Missile aerodynamic parameter rapid correction method based on residual learning neural network algorithm

Abstract

The invention discloses a missile aerodynamic parameter rapid correction method based on a residual learning neural network algorithm. A small number of pneumatic data points obtained through accurate calculation are fully utilized, a large number of pneumatic data sets obtained through learning rough calculation are fused, and therefore rapid and accurate correction of original pneumatic parameters is achieved. According to the method, a neural network algorithm based on residual learning is firstly provided, and a neural network is utilized to directly learn a residual term between a theoretical curve and high-fidelity simulation data, so that an original theoretical model is corrected based on residual prediction, and a fitting curve closer to high-precision data distribution is obtained. By combining the algorithm, efficient modeling under the condition of extremely small high-precision data volume is realized, an original low-precision theoretical model does not need to be modified, only a residual error part is modeled, limited high-precision data is smoothly fitted, and rapid and accurate correction of original aerodynamic parameters is realized.

Description

Technical Field

[0001] This invention relates to a method for rapid correction of missile aerodynamic parameters based on a residual learning neural network algorithm, specifically to the rapid correction of missile aerodynamic parameters. Background Technology

[0002] The aerodynamic performance of a missile is one of the key factors determining its flight characteristics and combat effectiveness. However, traditional methods for obtaining aerodynamic parameters all have certain limitations. Theoretical calculation methods are complex and limited by their complexity, and they also deviate from reality. Wind tunnel testing and flight testing methods face problems such as high cost and long testing cycles.

[0003] Currently, existing methods for fitting and correcting aerodynamic parameters mainly fall into two categories: traditional engineering fitting algorithms and emerging intelligent algorithms. Traditional engineering fitting algorithms, such as polynomial fitting, maximum likelihood fitting, and least squares fitting, primarily rely on the physical characteristics and statistical laws of aerodynamic forces, establishing mathematical relationships between aerodynamic forces and parameters such as flight state and aerodynamic shape through mathematical means. This method is suitable for local modeling with relatively small variations in state range. However, for aircraft with large variations in state parameters and complex aerodynamic shapes, the relationship between aerodynamic forces and various parameters is highly nonlinear, making it difficult for traditional mathematical modeling methods to accurately describe. While common intelligent algorithms such as neural networks possess powerful nonlinear fitting capabilities in aerodynamic modeling, they require a large amount of training data. Obtaining high-quality aerodynamic data is costly and time-consuming, and there is also a risk of overfitting, potentially leading to prediction errors under new operating conditions. The model's generalization ability is also limited by the training data, making it difficult to adapt to extreme operating conditions or special aerodynamic phenomena. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention proposes a rapid correction method for missile aerodynamic parameters based on a residual learning neural network algorithm. This method fully utilizes a small number of precisely calculated aerodynamic data points and fuses them with a large number of coarsely calculated aerodynamic data sets, thereby achieving rapid and accurate correction of the original aerodynamic parameters. The method includes the following steps:

[0005] Step 1: Provide the raw data, which includes two parts: a large set of data obtained from rough calculations and a small set of high-precision data. We select the aerodynamic parameters calculated using Datcom as the large set of data obtained from rough calculations, and the aerodynamic parameters calculated using Fluent as the small set of high-precision data.

[0006] Step Two: Establish a low-precision model, specifically using an MLP neural network structure. The training data consists of a large dataset obtained through rough calculation. The hidden layer has 20 neurons and two layers. The input layer has no activation function, the hidden layers use the sigmoid function, and the output layer uses the identity activation function. 80% of the training data is used for network training, and the remaining 20% ​​is used to verify the training results. The goal is for the final trained network to have a maximum relative error of no more than 1% on the test set. This trained neural network serves as a low-precision model, enabling the rapid output of low-precision drag coefficients under different input angles of attack and Mach numbers.

[0007] Step 3: Establish a residual learning neural network model, specifically using a multilayer perceptron (MLP) model, to establish the relationship between low-precision data and high-precision data, and use an autoregressive approach to express the correlation between different data, as shown in the following formula.

[0008] y h =f(x,y) l )

[0009] In the formula, x is the independent variable, and y h For high-precision data, y l Let f represent the functional relationship between low-precision and high-precision data. To obtain this functional relationship, this invention employs a neural network approximation method to obtain the linear relationship between multi-precision data. This method enables efficient modeling even with very limited high-precision data, without modifying the original low-precision theoretical model. It only models the residual part, requiring only a small number of samples to achieve a good fit. It can smoothly fit finite high-fidelity data, thus improving the robustness of the model.

[0010] Suppose a large number of low-precision data points are (x i ,y l (x i The low-precision fitting model is y. l (x), a small number of high-fidelity data points are (x) j ,y h (x j The corrected high-fidelity model is y. h The residual r(x) is defined as shown in the following equation.

[0011] r(x) = y h (x)-y l (x)

[0012] This invention trains an MLP (Multilayer Perceptron) model. To learn residuals The nonlinear mapping relationship between r(x) and the residual prediction error is minimized to obtain the optimal parameters, thereby modeling the residual and correcting the original model. The complete flowchart of the algorithm is shown below. Figure 1 As shown.

[0013] Due to the low dimensionality and small sample size of aerodynamic data, complex neural networks often struggle to achieve effective fitting. In the aerodynamic parameter correction problem, the model should have a compact structure and a moderate number of parameters. Based on this, this invention chooses to construct a residual learning MLP network, and the specific parameter settings are shown in the table below.

[0014] Table 1. Parameter settings for residual learning MLP networks

[0015]

[0016] The model uses the mean squared error loss function (MSEloss) as the training objective, and the objective function is shown in the following formula.

[0017]

[0018] After training, residual prediction is performed over the entire time axis, and the predicted residuals are superimposed on the original theoretical curves to obtain the output after residual correction, as shown in the following formula.

[0019]

[0020] Complete network structure such as Figure 2 As shown. Where x l to y l The mapping is a low-precision model, with low-precision data x as input. l To obtain low-precision predicted value y l MLP neural networks with residual learning are used to explore input x l The relationship between the residual r(x) and the output predicted residual. Prediction residuals in the unknown domain Compared with low-precision predicted value y l The corrected data y can be obtained by superimposing the data. h2 , will y h1 With y h2 Combined, we obtain the entire field x l The correction value y below hThe input to the residual learning neural network model is the low-precision model obtained in step two and a small amount of high-precision data from step one. The specific structure consists of two hidden layers, each with 64 neurons. The mean squared error loss function (MSEloss) is used as the training objective, the Adam optimizer is employed, the learning rate is set to 0.01, the ReLU activation function is used, and the training iterations are 1000. The trained residual learning neural network model outputs the predicted residual. Superimposing this predicted residual with the low-precision model over the entire domain yields the corrected drag coefficient curve.

[0021] Step 4: Verify the correction results. Select 20 additional high-precision data points as comparison and verification points. Compare the method proposed in this invention, the BP neural network algorithm in existing literature, the traditional quadratic function least squares fitting method in engineering, the uncorrected aerodynamic data, and the high-fidelity data of the test group, and calculate the relative error rate and mean square error loss.

[0022] The advantages and beneficial effects of this invention are as follows: This invention combines the above-mentioned algorithm to achieve efficient modeling under conditions of very small amounts of high-precision data. It does not require modification of the original low-precision theoretical model, but only models the residual part, smoothly fits the limited high-precision data, and achieves rapid and accurate correction of the original aerodynamic parameters. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the algorithm for correcting residual learning neural networks.

[0024] Figure 2 This is a schematic diagram of a residual learning-based neural network structure.

[0025] Figure 3 This is a schematic diagram of the shape of an example missile.

[0026] Figure 4a , Figure 4b , Figure 4c , Figure 4d This is a rough aerodynamic data point diagram for an example missile.

[0027] Figure 5a This is a mesh diagram of the projectile.

[0028] Figure 5b This is a surface mesh diagram of the flow field.

[0029] Figure 5c This is a three-dimensional view of the flow field grid.

[0030] Figure 5d This is a 3D detail diagram of the flow field mesh.

[0031] Figure 6a , Figure 6b , Figure 6c, Figure 6d , Figure 6e , Figure 6f , Figure 6g This is a convergence plot of aerodynamic parameters.

[0032] Figure 7a , Figure 7b , Figure 7c , Figure 7d , Figure 7e , Figure 7f , Figure 7g This is a pressure cloud map of the projectile surface.

[0033] Figure 8a , Figure 8b , Figure 8c , Figure 8d , Figure 8e , Figure 8f , Figure 8g This is a flow field pressure contour map.

[0034] Figure 9a , Figure 9b , Figure 9c , Figure 9d , Figure 9e , Figure 9f , Figure 9g This is a velocity contour map of the flow field.

[0035] Figure 10a , Figure 10b , Figure 10c , Figure 10d This is a schematic diagram illustrating the initial data error of an example missile.

[0036] Figure 11 This is a schematic diagram of the MLP network principle.

[0037] Figure 12 This is a schematic diagram illustrating the drag coefficient correction for an example missile.

[0038] Figure 13 This diagram illustrates the effect of different algorithms on the drag coefficient correction of an example missile. Detailed Implementation

[0039] The complete process of the residual learning neural network correction algorithm is as follows: Figure 1 As shown, firstly, based on a large set of data obtained through rough calculation, a low-precision model is obtained by fitting a neural network. Then, the low-precision model is compared with the high-precision data, and a residual learning neural network is used for training and fitting. After training, residual prediction is performed on the entire time axis, and the predicted residuals are superimposed with the low-precision model to obtain the corrected aerodynamic parameters.

[0040] To verify the specific implementation of the present invention, the Sparrow missile (AIM-7F) was selected as an example, and its external drawing is shown below. Figure 3As shown, the algorithm proposed in this invention is used below to correct only the drag coefficient CD of the example missile.

[0041] Step 1: Provide the raw data, which consists of two parts: a large set of data obtained from rough calculations and a small amount of high-precision data.

[0042] The example missile has a slender cylindrical body with a pointed, arched nose. Four all-moving, cruciform deltaic wings are located in the middle of the body, and four fixed triangular stabilizers are located at the tail. The all-moving wings and stabilizers are configured in a tandem XX pattern. The missile's reference area S, reference length l, aspect ratio λ, and control area S are given. f As shown in the following formula.

[0043]

[0044] In addition to the missile's basic aerodynamic parameters, it is also necessary to perform shape modeling on the missile. An example is given as follows: Figure 3 As shown.

[0045] The rough aerodynamic parameters of the missile were calculated using Missile Datcom software. This software employs a component assembly method, utilizing empirical formulas, experimental data, and mathematical formulas to calculate the missile's aerodynamic coefficients. It boasts fast calculation speed, low computer configuration requirements, and ease of use; calculations can be completed simply by inputting the missile's geometric parameters and flight conditions. The rough calculation of aerodynamic coefficients using Datcom software, converted to a velocity system, is shown below. Figure 4a , Figure 4b , Figure 4c , Figure 4d As shown.

[0046] The precise aerodynamic parameters of the missile were calculated using Ansys Fluent software, which employs the finite volume method, supports multiple physical models, and boasts powerful mesh processing capabilities and an efficient solver. The far-field boundary Mach number of the pressure was defined to correspond to the missile's flight Mach number, the incoming flow direction to the missile's flight attitude angle, the pressure was set to one standard atmosphere, and the temperature to 300K. The external fluid model used was the k-ω model within the turbulence model. The following figures illustrate the mesh generation, aerodynamic parameter convergence plot, pressure contour plot, and velocity contour plot during the Fluent calculation process. Figure 5a This is a mesh diagram of the projectile. Figure 5b This is a surface mesh diagram of the flow field. Figure 5c This is a 3D diagram of the flow field grid. Figure 5d This is a 3D detail diagram of the flow field mesh;

[0047] Figure 6a , Figure 6b , Figure 6c , Figure 6d , Figure 6e ,Figure 6f , Figure 6g This is a convergence plot of aerodynamic parameters; among which, Figure 6a The figure shows the convergence curves of drag coefficient, lift coefficient, side force coefficient, and three aerodynamic moments as a function of the number of wheels when α = ±30°. Figure 6b The figure shows the convergence curves of drag coefficient, lift coefficient, side force coefficient, and three aerodynamic moments as a function of the number of wheels when α = ±25°. Figure 6c The figure shows the convergence curves of the drag coefficient, lift coefficient, side force coefficient, and three aerodynamic moments as a function of the number of wheels when α = ±20°. Figure 6d The figure shows the convergence curves of drag coefficient, lift coefficient, side force coefficient, and three aerodynamic moments as a function of the number of wheels when α = ±15°. Figure 6e The figure shows the convergence curves of drag coefficient, lift coefficient, side force coefficient, and three aerodynamic moments as a function of the number of wheels when α = ±10°. Figure 6f The figure shows the convergence curves of the drag coefficient, lift coefficient, side force coefficient, and three aerodynamic moments as a function of the number of wheels when α = ±5°. Figure 6g The figure shows the convergence curves of the drag coefficient, lift coefficient, side force coefficient, and three aerodynamic moments as a function of the number of calculated wheels when α = 0°.

[0048] Figure 7a , Figure 7b , Figure 7c , Figure 7d , Figure 7e , Figure 7f , Figure 7g This is a pressure cloud map of the projectile surface; among which, Figure 7a The diagram shows the pressure distribution cloud map on the surface of the projectile at α = ±30°; Figure 7b The diagram shows the pressure distribution cloud map on the surface of the projectile at α = ±25°; Figure 7c The diagram shows the pressure distribution cloud map on the surface of the projectile at α = ±20°; Figure 7d The diagram shows the pressure distribution cloud map on the surface of the projectile at α = ±15°; Figure 7e The diagram shows the pressure distribution cloud map on the surface of the projectile at α = ±10°; Figure 7f The diagram shows the pressure distribution cloud map on the surface of the projectile at α = ±5°; Figure 7g The diagram shows the pressure distribution cloud map on the surface of the projectile when α = 0°.

[0049] Figure 8a , Figure 8b , Figure 8c , Figure 8d , Figure 8e , Figure 8f , Figure 8g This is a flow field pressure contour map; among which, Figure 8aThe diagram shows the pressure distribution contour map within the entire flow field computational domain when α = ±300. Figure 8b The diagram shows the pressure distribution contour map within the entire flow field computational domain at α = ±25°. Figure 8c The diagram shows the pressure distribution cloud map within the entire flow field computational domain at α = ±20°; Figure 8d The diagram shows the pressure distribution cloud map within the entire flow field computational domain at α = ±15°; Figure 8e The diagram shows the pressure distribution cloud map within the entire flow field computational domain when α = ±10°; Figure 8f The diagram shows the pressure distribution contour map within the entire flow field computational domain at α = ±5°; Figure 8g The diagram shows the pressure distribution cloud map within the entire flow field computational domain when α = 0°.

[0050] Figure 9a , Figure 9b , Figure 9c , Figure 9d , Figure 9e , Figure 9f , Figure 9g This is a flow field velocity contour map; where, Figure 9a The diagram shows the velocity distribution contour map within the entire flow field computational domain at α = ±30°. Figure 9b The diagram shows the velocity distribution contour map within the entire flow field computational domain at α = ±25°. Figure 9c The diagram shows the velocity distribution contour map within the entire flow field computational domain at α = ±20°; Figure 9d The diagram shows the velocity distribution contour map within the entire flow field computational domain at α = ±15°. Figure 9e The diagram shows the velocity distribution contour map within the entire flow field computational domain at α = ±10°. Figure 9f The diagram shows the velocity distribution contour plot within the entire flow field computational domain at α = ±5°. Figure 9g The diagram shows the velocity distribution contour map within the entire flow field computational domain when α = 0°.

[0051] Because Fluent software requires complete flow field simulation calculations, it is time-consuming. In actual simulations, under the same conditions, Fluent calculations took 20 hours, while Datcom calculations took approximately 30 seconds, roughly 10 times longer than Datcom. 4 Therefore, the example considers Fluent data as precise values ​​and Datcom data as approximate values. In practical applications, wind tunnel results can be used as precise data.

[0052] The calculation results of Fluent and Datcom were compared, and the aerodynamic parameter curves were plotted as follows: Figure 10a , Figure 10b , Figure 10c , Figure 10dAs shown, where, Figure 10a This figure shows a comparison of the calculation results of the lift coefficient CL versus angle of attack alpha under a given Mach number using the Fluent and Datcom methods. Figure 10b This figure shows a comparison of the calculation results of the drag coefficient CD versus angle of attack alpha under a given Mach number using the Fluent and Datcom methods. Figure 10c This figure shows a comparison of the curves showing the calculation results of the moment coefficient CMZ versus the angle of attack alpha under a given Mach number using the Fluent and Datcom methods. Figure 10d This chart compares the calculation results of the moment coefficient CMZ versus the rudder deflection angle delta using the Fluent and Datcom methods at a given Mach number. The maximum errors in aerodynamic parameters at the same Mach number are summarized in the table below.

[0053] Table 2 shows the error table of aerodynamic parameters calculated by Datcom and Fluent.

[0054]

[0055] As shown in the table above, the average maximum error between the data obtained by Datcom and Fluent exceeds 10%. Datcom has a faster calculation speed but lower accuracy, while Fluent has a slower calculation speed but is more accurate. Based on these results, the example uses the drag coefficient at Mach 0.5 to correct the angle-of-attack curve. The aerodynamic parameters calculated by Datcom are used as a large set of data (100 points in total) for rough calculation, while the aerodynamic parameters calculated by Fluent are used as a small set of high-precision data (10 points in total). The data format is point format (angle of attack, drag coefficient).

[0056] Step 2: Establish a low-precision model, specifically using an MLP neural network structure.

[0057] The training data consisted of a large dataset obtained through rough calculation. The hidden layer had 20 neurons and 2 hidden layers. The network structure was as follows: Figure 2 The neural network diagram is shown on the left. The input layer has no activation function, the hidden layer uses the sigmoid function, and the output layer uses the identity activation function. 80% of the training data is used for network training, and the remaining 20% ​​is used to test the training results. The goal is that the maximum relative error of the final trained network on the test set should not exceed 1%.

[0058] MLP network training involves propagating the error between the predicted and true values ​​backward from the input layer to the output layer. Its structural principle is as follows: Figure 11As shown, during propagation, the connection weights and thresholds of neurons in each layer are updated. Then, by repeatedly calculating the predicted value in the forward direction and repeatedly propagating the error between the predicted value and the true value, the error gradually converges to the target range. When the maximum relative error in the training set does not exceed 1%, a check is performed to verify that the maximum relative error in the test set does not exceed 1%. If the condition is not met, training continues; if it is met, training is considered successful.

[0059] Let n be the number of neurons in the input layer. In this example, the number of neurons in the input layer is 100, corresponding to the result calculated by Datcom (100 sets of data). m is the number of neurons in the output layer. In this example, the number of neurons in the output layer is 100, corresponding to the result calculated by Datcom (100 sets of data). The input vector X is the input of the 100 sets of data results calculated by Datcom, i.e., the angle of attack value. The label vector Y corresponding to the input vector is the output of the 100 sets of data results calculated by Datcom, i.e., the drag coefficient value. p is the number of neurons in the hidden layer. The net input vector S, input vector B, and actual output vector C of the output layer are intermediate parameters in the network update calculation process. In the process of using neural networks to correct missile aerodynamic parameters, the network itself mainly plays a fitting role. The internal hyperparameters are obtained by continuous training based on the input and output data, playing a role in fitting the data patterns.

[0060] The parameters are defined as follows:

[0061] X = (x1, x2, ..., x) n ) T

[0062] Y = (y1, y2, ..., y3) m ) T

[0063] S = (s1, s2, ..., s p ) T

[0064] L = (l1, l2, ..., l) m ) T

[0065] C = (c1, c2, ..., c m ) T

[0066] The weight matrix W from the input layer to the hidden layer, the weight matrix V from the hidden layer to the output layer, the threshold θ of a single neuron in the hidden layer, and the threshold γ of a single neuron in the output layer are set as follows:

[0067] W = {w ij}(i=1,2,…,n,j=1,2,…,p)

[0068] V = {v} jt}(j=1,2,…,p,t=1,2,…,m)

[0069] θ={θ j (i = 1, 2, ..., p)

[0070] γ={γ i}(t=1,2,…m)

[0071] In the formula, w ij Let v be the connection weight of the j-th neuron in the i-th hidden layer. jt Let θ be the link weight of the j-th neuron in the hidden layer of the last column to the t-th parameter of the output. j γ is the threshold of the j-th neuron in the hidden layer. i is the threshold of the i-th neuron in the output layer.

[0072] First, the parameters are initialized by randomly selecting values ​​from [-1, 1] and assigning them to the weight matrix W, V and the threshold θ, γ. Then, a sample is randomly selected from the sample dataset as the input data for the network model.

[0073] Next, the forward propagation process of the input data begins. The net input and output of the hidden layer neurons are calculated using the input vector X and the weight matrix W, as shown in the following equation:

[0074]

[0075] b j =f(s) j ), j = 1, 2, ..., p

[0076] In the formula, j represents the j-th neuron in the hidden layer, and s j b is the net input to the j-th neuron in the hidden layer. j x is the net output of the j-th neuron in the hidden layer. i Let f(·) be the i-th input parameter, and f(·) be the activation function. In this invention, the Sigmoid function is chosen, as shown in the following formula:

[0077]

[0078] In the formula, e is the natural logarithm, and x is the input quantity.

[0079] Then, the output of the hidden layer is used to calculate the net input and actual output of the output layer neurons, as shown in the following formula:

[0080]

[0081] ct =f(l t ), t=1,2,…m

[0082] In the formula, t represents the t-th neuron in the output layer, l i c is the net input to the i-th neuron in the hidden layer. t γ is the actual output of the i-th neuron in the hidden layer. t Let l be the value of the t-th neuron in the output layer in the training set. t Let f(t) be the actual value of the t-th neuron in the output layer, and f(·) be the activation function.

[0083] After the forward propagation of the input data is complete, the backward propagation of the error begins. First, the computational error d from the output layer to the neuron is calculated using the label vector Y corresponding to the input vector. t Using the mean squared error loss function, the computational error of a single neuron is shown in the following formula:

[0084]

[0085] The partial derivative of the computational error of a single neuron with respect to the connection weights, where the connection weights refer to each element in the weight matrices W and V, i.e., the connection weights of each neuron, can be obtained from this, as shown in the following formula:

[0086] d t =(y t -c t )c t ′

[0087] In the formula, (y t -c t ) represents the difference between the predicted output and the actual output of the output layer, c t Let ' be the partial derivative of the computational error of the t-th neuron in the output layer with respect to the connection weights. Using the obtained correction error d... t The correction error of the hidden layer neurons is calculated using the derivative of the activation function, as shown in the following formula:

[0088]

[0089] Let the learning rate from the output layer to the hidden layer be α (0 < α < 1). The weight matrix V from the output layer to the hidden layer and the threshold γ of the hidden layer neurons are corrected as follows:

[0090] Δv jt =αb j d t , j=1,2,…,p, t=1,2,…,m

[0091] △γ t =αdt ,t=1,2,…,m

[0092] In the formula, Δv jt Δγ represents the update error in the j-th row and t-th column of the weight matrix V from the output layer to the hidden layer. t This represents the error between the output value of the t-th parameter of the output layer and the corresponding value in the training set.

[0093] Let the learning rate from the input layer to the hidden layer be β (0 < β < 1). The weight matrix W from the input layer to the hidden layer and the threshold θ of a single neuron in the hidden layer are corrected as follows:

[0094] Δw jt =βX i e j ,i=1,2,…,n,j=1,2,…,p

[0095] Δθ t =βe j j = 1, 2, ..., p

[0096] In the formula, Δw jt X represents the update error in the j-th row and t-th column of the weight matrix W from the input layer to the hidden layer. i Represents the i-th input value, Δθ t This represents the error between the output value of the t-th parameter of the input layer and the corresponding value in the training set.

[0097] Then, a sample is randomly selected from the remaining samples as the input data for the network model, and the two calculation processes of forward propagation of input data and backpropagation of error are repeated until all samples have been learned.

[0098] The mean squared loss function E is used to calculate whether the network meets the accuracy requirement. If E meets the requirement, training ends; otherwise, the network's learning count is updated by incrementing it by 1. If the network reaches the specified number of learning counts, model training ends. The mean squared loss function is shown in the following formula:

[0099]

[0100] In the formula, q represents the number of training rounds.

[0101] The resulting trained neural network serves as a low-precision model, enabling the rapid output of low-precision drag coefficients at different angles of attack and Mach numbers.

[0102] Step 3: Establish a residual learning neural network model, specifically using an MLP (Multilayer Perceptron) model, such as... Figure 2 As shown.

[0103] Based on the low-precision model constructed in step two, i.e., the upper left part x in the figurel to y l The mapping, input low-precision data x l To obtain low-precision predicted value y l The MLP neural network based on residual learning established in step three is used to explore the input x. l The relationship between the residual r(x) and the output predicted residual. The specific principles and formulas are consistent with the MLP neural network introduced in Step Two, with the only difference being the network structure. Its input consists of the low-precision model obtained in Step Two and a small amount of high-precision data from Step One. The specific structure is designed with two hidden layers, each containing 64 neurons. The network structure is as follows: Figure 2 The right side of the diagram shows the neural network. The mean squared error loss function (MSEloss) is used as the training objective, the Adam optimizer is employed, the learning rate is set to 0.01, the ReLU activation function is used, and the training iterations are 1000. Compared to the network model in step two, the network in step three has stronger fitting capabilities and is suitable for small-sample refinement tasks, as detailed below.

[0104] Let n be the number of neurons in the input layer. In this example, the number of neurons in the input layer is 10, which corresponds to the portion of the Fluent calculation result used for training (10 sets of data in total). m is the number of neurons in the output layer. In this example, the number of neurons in the input layer is 10, which corresponds to the portion of the Fluent calculation result used for training (10 sets of data in total). p is the number of neurons in the hidden layer, which is related to the network structure; in this example, it is 64. The input vector X is the portion of the Fluent calculation result used for training, i.e., the angle of attack value. The label vector Y corresponding to the input vector is the portion of the Fluent calculation result used for training, i.e., the drag coefficient value. The hidden layer net input vector S, the input vector B, and the output layer actual output vector C are intermediate parameters in the network update calculation process. In the process of using the neural network to correct the missile's aerodynamic parameters, the network itself mainly plays a fitting role. The internal hyperparameters are obtained through continuous training based on the input and output data, playing a role in fitting the data patterns. Finally, the trained residual learning neural network model can output the predicted residual. By superimposing the predicted residual with the low-precision model over the entire domain, the corrected drag coefficient curve can be obtained.

[0105] Step 4: Verify the corrected results.

[0106] The initial data from step one, the results calculated by Datcom (100 sets of data), are used as the basic low-precision data. The results calculated by Fluent (31 sets of data) are used as follows: 10 sets are randomly selected as a small sample training set for training the correction neural network, and the remaining 21 sets are used as the test set to verify the model accuracy. This ensures that the number of low-precision data sets is more than 10 times that of the high-fidelity data sets. Simulation tests of the proposed aerodynamic parameter correction method based on multi-fidelity data fusion are performed, and the correction result curves are shown below. Figure 12 As shown, the formula for calculating the relative error rate between the corrected drag coefficient and the true drag coefficient is as follows:

[0107]

[0108] In the formula, CD is the actual drag coefficient of the example missile, and CD' is the drag coefficient of the example missile after being corrected by the algorithm proposed in this invention.

[0109] According to the above formula, the average error of the drag coefficient after correction decreased from the initial 9.3% to 0.41%, which fully demonstrates the effectiveness of the algorithm proposed in this invention. Below, we compare the results of the BP neural network algorithm proposed in existing literature, the traditional quadratic function least squares fitting method, and the residual learning neural network-based correction algorithm proposed in this invention, using the same original data. Simulation results are presented. Figure 13 As shown.

[0110] To better compare the algorithm proposed in this invention with other existing algorithms, in addition to calculating the relative error rate between the corrected resistance coefficient and the true resistance coefficient, the mean square error loss between the corrected resistance coefficient and the true resistance coefficient is also calculated, as shown in the following formula.

[0111]

[0112] The method proposed in this invention, the BP neural network algorithm in existing literature, the engineering traditional quadratic function least squares fitting, the uncorrected aerodynamic data, and the high-fidelity data of the test group were compared. The relative error rate and mean square error loss were calculated, and the results are summarized in the table below.

[0113] Table 3 Comparison of drag coefficient correction results of the proposed algorithm and other algorithms for the example.

[0114]

[0115] As can be seen from the comparison table above, from the perspectives of relative error rate and mean square error loss, the residual learning neural network correction algorithm proposed in this invention improves the accuracy by an order of magnitude and can complete the correction of aerodynamic parameters in a short time. This fully demonstrates the effectiveness of the residual learning neural network correction algorithm proposed in this invention.

[0116] In summary, this invention proposes a rapid aerodynamic parameter correction method for missiles based on a residual learning neural network algorithm. By combining a large amount of coarse aerodynamic data generated by Datcom with a small amount of precise aerodynamic data points calculated by Fluent, a residual learning multilayer perceptron model is used to achieve efficient correction of aerodynamic parameters. Simulations validate the proposed method using examples. The average error at the validation points decreased from the initial 9.3% to 0.41%. Compared with the BP neural network proposed in existing literature and the traditional quadratic function least squares fitting method used in engineering, the proposed method has a significant advantage in accuracy and can complete the aerodynamic parameter correction in a shorter time, demonstrating high engineering application value.

Claims

1. A method for rapid correction of missile aerodynamic parameters based on residual learning neural network algorithm, characterized in that: Includes the following steps: Step 1: Provide the raw data, which includes two parts: a large set of data obtained from rough calculation and a small set of high-precision data. Select the aerodynamic parameters calculated using Datcom as the large set of data obtained from rough calculation, and the aerodynamic parameters calculated using Fluent as the small set of high-precision data. Step 2: Establish a low-precision model, specifically using an MLP neural network structure; the training data is a large dataset obtained through rough calculation, with 20 neurons in the hidden layer and 2 hidden layers. The input layer has no activation function, the hidden layers use the Sigmoid function, and the output layer uses the identity activation function; 80% of the training data is used for network training, and the remaining 20% ​​is used to verify the training results. The requirement is that the maximum relative error of the network in the test set does not exceed 1%. The resulting trained neural network serves as a low-precision model, enabling rapid output of low-precision drag coefficients under different input angles of attack and Mach numbers. Step 3: Establish a residual learning neural network model, specifically using a multilayer perceptron (MLP) model, to establish the relationship between low-precision data and high-precision data, and use an autoregressive approach to express the correlation between different data, as shown in the following formula; y h =f(x,y l ) In the formula, x is the independent variable, and y h For high-precision data, y l For low-precision data, f represents the functional relationship between low-precision data and high-precision data; Step 4: Verify the corrected results; Twenty additional high-precision data points were selected as comparison and verification points, and the relative error rate and mean square error loss were calculated.

2. The method for rapid correction of missile aerodynamic parameters based on residual learning neural network algorithm according to claim 1, characterized in that: In step one, the missile has a slender cylindrical body with a pointed, arched nose. Four all-moving, cruciform deltaic wings are located in the middle of the body, and four fixed triangular stabilizers are located at the tail. The all-moving wings and stabilizers are arranged in tandem on the missile body. The missile's reference area S, reference length l, aspect ratio λ, and control area S are given. f As shown in the following formula; 3. A method for rapid correction of missile aerodynamic parameters based on a residual learning neural network algorithm according to claim 1 or 2, characterized in that: The missile's shape was modeled, and its coarse aerodynamic parameters were calculated using Missile Datcom software. The component assembly method was employed, and empirical formulas, experimental data, and mathematical formulas were used to calculate the missile's aerodynamic coefficients. The precise aerodynamic parameters were calculated using Ansys Fluent software, employing the finite volume method. The Mach number at the far-field boundary of the pressure was defined as the missile's flight Mach number, the incoming flow direction was defined as the missile's flight attitude angle, the pressure was set to one standard atmosphere, and the temperature was set to 300K. The external fluid model used the k-ω model in the turbulence model.

4. The method for rapid correction of missile aerodynamic parameters based on residual learning neural network algorithm according to claim 1, characterized in that: In step two, n is set as the number of neurons in the input layer, which is 100, corresponding to the 100 sets of data calculated by Datcom; m is set as the number of neurons in the output layer, which is 100, corresponding to the 100 sets of data calculated by Datcom; the input vector X is the input of the 100 sets of data calculated by Datcom, i.e., the angle of attack value; the label vector Y corresponding to the input vector is the output of the 100 sets of data calculated by Datcom, i.e., the drag coefficient value; p is the number of neurons in the hidden layer, and the net input vector S, input vector B, and actual output vector C of the output layer are intermediate parameters in the network update calculation process; The parameters are defined as follows: X=(x1,x2,…,x n ) T Y=(y1,y2,…,y m ) T S=(s1,s2,…,s p ) T L＝(l1,l2,…,l m ) T C=(c1,c2,…,c m ) T The weight matrix W from the input layer to the hidden layer, the weight matrix V from the hidden layer to the output layer, the threshold θ of a single neuron in the hidden layer, and the threshold γ of a single neuron in the output layer are set as follows: W={w ij }(i=1,2,…,n,j=1,2,…,p) V={v jt }(j=1,2,…,p,t=1,2,…,m) θ={θ j }(i=1,2,…,p) γ={γ i }(t=1,2,…m) In the formula, w ij Let v be the connection weight of the j-th neuron in the i-th hidden layer. jt Let θ be the link weight of the j-th neuron in the hidden layer of the last column to the t-th parameter of the output. j γ is the threshold of the j-th neuron in the hidden layer. i is the threshold of the i-th neuron in the output layer.

5. The method for rapid correction of missile aerodynamic parameters based on residual learning neural network algorithm according to claim 4, characterized in that: First, the parameters are initialized by randomly selecting values ​​in [-1, 1] and assigning them to the weight matrices W and V and the thresholds θ and γ. Then, a sample is randomly selected from the sample dataset as the input data for the network model. Next, the forward propagation process of the input data begins. The net input and output of the hidden layer neurons are calculated using the input vector X and the weight matrix W, as shown in the following equation: b j =f(s j ),j=1,2,…,p In the formula, j represents the j-th neuron in the hidden layer, and s j b is the net input to the j-th neuron in the hidden layer. j x is the net output of the j-th neuron in the hidden layer. i Let f(·) be the i-th input parameter, and f(·) be the activation function. We choose the Sigmoid function, as shown in the following equation: In the formula, e is the natural logarithm, and x is the input quantity; Then, the output of the hidden layer is used to calculate the net input and actual output of the output layer neurons, as shown in the following formula: c t =f(l t ),t=1,2,…m In the formula, t represents the t-th neuron in the output layer, l i c is the net input to the i-th neuron in the hidden layer. t γ is the actual output of the i-th neuron in the hidden layer. t Let l be the value of the t-th neuron in the output layer in the training set. t Let f(t) be the actual value of the t-th neuron in the output layer, and f(·) be the activation function.

6. The method for rapid correction of missile aerodynamic parameters based on residual learning neural network algorithm according to claim 5, characterized in that: After the forward propagation of the input data is completed, the backward propagation of the error begins. First, the computational error d from the output layer to the neuron is calculated using the label vector Y corresponding to the input vector. t Using the mean squared error loss function, the computational error of a single neuron is shown in the following formula: The partial derivative of the computational error of a single neuron with respect to the connection weights is calculated, where the connection weights refer to each element in the weight matrices W and V, i.e., the connection weights corresponding to each neuron. The resulting correction error for a single neuron is shown in the following formula: d t =(y t -c t )c t ′ In the formula, (y t -c t ) represents the difference between the predicted output and the actual output of the output layer, c t ′ represents the partial derivative of the computational error of the t-th neuron in the output layer with respect to the connection weights; using the obtained correction error d t The correction error of the hidden layer neurons is calculated using the derivative of the activation function, as shown in the following formula:

7. The method for rapid correction of missile aerodynamic parameters based on residual learning neural network algorithm according to claim 6, characterized in that: Let the learning rate from the output layer to the hidden layer be α (0 < α < 1). The weight matrix V from the output layer to the hidden layer and the threshold γ of the hidden layer neurons are corrected as follows: Δv jt =αb j d t ,j=1,2,…,p,t=1,2,…,m Dg t =αd t ,t=1,2,…,m In the formula, Δv jt Δγ represents the update error in the j-th row and t-th column of the weight matrix V from the output layer to the hidden layer. t This represents the error between the output value of the t-th parameter of the output layer and the corresponding value in the training set. Let the learning rate from the input layer to the hidden layer be β (0 < β < 1). The weight matrix W from the input layer to the hidden layer and the threshold θ of a single neuron in the hidden layer are corrected as follows: Δw jt =βX i e j ,i=1,2,…,n,j=1,2,…,p Dth t =βe j ,j=1,2,…,p In the formula, Δw jt X represents the update error in the j-th row and t-th column of the weight matrix W from the input layer to the hidden layer. i Represents the i-th input value, Δθ t This represents the error between the output value of the t-th parameter of the input layer and the corresponding value in the training set. Then, a sample is randomly selected from the remaining samples as the input data of the network model, and the two calculation processes of forward propagation of input data and backpropagation of error are repeated until all samples have been learned. The mean squared loss function E is used to calculate whether the network meets the accuracy requirement. If E meets the requirement, training ends; otherwise, the network learning count is updated by incrementing it by 1. If the network model reaches the specified number of learning counts, model training ends. The mean squared loss function is shown in the following formula: In the formula, q is the number of training rounds; The resulting trained neural network serves as a low-precision model, enabling the rapid output of low-precision drag coefficients at different angles of attack and Mach numbers.

8. The method for rapid correction of missile aerodynamic parameters based on residual learning neural network algorithm according to claim 1, characterized in that: In step three, let a large number of low-precision data points be (x i ,y l (x i The low-precision fitting model is y. l (x), a small number of high-fidelity data points are (x) j ,y h (x j The corrected high-fidelity model is y. h The residual r(x) is defined as follows; r(x)=y h (x)-y l (x) By training a multilayer perceptron (MLP) model To learn residuals The nonlinear mapping relationship between r(x) and the residual prediction error is used to obtain the optimal parameters, thereby modeling the residual and correcting the original model. We choose to construct a residual learning MLP network, and the model uses the mean squared error loss function (MSEloss) as the training objective. The objective function is shown in the following equation: After training, residual prediction is performed over the entire time axis, and the predicted residuals are superimposed on the original theoretical curves to obtain the output after residual correction, as shown in the following formula; Where, x l to y l The mapping is a low-precision model, with low-precision data x as input. l To obtain low-precision predicted value y l MLP neural networks with residual learning are used to explore input x l The relationship between the residual r(x) and the output predicted residual. Prediction residuals in the unknown domain Compared with low-precision predicted value y l The corrected data y is obtained by superposition. h2 , will y h1 With y h2 Combined, we obtain the entire field x l The correction value y below h .

9. The method for rapid correction of missile aerodynamic parameters based on residual learning neural network algorithm according to claim 1, characterized in that: In step four, the initial data from step one and the results calculated by Datcom are used as the basic low-precision data. The results calculated by Fluent are used as the basis. Ten groups are randomly selected as a small training set for training the corrected neural network, and the remaining 21 groups are used as the test set to verify the model's accuracy. This ensures that the number of low-precision data groups is more than 10 times that of the high-fidelity data. The formula for calculating the relative error rate between the corrected drag coefficient and the true drag coefficient is as follows: In the formula, CD is the actual drag coefficient of the example missile, and CD' is the drag coefficient of the example missile after algorithm correction.

10. A method for rapid correction of missile aerodynamic parameters based on a residual learning neural network algorithm according to claim 9, characterized in that: In addition to calculating the relative error rate between the corrected resistance coefficient and the true resistance coefficient, the mean square error loss between the corrected resistance coefficient and the true resistance coefficient was also calculated, as shown in the following formula.

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