Aircraft low sound detonation reverse design method based on transfer learning multi-fidelity neural network

Abstract

The invention relates to the technical field of aerodynamic configuration design of aircrafts, in particular to an aircraft low sound detonation reverse design method based on a transfer learning multi-fidelity neural network. According to the technical scheme, the near-field signal of the initial scheme is modified, the target near-field signal with smaller sound explosion is obtained through iteration in combination with the optimization method, and then the aircraft profile meeting the target near-field signal is obtained through the inverse design method. According to the method, the solvability of a generalized Burgers equation is adopted, a proxy optimization method is applied according to an initial scheme, and low-sound-explosion target near-field overvoltage distribution is determined; a multi-fidelity deep neural network is constructed based on transfer learning, the characteristic of low demand of fine tuning on data volume is utilized, the mapping relation between the aircraft profile and near-field overvoltage distribution can still be accurately captured when high-fidelity data is less, and due to the fact that the transfer learning does not need to be connected in series with multiple models, the accuracy of the multi-fidelity deep neural network is improved. Error accumulation caused by insufficient training of a single model during traditional multi-fidelity modeling can be avoided to a certain extent.

Description

Technical Field

[0001] A method for low-sonic detonation anti-design of aircraft based on transfer learning multi-fidelity neural networks. Background Technology

[0002] This application relates to the field of aircraft aerodynamic shape design technology, and in particular to an aircraft low-sonic blast inverse design method based on transfer learning multi-fidelity neural networks. Summary of the Invention

[0003] In the global development of aerospace technology, high-subsonic passenger aircraft have achieved great success. However, with the ever-increasing demand for air transport, supersonic civil aircraft have become a key direction for future civil aircraft development. However, some existing supersonic passenger aircraft have been forced out of the market due to sonic boom problems, which are inherent to supersonic flight and have resulted in poor economic and environmental performance. Sonic boom is a unique aeroacoustic phenomenon in supersonic flight, specifically manifested as a complex shock-expansion wave system generated in the near field of the aircraft during supersonic flight. This system propagates and evolves into intense sound waves on the ground, significantly impacting organisms and buildings along the flight path. These problems limit supersonic flight to specific areas with fewer people, deviating from the actual operating conditions for supersonic flight, leading to decreased aircraft performance and reduced economic efficiency.

[0004] In view of this, this application provides a low-detonation inverse design method for aircraft based on transfer learning multi-fidelity neural networks, which can effectively suppress the sonic boom of aircraft.

[0005] A low-sonic blast inverse design method for aircraft based on transfer learning multi-fidelity neural networks includes: obtaining the initial configuration of the aircraft; generating an initial near-field overpressure distribution based on the initial configuration information; parameterizing the initial near-field overpressure distribution and propagating the parameterized first near-field overpressure distribution to the far field; calculating the far-field sonic blast value based on the parameterized first near-field overpressure distribution; constructing a surrogate optimization model and, in conjunction with the far-field sonic blast value, optimizing and generating a target near-field overpressure distribution; and, based on the generated target near-field overpressure distribution, performing inverse design based on transfer learning multi-fidelity neural networks to obtain the target aircraft shape. Compared to the method of first obtaining the near-field overpressure distribution of the aircraft based on computational fluid dynamics (CFD) and then transferring it to the far field using acoustic methods to obtain the sonic blast value, this method specifies an ideal target feature and implements its low-sonic blast inverse design method. Compared to searching for the optimal feature among countless waveforms through forward search, this method effectively reduces the computational load of sonic blast analysis and improves design efficiency.

[0006] Specifically, an initial near-field overpressure distribution is generated based on the initial configuration information, including generating the initial near-field overpressure distribution through high-fidelity computational fluid dynamics (CFD) calculations based on the initial configuration information. Specifically, the initial near-field overpressure distribution is parameterized, including parameterizing the overpressure values ​​of key feature points in the initial near-field overpressure distribution. These key feature points include local extrema and the midpoint between two extrema in the initial near-field overpressure distribution. These key feature points are used as control points for spline curves, and the near-field overpressure distribution is parameterized through spline curves. Using the above scheme, the location and intensity of the shock wave can be effectively reflected.

[0007] Specifically, the parameterized first near-field overpressure distribution is propagated to the far field, including propagating the parameterized first near-field overpressure distribution to the far field based on the generalized Burgers equation. Using the above scheme, the generalized Burgers equation is easily solvable.

[0008] Specifically, the far-field sonic boom value is calculated based on the parameterized first near-field overpressure distribution, including calculating the ground sonic boom wave using the Mark VII method based on the parameterized first near-field overpressure distribution transmitted to the far field. Using the above scheme, calculating the ground sonic boom wave using Stevens' Mark VII method can improve the perceived sound pressure level (PLdB) of the ground sonic boom waveform, making the assessment of the ground sonic boom wave more accurate.

[0009] Specifically, a surrogate optimization model is constructed, which, in conjunction with the far-field sonic boom values, optimizes and generates the target near-field overpressure distribution. This includes using Latin hypercube sampling to generate initial sample points based on the far-field sonic boom values, calculating the objective function values ​​for these sample points, constructing a Kriging surrogate optimization model, and employing a point-addition method combining the standardized prediction error maximization criterion and the expected improvement criterion. Through multiple iterations and continuous expansion of sample points, the optimal solution is gradually approximated, generating the target near-field overpressure distribution. This approach achieves a balance between optimization efficiency and global optimization.

[0010] Furthermore, based on the output target near-field overpressure distribution, a reverse design is performed using a transfer learning multi-fidelity neural network to obtain the target aircraft's shape. This includes constructing a transfer learning-based method for predicting the near-field overpressure distribution of a multi-fidelity aircraft, and using a genetic algorithm to perform reverse design to obtain the target aircraft's shape based on the output target near-field overpressure distribution. By employing this approach and leveraging the powerful global search capability of the genetic algorithm, the problem of getting trapped in local optima within the performance space of multi-peak characteristics can be effectively avoided.

[0011] Specifically, a multi-fidelity near-field overpressure distribution prediction method for aircraft is constructed based on transfer learning. This includes building a multi-fidelity database, pre-training the model using low-fidelity near-field overpressure distribution data, and fine-tuning the model using high-fidelity near-field overpressure distribution data. This implicitly captures the relationship between high-fidelity and low-fidelity data, thus constructing a highly reliable near-field overpressure distribution prediction method. Using this approach, high-reliability near-field overpressure distribution prediction is achieved even with a limited number of high-fidelity samples.

[0012] Specifically, a near-field overpressure distribution database is constructed, including the deformation of the aircraft shape based on the freeform surface deformation method (FFD), and the perturbation of the freeform surface deformation control points of the initial shape of the aircraft using the Latin hypercube sampling method to obtain different aircraft shapes.

[0013] Specifically, the model is pre-trained based on low-fidelity near-field overpressure distribution data, including selecting an orthogonal Cartesian grid as the coarse grid, obtaining the low-fidelity near-field sonic boom overpressure distribution by solving the Euler equation, and based on the low-fidelity data (x L y L Training a low-fidelity neural network (NN) L Feature Z is extracted through the frozen layer FL. L The trainable layer TL performs low-fidelity predictions based on the extracted features. The formula is By optimizing low-fidelity neural networks The loss function improves low-fidelity prediction, and low-fidelity neural networks. The loss function is Where, θ F For the network parameters of the frozen layer, θ T,L For the network parameters of the trainable layers, x L Z is the input sample for low-fidelity data. L For the frozen layer FL to low-fidelity input x L Extracted feature vectors; Let TL be the predicted value of the low-fidelity output of the trainable layer, FL(▪) be the feature extraction operation of the frozen layer, and TL(▪) be the prediction operation of the trainable layer; m L The number of samples in the low-fidelity training dataset; y L,i Let y be the true value of the i-th low-fidelity sample; * L,i λ is the output value predicted by the network for the i-th low-fidelity sample; L θ is the regularization coefficient. i,F θ is the i-th parameter in the frozen layer FL; j,T,L Let j be the j-th parameter in the trainable layer TL.

[0014] Specifically, the model is fine-tuned using high-fidelity near-field overvoltage distribution data, including calculating the high-fidelity near-field overvoltage distribution based on the RANS equation, transferring the network architecture of the pre-trained network, and adjusting the parameters θ of the frozen layer FL. F Randomly initialize the network parameters θ of the trainable layer TL. T,H Using high-fidelity data (x H y H Training θ T,H Trainable layers implicitly capture the relationships between multi-fidelity data, constructing a high-fidelity neural network (NN). H The formula is: Among them, Z H For the frozen layer FL, high-fidelity input x H Extracted feature vector, x H For the input samples of high-fidelity data, FL(▪) is the feature extraction operation of the frozen layer FL, and θ F For the network parameters of the frozen layer, y * H Let θ be the prediction value of the high-fidelity output by the trainable layer TL, and TL(▪) be the prediction operation of the trainable layer TL. T，H For the network parameters of high-fidelity trainable layers, Loss H Let m be the total loss value of the high-fidelity neural network. H y represents the number of samples in the high-fidelity training dataset. H,i Let y be the true value of the i-th high-fidelity sample; H1,i λ is the predicted output value of the i-th high-fidelity sample; H To ensure high fidelity regularization coefficients and control parameter complexity; θ j,T,H Let j be the j-th parameter of the high-fidelity trainable layer.

[0015] The beneficial effects of this application are: 1. Taking advantage of the solvability of the generalized Burgers equation, a surrogate optimization method is applied based on the initial scheme to determine the target near-field overpressure distribution of low-sonic boom; 2. A multi-fidelity deep neural network based on transfer learning is adopted. Taking advantage of the low data requirement of fine-tuning, it can still accurately capture the mapping relationship between the aircraft shape and the near-field overpressure distribution even when there is little high-fidelity data. Furthermore, since transfer learning does not require multiple models to be connected in series, it can avoid the error accumulation caused by insufficient training of a single model in traditional multi-fidelity modeling to a certain extent. 3. By combining a high-reliability sonic boom prediction method based on transfer learning with a genetic algorithm, we can obtain an aircraft shape that satisfies the target's near-field signal. By utilizing the powerful global search capability of the genetic algorithm, we can effectively avoid the problem of getting trapped in local optima. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic diagram of a target near-field overvoltage distribution design using surrogate optimization according to this application; Figure 2 This is a schematic diagram of a target near-field overvoltage distribution inverse design using a genetic algorithm, as described in this application. Figure 3 This is a schematic diagram of the layout configuration of a certain supersonic passenger aircraft according to this application; Figure 4 This is a schematic diagram illustrating one method of selecting key characteristic points of near-field overpressure distribution as design variables in this application. Figure 5 This is a schematic diagram comparing the target near-field overvoltage distribution with the initial near-field overvoltage distribution according to this application; Figure 6 This is a schematic diagram comparing the target far-field waveform with the initial far-field waveform according to this application; Figure 7 This is a schematic diagram of a multi-fidelity overpressure distributed neural network training method based on transfer learning according to this application; Figure 8 This is a schematic diagram of a multi-fidelity deep neural network based on transfer learning according to this application; Figure 9 This is a schematic diagram comparing the near-field overvoltage distribution with different fidelities under one initial configuration of this application; Figure 10 is a schematic diagram of the prediction results of a custom network TF-DNN model according to this application; Figure 11 is a schematic diagram of the prediction results of a single-fidelity deep neural network (DNN-H) model according to this application; Figure 12 is a schematic diagram comparing an optimized scheme of this application with the initial near-field overpressure distribution; Figure 13 is a schematic diagram comparing an optimized scheme of this application with the initial far-field sonic boom waveform; Detailed Implementation

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to limit this application. The singular forms "a," "the," and "the" used in this application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise. It should also be understood that the term "and / or" as used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0020] An embodiment of an aircraft low-sonic blast inverse design method based on transfer learning multi-fidelity neural networks, with reference to... Figure 1 , Figure 2 This embodiment may include the following steps: S1: Obtain the initial configuration of the aircraft and generate an initial near-field overpressure distribution based on the initial configuration information; S2: Parametrically process the initial near-field overpressure distribution and propagate the parametrically processed first near-field overpressure distribution to the far field; S3: Calculate the far-field sonic boom value based on the parametrically processed first near-field overpressure distribution; S4: Construct a proxy optimization model and, in conjunction with the far-field sonic boom value, optimize and generate a target near-field overpressure distribution; S5: Based on the output target near-field overpressure distribution, perform reverse design to obtain the target aircraft shape. Using the above scheme, this application suppresses sonic booms through aircraft aerodynamic shape design, which is more effective than other approaches such as flow control and novel low-sonic-boom layouts. Specifically, the near-field signal of the initial scheme is first modified, and an optimization method is used iteratively to obtain a target near-field signal with a smaller sonic boom. Furthermore, expert experience can be combined to obtain a target near-field signal with an even smaller sonic boom. Then, a reverse design method is used to obtain an aircraft shape that satisfies the target near-field signal. Compared to searching for the optimal feature among countless waveforms through forward search, this application employs a low-detonation inverse design method. This method, which specifies an ideal target feature and implements it, effectively reduces the computational load of detonation analysis and improves design efficiency. The aircraft used in this application is a supersonic passenger aircraft, as illustrated below. The initial configuration of the supersonic passenger aircraft is as follows... Figure 3 As shown.

[0021] In some alternative embodiments, step S1 may employ high-fidelity computational fluid dynamics (CFD) methods to solve, for example... Figure 3 The near-field overpressure distribution of the initial configuration of the aircraft, i.e., the initial near-field overpressure distribution.

[0022] In some optional embodiments, step S2 parameterizes the initial near-field overpressure distribution, including parameterizing the overpressure values ​​of key feature points in the initial near-field overpressure distribution. These feature points include local extrema in the initial near-field overpressure distribution, which can mainly be local extrema and the midpoint between two extrema, serving as control points for spline curves. The initial near-field overpressure distribution can be parameterized using cubic spline curves. The above scheme can effectively reflect the position and intensity of the shock wave.

[0023] In some optional embodiments, step S2 can use the generalized Burgers equation to propagate the parameterized first near-field overpressure distribution to the far field. The generalized Burgers equation can take into account the effects of geometric acoustics, atmospheric stratification, thermoviscous absorption, and molecular relaxation on the propagation of the sonic boom. The waveform after propagation to the ground using the generalized Burgers equation is compared to... Figure 5 As shown, the perceived sound pressure level of the target near-field overpressure distribution decreased by 4.2%. This is in accordance with the classical Burgers equation. Adding terms to the right side representing geometric diffusion, atmospheric stratification, and relaxation effects (molecular relaxation), we obtain the dimensional form of the generalized Burgers equation: This equation can simulate the propagation of sound waves in a non-uniform, non-ideal gaseous medium. The five terms on the right correspond to five physical phenomena: nonlinear effects, classical dissipation, non-uniform medium, geometric diffusion, and relaxation effects. Here, S refers to the area of ​​the acoustic tube. The change in sound speed caused by the relaxation effect. Represents the relaxation time, subscript This represents the relaxation process for different atmospheric components. To solve this equation numerically, the dimensional form of the generalized Burgers equation is normalized to obtain the dimensionless form of the augmented Burgers equation: in, , Reference pressure, dimensionless distance Reference length Dimensionless time is The reference time is (Determined by the sampling rate of the near-field waveform). Dimensionless molecular relaxation time. dimensionless relaxation coefficient .

[0024] In some optional embodiments, step S3, after the initial near-field overpressure distribution propagates to the ground, calculates the ground sonic boom using Stevens' Mark VII method. This allows for the calculation of the perceived sound pressure level (PLdB) of the ground sonic boom waveform, making the assessment of the ground sonic boom more accurate. The Mark VII method can solve the generalized Burgers equation, combined with atmospheric physics effects models, to accurately simulate the propagation and distortion of the sonic boom waveform, and quantify its subjective loudness based on human hearing characteristics.

[0025] In some alternative embodiments, reference is made to Figure 1 As shown, in step S4, a surrogate optimization method can be used to generate the target near-field overpressure distribution, which is the near-field overpressure distribution with the lowest ground sonic boom loudness. Specifically, Latin hypercube sampling is used to generate initial sample points and calculate the objective function value of the sample points. The surrogate optimization model uses the Kriging model; the point addition (adaptive sampling) method uses the MSP criterion (Maximizing Standardized Predictive Error) and the EI criterion (Expected Improvement). Through multiple iterations and continuous expansion of sample points, the surrogate optimization method can gradually approach the optimal solution. The target near-field overpressure distribution is generated by judging whether it has converged; otherwise, a new near-field overpressure distribution sample point is obtained, and it is recalculated again using the generalized Burgers equation and the Mark VII method. The x-coordinate of the control point is kept unchanged, while its overpressure value is used as a design variable. The surrogate optimization method is used to adjust it to obtain the target near-field overpressure distribution with the minimum sonic boom value. The optimized target near-field overpressure distribution is compared with the near-field overpressure distribution of the initial scheme. Figure 4 As shown. The generalized Burgers equation is used to compare the waveform after propagation to the ground, for example... Figure 5 As shown in the figure, the perceived sound pressure level of the target's near-field overpressure distribution decreased by 4.2%. The aforementioned surrogate optimization method can balance optimization efficiency and global optimization. A comparison of the target's far-field waveform and the initial scheme's far-field waveform is also shown. Figure 6 As shown.

[0026] Because high-reliability computational fluid dynamics (CFD) solutions are very expensive—for the same aircraft shape—the mesh size required to solve for high-precision near-field overpressure distributions is typically 5-10 times that required to solve for aerodynamic forces. In engineering, modified linearization theory is often used to predict sonic boom signals based on the concept of lift equivalent cross-sectional area, replacing costly flow field solutions. However, it does not consider the nonlinear effects around complex aircraft shapes, resulting in inaccurate calculations. Deep neural networks, due to their superior data mining capabilities, are frequently used to construct mapping relationships between aircraft shapes and target performance, enabling rapid predictions. However, model construction relies on a large amount of high-fidelity data as training samples, leading to poor generalization performance when such data is scarce.

[0027] Therefore, after obtaining the target near-field overpressure distribution, step S6 can be adopted. Figure 2 The optimization framework shown is used to perform inverse design of the target near-field overvoltage distribution. Prior to this, refer to... Figure 7 As shown, this application proposes a multi-fidelity near-field overpressure distribution prediction method for aircraft based on transfer learning. A multi-fidelity database is constructed, and the model is pre-trained using low-fidelity near-field overpressure distribution data. Then, the model is fine-tuned using high-fidelity near-field overpressure distribution data. By implicitly capturing the relationship between high- and low-fidelity data, high-reliability near-field overpressure distribution prediction is achieved even with a limited number of high-fidelity samples. After constructing a fast prediction method using the above approach, it is combined with a genetic algorithm to build an aircraft sonic boom optimization framework. The genetic algorithm effectively avoids getting trapped in local optima in the performance space of multi-peak characteristics. Compared to using neural networks to capture the mapping relationship between aircraft shape and near-field overpressure distribution, which suffers from high computational cost and difficulty in large-scale sampling for high-fidelity near-field overpressure distribution, this application provides a fast and high-fidelity near-field overpressure distribution prediction method.

[0028] The calculation of high- and low-fidelity data is based on practical engineering considerations. To capture accurate near-field overpressure distribution, a dense mesh with 40 million grid points is used, but the computational cost remains high. In some optional embodiments, an orthogonal Cartesian mesh with 4-5 million grid points is used as the coarse mesh, and then the low-fidelity near-field sonic boom overpressure distribution is obtained by solving the Euler equation. The numerical results of solving the near-field overpressure distribution using the Euler equation have high accuracy, and the accuracy of the Cartesian mesh method can meet the accuracy requirements of the conceptual design stage. Therefore, this paper can use the Cartesian mesh and Euler solver to obtain a large number of low-fidelity near-field overpressure distributions (50 minutes at a time), and use a 10 times denser structured mesh and RANS solver (Reynolds-Averaged Navier-Stokes Solver) to obtain a small number of high-fidelity near-field overpressure distributions (10 hours at a time). Taking the initial shape as an example, the calculated near-field overpressure distribution is compared with... Figure 9 As shown, HF represents high fidelity and LF represents low fidelity.

[0029] In Cartesian coordinates, the conserved form of the Euler equations for three-dimensional inviscid, adiabatic, steady flow is: Where: conserved variable vector , It is the fluid density. They are The velocity component in the direction, It is the total energy per unit volume, and , It is the internal energy per unit mass. The flux vector. , It's fluid pressure. We still need to use the equation of state. To close the system of equations, It is the specific heat ratio, which is usually taken as air. .

[0030] Discretization is performed using the finite volume method: the three-dimensional computational domain is discretized into a series of non-overlapping control volumes (mesh elements). The volume integral is then applied to each control volume, and using the Gaussian divergence theorem, the volume integral is transformed into a surface integral over the control volume surface, yielding the discretized equations: in It's about controlling the volume. It is a surface that controls volume. It is the unit vector of the surface outward normal. The directional component. For calculating surface flux. The physical quantities on both sides of the control volume surface are interpolated using a first-order upwind scheme.

[0031] The second-order Runge-Kutta method uses time-progression to solve the discretized equations to obtain flow field solutions at different times. The time-progression process consists of two steps: prediction and correction. Prediction step: Calibration step: In some optional embodiments, the database construction process employs the Freeform Surface Deformation (FFD) method to deform the aircraft's shape. Under design conditions of Mach 1.8 and an angle of attack of 0.35, the initial shape of the aircraft is perturbed using the Latin hypercube sampling method at 33 FFD control points, successfully obtaining 600 different shapes. Subsequently, the Euler equation is used to calculate 600 low-fidelity near-field overpressure distributions using a Cartesian mesh. Next, for the structural mesh of the first 100 shapes, the RANS equation (Reynolds-averaged Navier-Stokes equations) is used to calculate their high-fidelity near-field overpressure distributions. The final database includes 600×33 FFD control points as the shape variable x and 600×1000 low-fidelity near-field overpressure distributions as variables. The high-fidelity near-field overvoltage distribution of the first 100 x values ​​(100×1000) is used as a variable. .

[0032] refer to Figure 8 As shown, the multi-fidelity deep neural network based on transfer learning follows the deep learning pre-training-fine-tuning paradigm and mainly includes the following two stages. The first stage is the pre-training stage, which uses a large amount of low-fidelity data. omnidirectional training of low-fidelity neural networks In this process, the frozen layers (FL) play a crucial role in feature extraction, and then the trainable layers (TL) perform low-fidelity prediction based on the extracted features. The formula is: By optimizing low-fidelity neural networks The loss function improves low-fidelity prediction; the loss function of a low-fidelity neural network is... , where θ F For the network parameters of the frozen layer, θ T,L For the network parameters of the trainable layers, x L Z is the input sample for low-fidelity data. L For the frozen layer FL to low-fidelity input x L Extracted feature vectors; Let TL be the predicted value of the low-fidelity output of the trainable layer, FL(▪) be the feature extraction operation of the frozen layer, and TL(▪) be the prediction operation of the trainable layer; m L The number of samples in the low-fidelity training dataset; y L,i Let y be the true value of the i-th low-fidelity sample; * L,i λ is the output value predicted by the network for the i-th low-fidelity sample; L θ is the regularization coefficient. i,F θ is the i-th parameter in the frozen layer FL; j,T,L Let be the j-th parameter in the trainable layer TL. The relationship between the loss function and low-fidelity prediction is: Low-fidelity loss function It consists of two parts, the first being the error term. The first step is to calculate the mean square error between the predicted and actual values, which directly reflects the degree of deviation between the "low-fidelity prediction result" and the "actual value," driving the network to learn to accurately map the low-fidelity input-output relationship; the second step is the regularization term. L2 regularization is applied to the parameters of the frozen layer and the trainable layer to constrain the parameter size, prevent the network from reducing its generalization ability due to overfitting to low-fidelity data, and indirectly ensure the stability and reliability of low-fidelity prediction.

[0033] The process of optimizing the loss function is as follows: First, initialize the parameters of the frozen layer randomly. and trainable layer parameters Forward propagation: passing low-fidelity input... The input network is processed by freezing layers to obtain features. The predicted value is then calculated by the trainable layer. Calculate the loss based on the true label. Calculated according to the loss function formula (Including error and regularization terms); Backpropagation, based on the chain rule, calculates the gradients of the network parameters from the loss value, such as for... Differentiate, Parameter updates are performed using the optimizer Adam to adjust the parameters of the trainable layers based on the gradients. ,Right now , Set the learning rate; iterate and optimize, repeating the process of "forward propagation → calculate loss → back propagation → parameter update" until the loss converges, thus completing the low-fidelity network training.

[0034] The second stage is the fine-tuning stage. At this stage, the custom TF-DNN network does not require rebuilding a new neural network model. Instead, it is fine-tuned by transferring the network architecture of the pre-trained network and the parameters of the frozen layer FL. Then, the network parameters of the trainable layers TL are randomly initialized. and utilize high-fidelity data train This enables trainable layers to implicitly capture relationships between multi-fidelity data, thereby achieving high-fidelity neural networks. The construction formula is as follows: Finally, the loss function was optimized to fine-tune the TL layer, thus perfecting the high-fidelity network training and the high-fidelity neural network NN. H The loss function is Among them, Z H For the frozen layer FL, high-fidelity input x H Extracted feature vector, x H For the input samples of high-fidelity data, FL(▪) is the feature extraction operation of the frozen layer FL, and θ F For the network parameters of the frozen layer, y * H Let θ be the prediction value of the high-fidelity output by the trainable layer TL, and TL(▪) be the prediction operation of the trainable layer TL. T，H For the network parameters of high-fidelity trainable layers, Loss H Let m be the total loss value of the high-fidelity neural network. H y represents the number of samples in the high-fidelity training dataset. H,i Let y be the true value of the i-th high-fidelity sample; H1,i λ is the predicted output value of the i-th high-fidelity sample; HTo ensure high fidelity regularization coefficients and control parameter complexity; θ j,T,H Let j be the j-th parameter of the high-fidelity trainable layer.

[0035] The process of optimizing the loss function involves initialization, randomly initializing the trainable layer parameters. Load the frozen layer parameters obtained from pre-training. Forward propagation transmits high-fidelity input. The input network is processed by freezing layers to obtain features. The predicted value is then calculated by the trainable layer. Calculate the loss based on the true label. Calculated according to the loss function formula (Including error and regularization terms); Backpropagation, based on the chain rule, calculates the gradients of the network parameters from the loss value, such as... Differentiate, Parameter updates are performed using the optimizer Adam to adjust the parameters of the trainable layers based on gradients. , Set the learning rate; iterate and optimize, repeating the process of "forward propagation → calculate loss → back propagation → parameter update" until the loss converges, thus completing the high-fidelity network training.

[0036] In some optional embodiments, the network architecture shown in Table 1 can be used during training, where the first three layers are fixed as frozen layers (FL) and the last layer is a trainable layer (TL). The pre-training phase uses 600 training samples. The dataset was divided into 512 training samples and 88 test samples. During the fine-tuning phase, 100 training samples were used. The dataset was divided into 92 training sets and 8 test sets. The network was trained using the Adam (Adaptive Moment Estimation) optimizer. During the pre-training phase, the epoch was 3000 and the batch size was 32. During the fine-tuning phase, the epoch was 6000 and the batch size was 8. Here, epoch refers to the process of the network completely traversing the entire training dataset once, batch refers to the number of training data sets, InputFeatures refers to the input features, and OutputFeatures refers to the output features.

[0037] Table 1. Multifidelity deep neural network architecture based on transfer learning

[0038] The training results are shown in Table 2. During the pre-training stage, thanks to the sufficient low-fidelity training samples, the model can achieve good prediction accuracy. TF-NNL is a low-fidelity neural network for transfer learning, TF-NNH is a high-fidelity neural network for transfer learning, Train_MSE is the mean square error of the training set, Test_MSE is the mean square error of the test set, and λ is the regularization coefficient.

[0039] Table 2. Prediction results of multi-fidelity deep neural networks based on transfer learning.

[0040] Further analysis was conducted using the TF-NNH model with λ=1e-2. Its maximum root mean square error (RMSE) was 9.84e-7, and its minimum RMS error was 2.34e-8. The root mean square error histogram was compared with the prediction result showing the largest error. Figure 10 As shown in the figure. Eight shapes (3, 14, 17, 28, 31, 35, 81, and 94) were selected from the test set to verify the model's sonic boom prediction accuracy. Specifically, the trained model was first used to obtain the predicted values ​​of the near-field overpressure distribution (HF) based on the shape. Then, the near-field overpressure distribution was transformed to the far-field using the Burgers equation, and the perceived sound pressure level (PLdB) was evaluated using Stevens' Mark VII method. The comparison results are detailed in Table 3. It can be seen that the absolute error of the sonic boom is within 2.7%, the relative error is within 2.7%, and the average relative error on the test set is 0.95%.

[0041] Table 3. Comparison of prediction accuracy for far-field sonic boom values ​​using multi-fidelity deep neural networks based on transfer learning (unit: PLDB)

[0042] Next, a single-fidelity deep neural network (DNN-H) was trained to learn from 100 sets of high-fidelity data, serving as a control group. 100 sets of high-fidelity near-field overpressure distributions were used as training samples, divided into 92 training sets and 8 test sets. A four-layer deep neural network was used to increase model complexity; in the table, FC represents a fully connected layer. The number of neurons in the first three layers increases approximately proportionally to effectively amplify the features of the input data. The difference lies in the number of neurons in the fourth layer (see Table 4). The network was trained using the Adam optimizer with epochs of 5000 and batches of 8. The training results are shown in Table 5.

[0043] Table 4 Single-fidelity deep neural network architecture design

[0044] Table 5 Analysis of Training Results of Single-Fidelity Deep Neural Networks

[0045] The choice of regularization coefficient λ has a certain impact on the model results, which may be due to both the model architecture and the characteristics of near-field sound pressure data. Further analysis was conducted using the DNN-H model with the best performance at λ=0.001 (maximum root mean square error of 2.03e-6, minimum root mean square error of 7.90e-8). The prediction results of its root mean square error histogram were compared with those of the model with the maximum root mean square error. Figure 11 As shown in Table 6, the prediction accuracy of sonic booms for all shapes in the test set was then compared. The maximum relative error was 4.05%, and the average relative error on the test set was 2.67%.

[0046] Table 6 Comparison of sonic boom values ​​predicted by single-fidelity deep neural networks (unit: PLDB)

[0047] Compared to the single-fidelity deep neural network model DNN-H, the multi-fidelity deep neural network TL-DNN based on transfer learning has significant advantages. In the high-fidelity near-field overpressure distribution prediction task, the error on the training set was reduced by one order of magnitude, the error on the test set was reduced by more than 50%, and the maximum prediction error for a single shape was reduced from 2e-6 to 3e-8, a reduction of approximately two orders of magnitude. Looking at the results of sonic boom prediction, the maximum relative error was significantly reduced from 4% to less than 0.6%, and the average relative error on the test set was reduced from 2.67% to 0.22%, resulting in a substantial improvement in prediction accuracy.

[0048] Then according to Figure 2 As shown, a high-reliability sonic boom prediction method is combined with a genetic algorithm for the inverse design of the target near-field overpressure distribution. The genetic algorithm can employ a gradient-free optimization algorithm (NSGA-II). For the genetic operators, different operations are selected to simulate the biological evolution process. The crossover operator uses two-point crossover, exchanging partial genes between two individuals to achieve gene recombination and increase population diversity. The mutation operator uses Gaussian mutation, mutating individual genes with a mean of 0 and a standard deviation of 0.2, with each gene having a mutation probability of 0.05. By introducing new gene information, the algorithm avoids getting trapped in local optima. The selection operator uses tournament selection, randomly selecting 5 individuals from the population each time, choosing the individual with the best fitness, retaining superior genes, and driving the population towards a better evolutionary direction.

[0049] The fitness evaluation function is crucial for measuring the quality of individuals. To improve the algorithm's fitness, an adaptive crossover and mutation probability adjustment mechanism was designed. Based on the fitness values ​​of individuals in the population, the crossover and mutation probabilities are dynamically adjusted. Individuals with high fitness have lower crossover and mutation probabilities, while individuals with low fitness have higher probabilities. This achieves a balance between global and local search, improving the algorithm's optimization efficiency and quality.

[0050] Initial population 50, optimization generations 100, optimization results as follows Figure 12 As shown, the waveform corresponding to the near-field overpressure distribution propagated to the ground using the generalized Burgers equation is as follows: Figure 13 As shown, the perceived ground sound pressure level obtained is 84.53 PLdB. Compared with the initial scheme, the loudness of the ground sonic boom is reduced by 3.6%.

Claims

1. A method for low-explosive anti-tank design of aircraft based on transfer learning multi-fidelity neural networks, characterized in that, include: Obtain the initial configuration of the aircraft and generate the initial near-field overpressure distribution based on the initial configuration information; The initial near-field overvoltage distribution is parameterized, and the parameterized first near-field overvoltage distribution is propagated to the far field. The far-field sonic boom value is calculated based on the parameterized first near-field overpressure distribution. A proxy optimization model is constructed, and the target near-field overpressure distribution is optimized by combining the far-field sonic boom value. Based on the generated target near-field overpressure distribution, the target aircraft shape is obtained through reverse design using a transfer learning multi-fidelity neural network.

2. The aircraft low-sonic blast anti-tank design method based on transfer learning multi-fidelity neural network according to claim 1, characterized in that, The initial near-field overpressure distribution is parameterized by parametrically representing the overpressure values ​​of key feature points in the initial near-field overpressure distribution. The key feature points include local extreme points and the midpoint between two extreme points in the initial near-field overpressure distribution. The key feature points are used as control points of spline curves, and the near-field overpressure distribution is parameterized by spline curves.

3. The aircraft low-sonic bomb anti-tank design method based on transfer learning multi-fidelity neural network according to claim 1, characterized in that, The parameterized first near-field overvoltage distribution is propagated to the far field, including propagating the parameterized first near-field overvoltage distribution to the far field based on the generalized Burgers equation.

4. The aircraft low-sonic bomb anti-tank design method based on transfer learning multi-fidelity neural network according to claim 1, characterized in that, The far-field sonic boom value is calculated based on the parameterized first near-field overpressure distribution, including calculating the ground sonic boom wave using the Mark VII method based on the parameterized first near-field overpressure distribution transmitted to the far field.

5. The aircraft low-sonic bomb anti-tank design method based on transfer learning multi-fidelity neural network according to claim 1, characterized in that, A surrogate optimization model is constructed, which, in conjunction with the far-field sonic boom value, optimizes and generates the target near-field overpressure distribution. This includes combining the far-field sonic boom value, using Latin hypercube sampling to generate initial sample points and calculating the objective function value of the sample points, constructing a Kriging surrogate optimization model, and using a point addition method based on the standardization prediction error maximization criterion and the expected improvement criterion. Through multiple iterations and continuous expansion of sample points, the optimal solution is gradually approximated to generate the target near-field overpressure distribution.

6. The aircraft low-sonic bomb anti-tank design method based on transfer learning multi-fidelity neural network according to claim 1, characterized in that, Based on the output target near-field overpressure distribution, the target aircraft shape is obtained by inverse design using a transfer learning multi-fidelity neural network. This includes constructing a multi-fidelity aircraft near-field overpressure distribution prediction method based on transfer learning, and using a genetic algorithm to inverse design the target aircraft shape based on the output target near-field overpressure distribution.

7. The method for low-sonic bombardment anti-tank design of aircraft based on transfer learning multi-fidelity neural networks according to claim 6, characterized in that, A multi-fidelity near-field overpressure distribution prediction method for aircraft is constructed based on transfer learning. This method includes building a multi-fidelity database, pre-training the model based on low-fidelity near-field overpressure distribution data, fine-tuning the model using high-fidelity near-field overpressure distribution data, implicitly capturing the relationship between high-fidelity and low-fidelity data, and constructing a highly reliable near-field overpressure distribution prediction method for aircraft.

8. The aircraft low-sonic bomb anti-tank design method based on transfer learning multi-fidelity neural network according to claim 7, characterized in that, A near-field overpressure distribution database was constructed, including the deformation of the aircraft shape based on the freeform surface deformation method (FFD), and the perturbation of the freeform surface deformation control points of the initial shape of the aircraft using the Latin hypercube sampling method to obtain different aircraft shapes.

9. The aircraft low-sonic bomb anti-tank design method based on transfer learning multi-fidelity neural network according to claim 7, characterized in that, The model was pre-trained based on low-fidelity near-field overpressure distribution data, including selecting an orthogonal Cartesian grid as the coarse grid, obtaining the low-fidelity near-field sonic boom overpressure distribution by solving the Euler equation, and based on the low-fidelity data (x L y L Training a low-fidelity neural network (NN) L Feature Z is extracted through the frozen layer FL. L The trainable layer TL performs low-fidelity predictions based on the extracted features. The formula is By optimizing low-fidelity neural networks The loss function improves low-fidelity prediction, and low-fidelity neural networks. The loss function is Where, θ F For the network parameters of the frozen layer, θ T,L For the network parameters of the trainable layers, x L Z is the input sample for low-fidelity data. L For the frozen layer FL to low-fidelity input x L Extracted feature vectors; Let TL be the predicted value of the low-fidelity output of the trainable layer, FL(▪) be the feature extraction operation of the frozen layer, and TL(▪) be the prediction operation of the trainable layer; m L The number of samples in the low-fidelity training dataset; y L,i Let y be the true value of the i-th low-fidelity sample; * L,i λ is the output value predicted by the network for the i-th low-fidelity sample; L θ is the regularization coefficient. i,F θ is the i-th parameter in the frozen layer FL; j,T,L Let j be the j-th parameter in the trainable layer TL.

10. The aircraft low-sonic bomb anti-tank design method based on transfer learning multi-fidelity neural network according to claim 7, characterized in that, The model was fine-tuned using high-fidelity near-field overvoltage distribution data, including calculating the high-fidelity near-field overvoltage distribution based on the RANS equation, transferring the network architecture of the pre-trained network, and adjusting the parameters θ of the frozen layer FL. F Randomly initialize the network parameters θ of the trainable layer TL. T,H Using high-fidelity data (x H y H Training θ T,H Trainable layers implicitly capture the relationships between multi-fidelity data, constructing a high-fidelity neural network (NN). H The formula is: Optimize the loss function and fine-tune the trainable layers TL to improve the training of the high-fidelity network. The loss function of the high-fidelity neural network NNH is: Among them, Z H For the frozen layer FL, high-fidelity input x H Extracted feature vector, x H For the input samples of high-fidelity data, FL(▪) is the feature extraction operation of the frozen layer FL, and θ F For the network parameters of the frozen layer, y * H Let θ be the prediction value of the high-fidelity output by the trainable layer TL, and TL(▪) be the prediction operation of the trainable layer TL. T，H For the network parameters of high-fidelity trainable layers, Loss H Let m be the total loss value of the high-fidelity neural network. H y represents the number of samples in the high-fidelity training dataset. H,i Let y be the true value of the i-th high-fidelity sample; H1,i λ is the predicted output value of the i-th high-fidelity sample; H To ensure high fidelity regularization coefficients and control parameter complexity; θ j,T,H Let j be the j-th parameter of the high-fidelity trainable layer.

Images