Product structure topological optimization design method considering aesthetic characteristics

Abstract

A product structure topological optimization design method considering aesthetic characteristics comprises the steps that an aesthetic scoring model based on a ResNet-18 network and a material field series expansion non-gradient topological optimization model based on a Kriging proxy model are constructed, the mechanical property of a product structure is used as an optimization target, and the volume fraction and the aesthetic score are used as constraint conditions; topological optimization design is carried out on the product, synchronous optimization design of mechanical properties and aesthetic characteristics of the product is achieved, and therefore the compound type requirement of a user for product function reliability and aesthetic experience is met.

Description

Technical Field

[0001] This invention relates to a design method, and more particularly to a product structure topology optimization design method that takes into account aesthetic characteristics, belonging to the interdisciplinary field of product aesthetics and structural optimization design. Background Technology

[0002] With the rapid development of industrial design, the requirements for the comprehensive performance of products are constantly increasing. As two parts that constitute the whole product, the mechanical performance and aesthetic characteristics of a product are often difficult to balance in the past due to the division of labor between designers and engineers. This not only seriously limits the efficiency of product development, but also leads to a disconnect between product functionality and aesthetics, resulting in a significant reduction in the product experience. Instead of being limited to single-function-oriented design that focuses on the aesthetic characteristics or mechanical performance of a product, multi-directional design that comprehensively considers various design needs has become a trend in industrial design research. Summary of the Invention

[0003] To address the challenge of balancing mechanical performance and aesthetic characteristics in traditional product design, this paper proposes a method for simultaneous optimization of product mechanical performance and aesthetic characteristics based on the KG-MFSE non-gradient topology optimization algorithm. This method aims to achieve simultaneous optimization of product mechanical performance and aesthetic characteristics. It employs a ResNet-18 network to construct a product aesthetic evaluation model, combines the MFSE method to establish a topology optimization model, and uses a Kriging surrogate model for non-gradient solution, verifying the feasibility of simultaneous optimization of mechanical performance and aesthetic characteristics. This framework enables simultaneous optimization of product mechanical performance and aesthetic characteristics, providing an interdisciplinary solution for multi-performance collaborative optimization in industrial design. The specific technical solution is as follows: A product structure topology optimization design method considering aesthetic characteristics, characterized by: constructing an aesthetic scoring model based on a ResNet-18 network and a material field series expansion non-gradient topology optimization model based on a Kriging surrogate model; using the product structure mechanical performance as the optimization objective and volume fraction and aesthetic score as constraints; and performing topology optimization design on the product to achieve simultaneous optimization of product mechanical performance and aesthetic characteristics, thereby meeting users' combined needs for product functional reliability and aesthetic experience.

[0004] Preferably, the product structure topology optimization design method considering aesthetic characteristics includes the following steps:

[0005] Step 1: Construct a product aesthetic evaluation model based on ResNet-18;

[0006] Step 2: Establishing a topology optimization model based on the KG-MFSE method;

[0007] Step 3: Establish a topology optimization model considering aesthetic characteristics;

[0008] Step 4: Non-gradient optimization algorithm based on Kriging surrogate model.

[0009] Beneficial effects

[0010] This invention achieves efficient prediction of aesthetic scores on small sample datasets through transfer learning from an aesthetic perspective, and constructs a product aesthetic evaluation model based on ResNet-18. From a mechanical perspective, it introduces the Material Field Series Expansion (MFSE) method to transform the topology optimization problem into a constrained optimization model with material field coefficients as design variables. Combined with the sequential sampling strategy of the Kriging surrogate model, it effectively reduces computational costs and improves global search capabilities. Attached Figure Description

[0011] Figure 1 Original helmet model and force distribution diagram;

[0012] Figure 2 Sample images of some road bike helmets;

[0013] Figure 3 Preprocessing of road bike helmet images;

[0014] Figure 4 Partial grayscale image;

[0015] Figure 5 (a) Partial three-part sample plot; (b) Partial seven-part sample plot;

[0016] Figure 6 Training diagram of ResNet-18 network;

[0017] Figure 7 (a) Result diagram of single constraint for working condition 1; (b) Model diagram of single constraint for working condition 1;

[0018] Figure 8 Single-constraint iterative graph;

[0019] Figure 9 (a) Result diagram of double constraint for working condition 1; (b) Model diagram of double constraint for working condition 1;

[0020] Figure 10 Double-constraint iterative graph;

[0021] Figure 11 Simulation results of single and double constraint optimization models. Detailed Implementation

[0022] This invention proposes a product structure topology optimization design method that considers aesthetic characteristics. This method constructs an aesthetic scoring model based on a ResNet-18 network and a material field series expansion (KG-MFSE) non-gradient topology optimization model based on a Kriging surrogate model. It uses the product's structural mechanical performance (such as structural deformation) as the optimization objective and volume fraction and aesthetic score (aesthetic characteristics) as constraints to perform topology optimization design on the product. This achieves simultaneous optimization of the product's mechanical performance and aesthetic characteristics, thereby meeting users' combined needs for product functional reliability and aesthetic experience.

[0023] To achieve the above objectives, the main technical solution of this invention is as follows:

[0024] A product mechanical performance and aesthetic characteristics simultaneous optimization design method based on KG-MFSE non-gradient topology optimization algorithm is proposed. The method mainly includes three parts: establishing a product aesthetic evaluation model, establishing a topology optimization model based on the KG-MFSE method, and establishing a topology optimization model considering aesthetic characteristics. The specific steps are as follows:

[0025] The first step is to construct a product aesthetic evaluation model based on ResNet-18.

[0026] 1.1) Select research subjects and use web crawling tools to collect a large number of product images of research subjects from domestic and foreign platform websites. After manual screening and deduplication, data augmentation is performed on the original collected data to expand the dataset.

[0027] 1.2) Preprocess the original product image, extract the main body of the product and convert it into an 8-bit grayscale image with numerical values ​​representing the presence or absence of materials. While preserving the product structural details, the data dimensionality is significantly reduced, and a standardized dataset that meets the requirements of machine learning is constructed.

[0028] 1.3) Data annotation is performed on the preprocessed standardized product images. The aesthetic score is organized into integer values ​​between 1 and 7. Images with different scores are placed in folders with corresponding score values ​​to form a labeled dataset for training the neural network.

[0029] 1.4) Training the ResNet-18 network. Regarding model architecture and training strategy design, this invention utilizes transfer learning based on the ResNet-18 network to construct a deep learning model suitable for aesthetic scoring. Addressing the differences between the original model's classification and regression tasks, the fully connected layer at the network's end is first adjusted from 1000 classification outputs to 7 classification outputs, enabling the network to directly output continuous aesthetic scores (1-7 points) while retaining the advantages of the pre-trained model in image feature extraction.

[0030] By calculating the squared deviation between predicted ratings and actual user ratings, the model is guided to learn the nonlinear mapping relationship between shape features and aesthetic preferences, which is more suitable for regression tasks compared to the cross-entropy loss function. For parameter initialization, a transfer learning method is used to load ImageNet pre-trained weights as the model's starting point. By freezing the low-level parameters of the first three convolutional blocks (out of four), only the high-level networks are fine-tuned. This leverages the powerful representational ability of the pre-trained model for general image features while avoiding the risk of overfitting due to the limited product data size. The product's shape feature contour curves are extracted and standardized input images are obtained through projection transformation. The ResNet-18 aesthetic evaluation model built based on transfer learning can be deconstructed into a composite nonlinear mapping:

[0031]

[0032] in, It is a weight matrix. This is a global average pooling operation. This represents the first... Feature maps output by the layer It is the input standardized image. It is a bias term. The activation function is the input image. Features are extracted using ResNet-18, dimensionality is reduced using global average pooling, and then the output is mapped to a scoring range using a fully connected layer and activation function to obtain the product aesthetic score. .

[0033] The product aesthetic evaluation algorithm proposed in this invention, based on transfer learning and deep residual networks, can solve the limitation of traditional convolutional neural networks for intelligent image decision-making under small sample dataset conditions, effectively improving the training speed and classification accuracy of the model. The trained aesthetic evaluation model lays the foundation for the subsequent simultaneous optimization of product mechanical performance and aesthetic characteristics.

[0034] The second step is to establish a topology optimization model based on the KG-MFSE method.

[0035] 2.1) To significantly reduce the number of design variables in non-gradient topology optimization while avoiding the checkerboard phenomenon, this invention employs a novel MFSE topology optimization method. Based on the Material Field Sequence Expansion (MFSE) method, the structural topology can be represented by a bounded field function with spatial correlation, such as... Figure 1 As shown, the side length of the rectangular design domain is . The expression for the MFSE topology optimization method is as follows:

[0036]

[0037] in, Design domain for topology optimization The bounded field function in the range of variation is , yes One of the points, and These represent holes and solid domains, respectively.

[0038] Based on the material field series expansion and truncation, only the field function is retained. The former MFSE coefficient Therefore, the field function can be expressed as:

[0039]

[0040] in, and Representing the correlation matrix respectively eigenvalues ​​and eigenvectors. and . yes A diagonal matrix. It is composed of eigenvectors The matrix. Additionally, the correlation matrix. Represented as:

[0041]

[0042] in, For the relevant function, it is represented as .

[0043] Based on the range of the field function And introduce the feature matrix The MFSE coefficient can be obtained. The range of variation is .

[0044] 2.2) To better realize the mapping process from field function to topological configuration, we... Performing Heaviside filtering is represented as

[0045]

[0046] in, This represents the smoothness coefficient. The following function is used for structural element material interpolation based on MFSE topology optimization:

[0047]

[0048] in, Represents the elastic modulus of a solid structure. , This represents the penalty coefficient.

[0049] Based on the above interpolation function, the topology optimization model based on MFSE can be expressed in the following form:

[0050]

[0051] and Let these represent the objective function and constraint function of the structure, respectively, and the MFSE coefficients. Represents the design variables of the optimization model. Represents the structural displacement vector. The equilibrium equations for finite element analysis of practical problems.

[0052] The third step is to establish a topology optimization model that considers aesthetic characteristics.

[0053] Combining the ResNet-18-based product aesthetic evaluation model built in the first step and the MFSE-based product mechanical performance optimization model built in the second step, a dual-constraint optimization algorithm based on KG-MFSE aesthetic score and volume fraction is constructed to achieve simultaneous optimization design of product mechanical performance and aesthetic characteristics. Compared to the single-constraint model of the second step that only considers volume fraction, this model considers both product mechanical performance and aesthetic characteristics (described as a dual-constraint model). The optimization model is as follows:

[0054]

[0055] Where S represents the aesthetic score of the current product design scheme calculated by the ResNet-18 network. This indicates a given aesthetic constraint on the product.

[0056] The fourth step is a non-gradient optimization algorithm based on the Kriging surrogate model.

[0057] Because it has advantages such as not requiring gradient information of the original problem, low computational cost, and ease of parallel computation, the Kriging surrogate model has become the preferred solution for solving non-gradient topology optimization problems.

[0058] After transformation, the unconstrained expression of the double-constraint function topology optimization problem in the above formula is as follows:

[0059]

[0060] in, As a penalty factor, set it to .

[0061] To obtain the globally optimal solution to the optimization problem in a given design domain, a Kriging surrogate model needs to be established and the optimization problem in the equation needs to be solved using a sequential sampling criterion. To ensure both global search capability and efficient solution, this invention combines two sampling criteria in the sequential sampling stage.

[0062] (i) Minimize the response surface criterion of the surrogate model, that is, add points to the minimum value of the response surface of the surrogate model.

[0063] (ii) is the maximization of expected value improvement criterion, i.e., the EI criterion. Since the adaptive adjustment strategy requires repeated collection of initial samples, even using only the MP criterion usually yields good optimization results. To further improve global search capabilities, the EI criterion can be used as a supplement, provided computational power is sufficient, to achieve even better global optimization performance.

[0064] Example

[0065] The specific embodiments of the present invention are described in detail below with reference to the technical solutions and accompanying drawings.

[0066] This invention proposes a design method for simultaneously optimizing the mechanical performance and aesthetic characteristics of products based on the KG-MFSE non-gradient topology optimization algorithm, and demonstrates the effectiveness of the model using a road bicycle helmet as an example. In terms of aesthetics, transfer learning is used to achieve efficient prediction of aesthetic scores on a small sample dataset, constructing a product aesthetic evaluation model based on ResNet-18. In terms of mechanics, the Material Field Series Expansion (MFSE) method is introduced, transforming the topology optimization problem into a constrained optimization model with material field coefficients as design variables. Combined with the sequential sampling strategy of the Kriging surrogate model, computational costs are effectively reduced and global search capabilities are improved. Furthermore, the effectiveness of the model is verified using a road bicycle helmet as an example. It is found that although the framework suffers a slight loss in mechanical performance, it significantly improves the aesthetic score, and exhibits high computational efficiency and strong engineering reliability. This provides an effective solution to the problems of high structural redundancy and weak aesthetic expressiveness caused by the fragmented division of labor in traditional design.

[0067] The image optimization issues that need to be addressed include: Figure 1 As shown, the optimization objective is set as the deformation at the loading point, and the volume fraction is set to... Aesthetic scoring constraints are set as follows: .

[0068] The first step is to construct a product aesthetic evaluation model based on ResNet-18.

[0069] 1.1) Considering the relatively simple structure of helmets, mainly composed of an outer shell and a buffer layer, it is easier to clearly define the direction and target when performing topology optimization. Therefore, helmets were selected as the research object. Web crawling tools were used to collect a large number of product images of the research object from domestic and international platforms. After manual screening and deduplication, a raw dataset containing 308 high-definition product images was finally formed. This dataset covers various design categories such as aerodynamic, lightweight, and ventilated helmets, and each image fully presents the distribution characteristics of ventilation holes on the helmet surface. The original 308 helmet images were expanded to 3028 images through enhancement operations such as geometric transformation (random horizontal flip, ±15° rotation, scaling), luminosity adjustment (brightness ±20%, contrast ±15%, Gaussian noise), and occlusion simulation (randomly erasing 10%~30% of the area), effectively covering visual variations in real-world scenarios such as lighting, angle, and local occlusion. Figure 2 The images shown are sample images of some road bicycle helmets, providing a sufficient visual information basis for subsequent structural analysis.

[0070] 1.2) In the image preprocessing stage, it is necessary to accurately extract the helmet subject from the original image, remove other interfering elements, and retain only the solid color background of the helmet subject. After extracting the subject, considering that the presence or absence of material in the structure is expressed by density values ​​during topology optimization, holes on the helmet model represent the absence of material, and the material density of this area is 0; solid units represent the presence of material. Therefore, the obtained color image of the road bike helmet needs to be converted into an 8-bit grayscale image where the presence or absence of material is represented by numerical values, significantly reducing the data dimensionality while preserving the product structural details. The road bike helmet image preprocessing is as follows: Figure 3 As shown, each pixel in the processed 224×224 pixel grayscale image is mapped to the density parameter of the 3D model, establishing a mathematical correspondence between grayscale values ​​and material distribution, forming a digital input that can be directly imported into subsequent topology optimization algorithms. Figure 4 As shown, through the above systematic processing methods, a standardized dataset that meets the requirements of machine learning is constructed.

[0071] 1.3) Data annotation was performed on the preprocessed standardized product images, and an online rating system was built. The questionnaire was designed to select valid users with actual cycling experience or helmet purchasing experience. Aesthetic ratings were compiled into integer values ​​between 1 and 7. Images with different scores were placed in folders corresponding to their respective scores, forming a labeled dataset for training the neural network. Scores 1-7 correspond to extremely unattractive to extremely attractive, respectively. Figure 5 As shown, (a) is a sample image with an aesthetic score of 3, and (b) is a sample image with an aesthetic score of 7. According to the images, the holes in the helmet are more evenly distributed and the edge curves of the holes are more in line with the outer contour curve of the helmet in the sample image with a score of 7, which represents the most beautiful appearance.

[0072] 1.4) Training the ResNet-18 network. Regarding model architecture and training strategy design, this invention utilizes transfer learning based on the ResNet-18 network to construct a deep learning model suitable for aesthetic scoring. Addressing the differences between the original model's classification and regression tasks, the fully connected layer at the network's end is first adjusted from 1000 classification outputs to 7 classification outputs, enabling the network to directly output continuous aesthetic scores (1-7 points) while retaining the advantages of the pre-trained model in image feature extraction.

[0073] By calculating the squared deviation between predicted ratings and actual user ratings, the model is guided to learn the non-linear mapping relationship between styling features and aesthetic preferences, which is more suitable for the needs of regression tasks compared to the cross-entropy loss function. For parameter initialization, a transfer learning method is used to load ImageNet pre-trained weights as the starting point of the model. By freezing the low-level parameters of the first three convolutional blocks (out of four), only the high-level networks are fine-tuned. This leverages the powerful representational ability of the pre-trained model for general image features while avoiding the risk of overfitting due to the limited scale of product data.

[0074] Figure 6 The changes in accuracy and loss during the training process of the ResNet-18 network are shown. Experimental results demonstrate that the network model exhibits excellent recognition performance during training, achieving an accuracy of 99.55% during the training phase, thus meeting the basic requirements for algorithm reliability.

[0075] The second step is to establish a topology optimization model based on the KG-MFSE method.

[0076] 2.1) Condition 1: The helmet is subjected to a vertically downward force at its center. The force diagram is shown below. Figure 1 As shown, this simulates the impact on a cyclist's head when colliding head-on with the ground. To address the elastic deformation of the helmet material, a load of 50N was selected to ensure that the helmet's PC material remains in the linear elastic stage (stress not exceeding the yield strength), facilitating observation of the helmet model's stress state through stress and strain contour plots.

[0077] 2.2) Optimizing product mechanical properties through a volume fraction constraint mechanism, considering only volume fraction as a constraint condition integrated into the optimization framework (described as a single-constraint model), forming a goal programming problem:

[0078]

[0079] in, Represents the volume of the i-th unit. Given the structural volume fraction constraint, The volume fraction is set to the volume of the structure when it is entirely composed of material. .

[0080] 2.3) A non-gradient optimization algorithm based on the Kriging surrogate model is used to solve the topology optimization problem without considering the aesthetic characteristics of the helmet. The unconstrained form of the optimization model is expressed as:

[0081]

[0082] The non-gradient algorithm solution process employs minimizing the surrogate model's prediction (MP criterion) and maximizing the expected improvement (EI criterion) as sequential sampling strategies, respectively. Furthermore, a design domain adjustment strategy is introduced during implementation to ensure the accuracy of the solution.

[0083] Optimization results are as follows Figure 7 As shown in (a). Simultaneously, the resulting image was input into the constructed aesthetic evaluation model, resulting in an aesthetic score of only 2 points. Based on the result image obtained from the optimization algorithm, the distribution of holes in the road bicycle helmet model was determined, and the initial model was "dug out" to complete the model reconstruction, as shown in (a). Figure 7 As shown in (b), finite element analysis and aesthetic evaluation were performed on the reconstructed helmet model, and the deformation at the loading point was obtained as follows. And the aesthetic score is .

[0084] The iterative history of a single-constraint optimization algorithm that only considers the mechanical properties of the product is as follows: Figure 8 As shown, after 15 sub-optimizations (a total of 2800 finite element analyses), the objective function value can stably converge to a single function value. ).

[0085] The third step is to establish a topology optimization model that considers aesthetic characteristics.

[0086] 3.1) Combining the ResNet-18-based product aesthetic evaluation model constructed in the first step and the MFSE-based product mechanical performance optimization model constructed in the second step, a dual-constraint optimization algorithm based on KG-MFSE aesthetic score and volume fraction is constructed to achieve simultaneous optimization design of product mechanical performance and aesthetic characteristics. Compared with the single-constraint model in the second step that only considers volume fraction, this model considers both product mechanical performance and aesthetic characteristics (described as a dual-constraint model). The optimization model is as follows:

[0087]

[0088] Where S represents the aesthetic score of the current product design scheme calculated by the ResNet-18 network. This represents a given product aesthetic constraint. The optimization objective is set as the deformation at the loading point, and the volume fraction is set to... Aesthetic scoring constraints are set as follows: .

[0089] 3.2) The topology optimization model that simultaneously considers the product's mechanical properties and aesthetic characteristics is also solved using a non-gradient optimization algorithm based on the Kriging surrogate model. The unconstrained form of this model is expressed as:

[0090]

[0091] The non-gradient algorithm solution process employs minimizing the surrogate model's prediction (MP criterion) and maximizing the expected improvement (EI criterion) as sequential sampling strategies, respectively. Furthermore, a design domain adjustment strategy is introduced during implementation to ensure the accuracy of the solution.

[0092] The topology optimization result for a road bike helmet, obtained using the above formula and a topology optimization model that simultaneously considers the product's mechanical properties and aesthetic characteristics, is as follows: Figure 9 As shown in (a), the optimized material distribution of the helmet structure under a specific load in condition 1 is illustrated. To verify the reliability of the helmet topology optimization design scheme and optimization algorithm, a reverse engineering method was used to conduct a full-process verification of the optimization results. Figure 9 (b) A road bike helmet model reconstructed based on the results obtained from the load applied directly above in condition 1, and the deformation at the loading point obtained from finite element analysis is: The reconstructed image was then input into the constructed aesthetic evaluation model, resulting in an aesthetic score of 7 points.

[0093] The iterative history of a dual-constraint optimization algorithm that simultaneously considers product mechanical performance and aesthetic characteristics is as follows: Figure 10 As shown, the horizontal axis represents the number of iterations, ranging from 0 to 3000, reflecting the iterative progress of the algorithm optimization; the vertical axis represents the deformation at the helmet loading point, with the objective function value converging to 0.469 mm. Figure 11 As can be seen, after 15 adjustments to the sub-design domain, the objective function can stably converge to a stable value.

[0094] Details of the optimization design results of the helmet structure under both constraint topology and single constraint topology are as follows: Figure 11 As shown. It can be concluded that under the same volume fraction constraint ( The topology-optimized structures under both constraints have the same structural mass (179.163g for dual-constraint optimization and 177.002g for single-constraint optimization). Furthermore, compared to the single-constraint optimization results, although the helmet structure experiences a slight loss in mechanical properties (deformation)... , However, considering the optimization results of the helmet structure's aesthetic characteristics, the aesthetic characteristics of the helmet product are significantly improved, that is, the aesthetic evaluation under dual constraints is... ( The aesthetic score for a single constraint is... Therefore, this demonstrates the effectiveness of the topology optimization proposed in this invention, which simultaneously considers the mechanical properties and aesthetic characteristics of the product, in synchronously improving overall performance.

[0095] This invention proposes a design method for simultaneously optimizing the mechanical performance and aesthetic characteristics of products based on the KG-MFSE non-gradient topology optimization algorithm, and demonstrates the effectiveness of the model using a road bicycle helmet as an example. In terms of aesthetics, transfer learning is used to achieve efficient prediction of aesthetic scores on a small sample dataset, constructing a product aesthetic evaluation model based on ResNet-18. In terms of mechanics, the Material Field Series Expansion (MFSE) method is introduced, transforming the topology optimization problem into a constrained optimization model with material field coefficients as design variables. Combined with the sequential sampling strategy of the Kriging surrogate model, computational costs are effectively reduced and global search capabilities are improved. Furthermore, the effectiveness of the model is verified using a road bicycle helmet as an example. It is found that although the framework suffers a slight loss in mechanical performance, it significantly improves the aesthetic score, and exhibits high computational efficiency and strong engineering reliability. This provides an effective solution to the problems of high structural redundancy and weak aesthetic expressiveness caused by the fragmented division of labor in traditional design.

[0096] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. A product structure topology optimization design method considering aesthetic characteristics, characterized by: This method constructs an aesthetic scoring model based on ResNet-18 network and a material field series expansion non-gradient topology optimization model based on Kriging surrogate model. With the product's structural mechanical performance as the optimization objective and volume fraction and aesthetic score as constraints, it performs topology optimization design on the product, achieving simultaneous optimization design of the product's mechanical performance and aesthetic characteristics, thereby meeting users' combined needs for product functional reliability and aesthetic experience.

2. The product structure topology optimization design method considering aesthetic characteristics according to claim 1, characterized by comprising the following steps: Step 1: Construct a product aesthetic evaluation model based on ResNet-18; Step 2: Establishing a topology optimization model based on the KG-MFSE method; Step 3: Establish a topology optimization model considering aesthetic characteristics; Step 4: Non-gradient optimization algorithm based on Kriging surrogate model.

3. The product structure topology optimization design method considering aesthetic characteristics according to claim 2, characterized in that, Step 1 further includes the following: selecting research objects, using web crawling tools to collect a large number of product images of research objects from domestic and foreign platform websites, and after manual screening and deduplication, performing data augmentation on the original collected data to expand the dataset; The original product image is preprocessed, the main body of the product is extracted and then converted into a multi-dimensional grayscale image with numerical values ​​representing the presence or absence of materials. While preserving the structural details of the product, the data dimensionality is significantly reduced, and a standardized dataset that meets the requirements of machine learning is constructed. Data annotation is performed on the preprocessed standardized product images, and the aesthetic scores are organized into integer values ​​between 1 and 7. Images with different scores are placed in folders with corresponding score values ​​to form a labeled dataset for training the neural network. In terms of model architecture and training strategy design, the ResNet-18 network is trained, and transfer learning is performed based on the ResNet-18 network to build a deep learning model suitable for aesthetic scoring; the differences between the original model's classification and regression tasks are addressed.

4. The product structure topology optimization design method considering aesthetic characteristics according to claim 2, characterized in that, Step 1 further includes the following: by calculating the squared deviation between the predicted score and the user's actual score, the model is guided to learn the nonlinear mapping relationship between styling features and aesthetic preferences; in terms of parameter initialization strategy, the transfer learning method is used to load ImageNet pre-trained weights as the starting point of the model, and by freezing the low-level parameters of the previous convolutional blocks, only the high-level network is fine-tuned, which utilizes the pre-trained model's ability to represent general image features and avoids the risk of overfitting due to the limited scale of product data; Extract the contour curves of the product's shape features and obtain a standardized input image through projection transformation. ; The ResNet-18 aesthetic evaluation model built based on transfer learning can be deconstructed into a composite nonlinear mapping: ； in, It is a weight matrix. This is a global average pooling operation. This represents the first... Feature maps output by the layer It is the input standardized image. It is a bias term; Activation function; input image Features are extracted using ResNet-18, dimensionality is reduced using global average pooling, and then the output is mapped to a scoring range using a fully connected layer and activation function to obtain the product aesthetic score. .

5. The product structure topology optimization design method considering aesthetic characteristics according to claim 2, characterized in that step 2 further includes the following: (1) Based on the material field sequence expansion MFSE method, the structural topology can be represented by a bounded field function with spatial correlation, where the side length of the rectangular design domain is ; the expression of the MFSE topology optimization method is as follows: ； in, Design domain for topology optimization The bounded field function in the range of variation is , yes One of the points, and They represent holes and solid fields, respectively. (2) In order to better realize the mapping process from field function to topological configuration, the field function is... Heaviside filtering is represented as follows: ； in, The smoothness coefficient is represented, and the structural element material interpolation based on MFSE topology optimization is performed using the function shown below: ； in, Represents the elastic modulus of a solid structure. , where p represents the penalty coefficient.

6. The product structure topology optimization design method considering aesthetic characteristics according to claim 5 is characterized in that it combines a product aesthetic evaluation model based on ResNet-18 and a product mechanical performance optimization model based on the MFSE optimization algorithm, and constructs an optimization algorithm based on KG-MFSE aesthetic score and volume fraction as dual constraints to achieve simultaneous optimization design of product mechanical performance and aesthetic characteristics. The dual constraint function model that simultaneously considers product mechanical performance and aesthetic characteristics is as follows: ； and Let these represent the objective function and constraint function of the structure, respectively, and the MFSE coefficients. Represents the design variables of the optimization model. Represents the structural displacement vector. The equilibrium equations for finite element analysis of practical problems.

7. The product structure topology optimization design method considering aesthetic characteristics according to claim 6, characterized in that step 4 further includes the following: the unconstrained expression form of the topology optimization problem of the double-constraint function model is as follows: ； in, As a penalty factor, set it to .

8. The product structure topology optimization design method considering aesthetic characteristics according to claim 6, characterized in that, in To ensure both global search capability and efficient solution, two sampling criteria are combined in the sequence sampling stage: (i) Minimize the response surface criterion of the surrogate model, that is, add points to the minimum value of the response surface of the surrogate model; (ii) is the maximization expectation improvement criterion, i.e., the EI criterion. Since the adaptive adjustment strategy requires repeated collection of initial samples, even using only the MP criterion usually yields good optimization results.

9. A non-volatile storage medium, characterized in that, The non-volatile storage medium includes a stored program, wherein the program, when executed, controls the device where the non-volatile storage medium is located to perform the method described in any one of claims 1 to 8.

10. A terminal device, characterized in that, The terminal device includes: a processor, a memory, a communication interface, and a bus; the processor, the memory, and the communication interface are connected through the bus and communicate with each other; the memory stores executable program code; the processor reads the executable program code stored in the memory to run a program corresponding to the executable program code, so as to perform the method as described in any one of claims 1-8 above.

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