Lightweight sunroof rail structure multi-objective optimization method based on machine learning

Abstract

This invention provides a multi-objective optimization method for lightweight sunroof guide rail structures based on machine learning, belonging to the technical field of automotive parts. The method includes: establishing a parametric model of the sunroof guide rail, using cross-sectional thickness, cross-sectional height, and chamfer radius as design variables, and employing non-uniform rational B-splines to represent the cross-section; extracting structural performance indicators through finite element simulation; establishing a motion characteristic analysis model to calculate friction time history, vibration amplitude, and sealing contact pressure; establishing a sealing and wear resistance prediction model to calculate leakage, equivalent wear depth, and fatigue life; establishing a motion mechanism constraint model, transforming friction, vibration amplitude, sealing contact pressure, and equivalent wear depth into four dimensionless inequality constraints; constructing a multi-performance surrogate model; and performing multi-objective optimization based on the surrogate model to obtain the Pareto optimal solution set and select the optimal lightweight solution. This method can achieve synergistic optimization of lightweighting, motion, sealing, and wear resistance performance.

Description

Technical Field

[0001] This application belongs to the technical field of automotive parts, specifically relating to a multi-objective optimization method for lightweight sunroof guide rail structures based on machine learning. Background Technology

[0002] With the development of lightweight structures and machine learning technologies, surrogate models and multi-objective optimization have been gradually applied to the design of complex structures. As a key moving load-bearing component in the automotive sunroof assembly, the sunroof guide rail needs to be lightweight while meeting requirements for load-bearing capacity, guidance, sealing, and wear resistance.

[0003] For example, Chinese invention patent CN120470663B discloses a multi-objective intelligent design and optimization method for arch dam shape based on machine learning. It improves design efficiency by replacing repetitive simulation calculations in traditional iterative design with machine learning models.

[0004] However, the aforementioned existing technologies address static hydraulic structures, focusing on static mechanical indicators such as strength and stability. They do not address the dynamic functional reliability requirements of moving components in terms of friction, vibration response, sealing contact state, and wear behavior. During operation, the sunroof guide rail must simultaneously withstand the coupled effects of multiple mechanical behaviors, including kinematic friction, vibration excitation, and sealing contact. Changes in its structural parameters will simultaneously affect the magnitude of friction, vibration response amplitude, sealing contact pressure distribution, and wear rate. These kinematic functional indicators are interrelated and conflict with structural quality. Existing technologies lack mathematical expressions for friction constraints, vibration amplitude constraints, sealing contact pressure constraints, and wear rate constraints, making it impossible to transform these kinematic functional requirements into calculable design constraint boundaries during the optimization process.

[0005] Due to the lack of functional constraint modeling methods for motion mechanisms, existing lightweight optimization methods are difficult to directly apply to moving structural components such as sunroof guide rails. If static structural optimization methods are directly applied, the resulting lightweight solution may fail to meet functional requirements such as smooth opening and closing, sealing reliability, and wear resistance because it does not consider the upper limit of friction, vibration amplitude limit, and minimum sealing contact pressure requirements under motion conditions.

[0006] Therefore, how to establish motion function reliability constraints in the multi-objective optimization of minimizing the mass of sunroof guide rails, so that the lightweight solution can take into account the requirements of friction, vibration, sealing and wear, has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] The purpose of this invention is to provide a multi-objective optimization method for lightweight sunroof guide rail structures based on machine learning, which can effectively solve the problems mentioned in the background art.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A multi-objective optimization method for lightweight sunroof guide rail structure based on machine learning includes: establishing a parametric model of the sunroof guide rail structure, using guide rail section thickness, guide rail section height and chamfer radius as core design variables, expressing the guide rail section through non-uniform rational B-spline curves, performing finite element simulation and extracting structural performance indicators; A multi-dimensional analysis model of the guide rail motion characteristics was established to calculate the friction force time history, vibration amplitude, and sealing contact pressure. Establish a prediction model for sealing performance and wear resistance, and calculate leakage, equivalent wear depth and fatigue life; A constraint inequality model of the motion mechanism is established, and the friction force, vibration amplitude, sealing contact pressure and equivalent wear depth are transformed into four normalized dimensionless inequality constraint functions. Construct a multi-performance proxy model to replace finite element simulation for rapid prediction; Multi-objective optimization is performed based on a multi-performance proxy model to obtain a Pareto optimal solution set, and the optimal lightweight solution is selected.

[0009] In summary, this application includes at least one of the following beneficial technical effects: 1. This application combines parametric modeling of sunroof guide rail structure, finite element simulation and multi-dimensional analysis of motion characteristics. With guide rail section thickness, section height and chamfer radius as core design variables, it can simultaneously obtain performance indicators such as mass, stress, displacement and friction, vibration amplitude and sealing contact pressure. Thus, it reflects the real force and motion state of sunroof guide rail during opening and closing under a unified framework, overcoming the shortcomings of existing static optimization methods that cannot take into account the requirements of motion function.

[0010] 2. This application transforms friction, vibration amplitude, sealing contact pressure, and equivalent wear depth into normalized dimensionless constraint functions through a sealing performance and wear resistance prediction model and a motion mechanism constraint inequality model. This allows the reliability requirements of motion functions to enter the multi-objective optimization process, providing calculable constraint boundaries for lightweight design and avoiding the failure of the optimized scheme to meet the requirements of smooth opening and closing, sealing reliability, and wear resistance due to neglecting motion conditions.

[0011] 3. This application constructs a multi-performance proxy model to replace finite element simulation for rapid prediction, and performs multi-objective optimization based on the model to obtain the Pareto optimal solution set. Then, the optimal lightweight scheme is selected by the superior-inferior solution distance method. This can reduce the mass of the guide rail and improve the optimization efficiency while ensuring the reliability of strength, stiffness and motion function. The reliability of the optimization method can be verified by experiments. Attached Figure Description

[0012] Figure 1A schematic diagram of the overall technical solution for a multi-objective optimization method for lightweight sunroof guide rail structures based on machine learning; Figure 2 A schematic diagram illustrating the core principle framework of a machine learning-driven multi-objective optimization algorithm; Figure 3 A logical flowchart for the data acquisition and preprocessing stage of the sunroof guide rail structure; Figure 4 This is a flowchart illustrating the logical flow framework of the iterative stage of multi-objective structural optimization based on lightweight constraints. Figure 5 This diagram illustrates the interaction and data flow between guide rail structure parameters, machine learning surrogate models, and multi-objective optimization functions. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of this invention clearer, the following description is provided in conjunction with the appendix. Figure 1 To be continued Figure 5 The present invention will be further described in detail below with reference to specific embodiments.

[0014] This embodiment provides a multi-objective optimization method for lightweight sunroof guide rail structures based on machine learning, encompassing six core technical modules: parametric modeling, motion characteristic analysis, sealing wear resistance prediction, constraint inequality construction, surrogate model construction, and multi-objective optimization solution. The embodiment of this application will be described in detail according to the above technical modules.

[0015] First, step S1 in the embodiment of this application is described: a parametric model of the sunroof guide rail structure is established. The three design variables control the geometry using independent scalar mapping. Thickness, height, and chamfer radius drive different sets of control points respectively. Each dimension is processed in parallel without performing overall vector or matrix operations.

[0016] Step S101: Determine the structural form, key geometric features, and core design variables of the sunroof guide rail. The sunroof guide rail is the core load-bearing component of the automotive sunroof assembly. A typical structure consists of an upper guide rail, a lower guide rail, and a middle connecting part, with a multi-chamber thin-walled cross-section. This structure is usually extruded from aluminum alloy and simultaneously undertakes functions such as glass component support, slider guidance, sealing strip installation, and body connection within a limited space.

[0017] The guide rail section thickness, guide rail section height, and chamfer radius are selected as core design variables to establish a three-dimensional parametric geometric expression system. Indicates the cross-sectional thickness. Indicates the cross-sectional height. Indicates the chamfer radius. Mapped to the set of wall thickness control points. Mapped to the upper and lower boundary control point sets. Mapping to the control point set in the corner region, the three control point sets are non-overlapping. The output consists of three sets of control point coordinates to be updated, which will be used directly in subsequent non-uniform rational B-spline curve calculations.

[0018] Step S102: Set the value range, reference value, scaling factor, and offset of the three design variables, and complete the control point update. The thickness value range is determined based on the material's mechanical properties and process constraints, with a typical value range being... to The guide rail section thickness parameter corresponds to the overall scaling factor of the guide rail wall thickness in the parametric model. Different wall thickness configuration schemes can be established through the scaling factor.

[0019] Input is design variable Reference thickness Pick The wall thickness scaling factor is calculated during processing. Then calculate the offset of the wall thickness control point along the direction of the external normal of the section. .use and Update the coordinates of the wall thickness control points. This represents the design variable for the guide rail cross-section thickness, with the dimension being mm; This indicates the reference thickness, measured in mm. This represents the wall thickness scaling factor, which is dimensionless.

[0020] This represents the offset of the wall thickness control point along the outward normal direction of the cross-section, in mm. The output includes the updated coordinates of the wall thickness control points and the updated cross-sectional geometry. The judgment criteria are... Design variable combinations that do not meet the value range will not be included in subsequent finite element simulations.

[0021] The guide rail section height parameter defines the overall dimension of the guide rail section in the vertical direction, and its value range is typically [value range missing]. to The guide rail section height parameter directly affects the guide rail's bending stiffness and overall weight. The chamfer radius parameter controls the corner transition form of the guide rail section, with a value range of [value missing]. to The size of the chamfer radius affects both the degree of local stress concentration and the material utilization rate.

[0022] Input is design variable and Reference height Pick Reference chamfer radius Pick Calculate the height scaling factor during processing. Multiply the vertical coordinates of the upper and lower boundary control points of the cross section by The horizontal coordinate remains unchanged. Simultaneously, the tangential offset of the chamfer control points is calculated. Move the control point in the corner area along the chamfer tangent direction. .

[0023] This represents the design variable for the guide rail cross-sectional height, with the dimension mm. This represents the design variable for the chamfer radius, measured in mm. Indicates the reference height, with the dimension mm; This indicates the reference chamfer radius, with the dimension of mm; This represents the height scaling factor, which is dimensionless. This represents the tangential offset of the chamfer control point, in mm. The output consists of the updated coordinates of the height control point and the chamfer control point. The judgment criteria are... and Design variable combinations that do not meet the value range will not be included in subsequent finite element simulations.

[0024] Step S103: The guide rail cross-section is represented using a non-uniform rational B-spline curve. The non-uniform rational B-spline curve is jointly defined by control vertices, node vectors, and weight factors. The control vertex symbols are... The basis function symbols are adopted To avoid repetition with subsequent penalty terms and normal contact pressure symbols, the mathematical expression is:

[0025] in, Represents the parameters on a non-uniform rational B-spline curve The corresponding position vector has the dimension of mm; The parameter values ​​are within the parameterization domain, and their range is... Dimensionless; To control vertex indices, from arrive , dimensionless integer; To control the maximum vertex index, the total number of vertices is controlled to be [value missing]. , dimensionless integer; For the first The spatial coordinate vectors of each control vertex, for a two-dimensional section. Determined by both horizontal and vertical coordinates, with units of mm; For the first The weight factors of each control vertex are positive real numbers and dimensionless. for The order non-uniform B-spline basis functions are dimensionless. Let be the order of the B-spline curve; in this embodiment, we take . , a dimensionless integer.

[0026] From node vectors Determined according to the Cox-deBoor recursive formula; For node vectors, For the first Each node value from arrive The node vectors satisfy a non-decreasing relationship. The node values ​​are dimensionless; the molecule The summation is a weighted summation of control vertices, with dimensions in mm; the denominator is... The summation is a weighted sum of weighted factors, dimensionless. Dividing the numerator by the denominator yields the position vector, with dimensions in mm, and the dimensional relationships are consistent.

[0027] By adjusting The cross-sectional shape can be changed by adjusting... The degree to which the curve approximates the control vertices can be changed. In this embodiment, the number of control vertices is set to... to One, weight factor initially taken Take the local chamfered area to The node vectors adopt a quasi-uniform distribution, and the repetition degree of the nodes at both ends is equal to... .

[0028] The input consists of the updated control point coordinates, weight factors, and node vectors from step S102. During processing, the position vectors on the cross-sectional curve are calculated using the formula described above. The output is a non-uniform rational B-spline curve of the guide rail cross-section. The criterion is that the maximum normal deviation between the cross-sectional curve and the target cross-sectional profile does not exceed [a certain value]. If the maximum normal deviation is exceeded, the control vertex coordinates or weight factors are adjusted and the calculation is repeated.

[0029] Step S104: Establish a data interface between the parametric geometric model and the finite element simulation software, and execute adaptive mesh density control. In the 3D computer-aided design software, a parametric guide rail model is created. This model uses design variables as parameters to drive the generation and modification of geometric features. When the values ​​of the design variables change, the parametric guide rail model automatically updates its geometry and generates an updated geometric model file.

[0030] The geometric model file is imported into the finite element simulation software via a standardized interface. After reading the geometric model, the finite element simulation software automatically performs mesh generation. This process ensures that the parameters of the 3D computer-aided design model and the finite element analysis model are consistent.

[0031] The input consists of the non-uniform rational B-spline curve of the guide rail cross-section and the three-dimensional parametric guide rail model generated in step S103. During processing, the geometric model is exported as a STEPAP214 format file and imported into the finite element simulation software through a standardized interface.

[0032] The output is a geometric model file that can be read by finite element simulation software. The judgment criteria are that the finite element simulation software can read the geometric model file without errors, and the imported geometric topology is consistent with the 3D computer-aided design model. If missing surfaces or incorrect edges appear, return to step S103 to regenerate the cross-sectional curves.

[0033] The mesh generation employs an adaptive mesh density control method, using smaller mesh sizes in areas of greater geometric curvature and larger mesh sizes in areas with gentler geometric features. For chamfers, cavity corners, and sealing contact areas in the skylight guide rail section, the mesh is automatically refined to capture stress concentrations and contact pressure gradients. For flat wall panel areas, the mesh is appropriately sparsed to reduce computational scale.

[0034] The input consists of the imported geometric model and its curvature distribution. During processing, the radius of curvature for each geometric region is calculated. When the radius of curvature is less than or equal to... At that time, the grid size is taken as When the radius of curvature is greater than and less than or equal to At that time, the grid size is taken as .

[0035] When the radius of curvature is greater than At that time, the grid size is taken as The output is a finite element mesh model. The judgment criterion is that the Jacobian value in the mesh quality check is greater than [value missing]. Warpage less than If any metric is not met, the grid size is adjusted and the grid is re-divided.

[0036] Step S105: Boundary conditions are applied using a parametric template. The finite element simulation software reads the preset boundary condition template file, which defines the constraint locations, constraint types, and load application methods. When the geometric model is updated, the boundary conditions are automatically remapped to the updated geometric surface. In the sunroof guide rail analysis, bolt connection fixing constraints, glass component gravity loads, drive motor opening and closing loads, and sealing contact boundaries are all managed uniformly through the boundary condition template file, avoiding the need to repeatedly set boundary conditions after each geometric update.

[0037] The input consists of the boundary condition template file and the finite element mesh model generated in step S104. During processing, fixed constraints are applied at the bolt hole locations, constraining 6 degrees of freedom. The weight of the sunroof glass is applied as a uniformly distributed load to the upper guide rail bearing surface, vertically downwards. The opening and closing load of the drive motor is applied as a horizontal concentrated force to the slider contact surface; the load magnitude is calculated based on the motor's rated torque and transmission efficiency.

[0038] The boundary conditions are remapped to the updated geometric surface using nearest-point projection. The output is a finite element analysis model with constraints and loads. The criteria for judgment are that all constraint locations and load application surfaces are successfully mapped to valid geometric surfaces, with no constraints missing or loads suspended. If any mapping failure occurs, return to step S104 to re-export the geometric model.

[0039] Step S106: Extract and store the performance indicators of the guide rail structure. After the finite element simulation is completed, extract the mass, stress distribution, and displacement response of the guide rail structure and store them in a unified data format file for subsequent analysis. The extracted mass, stress, and displacement data, together with the subsequent friction force, vibration amplitude, sealing contact pressure, and wear rate, constitute the dataset required for multi-objective optimization.

[0040] The input consists of the finite element analysis model and finite element simulation results generated in step S105. During processing, the guide rail structure mass, equivalent stress distribution, and key point displacement response are extracted from the simulation results. The mass is determined by the finite element software based on the updated geometric volume and the density of 6063-T5 aluminum alloy. calculate.

[0041] The equivalent stress is von Mises stress. Key point displacements are taken as the nodal displacements of the guide rail bearing surface and the slider contact surface. The output is a CSV or JSON data file containing mass, stress distribution, and displacement response. The judgment criterion is that all three types of data—mass, stress distribution, and displacement response—are present and not empty. If any data is missing, return to step S105 to check boundary conditions and solver settings.

[0042] Thus, step S1 forms a parametric modeling process for the sunroof guide rail, which uses design variables as input, automatically updates the geometric model, automatically executes finite element simulation, and outputs structural performance indicators in a unified manner.

[0043] After the above steps are completed, step S2 in this embodiment of the application will be described next. Step S2 focuses on three types of mechanical behaviors of the sunroof guide rail during opening and closing: friction, vibration, and sealing. A friction calculation model, a vibration amplitude prediction model, and a sealing contact pressure distribution model are established sequentially. Step S2 takes the design variables, finite element mesh, material properties, and boundary conditions output from step S1 as inputs, and outputs three types of motion performance indicators: friction, vibration amplitude, and sealing contact pressure. This provides a calculation basis for the sealing performance and wear resistance prediction in step S3 and the constraint inequality model of the motion mechanism in step S4.

[0044] Step S201: Establish the non-uniform time-varying contact friction integral model in the friction calculation model. The inputs are the friction coefficient, normal contact pressure distribution, and effective contact area. For the multi-chamber thin-walled structure of the sunroof guide rail and the slider guide contact, the contact pressure is non-uniformly distributed along the contact area and varies with the opening and closing stroke. Therefore, a non-uniform time-varying contact friction integral model is adopted:

[0045] The formula is derived from the classical friction formula. Discretization generalization. The classical friction formula calculates the total friction force using a single normal force and a single friction coefficient. This application discretizes the classical friction formula along the contact region as follows: Each infinitesimal element is represented by a first infinitesimal element. Normal contact pressure at each infinitesimal element, the first The area of ​​the first infinitesimal element and the... The frictional force of each infinitesimal element is calculated by taking the friction coefficient of each infinitesimal element, and then the total frictional force is obtained by summing the friction coefficients of all infinitesimal elements.

[0046] in, Represent design variables Corresponding time The frictional force, with dimensions in N. Represents a vector of design variables. The dimensions of each component are mm. This represents the total number of discrete infinitesimal elements in the contact region; it is a dimensionless integer. Indicates the contact element number, from 1 to .

[0047] Indicates the first The friction coefficient of a micro-element is dimensionless. The pairing of guide rail material and slider material is determined by friction and wear test or by referring to a material pairing experience table. In this embodiment, the guide rail material is 6063-T5 aluminum alloy and the slider material is polyoxymethylene. Take a value between 0.15 and 0.25. Indicates the first A microelement at time The normal contact pressure, in Pa. Indicates the first The area of ​​a infinitesimal element, with dimensions m 2 .

[0048] Multiplying the normal contact pressure by the area of ​​the infinitesimal element yields the normal force of that element, with dimensions in N. Multiplying this by the coefficient of friction yields the frictional force of that element, also with dimensions in N. Summing all the infinitesimal elements gives the total frictional force, with dimensions in N. The output is the frictional force time history. Its mean, peak value, and root mean square.

[0049] The criterion is that the peak friction force is less than or equal to the upper limit of allowable friction force. The upper limit of allowable friction force is calculated by dividing the product of the rated torque of the drive motor and the transmission efficiency by the equivalent radius of the transmission mechanism. In this embodiment, the rated torque is taken as 30 N·m, the transmission efficiency as 0.85, and the equivalent radius of the transmission mechanism as 0.05 m, resulting in an upper limit of allowable friction force of 510 N. If the peak friction force is greater than 510 N, then the design variables... Violation of the upper limit constraint on friction.

[0050] Step S202: Determine the input parameters of the friction calculation model. The inputs are the guide rail material, slider material, the self-weight of the sunroof glass assembly, the inertial force during the movement, the geometry of the guide rail cross section, and the slider support form.

[0051] The coefficient of friction is determined by referring to a table or by experience based on the material pairings. When the guide rail material is 6063-T5 aluminum alloy and the slider material is polyoxymethylene, the coefficient of friction is between 0.15 and 0.25. The output is the coefficient of friction. The criterion is that the coefficient of friction is within the range of 0.15 to 0.25. If it exceeds the range, the material pairing should be reselected or the surface treatment process should be adjusted.

[0052] The normal contact pressure is determined by the weight of the sunroof glass assembly and the inertial force during its motion. The time-domain response characteristics of the normal contact pressure are determined through dynamic analysis. The weight of the sunroof glass assembly is applied as a uniformly distributed load to the upper guide rail bearing surface, and the inertial force during motion is applied as an equivalent nodal force to the guide rail finite element model. The time-domain response characteristics of each contact element at time [time value missing] are then obtained. normal contact pressure .

[0053] The normal force is obtained by summing the products of the normal contact pressure and the area of ​​each contact element. The average normal contact pressure is obtained by dividing the normal force by the effective contact area. The outputs are the time-domain response of the normal contact pressure and the effective contact area. The criteria for judgment are that the peak value of the normal contact pressure does not exceed the allowable contact pressure of the material, and the effective contact area is greater than zero and consistent with the geometric dimensions.

[0054] The effective contact area depends on the geometry of the guide rail cross-section and the slider support configuration. Assuming the slider forms surface contact with the upper and lower surfaces of the guide rail cavity, the contact area is calculated as the product of the guide rail cross-section width and the slider length. The output is the effective contact area. The criteria for judgment are that the effective contact area is greater than zero and consistent with the geometric dimensions.

[0055] Step S203: Establish the modal analysis sub-model in the vibration amplitude prediction model. The inputs are the finite element mesh model generated in step S1, the material properties of 6063-T5 aluminum alloy, and the bolt fixing constraints.

[0056] The finite element method (FEM) is used to solve the eigenvalue problem of the guide rail structure. The homogeneous equations for undamped free vibration are solved using the Schwertner method or the Lanzos method, extracting the first six natural frequencies and their corresponding mode shapes. The output is a vector of natural frequencies and mode shapes. The criterion is that the first six natural frequencies cover the fundamental frequency of the drive motor and its higher harmonic frequencies. If they do not cover these frequencies, three more are extracted each time until coverage is achieved. The highest excitation frequency is also considered. Take the maximum value among the fundamental frequency of the drive motor excitation and its higher harmonic frequencies, with the dimension in Hz.

[0057] Step S204: Establish the contact-modal-transient coupled dynamic response analysis sub-model in the vibration amplitude prediction model. The inputs are the natural frequencies and mode shapes obtained from modal analysis, the periodic fluctuation excitation of the drive motor output torque, the friction force time history obtained in step S201, and the sealing lip contact force. The dynamic excitation is expressed as a simple harmonic excitation form, with frequency components including the fundamental frequency and its higher harmonics.

[0058] The structural displacement response is solved using contact-modal-transient coupled motion equations:

[0059] The formula is derived from the equations of motion in structural dynamics. The classical equations of motion in structural dynamics are: This application introduces a contact damping matrix between the guide rail and the slider based on the classical structural dynamics equations of motion. and contact stiffness matrix and will drive force Friction Contact force with sealing lip Together they form an external force term, resulting in a contact-modal-transient coupled motion equation.

[0060] in, This represents the mass matrix of the guide rail structure, with dimensions in kg. This represents the structural damping matrix, with dimensions in N·s / m. This represents the guide rail-slider contact damping matrix, with dimensions in N·s / m. This represents the structural stiffness matrix, with dimensions in N / m. This represents the guide rail-slider contact stiffness matrix, with dimensions in N / m.

[0061] This represents a displacement vector with dimensions in m. This represents the velocity vector, with dimensions in m / s. This represents the acceleration vector, with dimensions in m / s². 2 . This represents the excitation force for starting and stopping the drive motor, with the dimension N. The frictional force obtained in step S201 is expressed in N. This represents the contact force of the sealing lip, with dimensions in N.

[0062] Contact stiffness matrix and contact damping matrix The contact pressure distribution and contact area are determined based on the normal contact pressure distribution and contact area obtained in step S202. For the first... A contact element, the normal contact stiffness according to the... The normal contact pressure of the first contact element and the first contact element The product of the areas of each contact element, divided by the first contact element. The normal elastic deformation of the first contact element is determined, and the first... The normal elastic deformation of each contact micro-element is extracted from the contact finite element analysis results.

[0063] No. The normal contact damping of each contact element is multiplied by twice the contact damping ratio by the first contact element. The normal contact stiffness of the first contact element is related to the first... The square root of the equivalent mass product corresponding to each contact element is determined, and the contact damping ratio is taken as 0.02 to 0.1. The equivalent mass corresponding to each contact element is taken as the diagonal element of the mass matrix in the contact node set.

[0064] The normal contact stiffness of each contact element is placed in the contact stiffness matrix according to the contact element number. The diagonal elements are zero, and the off-diagonal elements are zero. The normal contact damping of each contact element is placed in the contact damping matrix according to the contact element number. The diagonal elements are zero, and the off-diagonal elements are zero.

[0065] The time step for transient dynamic analysis is taken as 1 / 20 of the highest excitation frequency.

[0066] The output is the time history of the displacement response at key points. The criterion is that the vibration amplitude is defined as half the peak-to-peak value of the displacement response at key points on the guide rail, i.e.:

[0067] The formula is derived from the definition of peak-to-peak vibration amplitude. The vibration amplitude is taken as half the difference between the maximum and minimum values ​​of the displacement response at the key point over the entire time history.

[0068] in, Represent design variables The corresponding vibration amplitude is measured in mm. Indicate key points At any moment The displacement is measured in mm. Indicate key points The maximum displacement over the entire response time, in mm. Indicate key points The minimum displacement over the entire response time, in mm.

[0069] The vibration amplitude value is less than or equal to the upper limit of the allowable vibration amplitude. The upper limit of the allowable vibration amplitude is the smaller value between the allowable value for sunroof operation stability and the allowable value for sealing performance. In this embodiment, the allowable value for stability is 0.15mm, and the allowable value for sealing performance is 0.12mm; therefore, the upper limit of the allowable vibration amplitude is 0.12mm. mm, then design variables Violation amplitude constraints were violated.

[0070] Step S205: Establish a sealing contact pressure distribution model. The inputs are the geometric models of the sealing lip structure and the guide rail substrate, the constitutive parameters of the sealing lip hyperelastic material, and the contact pair settings. The sealing lip is made of an elastomer, and the material constitutive relationship is described by the Mullin-Rivlin hyperelastic model, with the first material constant taken as 0.8 MPa and the second material constant taken as 0.2 MPa.

[0071] The penalty function method is used to handle the constraints between the contact interfaces. The contact constraints are embedded into the system equations through a penalty factor, which is taken as 0.1 to 1.0 times the elastic modulus of the sealing lip material. The sealing lip is set as the target surface, and the guide rail substrate is set as the contact surface. Nonlinear contact finite element analysis is performed. The output is the contact pressure distribution.

[0072] The criterion is that the minimum contact pressure in the contact pressure distribution is greater than or equal to the minimum contact pressure that guarantees sealing performance. The minimum contact pressure that guarantees sealing performance is taken as the larger value between the minimum contact pressure required by the sealing material preload and the minimum contact pressure required by the sealing specific pressure.

[0073] In this embodiment, the minimum contact pressure required for the preload of the sealing material is 0.05 MPa, and the minimum contact pressure required for the sealing specific pressure is 0.08 MPa. Therefore, the minimum contact pressure to ensure sealing performance is 0.08 MPa. If the minimum contact pressure is less than 0.08 MPa, then the design variables... Violation of seal contact pressure constraints.

[0074] Step S206: Extract the numerical solution of the sealing contact pressure and integrate the motion characteristic analysis results. The input is the contact element stress output obtained in step S205. Contact elements are set in the contact area between the sealing lip and the guide rail. The stress values ​​of the contact elements are read, and the contact normal stress component is taken as the numerical solution of the sealing contact pressure. The output is the numerical solution of the sealing contact pressure. The judgment criteria are that the contact pressure values ​​are not empty and have a reasonable distribution, and the minimum contact pressure is not less than 0.08 MPa.

[0075] Thus, step S2 forms a multi-dimensional analysis model of the guide rail's motion characteristics. This model unifies friction, vibration amplitude, and sealing contact pressure into a design variable-driven calculation framework, which, compared to optimization methods that only consider static strength, stiffness, and mass, can reflect the actual stress state of the sunroof guide rail during the opening and closing process.

[0076] The frictional time history is incorporated into the vibration equation, and the vibration response alters the sealing contact state. The sealing contact pressure then provides input for subsequent wear, leakage, and fatigue prediction. The motion performance indicators output in step S2, together with the mass, stress, and displacement output in step S1, constitute a multi-objective optimization input dataset. In step S4, this dataset is transformed into dimensionless inequality constraints, thereby supporting the synergistic optimization of the sunroof guide rail's lightweight design and motion function reliability.

[0077] Subsequently, step S3 in the embodiments of this application is described, which establishes a prediction model for sealing performance and wear resistance, including a leakage calculation model, a wear rate prediction model, and a fatigue life estimation model, as detailed below.

[0078] Step S301: Establish a leakage calculation model. The inputs are the radial clearance and axial clearance between the sealing lip structure and the guide rail base, the external environmental pressure of the sunroof, the internal pressure of the carriage, and the fluid density.

[0079] During the handling process, the leakage amount is calculated according to the orifice leakage formula, which is: Leakage channel cross-sectional area Determined by radial and axial clearances, for a rectangular cross-section leakage path, .in, This indicates the amount of leakage, with dimensions of . ; The flow coefficient is dimensionless and determined by the sealing structure and flow state. For typical flow states of the sunroof sealing gap, it is taken as 0.6 to 0.8. This represents the pressure difference between the external environmental pressure of the sealed structure and the internal pressure of the carriage, with dimensions of _____. ; This represents the cross-sectional area of ​​the leakage channel, with dimensions of . ; Represents fluid density, with dimensions of At room temperature and pressure, air is taken as 1.225. ; This represents the radial clearance between the sealing lip and the guide rail base, with dimensions of [missing information]. ; This indicates the axial clearance between the sealing lip and the guide rail base, with dimensions of .

[0080] The output is the leakage amount. The value is [value missing]. The criterion is that the leakage rate is less than or equal to the upper limit of the allowable leakage rate. The upper limit of the allowable leakage rate is determined according to the sunroof sealing level requirements.

[0081] The leakage rate is calculated using the orifice leakage formula during the handling process. Leakage rate. With pressure difference It is proportional to the square root and to the cross-sectional area of ​​the leakage channel. Proportional to, and with fluid dynamic viscosity Inversely proportional. Among them, This indicates the amount of leakage, with dimensions of . ; This represents the pressure difference between the external environmental pressure of the sealed structure and the internal pressure of the carriage, with dimensions of _____. ; This represents the cross-sectional area of ​​the leakage channel, with dimensions of . ; Represents the dynamic viscosity of a fluid, with dimensions of .

[0082] The output is the leakage amount. The value. The criterion is the leakage amount. Less than or equal to the maximum allowable leakage rate. The maximum allowable leakage rate is determined based on the sunroof sealing rating requirements.

[0083] Step S302: Determine the input parameters for the leakage calculation model. The input is the external environmental pressure of the sunroof. Pressure inside the carriage Wind speed and vehicle speed.

[0084] Calculate the pressure difference during processing. .in, This represents the external environmental pressure of the sunroof, with dimensions of ; This represents the pressure inside the carriage, with dimensions of . The pressure difference fluctuates with wind speed and vehicle speed. The output is the pressure difference. The time history. The criterion is that the peak pressure difference does not exceed the allowable pressure difference of the sealing structure, which is determined based on the strength of the sealing lip material.

[0085] Step S303: Establish a wear rate prediction model, with the wear coefficient as the input. Load Sliding distance and material hardness .

[0086] The wear volume is calculated according to the Arkad wear equation during processing. The wear volume equals the wear coefficient multiplied by the load multiplied by the sliding distance, then divided by the material hardness. Wherein, Represents the wear volume, with dimensions of ; This represents the wear coefficient, which is dimensionless. Represents load, with dimensions of ; Represents the sliding distance, with dimensions of ; The hardness of a material is expressed in units of 1 / 2π. The Arkad wear equation is a classical wear theory formula. This application considers the non-uniformity of stress distribution, transforms the wear volume into an equivalent wear depth, and establishes a mapping relationship between wear rate and stress distribution.

[0087] The output is the wear volume. The criterion is the wear volume. Less than or equal to the upper limit of allowable wear volume, which is determined based on the design service life and wear tolerance.

[0088] Step S304: Calculate the equivalent wear depth based on stress distribution. The inputs are the stress distribution in the guide rail contact area and the contact stress in each micro-element area. Local wear depth of each micro-element region and the area of ​​each infinitesimal region .

[0089] The equivalent wear depth was calculated using the stress-weighted average method during the processing. The formula is:

[0090] in, Represents the equivalent wear depth, with dimensions of ; Indicates the first The contact stress in a micro-element region has dimensions of ; Indicates the first The local wear depth of a micro-element region, with dimensions of ; Indicates the first The area of ​​a tiny region, with dimensions of ; Represents the total number of infinitesimal elements; a dimensionless integer. Dimensionality check: numerator. The dimensions are denominator The dimensions are Dividing the two yields ,and The dimensions are consistent.

[0091] The output is the equivalent wear depth. The criterion is the equivalent wear depth. Less than or equal to the upper limit of permissible wear depth. The upper limit of permissible wear depth is determined based on the sunroof's design service life and wear tolerance.

[0092] Step S305: Establish a fatigue life estimation model, with the input being the material stress-life curve and the stress time history data of the critical point location of the guide rail.

[0093] The process employs rainflow counting to iterate through the stress time history, counting the number of cycles at each stress amplitude level. The output shows each stress amplitude level and its corresponding cycle count. The judgment criterion is that the cycle count is complete and without omissions.

[0094] Fatigue life is calculated based on Miner's linear cumulative damage theory. The input is the actual number of cycles at each stress amplitude level. and the number of cycles allowed for the material .

[0095] Calculate cumulative damage during processing The cumulative damage is equal to the sum of the ratios of the number of cycles corresponding to each stress amplitude to the allowable number of cycles for that stress amplitude. Indicates the cumulative damage degree, dimensionless; Indicates the first The actual number of cycles at each stress amplitude level is a dimensionless integer. Indicates the first The number of permissible cycles for a material at a given stress amplitude level is a dimensionless integer. Miner's linear cumulative damage theory belongs to the classical fatigue theory.

[0096] when When the number of cycles reaches 1, the structure is considered to have suffered fatigue failure, and the corresponding total number of cycles is the fatigue life. The output is the fatigue life. The criterion for judgment is fatigue life. It is greater than or equal to the design service life requirement, which is determined based on the number of times the sunroof is opened and closed and the service life of the entire vehicle.

[0097] In summary, step S3 constructs a prediction model for sealing performance and wear resistance. The leakage amount, equivalent wear depth, and fatigue life, together with the mass, stress, and displacement data output from step S1, and the friction force, vibration amplitude, and sealing contact pressure output from step S2, constitute the input dataset for multi-objective optimization, and provide the calculation basis for sealing performance constraints, wear rate constraints, and fatigue life constraints for the motion mechanism constraint inequality model in step S4.

[0098] Based on the above analysis, step S4 in this embodiment is described, establishing a constraint inequality model for the motion mechanism. The friction force, vibration amplitude, sealing contact pressure obtained in step S2, and the equivalent wear depth obtained in step S3 are transformed into standard inequality constraint forms. Since the dimensions of each physical quantity are different, direct subtraction followed by square addition would lead to dimensional inconsistencies. Therefore, step S4 uses a normalized form to define the constraint functions, making all four inequality constraint functions dimensionless, which facilitates the calculation of the penalty term in step S6. The specific implementation process is described in detail below.

[0099] Step S401: Establish the first inequality constraint, corresponding to the upper limit constraint of friction force. The input is the design variable vector. The calculated friction force obtained in step S2 and the upper limit of permissible friction .

[0100] The first inequality constraint function is calculated using the normalization formula during processing:

[0101] in, Let denote the constraint function of the first inequality, which is dimensionless; Represents a vector of design variables. , This represents the design variable for the guide rail cross-section thickness, measured in mm. This represents the design variable for the guide rail cross-section height, in mm. This represents the design variable for the chamfer radius, measured in mm. Represent design variables The corresponding calculated value of friction force is in N. This indicates the upper limit of permissible friction, with dimensions in N.

[0102] The output is The value. The criterion is... Design variables Satisfy the upper limit constraint of friction; if Then design variables Violation of the upper limit constraint on friction. It is calculated from steps S201 to S204.

[0103] Maximum allowable friction The determination method is as follows: input the rated torque of the drive motor of the sunroof opening and closing mechanism. Transmission efficiency Equivalent radius of transmission mechanism The upper limit of the allowable friction force is taken as the product of the rated torque of the drive motor and the transmission efficiency, divided by the equivalent radius of the transmission mechanism. In this embodiment, the rated torque... Take 30 N·m, transmission efficiency Take 0.85, the equivalent radius of the transmission mechanism Taking 0.05m as an example, the upper limit of allowable friction force is calculated. It is 510N.

[0104] Step S402: Establish the second inequality constraint, corresponding to the vibration amplitude constraint, with the input being the design variable vector. The calculated vibration amplitude obtained in step S2 and the upper limit of permissible vibration amplitude .

[0105] The second inequality constraint function is calculated using the normalization formula during processing.

[0106] in, Let denote the constraint function of the second inequality, which is dimensionless; Represent design variables The corresponding calculated vibration amplitude is in mm. This indicates the upper limit of the permissible vibration amplitude, with the dimension in mm.

[0107] The output is The value. The criterion is... Design variables The vibration amplitude constraint is satisfied; if Then design variables Violation amplitude constraints were violated. It is calculated by steps S203 and S204.

[0108] Maximum allowable vibration amplitude The method for determining the vibration amplitude is as follows: input the smoothness requirements and sealing performance requirements for the sunroof operation; determine the allowable vibration amplitude value based on the smoothness requirements and the sealing performance requirements; and take the smaller of the two values ​​as the upper limit of the allowable vibration amplitude. In this embodiment, the smoothness requirement requires the vibration amplitude to not exceed 0.15mm, and the sealing performance requirement requires the vibration amplitude to not exceed 0.12mm. Therefore... Take 0.12mm.

[0109] Step S403: Establish the third inequality constraint, corresponding to the sealing contact pressure constraint, with the input being the design variable vector. The calculated value of the sealing contact pressure obtained in step S2 and the minimum contact pressure to ensure sealing performance .

[0110] The third inequality constraint function is calculated using the normalization formula during processing.

[0111] in, Let represent the constraint function of the third inequality, which is dimensionless; Represent design variables The corresponding calculated sealing contact pressure is in MPa. This indicates the minimum contact pressure required to ensure a sealing performance, measured in MPa.

[0112] The output is The value. The criterion is... Design variables Satisfy the sealing contact pressure constraint; if Then design variables Violation of seal contact pressure constraints. It is calculated by steps S205 and S206.

[0113] Minimum contact pressure The determination method is as follows: input the required preload of the sealing material and the sealing specific pressure; determine the minimum contact pressure based on the required preload of the sealing material and the minimum contact pressure based on the sealing specific pressure; take the larger of the two values ​​as the minimum contact pressure to ensure sealing performance. In this embodiment, the minimum contact pressure required by the required preload of the sealing material is 0.05 MPa, and the minimum contact pressure required by the sealing specific pressure is 0.08 MPa. Therefore... Take 0.08 MPa.

[0114] Step S404: Establish the fourth inequality constraint, corresponding to the wear rate constraint, with the input being the design variable vector. The wear rate calculation value obtained in step S3 and allowable wear rate limit .

[0115] The fourth inequality constraint function is calculated using the normalization formula during processing.

[0116] in, The fourth inequality constraint function is dimensionless. Represent design variables The corresponding wear rate is calculated using the equivalent wear depth, with the dimension in meters. This represents the upper limit of the allowable wear rate, expressed as the upper limit of the allowable wear depth, with the dimension in meters (m).

[0117] The output is The value. The criterion is... Design variables If the wear rate constraint is satisfied; Then design variables Violation of wear rate constraints. The equivalent wear depth calculated by steps S303 and S304 express.

[0118] Maximum allowable wear rate The determination method is as follows: input the design service life and wear tolerance of the sunroof, and determine the upper limit of the allowable wear rate based on the maximum allowable wear depth within the design service life. In this embodiment, the design service life is taken as... Next, the allowable wear is taken as 0.1 mm, which is 0.0001 μm. Therefore Take 0.0001m.

[0119] Step S405: Integrate the motion mechanism constraint inequality model and explain the symbols and dimensions. Steps S401 to S404 form the motion mechanism constraint inequality model. The four inequality constraints correspond to the upper limit of friction force, vibration amplitude, sealing contact pressure, and wear rate, respectively. The four inequality constraint functions are all dimensionless quantities, which together constitute the functional reliability constraint boundary of the motion mechanism.

[0120] Step S4 uses inequality constraint modeling, which is a standard constraint form in mathematical programming and does not involve deep learning models, convolutional layers, activation functions, training sets, loss functions, or hyperparameters. When design variables... Simultaneously satisfy , , and When determining design variables If it is a feasible solution, then it is considered an infeasible solution.

[0121] Taking a sunroof guide rail of a certain type of car as an example, the design variables are taken as follows: Step S2 calculates the frictional force. vibration amplitude Sealing contact pressure Step S3 calculates the equivalent wear depth. ,Right now .

[0122] Step S4 calculates the following: ,satisfy; ,violation; ,violation; This violates the original design and is not feasible.

[0123] After optimization steps S2 to S6, the vibration amplitude decreased to 0.10 mm, the sealing contact pressure increased to 0.09 MPa, and the equivalent wear depth decreased to 0.08 mm. , , All four inequality constraints are satisfied. The above example verifies that the constraint model can correctly identify feasible and infeasible solutions.

[0124] Therefore, step S4 forms a constraint inequality model for the motion mechanism, transforming motion characteristics and sealing wear resistance requirements into calculable constraint boundaries. All four normalized inequality constraint functions are dimensionless, providing a basis for determining constraint violations in step S6's multi-objective optimization solution, and supporting the coordinated optimization of the sunroof guide rail's lightweight design and motion function reliability.

[0125] Regarding step S5 in this embodiment, a multi-performance proxy model is constructed, including establishing a structural performance proxy model and a motion performance proxy model, and completing training sample generation and accuracy evaluation. The structural performance proxy model and the motion performance proxy model share the design variable input space and output structural performance indicators and motion performance indicators, respectively.

[0126] Step S501: Establish a structural performance surrogate model using the response surface methodology, with design variables as inputs. and performance response .

[0127] During processing, a quadratic polynomial response surface is fitted in the design variable space, and its mathematical expression is as follows:

[0128] in, It represents the performance response and is a scalar quantity; the dimensions of which are determined according to the specific performance indicators. Indicates the first There are 1 design variable, which is a scalar. From 1 to The dimension is mm; This indicates the number of design variables, in this embodiment. ; The coefficient of the constant term is a scalar with dimensions π / 2. same; The coefficient of the linear term is a scalar with dimensions . Divide the dimensions by mm; The coefficient of the quadratic term is a scalar with dimensions . Dimensions divided by mm 2 .

[0129] The cross term coefficient is a scalar. Dimensions are Dimensions divided by mm 2 ; The error term is a scalar with dimensions equal to or greater than 1. The same. All terms in the formula involve scalar operations; the summation symbol indicates the accumulation of scalar terms one by one; cross terms... This represents the multiplication of two scalars. The formula originates from the quadratic polynomial model in the classical response surface methodology.

[0130] The output is a response surface surrogate model. Response surface coefficients. , , , The estimation uses the least squares method. The inputs are the known design variable values ​​for sample points and the corresponding finite element simulation performance response values.

[0131] During processing, a design matrix is ​​constructed to minimize the sum of squared residuals between the predicted and simulated values, and the response surface coefficients are obtained by solving for them. The output is a vector of estimated response surface coefficients. The criterion is that the root mean square error of the response surface surrogate model in cross-validation is less than or equal to 5% of the simulated mean of the corresponding performance index. If it exceeds 5%, additional sample points are added for refitting.

[0132] Step S502: A structural performance surrogate model is constructed using a radial basis function network. The radial basis function network is a 3-layer feedforward neural network, including an input layer, a hidden layer, and an output layer.

[0133] The number of input layer nodes equals the number of design variables. In this embodiment The number of hidden layer nodes is between 10 and 20, and the activation function of the hidden layer is the Gaussian radial basis function, the expression of which is:

[0134] in, Indicates the first The output of each hidden layer node is a scalar, dimensionless. Represents a vector of design variables. The dimension is mm; Indicates the first The center vector of each hidden layer node, dimension and Same, dimensionless, in mm; Indicates the first The width parameter of each hidden layer node is a scalar with the dimension mm; Represents the design variable vector With the center vector The Euclidean distance between them is in mm. The output layer uses a linear combination to output the predicted performance response. The formula is derived from the Gaussian kernel function in classical radial basis function networks.

[0135] The input consists of design variables and performance response samples. Training data is generated into sample points in the design variable space through Latin hypercube sampling. Finite element simulations are performed on each sample point to obtain performance responses such as mass, stress, and displacement.

[0136] The k-means clustering method was used to determine the hidden layer centers during processing. The width parameter is determined based on the average distance between the centers. The least squares method is used to determine the weights of the output layer. The loss function is the mean squared error, with the input being the predicted values ​​from the surrogate model and the finite element simulation values, and the output being the squared mean of the prediction bias.

[0137] The training convergence objective is a mean squared error less than or equal to 0.001, or a change in the output layer weights less than 0.001. The output is a radial basis function (RBF) network surrogate model. The criterion is that the root mean square error of the RBF network surrogate model in cross-validation is less than or equal to 5% of the simulated mean of the corresponding performance index.

[0138] Step S503: Establish a motion performance proxy model, which is constructed using the multi-output Gaussian process regression method. Multi-output Gaussian process regression is a generalization of single-output Gaussian process regression to the multi-output case. It assumes that there is a correlation between multiple outputs and achieves joint modeling by constructing the covariance function between outputs.

[0139] The mathematical framework of multi-output Gaussian process regression is based on the multivariate Gaussian distribution, assuming that the output vector follows a Gaussian distribution determined by the mean function and the covariance function. The covariance function is a combination of the linear model covariance function and the noise covariance function. The linear model covariance function characterizes the correlation between outputs, while the noise covariance function describes the influence of observation noise. The formula is derived from classical Gaussian process regression theory.

[0140] The input consists of design variables and samples of motion performance indicators. These indicators include friction, vibration amplitude, sealing contact pressure, and equivalent wear depth. Training data is used to generate design variable samples via Latin hypercube sampling. Finite element simulation and motion characteristic analysis are performed on each sample to obtain the motion performance indicators.

[0141] The maximum marginal likelihood method is used to estimate the hyperparameters in the covariance function. The loss function is the negative marginal log-likelihood; the inputs are the training samples and the covariance function parameters, and the output is the negative marginal log-likelihood value. The training convergence objective is that the change in the negative marginal log-likelihood value is less than [a certain value]. The iteration count can be increased to a maximum of 500 iterations. The output is a multi-output Gaussian process regression surrogate model. The criterion for evaluation is that the root mean square error of the multi-output Gaussian process regression surrogate model in cross-validation is less than or equal to 5% of the simulated mean of the corresponding motion performance index.

[0142] Step S504: Generate training samples for the surrogate model. These are generated within the design variable space using the Latin hypercube sampling method. The inputs are the range of design variable values ​​and the number of samples. The range of design variable values ​​is: Take a thickness of 1.2mm to 3.5mm. Take 12mm to 28mm, The range is 0.5mm to 3.0mm. During processing, the value range of each design variable is divided into several equal intervals. One sample point is randomly selected from each interval, ensuring that the sample points are evenly distributed across all intervals. The output is a training sample set. The criterion is that the sample points are evenly distributed across all design variable intervals and there is no repetition.

[0143] Step S505: Determine the sample size. The inputs are the dimension of the design variables and the complexity of the surrogate model. The dimension of the design variables is 3. The initial sample size is set to 10 to 15 times the dimension of the design variables, i.e., 30 to 45 sample points. The performance index corresponding to a single sample is obtained through finite element simulation, and the simulation boundary conditions and load conditions are consistent with actual usage conditions. The output is the sample size value. The judgment criterion is that the sample size covers the design variable space and meets the training requirements of the surrogate model. In this embodiment, the initial sample size is 40.

[0144] Step S506: Evaluate the accuracy of the surrogate model, with the input being the surrogate model's predicted values ​​and the finite element simulation values.

[0145] The K-fold cross-validation method is used in the processing. The sample set is divided into K parts, and one part is used as the validation set in turn, while the remaining K-1 parts are used as the training set. The root mean square error between the surrogate model prediction value and the finite element simulation value is calculated. In this embodiment, K is set to 10. The output is the root mean square error.

[0146] The criteria for determining whether a surrogate model is ready for training are: the root mean square error (RMSE) of the structural performance surrogate model is less than or equal to 5% of the simulated mean of the corresponding performance index; and the root mean square error (RMSE) of the motion performance surrogate model is less than or equal to 5% of the simulated mean of the corresponding motion performance index. If the RMSE meets the criteria, the surrogate model is considered to have completed training; if the RMSE exceeds 5%, additional sample points are added for retraining.

[0147] Taking a sunroof guide rail for a certain type of car as an example, the material used is 6063-T5 aluminum alloy, and the slider material is polyoxymethylene. The design variables include the guide rail wall thickness, guide rail height, and chamfer radius. The wall thickness ranges from 1.5mm to 2.5mm, the height ranges from 16mm to 22mm, and the chamfer radius ranges from 1.0mm to 2.0mm.

[0148] Forty sets of design variable combinations were generated by Latin hypercube sampling. Finite element simulation analysis was performed on each combination to obtain structural performance indicators such as mass, stress, and displacement, as well as kinematic performance indicators such as friction, vibration amplitude, sealing contact pressure, and equivalent wear depth.

[0149] Based on simulation data, a response surface surrogate model was constructed to predict mass, a radial basis function network surrogate model was constructed to predict stress and displacement, and a multi-output Gaussian process regression surrogate model was constructed to predict motion performance indicators. After cross-validation to ensure the required accuracy, multi-objective optimization was performed. The optimization results yielded a solution set containing 15 Pareto optimal solutions. The best-to-best solution distance method was used to select the lightweight scheme with the best overall performance.

[0150] The optimal lightweight solution reduces the guide rail weight from 1.82 kg in the original design to 1.54 kg, achieving a weight reduction of 15.4%. At the same time, it ensures that the maximum equivalent stress is reduced from 156 MPa to 142 MPa and the maximum displacement is reduced from 0.38 mm to 0.31 mm, with all motion performance indicators meeting the constraints.

[0151] In summary, step S5 establishes the multi-performance surrogate model construction process. The structural performance surrogate model and the motion performance surrogate model share the design variable input space and output structural performance indicators and motion performance indicators, respectively. The structural performance indicators include mass, stress, and displacement, while the motion performance indicators include friction, vibration amplitude, sealing contact pressure, and equivalent wear depth. The surrogate model provides a fast predictive model for the multi-objective optimization solution in step S6, replacing the time-consuming finite element simulation calculation.

[0152] After the multi-performance proxy model is constructed, step S6 in this embodiment is described: multi-objective optimization is performed on the design variable space, and the optimization result is transformed into a workable lightweight solution. Let the design variable vector be... ,in This represents the design variable for the guide rail cross-section thickness, with the dimension being mm; This represents the design variable for the guide rail cross-sectional height, with the dimension mm. This represents the chamfer radius design variable, measured in mm. Original objective function vector. , This indicates the number of targets; in this embodiment, it is taken as... .

[0153] Each objective is defined as follows: This indicates the mass of the guide rail, with the dimension kg. This represents the maximum equivalent stress, with dimensions in MPa. This represents the maximum displacement, with dimensions in mm. This represents frictional force, with dimensions in N. This represents the vibration amplitude, with the dimension mm. The equivalent wear depth is represented by the unit m. All objectives are minimization objectives, and each objective value is predicted by the multi-performance surrogate model in step S5. Each objective dimension is calculated independently, without cross-objective matrix coupling.

[0154] Step S601: Construct the fitness function and adaptive penalty term, with the original objective function vector as input. Penalty items Current iteration number Maximum number of iterations Initial value of penalty coefficient Exponential decay coefficient To eliminate the dimensional differences among the objective functions, each objective function is first made dimensionless.

[0155] The first The original objective function values Divide by the objective function value at the initial point of the design variables. The dimensionless objective function value is obtained, i.e. .

[0156] in, Indicates the first A dimensionless objective function value, dimensionless; Indicates the first The original objective function value, with dimensions the same as the first... One target corresponds to; Indicates the first The objective function value of the first objective at the initial point of the design variables, with dimensions the same as the first objective. Each target corresponds to a specific value; the initial point of the design variable is taken from the baseline value in step S102, i.e. , , .

[0157] The augmented objective function is computed independently for each objective dimension: .

[0158] in, Indicates the first A fitness function for each objective dimension, dimensionless; Indicates the first A dimensionless objective function value, dimensionless; Indicates the first The penalty coefficient for the next iteration is dimensionless. This indicates a penalty term, which is dimensionless. This indicates the number of targets; in this embodiment, it is taken as... ; Represents a vector of design variables. The dimensions of each component are: .

[0159] The penalty term is defined as the sum of the penalty values ​​for all violations of constraints. For the four motion constraints in this application, the penalty term is calculated using the following formula:

[0160] in, This indicates a penalty term, which is dimensionless. Indicates the inequality constraint number, from 1 to 4; This indicates that step S4 establishes the first An inequality constraint function, dimensionless; Indicates taking 0 and The larger value in; Indicates to Summing each term from 1 to 4. When the constraints are satisfied... The penalty value is 0; when the constraint is violated. The penalty value is The square of.

[0161] The penalty coefficient is adaptively adjusted with the number of iterations, and is calculated using the exponential decay formula: .in, Indicates the first The penalty coefficient for the next iteration is dimensionless. This represents the initial value of the penalty coefficient, which is dimensionless. This represents the attenuation coefficient, which is dimensionless. Represents the current iteration number, a dimensionless integer; Represents the maximum number of iterations, a dimensionless integer.

[0162] In the initial optimization stage, a relatively large initial value for the penalty coefficient is set. This embodiment of the application takes... This results in a larger penalty value being imposed on infeasible solutions, guiding the search process towards the feasible region. As iterations proceed, the penalty coefficient decays exponentially according to the aforementioned formula. Set to 3, the current iteration number. With maximum number of iterations ratio As a component of the exponential term, the maximum number of iterations Take 200. Gradually decreasing from 100, when... hour This allows the search process to perform a fine search near the feasible region boundary and determine the location of the optimal solution.

[0163] The output is the fitness function value for each objective dimension. The criteria for judgment are: The smaller the value, the better the individual's performance in the first quarter. The better the fitness across all target dimensions; when all hour, The fitness function is equal to the dimensionless objective function value.

[0164] Step S602: Initialize the population and perform non-dominated sorting. The inputs are the range of design variables and the population size. The objective function vector for each individual and fitness function vector Randomly generated within the design variable range. Each individual corresponds to a set of design variable values, as described in this embodiment. Each individual Between 1.2mm and 3.5mm, Between 12mm and 28mm Those that do not meet the requirements (between 0.5mm and 3.0mm) will be regenerated.

[0165] The population is non-dominated and ordered, dividing it into several non-dominated front layers. The first front layer contains all non-dominated solutions, the second front layer contains all non-dominated solutions after removing the first front layer, and so on. If an individual Non-inferior in all objectives And at least one target exists that makes Strictly superior to ,but Dominate Individuals in the first front layer are not dominated by any other individual. The output includes the initial population, each front layer, and the layer to which each individual belongs. The criterion is that the number of individuals in the initial population equals the population size. There is no mutual domination relationship between individuals within each frontier layer.

[0166] Step S603: Perform crowding calculation, genetic operations, and iterative solution. The inputs are the target values ​​of individuals within the same frontier layer in each target dimension, parent population, non-dominated sorting level, crowding distance, and current iteration number. and maximum number of iterations For each target dimension, individuals within the frontier layer are sorted in ascending order of target value. For each individual, the difference between its target value and that of its neighboring individuals in each target dimension is calculated. The differences in each target dimension are normalized by dividing by the difference between the maximum and minimum values ​​of the target dimension within the current frontier layer. The normalized differences of all target dimensions are summed to obtain the crowding distance. A larger crowding distance indicates a sparser distribution of individuals on the Pareto front, and these individuals are given priority in subsequent selections.

[0167] The offspring population is generated based on tournament selection, simulated binary crossover, and multinomial mutation operators. In tournament selection, two individuals are randomly selected each time, prioritizing those with lower hierarchical levels; if levels are the same, those with greater crowding distance are selected. The simulated binary crossover probability is set to 0.9, and the distribution exponent is set to 20; the multinomial mutation probability is set to... The distribution index is 20. This indicates the number of design variables, as shown in the embodiments of this application. .

[0168] Merge parent and child generations, perform non-dominated sorting and crowding distance calculation, and select the first generation. Each individual is treated as a new generation of the population; the above process is repeated until the termination condition is met. The termination condition is the current iteration number. Reaching the maximum number of iterations Or the hypervolume change of the Pareto front for 20 consecutive generations is less than The output is the final Pareto optimal solution set. The decision criterion is: there is no dominance relationship between any two solutions in the Pareto optimal solution set; if the termination condition is met, the Pareto optimal solution set is output.

[0169] The multi-objective genetic algorithm is implemented using a reference-point-based non-dominated sorting genetic algorithm. This algorithm introduces a reference point mechanism into the standard non-dominated sorting genetic algorithm, guiding the population towards a uniformly distributed region at the Pareto front.

[0170] The algorithm's hierarchical structure is as follows: The input layer receives the design variable vector. The evaluation layer calculates the fitness function vector according to step S601. The sorting layer performs non-dominated sorting and divides the frontier layer; the diversity maintenance layer calculates the congestion distance and introduces a reference point; the genetic operation layer performs tournament selection, simulates binary crossover, and polynomial mutation; the output layer provides the Pareto optimal solution set. The congestion distance and reference point mechanism together maintain the distribution and convergence of the solution set, enabling the lightweight sunroof guide rail scheme to achieve a balance between mass, stress, displacement, friction, vibration amplitude, sealing contact pressure, and wear rate.

[0171] Step S604: Select the optimal lightweight solution based on the superior-inferior solution distance method. The input is the Pareto solution set containing the i-th solution. The objective function vector of each solution And the minimum value of each objective in the Pareto solution set. and maximum value For each target dimension Calculate the normalized target value independently. Specifically, calculate the first normalized target value. The solution of the first... The objective function value minus the minimum value of the objective in the Pareto solution set. Then divide by the target maximum value. and minimum value The difference between the maximum and minimum values ​​yields a normalized objective value between 0 and 1. If the maximum and minimum values ​​are equal, the normalized objective value is set to 0. The output is the normalized objective vector for each solution. The criterion is that each normalized objective value is between 0 and 1.

[0172] For each solution Calculate independently the Euclidean distance to the ideal point and the Euclidean distance to the negative ideal point. The ideal point is defined as the vector composed of the minimum values ​​of each objective; for a minimization problem, the ideal point is... The negative ideal point is defined as a vector composed of the maximum values ​​of all objectives. The distance calculation uses a normalized objective value, and all resulting distances are dimensionless. The output is the distance between each solution and the ideal point, and the distance to the negative ideal point. The criteria are: the smaller the distance to the ideal point, the closer the solution is to the ideal point; the larger the distance to the negative ideal point, the farther the solution is from the negative ideal point.

[0173] Calculate relative proximity:

[0174] in, Indicates the first The relative approximation of each Pareto solution is dimensionless; Indicates the first The normalized Euclidean distance between each solution and the ideal point is dimensionless. Indicates the first The normalized Euclidean distance between each solution and the negative ideal point is dimensionless. The output is the relative proximity of each Pareto solution. The criterion is: the larger the relative proximity, the closer the solution is to the ideal point and the farther it is from the negative ideal point, and the better the overall performance; the solution with the largest relative proximity is selected as the optimal lightweight scheme, and the calculation result is directly regarded as the best value.

[0175] Step S605: Machining the sample and building a motion performance testing platform. Inputs include the design variable values ​​for the optimal lightweight solution, the sunroof guide rail sample, the drive motor, the transmission mechanism, the displacement sensor, the force sensor, and the vibration sensor. Based on the design variable values, generate machining drawings and process parameters, and machine the sunroof guide rail sample. The deviation of the sample's key dimensions from the design variable values ​​must not exceed the machining tolerance requirements.

[0176] The drive motor, transmission mechanism, displacement sensor, force sensor, and vibration sensor are mounted on the test platform. The drive motor provides the power source for opening and closing the sunroof, the transmission mechanism converts the motor output into the linear motion of the slider, the displacement sensor measures the displacement response of the slider, the force sensor measures the contact force between the guide rail and the slider, and the vibration sensor measures the vibration acceleration response of the guide rail.

[0177] The output consists of a sunroof guide rail sample and a motion performance testing platform. The judgment criteria are: the key dimensions of the sample meet the machining tolerance requirements, and all sensors are correctly installed and their signal acquisition is normal.

[0178] Step S606: Collect measured data and compare it with the predicted values ​​of the multi-performance surrogate model. The inputs are the motion performance test platform, test conditions, measured data, and predicted values ​​of the multi-performance surrogate model. Drive the sunroof to open and close according to the preset conditions, collect measured data of key indicators such as friction, vibration amplitude, and sealing leakage, and calculate the relative error between the measured values ​​and the predicted values ​​of the multi-performance surrogate model.

[0179] The specific method is as follows: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error. The measured value of each performance indicator is subtracted from the predicted value of the multi-performance surrogate model, the absolute value is divided by the measured value of that performance indicator, and then multiplied by 100%. The output is the relative error. The judgment criteria are as follows: if the relative error of all key performance indicators is less than or equal to 5%, the prediction accuracy of the multi-performance surrogate model is deemed to meet the requirements and the optimization method is reliable; if the relative error of any indicator is greater than 5%, the multi-performance surrogate model is retrained with additional sample points and step S6 is repeated.

[0180] Finally, step S6 completes the multi-objective optimization solution and experimental verification. The adaptive penalty function handles the design scheme that violates the motion constraints. The non-dominated sorting genetic algorithm based on the reference point obtains a uniformly distributed Pareto optimal solution set. The superior-inferior solution distance method selects the lightweight scheme with the best overall performance. Sample testing verifies the prediction accuracy of the multi-performance surrogate model and the reliability of the optimization method.

[0181] Taking a sunroof rail of a certain type of car as an example, the specific application is explained. The sunroof rail material is 6063-T5 aluminum alloy with a density of 2700 kg / m³. 3The slider material is polyoxymethylene. Design variables include guide rail wall thickness, guide rail height, and chamfer radius. The wall thickness ranges from 1.5mm to 2.5mm, the height ranges from 16mm to 22mm, and the chamfer radius ranges from 1.0mm to 2.0mm.

[0182] Forty combinations of design variables were generated using Latin hypercube sampling. Finite element method (FEM) simulations were performed on each combination to obtain mass, stress, displacement, friction, vibration amplitude, sealing contact pressure, and equivalent wear depth. Based on the simulation data, a multi-performance surrogate model was constructed. The response surface model predicted mass, the radial basis function network model predicted stress and displacement, and the multi-output Gaussian process regression model predicted friction, vibration amplitude, sealing contact pressure, and equivalent wear depth. The root mean square error of the cross-validation results was less than 5% of the simulated mean of the corresponding performance indicators.

[0183] Perform multi-objective optimization according to the parameters described in steps S601 to S603, with the number of objectives q being 6, the population size N being 100, the maximum number of iterations T being 200, the crossover probability being 0.9, and the mutation probability being 1 / 3. The optimization result yields a solution set containing 15 Pareto optimal solutions. Following step S604, calculate the normalized Euclidean distance between each solution and the ideal point and the negative ideal point, and calculate the relative proximity. Select the solution with the highest relative proximity as the lightweight solution.

[0184] The guide rail wall thickness is 1.8mm, the guide rail height is 18mm, and the chamfer radius is 1.2mm. The guide rail weight is reduced from the original design of 1.82kg to 1.54kg, a weight reduction of 15.4%. The maximum equivalent stress is reduced from 156MPa to 142MPa, and the maximum displacement is reduced from 0.38mm to 0.31mm.

[0185] The friction force is 20N, which is less than the upper limit of allowable friction force of 510N. The vibration amplitude is 0.10mm, which is less than the upper limit of allowable vibration amplitude of 0.12mm. The sealing contact pressure is 0.09MPa, which is greater than the minimum contact pressure of 0.08MPa required to ensure sealing performance. The equivalent wear depth is 0.08mm, which is less than the upper limit of allowable wear depth of 0.10mm. All four inequality constraints established in step S4 are satisfied.

[0186] Following step S605, the sunroof guide rail sample was fabricated and a motion performance testing platform was built. Following step S606, measured data was collected. The relative errors between the measured friction force and the predicted values ​​of the multi-performance surrogate model were 3.2%, the relative error of vibration amplitude was 4.1%, and the relative error of sealing leakage was 3.8%, all less than 5%, verifying the prediction accuracy of the multi-performance surrogate model and the reliability of the optimization method.

[0187] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. Therefore, the embodiments should be regarded as exemplary and non-limiting in all respects.

[0188] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A multi-objective optimization method for lightweight sunroof guide rail structure based on machine learning, characterized in that: This includes establishing a parametric model of the sunroof guide rail structure, using the guide rail section thickness, guide rail section height, and chamfer radius as core design variables, expressing the guide rail section through a non-uniform rational B-spline curve, performing finite element simulation, and extracting structural performance indicators. A multi-dimensional analysis model of the guide rail motion characteristics was established to calculate the friction force time history, vibration amplitude, and sealing contact pressure. Establish a prediction model for sealing performance and wear resistance, and calculate leakage, equivalent wear depth and fatigue life; A constraint inequality model of the motion mechanism is established, and the friction force, vibration amplitude, sealing contact pressure and equivalent wear depth are transformed into four normalized dimensionless inequality constraint functions. Construct a multi-performance proxy model to replace finite element simulation for rapid prediction; Multi-objective optimization is performed based on a multi-performance proxy model to obtain a Pareto optimal solution set, and the optimal lightweight solution is selected.

2. The method according to claim 1, characterized in that: The establishment of a multi-dimensional analysis model of the guide rail motion characteristics includes: establishing a non-uniform time-varying contact friction integral model, discretizing the contact area into m micro-elements, calculating the micro-element friction force of each micro-element using the normal contact pressure at the j-th micro-element, the area of ​​the j-th micro-element, and the friction coefficient of the j-th micro-element, and then summing all micro-elements to obtain the total friction force time history; A modal analysis sub-model is established in the vibration amplitude prediction model. The eigenvalue problem of the guide rail structure is solved by the finite element method, and the first 6 natural frequencies and corresponding mode shapes are extracted. A contact-modal-transient coupled dynamic response analysis sub-model is established in the vibration amplitude prediction model. The contact damping matrix between the guide rail and the slider and the contact stiffness matrix between the guide rail and the slider are introduced into the structural dynamic motion equation. The contact-modal-transient coupled motion equation is adopted, and the starting and closing excitation force of the drive motor, the time history of friction force and the contact force of the sealing lip are taken as external force terms to solve the displacement response.

3. The method according to claim 1, characterized in that: Establishing a prediction model for sealing performance and wear resistance includes: establishing a leakage calculation model, calculating the leakage amount according to the orifice leakage formula, and determining the cross-sectional area of ​​the leakage channel by the radial and axial clearances between the sealing lip and the guide rail base; A wear rate prediction model was established, the wear volume was calculated according to the Akkad wear equation, and the equivalent wear depth was calculated using the stress-weighted average method. A fatigue life estimation model was established, and the stress time history was cyclically counted using the rainflow counting method. The cumulative damage degree and fatigue life were calculated based on Miner's linear cumulative damage theory.

4. The method according to claim 1, characterized in that: The sealing contact pressure distribution model is established as follows: the constitutive relation of the sealing lip material is described by the Mullin-Rivlin hyperelastic model, with the first material constant being 0.8 MPa and the second material constant being 0.2 MPa; The penalty function method is used to handle the contact interface constraint between the sealing lip and the guide rail substrate. The penalty factor is taken as 0.1 to 1.0 times the elastic modulus of the sealing lip material. Nonlinear contact finite element analysis was performed with the sealing lip as the target surface and the guide rail substrate as the contact surface, and the contact normal stress component was taken as the numerical solution of the sealing contact pressure.

5. The method according to claim 1, characterized in that: The construction of a multi-performance surrogate model includes: using the response surface methodology to construct a structural performance surrogate model to predict the quality of the guide rail, fitting a quadratic polynomial response surface in the design variable space, and estimating the response surface coefficients using the least squares method; A structural performance surrogate model is constructed using a radial basis function network to predict stress and displacement. The radial basis function network is a 3-layer feedforward neural network. The activation function of the hidden layer is Gaussian radial basis function. The number of hidden layer nodes is 10 to 20. The k-means clustering method is used to determine the center of the hidden layer. A motion performance surrogate model is constructed using a multi-output Gaussian process regression method to predict friction, vibration amplitude, sealing contact pressure, and equivalent wear depth. The covariance function adopts a combination of the linear model covariance function and the noise covariance function, and the hyperparameters in the covariance function are estimated using the maximum marginal likelihood method.

6. The method according to claim 1, characterized in that: The multi-objective optimization solution includes: performing dimensionless processing on each objective function, and dividing the value of the m-th original objective function by the value of the m-th original objective function at the initial point of the design variables; Construct an adaptive penalty term, which is the sum of the penalty values ​​for all violations of constraints. The penalty coefficient is adaptively adjusted with the number of iterations according to the exponential decay formula. Non-dominated sorting is performed on the population, and a reference point-based non-dominated sorting genetic algorithm is used for iterative solution. Offspring population is generated through tournament selection, simulated binary crossover and polynomial mutation operators. After merging the parent and offspring, non-dominated sorting and crowding distance calculation are performed, and the top N individuals are selected as the new generation population. The Pareto optimal solution set is screened based on the superior-inferior solution distance method. The normalized Euclidean distance between each solution and the ideal point and the negative ideal point is calculated, and the solution with the highest relative closeness is selected as the optimal lightweight solution.

7. The method according to claim 2, characterized in that: In the sub-model for contact-modal-transient coupled dynamic response analysis, the contact stiffness matrix and contact damping matrix are determined as follows: The normal contact stiffness of the j-th contact element is determined by multiplying the normal contact pressure of the j-th contact element by the area of ​​the j-th contact element and then dividing by the normal elastic deformation of the j-th contact element. The normal contact damping of the j-th contact element is determined by multiplying twice the contact damping ratio by the square root of the product of the normal contact stiffness of the j-th contact element and the equivalent mass corresponding to the j-th contact element, with the contact damping ratio ranging from 0.02 to 0.

1. The normal contact stiffness of each contact element is placed in the diagonal element of the contact stiffness matrix according to the contact element number, and the off-diagonal elements are zero. The normal contact damping of each contact element is placed in the diagonal element of the contact damping matrix according to the contact element number, and the off-diagonal elements are zero.

8. The method according to claim 1, characterized in that: In the finite element simulation and structural performance index extraction, the mesh generation adopts an adaptive mesh density control method. When the radius of curvature is less than or equal to 2.5 mm, the mesh size is 0.6 mm; when the radius of curvature is greater than 2.5 mm and less than or equal to 8 mm, the mesh size is 1.2 mm; and when the radius of curvature is greater than 8 mm, the mesh size is 2.0 mm. In the mesh quality check, the Jacobian value is greater than 0.7, and the warpage is less than 15°. The non-uniform rational B-spline curve is defined by control vertices, node vectors, and weight factors. The number of control vertices is 20 to 40, the initial weight factor is 1.0, and the weight factor in the local chamfered area is 0.8 to 1.

2. The node vector adopts a quasi-uniform distribution, the repeatability of the nodes at both ends is equal to p+1, p=3, and the maximum normal deviation between the cross-sectional curve and the target cross-sectional profile does not exceed 0.05 mm.

9. The method according to claim 1, characterized in that: In the constraint inequality model of the motion mechanism: The first inequality constraint function is the ratio of the calculated friction force to the upper limit of the allowable friction force minus 1. The upper limit of the allowable friction force is the product of the rated torque of the drive motor and the transmission efficiency divided by the equivalent radius of the transmission mechanism. The second inequality constraint function is the ratio of the calculated vibration amplitude to the upper limit of the allowable vibration amplitude minus 1. The upper limit of the allowable vibration amplitude is the smaller value between the allowable value of the stability requirement and the allowable value of the sealing performance requirement. The third inequality constraint function is 1 minus the ratio of the calculated value of the sealing contact pressure to the minimum contact pressure that guarantees the sealing performance. The minimum contact pressure is taken as the larger value between the minimum contact pressure required by the preload of the sealing material and the minimum contact pressure required by the sealing specific pressure. The fourth inequality constraint function is the ratio of the equivalent wear depth to the upper limit of the allowable wear depth minus 1. The upper limit of the allowable wear depth is determined based on the design service life and the wear tolerance.

10. The method according to claim 6, characterized in that: It also includes experimental verification steps: fabricating sunroof guide rail prototypes based on the design variable values ​​of the optimal lightweight scheme, and building a motion performance testing platform that includes a drive motor, transmission mechanism, displacement sensor, force sensor and vibration sensor; Drive the sunroof to open and close according to preset working conditions, and collect measured data on friction, vibration amplitude and sealing leakage. The relative error is obtained by subtracting the predicted value of the multi-performance proxy model from the measured value of the j-th performance index, taking the absolute value, dividing it by the measured value of the j-th performance index, and multiplying by 100%. If the relative error of all key performance indicators is less than or equal to 5%, the optimization method is deemed reliable; if the relative error of any indicator is greater than 5%, the multi-performance surrogate model is retrained by adding sample points and the multi-objective optimization solution is re-executed.

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