A multi-objective topology optimization method for aircraft design

Abstract

This invention discloses a multi-objective topology optimization method for aircraft design, belonging to the field of aerospace technology. The method includes: establishing a three-dimensional geometric model and defining the optimization region and aerodynamic preservation region; describing the structural boundary using level set functions; applying volume and manufacturing constraints with the objectives of maximizing stiffness and natural frequency; constructing a comprehensive objective function that minimizes the distance between ideal points using a compromise programming method; transforming the constraint problem using the augmented Lagrangian method; calculating shape sensitivity and deriving the normal velocity field; updating the level set functions to drive topology evolution; iterating until convergence to generate a Pareto front solution set; selecting the optimal solution and reconstructing it into a manufacturable three-dimensional model. This invention solves the multi-objective collaborative optimization problem while preserving the aerodynamic shape, resulting in clear boundaries, strong manufacturability, and significantly improved structural performance and engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to a multi-objective topology optimization method for aircraft design. Background Technology

[0002] Control components in an aircraft structure (such as spoilers and control surfaces) must perform functions such as adjusting lift, deceleration, and attitude control. Their structural design directly affects the aircraft's maneuverability, fuel efficiency, and structural safety. Therefore, achieving multi-performance synergistic optimization and lightweighting of such structures is a key issue in modern aerospace engineering.

[0003] The existing technology has the following limitations:

[0004] 1. Traditional design methods rely on manual experience and experimental verification, which are inefficient, costly, and difficult to simultaneously meet multiple performance objectives such as stiffness, frequency and mass, and are prone to getting trapped in local optima.

[0005] 2. Mainstream topology optimization methods (such as the SIMP density method) have inherent defects: gray-scale cells, checkerboard effect and boundary ambiguity are caused by discrete design variables; the geometric expression of the optimization results is not clear, resulting in poor manufacturing feasibility (e.g., it is impossible to directly generate a machinable model).

[0006] 3. Limited effectiveness of multi-objective optimization methods: Traditional linear weighted methods are sensitive to weight coefficients and have difficulty balancing objectives with significantly different magnitudes (such as stiffness and frequency); the resulting Pareto front solution set is unevenly distributed, reducing the diversity of solutions and their engineering practicality.

[0007] 4. Lack of aerodynamic shape preservation mechanism: Most methods do not consider aerodynamic profile constraints, and the optimization process may change the outer profile of the aircraft, affecting the stability of aerodynamic performance.

[0008] 5. Lack of manufacturing constraints: Optimization results often show unmanufacturable features such as "inverted" structures and isolated connections, which cannot meet the requirements of casting or additive manufacturing processes.

[0009] In summary, existing technologies have significant shortcomings in multi-objective collaborative optimization, aerodynamic shape preservation, manufacturing constraint integration, and boundary clarity, and there is an urgent need for an efficient topology optimization method applicable to key components of aircraft. Summary of the Invention

[0010] The purpose of this invention is to provide a multi-objective topology optimization method for aircraft design. While preserving the key aerodynamic shape of the aircraft structure, it introduces manufacturing constraints to improve manufacturing feasibility. By combining the level set method and the compromise programming strategy, it achieves synergistic optimization of performance such as stiffness, frequency, and mass, generating optimized design schemes with smooth boundaries, continuous structures, and direct manufacturability. This solves the multi-objective synergistic optimization problem and can thus solve at least one of the technical problems mentioned in the background art.

[0011] To solve the above-mentioned technical problems, the present invention is implemented as follows:

[0012] This invention provides a multi-objective topology optimization method for aircraft design, comprising the following steps:

[0013] Step S1: Establish a three-dimensional geometric model based on the geometry and outer contour dimensions of the aircraft structural components, and clearly define the optimization design area and the aerodynamic shape retention area.

[0014] Step S2: Construct the structural boundary representation function using the level set method;

[0015] Step S3: Set the maximization of stiffness and the maximization of natural frequency as optimization objectives, apply volume constraints and manufacturing constraints, and perform finite element analysis to solve the single-objective optimization of the aircraft structure response;

[0016] Step S4: Use the trade-off programming method to model the multi-objective problem and construct a comprehensive objective function that minimizes the distance to the ideal point;

[0017] Step S5: Transform the constrained optimization problem into an unconstrained form using the augmented Lagrange penalty function method, set the Lagrange multipliers and penalty parameters, and perform iterative updates.

[0018] Step S6: Calculate the shape sensitivity of the integrated objective function and constraint terms to the design variables, and derive the normal velocity field used for structural boundary evolution;

[0019] Step S7: Update the level set function through Hamilton-Jacobi partial differential equations to achieve structural boundary topology evolution and material distribution optimization;

[0020] Step S8: Determine whether the objective function meets the optimization convergence condition. If it does not meet the condition, return to step S5 to continue iteration. If it does meet the condition, terminate the optimization.

[0021] Step S9: Adjust the target weight coefficients, return to step S3 until all weight coefficients are traversed, and generate the Pareto front solution set;

[0022] Step S10: Based on the Pareto solution set, select the aircraft structure optimization scheme with the best comprehensive performance according to the mechanical performance required for actual application.

[0023] Step S11: Reconstruct the optimization results and output a three-dimensional aircraft structure model that is feasible for manufacturing.

[0024] Optionally, in step S1, by setting an aerodynamic shape preservation region in the three-dimensional geometric model, the outer contour surface of the aircraft structure and the critical width region are excluded from the scope of topology optimization variable updates.

[0025] Optionally, in step S2, the implicit level set function is used. Parametric description of the aircraft structural boundaries:

[0026] ;

[0027] in, Represents the design domain; These are the node coordinates within the design domain; Represents a structural domain containing solid material; for The boundary;

[0028] Boundary evolution is driven by Hamilton-Jacobi partial differential equations:

[0029] ;

[0030] in, This represents a hypothetical time parameter that controls the rate of boundary evolution. Represents the gradient operator; The gradient magnitude of the corresponding level set function; To construct the normal velocity vector for boundary evolution;

[0031] After discretization, we obtain the first... The first iteration Update equations for the node level set function values:

[0032] ;

[0033] in, Indicates the current number Step iteration; It is the grid node number; It refers to the first During the first iteration, the... The level set function values ​​at each node; It is a given time step; It is the first During the first iteration, the... The gradient magnitude at each node is calculated using the Hamilton-Jacobi weighted essentially non-oscillatory scheme; It is the first Normal velocity vector at each node.

[0034] Optionally, in step S3, constraints are created. Defined as:

[0035] ;

[0036] in, It is a continuously differentiable modified ramp function; level set function The gradient; The unit vector in the direction of the stiffening thickness; Let be the approximate Dirac function in the narrowband region.

[0037] Optionally, in step S4, the comprehensive objective function is:

[0038] ;

[0039] The constraints include:

[0040] ;

[0041] in, It is a multi-objective function value; Let the compliance objective function be... Representing the First natural frequency; The feature vector representing its association; These are the weighting coefficients for the relevant objectives; Represents structural volume; Represents the maximum permissible material volume; It is the force vector; It is a displacement vector; Represents the global linear stiffness matrix; Represents the global quality matrix; This represents the Heaviside function; and These represent the maximum and minimum values ​​of the overall structural flexibility before and after the aircraft structural optimization iteration; and These represent the maximum and minimum values ​​of the overall natural frequency before and after the aircraft structure optimization iteration.

[0042] Optionally, in step S11, the discretized boundary is converted into a three-dimensional geometric solid model by constructing a NURBS spatial spline surface fitted to the boundary, and the conversion from STL format to STEP format is realized.

[0043] Compared with the prior art, the advantages of this invention are as follows:

[0044] 1. This invention intelligently constrains the aerodynamic profile of the aircraft by precisely controlling the design space during the topology optimization process, ensuring that the optimized structure maintains improved performance while the original aerodynamic characteristics are not negatively affected. Through precise protection of the aerodynamic surface morphology, a dual balance between structural and flight performance is achieved, effectively avoiding drastic changes in aerodynamic shape, thereby ensuring the stability, efficiency, and controllability of the aircraft under different flight conditions.

[0045] 2. This invention effectively controls the evolution of structural features in the design domain, particularly the discontinuity in stiffening thickness, by introducing manufacturing process-related constraints during topology optimization. By constraining potentially discontinuous regions during structural evolution, the invention successfully suppresses the generation of inverted structures and isolated connections. This constraint not only significantly improves the manufacturing adaptability of the aircraft structure but also optimizes the stability and consistency of process implementation, ensuring the manufacturability of the design and the overall process integrity of the structure, thereby meeting the requirements for high-precision and high-reliability manufacturing.

[0046] 3. This invention introduces implicit level set functions to accurately parameterize the boundaries of the aircraft structure. This method achieves a continuous and smooth evolution process of the boundaries, overcoming the limitations of gray-scale elements and checkerboard effects caused by discrete design variables in the traditional density method (SIMP). This method not only significantly improves the geometric representation accuracy of the structural boundaries but also effectively avoids common boundary ambiguity or distortion problems in the optimization process. Through refined boundary description, the geometric features in the optimization process are accurately captured and expressed, which is beneficial for generating high-quality finite element meshes and accurately constructing manufacturable geometric models. This characteristic greatly enhances the manufacturability of the final optimized structure in engineering practice, while improving the adaptability and functionality of the structure in practical applications.

[0047] 4. This invention, by introducing a compromise planning strategy, achieves precise trade-offs and optimization among multiple design objectives, avoiding performance deviations or imbalances that may arise from single-objective optimization. By systematically adjusting the relative importance of each objective function, this strategy can find the optimal compromise solution among multiple dimensions such as the stiffness and natural frequency of the aircraft structure, thereby ensuring that the design scheme meets lightweight requirements while also possessing good engineering feasibility and economy. Compromise planning not only improves the multidimensional adaptability of the optimization results but also enhances the operability and applicability of the final design. Especially when facing complex design constraints and manufacturing limitations, it can better balance performance and cost, achieving optimal design results.

[0048] 5. This invention geometrically reconstructs the structural boundaries obtained from topology optimization, employing NURBS spatial spline surfaces for precise fitting of the boundaries. This smoothly transforms the discretized structural boundaries into a continuous, machinable 3D geometric solid model. During reconstruction, key topological features and functional performance are preserved, ensuring that the optimization results adapt to actual manufacturing requirements without affecting design objectives. Furthermore, this method achieves efficient conversion between STL format and standard engineering formats such as STEP, greatly facilitating subsequent engineering analysis and manufacturing processes. This reconstructed model not only provides an accurate geometric basis for finite element simulation analysis but can also be directly used for CNC machining path generation and additive manufacturing file extraction, achieving seamless integration from topology optimization to manufacturing and ensuring integrated application throughout the entire design and production process.

[0049] Experimental results show that the method provided by this invention constructs a complete integrated spoiler design process of "design-optimization-manufacturing", which has excellent adaptability, scalability and industrial application prospects, and is suitable for the automated optimization design of spoiler structures of various high-performance aircraft. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments 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, wherein:

[0051] Figure 1 A flowchart of a multi-objective topology optimization method for aircraft design provided by the present invention;

[0052] Figure 2 This is an initial design model diagram of an aircraft structure, taking a spoiler as an example, provided in Embodiment 1 of the present invention;

[0053] Figure 3 This is a schematic diagram of the complete Pareto solution set obtained during the optimization process provided in Embodiment 1 of the present invention;

[0054] Figure 4 This is an optimized result diagram of the aircraft spoiler structure provided in Embodiment 1 of the present invention after topology optimization and reconstruction. Detailed Implementation

[0055] The technical solutions of 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, not all, of the embodiments of the present invention. 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.

[0056] The terms "first," "second," etc., used in the specification and claims of this invention are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class and the number of objects is not limited; for example, a first object can be one or more. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0057] Please see Figure 1 As shown, this embodiment of the invention provides a multi-objective topology optimization method for aircraft design, comprising the following steps:

[0058] Step S1: Establish a three-dimensional geometric model based on the geometry and outer contour dimensions of the aircraft structural components, and clearly define the optimization design area and the aerodynamic shape retention area.

[0059] Step S2: Construct the structural boundary representation function using the level set method;

[0060] Step S3: Set the maximization of stiffness and the maximization of natural frequency as optimization objectives, apply volume constraints and manufacturing constraints, and perform finite element analysis to solve the single-objective optimization of the aircraft structure response;

[0061] Step S4: Use the trade-off programming method to model the multi-objective problem and construct a comprehensive objective function that minimizes the distance to the ideal point;

[0062] Step S5: Transform the constrained optimization problem into an unconstrained form using the augmented Lagrange penalty function method, set the Lagrange multipliers and penalty parameters, and perform iterative updates.

[0063] Step S6: Calculate the shape sensitivity of the integrated objective function and constraint terms to the design variables, and derive the normal velocity field used for structural boundary evolution;

[0064] Step S7: Update the level set function through Hamilton-Jacobi partial differential equations to achieve structural boundary topology evolution and material distribution optimization;

[0065] Step S8: Determine whether the objective function meets the optimization convergence condition. If it does not meet the condition, return to step S5 to continue iteration. If it does meet the condition, terminate the optimization.

[0066] Step S9: Adjust the target weight coefficients, return to step S3 until all weight coefficients are traversed, and generate the Pareto front solution set;

[0067] Step S10: Based on the Pareto solution set, select the aircraft structure optimization scheme with the best comprehensive performance according to the mechanical performance required for actual application.

[0068] Step S11: Reconstruct the optimization results and output a three-dimensional aircraft structure model that is feasible for manufacturing.

[0069] In step S1, by setting an aerodynamic shape retention area in the three-dimensional geometric model, the outer contour surface and key width area of ​​the aircraft structure are excluded from the update range of topology optimization variables. This can achieve full-process constraint on the original aerodynamic shape of the aircraft, thereby maintaining the overall aerodynamic stability during the structural topology evolution process and ensuring that the aerodynamic performance of the aircraft does not undergo undesirable changes during the optimization process.

[0070] In step S2, implicit level set functions are used. Parametric description of the aircraft structural boundaries:

[0071] ;

[0072] in, Represents the design domain; These are the node coordinates within the design domain; Represents a structural domain containing solid material; for The boundary;

[0073] Boundary evolution is driven by Hamilton-Jacobi partial differential equations:

[0074] ;

[0075] in, This represents a hypothetical time parameter that controls the rate of boundary evolution. Represents the gradient operator; The gradient magnitude of the corresponding level set function; To construct the normal velocity vector for boundary evolution;

[0076] After discretization, we obtain the first... The first iteration Update equations for the node level set function values:

[0077] ;

[0078] in, Indicates the current number Step iteration; It is the grid node number; It refers to the first During the first iteration, the... The level set function values ​​at each node; It is a given time step; It is the first During the first iteration, the... The gradient magnitude at each node is calculated using the Hamilton-Jacobi weighted essentially non-oscillatory scheme; It is the first Normal velocity vector at each node.

[0079] Step S2 introduces implicit level set functions to parametrically describe the aircraft structural boundary, achieving a continuous and smooth boundary evolution process. This effectively avoids the gray-scale element and checkerboard problems caused by discrete design variables in the density method (SIMP). This method improves the clarity of the structural boundary and the accuracy of the geometric representation, which is beneficial for generating high-quality finite element meshes and manufacturable geometric models, thereby enhancing the engineering manufacturability and practical application adaptability of the final structure.

[0080] In step S3, constraints are created. Defined as:

[0081] ;

[0082] in, It is a continuously differentiable modified ramp function used to measure the degree of deviation between the normal direction and the stiffening thickness direction; level set function The gradient; The unit vector in the direction of the stiffening thickness; For the approximate Dirac function in the narrow band region, ensure that the integral constraint mainly acts on the structural boundary region.

[0083] In step S3, manufacturing feasibility constraints are introduced. By functionally penalizing the distribution characteristics of discontinuous structures along the stiffening thickness direction in the design domain, the inverted structures and isolated connections that appear during the topology evolution process are effectively suppressed, thereby improving the overall manufacturability and process integrity of the aircraft structure.

[0084] In step S4, the multi-objective optimization model is constructed using a trade-off programming method. By minimizing the Euclidean distance between the normalized weighted objective vector and the ideal performance point, a comprehensive objective function with unified dimensions is established, where the comprehensive objective function is:

[0085] ;

[0086] The constraints include:

[0087] ;

[0088] in, It is a multi-objective function value; Let the compliance objective function be... Representing the First natural frequency; The feature vector representing its association; These are the weighting coefficients for the relevant objectives; Represents structural volume; Represents the maximum permissible material volume; It is the force vector; It is a displacement vector; Represents the global linear stiffness matrix; Represents the global quality matrix; This represents the Heaviside function; and These represent the maximum and minimum values ​​of the overall structural flexibility before and after the aircraft structural optimization iteration; and These are the maximum and minimum values ​​of the overall natural frequency before and after the aircraft structure optimization iteration, respectively. Their values ​​can be obtained from the single-objective stiffness optimization and single-objective basic natural frequency optimization in step S3.

[0089] Step S4 employs a compromise programming method, which effectively overcomes the problem that the traditional linear weighted method is prone to solution set bias and performance imbalance when dealing with multiple objectives with significant differences in magnitude. This results in a Pareto front solution set that is evenly distributed, has strong coverage, and has a reasonable performance trade-off, which can be used to guide the design and selection of multiple schemes for aircraft structures.

[0090] In step S11, 3D modeling software is used to geometrically reconstruct the boundary obtained from topology optimization. By constructing a NURBS spatial spline surface fitted to the boundary, the discretized boundary is converted into a continuous and machinable 3D geometric solid model. During the reconstruction process, key topological features and functional performance of the structure are preserved, and geometric conversion from STL format to standard engineering formats such as STEP is achieved, ensuring that the model has good manufacturability and integrability. This reconstructed structural model is not only suitable for subsequent finite element simulation analysis, but can also be directly used for CNC machining path generation and additive manufacturing file extraction, supporting integrated engineering applications throughout the entire process from topology optimization design to manufacturing implementation.

[0091] The multi-objective topology optimization method for aircraft design provided by the present invention will be described in detail below with reference to specific embodiment 1.

[0092] Example 1

[0093] The method provided by the present invention will be described using a spoiler as a typical aircraft structural component. The method includes the following steps:

[0094] Step S1: Based on the original geometric shape and aerodynamic profile dimensions of the spoiler assembly, construct a complete three-dimensional spoiler structural model, such as... Figure 2 As shown, the model includes an upper skin, lower skin, leading edge, trailing edge, and joint. The model area is divided into a structural optimization domain and an aerodynamic shape preservation domain. The upper and lower skins of the spoiler and the connecting joint are designated as non-evolvable regions to maintain the continuity of the aircraft's aerodynamic shape and the integrity of the sealed cavity. In the structural optimization domain, materials can be freely distributed during design iterations, allowing the topology to evolve. The initial skin thickness is uniformly set to 1 mm in the initial model as an initial baseline value to provide basic structural stiffness.

[0095] Step S2, using the level set function Implicit modeling is used to achieve a continuous and smooth evolution process of the boundary, effectively avoiding the gray-scale cell and checkerboard problem caused by discrete design variables in the density method (SIMP), and improving boundary clarity and structural manufacturability:

[0096] ;

[0097] in, Represents the design domain; These are the node coordinates within the structural design domain; Represents a structural domain containing solid material; for The boundary.

[0098] Step S3: Select compliance and first-order natural frequency as the objective functions for multi-objective topology optimization design. The compliance function characterizes the deformation performance of the structure under external loads, while the natural frequency index improves the dynamic stability of the structure. Volume is used as a constraint term, and the optimization variable is the material distribution function within the optimization design region. Simultaneously, to improve manufacturing feasibility, manufacturing constraints are introduced during modeling, setting the stiffening thickness direction as the positive Z-axis to avoid the structure exhibiting an "inverted" shape.

[0099] Manufacturing constraints are defined in the following integral form:

[0100] ;

[0101] in, It is a continuously differentiable modified ramp function used to measure the degree of deviation between the normal direction and the stiffening thickness direction; It is a level set function The gradient; The unit vector in the direction of the stiffening thickness; For the approximate Dirac function in the narrow band region, ensure that the integral constraint mainly acts on the structural boundary region.

[0102] The mathematical model for optimizing an aircraft spoiler under a horizontal set framework, with the single objective of maximizing stiffness (i.e., minimizing flexibility) and applying volume and manufacturing constraints, is as follows:

[0103] ;

[0104] in, Let the compliance objective function be... It is the force vector; For transpose; It is a displacement vector; Represents the global linear stiffness matrix; Represents structural volume; This represents the maximum permissible material volume.

[0105] The mathematical model for optimizing an aircraft spoiler under a level set framework, with the single objective of maximizing the basic natural frequency and applying volume and manufacturing constraints, is as follows:

[0106] ;

[0107] in, Represents the global stiffness matrix; Represents the global quality matrix; Representing the First natural frequency; The feature vector representing its association; This is a transpose.

[0108] Step S4: Based on the flexibility response index and the first-order natural frequency of the structure obtained in Step S2, a multi-objective optimization problem is constructed. A Pareto optimality theory combined with a trade-off programming method is used to establish the objective function model, incorporating different performance indices as parallel optimization objectives into a unified mathematical framework. Since flexibility and natural frequency differ significantly in magnitude, directly performing a linear weighted summation can easily lead to a bias in the optimization solution towards a particular objective, thereby weakening the overall performance synergy. Therefore, each objective function is normalized to maintain consistency in numerical scale, ensuring a reasonable balance and trade-off between improving structural stiffness and enhancing dynamic performance during the optimization process, resulting in a more engineering-practical optimal design scheme.

[0109] ;

[0110] in, It is a multi-objective function value; Let the compliance objective function be... Representing the First natural frequency; The feature vector representing its association; These are the weighting coefficients for the relevant objectives; Represents structural volume; It is the force vector; It is a displacement vector; Represents the global linear stiffness matrix; Represents the global quality matrix; This represents the Heaviside function; and These represent the maximum and minimum values ​​of the overall structural flexibility before and after the aircraft structural optimization iteration; and These are the maximum and minimum values ​​of the overall natural frequency before and after the aircraft structure optimization iteration, respectively. Their values ​​can be obtained from the single-target stiffness optimization and single-target basic natural frequency optimization in step three.

[0111] Step S5: Use the augmented Lagrangian penalty function method to transform the constrained optimization problem in the multi-objective problem into an unconstrained problem:

[0112] ;

[0113] in, Indicates the first Lagrange multipliers for step-by-step iteration; This represents the augmented Lagrange function.

[0114] Corresponding Lagrange multiplier Update according to the following plan:

[0115] ;

[0116] in, Indicates the first The penalty parameter for each iteration, which is related to... Simultaneously updated, therefore, the Lagrange multiplier It will provide a reasonable approximation of the exact Lagrange function through iterative updates.

[0117] Step S6, solve for sensitivity. Calculate the Lagrange shape derivative, choosing the normal velocity as the descent direction. The shape derivative is the sensitivity of the objective function to small changes in the shape region. In multi-objective problems, the advection velocity is solved as follows:

[0118] ;

[0119] The stiffness and sensitivity are solved as follows:

[0120] ;

[0121] in, This represents the transpose of the element nodal displacement vector; Represents the element stiffness matrix; Represents the displacement vector of the element node;

[0122] The basic natural frequency sensitivity is solved as follows:

[0123] ;

[0124] Based on the above analysis, within the established Lagrangian framework, coupling these two objective functions, the advection velocity that maximizes stiffness and fundamental natural frequency under volume constraints is:

[0125] ;

[0126] Step S7: Update the level set function to drive the evolution of the structural boundary. This is achieved by driving the level set function through the Hamilton-Jacobi partial differential equation. Evolutionary updates are performed to achieve surface and topological evolution of the spoiler structure and optimize its internal material distribution.

[0127] ;

[0128] in, Represents the level set function; This represents a hypothetical time parameter that controls the rate of boundary evolution. Represents the gradient operator; The gradient magnitude of the corresponding level set function; To construct the normal velocity vector for boundary evolution, discretize the above equation to obtain the first... Step iteration Update equations for the node level set function values:

[0129] ;

[0130] in, Indicates the current number Step iteration; It is the grid node number; It refers to the first During the first iteration, the... The level set function values ​​at each node; It is a given time step, and the gradient solution It is the first During the first iteration, the... The gradient magnitude at each node is calculated using the Hamilton-Jacobi weighted essentially non-oscillatory scheme; It is the first The normal velocity vector at each node; for the node The normal velocity obtained from the objective function shape sensitivity is equivalent to the steepest descent method in the Hamilton-Jacobi equation. This is when the normal velocity along the material interface... Convergence occurs when a very small zero tolerance range is satisfied.

[0131] Step S8: After each iteration, calculate the relative rate of change between the objective function value of the current spoiler structure and the result of the previous iteration, as the basis for convergence judgment. When the relative error of the objective function is lower than a preset threshold of 1%, the optimization process is considered to have converged, the iteration is terminated, and the optimized structure is output. If the convergence condition is not met, return to step S5 and continue iterative optimization.

[0132] Step S9: Adjust the target weight coefficients through the system, return to step S3, and repeat until all weight coefficients have been traversed to generate a Pareto front solution set covering various design preferences, such as... Figure 3 As shown.

[0133] Step S10: Based on the obtained Pareto solution set, and in combination with the aircraft design requirements and operational adaptability, select the spoiler structure layout scheme that is most suitable for engineering practice, so as to achieve a local optimal match between performance and manufacturability.

[0134] Step S11: In this embodiment, the target weight coefficient is selected. By constructing a NURBS spatial spline surface fitted to the boundary, the discretized structural boundary is smoothly transformed into a continuous and machinable three-dimensional geometric solid model of the spoiler, such as... Figure 4 As shown in Table 1, the optimized structure is compared with a traditional spoiler. The results show that, under approximately the same total mass, the optimized structure obtained by this invention exhibits significant advantages in both static stiffness and dynamic response. Specifically, the maximum displacement is reduced by approximately 32.35%, the maximum Von Mises stress is reduced by approximately 41.49%, and the first three natural frequencies are all improved, with the first modal frequency increasing by approximately 64.75%. This significantly enhances the structure's vibration resistance and dynamic stability, effectively reducing the risk of resonance.

[0135] Table 1. Performance Comparison of Two Spoiler Structures

[0136]

[0137] Figure 3This diagram illustrates the Pareto front solution set for a spoiler obtained using the multi-objective topology optimization method proposed in this invention. The horizontal axis represents the compliance index of the optimized structure, and the vertical axis represents the corresponding first-order natural frequency. Both performance indices have been normalized to eliminate bias caused by differences in magnitude. The multiple Pareto front points shown in the diagram are evenly distributed, exhibiting good continuity and monotonicity, fully demonstrating the high-quality non-dominated solution space generated by this method under different performance weighting coefficient settings. Figure 3 It is evident that the optimization strategy proposed in this invention can achieve diverse trade-offs between structural stiffness and dynamic response, providing designers with a flexible and adjustable design solution set, significantly enhancing the adaptability and controllability of spoiler structure design, and further verifying the effectiveness and engineering applicability of the method of this invention in dealing with multi-objective conflicts and achieving design diversity.

[0138] Figure 4 This paper presents a 3D model of a spoiler after geometric reconstruction based on the topology optimization results of this invention. The optimized structure has continuous and smooth boundaries, and the overall geometry exhibits good manufacturability, meeting the practical needs of CAD geometric reconstruction and subsequent engineering manufacturing processes. The material distribution shows clear and distinct boundaries, with a clear distinction between the non-structural area and the design area, avoiding non-manufacturable features such as grayscale units and inverted structures commonly found in traditional optimization results. While fully preserving the original aerodynamic profile, the reconstructed structure significantly improves its adaptability to various manufacturing paths, including additive manufacturing, mold forming, and CNC machining, providing direct data support for achieving a seamless transition from topology optimization results to engineering implementation of the spoiler.

[0139] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0140] Furthermore, it should be noted that the scope of the methods and systems in the embodiments of the present invention is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. In addition, features described with reference to certain examples may be combined in other examples.

[0141] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of the present invention.

Claims

1. A multi-objective topology optimization method for aircraft design, characterized in that, Includes the following steps: Step S1: Establish a three-dimensional geometric model based on the geometry and outer contour dimensions of the aircraft structural components, and clearly define the optimization design area and the aerodynamic shape retention area. Step S2: Construct the structural boundary representation function using the level set method; through implicit level set functions... Parametric description of the aircraft structural boundaries: ； in, Represents the design domain; These are the node coordinates within the design domain; Represents a structural domain containing solid material; for The boundary; Boundary evolution is driven by Hamilton-Jacobi partial differential equations: ； in, This represents a hypothetical time parameter that controls the rate of boundary evolution. Represents the gradient operator; The gradient magnitude of the corresponding level set function; To construct the normal velocity vector for boundary evolution; After discretization, we obtain the first... The first iteration Update equations for the node level set function values: ； in, Indicates the current number Step iteration; It is the grid node number; It refers to the first During the first iteration, the... The level set function values ​​at each node; It is a given time step; It is the first During the first iteration, the... The gradient magnitude at each node is calculated using the Hamilton-Jacobi weighted essentially non-oscillatory scheme; It is the first Normal velocity vector at each node; Step S3: Set maximizing stiffness and maximizing natural frequency as optimization objectives, apply volume constraints and manufacturing constraints, and perform finite element analysis to solve for the single-objective optimization of the aircraft structure response; manufacturing constraints Defined as: ； in, It is a continuously differentiable modified ramp function; level set function The gradient; The unit vector in the direction of the stiffening thickness; This is the approximate Dirac function in the narrowband region; Step S4: Use the trade-off programming method to model the multi-objective problem and construct a comprehensive objective function that minimizes the distance to the ideal point; Step S5: Transform the constrained optimization problem into an unconstrained form using the augmented Lagrange penalty function method, set the Lagrange multipliers and penalty parameters, and perform iterative updates. Step S6: Calculate the shape sensitivity of the integrated objective function and constraint terms to the design variables, and derive the normal velocity field used for structural boundary evolution; Step S7: Update the level set function through Hamilton-Jacobi partial differential equations to achieve structural boundary topology evolution and material distribution optimization; Step S8: Determine whether the objective function meets the optimization convergence condition. If it does not meet the condition, return to step S5 to continue iteration. If it does meet the condition, terminate the optimization. Step S9: Adjust the target weight coefficients, return to step S3 until all weight coefficients are traversed, and generate the Pareto front solution set; Step S10: Based on the Pareto solution set, select the aircraft structure optimization scheme with the best comprehensive performance according to the mechanical performance required for actual application. Step S11: Reconstruct the optimization results and output a three-dimensional aircraft structure model that is feasible for manufacturing.

2. The method according to claim 1, characterized in that, In step S1, by setting an aerodynamic shape preservation region in the three-dimensional geometric model, the outer contour surface of the aircraft structure and the critical width region are excluded from the scope of topology optimization variable update.

3. The method according to claim 1, characterized in that, In step S4, the comprehensive objective function is: ； The constraints include: ； in, It is a multi-objective function value; Let the compliance objective function be... Representing the First natural frequency; The feature vector representing its association; These are the weighting coefficients for the relevant objectives; Represents structural volume; Represents the maximum permissible material volume; It is the force vector; It is a displacement vector; Represents the global linear stiffness matrix; Represents the global quality matrix; This represents the Heaviside function; and These represent the maximum and minimum values ​​of the overall structural flexibility before and after the aircraft structural optimization iteration; and These represent the maximum and minimum values ​​of the overall natural frequency before and after the aircraft structure optimization iteration.

4. The method according to claim 1, characterized in that, In step S11, by constructing a NURBS spatial spline surface fitted to the boundary, the discretized boundary is converted into a three-dimensional geometric solid model, and the conversion from STL format to STEP format is realized.

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