterized in that: In step 3, the baseline aerodynamic layout of the hypersonic winged reentry vehicle is a twin vertical tail (TVT) winged reentry vehicle; the fuselage cross-section is D-shaped, with two triangular wings on both sides of the fuselage with sweep angles of 10° and 45° respectively. A pair of elevator surfaces on both sides control the pitch channel, and the twin vertical tail design controls the lateral flight channel.

4. The multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle according to claim 1, characterized in that: In step 4, based on the aforementioned winged reentry vehicle geometry samples, computational fluid dynamics (CFD) and engineering estimation methods are applied to the geometry samples at different flight state points to obtain high-confidence and low-confidence data sets. Specifically, the flight state points are defined based on actual conditions. Aerodynamic shape optimization requires B flight state points, and aerodynamic analysis is performed at all flight state points. Get the aerodynamic data of each flight state point, namely C i =[C Li C Di C Mi ],i=1,...,B,C Li is the lift coefficient of state point i; C Di is the resistance coefficient of state point i; C Mi is the pitching moment coefficient at state point i, select the key aerodynamic data, and assume the number is K; Based on the design variable sample, aerodynamic simulation is performed at each flight state point i, i = 1, ..., B, using the CFD fluid calculation method to obtain a high-confidence data set: M H ={S1,Y H }; Where Y H Represents high-fidelity aerodynamic data; represents the jth key aerodynamic coefficient calculated by CFD simulation for the i-th high-fidelity design variable sample; Based on the design variable samples, a quick estimation is performed at each flight state point i using the engineering estimation method, where i = 1, ..., B, to obtain a low-confidence data set: M H ={S2,Y L }; Where Y L Represents low-fidelity aerodynamic data; represents the jth key aerodynamic coefficient calculated using the engineering estimation method for the i-th low-fidelity design variable sample.

5. The multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle according to claim 1, characterized in that: In step 5, based on a deep learning neural network, the high- and low-fidelity data sets are fused to construct a multi-fidelity data fusion proxy model for high-fidelity aerodynamic parameter prediction of design variables. The specific steps include the following: Step 51: Based on the low-fidelity data set, a deep learning neural network is used to construct a low-fidelity proxy model for predicting low-fidelity aerodynamic parameters; Step 52: Input the high-fidelity dataset into the low-fidelity proxy model to obtain a low-fidelity prediction value. The low-fidelity prediction value and the high-fidelity dataset are used to train a deep learning neural network to construct a prediction value correction proxy model. Step 53: Based on the low-fidelity proxy model and the predicted value modified proxy model, the low-fidelity data set design variables are used as initial input variables, and the two models are connected in series to form a multi-fidelity data fusion proxy model; Step 54: Based on the Latin hypercube sampling method and the CFD simulation method, a validation data set is obtained, and the goodness of fit is used as an indicator to test the iterative optimization and evaluate the accuracy of the surrogate model.

6. The multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle according to claim 1, characterized in that: In step 6, based on the linear weighting method, the aerodynamic data predicted by the multi-fidelity data fusion proxy model at multiple flight state points are integrated to obtain the comprehensive aerodynamic indicators for the two-section wing shape optimization. Based on the comprehensive aerodynamic indicators, an aerodynamic optimization proxy model is constructed. The proxy model generation method is a radial basis function neural network, which specifically includes the following steps: Step 61: Generate an objective function and a constraint range of the design variables at each flight state point, and generate a comprehensive aerodynamic index using a linear weighted method based on the optimization objectives of all flight state points; Step 62: construct an aerodynamic optimization proxy model based on the comprehensive aerodynamic index. The proxy model is generated using a radial basis function neural network to construct a mapping relationship between the design variables and the comprehensive aerodynamic index. Step 63: Based on the Latin hypercube sampling method and the CFD simulation method, an interpolated data set and an extrapolated data set are obtained, and accuracy verification and generalization testing are performed respectively to evaluate the accuracy and generalization ability of the aerodynamic optimization proxy model.

7. The multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle according to claim 6, characterized in that: In step 61, the optimization objective is to integrate the key aerodynamic parameters of multiple flight state points: F i The objective function established for the aerodynamic data of the i-th flight state point; f i is the mapping relationship between the aerodynamic data of the i-th flight state point and the objective function; The objective functions at different state points are normalized and weighted to generate comprehensive aerodynamic indicators for the two-section wing shape optimization: Among them (F i )0 represents the normalization process of the i-th objective function, and the normalization method is one of the maximum and minimum normalization, z-score normalization, L2 norm normalization, or it is assumed that the normalization method is given; k i represents the weighted coefficient of the i-th objective function; High-fidelity aerodynamic parameter predictions based on a multi-fidelity data fusion surrogate model Generate comprehensive aerodynamic indicators: F S is the comprehensive aerodynamic index function of each flight state point; f S It is the mapping relationship between high-fidelity aerodynamic parameter prediction values ​​and comprehensive aerodynamic indicators.

8. The multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle according to claim 6, characterized in that: In step 62, the input layer, hidden layer, and output layer of the radial basis function neural network are defined according to the actual situation. In this example, the deep learning neural network structure is: input layer, hidden layer, and output layer. The number of neuron nodes in the input layer is 2; the number of neuron nodes in each hidden layer is M; and the number of neuron nodes in the output layer is 1. Take S2 ​​as input value, F S is the true label; Initialize the training data points and the expected output vector: Where X i represents the i-th design variable sample; d j represents the expected output value of the jth sample; The radial basis function neural network agent model is: In the formula is the interpolation matrix, where: Radial Basis Function is one of the Gauss function, inverse S-function, inverse multiquadratic function, or the radial basis function is assumed to be given; For each sample data X j ,get Self-organizing learning selects the radial basis function center: Select M samples from the training data X and initialize the cluster center t i , i=1,...,M; continue to assign M samples in X to cluster center t according to the nearest neighbor rule i , forming a sample cluster set θ i , and the following relations are satisfied: Among them L i represents the minimum Euclidean distance; Calculate the set θ i The average value of the samples in is used as the new cluster center: Among them, P i is θ i The number of input samples; According to regularization theory: Where D is the linear differential operator, which represents the F (X) prior knowledge; λ is the regularization parameter, and λ∈R + , represents the relative importance of the regularization term; represents the standard error term; represents the regularization term; The weight vector of the regularization problem is solved: W=G + d In the formula is the Green matrix; G + represents the pseudo-inverse matrix of G; where: g ip =G(X i -X p ),i=1,...,N2;p=1,...,M Defining Green's function with Gaussian function: Where σ j is the model hyperparameter; here d m is the maximum distance between cluster centers; The obtained aerodynamic optimization agent model can be summarized as follows:

9. The multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle according to claim 6, characterized in that: In step 63, the interpolation test sample S obtained based on the Latin hypercube sampling method is I , the number of samples is N4; and the extrapolation test sample S O , the number of samples is N5; CFD simulation method is used to perform fluid calculation at each flight state point to obtain interpolated data set and extrapolated data set: Where Y I represents the high-fidelity aerodynamic data of the interpolated dataset samples; Y O represents high-fidelity aerodynamic data of the extrapolated dataset samples; Constructing comprehensive aerodynamic indicators of real aerodynamic data of interpolated and extrapolated datasets: F S (I) =f S (Y I ) F S (O) =f S (Y O ) The design variable sample S I and S O Input the aerodynamic optimization agent model to obtain the predicted value of comprehensive aerodynamic indicators: In the formula represents the predicted value of comprehensive aerodynamic index of interpolated samples; represents the predicted value of comprehensive aerodynamic index of extrapolated samples; Construct a goodness-of-fit based on the interpolated and extrapolated datasets: Among them F S,i (I) and F S,i (O) are the true values ​​of the i-th comprehensive aerodynamic index of the interpolated data set and the extrapolated data set, respectively; and are the predicted values ​​of the i-th comprehensive aerodynamic index of the interpolated data set and the extrapolated data set, respectively; is the mean of the interpolated sample prediction values; is the mean of the extrapolated sample prediction values; and is the goodness of fit judgment value; If the surrogate model does not meet the goodness-of-fit criteria, expand the design variable sample and return to step 2; if it meets the criteria, proceed to step 7.

10. The multi-objective optimization method for the aerodynamic shape of a second-segment wing of a hypersonic winged reentry vehicle according to claim 1, characterized in that: In step 7, the aerodynamic optimization agent model constructed based on the deep learning neural network is optimized using the simulated annealing algorithm to find the optimal value within the range of the design variables. The optimal comprehensive optimization index and the optimal design variables corresponding to the index are obtained as follows: Initialize the simulated annealing parameters: T0 represents the initial temperature for annealing; x0 is the randomly generated initial solution; E(x0) is the internal energy corresponding to x0, that is, the objective function value; For the current solution x k Apply random perturbations to generate a new solution x in its domain k+1 : Calculate the difference in internal energy between the new solution and the current solution: ΔE=E(x k+1 )-E(x k ) Based on the Metropolis criterion, the acceptance probability is: If we accept the new solution, then x′ k =x k+1 Otherwise, x′ k =x k ; Repeat the perturbation process and the acceptance process L times, where L is the length of the Markov chain; update the simulated annealing temperature: T′ = αT; where α is the temperature drop rate and α∈[0,1]; repeat step 7 for iterative optimization until the following termination condition is met: ΔT=T-T f <0 Where T f is the termination temperature.

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