Topological optimization design method and device integrating subjective preference and storage medium

Abstract

The invention relates to the field of computer-aided engineering and intelligent manufacturing, and provides a topological optimization design method integrating subjective preferences. The method comprises the following steps: initializing material density distribution in a design domain, and intelligently recommending an initial density distribution scheme according to a subjective preference type selected by a user; calculating an objective response value and sensitivity thereof; calling a pre-trained subjective preference scoring model to subjectively evaluate the current material density distribution, outputting a subjective evaluation value, and calculating the sensitivity of the subjective evaluation value based on a numerical perturbation method; the objective response value, the sensitivity of the objective response value, the subjective evaluation value and the sensitivity of the subjective evaluation value are input into an MMA optimizer for iterative calculation, and material density distribution is dynamically updated to balance subjective preference and objective constraint; and judging whether the updated material density distribution meets a convergence condition set by a user, if so, performing post-processing visualization on the optimized material density distribution, and outputting a final topological configuration, otherwise, returning to a new round of iteration.

Description

Technical Field

[0001] This application relates to the fields of computer-aided engineering and intelligent manufacturing, and in particular to a topology optimization design method, apparatus and storage medium that integrates subjective preferences. Background Technology

[0002] Topology optimization, as one of the core technologies in structural optimization, plays a vital role in modern engineering design. Its core objective is to automatically find the optimal material distribution within a given design space, load conditions, and performance constraints, thereby achieving the design goal of meeting performance requirements with minimal material or maximizing structural performance (e.g., strength, stiffness, and vibration resistance) with a fixed material quantity. Unlike traditional size or shape optimization, topology optimization can generate innovative structural solutions from scratch, combining functionality and economy, and is therefore widely used in automotive, aerospace, consumer electronics, and construction industries. Through numerical simulation techniques such as finite element analysis, topology optimization can efficiently handle complex physical field problems, providing a scientific basis for engineering decisions.

[0003] In existing technologies, topology optimization typically relies on objective mathematical constraints to guide the optimization process. Common constraint types include stress constraints, displacement constraints, frequency constraints, and stability constraints, among others. These constraints are expressed through explicit mathematical formulas and integrated into the optimization algorithm, forming a standardized process.

[0004] However, existing technologies have significant drawbacks: they can only handle objective responses and cannot effectively integrate subjective preferences. In practical engineering, the design of many products not only needs to meet performance constraints but also needs to consider subjective factors such as visual aesthetics and proportional harmony. These factors directly affect the product's market acceptance and user satisfaction. However, because subjective preferences are difficult to quantify through mathematical formulas, traditional topology optimization methods lack corresponding mechanisms to dynamically incorporate these preferences. This can lead to optimization results that are overly technical and neglect human-centered design, thus limiting their overall effectiveness in practical applications. Summary of the Invention

[0005] This application provides a topology optimization design method, apparatus, and storage medium that integrates subjective preferences, thereby improving the practicality and overall quality of topology optimization design by integrating subjective preferences with objective constraints.

[0006] On the one hand, this application provides a topology optimization design method integrating subjective preferences, the method comprising: Step S101: Initialize the material density distribution within the design domain and intelligently recommend an initial density distribution scheme based on the user's selected subjective preference type; Step S102: Perform finite element analysis based on the current material density distribution to calculate the objective response value and its sensitivity; Step S103: Call the pre-trained subjective preference rating model to subjectively evaluate the current material density distribution, output the subjective evaluation value, and calculate the sensitivity of the subjective evaluation value based on the numerical perturbation method; Step S104: Input the objective response value and its sensitivity, as well as the subjective evaluation value and its sensitivity, into the moving asymptote method MMA optimizer for iterative calculation, and dynamically update the material density distribution to balance subjective preferences and objective constraints; Step S105: Determine whether the updated material density distribution meets the convergence condition set by the user. If it does, proceed to step S106; otherwise, return to step S102 for a new round of iteration. Step S106: Post-process and visualize the optimized material density distribution, and output the final topology configuration.

[0007] On the other hand, this application provides a topology optimization design apparatus that integrates subjective preferences, the apparatus comprising: The initialization module is used to initialize the material density distribution within the design domain and intelligently recommend an initial density distribution scheme based on the user's selected subjective preference type. The objective response processing module is used to perform finite element analysis based on the current material density distribution and calculate the objective response value and its sensitivity. The subjective response processing module is used to call a pre-trained subjective preference scoring model to subjectively evaluate the current material density distribution, output the subjective evaluation value, and calculate the sensitivity of the subjective evaluation value based on the numerical perturbation method. The iterative module is used to input the objective response value and its sensitivity, as well as the subjective evaluation value and its sensitivity, into the moving asymptote method MMA optimizer for iterative calculation, and dynamically update the material density distribution to balance subjective preferences and objective constraints. The judgment module is used to determine whether the updated material density distribution meets the convergence conditions set by the user. If it does, it will switch to the post-processing module for execution; otherwise, it will return to the objective response processing module for a new round of iteration. The post-processing module is used to post-process and visualize the optimized material density distribution and output the final topology configuration.

[0008] Thirdly, this application provides an apparatus comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the technical solution of the topology optimization design method integrating subjective preferences as described above.

[0009] Fourthly, this application provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of the technical solution of the topology optimization design method integrating subjective preferences as described above.

[0010] As can be seen from the technical solution provided in this application, on the one hand, by introducing a pre-trained subjective preference scoring model into the optimization process and calculating the sensitivity of subjective responses, the problem of neglecting subjective factors in traditional methods is avoided. This ensures that the final output topology configuration not only meets objective constraints such as strength and stiffness but also reflects visual harmony or user interaction comfort. On the other hand, since subjective responses are quantified into computable parameters and input into the MMA optimizer along with objective responses, the optimization algorithm can explore the design space more comprehensively. This not only enhances the flexibility of the optimization process but also avoids getting trapped in local optima and improves convergence efficiency. In summary, the technical solution of this application improves the practicality and overall quality of topology optimization design by integrating subjective preferences and objective constraints. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart of the topology optimization design method integrating subjective preferences provided in the embodiments of this application; Figure 2 This is a schematic diagram of the structure of the topology optimization design device integrating subjective preferences provided in the embodiments of this application; Figure 3 This is a schematic diagram of the device provided in the embodiments of this application. Detailed Implementation

[0013] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0014] In this specification, adjectives such as "first" and "second" are used only to distinguish one element or action from another, without necessarily requiring or implying any actual such relationship or order. Where circumstances permit, reference to an element or component or step (etc.) should not be construed as being limited to only one of the elements, components, or steps, but may be one or more of the elements, components, or steps, etc.

[0015] For ease of description, the dimensions of the various parts shown in the accompanying drawings are not drawn to actual scale.

[0016] In existing technologies, topology optimization typically relies on objective mathematical constraints to guide the optimization process. Common constraint types include stress constraints, displacement constraints, frequency constraints, and stability constraints, among others. These constraints are expressed through explicit mathematical formulas and integrated into the optimization algorithm, forming a standardized process. For example, traditional methods first obtain physical quantities such as displacement and stress through finite element analysis, then calculate the response values ​​and their sensitivities, and finally input them into an MMA optimizer for iterative updates. This method can effectively handle objective performance indicators, but overall it focuses on optimizing purely technical parameters. However, existing technologies have a significant drawback: they can only handle objective responses (e.g., displacement, stress) and cannot effectively integrate subjective preferences (e.g., aesthetic considerations, user experience, or human-computer interaction needs). In practical engineering, the design of many products (e.g., automotive exteriors, electronic product casings, or building structures) not only needs to meet performance constraints but also needs to consider subjective factors such as visual aesthetics and proportional harmony. These factors directly affect the product's market acceptance and user satisfaction. However, since subjective preferences are difficult to quantify through mathematical formulas, traditional topology optimization methods lack corresponding mechanisms to dynamically incorporate such preferences, which may lead to optimization results that are too technical and neglect human-centered design, thus limiting their overall effectiveness in practical applications.

[0017] To address the aforementioned problems in existing technologies, this application proposes a topology optimization design method integrating subjective preferences. This method can be applied to engineering product design scenarios, such as automobile exteriors, consumer electronics casings, or architectural structural forms. A flowchart of this method is attached. Figure 1 As shown, the main steps include S101 to S106, which are detailed below: Step S101: Initialize the material density distribution within the design domain and intelligently recommend an initial density distribution scheme based on the user's selected subjective preference type.

[0018] Traditional topology optimization methods often initialize material density distribution in the initialization phase using random, uniform, or historical data-based density distributions. This approach completely ignores the subjective preferences specific to the design problem. For example, completely random initialization requires numerous iterations to find a feasible direction, uniform initialization lacks guidance based on specific preferences, and historical data-based initialization requires a large number of similar cases and struggles to adapt to new design requirements. To address these issues, this application proposes an initial density distribution scheme within the design domain, intelligently recommending an initial density distribution scheme based on the user's selected subjective preference type. Specifically, each finite element element is assigned an initial density value within the design domain, reflecting the probability or density level of material presence in that region. These density values ​​typically range from 0 to 1, where 0 represents complete emptiness, 1 represents complete material filling, and intermediate values ​​represent partial material filling. This approach, by intelligently matching subjective preference characteristics, provides the optimization process with a clearly oriented initial state, accelerating convergence and providing subsequent iterations with search directions aligned with the design intent, effectively preventing the optimization process from wasting computational resources in irrelevant regions. As an embodiment of this application, the intelligent recommendation of the initial density distribution scheme based on the subjective preference type selected by the user can be as follows: matching the corresponding preference features from the model library according to the subjective preference type selected by the user; generating an initial density distribution based on the matched preference features, wherein the density distribution preferentially satisfies symmetry or minimum size constraints. It should be noted that the above-mentioned intelligent recommendation of the initial density distribution scheme based on the user's selected subjective preference type is actually a dynamic adjustment process. The purpose is to reduce the number of iterations and avoid local optima. That is, as another embodiment of this application, the intelligent recommendation of the initial density distribution scheme based on the user's selected subjective preference type can also be as follows: receiving the user's selected subjective preference type as an input signal; performing feature matching query in a pre-built model library according to the subjective preference type, wherein the model library stores the topological feature patterns corresponding to different preference types; obtaining the matching preference feature parameter set, including symmetry weight coefficient, minimum size threshold, and material distribution tendency index; generating candidate initial density distribution schemes based on the matching preference feature parameter set; verifying the feasibility of the candidate schemes and checking whether they meet the preset geometric and physical constraints; when the candidate scheme fails the verification, adaptively adjusting the preference feature parameter weights and regenerating the density distribution scheme; iteratively optimizing until an initial density distribution that meets all constraints is generated; and using the finally determined density distribution as the initial state of the topology optimization process.

[0019] Step S102: Perform finite element analysis based on the current material density distribution to calculate the objective response value and its sensitivity.

[0020] Existing methods for finite element analysis and objective response calculation generally employ simplified structural mechanics models (i.e., simplified theories) or empirical safety factor methods based on historical data with amplified loads. However, these methods fail to accurately capture structural behavior under complex loading conditions, potentially leading to substandard performance in practical engineering. For example, simplified theories exhibit significant errors when dealing with complex three-dimensional structures, while empirical safety factor methods are conservative and lack specificity. The proposed solution, however, utilizes finite element analysis based on the current material density distribution to calculate objective response values ​​and their sensitivities. Calculating objective response values ​​and their sensitivities involves obtaining nodal displacements and stress fields through finite element analysis and using the adjoint variable method to solve for sensitivity, thereby optimizing computational efficiency. Specifically, for objective responses, topology optimization can solve for the numerical values ​​of relevant physical responses and their sensitivity to design variables based on the mathematical expressions corresponding to specific objective functions and constraints. Objective response values ​​typically include key performance indicators such as structural displacement, stress, strain energy density, and compliance. To accurately solve for these objective response values, finite element analysis can be performed to obtain the field variable distribution within the design domain. Field variables typically refer to physical quantities such as nodal displacements, element stresses, and strains, which reflect the mechanical behavior of a structure under given loads and boundary conditions. By performing a complete finite element analysis on the current material density distribution, the mechanical behavior of the structure under actual working conditions can be accurately simulated, ensuring that each iteration step in the optimization process is based on the true physical response, thereby improving the engineering practicality and reliability of the final design scheme.

[0021] It should be noted that the objective response values ​​in the above embodiments refer to the calculated physical quantity results, while the sensitivity of the objective response values ​​refers to the degree to which these objective response values ​​are sensitive to density changes in each tiny unit within the design domain. Taking an electric vehicle manufacturer's need to design a suspension bracket connecting the battery pack and the vehicle chassis as an example, the displacement (deformation) of key points of the bracket, the maximum stress (whether it exceeds the material strength), and the overall compliance (the reciprocal of stiffness, the smaller the value, the greater the stiffness), etc., are all objective performance indicators that can be clearly measured by physical laws, and are also objective response values ​​that can be calculated.

[0022] Step S103: Call the pre-trained subjective preference rating model to subjectively evaluate the current material density distribution, output the subjective evaluation value, and calculate the sensitivity of the subjective evaluation value based on the numerical perturbation method.

[0023] Traditionally, subjective aesthetic preferences are considered difficult to quantify, which has prevented the systematic integration of human-centered design factors into the topology optimization process. Existing solutions often involve post-processing aesthetic enhancement (appearance modification after topology optimization) or parametric shape constraints (limiting the range of geometric variations). However, post-processing aesthetic enhancement may compromise mathematical optimality, while parametric constraints restrict innovation. To achieve a harmonious balance between visual appeal and functional performance in the final design, this application employs a pre-trained subjective preference scoring model to subjectively evaluate the current material density distribution, outputting a subjective evaluation value, and calculating the sensitivity of this value using a numerical perturbation method. This approach achieves a quantitative description of subjective preferences, allowing aesthetic factors to participate in optimization decisions with equal importance to engineering performance.

[0024] In the above embodiments, the subjective evaluation value is a score output by a pre-trained subjective preference scoring model after "aesthetically" evaluating a certain geometric configuration. Taking the example of an electric vehicle manufacturer needing to design a suspension bracket connecting the battery pack and the vehicle chassis, the subjective evaluation value is the score given by the pre-trained subjective preference scoring model to the current bracket's geometric configuration, outputting a score, for example, 0.85 (out of 1.0). This score is the subjective evaluation value, which quantifies the degree to which the current design conforms to the subjective preference of "streamlined." The sensitivity of the subjective evaluation value is calculated through the difference quotient, answering the question, "How much will increasing the density of a certain unit improve the 'streamlined' score of the bracket?" This indicates to the optimization algorithm how to adjust the density to improve aesthetics.

[0025] It should be noted that the pre-trained subjective preference rating model mentioned above can be trained using reinforcement learning methods based on human feedback. The specific training process is as follows: collect rating data from human evaluators on various topological configurations to construct a preference dataset; design the state space and action space of the subjective preference rating model, where the state space includes density distribution features and the action space includes the rating output; and use a reinforcement learning algorithm, with the preference dataset as the reward signal, to train the subjective preference rating model to learn subjective evaluation strategies. Through the above reinforcement learning method based on human feedback, this application can train subjective preference rating models such as symmetric preference, porous preference, connectivity preference, and user-personalized preference.

[0026] Understandably, the state space is a core component of reinforcement learning agents' observation and perception of their environment, defining the input information the agent relies on when evaluating topological structures. In traditional topology optimization, the state space may only contain basic physical parameters (e.g., density distribution, stress values, etc.), but these data are low-level and mathematical, making it difficult to directly map to human subjective preferences (e.g., aesthetics, symmetry). However, subjective preference rating models often need to handle structures with complex geometries and physical properties generated during topology optimization. If the state space only contains basic physical parameters such as density distribution and stress values, it is insufficient for accurate evaluation. In other words, the richness of the state space directly determines whether the model can understand the visual and functional characteristics of the structure. Considering that geometric feature parameters are high-level attributes quantified from the density distribution of the topology through image processing techniques (e.g., edge detection, shape descriptor extraction, or contour analysis), such as symmetry measures, continuity scores, hole distribution patterns, or contour smoothness, these parameters are highly aligned with the cognitive process of human subjective evaluation. For example, when humans evaluate a design (e.g., a car's exterior or building structure), the brain automatically extracts geometric features (e.g., symmetry, proportion) rather than directly processing raw grid data. By incorporating geometric feature parameters into the state space, subjective preference rating models can simulate this process, making the ratings closer to human judgment. Therefore, to enhance the accuracy of subjective evaluations, the state space of the subjective preference rating model in the above embodiments can also include topological geometric feature parameters extracted through image processing techniques. On the one hand, geometric feature parameters provide discriminative information, enabling the subjective preference rating model to accurately capture preference differences; on the other hand, through geometric features, the subjective preference rating model learns high-level abstract rules such as "higher symmetry scores result in higher scores," rather than memorizing specific density patterns. This improves its adaptability to new topological structures and rating consistency, i.e., enhances the generalization ability of the subjective preference rating model. As for how to extract topological geometric feature parameters through image processing techniques, the specific methods could be as follows: convert the material density distribution into a grayscale image, where the density value is mapped to pixel intensity; apply image processing algorithms (e.g., Fourier transform for periodic analysis or morphological operations for hole recognition, etc.) to extract feature parameters, such as calculating symmetry coefficients through mirror comparison, analyzing connectivity indices based on skeleton extraction or connected component analysis, and quantifying contour complexity through boundary curvature variance, etc.; input these feature parameters as additional dimensions of the state space into the agent, combining them with the original density data to provide a more comprehensive representation of the environment.

[0027] Traditional topology optimization suffers from a lack of mathematical quantification methods, preventing subjective preferences from directly participating in the iteration process. Even with the introduction of subjective rating models, these models are typically black-box functions (e.g., various types of neural networks) lacking analytic derivatives, making it impossible to calculate their sensitivity or integrate them with gradient basis optimization algorithms. To provide computable gradient information for the pre-trained subjective preference rating model, accurately capture the response of subjective evaluation values ​​to local density changes, and avoid global approximation errors, the sensitivity of the subjective evaluation value output by the subjective preference rating model based on the numerical perturbation method in the above embodiment can be achieved as follows: Calculate the subjective evaluation value based on the current material density distribution. Apply a size of [value] to each unit in sequence. The density perturbation is used to calculate the subjective evaluation value after the perturbation. Using the difference quotient formula Calculate the sensitivity of the subjective evaluation value for each element. In the above embodiments, the element refers to the basic mesh element of the discretized design domain in finite element analysis. Specifically, it can be a large number of tiny elements (e.g., triangular, quadrilateral, or hexahedral elements, etc.) divided into continuous design domains in topology optimization. Each element is assigned a density value (between 0 and 1), representing the probability of material presence or absence. Density perturbation. The value of can range from 0.001 to 0.01. This range is based on finite difference theory to balance accuracy and stability. This range has been verified to avoid nonlinear abrupt changes in the subjective rating model while ensuring the validity of the difference quotient result. Furthermore, the reason for sequentially perturbing each unit and calculating the sensitivity of each unit's subjective evaluation value using the difference quotient formula, rather than using global perturbation and a simplified formula, is that global perturbation cannot accurately reflect the impact of local density changes. The difference quotient formula is a first-order approximation of the derivative, mathematically guaranteeing that the sensitivity points in the gradient descent direction. This transforms subjective preferences into actionable optimization guidelines and allows the Moving Asymptote Method (MMA) algorithm to simultaneously coordinate subjective and objective objectives.

[0028] Furthermore, considering that in topology optimization, high-density gradient regions are areas where density values ​​change drastically (e.g., the transition zone from density 1 (solid material) to density 0 (void)), these regions typically correspond to key structural features, such as boundaries, void edges, or load transfer paths, significantly impacting structural performance such as stress concentration and deformation. Conversely, low-density gradient regions (e.g., homogeneous material regions or void regions) have lower sensitivity, and perturbing these elements has limited guidance for the optimization direction. On the other hand, the topology optimization design domain may contain tens of thousands of elements. Perturbing each element sequentially would be computationally expensive, while prioritizing perturbations of high-gradient regions allows for the early acquisition of key sensitivity information, enabling the optimization algorithm to identify important search directions more quickly. Once the sensitivity of these regions is calculated, the optimization iteration can converge earlier or skip the detailed calculation of low-sensitivity elements, thereby reducing the total number of perturbations. Therefore, in the above embodiment, a value of [missing information] is applied sequentially to each element. When performing density perturbations, priority can be given to perturbing cells in high-density gradient regions. This reduces the number of perturbations, accelerating iterative convergence. While reducing computational load and improving the overall optimization efficiency, the priority perturbation does not significantly sacrifice the accuracy of subjective evaluation because high-density gradient regions dominate the optimization direction, ensuring that the optimization process efficiently and accurately reflects human preferences.

[0029] Step S104: Input the objective response value and its sensitivity, as well as the subjective evaluation value and its sensitivity, into the moving asymptote method MMA optimizer for iterative calculation, and dynamically update the material density distribution to balance subjective preferences and objective constraints.

[0030] It should be noted that during topology optimization, if only mechanical performance targets are considered while ignoring actual manufacturing process constraints, the optimization results cannot be directly used for production. For example, excessively fine structures may be generated that cannot be processed, or suspended areas may be impossible to demold. Therefore, in order to place manufacturing constraints at the forefront of the optimization stage, significantly reduce the cost of later modifications, and resolve the conflict between manufacturing constraints and subjective preferences in specific situations, this application also performs a manufacturing constraint application operation before step S104. Specifically, this includes: selecting at least one of the manufacturing constraints according to the manufacturing process, wherein the manufacturing constraints include minimum size control, draft direction constraints, and material continuity; converting the manufacturing constraints into mathematical constraints and integrating them into the MMA optimizer; and prioritizing the activation of one of the manufacturing constraints based on user configuration when there is a conflict between manufacturing constraints and subjective preferences. Furthermore, in order to find the optimal balance between manufacturing feasibility and subjective aesthetics, achieve manufacturable aesthetic design, and automate feature recognition to reduce manual intervention to meet the needs of large-scale design problems, the application of manufacturing constraints in the above embodiments is achieved through geometric feature recognition, including detecting suspended areas or minimum tilt angles, and interacting with the subjective scoring model to adjust the constraint strength.

[0031] Existing optimization methods often employ simple weighted summation when dealing with multiple subjective and objective objectives, failing to effectively handle complex trade-offs between objectives and leading to instability in the optimization process. For example, weighted summation requires prior knowledge to determine weights, and hierarchical optimization may overlook important trade-offs of low-priority objectives. To efficiently find equilibrium points in complex design spaces and ensure smooth convergence of the optimization process to a practical solution that meets multiple requirements, this application inputs objective response values ​​and their sensitivities, as well as subjective evaluation values ​​and their sensitivities, into a Moving Asymptotes (MMA) optimizer for iterative calculation, dynamically updating the material density distribution to balance subjective preferences and objective constraints. Specifically, as an embodiment of this application, inputting objective response values ​​and their sensitivities, as well as subjective evaluation values ​​and their sensitivities, into the MMA optimizer for iterative calculation, and dynamically updating the material density distribution can be achieved by: combining subjective and objective responses into a multi-objective function; dynamically adjusting the asymptote movement step size using sensitivity information to balance convergence speed and stability; and dynamically adjusting the weight coefficients of the subjective response based on user input or historical data during the iteration process of the MMA optimizer to adaptively optimize the process.

[0032] In the above embodiments, dynamically adjusting the asymptote movement step size using sensitivity information to balance convergence speed and stability can specifically be achieved by analyzing the local curvature characteristics of the optimization problem based on sensitivity information. That is, if the sensitivity value is large (indicating drastic changes in the objective function), the asymptote movement step size is reduced to enhance stability; if the sensitivity value is small and changes gradually, the step size is increased to accelerate convergence. The step size adjustment factor used to adjust the step size can be referenced by the following formula: ,in, For the sensitivity norm, α and β These are empirical parameters; based on the step size adjustment factor, the asymptotic boundaries in the MMA algorithm (e.g., upper bound asymptotic U and lower bound asymptotic L) are updated using the following formula: ,in, δ As the base step size, For the existing asymptote boundary, The updated asymptote boundaries are used; the adjusted asymptotes are used to solve the subproblem, generating a new density distribution, completing this iteration. During the iteration process of the MMA optimizer, the weight coefficients of subjective responses are dynamically adjusted based on user input or historical data to adaptively optimize the process. Specifically, during the MMA iteration, two types of signals are detected in real time: user input signals (e.g., preference intensity adjustment instructions in the interactive interface) and historical data signals (e.g., the changing trend of subjective evaluation values ​​or convergence stability indicators in the past few iterations). Weight changes are quantified based on trigger conditions; that is, if the user input requests to strengthen subjective preferences, the weight of the subjective response is increased; if historical data shows oscillations in subjective ratings, the weight is decreased to prioritize stabilizing objective constraints. Weight adjustments can be based on rule engines or machine learning models, for example... ,in, w Subjective weighting, k The weights are the gain coefficients; the adjusted weight coefficients are substituted into the multi-objective function, for example, ,in, and The objective functions are subjective and objective; perform one trial iteration and check whether the convergence metric (e.g., rate of change of objective function) improves under the new weights; if not, roll back the weights and re-trigger the adjustment.

[0033] Step S105: Determine whether the updated material density distribution meets the convergence conditions set by the user. If it does, proceed to step S106; otherwise, return to step S102 for a new round of iteration.

[0034] In this embodiment, the updated material density distribution can be determined to meet the user-defined convergence conditions by monitoring at least one of the objective function's rate of change, the density distribution's norm of change, or the maximum number of iterations. The rate of change threshold is dynamically set based on subjective preferences; for example, a smaller threshold is set for high-precision preferences (e.g., strict appearance requirements), while a default threshold can be used for less stringent preferences. Furthermore, if the updated material density distribution does not meet the user-defined convergence conditions, the mesh density or load conditions of the finite element analysis can be automatically adjusted first. If the user-defined convergence conditions are still not met, the process returns to step S102 for a new round of iteration. The automatic adjustment of the mesh density in the finite element analysis can identify locally optimal regions and refine the mesh to improve computational accuracy, while the automatic adjustment of the load conditions can dynamically adjust the load step size based on historical convergence data. When the updated material density distribution meets the user-defined convergence conditions, instead of directly returning to step S102 for a new round of iteration, the mesh density or load conditions of the finite element analysis are automatically adjusted. If the user-defined convergence conditions are still not met, the process returns to step S102 for a new round of iteration. Adjusting the calculation parameters can help the optimization process escape local optima and avoid excessive iteration in invalid regions, thus accelerating global convergence.

[0035] Step S106: Post-process and visualize the optimized material density distribution to output the final topology configuration.

[0036] In existing technologies, topology optimization results often contain a large number of intermediate density cells, making them difficult to use directly in engineering manufacturing and requiring effective post-processing methods. For example, simply setting a truncation threshold may result in the loss of important structural features, while using a simplified projection method may introduce new numerical problems. In order to transform mathematical optimization results into manufacturable engineering drawings while maintaining the complete communication of design intent and providing reliable input for subsequent manufacturing processes, this application can perform post-processing visualization of the optimized material density distribution and output the final topology configuration. Specifically, this includes: converting the density distribution into an isosurface model and using color mapping to highlight subjectively preferred areas, while generating an optimization report; verifying the manufacturability of the topology configuration in the post-processing stage, checking dimensional feasibility through simulated processing technology, and feeding the results back to the initialization process in step S101.

[0037] The entire optimization process in the above embodiment is implemented through a parallel computing architecture, wherein the finite element analysis in step S102, the subjective scoring in step S103, and the MMA optimizer iteration in step S104 are distributed and executed synchronously on different computing nodes to improve the processing efficiency of large-scale design problems.

[0038] To better understand the technical solutions of the embodiments of this application described above, an application scenario of this application will be used as an example for illustration below.

[0039] Suppose a research and development engineer is tasked with designing a suspension bracket connecting a battery pack to the vehicle body. The core challenge lies in ensuring the bracket meets stringent safety standards (i.e., deformation must be below a threshold and stress below the material's yield strength under severe vibration) while simultaneously exhibiting smooth, dynamic aesthetic lines consistent with the brand's character. Existing design methods often require repeated compromises between these two goals, while this application offers an integrated intelligent solution. At the start of the design process, the engineer defines the approximate design space for the bracket in the software and selects a "streamlined preference" as the aesthetic objective. Based on this, the system intelligently generates an initial material distribution scheme, which already possesses a smooth outline rather than a traditional uniform layout, laying a solid foundation for subsequent efficient optimization. Subsequently, the system's core workflow is initiated. It first performs finite element analysis based on the current material density distribution, simulating real-world conditions and accurately calculating objective response values ​​representing structural performance, such as displacement and maximum stress at key points, etc. Simultaneously, the sensitivity of these objective responses is calculated—that is, how much a change in material density in each tiny region affects the displacement or stress values. Then, the system activates a pre-trained agent specializing in "streamlined" aesthetic evaluation—the subjective preference scoring model. This agent examines the geometry of the current support structure and outputs a quantified subjective evaluation value, for example, 0.85 out of 1.0, intuitively reflecting the aesthetic appeal of the current design. To also provide direction for aesthetic optimization, the system employs a clever numerical probing method: it slightly perturbs each of the tens of thousands of elements within the design domain, observing the change in aesthetic score after each perturbation, thereby calculating the sensitivity of the subjective evaluation value. This clearly indicates which part of the material, strengthening or weakening it, can more effectively enhance the overall streamlined feel. The subjective preference scoring model possesses all the information from both the "performance" and "aesthetic" dimensions—that is, their respective current values ​​(response values) and optimization directions (sensitivity). It inputs all this data into the core MMA optimizer. The optimizer, like an experienced decision-maker, no longer treats these two objectives as opposites, but rather processes them collaboratively. Based on sensitivity information, it intelligently adjusts material distribution: it might reinforce a connection point to reduce stress, while smoothing a transition region to improve streamline performance. Each iteration is an intelligent exploration towards a better, more aesthetically pleasing design while meeting all hard constraints. This process is cyclical. After each iteration, the system automatically determines whether the result is sufficiently ideal (converged). If it hasn't reached the optimal state, the optimization process will perform finite element analysis and subjective evaluation again with the updated design, repeating this cycle step by step. Finally, when the system determines that the design can no longer be significantly improved through further fine-tuning, a support topology configuration that combines high strength, high stiffness, and an elegant streamlined shape is automatically generated and can be directly used for subsequent engineering manufacturing.This scenario demonstrates that by quantifying subjective preferences and placing them within the same optimization framework as objective performance, this application empowers computers to simultaneously pursue both "ease of use" and "aesthetic appeal," thereby significantly improving the efficiency and quality of innovative designs.

[0040] From the above appendix Figure 1 As illustrated by the example of the integrated subjective preference topology optimization design method, on the one hand, by introducing a pre-trained subjective preference scoring model into the optimization process and calculating the sensitivity of subjective responses, the problem of neglecting subjective factors in traditional methods is avoided. This ensures that the final output topology configuration not only meets objective constraints such as strength and stiffness but also reflects visual harmony or user interaction comfort. On the other hand, because subjective responses are quantified into computable parameters and input into the MMA optimizer along with objective responses, the optimization algorithm can explore the design space more comprehensively. This not only enhances the flexibility of the optimization process but also avoids getting trapped in local optima and improves convergence efficiency. In summary, the technical solution of this application improves the practicality and overall quality of topology optimization design by integrating subjective preferences and objective constraints.

[0041] Please see the appendix Figure 2 This application provides a topology optimization design device integrating subjective preferences. The device may include an initialization module 201, an objective response processing module 202, a subjective response processing module 203, an iteration module 204, a judgment module 205, and a post-processing module 206, as detailed below: Initialization module 201 is used to initialize the material density distribution within the design domain and intelligently recommend an initial density distribution scheme based on the user's selected subjective preference type. The objective response processing module 202 is used to perform finite element analysis based on the current material density distribution and calculate the objective response value and its sensitivity. The subjective response processing module 203 is used to call a pre-trained subjective preference scoring model to subjectively evaluate the current material density distribution, output the subjective evaluation value, and calculate the sensitivity of the subjective evaluation value based on the numerical perturbation method. The iteration module 204 is used to input the objective response value and its sensitivity, as well as the subjective evaluation value and its sensitivity, into the moving asymptote method MMA optimizer for iterative calculation, and dynamically update the material density distribution to balance subjective preferences and objective constraints. The judgment module 205 is used to determine whether the updated material density distribution meets the convergence conditions set by the user. If it does, it will switch to the post-processing module for execution; otherwise, it will return to the objective response processing module for a new round of iteration. The post-processing module 206 is used to perform post-processing visualization of the optimized material density distribution and output the final topology configuration.

[0042] From the above appendix Figure 2As illustrated by the example of the integrated subjective preference topology optimization design device, on the one hand, by introducing a pre-trained subjective preference scoring model into the optimization process and calculating the sensitivity of subjective responses, the problem of neglecting subjective factors in traditional methods is avoided. This ensures that the final output topology configuration not only meets objective constraints such as strength and stiffness but also reflects visual harmony or user interaction comfort. On the other hand, because subjective responses are quantified into computable parameters and input into the MMA optimizer along with objective responses, the optimization algorithm can explore the design space more comprehensively. This not only enhances the flexibility of the optimization process but also avoids getting trapped in local optima and improves convergence efficiency. In summary, the technical solution of this application improves the practicality and overall quality of topology optimization design by integrating subjective preferences and objective constraints.

[0043] Figure 3 This is a schematic diagram of the structure of a device provided in one embodiment of this application. For example... Figure 3 As shown, the device 3 in this embodiment mainly includes: a processor 30, a memory 31, and a computer program 32 stored in the memory 31 and executable on the processor 30, such as a program for a topology optimization design method integrating subjective preferences. When the processor 30 executes the computer program 32, it implements the steps in the above-described embodiment of the topology optimization design method integrating subjective preferences, for example... Figure 1 The steps S101 to S106 are shown. Alternatively, when the processor 30 executes the computer program 32, it implements the functions of each module / unit in the above-described device embodiments, for example... Figure 2 The functions of the initialization module 201, objective response processing module 202, subjective response processing module 203, iteration module 204, judgment module 205, and post-processing module 206 are shown.

[0044] For example, the computer program 32 integrating subjective preference-based topology optimization design mainly includes: initializing the material density distribution within the design domain and intelligently recommending an initial density distribution scheme based on the user-selected subjective preference type; performing finite element analysis based on the current material density distribution to calculate the objective response value and its sensitivity; calling a pre-trained subjective preference scoring model to subjectively evaluate the current material density distribution, outputting the subjective evaluation value, and calculating the sensitivity of the subjective evaluation value based on the numerical perturbation method; inputting the objective response value and its sensitivity, as well as the subjective evaluation value and its sensitivity, into the moving asymptote method MMA optimizer for iterative calculation, dynamically updating the material density distribution to balance subjective preferences and objective constraints; determining whether the updated material density distribution meets the convergence conditions set by the user; if it does, post-processing and visualizing the optimized material density distribution, outputting the final topology configuration; otherwise, returning to a new round of iteration. The computer program 32 can be divided into one or more modules / units, which are stored in the memory 31 and executed by the processor 30 to complete this application. One or more modules / units can be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program 32 in the device 3. For example, computer program 32 can be divided into the functions of a synchronous acquisition module 201, a data fusion module 202, a data storage module 203, and a diagnostic tracing module 204 (a module in the virtual device). The specific functions of each module are as follows: Initialization module 201 is used to initialize the material density distribution within the design domain and intelligently recommend an initial density distribution scheme based on the user's selected subjective preference type; Objective response processing module 202 is used to perform finite element analysis based on the current material density distribution and calculate the objective response value and its sensitivity; Subjective response processing module 203 is used to call a pre-trained subjective preference scoring model to perform subjective evaluation on the current material density distribution. The system performs a series of steps: 1) Pricing; 2) Outputting subjective evaluation values ​​and calculating the sensitivity of these values ​​based on the numerical perturbation method; 3) Iteration module 204, which inputs the objective response values ​​and their sensitivities, along with the subjective evaluation values ​​and their sensitivities, into the Moving Asymptote Method (MMA) optimizer for iterative calculation, dynamically updating the material density distribution to balance subjective preferences and objective constraints; 4) Judgment module 205, which determines whether the updated material density distribution meets the user-defined convergence conditions. If it does, the system proceeds to the post-processing module; otherwise, it returns to the objective response processing module for a new round of iteration; 5) Post-processing module 206, which visualizes the optimized material density distribution and outputs the final topology.

[0045] Device 3 may include, but is not limited to, processor 30 and memory 31. Those skilled in the art will understand that... Figure 3This is merely an example of device 3 and does not constitute a limitation on device 3. It may include more or fewer components than shown, or combine certain components, or different components. For example, the device may also include input / output devices, network access devices, buses, etc.

[0046] The processor 30 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0047] The memory 31 can be an internal storage unit of the device 3, such as a hard disk or RAM of the device 3. The memory 31 can also be an external storage device of the device 3, such as a plug-in hard disk, Smart MediaCard (SMC), Secure Digital (SD) card, or Flash Card equipped on the device 3. Furthermore, the memory 31 can include both internal and external storage units of the device 3. The memory 31 is used to store computer programs and other programs and data required by the device. The memory 31 can also be used to temporarily store data that has been output or will be output.

[0048] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed. That is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above-described device can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0049] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0050] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0051] In the embodiments provided in this application, it should be understood that the disclosed apparatus / device and method can be implemented in other ways. For example, the apparatus / device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another device, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0052] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0053] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0054] If an integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a storage medium. Based on this understanding, all or part of the processes in the above-described embodiments can be implemented by a computer program instructing related hardware. The computer program integrating the subjective preference topology optimization design method can be stored in a storage medium. When the computer program is executed by a processor, it can implement the steps of the above-described method embodiments, namely: initializing the material density distribution within the design domain and intelligently recommending an initial density distribution scheme based on the user-selected subjective preference type; performing finite element analysis based on the current material density distribution to calculate the objective response value and its sensitivity; calling a pre-trained subjective preference scoring model to subjectively evaluate the current material density distribution, outputting the subjective evaluation value, and calculating the sensitivity of the subjective evaluation value based on the numerical perturbation method; inputting the objective response value and its sensitivity, as well as the subjective evaluation value and its sensitivity, into the moving asymptote method MMA optimizer for iterative calculation, dynamically updating the material density distribution to balance subjective preferences and objective constraints; determining whether the updated material density distribution meets the user-defined convergence conditions. If it does, post-processing and visualizing the optimized material density distribution and outputting the final topology configuration; otherwise, returning to a new round of iteration. Computer programs include computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. Storage media can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the contents of storage media can be appropriately added or removed according to the requirements of legislation and patent practice in a jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, storage media do not include electrical carrier signals and telecommunication signals.

[0055] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application. The specific embodiments described above further illustrate the purpose, technical solutions, and beneficial effects of this application. It should be understood that the above descriptions are merely specific embodiments of this application and are not intended to limit the protection scope of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A topology optimization design method integrating subjective preferences, applied to engineering product design scenarios, characterized in that, The method includes: Step S101: Initialize the material density distribution within the design domain and intelligently recommend an initial density distribution scheme based on the user's selected subjective preference type; Step S102: Perform finite element analysis based on the current material density distribution to calculate the objective response value and its sensitivity; Step S103: Call the pre-trained subjective preference rating model to subjectively evaluate the current material density distribution, output the subjective evaluation value, and calculate the sensitivity of the subjective evaluation value based on the numerical perturbation method; Step S104: Input the objective response value and its sensitivity, as well as the subjective evaluation value and its sensitivity, into the moving asymptote method MMA optimizer for iterative calculation, and dynamically update the material density distribution to balance subjective preferences and objective constraints; Step S105: Determine whether the updated material density distribution meets the convergence condition set by the user. If it does, proceed to step S106; otherwise, return to step S102 for a new round of iteration. Step S106: Post-process and visualize the optimized material density distribution to output the final topology configuration.

2. The topology optimization design method integrating subjective preferences as described in claim 1, characterized in that, The intelligent recommendation of the initial density distribution scheme based on the user's selected subjective preference type includes: Based on the user's selected subjective preference type, the corresponding preference features are matched from the model library; An initial density distribution is generated based on the matched preference features, wherein the density distribution preferentially satisfies symmetry or minimum size constraints.

3. The topology optimization design method integrating subjective preferences as described in claim 1, characterized in that, The sensitivity of calculating the subjective evaluation value based on the numerical perturbation method includes: Subjective evaluation value calculated based on the current material density distribution. ; Apply a size of [value] to each unit in sequence. The density perturbation is used to calculate the subjective evaluation value after the perturbation. ; Using the difference quotient formula Calculate the sensitivity of the subjective evaluation value for each unit.

4. The topology optimization design method integrating subjective preferences as described in claim 1, characterized in that, The step of inputting the objective response value and its sensitivity, as well as the subjective evaluation value and its sensitivity, into the moving asymptote optimizer for iterative calculation and dynamically updating the material density distribution includes: Combine subjective and objective responses into a multi-objective function; The asymptote movement step size is dynamically adjusted using sensitivity information to balance convergence speed and stability; During the iteration process of the MMA optimizer, the weight coefficients of the subjective response are dynamically adjusted based on user input or historical data to adaptively optimize the process.

5. The topology optimization design method integrating subjective preferences as described in claim 1, characterized in that, The method further includes: Prior to step S104, at least one of the manufacturing constraints is selected according to the manufacturing process, the manufacturing constraints including minimum size control, draft direction constraint and material continuity; The manufacturing constraints are transformed into mathematical constraints and integrated into the MMA optimizer. When the manufacturing constraints conflict with subjective preferences, one option is selected to be enabled based on the user configuration.

6. The topology optimization design method integrating subjective preferences as described in claim 5, characterized in that, The manufacturing constraints are applied through geometric feature recognition, including detecting suspended areas or minimum tilt angles, and interacting with a subjective scoring model to adjust the constraint strength.

7. The topology optimization design method integrating subjective preferences as described in claim 1, characterized in that, The entire optimization process is implemented through a parallel computing architecture, with the finite element analysis in step S102, the subjective scoring in step S103, and the MMA optimizer iteration in step S104 being executed synchronously on different computing nodes.

8. A topology optimization design device integrating subjective preferences, characterized in that, The device includes: The initialization module is used to initialize the material density distribution within the design domain and intelligently recommend an initial density distribution scheme based on the user's selected subjective preference type. The objective response processing module is used to perform finite element analysis based on the current material density distribution and calculate the objective response value and its sensitivity. The subjective response processing module is used to call a pre-trained subjective preference scoring model to subjectively evaluate the current material density distribution, output the subjective evaluation value, and calculate the sensitivity of the subjective evaluation value based on the numerical perturbation method. The iterative module is used to input the objective response value and its sensitivity, as well as the subjective evaluation value and its sensitivity, into the moving asymptote method MMA optimizer for iterative calculation, and dynamically update the material density distribution to balance subjective preferences and objective constraints. The judgment module is used to determine whether the updated material density distribution meets the convergence conditions set by the user. If it does, it will switch to the post-processing module for execution; otherwise, it will return to the objective response processing module for a new round of iteration. The post-processing module is used to post-process and visualize the optimized material density distribution and output the final topology configuration.

9. An apparatus comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 7.

10. A storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

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