Variable-resolution material distribution determination method for shape-deformed soft material

Abstract

The invention discloses a variable-resolution material distribution determination method for a shape deformation soft material. The method is characterized by comprising the following steps: S1, constructing a prediction model from material distribution of the shape deformation soft material to a shape deformation result under given external excitation; s2, establishing an evaluation index to quantify the difference between the shape deformation prediction result and the target shape; s3, roughly dividing the shape-deformed soft material to obtain low-resolution material voxels; s4, further subdividing the low-resolution material voxels to obtain high-resolution material voxels; s5, judging whether the high-resolution material voxel optimization result obtained in the step S4 meets a preset threshold value or not, and if yes, outputting optimal material distribution; and if not, regarding the high-resolution material voxel and the optimization result as a new low-resolution material voxel and the optimization result, and repeating the step S4 until the result meets the requirement. According to the method, high-dimensional voxel-level material distribution can be accurately designed, so that specific shape deformation is realized.

Description

Technical Field

[0001] This invention relates to the field of machine learning technology, and in particular to a method for determining the variable resolution material distribution of soft materials with shape deformation. Background Technology

[0002] Shape-deformable soft materials are composed of responsive materials with different properties. They can deform in shape upon exposure to external stimuli such as heat, light, water, electric fields, and magnetic fields. Examples include magnetic soft materials, liquid crystal elastomers, reactive composite materials, and hydrogels, which have broad application prospects in soft robotics, biomedical devices, and other fields. The deformation behavior of shape-deformable soft materials depends on the spatial distribution of material properties, such as the distribution of magnetization intensity and direction in magnetic soft materials, the distribution of molecular chain orientation in liquid crystal elastomers, and the distribution of thermal expansion coefficients in reactive composite materials. Accurately realizing the complex shape deformation of soft materials requires the design of voxel-level material distributions. The numerous design variables and large design space make the precise design of voxel-level material distributions challenging.

[0003] Genetic algorithms, as optimization algorithms that simulate the natural evolutionary process, can efficiently explore the design space by simulating the selection, crossover, and mutation mechanisms in biological evolution. Combining them with finite element simulation models or data-driven surrogate models can achieve voxel-level material distribution design for shape-deformable soft materials. However, existing methods directly optimize material voxels at a fixed resolution. For material distribution design problems involving large-scale voxels, the design variables are highly dimensional, direct optimization is difficult, and it is easy to get trapped in local optima, making it difficult to obtain the optimal material distribution that meets the target shape deformation requirements. Therefore, this invention proposes a variable-resolution material distribution determination method for shape-deformable soft materials. First, an evaluation index is established to quantify the difference between the predicted shape deformation and the target shape. Second, low-resolution material voxels are obtained through coarse partitioning and optimized to obtain low-resolution material voxel optimization results that reflect the overall deformation trend. Then, the low-resolution material voxels are subdivided to obtain high-resolution material voxels, and the low-resolution material voxel optimization results are used as the initial solution for further optimization. The voxel subdivision and optimization process is repeated until a preset threshold is met, ultimately achieving accurate voxel-level material distribution design for a given target shape. Summary of the Invention

[0004] The purpose of this invention is to address the problems in existing voxel-level material distribution design for shape-deformable soft materials, such as high dimensionality of design variables, difficulty in direct optimization, easy getting trapped in local optima, and difficulty in obtaining the optimal material distribution that meets the target shape deformation requirements. The invention proposes a variable resolution material distribution determination method for shape-deformable soft materials, which realizes voxel-level material distribution design for shape-deformable soft materials through a variable resolution optimization strategy.

[0005] The technical solution of this invention is:

[0006] A method for determining the variable resolution material distribution of shape-deformable soft materials, characterized by the following steps:

[0007] S1. Construct a predictive model between the material distribution of a soft material deformed under a given external excitation and the shape deformation result;

[0008] S2. Establish evaluation indicators to quantify the difference between the predicted shape deformation and the target shape;

[0009] S3. Coarsely divide the soft material with shape deformation to obtain low-resolution material voxels. Use an optimization algorithm to minimize the evaluation index. During the optimization process, obtain the shape deformation results corresponding to different material distributions through a prediction model, thereby obtaining a set of low-resolution material voxel optimization results.

[0010] S4. Further subdivide the low-resolution material voxels to obtain high-resolution material voxels. Use the optimization results of the low-resolution material voxels as the initial solution, and use optimization algorithms and prediction models to obtain the optimization results of the high-resolution material voxels.

[0011] S5. Determine whether the high-resolution material voxel optimization result obtained in S4 meets the preset threshold. If it does, output the optimal material distribution. If it does not, treat the high-resolution material voxel and optimization result as the new low-resolution material voxel and optimization result, and repeat S4 until the result meets the requirements.

[0012] Preferably, in S1, the prediction model can be a numerical simulation model built based on the deformation mechanism, or a surrogate model trained with simulation data. Specifically, the surrogate model is an artificial intelligence model capable of predicting material distribution and shape deformation results, including one or more combinations of fully connected neural networks, convolutional neural networks, graph neural networks, graph neural operators, Fourier neural operators, wavelet neural operators, and manifold neural operators.

[0013] Preferably, in S2, the evaluation index established in S2 is used to quantify the difference between the predicted shape deformation and the target shape, specifically in one or a combination of the following ways:

[0014] a) Establish evaluation index based on spatial domain statistical information: Take multiple points on the shape deformation prediction result and the target shape, calculate the distance between each point on the shape deformation prediction result and the corresponding point on the target shape, and establish evaluation index by calculating the maximum value and average value of multiple distances.

[0015] b) Establishing evaluation metrics based on eigendomain decomposition coefficients: Project the shape deformation prediction result and the target shape onto the same set of eigenvalue basis functions. Quantify the difference between the shape deformation prediction result and the target shape by calculating the error between their coefficient vectors after projection. The eigenvalue basis functions can be Laplace-Beltrami operator eigenfunctions obtained from the geometry of soft materials or basis functions obtained through intrinsic orthogonal decomposition and kernel principal component analysis. Project the shape deformation prediction result and the target shape onto the eigenvalue basis functions to obtain the coefficient vectors of the shape deformation prediction result and the target shape. Establish evaluation metrics by calculating the maximum error, average error, average absolute error, mean square error, root mean square error, or relative L2 error between the coefficient vectors of the shape deformation prediction result and the target shape.

[0016] Preferably, the optimization algorithms in S3 and S4 are one of the following: genetic algorithm, Bayesian optimization, particle swarm optimization algorithm, and annealing algorithm.

[0017] Preferably, in S4, the low-resolution material voxels are further subdivided to obtain high-resolution material voxels, and the optimization results of the low-resolution material voxels are used as the initial solution. Specifically, the subdivision can be either overall or local.

[0018] (1) Overall subdivision refers to the process of re-dividing each voxel in the low-resolution material voxel into multiple smaller voxels to obtain a high-resolution material voxel. After subdivision, the optimization results of the low-resolution material voxels are assigned to each voxel of the high-resolution material voxel as the initial solution.

[0019] (2) Local subdivision refers to calculating the error field between the shape deformation prediction result and the target shape based on the low-resolution material voxel optimization result obtained from S3, identifying local regions with significant errors, and then subdividing the voxels contained in these local regions to obtain high-resolution material voxels. The identification method for local regions with significant errors can be to set a fixed error threshold and select local regions with errors exceeding the preset threshold; or it can be to segment the error field through a clustering algorithm and select local regions with large errors. After subdivision, the optimization result of the low-resolution material voxels is assigned to each voxel of the high-resolution material voxel as the initial solution.

[0020] The beneficial effects of this invention are:

[0021] This invention employs a variable resolution optimization strategy. First, it optimizes and confirms the macroscopic material distribution on low-resolution material voxels. Then, using the optimization results of the low-resolution material distribution as the initial solution, it further optimizes on high-resolution material voxels, ultimately achieving voxel-level material distribution design for complex-shaped deformable soft materials. Attached Figure Description

[0022] Figure 1This is a flowchart illustrating an embodiment of the present invention.

[0023] Figure 2 This represents the initial shape of the active composite material in this embodiment of the invention.

[0024] Figure 3 This is the design result of the active composite material in the embodiments of the present invention.

[0025] Figure 4 This is a comparison chart of the design results and the Z-coordinate variation trend of the target shape along the diagonal in the embodiments of the present invention. Detailed Implementation

[0026] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0027] like Figure 1-4 As shown.

[0028] A variable-resolution material distribution determination method for shape-deformable soft materials is proposed, which is used to design the voxel-level material distribution of shape-deformable soft materials to achieve specific shape deformations, such as... Figure 1 As shown. The shape-deformable soft material used in this embodiment is specifically a thermally responsive active composite material composed of active and passive materials. The active material is heat-sensitive and undergoes significant volume expansion upon heating; the passive material is insensitive to temperature changes and can remain relatively stable at different temperatures. The purpose of this embodiment is to achieve a given shape deformation by designing the voxel-level material distribution of active and passive materials on the active composite material. This includes the following steps:

[0029] S1. Construct a predictive model between the material distribution of a soft material deformed under a given external excitation and the shape deformation result.

[0030] This embodiment constructs a manifold neural operator model for thermally excited reactive composite materials to predict the results from material distribution to shape deformation. The initial shape of the reactive composite material is as follows: Figure 2 As shown, in this embodiment, the active composite material is first divided into 290 voxels. Each voxel can be assigned an active material with a coefficient of thermal expansion of 0.001 or a passive material with a coefficient of thermal expansion of 0. Next, 50,000 material distributions are randomly generated within the material distribution design space using a random sampling method. Then, Abaqus finite element simulation software is used to perform batch calculations for a temperature increase of 60°C. The shape deformation results were used to construct a dataset. The manifold neural operator model consists of one channel dimensionality increase layer, eight operator learning layers, and one channel dimensionality decrease layer. The operator learning layer comprises an encoder, an approximator, and a decoder, employing 128 Laplacian operator feature functions and the GeLU activation function for nonlinear activation. During training, the average relative L2 error was used as the loss function, and AdamW with weighted decay was used as the optimization method. The initial learning rate was set to 0.001, and the batch size to 16. After 500 iterations of training, the manifold neural operator model connecting the material distribution of the thermally excited reactive composite material to the shape deformation results was constructed.

[0031] S2. Establish evaluation indicators to quantify the difference between the predicted shape deformation and the target shape.

[0032] This embodiment establishes an evaluation index based on spatial domain statistical information: First, the geometric domain of the shape-deformable soft material is discretized into a mesh, and the distance between each node in the shape deformation prediction result and the corresponding node of the target shape is calculated. The evaluation index is established by calculating the average value of multiple distances.

[0033] S3. Coarsely divide the soft material with shape deformation to obtain low-resolution material voxels. Use an optimization algorithm to minimize the evaluation index established in S2. During the optimization process, obtain the shape deformation results corresponding to different material distributions through the prediction model constructed in S1, thereby obtaining a set of low-resolution material voxel optimization results.

[0034] In this embodiment, the initial shape-deformable soft material is coarsely divided into 106 large voxels, forming low-resolution material voxels. With the goal of minimizing the evaluation index established in S2, a genetic algorithm is used to optimize the low-resolution material voxels. During the optimization process, the prediction model established in S1 is used for prediction. The population size is set to 1000, the crossover probability to 0.75, and the mutation probability to 0.2. After 100 rounds of iterative optimization, the top 100 optimal results are taken as the optimized low-resolution material voxels.

[0035] S4. Further subdivide the low-resolution material voxels to obtain high-resolution material voxels. Use the optimization results of the low-resolution material voxels as the initial solution, and use the optimization algorithm to minimize the evaluation index established in S2. During the optimization process, obtain the shape deformation results corresponding to different material distributions through the prediction model constructed in S1, thereby obtaining the optimization results of high-resolution material voxels.

[0036] This embodiment employs a global subdivision strategy, subdividing the 106 voxels in the low-resolution material voxel into smaller voxels, resulting in 290 smaller voxels, forming the high-resolution material voxel. The optimization results of the low-resolution material voxels in S3 are then assigned to each voxel of the high-resolution material voxel as the initial solution. With the goal of minimizing the evaluation index established in S2, a genetic algorithm and prediction model are used to perform optimization search on the high-resolution material voxel. After 100 iterations, the optimization results of the high-resolution material voxel are obtained.

[0037] S5. Determine whether the optimization results of the high-resolution material voxels meet the preset threshold. If they do, output the optimal material distribution. If they do not, treat the high-resolution material voxels and optimization results obtained in S4 as new low-resolution material voxels and optimization results, and repeat S4 until the results meet the requirements.

[0038] The preset threshold used in this embodiment is that the average distance between the predicted shape deformation result and all corresponding nodes on the target shape is no higher than 0.5 mm. After a high-resolution overall subdivision optimization in S4, the design result is as follows: Figure 3 As shown, the average distance between the predicted shape deformation result and the nodes of the target shape is less than 0.5 mm, which meets the design requirements, and further iteration S4 is not necessary. Figure 4 As shown, by comparing the design result with the target shape along the diagonal... The coordinate change trend shows that the two are highly consistent, which once again verifies the consistency between the design result and the target shape.

[0039] The results show that the variable resolution material distribution determination method for shape-deformable soft materials proposed in this invention can achieve excellent optimization results.

[0040] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

[0041] The parts not covered in this invention are the same as or can be implemented using existing technologies.

Claims

1. A variational resolution material distribution determination method for a shape morphing soft material, characterized by: Includes the following steps: S1. Construct a predictive model between the material distribution of a soft material deformed under a given external excitation and the shape deformation result; S2. Establish evaluation indicators to quantify the difference between the predicted shape deformation and the target shape; S3. Coarsely divide the soft material with shape deformation to obtain low-resolution material voxels. Use an optimization algorithm to minimize the evaluation index. During the optimization process, obtain the shape deformation results corresponding to different material distributions through a prediction model, thereby obtaining a set of low-resolution material voxel optimization results. S4. Further subdivide the low-resolution material voxels to obtain high-resolution material voxels. Use the optimization results of the low-resolution material voxels as the initial solution, and use optimization algorithms and prediction models to obtain the optimization results of the high-resolution material voxels. S5. Determine whether the high-resolution material voxel optimization result obtained in step S4 meets the preset threshold. If it does, output the optimal material distribution. If it does not, treat the high-resolution material voxel and optimization result as the new low-resolution material voxel and optimization result, and repeat S4 until the result meets the requirements.

2. The method of claim 1, wherein: The prediction model in step S1 is a numerical simulation model built based on the deformation mechanism, or a surrogate model trained through simulation data.

3. The method according to claim 2, characterized in that: The surrogate model is specifically an artificial intelligence model capable of predicting material distribution and shape deformation results, including one or more combinations of fully connected neural networks, convolutional neural networks, graph neural networks, graph neural operators, Fourier neural operators, wavelet neural operators, and manifold neural operators.

4. The method according to claim 1, characterized in that: The establishment of evaluation indicators in step S2 to quantify the difference between the shape deformation prediction result and the target shape can be achieved through one or a combination of the following methods: a) Establish evaluation index based on spatial domain statistical information: Take multiple points on the shape deformation prediction result and the target shape, calculate the distance between each point on the shape deformation prediction result and the corresponding point on the target shape, and establish evaluation index by calculating the maximum value and average value of multiple distances. b) Establishing evaluation indicators based on feature domain decomposition coefficients: Project the shape deformation prediction result and the target shape onto the same set of feature basis functions respectively, and quantify the difference between the shape deformation prediction result and the target shape by calculating the error of the coefficient vectors of the two after projection; the feature basis functions are the Laplace-Beltrami operator feature functions obtained through the geometry of soft materials or the basis functions obtained through intrinsic orthogonal decomposition and kernel principal component analysis; project the shape deformation prediction result and the target shape onto the feature basis functions to obtain the coefficient vector of the shape deformation prediction result and the coefficient vector of the target shape, and establish evaluation indicators by calculating the maximum error, average error, average absolute error, mean square error, root mean square error or relative L2 error between the coefficient vector of the shape deformation prediction result and the coefficient vector of the target shape.

5. The method according to claim 1, characterized in that: The optimization algorithm in steps S3 and S4 is one of the following: genetic algorithm, Bayesian optimization, particle swarm optimization algorithm, or annealing algorithm.

6. The method according to claim 1, characterized in that: In step S4, the low-resolution material voxels are further subdivided to obtain high-resolution material voxels. The optimization result of the low-resolution material voxels is used as the initial solution. Specifically, the subdivision can be either global or local. (1) Overall subdivision refers to the process of re-dividing each voxel in the low-resolution material voxel into multiple smaller voxels to obtain a high-resolution material voxel; after subdivision, the optimization results of the low-resolution material voxel are assigned to each voxel of the high-resolution material voxel as the initial solution. (2) Local subdivision refers to calculating the error field between the shape deformation prediction result and the target shape based on the low-resolution material voxel optimization result obtained in step S3, identifying local regions with significant errors, and then subdividing the voxels contained in these local regions to obtain high-resolution material voxels. The identification method for local regions with significant errors can be to set a fixed error threshold and select local regions with errors exceeding the preset threshold; or to segment the error field through a clustering algorithm and select local regions with large errors. After subdivision, the optimization result of the low-resolution material voxels is assigned to each voxel of the high-resolution material voxel as the initial solution.

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