Supersonic civil aircraft self-adaptive low-sound-explosion optimization design method based on proxy model

Abstract

The invention aims to provide a supersonic civil aircraft self-adaptive low-sound-explosion optimization design method based on an agent model. According to the method, a dynamic mesh (FFD) parameterization technology, a radial basis function (RBF) proxy model, a differential evolution (DE) global optimization algorithm and an innovative hybrid adaptive point adding strategy (GHOTM-RBF) are systematically integrated, the aerodynamic configuration of the supersonic civil aircraft which meets multiple engineering constraints and is remarkably reduced in acoustic explosion can be efficiently obtained at an acceptable calculation cost, and the aerodynamic configuration of the supersonic civil aircraft can be used for solving the problem that the aerodynamic configuration of the supersonic civil aircraft meets the requirements of multiple engineering constraints and is remarkably reduced in acoustic explosion. And an efficient and engineering-usable low-sound-explosion optimization design idea can be provided for future supersonic civil aircraft development.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to the aerodynamic design of supersonic aircraft, and particularly to an aerodynamic shape optimization design method for reducing the sonic boom intensity of supersonic civil aircraft. Background Technology

[0002] Since the mid-20th century, supersonic aircraft design technology has made significant progress, but its commercial application in civil aviation has consistently faced a formidable obstacle—sonic boom. When an aircraft flies at supersonic speeds, the compression waves it generates converge around the fuselage to form shock waves. These shock waves propagate outward in a cone shape, forming N-type pressure waves upon reaching the ground, which are perceived by the human ear as two loud explosions—a sonic boom. Intense sonic booms not only disturb people on the ground but can also damage buildings. For this reason, most countries around the world have laws prohibiting supersonic flight of civil aircraft over land, which severely limits the route planning and commercial value of supersonic aircraft.

[0003] To achieve "quiet" supersonic land flight, the development of low-sonic-boom design technology has become a research hotspot in the global aviation industry. The core idea of ​​low-sonic-boom design is to actively control the distribution of the pressure field generated by the aircraft through precise aerodynamic design, so that the near-field pressure signal, when propagating to the far field (ground), forms a waveform with a relatively gentle pressure rise and low peak value, rather than the traditional N-type wave. An ideal low-sonic-boom waveform is typically designed as a "minimum-perceived" waveform, with a far-field perceived loudness decibel (PLdB) far lower than that of conventional supersonic aircraft. To achieve this goal, researchers have developed various low-sonic-boom optimization design methods. Early research mainly relied on modified linearization theory (Whitham's theory) and gradient optimization algorithms. These methods are computationally fast and can provide preliminary design directions, but their accuracy is limited, especially for aircraft with complex three-dimensional shapes, where the assumptions of linearization theory often no longer hold.

[0004] With the rapid development of computer performance, optimization design methods based on high-precision computational fluid dynamics (CFD) have become mainstream. CFD can accurately solve Euler or Reynolds-averaged Navier-Stokes (RANS) equations, and accurately predict the flow field and near-field pressure distribution around complex-shaped aircraft. However, directly embedding CFD into the optimization loop faces two major challenges: the "curse of dimensionality" and "computational cost." On the one hand, to accurately describe the shape of a complex aircraft, a large number of geometric design variables are needed, forming a high-dimensional design space; on the other hand, a single high-precision three-dimensional CFD simulation can easily require hours or even tens of hours of computation time. Traditional optimization algorithms, such as genetic algorithms or particle swarm optimization, typically require thousands or even tens of thousands of objective function evaluations to converge. If a CFD simulation is called for each evaluation, the entire optimization process would be astronomically time-consuming, making it impractical in engineering.

[0005] To address this challenge, Surrogate-Based Optimization (SBO) has emerged. A surrogate model, also known as a response surface model or meta-model, is a computationally inexpensive mathematical model used to approximate high-cost CFD simulations. Its basic process is as follows: First, an initial surrogate model is constructed using a small number of high-precision simulation sample points. Then, extensive optimization searches are performed on the inexpensive surrogate model to find potential optimal solutions. Next, a "point addition strategy" is used to select new, most valuable points for high-precision simulation, and the new sample points are added to a database to update and improve the accuracy of the surrogate model. This process is iterated until convergence.

[0006] While surrogate model optimization methods have been applied to some extent in the field of aerospace design, several technical bottlenecks remain in addressing the specific and highly challenging problem of low sonic booms in supersonic civil aircraft: 1. Limitations of parametric methods: Traditional parametric methods are difficult to provide a sufficiently rich and flexible design space to capture the fine shape features required for low-sound boom while ensuring the smoothness of the shape.

[0007] 2. Efficiency issues in optimization algorithms: In high-dimensional design spaces, many traditional optimization algorithms are prone to getting trapped in local optima or have slow convergence speeds. Choosing an efficient optimizer with strong global search capabilities is crucial.

[0008] 3. The Balance of Sampling Strategies: Sampling strategies are the core of surrogate model optimization methods, determining optimization efficiency. A good sampling strategy requires a delicate balance between "sampling in regions of high model uncertainty to improve global accuracy" and "sampling near the current predicted optimal solution to accelerate convergence." Some existing sampling strategies struggle to simultaneously meet the dual requirements of global optimum and efficient convergence in hyposonic blast design.

[0009] 4. Handling Complex Constraints: Low-detonation optimization design not only needs to reduce sonic booms but also must meet a series of complex engineering constraints, such as ensuring sufficient fuselage volume to accommodate passengers and cargo, ensuring sufficient wing volume to carry fuel, and maintaining the necessary wing area to generate lift. How to efficiently and accurately handle these nonlinear constraints is key to the success of the optimization design.

[0010] Therefore, there is an urgent need for a systematic optimization design method for low-sonic blasts of supersonic civil aircraft that integrates efficient parameterization methods, powerful optimization algorithms, intelligent point addition strategies, and reliable constraint processing mechanisms, in order to meet the above challenges and realize the leap from theoretical research to engineering application of low-sonic blast design. Summary of the Invention

[0011] This invention aims to solve the technical problems existing in the optimization design method for low-detonation supersonic civil aircraft, such as high computational cost, low optimization efficiency, and difficulty in handling high-dimensional complex constraints.

[0012] The purpose of this invention is to provide an adaptive low-detonation optimization design method for supersonic civil aircraft based on a surrogate model. This method systematically integrates moving mesh (FFD) parameterization technology, radial basis function (RBF) surrogate model, differential evolution (DE) global optimization algorithm, and an innovative hybrid adaptive point addition strategy (GHOTM-RBF). It can efficiently obtain a supersonic civil aircraft aerodynamic shape that satisfies multiple engineering constraints and significantly reduces detonation at an acceptable computational cost.

[0013] The technical solution of this invention provides an adaptive low-detonation optimization design method for supersonic civil aircraft based on a surrogate model, the core process of which includes: 1. Establish a high-dimensional, flexible geometric parameterization model of the aircraft. This invention employs the Moving Mesh Function (FFD) method to parameterize the aerodynamic shape of a benchmark supersonic civil aircraft. The FFD method constructs a control volume outside the aircraft geometry and embeds the geometric shape within it. By moving control points on the control volume, smooth and continuous deformation of the internal geometry can be driven. The advantages of FFD lie in its topology being independent of the original geometry, its ability to handle arbitrarily complex shapes, and the ability to easily control the dimensionality of the design space and the degrees of freedom of local deformations by adjusting the number and distribution of control points. This invention selects the coordinates of some control points on the FFD control volume as design variables, thereby constructing a high-dimensional design space capable of precisely describing the shape changes of key components such as the nose, fuselage, and wings.

[0014] 2. Construct an accurate and complete mathematical model for the optimization problem. The optimization objective of this invention is to minimize the far-field perceived sound pressure level (PLdB) on the ground path directly beneath the aircraft during its design cruise state (e.g., Mach 1.6). PLdB is an acoustic metric that comprehensively considers the waveform, intensity, frequency, and auditory characteristics of a sonic boom, and is currently the internationally recognized standard for low sonic boom design evaluation. Furthermore, to ensure the engineering practicality of the optimization results, this invention sets strict constraints: (1) Inequality geometric constraints: The optimized fuselage volume is required to be no less than the initial volume, the wing volume is required to be no less than the initial volume, and the wing projected area is required to be no less than the initial area. These constraints ensure that the aircraft's payload capacity, fuel loading capacity, and aerodynamic lift characteristics will not be degraded due to shape optimization.

[0015] (2) Boundary constraints: Set reasonable upper and lower movement boundaries for each design variable (i.e., FFD control point coordinates) to prevent unrealistic or distorted geometric shapes.

[0016] The constraints are integrated into the objective function using the penalty function method, forming an augmented objective function that is easier for the optimization algorithm to solve.

[0017] 3. Build and iteratively update a high-precision proxy model This invention employs a radial basis function (RBF) neural network to construct a surrogate model. The RBF model has advantages such as strong approximation capability for high-dimensional nonlinear functions and simple model construction. The optimization process begins with an initial stage: firstly, a set of uniformly distributed initial sample points is generated within the design space using the Latin hypercube sampling (LHS) method. For the geometry represented by each sample point, a high-cost "black box function"—namely, high-precision CFD simulation combined with sonic boom propagation calculation—is invoked to obtain its true PLdB value and the values ​​of each constraint function. Based on this set of "design variable-response value" data pairs, an initial RBF surrogate model is constructed. In subsequent iterations, the surrogate model is continuously updated through an adaptive point addition strategy, and its accuracy gradually improves accordingly.

[0018] 4. Combine differential evolution algorithm with hybrid adaptive point addition strategy for efficient iterative optimization. This is the core innovation of this invention. The entire iterative optimization loop consists of the following key steps: (1) Global Optimization: On the currently constructed RBF surrogate model, this invention uses the Differential Evolution (DE) algorithm for global search. The DE algorithm is a population-based metaheuristic algorithm that optimizes by simulating the "survival of the fittest" mechanism in the biological world. Compared with other algorithms such as genetic algorithms, the DE algorithm has fewer control parameters and is less sensitive to initial values. It exhibits stronger global convergence ability and robustness, especially when dealing with complex optimization problems with high dimensions and multiple peaks. Since the evaluation cost of the RBF surrogate model is extremely low, the DE algorithm can perform tens of thousands or even hundreds of thousands of evaluations on it, thereby efficiently finding the global optimal solution on the current surrogate model.

[0019] (2) Intelligent Point Addition: After finding the optimal solution on the surrogate model, the next key step is to determine the next new sample point that needs to be used for high-precision CFD simulation, i.e., "point addition". This invention adopts an innovative hybrid adaptive point addition strategy, named GHOTM-RBF. This strategy selects a new point with the most informational value by considering both the predicted optimal value and the prediction uncertainty through a mathematical criterion.

[0020] (3) Model Update: High-precision CFD simulation is performed on the selected new points to obtain their true response values. Then, this new "knowledge" point is added to the sample database, and the RBF surrogate model is retrained using the updated database. The updated model will have improved prediction accuracy because it contains more information.

[0021] By continuously repeating the cycle of "global optimization - intelligent point addition - model update", the surrogate model will increasingly approximate the real high-precision CFD model, and the optimal solution searched by the DE algorithm will gradually converge to the real global optimum. The optimization process terminates when the preset convergence conditions (such as the upper limit of the number of iterations or the stability of the objective function value) are met.

[0022] Compared with the prior art, the present invention has the following significant advantages: (1) Extremely high computational efficiency: This invention replaces most of the time-consuming high-precision CFD simulation with a proxy model. The entire optimization process may only require tens to hundreds of CFD calls, which is 1 to 2 orders of magnitude lower than the thousands or tens of thousands of calls required by traditional direct optimization methods, making it possible to complete the optimization of low-sonic booms of complex three-dimensional shapes in a limited time.

[0023] (2) Powerful global optimization capability: The combination of differential evolution (DE) algorithm and hybrid adaptive point addition strategy (GHOTM-RBF) ensures that the optimization process can effectively avoid getting trapped in local optima in the high-dimensional and complex design space, and significantly improves the probability of finding the globally optimal low-sound boom shape. The adaptive characteristics of the GHOTM-RBF strategy enable the algorithm to intelligently switch between global exploration and local development, making the optimization path more efficient.

[0024] (3) Flexibility and practicality of design space: The FFD parametric method provides a broad and flexible design space for finding innovative low sonic boom shapes. At the same time, by strictly applying multiple engineering constraints such as fuselage volume, wing volume and area, it is ensured that the optimization results not only have low sonic boom, but also have practical engineering application value, avoiding the infeasibility of the solution caused by "sonic boom theory".

[0025] (4) Systematic and automated approach: This invention integrates a complete process from parameterization, CFD simulation, sonic boom prediction to surrogate model optimization, enabling a highly automated design cycle. Designers only need to set the initial configuration, optimization objectives, and constraints, and the system can automatically execute the optimization process and output the final design scheme, greatly freeing up manpower and shortening the design cycle.

[0026] (5) Significant noise reduction effect: Through the application verification in a typical supersonic research model of a large swept delta wing-body (DWB) supersonic, the method of the present invention successfully reduced the far-field perceived sound pressure level (PLdB) from 87.22 dB to 83.12 dB, a reduction of 4.7%, while satisfying all geometric constraints. The significant reduction in sonic boom intensity proves the effectiveness and advancement of the present invention.

[0027] In summary, this invention proposes an innovative, efficient, and practical low-detonation optimization design method for supersonic civil aircraft, successfully overcoming many bottlenecks in existing technologies and providing strong key technical support for the development of a new generation of environmentally friendly and quiet supersonic civil aircraft. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the overall process of the low-sound blast optimization design method according to an embodiment of the present invention.

[0029] Figure 2 This is a schematic diagram illustrating the principle of the dynamic mesh (FFD) parameterization method used in this invention, showing the FFD control volume, control points, and the driving deformation effect on the internal geometry.

[0030] Figure 3 This is a comparison diagram of the shape of the DWB configuration of a supersonic civil aircraft before and after optimization in one embodiment of the present invention.

[0031] Figure 4 This is a comparison curve of the far-field N-type wave sonic boom signal propagating to the ground before and after optimization in one embodiment of the present invention.

[0032] Figure 5 This is a convergence history curve of the objective function (far-field perceived sound pressure level PLdB) during the optimization process in one embodiment of the present invention. Detailed Implementation

[0033] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] Example This embodiment uses a typical high-sweep delta wing body (DWB) supersonic civil aircraft as the optimization object to illustrate in detail the specific application process of the low sonic boom optimization design method described in this invention. The aircraft is designed for a cruise state of Mach number Ma=1.6 and a flight altitude of 16km.

[0035] Reference Figure 1 The overall process of the low-sound explosion optimization design method of the present invention mainly includes the following modules: geometric parameterization module 110, optimization problem definition module 120, high-precision evaluation module 130, and core proxy model optimization engine 140.

[0036] Step 1: Aircraft geometry parameterization (corresponding to...) Figure 1 Module 110) This embodiment uses the dynamic mesh (FFD) method to parameterize the baseline DWB configuration. (Refer to...) Figure 2 First, a tightly fitted three-dimensional cuboid control body, consisting of several control points, is constructed around the three-dimensional geometric model of the DWB configuration. In this embodiment, the size of the control body and the number of control points are carefully designed to focus on covering areas that significantly affect the sonic boom characteristics, such as the nose, fuselage, wing root, and wingtip.

[0037] The mathematical principle of FFD is that the coordinate transformation (deformation) of any point P in space is its transformation in the local coordinate system of the control volume. All control points below The weighted sum of displacements. Its formula can be expressed as:

[0038] in, The Cartesian coordinates of the control box points. For any point on the object to be deformed The local coordinates satisfy ,and Actual representation Cartesian coordinates, They are respectively For the basis functions, Bernstein basis functions, B-Spline basis functions, or NURBS basis functions can be selected. Considering that the latter two basis functions have stronger local control capabilities, and the layout optimization in this embodiment aims to retain features such as the leading and trailing edges of straight lines in the original DWB configuration, overly refined local control capabilities are not required. Therefore, cubic Bernstein basis functions are used. A total of N control points are selected as design variables x = {x1, x2, ..., x...}, with their displacements in a specific direction (such as the vertical Z-axis). N These design variables collectively constitute an N-dimensional design space. By changing the values ​​of these variables, the DWB configuration can be driven to produce smooth and continuous complex three-dimensional deformations, such as changing the bluntness of the nose, the torsion and camber distribution of the wing, and the morphology of the wing-body blending zone. This parametric method ensures design flexibility while avoiding the geometric non-smoothness problems caused by directly manipulating mesh points. Assume the coordinates of the changed control box points are... Then the coordinates of the points on the surface of the deformed object are:

[0039] Step 2: Define the mathematical model for the optimization problem (corresponding to...) Figure 1 Module 120) The optimization problem is formally defined as: finding the vector of design variables. And minimizing the far-field perceived sound pressure level PLdB ( The following constraints must be met: (1) (Fuse volume constraints) (2) (Wing volume constraints) (3) .1 (Wing area constraint) (4) x_lower ≤ x ≤ x_upper (design variable boundary constraint) Where V represents volume, S represents area, and the subscript 0 indicates the initial value before optimization.

[0040] To facilitate the solution, this embodiment employs the penalty function method to handle the aforementioned inequality constraints, transforming the constrained problem into an unconstrained one. Augmented objective function. Defined as:

[0041] Here, W is a sufficiently large penalty factor. When all constraints are satisfied, the penalty term is 0; when any constraint is violated, a large penalty value is added to the objective function, thus guiding the optimization algorithm to search the feasible region. For example, considering the changes in the aforementioned constraint quantities in sonic boom optimization, and based on design practice, the difference is multiplied by 10000 when it exceeds 1.1 times the wing area, and by 5000 when it is less. The wing and fuselage volumes are multiplied by 6000000 and 1000000 respectively due to their dimensional relationships.

[0042] Step 3: High-precision evaluation module (corresponding to) Figure 1 Module 130) This module is the source of the "true" response values, although its calls are strictly controlled. For a given design variable vector x, the high-precision evaluation process is as follows: (1) Geometry and Mesh Generation: Based on the value of x, a new DWB geometry is generated through FFD transformation. Subsequently, dynamic meshing technology (volume spline interpolation method is used in this embodiment) is invoked to automatically update the mesh node positions to adapt to the new shape boundary based on the high-quality computational mesh of the initial configuration, generating a new computational mesh. This avoids re-meshing each time, greatly saving time.

[0043] (2) CFD simulation: A mature CFD solver is used to simulate the inviscid flow field around the aircraft under cruise conditions of Ma=1.6 by solving the three-dimensional Euler equation. After the calculation converges, the pressure distribution data at a certain distance below the aircraft (usually 1-2 times the fuselage length) is extracted, i.e., the near-field pressure signal.

[0044] (3) Sonic boom propagation and assessment: Using the near-field pressure signal obtained from CFD as input, a sonic boom propagation program based on the modified Burgers equation was used to simulate the propagation of the pressure wave from flight altitude to the ground, considering atmospheric non-uniformity and nonlinear effects. The far-field sonic boom waveform at the ground was finally obtained, and the far-field perceived sound pressure level (PLdB) was calculated based on this waveform. Simultaneously, constraint function values ​​such as fuselage volume, wing volume, and wing area were obtained through calculations of the geometric model.

[0045] This complete process constitutes a high-precision evaluation, the output of which is PLdB and the values ​​of three g(x).

[0046] Step 4: Adaptive Optimization Engine Based on Agent Model (corresponding to) Figure 1 Module 140) (a) Initialization Using the Latin hypercube sampling (LHS) method, M initial sample points (M=50 in this embodiment) are generated within the boundary range of the design variable x. LHS ensures that the sample points are distributed as uniformly as possible in the design space. For each of these M sample points, the high-precision evaluation module 130 is called to obtain their corresponding true PLdB and constraint values. Thus, we obtain an initial sample database. ,in Represents PLdB, This represents the constraint vector.

[0047] (b) Constructing a proxy model Based on sample database We construct radial basis function (RBF) surrogate models for the objective function and constraint functions, respectively. The RBF model form can be unified using the surrogate model form. ,in It is the first k A radial basis function (Gaussian function is used in this embodiment), which is composed of... The relationship with the sample input determines this; The weights of the basis functions are determined by the sample data. These weights are determined by solving a system of linear equations, ensuring that the surrogate model is exactly equal to the true value at all known sample points.

[0048] (c) Global optimization A large-scale search is performed on the aforementioned surrogate model. This embodiment employs the Differential Evolution (DE) algorithm to find the augmented objective function. Minimum design point The DE algorithm iteratively evolves a population by maintaining it and performing mutation, crossover, and selection operations. Because... The evaluation is extremely rapid; the DE algorithm can complete hundreds of thousands of evaluations in seconds, thus having a high probability of finding the global optimum on the surrogate model. .

[0049] (d) Adaptive point addition This is key to improving optimization efficiency. A hybrid point-addition strategy using GHOTM-RBF is employed to determine the next point requiring high-precision evaluation. The goal of this strategy is to find a point that is either the true optimal solution or one that minimizes uncertainty in the unknown regions of the model. This is achieved by solving an auxiliary optimization problem whose objective function combines the surrogate model's predictions and prediction errors (estimated through methods such as cross-validation).

[0050] (e) Updates and Iterations Will Submitted to the high-precision evaluation module to obtain its true ( , Then, this new sample point ( , , The expanded database is then added to the sample database, making its size M+1. The process then returns to step (b), where the expanded database is used to rebuild a more accurate RBF proxy model. This cycle of "model building - optimization - addition - update" continues.

[0051] (f) Convergence judgment After each iteration, the convergence condition is checked. In this embodiment, the convergence condition is: optimization terminates when the number of iterations reaches a preset upper limit (e.g., 200 high-precision evaluations). Finally, from all evaluated sample points, the point that satisfies all constraints and has the smallest PLdB value is selected, and its corresponding geometry is the final optimization result.

[0052] Results and Analysis After approximately 200 iterations (i.e., 200 CFD simulation calls), the optimization process in this embodiment converged. (Refer to...) Figure 5 The figure illustrates the convergence history of the PLdB value during the optimization process. It shows that as the number of iterations increases, the algorithm continuously finds solutions with lower PLdB values, eventually stabilizing around 83.12 dB. This indicates that the optimization process is effective and convergent.

[0053] Reference Figure 3The shape of the DWB configuration before and after optimization was compared. It can be observed that the optimized configuration has undergone significant and subtle geometric changes compared to the initial configuration: the nose section has become fuller and more blunt, which helps to generate a smoother initial pressure rise at the nose, rather than a sharp shock wave; the cross-sectional shape and torsional distribution of the wing leading edge have been redesigned, making the wing lift distribution in the spanwise and chordal directions more reasonable, avoiding strong shock waves caused by excessive lift concentration; the transition of the wing-body blending area is smoother, reducing the mutual interference and superposition of shock waves between different components.

[0054] These geometric changes directly lead to an improvement in near-field pressure distribution, which is directly reflected in the far-field sonic boom signal. Experimental results show that the initial configuration of the far-field sonic boom waveform propagating to the ground produces a strong N-type wave with a high overpressure peak. The optimized configuration produces a waveform with a much smoother pressure rise and fall, a significantly reduced peak overpressure, and a waveform closer to the ideal low-sonic boom "flat-top" waveform. Quantitative results show that the method of this invention successfully reduced the perceived far-field sound pressure level by 4.1 dB (from 87.22 to 83.12, a reduction of 4.7%) while fully satisfying all geometric constraints (no reduction in fuselage and wing volume or wing area). This reduction is acoustically significant, meaning a substantial decrease in the perceived intensity of the sonic boom.

[0055] In summary, this embodiment fully demonstrates the effectiveness, efficiency, and engineering applicability of the proposed surrogate model-based adaptive low-detonation optimization design method for supersonic civil aircraft.

Claims

1. A supersonic civil aircraft adaptive low-detonation optimization design method based on a surrogate model, characterized in that, Includes the following steps: (a) The initial aerodynamic shape of the supersonic civil aircraft is parameterized using the dynamic mesh method. A set of control point coordinates on the FFD control volume is selected as design variables to construct a high-dimensional design space that describes the shape change. (b) Set the optimization objective as minimizing the far-field perceived sound pressure level generated by the aircraft during cruise; Set constraints, including geometric constraints to maintain or increase fuselage volume, wing volume and wing area, as well as boundary constraints on the range of design variables; (c) An initial sample point set is generated in the design space using the Latin hypercube sampling method; for each sample point, the near-field pressure signal is obtained through high-precision computational fluid dynamics simulation, and the corresponding far-field perceived sound pressure level and constraint function value are calculated through the sonic boom propagation theory; based on the initial sample point set and its corresponding response value, a radial basis function surrogate model is constructed to approximate the objective function and constraint function respectively. (d) Use the differential evolution algorithm to perform an efficient global optimization search on the currently constructed RBF surrogate model to find the optimal solution that minimizes the objective function value predicted by the surrogate model; (e) A hybrid point-addition strategy that takes into account both global exploration and local development is adopted. The point-addition is determined in the design space by a combination of criteria that maximize the expected improvement and minimize the prediction uncertainty. The point-addition is the design state that is most worthy of high-precision CFD simulation at present. (f) Perform high-precision CFD simulation and sonic boom prediction calculation on the new sample points determined in step (e) to obtain their true response values; add the new sample points and their response values ​​to the sample point database, and use the updated database to retrain and build a more accurate RBF surrogate model. (g) Determine convergence and output the result: Repeat steps (d) to (f) until the preset convergence criterion is met, such as reaching the maximum number of iterations or the change in the objective function value is less than the threshold; finally output the optimized shape of the supersonic civil aircraft that satisfies all constraints and has the minimum far-field perceived sound pressure level.

2. The method according to claim 1, characterized in that, The free-form deformation method in step (a) sets up a three-dimensional control volume around the geometric shape of the aircraft and uses Bernstein basis functions in the form of tensor products as weight functions to control the mapping relationship between the displacement of the control point and the displacement of the point on the surface of the geometric shape, thereby ensuring the smoothness and continuity of the shape deformation.

3. The method according to claim 1, characterized in that, In step (b), the constraint handling adopts the penalty function method, which transforms the geometric constraints into a penalty term in the objective function, thereby transforming the constrained optimization problem into an unconstrained optimization problem for solution.

4. The method according to claim 1, characterized in that, In steps (c) and (f), high-precision computational fluid dynamics simulations are used to obtain near-field pressure signals by solving the Euler equation or the Reynolds-averaged Navier-Stokes equation; and the sonic boom propagation theory is combined with the modified Burgh's equation for far-field propagation to calculate the far-field perceived sound pressure level.

5. The method according to claim 1 or 4, characterized in that, During CFD simulation, when the aircraft's geometry changes according to design variables, a dynamic meshing technique based on volume spline interpolation is used to automatically update the computational mesh to adapt to the changes in shape, avoiding the time cost of regenerating the mesh.

6. The method according to claim 1, characterized in that, The differential evolution algorithm used in step (d) simulates the biological evolution process on the surrogate model through mutation, crossover and selection operations. Because of its few parameters, strong robustness and outstanding global search ability, it is particularly suitable for dealing with the high-dimensional and nonlinear complex optimization problems involved in this invention.

7. The method according to claim 1, characterized in that, The hybrid adaptive point addition strategy in step (e) selects new sample points based on the following criteria: (I) Use the differential evolution algorithm to find the current optimal solution on the surrogate model to enhance local exploitation capabilities; (II) Find the point in the design space where the surrogate model has the greatest uncertainty in prediction, so as to enhance the global exploration capability and thus achieve a balance between optimization efficiency and global convergence.

8. The method according to claim 1, characterized in that, The convergence criterion is: the relative change of the optimal objective function value in a series of iterations is less than a preset minimum value, or the computational resource consumption reaches a preset upper limit.

Images