Low-resistance and low-sound-explosion optimization method for aircraft

Abstract

The invention relates to a low-resistance and low-sound-explosion optimization method for an aircraft, and belongs to the technical field of pneumatic and acoustic comprehensive design of aircrafts. The method comprises the following steps: step 1, constructing an aircraft performance database; 2, constructing a multi-fidelity deep neural network model AMF-DNN based on a linear and nonlinear comprehensive correction strategy; step 3, training and sound explosion prediction are carried out by using the multi-fidelity deep neural network model AMF-DNN; 4, constructing a high-fidelity aerodynamic neural network model DNN-AERO and a low-fidelity near-field overvoltage distribution neural network model DNN-L; and step 5, combining a high-credibility performance prediction method with a genetic algorithm to construct an aircraft acoustic explosion optimization system for optimization design. According to the method, the genetic algorithm is preferably selected as a global optimization method, and especially in a comprehensive optimization scene oriented to double targets of aerodynamic performance and acoustic detonation characteristics of the aircraft, collaborative optimization of two project targets of aerodynamic efficiency improvement and acoustic detonation intensity suppression is achieved.

Description

Technical Field

[0001] This invention relates to the field of aircraft aerodynamic shape design technology, and more particularly to the field of low-drag, low-detonation optimization design technology for supersonic aircraft, specifically a low-drag, low-detonation optimization method for aircraft that integrates a multi-fidelity neural network with correction strategies. Background Technology

[0002] In the global development of aerospace technology, although high-subsonic passenger aircraft have achieved great success, with the ever-increasing demand for air transport, supersonic passenger aircraft have become the key direction for future civil aircraft development. Currently, the development of supersonic passenger aircraft faces two urgent problems: sonic boom and fuel efficiency.

[0003] The sonic boom problem was the root cause of the failures of early supersonic passenger aircraft like the Concorde and Tu-144, ultimately forcing them out of the market. The massive sonic boom limited the aircraft to supersonic flight only over the ocean or in remote, sparsely populated areas of land, deviating from their supersonic design conditions and leading to a sharp decline in performance and economic efficiency. Especially in my country's domestic air routes, which are almost entirely over land, future supersonic passenger aircraft must possess supersonic cruise capability over land to fully leverage their speed advantage. Therefore, sonic boom assessment and suppression technologies have become core and critical technologies that must be overcome.

[0004] Low fuel efficiency leads to economic problems such as excessively high aircraft operating costs. Reducing overall drag is one of the most effective ways to improve fuel economy. Among various drag reduction methods, aerodynamic optimization design technology has gradually become an efficient and practical approach in modern aircraft design.

[0005] The design of supersonic passenger aircraft is inherently a multidisciplinary problem. Aerodynamic and sonic boom characteristics are coupled yet contradictory in the design process. Considering only one discipline often leads to the deterioration of the other characteristic, resulting in poor engineering practicality. Currently, most designs for supersonic passenger aircraft still separate the design of aerodynamic and sonic boom characteristics, with few comprehensively considering both disciplines and employing high-precision methods for the evaluation and design of supersonic passenger aircraft. Summary of the Invention

[0006] This invention aims to propose a method for optimizing low-drag and low-sonic-bang aircraft, specifically involving multi-fidelity neural network modeling and evolutionary optimization techniques that integrate correction strategies. Addressing the challenge of multi-peak distribution in the three-dimensional aircraft design space and the tendency of traditional optimization methods to get trapped in local optima, this invention employs a genetic algorithm as a global optimization tool. By simulating natural selection and genetic mechanisms, it starts from multiple initial designs and combines genetic operators such as crossover and mutation to perform a global search in the high-dimensional design space, possessing the ability to escape local optima. Especially in the dual-objective optimization of aircraft aerodynamic performance and sonic boom characteristics, the genetic algorithm can explore multiple potential optimal solution regions in parallel, avoiding getting trapped in local optima due to a single indicator. This achieves synergistic optimization of aerodynamic efficiency improvement and sonic boom intensity suppression, enhancing the convergence and globality of multi-objective optimization. This method is applicable to multi-objective and multi-constraint design scenarios in the overall layout optimization of aircraft.

[0007] Step 1: Constructing the Aircraft Performance Database. Based on the initial aircraft shape, parametric shape modeling is performed using the Freeform Surface Deformation (FFD) method; perturbation sampling is performed on multiple control points to obtain several deformable shapes; computational fluid dynamics methods are used to solve the coarse mesh to obtain low-fidelity near-field overpressure distribution and high-fidelity aerodynamic data corresponding to each shape; for some shapes, structured meshes and high-precision equations are used to solve their high-fidelity near-field overpressure distribution, constructing a multi-fidelity database containing shape parameters, low-fidelity sonic boom data, and high-fidelity data.

[0008] Based on orthogonal Cartesian grids and combined with the Euler equations, low-fidelity near-field overpressure distribution and corresponding aerodynamic data are obtained; at the same time, structured grids are used and RANS equations are solved to obtain high-fidelity near-field sonic boom overpressure distribution.

[0009] Step 2: Construct a multi-fidelity deep neural network model AMF-DNN based on a combined linear and nonlinear correction strategy. Specifically, this includes: constructing a generalized autoregressive structure that includes the relationship between low-fidelity and high-fidelity data, with the correlation function consisting of linear and nonlinear subnetworks; and dynamically adjusting the weight distribution of the linear and nonlinear networks according to the correlation between the data by adjusting the adaptive parameters to achieve adaptive learning of multi-fidelity relationships by the model.

[0010] The loss function of the multifidelity deep neural network model AMF-DNN includes a main loss term, a regularization term, and an adaptive search term; two independent networks are used. and Let's learn separately. and Used to explore the relationship between low-fidelity and high-fidelity data, among which, To explore the linear part Networks with interconnected relationships do not contain activation functions; To explore the nonlinear part A network of relationships containing non-linear activation functions.

[0011] Step 3: Training and sonic boom prediction using the multi-fidelity deep neural network model AMF-DNN, specifically including: training and testing the AMF-DNN model using the constructed multi-fidelity database; combining the near-field sonic boom prediction results with the propagation model to convert the near-field signal into a far-field sonic boom signal and evaluating the ground-sensing sound pressure level; verifying the model's sonic boom prediction accuracy on different shapes by comparing it with actual high-fidelity data; then training a benchmark neural network model as a performance comparison, specifically including: constructing a single-fidelity deep neural network model DNN-H, using high-fidelity data as input training samples; comparing the differences between this model and the multi-fidelity deep neural network model AMF-DNN in terms of prediction accuracy and generalization ability.

[0012] A high-reliability, fast sonic boom prediction method is developed, which uses the generalized Burgers equation to transform the near-field overpressure distribution to the far-field and evaluates the perceived sound pressure level by the human ear using the Stevens' Mark VII method. A benchmark neural network model is further trained as a performance comparison, specifically including: constructing a single-fidelity deep neural network model DNN-H with high-fidelity data as input training samples; and comparing the differences between this model and the multi-fidelity deep neural network model AMF-DNN in terms of prediction accuracy and generalization ability.

[0013] Step 4: Construct a high-fidelity aerodynamic neural network model DNN-AERO and a low-fidelity near-field overpressure distribution neural network model DNN-L.

[0014] Traditional neural network modeling relies heavily on high-fidelity data and suffers from insufficient performance when samples are scarce. Furthermore, the grid size required for high-precision overpressure distribution calculations is typically 5–10 times that of aerodynamic calculations, making it difficult to obtain high-fidelity samples in batches. Therefore, this invention proposes a multi-fidelity modeling method that integrates linear / nonlinear correction strategies with adaptive search, making full use of a large number of low-fidelity samples to improve modeling accuracy under conditions of scarce high-fidelity samples.

[0015] Step 5: A high-reliability performance prediction method combined with a genetic algorithm is used to construct an aircraft sonic boom optimization system for optimization design. Specifically, this includes: setting the shape parameters as design variables, with the optimization objectives being low sonic boom and high lift-to-drag ratio; setting multiple genetic operators (such as crossover, mutation, and selection), combined with an adaptive parameter adjustment mechanism to improve search efficiency and robustness; and achieving multi-objective evolutionary optimization with the support of neural network prediction to obtain the optimal shape solution that combines low sonic boom and high aerodynamic performance.

[0016] A genetic algorithm optimization process was constructed, setting the shape parameters as design variables and low sonic boom and high lift-to-drag ratio as optimization objectives. Multiple genetic operators, including crossover, mutation, and selection, were implemented to improve search efficiency. Different operations were selected to simulate the biological evolution process. The crossover operator used two-point crossover, exchanging partial genes from two individuals to achieve gene recombination and increase population diversity. The mutation operator employed Gaussian mutation, introducing new genetic information to avoid the algorithm getting trapped in local optima. An adaptive parameter adjustment mechanism was adopted to dynamically adjust genetic parameters based on individual fitness, achieving global and local balance in the optimization process. With model prediction support, multi-objective evolutionary optimization of the aircraft's shape was performed to obtain the optimal shape solution that meets the requirements of low sonic boom and high aerodynamic performance.

[0017] This invention provides an efficient and feasible aerodynamic shape optimization design method for low-drag, low-sonic-bang aircraft design. The beneficial effects of this invention are: I. A multi-fidelity deep neural network is constructed using a linear / nonlinear integrated correction strategy that integrates adaptive search methods, so that the mapping relationship between the aircraft shape and the near-field overpressure distribution can still be accurately captured even when high-fidelity data is scarce. II. A high-reliability, fast sonic boom prediction method is adopted, which uses a neural network to predict the aircraft shape to the near-field overpressure distribution, then uses the generalized Burgers equation to transform the near-field overpressure distribution to the far field, and evaluates the sound pressure level perceived by the human ear as the sonic boom value using the Stevens' Mark VII method. Third, by utilizing the accuracy of aerodynamic force calculations based on low-fidelity near-field overpressure distribution to achieve the standard of high-fidelity aerodynamic force, and with sufficient sampling calculations, there is no need to separately sample aerodynamic force and incur additional costs, allowing for the direct construction of a highly reliable drag prediction model. Fourth, a high-reliability sonic boom prediction model and drag prediction model are combined with a genetic algorithm to construct a sonic boom optimization framework for aircraft. The genetic algorithm is used to carry out a multi-objective optimization problem of finding the aerodynamic and sonic boom objectives of the aircraft. It can search in multiple possible optimal solution regions and is not limited to a certain local optimal combination, thus it is possible to find a better solution that simultaneously satisfies the requirements of aerodynamic optimization and low sonic boom. Attached Figure Description

[0018] Figure 1 Schematic diagram of a high-reliability, low-drag, low-sonic-bang optimization system for aircraft.

[0019] Figure 2 Schematic diagram of the database construction process.

[0020] Figure 3 A schematic diagram of a multi-fidelity deep neural network that integrates linear / nonlinear comprehensive correction strategies with adaptive search methods.

[0021] Figure 4 A schematic diagram of the layout configuration of a supersonic passenger aircraft.

[0022] Figure 5 Schematic diagrams of meshes with different fidelities under the initial configuration.

[0023] Figure 6 A schematic diagram comparing the near-field overvoltage distribution at different fidelities under the initial configuration.

[0024] Figure 7 A schematic diagram of the prediction results of the AMF-DNN model.

[0025] Figure 8 A schematic diagram of the prediction results of the DNN-H model.

[0026] Figure 9 A schematic diagram of a single-fidelity deep neural network.

[0027] Figure 10 Pareto leading edge for sonic boom and lift-to-drag ratio.

[0028] Figure 11 Comparison of geometric shapes before and after optimization.

[0029] Figure 12 Comparison of near-field overvoltage distribution before and after optimization.

[0030] Figure 13 Comparison of far-field overvoltage signals before and after optimization. Detailed Implementation

[0031] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are merely descriptive and not limiting, and should not be construed as limiting the scope of protection of the present invention.

[0032] like Figure 1 A schematic diagram of an aircraft sonic boom optimization framework constructed by combining a high-reliability sonic boom prediction method with a genetic algorithm is shown. An aircraft sonic boom multi-fidelity optimization method that integrates an adaptive search comprehensive correction strategy consists of the following steps.

[0033] Step 1: Constructing the Aircraft Performance Database. Based on the initial aircraft shape, parametric shape modeling is performed using the Freeform Surface Deformation (FFD) method; perturbation sampling is performed on multiple control points to obtain several deformable shapes; computational fluid dynamics methods are used to solve the coarse mesh to obtain low-fidelity near-field overpressure distribution and high-fidelity aerodynamic data corresponding to each shape; for some shapes, structured meshes and high-precision equations are used to solve their high-fidelity near-field overpressure distribution, constructing a multi-fidelity database containing shape parameters, low-fidelity sonic boom data, and high-fidelity data.

[0034] Based on the initial shape and parameters of the aircraft, multiple perturbation shapes are generated using the freeform surface deformation (FFD) method; in one embodiment, the aircraft is a supersonic aircraft, based on... Figure 4 The layout configuration of a certain supersonic passenger aircraft shown is used as the initial shape. Its fuselage length is 49m, its wingspan is 16.8m, and its reference area is 72m². 2 The cruising Mach number is set to 1.8, and the cruising altitude is 18km.

[0035] The calculation of high-fidelity and low-fidelity data is based on practical engineering considerations. In one embodiment, to capture accurate near-field overpressure distribution, a dense grid with 40 million grid points is used, which remains computationally expensive even when using the Eluer equation. Therefore, an orthogonal Cartesian grid with 4-5 million grid points is used as a coarse grid. Then, the low-fidelity near-field overpressure distribution and high-fidelity aerodynamic forces are obtained by solving the Eluer equation. The numerical results of solving the near-field overpressure distribution using the Eluer equation have high accuracy. Although the Cartesian grid method may have difficulty capturing minute changes in shock waves, the accuracy still meets the requirements of the conceptual design stage. Therefore, this invention uses a Cartesian grid and the Eluer equation to obtain a large number of low-fidelity near-field overpressure distributions.

[0036] In one embodiment, a small number of high-fidelity near-field overpressure distributions are obtained using a 10x denser structured mesh and a RANS solver. Taking the initial shape as an example, the mesh used is the calculated near-field overpressure distribution, as shown below. Figure 5 and Figure 6 As shown. Figure 5 These are schematic diagrams of meshes with different fidelity levels under the initial configuration. The left (a) is a schematic diagram of the Cartesian coarse mesh, and the right (b) is a schematic diagram of the structured mesh. Both sets of meshes have been refined in the near field to improve the accuracy of the near-field wave system as much as possible during low-fidelity calculations. Figure 6 This is a schematic diagram comparing the near-field overvoltage distribution at different fidelities under the initial configuration.

[0037] Database construction process as follows Figure 2 As shown, specifically, in one embodiment, under the design conditions of Mach 1.8 and an angle of attack of 0.35, the initial shape's 33 freeform surface deformation (FFD) control points were perturbed using the Latin hypercube sampling method, successfully obtaining 600 different shapes. Subsequently, the Euler equation was used to calculate 600 low-fidelity near-field overpressure distributions and high-fidelity aerodynamic forces using a Cartesian mesh. Next, for the structural mesh of the first 100 shapes, the RANS equation was used to calculate their high-fidelity near-field overpressure distributions. The final database covers 600×33 freeform surface deformation (FFD) control points as shape variables. xA low-fidelity near-field overvoltage distribution of 600×1000 and a high-fidelity near-field overvoltage distribution of 100×1000 (corresponding to the first 100 x's) are used as variables. .

[0038] Step 2: Construct a multi-fidelity deep neural network model AMF-DNN based on a combined linear and nonlinear correction strategy. Specifically, this includes: constructing a generalized autoregressive structure that includes the relationship between low-fidelity and high-fidelity data, with the correlation function consisting of linear and nonlinear subnetworks; and dynamically adjusting the weight distribution of the linear and nonlinear networks according to the correlation between the data by adjusting the adaptive parameters to achieve adaptive learning of multi-fidelity relationships by the model.

[0039] First, a multi-fidelity deep neural network model, AMF-DNN, is constructed based on a combined linear and nonlinear correction strategy, such as... Figure 3 As shown, its theoretical core is the generalized autoregressive scheme in formula (1):

[0040] in, For low-fidelity input, For low-fidelity data, For high-fidelity input, This is a low-fidelity result when inputting high-fidelity data. For high-fidelity data, F This represents the association function between high-fidelity data and low-fidelity data, and... F Further decomposed into linear parts and nonlinear part .

[0041] Use two independent networks and Let's learn separately. and Used to explore the relationship between low-fidelity and high-fidelity data, among which, To explore the linear part Networks with interconnected relationships do not contain activation functions; To explore the nonlinear part The network of relationships includes a non-linear activation function. Both types of networks use high-fidelity inputs. and its corresponding low-fidelity result when inputting high-fidelity data. The output is and .in, This represents the output of the linear layer. This represents the output of the nonlinear layer.

[0042] Furthermore, in practice, the specific correlations between data points are often unknown beforehand. Therefore, a key aspect of model design is designing a function g that enables the model to adaptively explore the linear and nonlinear correlations between high / low fidelity data.

[0043] Initially, the distinction between linear and nonlinear relationships relied primarily on the regularization of network parameters. When the regularization coefficient was too small, the model tended to approximate a linear relationship using a nonlinear function due to the inherent nonlinearity of the neural network, leading to frequent overfitting. Conversely, when the regularization coefficient was too large, the model's nonlinearity was weakened, resulting in underfitting. Since the optimal value of the regularization coefficient depends on multiple factors, including data distribution, model complexity, and problem characteristics, it requires extensive experimentation and tuning. Furthermore, obtaining the optimal regularization coefficient is difficult when high-fidelity validation datasets are lacking.

[0044] To address the aforementioned problems, this invention sets an adaptive search term to determine the weights of linear and nonlinear relationships in the prediction. Specifically, the loss function corresponding to the linear relationship between multi-fidelity data is used... Loss function added to the model In the middle, and the network's prediction values ​​for high-fidelity data. and Parameters that change The correlation is shown in formulas (3)-(5).

[0045] Where c is a constant, with a recommended value of 100. This is so that when the relationship between multifidelity data is non-linear, the parameter... The closer to 1, the better, especially when there is a linear relationship between multifidelity data. parameters It will tend to become 0. Thus, Able to be based on The value of is adaptively adjusted, thus determining the weights of linear and nonlinear relationships in the prediction. Its model's loss function for

[0046] In the formula, Indicates the number of samples. Represents the regularity coefficient. The regularization coefficients of a high-fidelity network are represented. This represents the sum of squares of the parameters of a high-fidelity network.

[0047] Step 3: Training and sonic boom prediction using the multi-fidelity deep neural network model AMF-DNN, specifically including: training and testing the AMF-DNN model using the constructed multi-fidelity database; combining the near-field sonic boom prediction results with the propagation model to convert the near-field signal into a far-field sonic boom signal and evaluating the ground-sensing sound pressure level; verifying the model's sonic boom prediction accuracy on different shapes by comparing it with actual high-fidelity data; then training a benchmark neural network model as a performance comparison, specifically including: constructing a single-fidelity deep neural network model DNN-H, using high-fidelity data as input training samples; comparing the differences between this model and the multi-fidelity deep neural network model AMF-DNN in terms of prediction accuracy and generalization ability.

[0048] In one embodiment, the network architecture shown in Table 1 is used. The training samples are the relevant data corresponding to the first 100 shapes, which are divided into 92 training sets and 8 test sets. The network is trained using the Adam optimizer, with epoch=30000 and batch=8. FC1, FC2, and FC3 represent fully connected layers 1, 2, and 3, respectively.

[0049] Table 1. Design of Multifidelity Deep Neural Network Architecture Based on Linear / Nonlinear Synthetic Correction

[0050] The training results after independent normalization of high-fidelity and low-fidelity data are shown in Table 2, and the results after mixing and then normalizing are shown in Table 3. Combining the two tables, it can be seen that the normalization method has minimal impact on the model, and the regularization coefficient also has a limited impact on the two models. This indicates that the adaptive search method effectively captures both linear and nonlinear relationships between the data, improving the robustness of the multi-fidelity deep neural network model AMF-DNN (hereinafter referred to as the "AMF-DNN model").

[0051] Since the normalization method has a minimal impact, this invention is based on the results of the more commonly used independent normalization. According to Table 2, the AMF-DNN model with a regularization coefficient λ=0.001 (its maximum root mean square error is 3.11e-8, and its minimum root mean square error is 1.14e-9) is selected for further analysis. Its root mean square error histogram is shown below. Figure 7 See (a) for a comparison with the prediction result with the largest error. Figure 7 (b)

[0052] Table 2. Training results of AMF-DNN after independent normalization

[0053] Table 3. Training results of AMF-DNN after hybrid normalization.

[0054] Given the severe overfitting of the model, eight shapes (3, 14, 17, 28, 31, 35, 81, and 94) from the test set, and shape 4 (with the largest error in the training set), were selected as representatives to verify the model's sonic boom prediction accuracy. Specifically, considering the ease of solving the generalized Burgers equation in acoustic methods (approximately 3 minutes per calculation), the cost of sonic boom calculation is mainly concentrated on CFD calculation of the near-field overpressure distribution. Therefore, this invention proposes to first use the trained model to obtain the predicted value of the near-field overpressure distribution based on the shape, and then use the generalized Burgers equation to transform the near-field overpressure distribution to the far field and evaluate the perceived sound pressure level by the human ear using the Stevens' Mark VII method as a high-reliability and fast sonic boom prediction method.

[0055] The comparison results are detailed in Table 4. The absolute error of the sonic boom was controlled within 0.5%, and the relative error was controlled within 0.6%. The average relative error of AMF-DNN on the test set was 0.24%. The sonic boom prediction results further demonstrate that AMF-DNN can effectively capture the relationship between high-fidelity and low-fidelity data. In Table 4 below, PLdB is the sonic boom value, and HF(PLdB) is the sonic boom value considering human subjective perception factors.

[0056] Table 4 Comparison of AMF-DNN Far-Field Sonic Boom Prediction Accuracy

[0057] Next, a single-fidelity deep neural network model, DNN-H, was trained to learn from 100 sets of high-fidelity data, serving as a control group for this invention. Its model architecture is as follows: Figure 9 As shown in Table 5, 100 sets of high-fidelity near-field overvoltage 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, with the number of neurons in the first three layers increasing 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 5). The network was trained using the Adam optimizer with epoch=5000 and batch=8. The training results are shown in Table 6.

[0058] Table 5 Single-fidelity deep neural network architecture design

[0059] Table 6 Analysis of Training Results of Single-Fidelity Deep Neural Networks

[0060] 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 the near-field sound pressure data. Further analysis was conducted using the DNN-10000 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). Its root mean square error histogram is shown below. Figure 8 In (a), the prediction results of shape 3 with the maximum mean square error are compared as follows: Figure 8 As shown in (b). Next, the sonic boom prediction accuracy for all shapes in the test set was compared. The results are shown in the table, with a maximum relative error of 4.05% and an average relative error of 2.67% on the test set.

[0061] Table 7 Comparison of Predicted Sonic Boom Values ​​by Single-Fidelity Deep Neural Networks

[0062] Compared to the single-fidelity deep neural network model DNN-H, the multi-fidelity deep neural network AMF-DNN based on linear / nonlinear integrated correction 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.

[0063] Step 4: Construct a high-fidelity aerodynamic neural network model DNN-AERO and a low-fidelity near-field overpressure distribution neural network model DNN-L.

[0064] Furthermore, traditional single-fidelity neural network modeling methods rely on a large amount of high-fidelity data as training samples, resulting in poor model generalization performance when such data is scarce. For the same shape, the grid size required to solve for high-precision near-field overpressure distribution is typically 5-10 times that required to solve for aerodynamic forces, making it difficult to provide a large amount of high-fidelity datasets for training. Therefore, this invention proposes a multi-fidelity modeling method that integrates an adaptive search method with a linear / nonlinear comprehensive correction strategy. This method constructs the model by combining a large amount of low-fidelity data, aiming to achieve relatively ideal prediction accuracy even when high-fidelity data is limited.

[0065] In one embodiment, both the high-fidelity aerodynamic neural network model DNN-AERO and the low-fidelity near-field overpressure distribution neural network model DNN-L are constructed using a 3-layer single-fidelity fully connected deep neural network, such as... Figure 9As shown, the model framework is presented in Table 8. The training samples for the DNN-AERO model consist of 600 sets of high-fidelity aerodynamic coefficients (specifically, lift-to-drag ratio), while the training samples for the DNN-L model consist of 600 sets of low-fidelity near-field overpressure distributions. This dataset is divided into 512 training sets and 88 test sets.

[0066] Table 8 Single-fidelity deep neural network architecture

[0067] The model training accuracy is shown in Table 9. The lift-to-drag ratio error predicted by DNN-AERO is 0.025, and the low-fidelity near-field overvoltage distribution error predicted by DNN-L is 0.00038, which meets the accuracy requirements.

[0068] Table 9 Prediction Accuracy of Single-Fidelity Neural Networks

[0069] Since aerodynamic drag directly affects an aircraft's flight performance, fuel efficiency, and operating costs, accurate drag prediction is crucial. In the aforementioned sonic boom prediction model, a high-fidelity and low-fidelity data fusion strategy was employed. The aerodynamic accuracy obtained from the low-fidelity near-field overpressure distribution calculation already meets the requirements of high-fidelity aerodynamic calculation, thus eliminating the need for separate aerodynamic sampling. Furthermore, due to the sufficient sample size from the low-fidelity near-field overpressure distribution calculation, a multi-fidelity sampling method is not required when constructing the high-confidence drag prediction neural network; a simple single-fidelity neural network suffices.

[0070] Step 5: A high-reliability performance prediction method combined with a genetic algorithm is used to construct an aircraft sonic boom optimization system for optimization design. Specifically, this includes: setting shape parameters as design variables, with low sonic boom and high lift-to-drag ratio as optimization objectives; setting multiple genetic operators, including crossover, mutation, and selection operations, to improve search efficiency; employing an adaptive parameter adjustment mechanism to dynamically adjust genetic parameters based on individual fitness, achieving global and local balance in the optimization process; and, with model prediction support, performing multi-objective evolutionary optimization of the aircraft shape to obtain the optimal shape solution that meets the requirements of low sonic boom and high aerodynamic performance.

[0071] A high-reliability performance prediction method combined with a genetic algorithm was used to construct an optimization system for aircraft sonic booms. To make the genetic algorithm more efficient in finding the optimal solution, fine-tuning was performed on genetic operators and fitness evaluation. For genetic operators, different operations were 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; in one embodiment, individual genes are mutated 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.

[0072] 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.

[0073] An initial population of 100 was set, with 500 generations for optimization. The optimization objectives were set as the reciprocals of the ground-sense sound pressure level and lift-to-drag ratio. Multi-objective optimization of sonic boom and aerodynamics was performed on the supersonic aircraft shown in Figure 4. The optimized Pareto leading edge for sonic boom and lift-to-drag ratio is shown below. Figure 10 As shown in the figure. The horizontal axis represents the lift-to-drag ratio (K), and the vertical axis represents the sonic boom value (PLdB). The solution with a sonic boom value of around 90 dB is selected as the optimal solution. Figure 11 The image shows a comparison of the aerodynamic shape before and after optimization. The red shape represents the optimized shape, and the blue shape represents the initial shape. Figure 12 To compare the near-field overvoltage distribution before and after optimization, the red solid line represents the optimized near-field sonic boom signal, and the blue solid line represents the near-field sonic boom signal of the initial shape. Figure 13 The comparison of far-field overvoltage signals before and after optimization is given. The red solid line represents the optimized ground sonic boom signal, and the blue dashed line represents the ground sonic boom signal of the initial shape.

[0074] Table 10 Results of sonic boom and aerodynamic optimization

[0075] Table 10 lists the sonic boom values ​​and lift-to-drag ratios for the optimized and initial shapes. Among them, This represents the difference between the optimized result and the initial shape.

[0076] In summary, the proposed low-drag, low-sonic-bang optimization method for aircraft, through the integration of an adaptive search multi-fidelity deep neural network, can accurately establish the mapping relationship between the aircraft's shape and near-field overpressure distribution even under conditions of limited high-fidelity data. Based on the neural network prediction results, combined with the generalized Burgers equation and Stevens' Mark VII method, it achieves high-reliability, fast sonic bang prediction. Simultaneously, leveraging the advantages of low-fidelity near-field overpressure distribution in aerodynamic accuracy and sampling sufficiency, it directly constructs a high-reliability drag prediction model. Finally, it combines the sonic bang and drag prediction models with a genetic algorithm to form a multi-objective optimization framework that considers both aerodynamic performance and the low-sonic-bang target, effectively avoiding local optima and improving the overall optimization effect.

[0077] It should be noted that, for those skilled in the art, the technical features in the above embodiments can be freely combined, and the resulting technical solutions also belong to the embodiments disclosed in this invention.

[0078] Furthermore, without departing from the principles of this invention, several improvements and modifications can be made to this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A method for optimizing low-drag and low-sonic-bang performance in aircraft, characterized in that, The steps are as follows: Step 1: Construct an aircraft performance database; based on the initial aircraft shape, use the freeform surface deformation method to perform parametric shape modeling; perform perturbation sampling on multiple control points to obtain several deformable shapes; solve the coarse mesh using computational fluid dynamics methods to obtain low-fidelity near-field overpressure distribution and high-fidelity aerodynamic data corresponding to each shape; for some shapes, use structured meshes and high-precision equations to solve their high-fidelity near-field overpressure distribution, and construct a multi-fidelity database containing shape parameters, low-fidelity sonic boom data, and high-fidelity data; Step 2: Construct a multi-fidelity deep neural network model AMF-DNN based on a combined linear and nonlinear correction strategy. Specifically, this includes: constructing a generalized autoregressive structure that includes the relationship between low-fidelity and high-fidelity data, with the correlation function consisting of linear and nonlinear subnetworks; and dynamically adjusting the weight distribution of the linear and nonlinear networks according to the correlation between the data by adjusting the adaptive parameters to achieve adaptive learning of the multi-fidelity relationship by the model. Step 3: Training and sonic boom prediction using the multi-fidelity deep neural network model AMF-DNN, specifically including: training and testing the AMF-DNN model using the constructed multi-fidelity database; combining the near-field sonic boom prediction results with the propagation model to convert the near-field signal into a far-field sonic boom signal and evaluate the far-field perceived sound pressure level; verifying the model's sonic boom prediction accuracy on different shapes by comparing it with actual high-fidelity data. Step 4: Construct a high-fidelity aerodynamic neural network model DNN-AERO and a low-fidelity near-field overpressure distribution neural network model DNN-L; Step 5: Utilize a combination of highly reliable performance prediction methods and genetic algorithms to construct an aircraft sonic boom optimization system for optimization design.

2. The method for optimizing low-drag and low-sonic-bang aircraft according to claim 1, characterized in that, In step one, based on orthogonal Cartesian grids and combined with the Euler equations, low-fidelity near-field overpressure distribution and corresponding aerodynamic data are obtained; at the same time, structured grids are used and RANS equations are solved to obtain high-fidelity near-field sonic boom overpressure distribution.

3. The method for optimizing low-drag and low-sonic-bang aircraft according to claim 1, characterized in that, In step two, a generalized autoregressive scheme is constructed that includes the relationships between low-fidelity and high-fidelity data: in, For low-fidelity input, For low-fidelity data, For high-fidelity input, This is a low-fidelity result when inputting high-fidelity data. For high-fidelity data, F This represents the association function between high-fidelity data and low-fidelity data, and... F It can be further decomposed into linear and nonlinear parts.

4. The method for optimizing low-drag and low-sonic-bang performance of an aircraft according to claim 1, characterized in that, In step two, the loss function of the multifidelity deep neural network model AMF-DNN is set to include a main loss term, a regularization term, and an adaptive search term. The loss function of the AMF-DNN model is as follows: , In the formula, Indicates the number of samples. For high-fidelity data, This represents the output of the linear layer. This represents the output of the nonlinear layer. The regularization coefficients of a high-fidelity network are represented. This represents the sum of squares of the parameters of a high-fidelity network.

5. The method for optimizing low-drag and low-sonic-bang aircraft according to claim 1, characterized in that, In step two, two independent networks are used. and Let's learn separately. and Used to explore the relationship between low-fidelity and high-fidelity data, among which, To explore the linear part Networks with interconnected relationships do not contain activation functions; To explore the nonlinear part A network of relationships containing non-linear activation functions.

6. The method for optimizing low-drag and low-sonic-bang aircraft according to claim 1, characterized in that, In step three, the near-field overpressure distribution is transformed to the far field using the generalized Burgers equation, and the perceived sound pressure level of the human ear is evaluated using the Stevens' Mark VII method as a high-confidence fast sonic boom prediction method.

7. A method for optimizing low-drag and low-sonic-bang performance of an aircraft according to claim 1 or 6, characterized in that, In step three, a benchmark neural network model is further trained as a performance comparison. Specifically, this includes: constructing a single-fidelity deep neural network model DNN-H, using high-fidelity data as input training samples; and comparing the differences between this model and the multi-fidelity deep neural network model AMF-DNN in terms of prediction accuracy and generalization ability.

8. The method for optimizing low-drag and low-sonic-bang aircraft according to claim 1, characterized in that, In step four, the models are constructed using a 3-layer single-fidelity fully connected deep neural network. The training samples for model DNN-AERO consist of 600 sets of high-fidelity aerodynamic coefficients, while the training samples for model DNN-L consist of 600 sets of low-fidelity near-field overpressure distributions.

9. The method for optimizing low-drag and low-sonic-bang aircraft according to claim 1, characterized in that, Step five specifically includes: constructing a genetic algorithm optimization process, setting the shape parameters as design variables, and low sonic boom and high lift-to-drag ratio as optimization objectives; setting multiple genetic operators, including crossover, mutation, and selection operations, to improve search efficiency; adopting an adaptive parameter adjustment mechanism to dynamically adjust genetic parameters according to individual fitness to achieve global and local balance in the optimization process; and, with the support of model prediction, performing multi-objective evolutionary optimization on the aircraft shape to obtain the optimal shape solution that meets the requirements of low sonic boom and high aerodynamic performance.

10. The method for optimizing low-drag and low-sonic-bang performance of an aircraft according to claim 9, characterized in that, In step five, different operations were selected to simulate the biological evolution process in terms of genetic operators; the crossover operator uses two-point crossover to achieve gene recombination by exchanging some genes of two individuals, thereby increasing the diversity of the population; the mutation operator uses Gaussian mutation to avoid the algorithm getting trapped in local optima by introducing new gene information.

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