Automobile front-end module optimization method based on multi-working-condition topology

Through the multi-case topology optimization method, the problem of taking into account both performance and lightweight of the automotive front-end module is solved, and the goal of structural performance optimization and weight reduction is achieved, reducing design costs and improving market competitiveness.

CN119473270APending Publication Date: 2025-02-18HEFEI HENGXIN LIGHTWEIGHT TECH DEVELOPENT CO LTD
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Patent Information

Application Number
CN202411405782.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-10-10
Publication Date
2025-02-18

AI Technical Summary

Technical Problem

Existing automotive front-end modules are difficult to balance between performance and lightweight, resulting in low material utilization and high cost.

Method used

Adoption method based on multi-case topology, by building a three-dimensional assembly model, setting multi-case boundary conditions, defining design response and objective function, topology optimization is performed using orthogonal penalization material density method, and the topology structure of the front-end module is optimized to achieve the maximum Excellent design plan.

Benefits of technology

It achieves the reduction of weight and cost while meeting the structural performance of the front-end module of the automobile while reducing the weight and reducing costs, improving material utilization and market competitiveness.

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Abstract

The invention provides an automobile front-end module optimization method based on multi-working-condition topology, and the method comprises the steps: 1, constructing a three-dimensional assembly model, and carrying out the geometric repair and finite element mesh division of the three-dimensional assembly model; defining a design domain and a non-design domain; 2, setting a multi-working-condition boundary condition and a fixed constraint of the three-dimensional assembly model, and defining a design response; 3, the minimum flexibility is defined as a target function of front-end module design, and manufacturing process constraint parameters are set; step 4, adopting an orthogonal penalty material density method topological optimization algorithm to carry out multiple iterative calculations to obtain a front-end module after topological optimization; 5, performing reanalysis on the front-end module after topological optimization, and judging and checking whether the rigidity performance of each working condition of the optimized model meets the requirements or not; if yes, model reconstruction shaping of the final front-end module is carried out; otherwise, returning to the step 1. The method has the advantages of simple logic, convenience, reliability and the like, and meanwhile, the development and design period of the front-end module is greatly shortened.
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Description

Technical Field

[0001] The present invention relates to the technical field of automobile front-end module optimization, and in particular to an automobile front-end module optimization method based on multi-operating condition topology. Background Art

[0002] With the rapid development of the new car market, the development cycle of automotive parts has been drastically shortened. As one of the important automotive parts, the front-end frame has a wide variety of performance indicators and very strict target requirements. Therefore, it is difficult to design a full-plastic front-end frame that meets all performance indicators and optimizes weight within a limited development cycle. Topology optimization is a conceptual design method that calculates the optimal design solution in a predetermined design space, and its application in automotive lightweight design is becoming more and more widespread, mainly because topology optimization can achieve efficient product design.

[0003] At present, the development and design of products is still in the empirical design stage. The designed rib thickness, rib position and direction are too complicated, which makes it impossible for the product to achieve the optimal solution for lightweight performance, thereby indirectly affecting the material utilization rate and cost of the product. This method uses the topological optimization method of finite element theory to perform topological optimization design on the front-end module of the automobile, effectively solving and realizing the optimal solution problem of stiffness of each installation point of the front-end module of the automobile, thereby achieving the goal of lightweight while meeting the structural performance of the front-end module of the automobile. Summary of the invention

[0004] In view of the deficiencies in the prior art, the purpose of the present invention is to provide an automobile front-end module optimization method and device based on a multi-operating condition topology, which can solve the existing problems.

[0005] In order to achieve the above object, the technical solution of the present invention is as follows:

[0006] The present invention is implemented by the following technical solution: an automobile front-end module optimization method based on multi-operating condition topology, comprising the following steps:

[0007] Step 1: Construct a 3D assembly model of the front-end module, anti-collision beam, connecting sheet metal and energy absorption box, and perform geometric repair and finite element meshing on the 3D assembly model; define the design domain and non-design domain based on the divided mesh;

[0008] Step 2: setting multi-condition boundary conditions and fixed constraints of the three-dimensional assembly model, and defining design responses, including volume fraction response and weighted compliance response;

[0009] Step 3: Define the minimization of flexibility as the objective function of the front-end module design and set the manufacturing process constraint parameters;

[0010] Step 4: Use the orthogonal penalty material density method topology optimization algorithm to perform multiple iterative calculations to obtain the front-end module after topology optimization;

[0011] Step 5: Re-analyze the front-end module after topology optimization to determine whether the stiffness performance of each working condition of the optimized model meets the requirements;

[0012] If satisfied, the model of the front-end module after final optimization is reconstructed and finalized;

[0013] If not satisfied, repeat steps 1 to 5.

[0014] Furthermore, the design domain and the non-design domain are defined according to the divided grids, including defining the front-end module as the design domain, and defining the anti-collision beam, the connecting sheet metal and the energy absorption box as the non-design domain.

[0015] Furthermore, the multi-operating condition boundary conditions include the static stiffness of the hood lock area in the X / Z direction, the static stiffness of the headlight in the Z direction, the static stiffness of the radiator in the X / Z direction, and the static stiffness of the buffer block in the Z direction.

[0016] Furthermore, the manufacturing process constraint parameters are set to include checkerboard phenomenon control, maximum / minimum size constraints and draft / extrusion constraints.

[0017] Furthermore, the re-analyzing the front-end module after topology optimization includes re-analyzing the front-end module after topology optimization using the OSSmooth module in the optistruct software.

[0018] Furthermore, the OSSmooth module in the optistruct software is used to re-analyze the front-end module after topology optimization, including:

[0019] Import the topology optimization results into OptiStruct software;

[0020] Configure the parameters of the OSSmooth module;

[0021] Run the OSSmooth module to generate a smoothed model;

[0022] Reanalyze the smoothed model;

[0023] Based on the results of the reanalysis, evaluate whether the smoothed model meets the design requirements.

[0024] Furthermore, the calibration of image data includes: image classification, target detection and semantic segmentation.

[0025] An automobile front-end module optimization device based on multi-operating condition topology includes a processor and a memory; the memory is used to store programs; the processor executes the program to implement any of the methods described above.

[0026] A computer-readable storage medium stores a program, wherein the program is executed by a processor to implement any of the methods described above.

[0027] Compared with the prior art, the beneficial effects of the present invention include:

[0028] The automotive front-end module optimization method based on multi-operating-condition topology of the present invention has the advantages of being able to simultaneously perform structural topology optimization of multiple operating conditions, obtaining the optimal design solution through structural topology optimization, improving the structural rigidity while reducing the structural weight, and achieving the lightweight goal of reducing costs and increasing efficiency; the second advantage is that the optimized front-end module can be directly re-analyzed and the model reconstructed, further shortening the development cycle of the front-end module, thereby achieving the goal of saving design costs to enhance market competitiveness. The present invention has the advantages of simple logic, convenience and reliability, and greatly shortens the cycle of front-end module development and design. It has extremely high practical value and promotion significance in the automotive field, especially in the field of lightweight optimization technology for automotive front-end modules. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The disclosure of the present invention is described with reference to the accompanying drawings. It should be understood that the drawings are only for illustrative purposes and are not intended to limit the scope of protection of the present invention. In the drawings, the same reference numerals are used to refer to the same components. Among them:

[0030] Figure 1 It is a schematic flow chart of the automobile front-end module optimization method based on multi-operating condition topology of the present invention;

[0031] Figure 2 A schematic diagram of a three-dimensional assembly model of a front-end module, a connecting sheet metal, an energy absorption box and an anti-collision beam in an embodiment of the present invention;

[0032] As shown in the figure: 1. Front end module; 2. Connecting sheet metal; 3. Energy absorption box; 4. Anti-collision beam. DETAILED DESCRIPTION

[0033] It is easy to understand that according to the technical solution of the present invention, without changing the essential spirit of the present invention, a person skilled in the art can propose a variety of interchangeable structural modes and implementation modes. Therefore, the following specific implementation modes and drawings are only exemplary descriptions of the technical solution of the present invention, and should not be regarded as the whole of the present invention or as a limitation or restriction to the technical solution of the present invention.

[0034] The present invention provides an automobile front-end module optimization method based on multi-operating condition topology, comprising the following steps:

[0035] Step 1: Construct a 3D assembly model of the front-end module, anti-collision beam, connecting sheet metal and energy absorption box, and perform geometric repair and finite element meshing on the 3D assembly model; define the design domain and non-design domain based on the divided mesh;

[0036] In the present invention, the front-end module is defined as the design area, and the anti-collision beam, connecting sheet metal and energy absorption box are defined as the non-design area;

[0037] Define the 3D assembly model to efficiently and accurately extract the model mid-face and generate high-quality meshes to improve calculation efficiency and accuracy. This step is the basis of the entire optimization process. High-quality models and meshes are the prerequisites for all subsequent analysis and optimization.

[0038] Specifically, the 3D assembly model is constructed using CAD software such as SolidWorks, CATIA, SiemensNX, or Fusion 360. The steps are:

[0039] To create a single part model:

[0040] Front-end module: Create a 3D model of the front-end module according to design requirements.

[0041] Crash beam: Create a 3D model of the crash beam, paying attention to its cross-sectional shape and length.

[0042] Connecting sheet metal: Create a 3D model of the connecting sheet metal to ensure it can properly connect the front end module and the anti-collision beam.

[0043] Crash Box: Create a 3D model of a crash box, taking into account its internal structure and material properties.

[0044] Assembly parts:

[0045] Create an assembly file in your CAD software.

[0046] Import the above parts into the assembly file one by one; Figure 2 As shown in the figure, the front end module 1, the connecting sheet metal 2, the energy absorption box 3 and the anti-collision beam 4 are modeled and assembled as shown in the figure. Figure 2 shown.

[0047] Use constraints such as fit, alignment, distance, etc. to fit the parts together correctly.

[0048] Geometry repair Use geometry repair tools such as Autodesk Meshmixer, Geomagic Design X, or the repair function of the CAD software. The steps are:

[0049] Check geometry model: Import assembly model into geometry repair tool.

[0050] Check the model for geometric problems such as gaps, overlaps, discontinuities, etc.

[0051] Fix Geometry Issues: Fill Gaps: Use the Fill tool to fill small gaps in your model.

[0052] Fix overlaps: adjust geometry positions or remove redundant geometry parts.

[0053] Smooth Surface: Use the Smooth tool to improve the surface quality of your model.

[0054] Patch Holes: Use the Patch tool to fill holes in your model.

[0055] Finite element analysis software used for finite element meshing: such as ANSYS, Abaqus, or HyperMesh. The steps are:

[0056] Import geometric model: Import the repaired geometric model into finite element analysis software.

[0057] Define mesh type: Select the appropriate mesh type (such as tetrahedron, hexahedron, shell element, etc.).

[0058] Set mesh parameters: define mesh size, density, and quality criteria.

[0059] Finer meshes can be used for critical areas (such as joints and stress concentration areas).

[0060] Generate mesh: Run the meshing command to generate the finite element mesh.

[0061] Check the mesh quality to ensure there are no distorted or oversized elements.

[0062] Define the design domain and non-design domain. The steps are:

[0063] Selecting the design domain: determining which parts are the target areas (design domains) for design optimization. Exemplarily, the design domain front-end module of the present invention selects these areas in the finite element model and marks them as design domains.

[0064] Select non-design domain: determine which parts are fixed areas (non-design domains) that do not need to be optimized. For example, the present invention defines the connecting sheet metal, anti-collision beam and energy absorption box as non-design domains. Select these areas in the finite element model and mark them as non-design domains.

[0065] Step 2: setting multi-condition boundary conditions and fixed constraints of the three-dimensional assembly model, and defining design responses, including volume fraction response and weighted compliance response;

[0066] The multi-condition boundary conditions and fixed constraints of the model are set to simulate the actual assembly constraints and the actual working condition loading conditions. The multi-conditions include but are not limited to the X / Z static stiffness of the hood lock area, the Z static stiffness of the headlight, the X / Z static stiffness of the radiator, and the Z static stiffness of the buffer block. The X / Z static stiffness of the lock area simulates the stiffness requirements of the lock area in the X and Z directions; the Z static stiffness of the headlight simulates the stiffness requirements of the headlight in the Z direction; the X / Z static stiffness of the radiator simulates the stiffness requirements of the radiator in the X and Z directions; and the Z static stiffness of the buffer block simulates the stiffness requirements of the buffer block. The lock area refers to the designated areas that are not involved in the optimization during the topology optimization process, and their original geometric shape and material distribution are maintained.

[0067] Set fixed constraints for the model to simulate the constraints in the actual assembly. For example, fix the position of certain key components to prevent them from moving during the analysis process.

[0068] Volume fraction response: Defines the volume fraction response, which is used to control the volume of the optimized model. The volume fraction usually represents the material density distribution of the optimized model.

[0069] Weighted Flexibility Response: Define a weighted flexibility response that takes the performance requirements from the multi-case boundary conditions and fixed constraints of the model as weighted flexibility responses. Flexibility is the inverse of stiffness, so minimizing flexibility is the same as maximizing stiffness.

[0070] Step 3: Define the minimization of flexibility as the objective function of the front-end module design and set the manufacturing process constraint parameters;

[0071] Minimizing flexibility is to maximize stiffness; setting manufacturing process constraint parameters, including but not limited to checkerboard phenomenon control, maximum / minimum size constraints, draft / extrusion constraints, etc., to control the actual manufacturability of the optimized model;

[0072] Minimizing compliance (i.e. maximizing stiffness) is a common optimization goal in front-end module design. By minimizing compliance, it is possible to ensure that the structure has higher stiffness when subjected to external loads, thereby reducing deformation and improving overall performance.

[0073] Step 4: Use the orthogonal penalty material density method topology optimization algorithm to perform multiple iterative calculations to obtain the front-end module after topology optimization;

[0074] The method of topology optimization using orthogonal penalty material density method (SIMP, Solid Isotropic Material with Penalization) includes the following specific steps:

[0075] Problem definition

[0076] First, the optimization goal and constraints are clarified. Step 3 has already introduced that the goal of the present invention is to minimize flexibility (maximize stiffness).

[0077] The constraint parameters are: checkerboard phenomenon control, maximum / minimum size constraint, draft / extrusion constraint, etc.

[0078] 4.2. Grid division

[0079] In step 1, the front-end module is assembled into a 3D model and then divided into finite element meshes. The fineness of the mesh will affect the calculation accuracy and calculation time.

[0080] 4.3. Initializing design variables

[0081] Define the design variables (x_i) to represent the material density of each element. The initial value is usually set to an intermediate value (such as 0.5), indicating that all elements are partially filled with material.

[0082] 4.4. Constructing the stiffness matrix

[0083] According to the current design variables (x_i), the stiffness matrix (K) of the structure is constructed. The SIMP method controls the nonlinear behavior of the material by introducing a penalty factor (p): [E(x_i)=E_0x_i^p] where:

[0084] (E_0) is the elastic modulus of the material.

[0085] (p) is a penalty factor, usually 3 or higher, to promote the binarization of the material (0 or 1).

[0086] 4.5. Solving for displacement

[0087] Use the finite element method to solve for the displacement (\mathbf{u}): [K\mathbf{u}=\mathbf{F}]

[0088] 4.6. Calculation of flexibility

[0089] According to the displacement (\mathbf{u}), calculate the flexibility (C): [C=\mathbf{u}^T\mathbf{F}]

[0090] 4.7. Update design variables

[0091] Use optimization algorithms (such as gradient descent method, optimization criterion method, etc.) to update the design variables (x_i). Common update formulas include: [x_i^{k+1}=x_i^k-\alpha\frac{\partial C}{\partial x_i}] where:

[0092] (k) is the number of iterations.

[0093] (\alpha) is the step size parameter.

[0094] (\frac{\partial C}{\partial x_i}) is the sensitivity of the flexibility to the design variables.

[0095] 4.8. Checking convergence conditions

[0096] Check whether the convergence conditions are met, such as the change of the design variable is less than a certain threshold or the maximum number of iterations is reached. If not, return to step 4.4 to continue iterating.

[0097] 4.9. Output optimization results

[0098] When the convergence conditions are met, the optimized design variables (x_i) are output and the optimization results are visualized.

[0099] Step 5: Re-analyze the front-end module after topology optimization to determine whether the stiffness performance of each working condition of the optimized model meets the requirements;

[0100] If satisfied, the model of the front-end module after final optimization is reconstructed and finalized;

[0101] If not satisfied, repeat steps 1 to 5.

[0102] Furthermore, the OSSmooth module in the optistruct software was used to re-analyze the front-end module after topology optimization to verify whether the stiffness performance of each working condition of the optimized model meets the requirements.

[0103] The OSSmooth module is used to smooth and refine the topology optimization results to make them more in line with actual manufacturing requirements. The specific steps are as follows:

[0104] 5.1 Import optimization results

[0105] The topology optimization results were imported into OptiStruct software.

[0106] 5.2 Configure OSSmooth parameters

[0107] Configure the parameters of the OSSmooth module to ensure that the smoothed model meets the design requirements. Common parameters include:

[0108] Smoothing degree: Controls the degree of smoothing. Too high a value may result in loss of details, while too low a value may not result in a smoothing effect.

[0109] Minimum thickness: Ensure that the smoothed model has sufficient minimum thickness to avoid manufacturing difficulties.

[0110] Boundary Treatment: Select how to treat the model's boundaries, such as keeping the boundaries unchanged or allowing them to vary.

[0111] 5.3 Run OSSmooth

[0112] Run the OSSmooth module to generate a smoothed model.

[0113] 5.4. Reanalysis

[0114] Reanalyze the smoothed model to verify whether its performance meets the design requirements. This step usually includes:

[0115] Static analysis: Check stress, displacement and other indicators.

[0116] Modal Analysis: Evaluate the vibration characteristics of your model.

[0117] Thermal analysis (if necessary): Evaluate thermal stresses and temperature distribution.

[0118] 5.5. Results Evaluation

[0119] Based on the results of the reanalysis, evaluate whether the smoothed model meets the design requirements. If necessary, adjust the OSSmooth parameters and repeat the above steps until a satisfactory result is obtained.

[0120] 5.6. Prepare for manufacturing

[0121] Once the model meets all design and performance requirements, it can be prepared for manufacturing. This may include generating CAM files, 3D printing files, etc.

[0122] Precautions

[0123] Maintain design intent: Ensure that the basic design intent of the model is not changed during the smoothing process.

[0124] Verify results: Verify after each modification to ensure that the performance of the model has not degraded.

[0125] Comparison of multiple solutions: Try different smoothing parameters, compare the effects of different solutions, and select the optimal solution.

[0126] The present invention also provides an automobile front-end module optimization device based on multi-operating condition topology, comprising a processor and a memory; the memory is used to store programs; the processor executes the program to implement any of the above methods.

[0127] The automotive front-end module optimization method based on multi-operating-condition topology of the present invention has the advantages of being able to simultaneously perform structural topology optimization of multiple operating conditions, obtaining the optimal design solution through structural topology optimization, improving the structural rigidity while reducing the structural weight, and achieving the lightweight goal of reducing costs and increasing efficiency; the second advantage is that the optimized front-end module can be directly re-analyzed and the model reconstructed, further shortening the development cycle of the front-end module, thereby achieving the goal of saving design costs to enhance market competitiveness. The present invention has the advantages of simple logic, convenience and reliability, and greatly shortens the cycle of front-end module development and design. It has extremely high practical value and promotion significance in the automotive field, especially in the field of lightweight optimization technology for automotive front-end modules.

[0128] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in terms of function in the above description. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this article.

[0129] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0130] In the several embodiments provided herein, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic, for example, the division of the units is only a logical function division, and there may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, or can be electrical, mechanical or other forms of connection.

[0131] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the embodiments of this article.

[0132] In addition, each functional unit in each embodiment of this invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above integrated unit may be implemented in the form of hardware or in the form of software functional unit.

[0133] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this article is essentially or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of this article. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program code.

[0134] Specific embodiments are used in this article to illustrate the principles and implementation methods of this article. The description of the above embodiments is only used to help understand the methods and core ideas of this article. At the same time, for general technicians in this field, according to the ideas of this article, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be understood as a limitation on this article.

Claims

1. An automotive front-end module optimization method based on multi-operating condition topology, characterized in that: The following steps are involved: Step 1: Construct a 3D assembly model of the front-end module, anti-collision beam, connecting sheet metal and energy absorption box, and perform geometric repair and finite element meshing on the 3D assembly model; define the design domain and non-design domain based on the divided mesh; Step 2: setting multi-condition boundary conditions and fixed constraints of the three-dimensional assembly model, and defining design responses, including volume fraction response and weighted compliance response; Step 3: Define the minimization of flexibility as the objective function of the front-end module design and set the manufacturing process constraint parameters; Step 4: Use the orthogonal penalty material density method topology optimization algorithm to perform multiple iterative calculations to obtain the front-end module after topology optimization; Step 5: Re-analyze the front-end module after topology optimization to determine whether the stiffness performance of each working condition of the optimized model meets the requirements; If satisfied, the model of the front-end module after final optimization is reconstructed and finalized; If not satisfied, repeat steps 1 to 5.

2. The automotive front-end module optimization method based on multi-operating-condition topology according to claim 1, characterized in that: The design domain and the non-design domain are defined according to the divided grids, including defining the front-end module as the design domain, and defining the anti-collision beam, the connecting sheet metal and the energy absorption box as the non-design domain.

3. The automotive front-end module optimization method based on multi-operating-condition topology according to claim 1, characterized in that: The multi-operating condition boundary conditions include the X / Z-direction static stiffness of the hood lock area, the Z-direction static stiffness of the headlight, the X / Z-direction static stiffness of the radiator, and the Z-direction static stiffness of the buffer block.

4. The automotive front-end module optimization method based on multi-operating-condition topology according to claim 1, characterized in that: The manufacturing process constraint parameters are set to include checkerboard phenomenon control, maximum / minimum size constraints, and draft / extrusion constraints.

5. The automotive front-end module optimization method based on multi-operating-condition topology according to claim 1, characterized in that: The re-analyzing the front-end module after topology optimization includes re-analyzing the front-end module after topology optimization using the OSSmooth module in the optistruct software.

6. The automotive front-end module optimization method based on multi-operating-mode topology according to claim 5 is characterized in that: The OSSmooth module in the optistruct software is used to re-analyze the front-end module after topology optimization, including: Import the topology optimization results into OptiStruct software; Configure the parameters of the OSSmooth module; Run the OSSmooth module to generate a smoothed model; Reanalyze the smoothed model; Based on the results of the reanalysis, evaluate whether the smoothed model meets the design requirements.

7. An automotive front-end module optimization device based on multi-operating condition topology, characterized in that: It comprises a processor and a memory; the memory is used to store a program; the processor executes the program to implement the method as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that: The storage medium stores a program, and the program is executed by a processor to implement the method according to any one of claims 1 to 6.