High initial tack optimization method based on modeling of compression and rebound performance of foam structure

Abstract

The application relates to a high-initial-adhesion optimization method based on modeling of compression and rebound performance of a foam structure, and comprises the following steps: S1: defining a structured parameter space, and generating candidate structure parameters in the parameter space by using a Latin hypercube; for each group of parameters, a representative volume element model of the foam is established by using finite element software, simulation is performed, and a virtual data set is obtained; S2: according to the virtual data set, a foam structure-performance proxy model based on a graph neural network is constructed; S3: a variational autoencoder is constructed, and candidate structures are obtained according to the structured parameter space; S4: according to the foam structure-performance proxy model and the candidate structures, a global optimal structure search based on multi-objective Bayesian optimization is performed to obtain optimal structure parameters; and S5: according to the optimal structure parameters and actual manufacturing process parameters of the foam, material process parameter collaborative optimization based on deep reinforcement learning is adopted. The application obtains an optimal process formula, and effectively improves process formula optimization efficiency and reliability.

Description

Technical Field

[0001] This invention relates to the field of formulation optimization, and in particular to a high initial viscosity optimization method based on modeling the compression and resilience properties of foam structures. Background Technology

[0002] Foam double-sided tape consists of a foam substrate and pressure-sensitive adhesive layers on both sides, and is widely used in automotive manufacturing, electronic equipment assembly, building decoration, and new energy battery pack fixing. In practical applications, this type of material typically needs to simultaneously meet two seemingly contradictory mechanical requirements: on the one hand, it must possess high initial tack at the moment of bonding to ensure rapid positioning and initial adhesive strength; on the other hand, it must withstand continuous pressure or cyclic vibration during long-term service, requiring the foam substrate to have good resistance to compression deformation and resilience to prevent slippage or failure of the adhesive interface due to creep. Traditional foam double-sided tape often emphasizes one aspect of performance—improving initial tack usually requires reducing the surface modulus of the foam to increase the contact area, but this exacerbates compression set and stress relaxation; while enhancing compression resistance requires increasing the stiffness and cross-linking density of the foam, which weakens initial tack. This inherent "soft-hard" contradiction restricts the further application of foam double-sided tape in high-end manufacturing fields.

[0003] In existing technologies, the optimization of foam structures mainly relies on empirical formulation adjustments and extensive physical experimentation. Designers control initial tack or compression rebound by changing foaming process parameters (such as foaming agent dosage, temperature, and pressure) or adhesive formulations. However, these variables have complex coupling relationships, and the mapping mechanism between the internal pore structure of the foam (porosity, pore size distribution, wall thickness, gradient structure, etc.) and macroscopic mechanical properties remains unclear. Although finite element simulation can simulate the compression rebound behavior of foam, establishing an accurate representative volume element model requires a large amount of computation and is difficult to use to guide multi-objective optimization in high-dimensional parameter space (simultaneously maximizing initial tack, minimizing compression set, and stress relaxation rate). Therefore, traditional methods have limitations such as long development cycles, high costs, and low performance ceilings, making it difficult to systematically achieve the synergistic design of high initial tack and excellent compression resistance. Summary of the Invention

[0004] To address the aforementioned issues, the present invention aims to provide a high initial viscosity optimization method based on foam structure compression and rebound performance modeling, which effectively improves the efficiency and reliability of process formulation optimization.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A high initial viscosity optimization method based on modeling the compression and rebound performance of foam structures includes the following steps: S1: Define a structured parameter space and use Latin hypercube to generate candidate structural parameters in the parameter space. For each set of parameters, use finite element software to build a representative volume element model of foam, perform virtual compression-springback-creep simulation, and obtain a virtual dataset. S2: Construct a foam structure-performance proxy model based on a graph neural network, using a virtual dataset; S3: Construct a variational autoencoder and obtain a candidate set of structures based on the structured parameter space; S4: Based on the foam structure-performance proxy model and the candidate structure set, the optimal structure parameters are obtained by global optimal structure search based on multi-objective Bayesian optimization; S5: Based on the optimal structural parameters and the actual manufacturing process parameters of the foam, the optimal process formula is obtained by co-optimizing the material process parameters using deep reinforcement learning.

[0006] Furthermore, a structured parameter space is defined, and candidate structure parameters are generated within the parameter space using Latin hypercubes, as detailed below: The parameterized space Ω of the foam structure is defined, containing key geometric and structural parameters that affect the compression resilience and initial tack of the foam double-sided tape. These parameters are divided into continuous and discrete variables. The continuous variables include the overall porosity φ and the average pore size d. p Hole wall thickness t w Thickness gradient factor α=φ skin / φ core , where φ skin φ represents the surface porosity. core The core porosity and the column diameter D of the local micropillar reinforcement structure in the core layer are given. c And the ratio of column spacing to diameter β=L c / D c Discrete variables include aperture distribution type t pore and the micro-column arrangement method t lat All parameters constitute a d-dimensional structured parameter vector: x=[φ,d p ,t w ,α,Dc,β,t pore ,t lat ] T ; N sets of candidate structural parameters are generated in the parameter space Ω using Latin hypercube sampling. The range of values ​​for each continuous parameter dimension j Divide the interval into N non-overlapping subintervals, such that the probability of each subinterval is 1 / N; for the j-th dimension, independently and randomly select a value u within each subinterval. ijThen, for each sample i, the extracted values ​​of each dimension are randomly combined to finally generate a sample matrix X=[x1,x2,…,x…]. i ,…,x N ] T .

[0007] Furthermore, a representative volumetric element model of the foam was established using finite element software, and a virtual compression-springback-creep simulation was performed to obtain a virtual dataset, as detailed below: For each set of candidate parameters x i A representative volumetric element model (RVE) of the foam was established using finite element method (FEM) software. Based on the given porosity, pore size, and pore wall thickness, a three-dimensional open-cell foam structure was generated using a random sequential adsorption algorithm. For gradient porosity, different porosities were assigned to layers along the thickness direction. Local micropillar reinforcement involved inserting cylindrical solid elements into designated areas of the core layer. The model mesh used hexahedrons, and the material constitutive model was hyperelastic. The parameters were calibrated by uniaxial tensile tests on the substrate, and the strain energy density function adopted the Ogden form. Where, λ i The main elongation ratio is J, the volume ratio is μp, αp, and Dp are temperature-dependent material parameters calibrated by uniaxial tensile tests on the substrate; the viscoelastic effect is introduced into the relaxation modulus through the superposition of Prony series. ; Among them, G ∞ For long-term modulus, G i and τ i These are the modulus and relaxation time of the i-th relaxation mode, respectively; Virtual compression-springback-creep simulations were performed to model the mechanical response of foam in actual use. Based on elastic contact theory, the initial tack force was estimated using the local surface contact pressure distribution obtained from the simulation. (Proportional to the product of effective contact area and interfacial adhesion energy), for each candidate parameter x_i, the simulation outputs the corresponding performance vector y. i ; All simulation results were compiled, cleaned, and standardized to form a virtual dataset D. virtual ={(x i , y i ) | i=1..N}.

[0008] Furthermore, based on the virtual dataset, a foam structure-performance proxy model based on graph neural networks is constructed as follows: Based on the obtained virtual dataset D virtual = {(x i , y iA graph neural network is used to abstract the microscopic pore structure of foam into graph data for end-to-end learning, given structural parameters x. i The corresponding representative volume element of the foam is transformed into a property graph G. i =(V,E,H V H E In the equation (RVE), V is the set of nodes, where each node represents a pore in the foam, and the number of nodes equals the number of pores in RVE; E is the set of edges, where an undirected edge is established between two pores if they are spatially adjacent; adjacency is determined by the nearest neighbor method based on Euclidean distance; H... V The node feature matrix is ​​given, and the eigenvector of the v-th node includes the local pore size d of the pore. p (v), local porosity φ(v) (calculated within a spherical neighborhood centered on the node), normalized spatial coordinates (x) v ,y v ,z v ), whether it is located on the gradient surface, and whether the pore is adjacent to the micropillar reinforcement region; H E Let be the edge feature matrix, where the features of the e-th edge include the Euclidean distance l between the two pore centers. e Average thickness t of shared hole wall w (e) and the local stiffness enhancement factor of the hole wall material; A graph isomorphic network with edge updates is chosen as the basic architecture of the surrogate model. The network consists of L graph convolutional layers and global pooling layers. The node update formula for the layer is: Where, is the node v at the th ? Hidden features of the layer, initial ; It is the set of neighboring nodes of node v; e uv The edge features connecting nodes u and v It is a weight matrix It is a scalar parameter used to balance information about itself and its neighbors. It is a two-layer multilayer perceptron; [·;·] denotes vector concatenation; After L layers of graph convolution, node features It aggregates the structural information of the entire graph; All node features are aggregated into a fixed-length vector using a combination of global mean pooling and global max pooling. ; Here, ⊕ represents vector concatenation; this vector is then regressed to the performance label through an output header: ; in, Corresponding to standardized predictability .

[0009] Furthermore, a variational autoencoder (VAE) is constructed to obtain a candidate set of structures based on the structured parameter space. Specifically, a VAE is introduced to learn a low-dimensional latent representation of the structured parameter space Ω, and new structure parameters are generated by randomly sampling the latent space, thereby expanding the optimization search range. The VAE consists of an encoder network q. φ (z∣x) and a decoder network p θ The input vector is composed of (x|z), where x∈Ω is the original structural parameter vector and z is the latent variable. The encoder maps the input x to the mean and logarithm of the Gaussian distribution in the latent space, i.e.: ; The decoder then reconstructs the original parameters from the latent variable z. That is, p θ (x|z)=N(x;μ) θ (z), I), the training objective is to maximize the lower bound of evidence: Where p(z)=N(0,I) is the standard normal prior, and the KL divergence term is used as a regularization to make the latent distribution approximate the standard normal.

[0010] Furthermore, based on the foam structure-performance surrogate model and the candidate structure set, the optimal structure parameters are obtained through a global optimal structure search based on multi-objective Bayesian optimization, as follows: The candidate structure set X generated in step S3 cand We randomly select n0 points as initial design points, conduct real experiments to evaluate these initial points, obtain the real target vector, and add it to the real dataset D. real ; Based on D real Update the surrogate model and calculate the current Pareto front P and hypervolume HV(P); In each iteration, except for X cand The points in the dataset also include new points generated by VAE or perturbation points within the neighborhood of the current optimal solution, and all evaluable points are denoted as X. pool ; For X pool For each point x in the model, the predicted mean μ(x) and standard deviation σ(x) are calculated using a surrogate model, and then the EHVI value is calculated. Select the next assessment point: ; Get x nextReal performance of foam samples ,Will Join D real Recalculate the Pareto front P and hypervolume; Using the amplified D real Fine-tuning the graph neural network to improve local accuracy is performed when the maximum value of EHVI is less than a threshold ε in a series of consecutive iterations, or when the preset maximum number of iterations N is reached. iter It will stop when it converges to the maximum volume.

[0011] Furthermore, the multi-objective Bayesian optimization surrogate function adopts M... GNN and M GNN The mean and variance of the output are considered as the GP posterior for each target. For the j-th target, the predicted mean is defined as... Prediction standard deviation Then the posterior distribution of the objective function value is approximately: ; In multi-objective Bayesian optimization, the acquisition function employs the desired hypervolume improved EHVI. The hypervolume HV refers to the volume of the region enclosed between the Pareto front and the reference point. Given the currently known Pareto front P and reference point r, the hypervolume is defined as: ; Where λ is the Lebesgue measure, and [y,r] represents a hyperrectangle with y and r as diagonal vertices; For a candidate point x, its hypervolume improvement HVI is defined as: ; Since f(x) is unknown, we calculate the expectation using its probability distribution: .

[0012] Furthermore, based on the optimal structural parameters and the actual manufacturing process parameters of the foam, a collaborative optimization of material process parameters based on deep reinforcement learning is adopted to obtain the optimal process formula, as follows: This problem is modeled as a Markov Decision Process (MDP). A deep reinforcement learning agent is used to automatically learn the optimal process strategy. The MDP quadruple (S, A, R, P) is defined as follows: the state space S includes the current structural parameters and the real-time process parameter vector p; the action space A represents the adjustment amount for each process parameter, which are continuous actions; the state transition probability P is determined by the response characteristics of the actual manufacturing environment; the reward function R is designed as a comprehensive performance index, guiding the agent to maximize the initial viscous force and minimize compressive permanent deformation and stress relaxation rate while satisfying constraints. ; Where w1, w2, and w3 are weighting coefficients. As a normalization benchmark, 1 fail Indicates process failure; The goal of MDP is to find the optimal policy π. (a|s) maximizes the cumulative discount reward, with a discount factor γ=0.95; The double-delay deep deterministic policy gradient algorithm is selected, which effectively alleviates the overestimation problem through a double Q-network and delayed policy updates. The agent structure includes an Actor network π. φ (s) Outputs a deterministic action a, two Critic networks Evaluate the value of actions; train the agent, and after training converges, extract the optimal structural parameters X for each group from the agent's policy. opt The deterministic action sequence, since the policy has learned the adjustment path from the initial process to a stable high-performance state, the final output process formula is the process parameter value of the agent in steady state.

[0013] The high initial viscosity optimization system based on foam structure compression and rebound performance modeling includes a processor, a memory, and a computer program stored in the memory. When the processor executes the computer program, it specifically performs the steps in the high initial viscosity optimization method based on foam structure compression and rebound performance modeling as described above.

[0014] A computer storage medium storing a plurality of instructions adapted for loading by a processor and executing the method steps described above.

[0015] The present invention has the following beneficial effects: 1. This invention generates a virtual dataset through Latin hypercube sampling and constructs a graph neural network surrogate model, which effectively improves the prediction speed of structure-performance mapping and has a generalization ability far exceeding that of the response surface methodology. Furthermore, it combines variational autoencoders for generative design, which automatically generates novel foam structures that exceed empirical boundaries in a high-dimensional parameter space (such as the combination of gradient porosity and micropillar reinforcement), significantly expanding the search range of high-quality candidate solutions. 2. This invention employs a multi-objective Bayesian optimization framework that utilizes the uncertainty quantification information of the surrogate model and uses the expected hypervolume improvement as the acquisition function. It can approach the Pareto optimal frontier in a very small number of real experimental iterations, solving the problem that traditional optimization is difficult to traverse multiple objectives due to high experimental costs. 3. This invention optimizes structural parameters and manufacturing process parameters (such as foaming temperature, pressure, and UV curing dosage) together. By learning the optimal action strategy, it compensates for the deviation between simulation and reality, ensuring that the high initial viscosity and compression resistance design is not only theoretically optimal, but also achievable on the actual production line. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: refer to Figure 1 In this embodiment, a high initial viscosity optimization method based on foam structure compression and rebound performance modeling is provided, including the following steps: S1: Define a structured parameter space and use Latin hypercube to generate candidate structural parameters in the parameter space. For each set of parameters, use finite element software to build a representative volume element model of foam, perform virtual compression-springback-creep simulation, and obtain a virtual dataset. S2: Construct a foam structure-performance proxy model based on a graph neural network, using a virtual dataset; S3: Construct a variational autoencoder and obtain a candidate set of structures based on the structured parameter space; S4: Based on the foam structure-performance proxy model and the candidate structure set, the optimal structure parameters are obtained by global optimal structure search based on multi-objective Bayesian optimization; S5: Based on the optimal structural parameters and the actual manufacturing process parameters of the foam, the optimal process formula is obtained by co-optimizing the material process parameters using deep reinforcement learning.

[0018] In this embodiment, a structured parameter space is defined, and candidate structure parameters are generated within the parameter space using Latin hypercubes, as detailed below: The parameterized space Ω of the foam structure is defined, containing key geometric and structural parameters that affect the compression resilience and initial tack of the foam double-sided tape. These parameters are divided into continuous and discrete variables. The continuous variables include the overall porosity φ (range 0.3 ≤ φ ≤ 0.85) and the average pore size d. p (50 μm≤dp≤300 μm), pore wall thickness t w (5 μm≤t) w ≤30 μm), thickness gradient factor α=φ skin / φ core , where φ skin φ represents the surface porosity. core The core porosity is defined as α ≤ 2.5, and the column diameter D of the locally reinforced micropillar structure in the core layer is also defined as α ≤ 2.5. c (50 μm≤D) c ≤200 μm) and the ratio of column spacing to diameter β=L c / D c (0.1≤β≤0.5); discrete variables include aperture distribution type t pore (t) pore∈{0,1}, where 0 represents a single peak and 1 represents a double peak, and the micro-pillar arrangement t lat (tlat∈{0,1}, where 0 represents a square grid and 1 represents a hexagonal close-packed grid); all parameters constitute a d-dimensional structure parameter vector: x=[φ,d p ,t w ,α,Dc,β,t pore ,t lat ] T ; N sets of candidate structural parameters are generated in the parameter space Ω using Latin hypercube sampling. The range of values ​​for each continuous parameter dimension j Divide the interval into N non-overlapping subintervals, such that the probability of each subinterval is 1 / N; for the j-th dimension, independently and randomly select a value u within each subinterval. ij Then, for each sample i, the extracted values ​​of each dimension are randomly combined to finally generate a sample matrix X=[x1,x2,…,x…]. i ,…,x N ] T .

[0019] In this embodiment, a representative volumetric element model of the foam is established using finite element software, and a virtual compression-springback-creep simulation is performed to obtain a virtual dataset, as detailed below: For each set of candidate parameters x i A representative volumetric element model (RVE) of the foam was established using finite element method (FEM) software. Based on the given porosity, pore size, and pore wall thickness, a three-dimensional open-cell foam structure was generated using a random sequential adsorption algorithm. For gradient porosity, different porosities were assigned to layers along the thickness direction. Local micropillar reinforcement involved inserting cylindrical solid elements into designated areas of the core layer. The model mesh used hexahedrons, and the material constitutive model was hyperelastic. The parameters were calibrated by uniaxial tensile tests on the substrate, and the strain energy density function adopted the Ogden form. Where, λ i The main elongation ratio is J, the volume ratio is μp, αp, and Dp are temperature-dependent material parameters calibrated by uniaxial tensile tests on the substrate; the viscoelastic effect is introduced into the relaxation modulus through the superposition of Prony series. ; Among them, G ∞ For long-term modulus, G i and τ i These are the modulus and relaxation time of the i-th relaxation mode, respectively. Usually, n=3 is sufficient to capture the long-term creep behavior of foam. A virtual compression-rebound-creep simulation was performed to simulate the mechanical response of foam in actual use. The simulation loading process was divided into three stages: the first stage was the loading stage, where the RVE model was compressed to 50% strain at a speed of 1 mm / min, and the instantaneous stress-strain curve was recorded to extract the instantaneous elastic modulus E0; the second stage was the pressure-holding creep stage, where the model was held at 50% strain for 72 hours (the virtual time can be accelerated using algorithms such as scaling the relaxation time spectrum using the Prony series viscoelastic constitutive model), and the stress decay curve over time was recorded to calculate the 24-hour creep compliance J(24h) and stress relaxation rate SR (the ratio of stress at the end of the pressure-holding stage to the initial stress); the third stage was the unloading recovery stage, where the model was unloaded to zero stress at the same speed, and allowed to recover freely for 24 hours, during which the residual strain was measured and the compression permanent deformation C was calculated. S = Residual strain / 50%; Based on elastic contact theory, the initial viscous force is estimated using the local surface contact pressure distribution obtained through simulation. (Proportional to the product of effective contact area and interfacial adhesion energy), for each candidate parameter x_i, the simulation outputs the corresponding performance vector y. i = [E0, J(24h), CS, SR, ]; All simulation results are compiled, and after data cleaning (removing non-convergent or physical outliers) and standardization (zero mean, unit variance), a virtual dataset D is formed. virtual = {(x i , y i ) | i=1..N}.

[0020] In this embodiment, a foam structure-performance proxy model based on a graph neural network is constructed according to the virtual dataset, as follows: Based on the obtained virtual dataset D virtual = {(x i , y i A graph neural network is used to abstract the microscopic pore structure of foam into graph data for end-to-end learning, given structural parameters x. i The corresponding representative volume element of the foam is transformed into a property graph G. i =(V,E,H V H E In the RVE (Real-Volume Equation), V is the set of nodes, where each node represents a pore in the foam, and the number of nodes equals the number of pores in the RVE; E is the set of edges, where an undirected edge is established between two pores if they are spatially adjacent (i.e., sharing a wall or connected by a channel); adjacency is determined by the nearest neighbor method based on Euclidean distance (the distance threshold is set to 1.5 times the average pore diameter); H VThe node feature matrix is ​​given, and the eigenvector of the v-th node includes the local pore size d of the pore. p (v), local porosity φ(v) (calculated within a spherical neighborhood centered on the node), normalized spatial coordinates (x) v ,y v ,z v ), whether it is located on the gradient surface (binary indicator), and whether the pore is adjacent to the micropillar reinforcement region (binary indicator); H E Let be the edge feature matrix, where the features of the e-th edge include the Euclidean distance l between the two pore centers. e Average thickness t of shared hole wall w (e) and the local stiffness enhancement factor of the hole wall material; A graph isomorphic network with edge updates is chosen as the basic architecture of the surrogate model. The network consists of L graph convolutional layers and global pooling layers. The node update formula for the layer is: Where, is the node v at the th ? Hidden features of the layer, initial ; It is the set of neighboring nodes of node v; e uv The edge features connecting nodes u and v It is a weight matrix It is a scalar parameter used to balance information about itself and its neighbors. It is a two-layer multilayer perceptron; [·;·] represents vector concatenation; during the update process, edge features are concatenated into the features of neighboring nodes, enabling the network to perceive hole wall thickness and distance information; After L layers of graph convolution, node features It aggregates the structural information of the entire graph; All node features are aggregated into a fixed-length vector using a combination of global mean pooling and global max pooling. ; Here, ⊕ represents vector concatenation; this vector is then passed through an output head (two MLP layers, with 128 and 64 neurons respectively, and the last layer being linear activation) to regress to the performance label: ; in, Corresponding to standardized predictability .

[0021] In this embodiment, a variational autoencoder (VAE) is constructed to obtain a candidate set of structures based on the structured parameter space. Specifically, a VAE is introduced to learn a low-dimensional latent representation of the structured parameter space Ω, and new structure parameters are generated by randomly sampling the latent space, thereby expanding the optimization search range. The VAE consists of an encoder network q. φ (z∣x) and a decoder network p θ The input vector is composed of (x|z), where x∈Ω is the original structural parameter vector and z is the latent variable. The encoder maps the input x to the mean and logarithm of the Gaussian distribution in the latent space, i.e.: ; The decoder then reconstructs the original parameters from the latent variable z. That is, p θ (x|z)=N(x;μ) θ (z),I) (The training objective is to maximize the lower bound of evidence (ELBO): Where p(z)=N(0,I) is the standard normal prior, and the KL divergence term is used as a regularization to make the latent distribution approximate the standard normal. Preferably, in this embodiment, the encoder has: an input layer dimension d=8; two hidden layers, each with 128 neurons, activated using ReLU; and an output branch with a mean μφ dimension m, logarithmic... Dimension m; Decoder: Input layer dimension m; two hidden layers, 128 neurons each, ReLU activation; output layer dimension d, using linear activation for continuous variables (outputting reconstructed continuous values), and using Sigmoid activation with binary cross-entropy loss for discrete variables. Discrete variable t pore and t lat It is used as part of the input during encoding and processed separately during decoding; Loss function for handling mixed-type data: The reconstruction loss for continuous variables and discrete variables is calculated separately. Let x = [x...] c ;x d ], where x c For continuous variables (6 dimensions), x d Let the variables be discrete (2-dimensional). Then the reconstruction loss is: The continuous part uses Gaussian negative log-likelihood (MSE loss is equivalent to Gaussian likelihood with fixed variance): The discrete part uses binary cross-entropy (independent for each discrete dimension): ; in .

[0022] From the design matrix X=[x1,x2,…,x] in S1 i ,…,x N ] T Randomly select N VAE We have samples as the unsupervised training set. All continuous variables are pre-normalized to the [0,1] interval (Min-Max scaling), while discrete variables remain unchanged. The optimizer uses Adam with a learning rate of 1×10⁻⁶. -3 The batch size is 256, and the training duration is 200 epochs. After each epoch, the ELBO and reconstruction error are calculated on the validation set (10% of the samples). To prevent posterior collapse (i.e., the latent distribution of all samples tends to the prior), a KL annealing strategy can be used: in the first 50 epochs, the KL loss is multiplied by a linearly increasing weight β, which gradually increases from 0 to 1, i.e., in the form of β-VAE. This scheme uses β=0.5 (final stable value) to ensure the decoupling of potential structures while avoiding excessive regularization; After training, a VAE model capable of generating reasonable structure parameters is obtained. To obtain a novel and diverse set of structure candidates, the following four strategies are used for sampling in the latent space: Random sampling: directly from the prior distribution M1 latent vectors zrzr are randomly selected from the dataset, and the corresponding structural parameters are generated by the decoder. These parameters may deviate from the distribution of the original training data, but the randomness is guaranteed by the reparameterization technique, which enables the exploration of unknown regions.

[0023] Linear interpolation: the latent encoding z of two training samples randomly selected from the latent space. i and z j Interpolate at equal intervals along a straight line: z λ =(1-λ)z i +λz j λ∈(0,1) takes 5 to 10 values. Decoding yields an intermediate structure between the two training structures. Gaussian perturbation sampling: For high-potential regions in the training data (e.g., samples with good initial performance), the latent mean μ is first calculated by the encoder. φ (x k Then add Gaussian noise around it: ,in ; Boundary extrapolation sampling: Sampling is performed in the edge regions of the potential space (e.g., regions with a radius greater than 2 from the origin), and then reconstructed using a decoder. These generated structures are often extreme (e.g., extremely high or extremely low porosity) and may exceed the boundaries of the original parameters, requiring subsequent evaluation of their feasibility using a surrogate model.

[0024] Combining the four methods described above, a total of M = M1 + M2 + M3 + M4 candidate structures are generated. For each generated candidate structure, post-processing is performed to ensure physical rationality: continuous variables are pruned to their original domain, and discrete variables are binarized through rounding or thresholding operations.

[0025] All generated candidate structures: Input the graph neural network surrogate model M in step S2 GNN The performance vector is predicted. A coarse filter is performed based on a preset initial performance threshold, eliminating obviously unqualified candidates. The number of retained candidates is denoted as Mpass (typically 200-500), forming the final candidate structure set X. cand .

[0026] In this embodiment, based on the foam structure-performance surrogate model and the candidate structure set, the optimal structure parameters are obtained through a global optimal structure search using multi-objective Bayesian optimization, as follows: The candidate structure set X generated in step S3 cand Randomly select n0 points as initial design points, perform real experiments on these initial points (prepare samples, test performance) to obtain the real target vector, and add it to the real dataset D. real ; Based on D real Update the surrogate model and calculate the current Pareto front P and hypervolume HV(P); In each iteration, except for X cand The points in the dataset also include new points generated by VAE or perturbation points within the neighborhood of the current optimal solution, and all evaluable points are denoted as X. pool ; For X pool For each point x in the model, the predicted mean μ(x) and standard deviation σ(x) are calculated using a surrogate model, and then the EHVI value is calculated. Select the next assessment point: ; Get x next Real performance of foam samples ,Will Join D real Recalculate the Pareto front P and hypervolume; Using the amplified D realFine-tuning of the graph neural network (with only a few epochs, such as 10-20) is performed to improve local accuracy. This is done when the maximum value of EHVI is less than the threshold ε = 0.001 (normalized hypervolume) in several consecutive iterations, or when the preset maximum number of iterations N is reached. iter Stop when the volume converges (the change between two adjacent changes is less than 0.1%).

[0027] In this embodiment, the multi-objective Bayesian optimization surrogate function adopts M GNN and M GNN The mean and variance of the output are considered as the GP posterior for each target. For the j-th target, the predicted mean is defined as... Prediction standard deviation (From the MC Dropout uncertainty quantization in step S2), the posterior distribution of the objective function value is approximately: ; In multi-objective Bayesian optimization, the acquisition function employs the desired hypervolume improved EHVI. The hypervolume HV refers to the volume of the region enclosed between the Pareto front and the reference point. Given the currently known Pareto front P and reference point r, the hypervolume is defined as: ; Where λ is the Lebesgue measure, and [y,r] represents a hyperrectangle with y and r as diagonal vertices; For a candidate point x, its hypervolume improvement HVI is defined as: ; Since f(x) is unknown, we calculate the expectation using its probability distribution: .

[0028] In this scheme, design variables x∈X are defined, where X is the structured parameter space defined in step S1. The objective function is a vector-valued function: f(x)=[f1(x),f2(x),f3(x),f4(x)] T ; in: (Take the negative to minimize, because optimization usually solves a minimization problem); f2(x) = -RLT(x) (negative cryogenic retention rate); f3(x) = CS(x); f4(x) = SR(x); In actual calculations, f j The value of (x) is predicted by the surrogate model MGNN. The goal of multi-objective optimization is to find a Pareto optimal set of solutions such that there is no other x′ that is not inferior to x on all objectives and is strictly superior on at least one objective.

[0029] With four targets, the analytical expression for EHVI is quite complex. This approach uses the Monte Carlo approximation, drawing S=1000 samples from the posterior distribution for each x. ,calculate: In practice, a dynamically updated Pareto front can be maintained. (Including all points that have been truly evaluated), the reference point r is set to the maximum value of the current observation of each target plus a relaxation amount.

[0030] In this embodiment, based on the optimal structural parameters and the actual manufacturing process parameters of the foam, a material process parameter collaborative optimization based on deep reinforcement learning is adopted to obtain the optimal process formula, as follows: Step S4 has yielded the Pareto optimal structural parameters X. opt (For example, equilibrium solutions, initial tack optimal solutions, and compression resistance optimal solutions), however, the foam performance corresponding to these structural parameters is highly dependent on the actual manufacturing process parameters. Due to the presence of multiple process variables during material preparation, such as foaming temperature, molding pressure, curing time, and IPN ultraviolet irradiation dose, and the complex coupling effects between these variables and with the structural parameters, this step models the problem as a Markov Decision Process (MDP). A deep reinforcement learning agent is used to automatically learn the optimal process strategy. The MDP quadruple (S, A, R, P) is defined as follows: the state space S includes the current structural parameters (fixed at X). opt This is related to the real-time process parameter vector p, specifically the foaming temperature T∈[120,180]. C. Molding pressure P∈[0.5,3.0]MPa, holding time t hold ∈[300,1200]、IPN UV radiation dose D UV ∈[200,800]mJ / cm 2 and cooling rate v cool ∈[0.5,5] C / s; the action space A is the adjustment amount for each process parameter, which is a continuous action, and its value range is Δp∈[-0.1,0.1]×(relative change ratio of each dimension); the state transition probability P is determined by the response characteristics of the actual manufacturing environment (unknown but deterministically observable); the reward function R is designed as a comprehensive performance index to guide the agent to maximize the initial viscous force and minimize the compression permanent deformation and stress relaxation rate under the premise of satisfying the constraints. ; Where w1=0.4, w2=0.3, w3=0.3 are weighting coefficients. As a normalization benchmark, 1 fail A bonus of -10 is awarded for process failure indications (such as sample breakage or inability to demold). The goal of MDP is to find the optimal policy π. (a|s) maximizes the cumulative discount reward, with a discount factor γ=0.95; The dual-delay deep deterministic policy gradient algorithm is selected. Through a dual-Q network and delayed policy updates, it effectively alleviates the overestimation problem, making it suitable for high-precision process optimization. The agent structure includes an Actor network π. φ (s) Outputs a deterministic action a, two Critic networks Evaluate action value; the training process is as follows: initialize the Actor and Critic networks and the target network; set up the experience replay pool D with a capacity of 10. 5 Run 2000 episodes in a virtual environment, each episode starting from the initial process parameters p. 0 Start, and choose an action based on the current state at each step. (Ornstein-Uhlenbeck noise is used for exploration). After execution, the next state and reward are obtained and stored in D. Every 100 steps, a mini-batch (size 256) is sampled from D to update the Critic and Actor (Critic minimizes the TD error, Actor maximizes the Q value). After virtual training is completed, the Actor strategy is transferred to the real production line. Data is collected in the real environment, and the model is updated every 50 real steps until the process output performance stably meets CS≤10%, SR≤20%, F tack ≥8N / cm 2 Furthermore, the performance fluctuation of 10 consecutive product batches is less than 5%; Then, training is performed, and after training converges, the optimal structural parameters X for each group are extracted from the agent's policy. opt The deterministic sequence of actions, since the policy has learned the adjustment path from the initial process to a stable high-performance state, ultimately outputs the process formula as the agent's steady-state process parameter values, i.e. Simultaneously, the corresponding performance prediction range is output (given through multiple repeated simulations or a small number of reproducible tests). This optimal process formulation can be directly used to guide the production of foam double-sided tape: for example, for the equilibrium solution structure, the final formulation is "foaming temperature 155±2℃, molding pressure 1.8MPa, holding time 720s, UV dose 550mJ / cm". 2 Cooling rate: 2.5℃ / s.

[0031] The high initial viscosity optimization system based on foam structure compression and rebound performance modeling includes a processor, a memory, and a computer program stored in the memory. When the processor executes the computer program, it specifically performs the steps in the high initial viscosity optimization method based on foam structure compression and rebound performance modeling as described above.

[0032] A computer storage medium storing a plurality of instructions adapted for loading by a processor and executing the method steps described above.

[0033] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0034] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0035] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0036] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0037] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A high initial viscosity optimization method based on modeling the compression and rebound performance of foam structures, characterized in that, Includes the following steps: S1: Define a structured parameter space and use Latin hypercube to generate candidate structural parameters in the parameter space. For each set of parameters, use finite element software to build a representative volume element model of foam, perform virtual compression-springback-creep simulation, and obtain a virtual dataset. S2: Construct a foam structure-performance proxy model based on a graph neural network, using a virtual dataset; S3: Construct a variational autoencoder and obtain a candidate set of structures based on the structured parameter space; S4: Based on the foam structure-performance proxy model and the candidate structure set, the optimal structure parameters are obtained by global optimal structure search based on multi-objective Bayesian optimization; S5: Based on the optimal structural parameters and the actual manufacturing process parameters of the foam, the optimal process formula is obtained by co-optimizing the material process parameters using deep reinforcement learning.

2. The high initial viscosity optimization method based on foam structure compression and rebound performance modeling according to claim 1, characterized in that, The definition of the structured parameter space and the generation of candidate structure parameters within the parameter space using Latin hypercube are as follows: The parameterized space Ω of the foam structure is defined, containing key geometric and structural parameters that affect the compression resilience and initial tack of the foam double-sided tape. These parameters are divided into continuous and discrete variables. The continuous variables include the overall porosity φ and the average pore size d. p Hole wall thickness t w Thickness gradient factor α=φ skin / φ core , where φ skin φ represents the surface porosity. core The core porosity and the column diameter D of the local micropillar reinforcement structure in the core layer are given. c And the ratio of column spacing to diameter β=L c / D c ; Discrete variables include aperture distribution type t pore and the micro-column arrangement method t lat All parameters constitute a d-dimensional structured parameter vector: x=[φ,d p ,t w ,α,Dc,β,t pore ,t lat ] T ; N sets of candidate structural parameters are generated in the parameter space Ω using Latin hypercube sampling. The range of values ​​for each continuous parameter dimension j Divide the interval into N non-overlapping subintervals, such that the probability of each subinterval is 1 / N; for the j-th dimension, independently and randomly select a value u within each subinterval. ij Then, for each sample i, the extracted values ​​of each dimension are randomly combined to finally generate a sample matrix X=[x1,x2,…,x…]. i ,…,x N ] T .

3. The high initial viscosity optimization method based on foam structure compression and rebound performance modeling according to claim 2, characterized in that, The process involves using finite element software to establish a representative volumetric element model of the foam, performing virtual compression-rebound-creep simulations, and obtaining a virtual dataset, as detailed below: For each set of candidate parameters x i A representative volumetric element model (RVE) of the foam was established using finite element method (FEM) software. Based on the given porosity, pore size, and pore wall thickness, a three-dimensional open-cell foam structure was generated using a random sequential adsorption algorithm. For gradient porosity, different porosities were assigned to layers along the thickness direction. Local micropillar reinforcement involved inserting cylindrical solid elements into designated areas of the core layer. The model mesh used hexahedrons, and the material constitutive model was hyperelastic. The parameters were calibrated by uniaxial tensile tests on the substrate, and the strain energy density function adopted the Ogden form. ； Where, λ i The main elongation ratio is J, the volume ratio is μp, αp, and Dp are temperature-dependent material parameters calibrated by uniaxial tensile tests on the substrate; the viscoelastic effect is introduced into the relaxation modulus through the superposition of Prony series. ； Among them, G ∞ For long-term modulus, G i and τ i These are the modulus and relaxation time of the i-th relaxation mode, respectively; Virtual compression-springback-creep simulations were performed to model the mechanical response of foam in actual use. Based on elastic contact theory, the initial tack force was estimated using the local surface contact pressure distribution obtained from the simulation. For each candidate parameter x_i, the simulation outputs the corresponding performance vector y. i ; All simulation results were compiled, cleaned, and standardized to form a virtual dataset D. virtual = {(x i ,y i ) | i=1..N}.

4. The high initial viscosity optimization method based on foam structure compression and rebound performance modeling according to claim 1, characterized in that, The foam structure-performance proxy model based on a graph neural network is constructed using the virtual dataset, as detailed below: Based on the obtained virtual dataset D virtual = {(x i , y i A graph neural network is used to abstract the microscopic pore structure of foam into graph data for end-to-end learning, given structural parameters x. i The corresponding representative volume element of the foam is transformed into a property graph G. i =(V,E,H V H E In the equation (RVE), V is the set of nodes, where each node represents a pore in the foam, and the number of nodes equals the number of pores in RVE; E is the set of edges, where an undirected edge is established between two pores if they are spatially adjacent; adjacency is determined by the nearest neighbor method based on Euclidean distance; H... V The node feature matrix is ​​given, and the eigenvector of the v-th node includes the local pore size d of the pore. p (v), local porosity φ(v) (calculated within a spherical neighborhood centered on the node), normalized spatial coordinates (x) v ,y v ,z v ), whether it is located on the gradient surface, and whether the pore is adjacent to the micropillar reinforcement region; H E Let be the edge feature matrix, where the features of the e-th edge include the Euclidean distance l between the two pore centers. e Average thickness t of shared hole wall w (e) and the local stiffness enhancement factor of the hole wall material; A graph isomorphic network with edge updates is chosen as the basic architecture of the surrogate model. The network consists of L graph convolutional layers and global pooling layers. The node update formula for the layer is: ； Where, is the node v at the th ? Hidden features of the layer, initial ; It is the set of neighboring nodes of node v; e uv The edge features connecting nodes u and v It is a weight matrix It is a scalar parameter used to balance information about itself and its neighbors. It is a two-layer multilayer perceptron; [·;·] denotes vector concatenation; After L layers of graph convolution, node features It aggregates the structural information of the entire graph; All node features are aggregated into a fixed-length vector using a combination of global mean pooling and global max pooling. ； Here, ⊕ represents vector concatenation; this vector is then regressed to the performance label through an output header: ； in, Corresponding to standardized predictability .

5. The high initial viscosity optimization method based on foam structure compression and rebound performance modeling according to claim 1, characterized in that, The construction of the variational autoencoder (VAE) involves obtaining a candidate set of structures based on the structured parameter space. Specifically, a VAE is introduced to learn a low-dimensional latent representation of the structured parameter space Ω, and new structure parameters are generated by randomly sampling the latent space, thereby expanding the optimization search range. The VAE consists of an encoder network q. φ (z∣x) and a decoder network p θ The input vector is composed of (x|z), where x∈Ω is the original structural parameter vector and z is the latent variable. The encoder maps the input x to the mean and logarithm of the Gaussian distribution in the latent space, i.e.: ； The decoder then reconstructs the original parameters from the latent variable z. That is, p θ (x|z)=N(x;μ) θ (z), I), the training objective is to maximize the lower bound of evidence: ； Where p(z)=N(0,I) is the standard normal prior, and the KL divergence term is used as a regularization to make the latent distribution approximate the standard normal.

6. The high initial viscosity optimization method based on foam structure compression and rebound performance modeling according to claim 1, characterized in that, The optimal structure parameters are obtained by performing a global optimal structure search based on a multi-objective Bayesian optimization method, using the foam structure-performance proxy model and a candidate structure set. The specific steps are as follows: The candidate structure set X generated in step S3 cand We randomly select n0 points as initial design points, conduct real experiments to evaluate these initial points, obtain the real target vector, and add it to the real dataset D. real ; Based on D real Update the surrogate model and calculate the current Pareto front P and hypervolume HV(P); In each iteration, except for X cand The points in the dataset also include new points generated by VAE or perturbation points within the neighborhood of the current optimal solution, and all evaluable points are denoted as X. pool ; For X pool For each point x in the model, the predicted mean μ(x) and standard deviation σ(x) are calculated using a surrogate model, and then the EHVI value is calculated. Select the next assessment point: ； Get x next Real performance of foam samples ,Will Join D real Recalculate the Pareto front P and hypervolume; Using the amplified D real Fine-tuning the graph neural network to improve local accuracy is performed when the maximum value of EHVI is less than a threshold ε in a series of consecutive iterations, or when the preset maximum number of iterations N is reached. iter It will stop when it converges to the maximum volume.

7. The high initial viscosity optimization method based on foam structure compression and rebound performance modeling according to claim 6, characterized in that, The multi-objective Bayesian optimization surrogate function adopts M... GNN and M GNN The mean and variance of the output are considered as the GP posterior for each target. For the j-th target, the predicted mean is defined as... Prediction standard deviation Then the posterior distribution of the objective function value is approximately: ； In multi-objective Bayesian optimization, the acquisition function employs the desired hypervolume improved EHVI. The hypervolume HV refers to the volume of the region enclosed between the Pareto front and the reference point. Given the currently known Pareto front P and reference point r, the hypervolume is defined as: ； Where λ is the Lebesgue measure, and [y,r] represents a hyperrectangle with y and r as diagonal vertices; For a candidate point x, its hypervolume improvement HVI is defined as: ； Since f(x) is unknown, we calculate the expectation using its probability distribution: 。 8. The high initial viscosity optimization method based on foam structure compression and rebound performance modeling according to claim 1, characterized in that, The optimal process formula is obtained by collaboratively optimizing material process parameters based on deep reinforcement learning, using the optimal structural parameters and the actual manufacturing process parameters of the foam. The specific details are as follows: This problem is modeled as a Markov Decision Process (MDP). A deep reinforcement learning agent is used to automatically learn the optimal process strategy. The MDP quadruple (S, A, R, P) is defined as follows: the state space S includes the current structural parameters and the real-time process parameter vector p; the action space A represents the adjustment amount for each process parameter, which are continuous actions; the state transition probability P is determined by the response characteristics of the actual manufacturing environment; the reward function R is designed as a comprehensive performance index, guiding the agent to maximize the initial viscous force and minimize compressive permanent deformation and stress relaxation rate while satisfying constraints. ； Where w1, w2, and w3 are weighting coefficients. As a normalization benchmark, 1 fail Indicates process failure; The goal of MDP is to find the optimal policy π. (a|s) maximizes the cumulative discount reward, with a discount factor γ=0.95; The double-delay deep deterministic policy gradient algorithm is selected, which effectively alleviates the overestimation problem through a double Q-network and delayed policy updates. The agent structure includes an Actor network π. φ (s) Outputs a deterministic action a, two Critic networks Evaluate the value of actions; train the agent, and after training converges, extract the optimal structural parameters X for each group from the agent's policy. opt The deterministic action sequence, since the policy has learned the adjustment path from the initial process to a stable high-performance state, the final output process formula is the process parameter value of the agent in steady state.

9. A high initial viscosity optimization system based on modeling the compression and rebound performance of foam structures, characterized in that, It includes a processor, a memory, and a computer program stored in the memory. When the processor executes the computer program, it specifically performs the steps in the high initial viscosity optimization method based on foam structure compression and rebound performance modeling as described in any one of claims 1-8.

10. A computer storage medium, characterized in that, The computer storage medium stores a plurality of instructions adapted for loading by a processor and executing the method steps as claimed in any one of claims 1-8.

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