Method for reducing high-temperature compression deformation of EVA foamed shoe sole material

Abstract

This invention provides a method for reducing the high-temperature compression deformation of EVA foam shoe sole materials, belonging to the technical field of foam shoe sole materials. The invention obtains a compound by plasticizing the components in a mixer, constructing a Pareto front in a three-dimensional parameter space using high-throughput response surface methodology to determine optimal process parameters, inputting these parameters into a non-equilibrium statistical mechanics creep rate field algorithm for thermodynamically self-consistent creep rate field verification, performing micro-computed tomography on the sample, and extracting the cell shape parameter set and anisotropy index using an artificial intelligence-based three-dimensional cell reconstruction and shape parameterization model, outputting a long-term creep prediction curve, and finally generating an optimized formulation through a flow-matching reverse design algorithm and performing closed-loop verification. This solves the technical problems of excessively high high-temperature compression set in EVA foam shoe sole materials and the lack of closed-loop quantitative prediction and reverse design capabilities from formulation design to process optimization.

Description

Technical Field

[0001] This invention belongs to the field of foamed shoe sole material technology, and more specifically, relates to a method for reducing high-temperature compression deformation of EVA foamed shoe sole material. Background Technology

[0002] Ethylene-vinyl acetate copolymer foam materials are widely used in sports shoe soles due to their lightweight and excellent cushioning properties. In traditional manufacturing processes, formulation development relies on engineers' experience to conduct forward experiments, adjusting parameters such as the amount of dicumyl peroxide, the proportion of foaming agent, and vulcanization temperature and time, followed by compression set tests to evaluate product performance. Existing technologies have employed response surface methodology to optimize vulcanization parameters, used the time-temperature equivalence principle to predict creep behavior, and employed finite element simulation to assess the impact of cell structure on mechanical properties. These methods have achieved certain results under normal temperature conditions.

[0003] However, under high-temperature operating conditions, since the crosslinked network of ethylene-vinyl acetate copolymer is simultaneously driven by multiple fields including thermal field, force field and chemical potential field, traditional response surface optimization only establishes a formulation-performance mapping for a single temperature point. It cannot capture the nonlinear distribution of creep rate field caused by changes in crosslinking density at high temperatures, resulting in significant creep exceeding the standard problem in samples prepared with optimized parameters under actual high-temperature compression conditions.

[0004] Specifically, when shoe sole materials are subjected to prolonged high-temperature compression conditions, traditional power-law creep models introduce systematic biases due to the artificially assumed creep exponent, failing to accurately predict the long-term creep behavior of cross-linked networks. Simultaneously, two-dimensional cross-sectional analysis underestimates the contribution of the three-dimensional anisotropy of the foam cells to creep, resulting in a significant discrepancy between finite element predictions and measured results. Furthermore, the forward experimental path from formulation to performance lacks reverse design capabilities, making it difficult to automatically generate optimized formulations that meet constraints based on the target compression set. In other words, existing technologies suffer from the technical problem of excessively high high-temperature compression set rates in EVA foam shoe sole materials and a lack of closed-loop quantitative prediction and reverse design capabilities from formulation design to process optimization. Summary of the Invention

[0005] In view of this, the present invention provides a method for reducing the high-temperature compression deformation of EVA foam shoe sole materials, which can solve the technical problems in the prior art where the high-temperature compression permanent deformation rate of EVA foam shoe sole materials is too high and there is a lack of closed-loop quantitative prediction and reverse design capabilities from formulation design to process optimization.

[0006] This invention is achieved as follows: This invention provides a method for reducing high-temperature compression deformation of EVA foam shoe sole materials, comprising the following steps:

[0007] After mixing the components according to the basic formula, plasticize them in an internal mixer to obtain the compounded rubber.

[0008] High-throughput response surface methodology was employed to scan the three-dimensional parameter space of temperature, time and dicumyl peroxide dosage on a flat vulcanizing machine matrix experimental platform. Pareto front was constructed with gel content and compression set as dual objectives to determine the positive vulcanization window and optimize process parameters.

[0009] The preferred process parameters are input into the non-equilibrium statistical mechanics creep rate field algorithm to obtain the creep rate field distribution results. Based on the comparison between the creep rate field mean and the preset creep rate threshold, if the creep rate field mean exceeds the preset creep rate threshold, return to the previous step to adjust the parameters; otherwise, proceed to the next step.

[0010] The sample prepared under the preferred process parameters is subjected to micro-computed tomography. The three-dimensional morphology of the bubble is reconstructed using bubble 3D reconstruction and shape parameterization model. The bubble shape parameter set and anisotropy index are extracted. If the anisotropy index exceeds the preset anisotropy threshold, the mold flow channel size or injection direction is adjusted and the sample is remade. Otherwise, proceed to the next step.

[0011] Multi-temperature short-time compression creep experiments were conducted on the samples. The creep experiment data and the set of pore shape parameters were input into the creep prediction model, and the long-time creep prediction curve containing confidence intervals was output. If the confidence interval width exceeded the preset confidence width threshold, the number of experimental temperature points was increased and the data was collected again. Otherwise, the process proceeded to the next step.

[0012] The long-term creep prediction curve is matched with the input stream of the cell shape parameter set to design an inverse algorithm. An optimized formula is generated with the target compression set and the target springback rate as conditions. The optimized formula is then validated by sample preparation and compression set test to complete the closed-loop validation.

[0013] The basic formula is based on 100 parts by weight of ethylene-vinyl acetate copolymer. The components include ethylene-vinyl acetate copolymer, dicumyl peroxide, azodicarbonamide, zinc oxide, stearic acid, silica, and triallyl isocyanurate. The components are mixed in an internal mixer at a specified temperature for a specified time before being discharged.

[0014] Among them, the high-throughput response surface experimental design adopts the response surface method combined with Taguchi orthogonal design. The Pareto front is obtained by multi-objective optimization of the response surface fitting data through a non-dominated sorting genetic algorithm. The objective function is that the gel content is higher than the target value of gel content and the compression set is lower than the target value of compression set.

[0015] Among them, the non-equilibrium statistical mechanics creep rate field algorithm is based on the Onsager linear irreversible thermodynamic framework. It describes the high-temperature creep of the ethylene-vinyl acetate copolymer crosslinked network as a process of minimizing the entropy generation rate and constructs the Onsager coefficient matrix between generalized forces and generalized flows. The matrix satisfies the symmetric positive definite condition.

[0016] Among them, the non-equilibrium statistical mechanics creep rate field algorithm discretizes the creep equation into a finite volume scheme, minimizes the global entropy generation functional under the constraint that the local entropy generation rate is greater than or equal to zero, and adopts the block preconditional conjugate gradient method for iterative solution.

[0017] The encoder of the bubble 3D reconstruction and shape parameterization model adopts a multi-level downsampling path composed of 3D residual convolutional units, and the decoder adopts a symmetrical multi-level upsampling path with skip connections at each level. The output layer outputs a voxel-by-voxel bubble assignment probability map.

[0018] The set of bubble shape parameters is composed of the coefficients of spherical harmonic functions extracted from each connected bubble region. The anisotropy index is defined as the ratio of the maximum to the minimum length of the three principal axes of the bubble, which is obtained by principal component analysis of the bubble voxel coordinate set.

[0019] The creep prediction model adopts a dual-stream parallel coding architecture. The first stream uses a temporal convolutional network to extract local features from short-term stress relaxation signals, while the second stream uses a bidirectional long short-term memory network to perform global temporal modeling of medium- and long-term creep curves. The features from the two streams are fused through a cross-attention mechanism.

[0020] The creep prediction model incorporates a physical condition location encoding module at its top layer. This module generates a physical condition location encoding vector using temperature, crosslinking density, and vinyl acetate content as conditional variables. A time-temperature superposition shift factor is embedded in the network as a learnable scalar parameter.

[0021] In the creep prediction model, a Monte Carlo random deactivation strategy is used to output confidence intervals during inference. The internal iterative feedback loop re-encodes the predicted long-term creep curve and feeds it back to the initial hidden state of the long short-term memory network for refined prediction.

[0022] In the creep prediction model training process, a creep prediction dynamic learning rate adjustment function is used. The comprehensive adjustment index is calculated based on three data: the Huber loss of the validation set in the current training round, the current confidence interval coverage, and the gradient norm of the learnable parameters of the current time-temperature superimposed shift factor. The learning rate is then adjusted according to the interval of the comprehensive adjustment index.

[0023] Among them, the flow matching reverse design algorithm models the recipe reverse design as a conditional flow matching problem. The flow field is parameterized by a neural network, and the training objective is to minimize the mean square error between the predicted flow velocity and the reference flow velocity derived from the optimal transport theory.

[0024] Among them, the flow matching reverse design algorithm embeds the physical feasible region of the recipe as a hard boundary in the flow field. The flow matching on the Riemann manifold ensures that the generated recipe is always within the physical feasible region. In the inference stage, a fourth-order Runge-Kutta-Dormand solver is used to numerically integrate the flow field of the ordinary differential equation.

[0025] The preset creep rate threshold is obtained by preparing gel content gradient samples with a basic formula, conducting compression creep experiments for a specified duration at a specified temperature, and determining the average creep rate field value corresponding to the compression permanent deformation rate being exactly equal to the compression permanent deformation rate threshold as the preset creep rate threshold. This process is repeated multiple times to obtain the arithmetic mean value.

[0026] The basic formulation includes an ethylene-vinyl acetate copolymer with a vinyl acetate content of 18%–28%, dicumyl peroxide at 1.0–2.5 parts by weight, azodicarbonamide at 3.0–6.0 parts by weight, zinc oxide at 1.0–3.0 parts by weight, stearic acid at 0.5–1.5 parts by weight, silica at 5.0–15.0 parts by weight, and triallyl isocyanurate at 0.5–2.0 parts by weight. The mixing temperature is 100–120℃, the mixing time is 8–12 minutes, and the discharge temperature does not exceed 125℃. The high-throughput response surface methodology scanning temperature is also specified. The temperature range is 155–175℃, and the time range is 8–20 minutes; the target gel content is 75%, and the target compression set is 30%; the anisotropy threshold is determined by statistically analyzing the correlation between the anisotropy index and the finite element simulation prediction error, with the mean anisotropy index corresponding to the first time the finite element simulation prediction error exceeds 15% as the standard; the preset confidence width threshold is 50% of the mean width of the long-term prediction confidence interval after the Williams-Landel-Ferry equation is superimposed on temperature; the compression set threshold is 25%, and the preset creep rate threshold is repeated 3 times and the arithmetic mean is taken.

[0027] This invention solves the technical problem that traditional methods cannot accurately capture the creep behavior of cross-linked networks under high-temperature multi-field coupling conditions by constructing a process parameter screening mechanism that combines high-throughput response surface experiments with non-equilibrium statistical mechanics creep rate field algorithm.

[0028] This invention utilizes 3D cell reconstruction and shape parameterization models to quantitatively describe the 3D anisotropic morphology of cells, overcoming the prediction bias caused by underestimating cell non-uniformity in 2D cross-sectional analysis. This allows the creep prediction model to obtain physically meaningful morphological feature inputs. The invention employs a dual-stream parallel coding architecture for the creep prediction model, integrating short-term stress relaxation local features with medium- to long-term creep global features. Furthermore, it embeds prior information such as temperature and crosslinking density into the network through physical condition location coding, achieving accurate extrapolation of long-term creep behavior across formulations and temperature conditions.

[0029] In summary, this invention solves the technical problems mentioned in the background art, namely, the excessively high high-temperature compression permanent deformation rate of EVA foam shoe sole materials and the lack of closed-loop quantitative prediction and reverse design capabilities from formulation design to process optimization. Attached Figure Description

[0030] Figure 1 This is a flowchart of the method of the present invention.

[0031] Figure 2 The Pareto front and optimal process parameter distribution diagram for response surface methodology.

[0032] Figure 3 A visualization of the 3D reconstruction of the bubble structure and the anisotropy index.

[0033] Figure 4 The image shows the long-term creep prediction curve and 95% confidence interval plot output by the creep prediction model.

[0034] Figure 5 This is a comparison chart of the compression creep curves of the experimental example and the comparative example at 60℃.

[0035] Figure 6 Generate a diagram showing the relationship between recipe distribution and performance condition vector constraints for the flow matching reverse design algorithm. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0037] like Figure 1 The diagram shown is a flowchart of a method for reducing high-temperature compression deformation of EVA foam shoe sole material provided by the present invention. This method includes the following steps:

[0038] S01. Mix the components according to the basic formula and then plasticize them in an internal mixer to obtain the compounded rubber.

[0039] S02. High-throughput response surface methodology was used to scan the three-dimensional parameter space of temperature, time and dicumyl peroxide dosage on a flat vulcanizing machine matrix experimental platform. Pareto front was constructed with gel content and compression set as dual objectives to determine the positive vulcanization window and optimize process parameters.

[0040] S03. Input the preferred process parameters obtained in step S02 into the non-equilibrium statistical mechanical creep rate field algorithm to obtain the creep rate field distribution result; according to the comparison result between the creep rate field average value and the preset creep rate threshold, if the creep rate field average value exceeds the preset creep rate threshold, return to step S02 to adjust the parameters, otherwise proceed to step S04.

[0041] S04. Perform micro-computed tomography on the sample prepared under the preferred process parameters obtained in step S02, and reconstruct the three-dimensional morphology of the bubble using three-dimensional bubble reconstruction and shape parameterization model, and extract the bubble shape parameter set and anisotropy index; if the anisotropy index exceeds the preset anisotropy threshold, adjust the mold flow channel size or injection direction and re-prepare the sample, otherwise proceed to step S05.

[0042] S05. Perform multi-temperature short-time compression creep experiments on the samples obtained in step S04. Input the creep experiment data and the set of bubble shape parameters obtained in step S04 into the creep prediction model and output a long-time creep prediction curve with a 95% confidence interval. If the confidence interval width exceeds the preset confidence width threshold, increase the number of experimental temperature points and re-collect data; otherwise, proceed to step S06.

[0043] S06. The long-term creep prediction curve obtained in step S05 is matched with the input flow of the cell shape parameter set obtained in step S04 to design an inverse algorithm, and an optimized formula is generated under the conditions of target compression set and target springback. The optimized formula is verified by sample preparation and compression set test to complete the closed-loop verification.

[0044] The basic formulation is based on 100 parts by weight of ethylene-vinyl acetate copolymer, and the components and their parts by weight are as follows: 100 parts by weight of ethylene-vinyl acetate copolymer (vinyl acetate content 18%–28%), 1.0–2.5 parts by weight of dicumyl peroxide, 3.0–6.0 parts by weight of azodicarbonamide, 1.0–3.0 parts by weight of zinc oxide, 0.5–1.5 parts by weight of stearic acid, 5.0–15.0 parts by weight of silica, and 0.5–2.0 parts by weight of triallyl isocyanurate. All components are mixed in an internal mixer at 100–120°C for 8–12 minutes, and then discharged at a discharge temperature not exceeding 125°C.

[0045] The high-throughput response surface methodology (RSM) experimental design combines RSM with Taguchi orthogonal design, with a scanning temperature range of 155–175 °C, a time range of 8–20 minutes, and a dicumyl peroxide (DPO) dosage range of 1.0–2.5 parts by mass. The Pareto front is obtained through multi-objective optimization of the RSM fitting data using a non-dominated sorting genetic algorithm. The objective function is a gel content higher than 75% and a compression set lower than 30%. The positive vulcanization window is the parameter combination region in the three-dimensional parameter space of temperature-time-DPO, where the crosslinking and foaming reactions proceed synergistically, the cell structure is intact, and both gel content and compression set simultaneously meet the target values. The preferred process parameters are the combination of temperature, time, and DPO dosage on the Pareto front that achieves the optimal balance between gel content and compression set.

[0046] The preset creep rate threshold is obtained by preparing a gel content gradient sample with the basic formula, conducting a 100-hour compression creep experiment at 60°C, and determining the average creep rate corresponding to when the compression permanent deformation rate is exactly equal to 25% as the preset creep rate threshold. This process is repeated 3 times and the arithmetic mean is taken.

[0047] The non-equilibrium statistical mechanics creep rate field algorithm is based on the Onsager linear irreversible thermodynamic framework, describing the high-temperature creep of the ethylene-vinyl acetate copolymer crosslinked network as a process of minimizing entropy generation rate. An Onsager coefficient matrix is ​​constructed between generalized forces (temperature gradient, stress gradient, chemical potential gradient) and generalized flows (heat flow, deformation rate, crosslinking density change rate), and this matrix satisfies... This significantly reduces the number of independent parameters. The algorithm discretizes the creep equation into a finite volume format and minimizes the global entropy generation functional within each computational unit under the constraint that the local entropy generation rate is greater than or equal to zero, thereby obtaining the optimal creep rate field distribution. The iterative solution employs the block-based preconditioned conjugate gradient method. The technical effects of the non-equilibrium statistical mechanics creep rate field algorithm are as follows: it automatically captures the thermo-mechanical-chemical multi-field coupling effect of the cross-linked network through a rigorous thermodynamic framework, avoiding the systematic bias introduced by the artificial assumption of the creep exponent in the traditional power-law creep model; the symmetric positive definiteness of the Onsager coefficient matrix ensures stable convergence of the iteration; and it provides a physically consistent benchmark creep rate field for the creep prediction model, making the creep prediction results of the entire scheme thermodynamically self-consistent.

[0048] The 3D reconstruction and shape parameterization model (TSRM model) of the bubble pores is used for 3D segmentation and parameterized description of bubble pore morphology in micro-computed tomography images. The specific structure of the TSRM model is as follows: the encoder employs a five-level downsampling path composed of 3D residual convolutional units, with each level containing two 3D convolutional layers (kernel size...). The encoder employs a batch normalization layer with channel numbers of 16, 32, 64, 128, and 256, respectively. The decoder uses a symmetrical five-level upsampling path, with each level containing a 3D transposed convolutional layer and skip connections. The corresponding level feature maps from the encoder and decoder are concatenated along the channel dimension and then fed into two 3D convolutional layers. The output layer is... The convolutional layer is activated by a Sigmoid function, outputting a voxel-by-voxel cell assignment probability map. Based on the segmentation results, spherical harmonic function coefficients of orders 0 to 4 (25 in total) are extracted from each connected cell region to form a cell shape parameter set. The anisotropy index is defined as the ratio of the maximum to minimum lengths of the three principal axes of the cell, obtained by principal component analysis of the cell voxel coordinate set. The specific steps for establishing the training dataset of the TSRM model include: collecting 50 groups of ethylene-vinyl acetate copolymer foaming samples under different formulations and process conditions, and cutting out samples from each group. Samples with 3-5 High-resolution computed tomography (CT) scans were performed. Three professionals independently annotated the bubble boundaries of each image set, and the intersection of their annotations was used as the final label. Data augmentation methods included random rotation (0–360°), random flipping (independent on all three axes), and random elastic deformation (deformation amplitude of 0–2 voxel sizes). The TSRM model training steps specifically included: using the Adam optimizer with an initial learning rate of 0.001, multiplied by 0.5 every 20 rounds; the loss function was a weighted sum of Dice loss and cross-entropy loss, with a weight ratio of 7:3; the input sub-block size was… The voxels are set to a batch size of 2; the training rounds are 200, with early stopping conditioned on a Dice coefficient on the validation set not increasing for 10 consecutive rounds; during inference, a sliding window strategy is used to infer and stitch together the complete 3D image block by block. The technical benefits of the TSRM model to the solution are as follows: 3D semantic segmentation completely restores the anisotropic 3D morphology of the bubble ellipsoid, eliminating the prediction bias of the finite element model introduced by the underestimation of bubble non-uniformity in the 2D section; the spherical harmonic function coefficients describe the 3D bubble geometry with high fidelity using a small number of parameters, providing physically meaningful morphological feature inputs for the flow matching reverse design algorithm, and establishing a quantitative correspondence between the formulation optimization results and the bubble structure.

[0049] The preset anisotropy threshold is obtained by performing micro-computed tomography and uniaxial compression finite element simulation on 20 samples prepared under different process conditions, statistically analyzing the correlation between the anisotropy index and the finite element simulation prediction error, and determining the mean anisotropy index corresponding to the first time the finite element simulation prediction error exceeds 15% as the preset anisotropy threshold.

[0050] The creep prediction model (TA-TCN model) is used to fuse multi-temperature short-time compression creep experimental data with a set of bubble shape parameters, outputting a long-time creep prediction curve with a 95% confidence interval. The specific structure of the TA-TCN model is as follows: the model adopts a dual-stream parallel coding architecture. The first stream uses a temporal convolutional network to extract local features from the 0-100 second short-time stress relaxation signal. The temporal convolutional network consists of 6 causal dilated convolutional layers with a kernel size of 3 and dilation coefficients of [missing information]. Each layer has 64 channels, and each subsequent layer is normalized and ReLU activated. The second stream uses a three-layer bidirectional long short-term memory network to perform global temporal modeling of the medium-to-long-term creep curve from 100 to 10000 seconds. Each layer has 128 hidden units, and the bidirectional outputs are concatenated along the time dimension to have a dimension of 256. The features from both streams are fused through a cross-attention mechanism. The local features output by the temporal convolutional network are used as the query, and the global hidden states of the long short-term memory network are used as the key and value. The attention weight matrix has a dimension of [missing information]. After scaling dot product attention calculation, the output fused feature vector is 128-dimensional. The top layer of the network embeds a physical conditional location encoding module, using temperature, crosslinking density, and vinyl acetate content as conditional variables. This module generates a physical conditional location encoding vector through a three-layer fully connected network (dimensions 32, 64, and 128 respectively), which is then element-wise added to the fused feature vector before being fed into the output layer. The output layer is a two-layer fully connected network (dimensions 64 and 1 respectively), outputting normalized creep strain prediction values. An internal iterative feedback loop re-encodes the predicted long-term creep curve and feeds it back to the initial hidden state of the Long Short-Term Memory network for refined prediction, iterating a maximum of 3 times, with Huber loss used to measure iterative convergence. A time-temperature superposition shift factor is embedded in the network as a learnable scalar parameter, participating in the physical conditional location encoding calculation along with the temperature conditional variable. During inference, Monte Carlo random deactivation (random deactivation probability of 0.1, sampling count of 100 times) is used to provide a 95% confidence interval. The specific design of the TA-TCN model in terms of resource allocation is as follows: the dilation coefficient of the temporal convolutional network... to The first three layers are allocated to CUDA stream 0 of the first graphics processing unit, with an expansion coefficient. to The last three layers are allocated to CUDA stream 1 of the second graphics processing unit (GPU), and the computation results of the two streams are directly transferred and merged through point-to-point memory transfer. The forward and backward computations of the bidirectional long short-term memory network are allocated to CUDA streams 2 and 3 of the two GPUs, respectively. The calculations of the query matrix and key-value matrix across the attention mechanism are executed in parallel on the two GPUs, and the attention weight matrix is ​​normalized and weighted summed on the first GPU. The hidden state of the long short-term memory network in the internal iterative feedback loop is cached in a fixed memory area of ​​the GPU and is not released between iterations. The 100 samples of Monte Carlo random deactivation are grouped into batches of 20 and executed alternately on the two CUDA streams, and the sampling results are accumulated and stored in the host memory. The GPU memory allocation ratio (temporal convolutional network: long short-term memory network: cross-attention mechanism: iterative feedback cache: Monte Carlo buffer) is 3:3:2:1:1, and the ratio is determined by statistically analyzing the peak memory sampling of each module every 10 rounds during training. When the number of experimental temperature points in step S05... When changes occur, the memory allocation ratio across attention mechanism modules is adjusted according to the following formula:

[0051] ;

[0052] in Allocate memory (units) for cross-attention mechanism modules ), Total available video memory for graphics processing units (in units) ), The number of reference temperature points (value is 5). The number of actual experimental temperature points in step S05 is adjusted, and the remaining modules are compressed proportionally according to the original ratio. The specific steps for establishing the training dataset of the TA-TCN model include: collecting foamed samples of ethylene-vinyl acetate copolymer with a vinyl acetate content of 18% to 28% and a dicumyl peroxide content of 1.0 to 2.5 parts by mass; conducting compression creep experiments for 0.1 to 10000 seconds at 40 to 80℃ (5 temperatures in 10℃ intervals); the sampling frequency for the 0 to 100 second segment is 10Hz, and the sampling frequency for the 100 to 10000 second segment is 0.1Hz; each formulation is repeated 3 times at each temperature and the average value is taken; the dataset contains no less than 200 formulation condition combinations and a total of no less than 600 creep curves; the creep strain value is normalized by dividing by the initial strain, and the time axis is normalized to the 0 to 1 interval after taking the logarithm to the base 10. The specific training steps of the TA-TCN model include: using the AdamW optimizer with an initial learning rate of 0.0005 and a weight decay coefficient of 0.01; training for 500 epochs, with the early stopping condition being that the root mean square error of the verification set does not decrease for 20 consecutive epochs; a batch size of 32; setting the gradient update step size of the learnable parameters of the time-temperature superimposed shift factor to 0.1 times the step size of the other parameters; and using the total loss function as the sum of the Huber loss and the confidence interval coverage penalty term, with the confidence interval coverage penalty term taking a positive value when the coverage is below 95%. The technical benefits of the TA-TCN model are as follows: the dual-stream parallel coding architecture simultaneously captures the local fast dynamic features of short-term stress relaxation and the global slow dynamic features of medium- to long-term creep curves; the cross-attention mechanism enables adaptive fusion of the two types of time-scale information in the feature space; the physical condition location coding enables the network to have prior perception of the differences in creep time-scales of different formulations, and can still accurately extrapolate creep behavior across formulations and temperatures even with limited training data; the 95% confidence interval of the Monte Carlo random inactivation output provides a quantitative basis for engineering reliability decisions, effectively making up for the shortcomings of the traditional time-temperature equivalence principle in nonlinear viscoelastic crosslinking systems with excessively wide confidence intervals.

[0053] The method for obtaining the preset confidence width threshold is as follows: compression creep experiments are conducted on 10 groups of gel content gradient samples at 5 temperatures. The mean of the long-term prediction confidence interval width is calculated by superimposing the time and temperature using the Williams-Landel-Ferry equation. 50% of the mean value is used as the preset confidence width threshold, and the consistency is verified by repeating the experiment twice.

[0054] To adjust the learning rate during the training process of the TA-TCN model, a creep prediction dynamic learning rate adjustment function is designed. This creep prediction dynamic learning rate adjustment function is based on the Huber loss of the validation set in the current training round. Current confidence interval coverage The gradient norm of the learnable parameter of the shift factor superimposed with the current time temperature The comprehensive adjustment index is calculated from three data points. The formula is expressed as follows:

[0055] ;

[0056] in Huber loss for the initial validation set (units) same), The initial gradient norm (unit: ) same), and These are dimensionless weighting coefficients. Take 1.5, The value is set to 0.5, determined by performing a grid search on 20 sets of training curves. When, the learning rate is multiplied by 0.5; when When the learning rate remains constant; when When, the learning rate is multiplied by 1.2; when At that time, the learning rate is multiplied by 1.5 and the gradient update step size of the learnable parameters of the time-temperature superimposed shift factor is restored to the same step size as the other parameters.

[0057] The flow-matching reverse design algorithm models the reverse design of the ethylene-vinyl acetate copolymer formulation as a conditional flow-matching problem. A performance condition vector is constructed using the target compression set, target springback rate, and the set of cell shape parameters obtained in step S04. The algorithm learns the optimal transport flow field from a standard normal distribution to a formulation distribution that satisfies the performance constraints. The flow field is generated by a neural network. Parameterization, where For the recipe vector, For the streaming time (value range 0 to 1). The performance condition vector is used for training. The training objective is to minimize the mean square error between the predicted flow velocity and the reference flow velocity derived from the optimal transport theory. A physical feasible region (constraints on the amount of each component and stoichiometry) is embedded in the flow field as a hard boundary. Flow matching on the Riemann manifold ensures that the generated formula always remains within the physical feasible region. During the inference phase, a fourth-order Runge-Kutta-Dormand solver is used to numerically integrate the flow field of the ordinary differential equations, generating an optimized formula that satisfies the performance condition vector constraints from standard normal noise in 10 steps. The technical benefits of the flow matching reverse design algorithm are as follows: by learning a continuous deterministic flow field from the noise distribution to the feasible formula distribution, the accumulated error from multi-step random denoising is avoided, resulting in higher physical feasibility of the generated formula under the constraints of the physical feasible region; flow matching on the Riemann manifold naturally satisfies the non-negativity of the amount of each component and the stoichiometry constraints during the generation process, eliminating the need for post-processing corrections; and incorporating the cell shape parameter set into the performance condition vector allows the reverse design to simultaneously constrain mechanical properties and cell morphology, achieving an end-to-end closed-loop design from performance objectives to formula composition.

[0058] Optionally, the present invention also provides a method system for reducing high-temperature compression deformation of ethylene-vinyl acetate copolymer foamed shoe sole material by means of a computer, wherein the computer is provided with a readable storage medium, the readable storage medium storing program instructions, and the program instructions can execute the above method when running in the computer.

[0059] The specific implementation method of step S01 is as follows: Ethylene-vinyl acetate copolymer, dicumyl peroxide, azodicarbonamide, zinc oxide, stearic acid, silica, and triallyl isocyanurate are weighed according to the basic formula and added to an internal mixer, and mixed at 100-120°C for 8-12 minutes. During the mixing process, the rotor shearing action of the internal mixer ensures that each component is uniformly dispersed in the ethylene-vinyl acetate copolymer matrix. The addition of silica and triallyl isocyanurate helps to improve the density of the subsequent crosslinking network. The discharge temperature must be strictly controlled not to exceed 125°C to avoid premature decomposition of dicumyl peroxide and azodicarbonamide during the mixing stage, ensuring that the chemical activity of the mixed rubber compound remains intact.

[0060] The specific implementation of step S02 is as follows: Using a response surface methodology combined with Taguchi orthogonal design as the experimental design framework, a systematic scan of the parameter space was conducted on a flat vulcanizing machine matrix experimental platform, focusing on three dimensions: temperature (155–175°C), time (8–20 minutes), and dicumyl peroxide dosage (1.0–2.5 parts by mass). After each experiment, the gel content and compression set were measured. The response surface methodology was used to fit the experimental data using a second-order polynomial to establish a surrogate model of gel content and compression set with respect to the three-dimensional parameters. Subsequently, a non-dominated sorting genetic algorithm was used to optimize the surrogate model using multiple objectives. The objective function was set to a gel content higher than 75% and a compression set lower than 30%, outputting the Pareto front. The positive vulcanization window was defined as the parameter combination region in the three-dimensional parameter space where crosslinking and foaming reactions proceeded synergistically, the cell structure was intact, and both objectives were simultaneously satisfied. The optimal process parameters were selected from the combination of temperature, time, and dicumyl peroxide dosage at the Pareto front, which provided the comprehensive best results.

[0061] The specific implementation of step S03 is as follows: The optimized process parameters obtained in step S02 are used as input and fed into the non-equilibrium statistical mechanics creep rate field algorithm for thermodynamic self-consistency verification. This algorithm, based on the Onsager linear irreversible thermodynamic framework, describes the creep behavior of the ethylene-vinyl acetate copolymer crosslinked network at high temperatures as a process of minimizing entropy generation rate. The algorithm constructs an Onsager coefficient matrix between temperature gradient, stress gradient, chemical potential gradient (generalized force), and heat flux, deformation rate, and crosslinking density change rate (generalized flow). This matrix satisfies the symmetric positive definite condition, thereby significantly reducing the number of independent parameters and ensuring stable convergence of the iteration. The creep equation is discretized into a finite volume scheme. Within each computational unit, the global entropy generation functional is minimized under the thermodynamic constraint that the local entropy generation rate is greater than or equal to zero. The block-preconditioned conjugate gradient method is used for iterative solution, and the creep rate field distribution result is finally output. If the average creep rate exceeds the preset creep rate threshold (reference value: the average creep rate corresponding to when the compression permanent deformation rate is exactly 25%, repeated 3 times and the arithmetic mean is taken), then return to step S02 to adjust the parameters; otherwise, proceed to step S04.

[0062] The specific implementation of step S04 is as follows: cut the sample prepared under the preferred process parameters in step S02. Samples, with 3 to 5 High-resolution computed tomography (CT) scans were performed. The scanned images were then input into a 3D bubble reconstruction and shape parameterization model for processing. The encoder of this model consists of a five-level downsampling path composed of 3D residual convolutional units, with channel numbers of 16, 32, 64, 128, and 256 respectively. The decoder employs a symmetrical five-level upsampling path, with skip connections at each level. The corresponding level feature maps from the encoder and decoder are concatenated along the channel dimension and then processed by 3D convolution. The output layer is activated by a sigmoid function to output a voxel-by-voxel bubble assignment probability map, achieving 3D semantic segmentation. Based on the segmentation results, 25 spherical harmonic function coefficients (0-4 orders) are extracted from each connected bubble region to form a bubble shape parameter set, providing a high-fidelity description of the 3D bubble geometry. The anisotropy index is defined as the ratio of the maximum to minimum lengths of the three principal axes of the bubble, obtained through principal component analysis of the bubble voxel coordinate set. If the anisotropy index exceeds the preset anisotropy threshold (reference value: the average anisotropy index corresponding to the first time the finite element simulation prediction error exceeds 15%), then adjust the mold flow channel size or injection direction and re-make the sample; otherwise, proceed to step S05.

[0063] The specific implementation of step S05 is as follows: Short-time compression creep experiments are conducted on the samples obtained in step S04 at multiple temperature points (reference range 40–80℃, 5 temperature points with 10℃ intervals). The sampling frequency is 10Hz for the 0–100 second segment and 0.1Hz for the 100–10000 second segment. Each temperature is repeated 3 times, and the average value is taken. The creep experiment data and the bubble shape parameter set obtained in step S04 are input into the creep prediction model. This model adopts a dual-stream parallel coding architecture: the first stream uses a temporal convolutional network to extract local features from the 0–100 second short-time stress relaxation signal, consisting of 6 causal dilated convolutional layers with dilation coefficients as follows: to The second stream uses a bidirectional long short-term memory network to perform global temporal modeling of medium- to long-term creep curves ranging from 100 to 10,000 seconds; the features of the two streams are adaptively fused through a cross-attention mechanism. The top-level physical condition location encoding module embeds temperature, crosslinking density, and vinyl acetate content into the network, with the time-temperature superposition shift factor used as a learnable scalar parameter in the location encoding calculation. During inference, Monte Carlo random deactivation (random deactivation probability of 0.1, 100 samplings) is used to output a long-term creep prediction curve with a 95% confidence interval. If the confidence interval width exceeds the preset confidence width threshold (reference value: 50% of the average width of the long-term prediction confidence interval after time-temperature superposition in the Williams-Landel-Ferry equation), the number of experimental temperature points is increased and data is re-acquired.

[0064] The specific implementation of step S06 is as follows: The long-term creep prediction curve obtained in step S05 is input into a flow matching reverse design algorithm with the pore shape parameter set obtained in step S04. This algorithm uses the target compressive set rate, target springback rate, and pore shape parameter set to form a performance condition vector, modeling the formulation reverse design as a conditional flow matching problem. It parameterizes the optimal transport flow field from a standard normal distribution to a formulation distribution that satisfies performance constraints through a neural network. The training objective is to minimize the mean square error between the predicted flow velocity and the reference flow velocity derived from the optimal transport theory. The algorithm applies hard boundary constraints (the range of component dosages and stoichiometry constraints) to the Riemannian manifold to ensure that the generated formulation naturally satisfies the non-negativity and stoichiometry requirements. In the inference stage, a fourth-order Runge-Kutta-Dormand solver is used to numerically integrate the ordinary differential equation flow field, generating an optimized formulation that satisfies the performance condition vector constraints from standard normal noise in 10 steps. Finally, the optimized formulation is validated through sample preparation and compressive set testing to complete the closed-loop validation.

[0065] It should be noted that the key technologies of this invention include: the non-equilibrium statistical mechanics creep rate field algorithm is based on the Onsager linear irreversible thermodynamic framework. By constructing a generalized force-generalized flow coefficient matrix that satisfies the symmetric positive definite condition, it rigorously captures the high-temperature multi-field coupling effect from a physical perspective, avoiding the systematic bias introduced by the artificial assumption of the creep exponent in the traditional power-law creep model, while ensuring the stable convergence of the iterative solution; the three-dimensional reconstruction and shape parameterization model of the bubble cavity transforms the three-dimensional anisotropic morphology of the bubble cavity into a quantitative feature with clear physical meaning through three-dimensional semantic segmentation and spherical harmonic function coefficient extraction. This eliminates the prediction bias caused by the underestimation of the non-uniformity of the bubble cavity in two-dimensional cross-section analysis, providing quantitative morphological input for creep prediction models and reverse design algorithms. The dual-stream parallel creep prediction model captures short-term local fast dynamics and medium-to-long-term global slow dynamics through a temporal convolutional network and a bidirectional long short-term memory network, respectively. The cross-attention mechanism enables the adaptive fusion of the two types of information in the feature space. The physical condition location encoding gives the network the ability to perceive the differences in creep time scales of different formulations, thereby achieving accurate extrapolation of long-term creep behavior across formulations and temperature conditions. The synergistic effect of the three is that the creep rate field algorithm provides a thermodynamically self-consistent reference rate field for the creep prediction model, the bubble shape parameter set provides morphological constraints for creep prediction and reverse design, and the output curve of the creep prediction model drives the flow matching reverse design algorithm to generate optimized formulations that meet the constraints, ultimately forming a complete closed loop from process parameters to formulation composition.

[0066] It should be noted that under high temperature and long-term compression conditions, EVA foam shoe soles are subjected to the superposition effect of creep at multiple temperature points and under multiple formulation conditions. Moreover, the creep data at each temperature point is often limited in quantity due to high acquisition costs. This results in the traditional time-temperature equivalence principle having an excessively wide prediction confidence interval in nonlinear viscoelastic crosslinking systems, and engineering decisions lacking a reliable quantitative uncertainty basis.

[0067] The above technical problem arises because the creep behavior of the ethylene-vinyl acetate copolymer crosslinking system exhibits obvious nonlinear viscoelastic characteristics at different temperatures. The construction of the time-temperature superposition master curve relies on the linear assumption of the Williams-Landel-Ferry equation. However, the creep mechanism of actual materials changes over a wide temperature range, causing the shift factor to deviate from the linear prediction. Consequently, the confidence interval of the long-term extrapolation curve expands sharply as the prediction time increases, ultimately failing to meet the accuracy requirements of engineering reliability decision-making.

[0068] To address the aforementioned technical issues, common solutions include increasing the number of experimental temperature points to broaden the coverage of time-temperature superposition, or employing more complex viscoelastic constitutive models (such as the generalized Maxwell model) to fit the creep data. However, increasing the number of experimental temperature points significantly increases experimental costs and time; the number of parameters in the generalized Maxwell model increases dramatically with the dispersion of the relaxation time spectrum, making it prone to overfitting when training data is limited, and neither model can incorporate the three-dimensional morphology information of the cells into the prediction framework, resulting in insufficient cross-formulation extrapolation capabilities.

[0069] This invention effectively solves this technical problem. The creep prediction model directly embeds prior physical information such as temperature, crosslinking density, and vinyl acetate content into the network structure through physical condition location encoding. This enables the model to have prior perception of the differences in creep timescales of different formulations, and can still achieve accurate extrapolation across formulations and temperature conditions even with limited training data. The Monte Carlo random deactivation strategy applies random perturbations to the network weights and samples multiple times to statistically quantify the uncertainty of the model prediction, outputting a long-term creep prediction curve with a 95% confidence interval. This effectively compensates for the shortcomings of the traditional time-temperature equivalence principle in nonlinear viscoelastic crosslinking systems, which has an excessively wide confidence interval. At the same time, the introduction of the cell shape parameter set enables the creep prediction framework to quantitatively distinguish the contribution of different cell three-dimensional morphologies to creep behavior, further improving the accuracy of cross-formulation prediction, thereby providing a quantitative uncertainty basis for engineering reliability decisions.

[0070] Specifically, the principle of this invention is:

[0071] The fundamental reason why this invention can solve the above-mentioned core technical problems is that it constructs a complete quantitative mapping chain from material formulation, process parameters, cell morphology to creep behavior, and on this basis realizes a reverse closed-loop design from performance target to formulation composition.

[0072] First, at the level of process parameter optimization, traditional methods only establish the formula-performance relationship at a single temperature point, failing to reflect the complex nonlinear characteristics of the parameter space when crosslinking and foaming reactions occur synergistically at high temperatures. This invention employs a response surface methodology combined with a multi-objective genetic algorithm to construct a Pareto front in a three-dimensional parameter space. This ensures that the two mutually constraining objectives of gel content and compression set simultaneously meet engineering requirements, fundamentally avoiding performance imbalances caused by single-objective optimization. Building upon this, a non-equilibrium statistical mechanics creep rate field algorithm is introduced. Based on the Onsager linear irreversible thermodynamic framework, high-temperature creep is described as a process of minimizing entropy generation rate. By constructing a symmetric positive definite Onsager coefficient matrix between generalized forces and generalized flows, the thermo-mechanical-chemical multi-field coupling effect is rigorously captured. This ensures the thermodynamic self-consistency of the creep rate field distribution results from a physical perspective, avoiding the systematic bias introduced by the artificial assumption of creep exponents in traditional power-law models.

[0073] Secondly, in terms of cell morphology characterization, traditional two-dimensional cross-sectional analysis can only obtain the statistical mean of cell size, failing to reconstruct the three-dimensional anisotropic ellipsoidal morphology of the cells. This invention utilizes three-dimensional cell reconstruction and a shape parameterization model to perform three-dimensional semantic segmentation on micro-computed tomography images, extracting spherical harmonic function coefficients to construct a cell shape parameter set, and using the anisotropy index as a process feedback control index. The introduction of three-dimensional cell morphology information eliminates the finite element prediction bias caused by the underestimation of cell non-uniformity in two-dimensional cross-sections, providing physically meaningful morphological feature inputs for subsequent creep prediction models and reverse design algorithms, thus establishing a quantitative correspondence between the formulation optimization results and the cell structure.

[0074] Furthermore, in terms of long-term creep prediction, the traditional time-temperature equivalence principle has an excessively wide confidence interval in nonlinear viscoelastic crosslinking systems, making it difficult to provide a reliable basis for engineering decisions. This invention employs a dual-stream parallel coding creep prediction model, using a temporal convolutional network to capture local fast dynamic features of short-term stress relaxation and a bidirectional long short-term memory network to capture global slow dynamic features of medium- to long-term creep. The two types of time-scale information are then adaptively fused through a cross-attention mechanism. The physical condition location coding module embeds prior information such as temperature, crosslinking density, and vinyl acetate content into the network, enabling the model to accurately extrapolate creep behavior across formulations and temperatures even with limited training data. A Monte Carlo random deactivation strategy outputs a long-term creep prediction curve with a 95% confidence interval, providing quantitative uncertainty basis for engineering reliability decisions.

[0075] Finally, at the reverse design level, traditional forward testing cannot automatically generate optimized formulations that meet constraints based on target performance. This invention employs a flow-matching reverse design algorithm, modeling the formulation reverse design as a conditional flow-matching problem. By learning the optimal transport flow field from a standard normal distribution to a formulation distribution that meets performance constraints, and applying hard boundary constraints on the formulation's physical feasible region on the Riemannian manifold, it ensures that the generated formulation naturally satisfies the non-negativity of each component's dosage and stoichiometric constraints, thus achieving an end-to-end closed-loop design from performance target to formulation composition.

[0076] The above four levels are interconnected, forming a complete technical closed loop from process optimization, morphology characterization, creep prediction to formula reverse design. Therefore, it can fundamentally solve the core technical problem of EVA foam shoe sole material having too high high temperature compression permanent deformation rate and lacking closed-loop quantitative prediction and reverse design capabilities.

[0077] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0078] The specific implementation method of step S01 is as follows: Based on 100 parts by weight of ethylene-vinyl acetate copolymer, 1.0-2.5 parts by weight of dicumyl peroxide, 3.0-6.0 parts by weight of azodicarbonamide, 1.0-3.0 parts by weight of zinc oxide, 0.5-1.5 parts by weight of stearic acid, 5.0-15.0 parts by weight of silica, and 0.5-2.0 parts by weight of triallyl isocyanurate are added sequentially. The mixture is then mixed in an internal mixer at 100-120°C for 8-12 minutes, and the discharge temperature does not exceed 125°C to obtain the compound.

[0079] The specific implementation of step S02 is as follows: using response surface methodology combined with Taguchi orthogonal design, the vulcanization temperature is scanned in a three-dimensional parameter space. (Unit: °C) Vulcanization time (unit Dosage of dicumyl peroxide (per unit mass portion), the gel content of samples at each experimental point was determined separately. (Unit: %) and compressive permanent deformation rate (Unit: %), after fitting the response surface model, the following multi-objective optimization problem is solved using a non-dominated sorting genetic algorithm:

[0080] ;

[0081] In the formula, The reference value for the compression permanent deformation rate is 30%. The gel content reference value is 75%; both target items, divided by their corresponding reference values, are dimensionless; the constraints are as follows: and The non-dominated sorting genetic algorithm iteratively sorts the response surface fitting data to obtain the Pareto front, and selects the most suitable data from the Pareto front. and The optimal combination of parameters As preferred process parameters, the positive vulcanization window (i.e., the parameter combination region in the three-dimensional parameter space that simultaneously satisfies the constraint conditions and has a complete cell structure) is also determined.

[0082] The specific implementation of step S03 is as follows: Select the preferred process parameters... Input a non-equilibrium statistical mechanics creep rate field algorithm. This algorithm, based on the Onsag linear irreversible thermodynamic framework, describes the high-temperature creep of cross-linked networks as a process that minimizes the entropy generation rate. Define a generalized force vector. ,in Temperature gradient (units) ), Stress gradient (unit) ), Chemical potential gradient (units) Define the generalized flow vector. ,in Heat flux (unit) ), Deformation rate (unit) ), Crosslinking density change rate (unit) Both are obtained through the Onsager coefficient matrix. Related:

[0083] ;

[0084] In the formula, The elements of the Onsager coefficient matrix satisfy the symmetry condition. diagonal elements The unit is , The unit is , The unit is off-diagonal elements ( The units of are derived from the dimensions of the corresponding generalized flow and generalized force, and determined by experimental fitting; the positive definiteness of the matrix guarantees stable convergence of the iteration. Local entropy generation rate. (unit ) is defined as:

[0085] ;

[0086] In the formula, For the first Line number The dimension transformation coefficients of the coupling terms (obtained through experimental calibration) are used to normalize the dimensions of each coupling term. diagonal terms (Dimensionless), off-diagonal terms ( The creep equation was determined by experimental calibration. The creep equation was discretized into a finite volume scheme, and the computational domain was divided into... Each computational unit generates a functional from the global entropy. (unit )for:

[0087] ;

[0088] In the formula, For the first Unit local entropy generation rate (unit) ), For the first Unit volume (unit) ); in constraints Minimize The optimal creep rate field distribution was obtained by iteratively solving the problem using the block preconditioning conjugate gradient method. (unit ), calculate the field-average creep rate:

[0089] ;

[0090] In the formula, The creep rate is the field-averaged value (unit: ). ), For the first Unit creep rate (unit) Preset creep rate threshold (unit The method for obtaining the gel content gradient sample is as follows: A compression creep test is conducted at 60℃ for 100 hours, and the sample is obtained when the compression set is exactly 25%. The mean was determined as Repeat 3 times and take the arithmetic mean. If If the condition is met, return to step S02 to adjust the parameters; otherwise, proceed to step S04.

[0091] The specific implementation of step S04 is as follows: Perform microcomputed tomography (CT) on the sample obtained in step S02, with a resolution of 3–5. The scanned image is input into a bubble pore 3D reconstruction and shape parameterization model for 3D semantic segmentation. The encoder of this model employs a five-level 3D residual convolutional downsampling path, with each level containing two convolutional kernels of size [missing information]. The system consists of a 3D convolutional layer and a batch normalization layer, with channel numbers of 16, 32, 64, 128, and 256 respectively. The decoder employs a symmetrical five-level upsampling path, where each level uses skip connections to concatenate the corresponding level feature map from the encoder and the decoder along the channel dimension before feeding them into two 3D convolutional layers. The output layer is... Convolutional layer Activation function, outputting a voxel-by-voxel pore assignment probability map. (Dimensionless). Extract the coefficients of spherical harmonic functions from order 0 to 4 for each connected bubble region. The expansion of the spherical harmonic function is:

[0092] ;

[0093] In the formula, Radial distance function of bubble surface (units) ), Polar angle (unit) ), Azimuth (unit) ), for Step Subreal spherical harmonic basis functions (dimensionless). For the corresponding spherical harmonic coefficients (units) ), It is the order (values ​​from 0 to 4, dimensionless integers). For the number of times (values) ~ (dimensionless integers); all 25 coefficients constitute the bubble shape parameter set. Anisotropy index The coordinates of the pore voxels were obtained through principal component analysis, with the lengths of the three principal axes set as follows: (unit ),but:

[0094] ;

[0095] In the formula, It is a dimensionless quantity. and These are the maximum and minimum spindle lengths (units) among the three spindles of the bubble cavity. Preset anisotropy threshold. The dimensionless value was obtained by performing micro-computed tomography and uniaxial compression finite element simulation on 20 groups of samples, and statistically analyzing the results. With finite element simulation prediction error Correlation (in %), in When it first exceeds 15% The mean was determined as .like If the mold flow channel size or injection direction is not adjusted, the sample should be remade; otherwise, proceed to step S05.

[0096] The specific implementation method of step S05 is as follows: the sample obtained in step S04 is subjected to a temperature range of 40-80℃ (5 temperature points at 10℃ intervals) for 0.1-10000 seconds. Multi-temperature short-time compression creep test, 0–100 The segment sampling frequency is 10 100 to 10000 The segment sampling frequency is 0.1. For each formulation and temperature, the experiment was repeated three times, and the average value was taken. The creep strain value was then normalized by dividing the initial strain by the creep strain. The time axis was normalized to the 0-1 range after taking the logarithm to base 10. The creep experimental data were then compared with the cell shape parameter set. The input creep prediction model is used for long-term creep prediction. This model employs a two-stream parallel coding architecture: the first stream uses a temporal convolutional network to process values ​​from 0 to 100. The short-term stress relaxation signal consists of 6 causal dilated convolutional layers with a kernel size of 3 and dilation coefficients of [missing information]. Each layer has 64 channels; the second stream uses a three-layer bidirectional long short-term memory network to process 100 to 10000. The creep curve for medium to long durations is shown, with 128 hidden units per layer. The bidirectional outputs, after concatenation along the time dimension, have a dimension of 256. The two streams of features are fused via a cross-attention mechanism, resulting in a local feature vector output by the temporal convolutional network. (Dimensionless) as the query vector, the global hidden state of the Long Short-Term Memory network (Dimensionless) As the key vector and value vector, the scaled dot product attention is calculated as follows:

[0097] ;

[0098] In the formula, (dimension) (dimensionless) is the query matrix. (dimension) (dimensionless) is the bond matrix. (dimension) (dimensionless) is a value matrix. , , It is a learnable projection matrix (dimensionless). The dimension of the key vector is dimensionless. and All outputs are dimensionless. The output fused feature vector has a dimension of (Dimensionless); After fusion across attention mechanisms, a linear transformation yields a fused feature vector of dimension 128 (dimensionless). A physical conditional location encoding module is embedded at the top layer of the network, using temperature... (Unit: °C), Crosslinking density (unit (The content of vinyl acetate was obtained by combining swelling experiments with the Florey-Rayner equation.) (Unit: %, directly given by raw material specifications) is used as a conditional variable, and a physical conditional location encoding vector is generated through a three-layer fully connected network (dimensions are 32, 64, and 128 respectively). (Dimensionless), the normalized creep strain prediction value is fed into the output layer (two fully connected layers with dimensions of 64 and 1 respectively) after element-wise addition with the fused feature vector. (Dimensionless). Time-temperature superposition shift factor The dimensionless parameter is embedded in the network as a learnable scalar parameter, with its gradient update step size defaulting to 0.1 times that of the other parameters. It participates in the physical condition location encoding calculation along with the temperature condition variable. An internal iterative feedback loop re-encodes the predicted long-term creep curve and feeds it back to the initial hidden state of the Long Short-Term Memory network for refined prediction, iterating a maximum of 3 times. Huber loss is used to measure iterative convergence. During inference, Monte Carlo random deactivation (random deactivation probability of 0.1, sampling count of 100) is used to provide a 95% confidence interval. (Dimensionless), confidence interval width is (Dimensionless). Hubel loss during creep prediction model training. The formula is expressed as follows:

[0099] ;

[0100] In the formula, The sample size is a dimensionless positive integer. For the first Normalized creep strain prediction values ​​(dimensionless) for each sample. For the first Normalized true creep strain values ​​(dimensionless) for each sample. Let the element-wise Hubel function be the residual. (dimensionless), then: when hour ;when hour ;in The piecewise threshold (dimensionless) for the Hubel function is empirically set to 0.1. and All are dimensionless quantities. Total loss function The formula for (dimensionless) is as follows:

[0101] ;

[0102] In the formula, This represents the current confidence interval coverage (dimensionless). Target coverage (dimensionless). The denominator 1 is a dimensionless reference value, ensuring that all quantities within the parentheses are dimensionless. is a dimensionless penalty weighting coefficient, with an empirical value of 1.0; when The penalty term takes a positive value. The dynamic learning rate adjustment function is based on the Hubel loss on the validation set. (Dimensionless) Confidence Interval Coverage (Dimensionless) Gradient norm of the shift factor superimposed with time and temperature (Dimensionless) Calculation of the comprehensive adjustment index (Dimensionless), the formula is expressed as follows:

[0103] ;

[0104] In the formula, Hubel loss for the initial validation set (dimensionless, unit 1) same), The initial value of the gradient norm of the time-temperature superposition shift factor (dimensionless, unit: ...). same), This is a dimensionless weighting coefficient with a value of 1.5. The dimensionless weighting coefficient is set to 0.5. The values ​​of both were determined through a grid search of 20 training curves. The denominator 1 is a dimensionless reference value, making the terms on the right side of the formula equal to... The dimensions are unified to dimensionless; when Multiply the learning rate by 0.5; when The learning rate remains constant; when Multiply the learning rate by 1.2; when Multiply the learning rate by 1.5 and simultaneously The gradient update step size is restored to the same size as the other parameters. This applies when the number of experimental temperature points... When the (dimensionless positive integer) changes, the memory allocation ratio across attention mechanism modules is adjusted according to the following formula:

[0105] ;

[0106] In the formula, Allocate memory (units) for cross-attention mechanism modules ), Total available video memory for graphics processing units (in units) The ratio of the two is a dimensionless quantity. The number of reference temperature points (dimensionless positive integer), with a value of 5. For dimensionless ratios, all terms on the right-hand side of the formula are dimensionless, and the ratios on the left-hand side are also dimensionless. Units are standardized; after adjustment, the remaining modules are compressed proportionally to their original proportions. A preset signal width threshold is set. The dimensionless value was obtained by conducting compression creep experiments on 10 groups of gel content gradient samples at 5 different temperatures. The mean width of the long-term prediction confidence interval was statistically calculated after time-temperature superposition using the Williams-Randall-Ferry equation, and 50% of this mean was used as the threshold value. Repeat the consistency verification twice. If the number of experimental temperature points is increased, data will be collected again; otherwise, proceed to step S06.

[0107] The specific implementation of step S06 is as follows: The long-term creep prediction curve is compared with the set of bubble shape parameters. Input stream matching reverse design algorithm to target compression permanent deformation rate (Unit: %) Target rebound rate (unit %) and Constructing a performance condition vector The algorithm learns from the standard normal distribution To achieve a formulation distribution that meets performance constraints The optimal transport flow field between them, the flow field is determined by a neural network. Parameterization, where This is the formula vector (parts by mass). The flow time is dimensionless. The performance condition vector is used for training purposes.

[0108] ;

[0109] In the formula, For flow time The recipe vector (parts by mass) at time t. Predict flow rate (parts by mass) for neural networks. Reference flow rate (unit mass parts) derived from optimal transport theory. For reference flow velocity scale (unit mass fraction), all three have the same dimensions, and the difference is divided by... The quantity in parentheses is dimensionless. It is the Euclidean norm (dimensionless). For the learnable parameters (dimensionless) of the neural network, the expected value is... The internal components are dimensionless; the physical feasible region constraints (the range of each component's dosage and stoichiometry constraints) are embedded as hard boundaries in the Riemannian manifold to ensure that the generated formulation always lies within the feasible region; during the inference stage, a fourth-order Runge-Kutta-Dollmann solver is used to solve the ordinary differential equations. Numerical integration was performed to generate an optimized formulation that satisfies the performance condition vector constraints from standard normal noise through 10 steps. The obtained optimized formulation was then validated through sample preparation and compression set testing to complete closed-loop validation.

[0110] To better understand and implement this invention, the following is a specific application scenario of the invention, Example 2: To verify the effect of the invention, the technicians set up a test environment, selected ethylene-vinyl acetate copolymer (vinyl acetate content of 23%) as the matrix material, and mixed each component in an internal mixer at 110°C for 10 minutes according to step S01. The discharge temperature was controlled at 123°C to prepare the compounded rubber. Based on this, the implementation and verification of the complete process were carried out.

[0111] In step S02, technicians used a response surface methodology combined with Taguchi orthogonal design on a flat vulcanizing machine matrix experimental platform to scan the three-dimensional parameter space of temperature (155℃, 162℃, 168℃, 175℃), time (8 minutes, 12 minutes, 16 minutes, 20 minutes), and dicumyl peroxide dosage (1.0 part, 1.5 part, 2.0 part, 2.5 parts), designing a total of 64 sets of experimental conditions. After each set of experiments, the gel content and compression set were measured. The experimental results showed that the gel content ranged from 61% to 88%, and the compression set ranged from 18% to 47%. A non-dominated sorting genetic algorithm was used to perform multi-objective optimization on the response surface fitting data, constructing a Pareto front. The objective function was set to a gel content higher than 75% and a compression set lower than 30%. The final optimized process parameters were determined to be a temperature of 168℃, a time of 14 minutes, and a dicumyl peroxide dosage of 1.8 parts by mass. Figure 2 As shown, the Pareto front clearly distinguishes the trade-off between gel content and compression set, with the preferred process parameters located in the overall optimal region.

[0112] In step S03, the aforementioned preferred process parameters are input into the non-equilibrium statistical mechanics creep rate field algorithm. Based on the Onsager linear irreversible thermodynamic framework, a symmetric positive definite Onsager coefficient matrix between generalized forces and generalized flows is constructed. The functional is generated by minimizing the global entropy under a finite volume scheme, and the block preconditioned conjugate gradient method is used for iterative solution to obtain the creep rate field distribution. The calculated mean creep rate field value is... Below the preset creep rate threshold (Determined by the field-average creep rate corresponding to when the compression permanent deformation rate is exactly equal to 25%, and the arithmetic mean is taken after repeating 3 times), the optimal process parameters are determined to be thermodynamically self-consistent and proceed to step S04.

[0113] In step S04, the sample prepared under the preferred process parameters is cut. Sample, with 4 High-resolution computed tomography (CT) scans were performed. The scanned images were input into a 3D reconstruction and shape parameterization model of the bubble pores. After 3D semantic segmentation, 25 spherical harmonic function coefficients (0-4 orders) were extracted from each connected bubble pore region, forming a bubble pore shape parameter set. For example... Figure 3 As shown, the 3D reconstruction results clearly present the ellipsoidal anisotropic 3D morphology of the bubble cells, with the lengths of the three principal axes of the bubble cells being... , and The anisotropy index was calculated to be 1.11, which is lower than the preset anisotropy threshold of 1.35 (determined by the mean anisotropy index corresponding to the first time the finite element simulation prediction error exceeds 15%). Therefore, the uniformity of the bubble morphology is determined to meet the requirements, and the process proceeds to step S05.

[0114] In step S05, compression creep experiments were conducted on the samples obtained in step S04 at five temperature points: 40℃, 50℃, 60℃, 70℃, and 80℃. The sampling frequency was 10Hz for the 0–100 second range and 0.1Hz for the 100–10000 second range. Each temperature was repeated three times, and the average value was taken. The creep experiment data and the set of cell shape parameters were input into the creep prediction model. After processing using a dual-stream parallel coding architecture, a long-term creep prediction curve containing a 95% confidence interval was output through Monte Carlo random deactivation (random deactivation probability of 0.1, sampling 100 times). Figure 4 As shown, the confidence interval width of the prediction curve is 0.038 (normalized creep strain unit) at 10000 seconds, which is lower than the preset confidence interval width threshold of 0.06 (50% of the average confidence interval width of the long-term prediction after the time-temperature superposition of the Williams-Landel-Ferry equation). Therefore, the prediction result is determined to meet the engineering reliability requirements, and the process proceeds to step S06.

[0115] In step S06, the long-term creep prediction curve and the set of cell shape parameters are input into the flow matching inverse design algorithm. An optimized formulation is generated based on the target compressive permanent deformation rate of 22% and the target springback rate of 62%. The flow matching algorithm applies hard boundary constraints to the physical feasible region of the formulation on the Riemannian manifold. The optimized formulation is generated through 10 steps of numerical integration using a fourth-order Runge-Kutta-Dormand solver. The amounts of each component are shown in Table 1.

[0116] Table 1 Comparison of component dosages between the basic and optimized formulations

[0117]

[0118] Samples were prepared according to the optimized formula under the preferred process parameters (168℃, 14 minutes) and subjected to compression set tests. At the same time, a comparative example (using only traditional empirical formulas and single-objective response surface optimization parameters, without introducing the closed-loop mechanism of each step of the present invention) was set up for comparison and verification. The test results are shown in Table 2.

[0119] Table 2 Comparison of Compressive Permanent Deformation and Springback Rate Test Results between Experimental Example and Comparative Example

[0120]

[0121] As shown in Table 2, the compression set of the experimental example at 60℃ and 80℃ was significantly lower than that of the comparative example, while the rebound rate was significantly higher and the gel content was also higher. This indicates that the closed-loop optimization path of the present invention has a significant performance improvement effect under high-temperature compression conditions. The anisotropy index of the comparative example exceeded the preset threshold of 1.35, indicating that the pore morphology of the sample prepared by the traditional method has strong anisotropy, further confirming the importance of three-dimensional morphology characterization for performance prediction.

[0122] like Figure 5 As shown, the compression creep curves of the experimental example and the comparative example were compared at 60℃. The slope of the creep curve of the experimental example was significantly lower than that of the comparative example, and the creep rate field remained below the threshold level throughout the entire test time. This proves that the present invention can effectively suppress the development of creep rate at high temperature through thermodynamic self-consistent creep rate field verification and quantitative constraint of three-dimensional morphology of the pores.

[0123] The advancements of this invention compared to traditional methods are reflected in the following aspects. First, traditional methods rely on engineers' experience for forward experiments, and the formula-performance mapping is only established at a single temperature point, failing to capture the nonlinear distribution of the creep rate field under high-temperature multi-field coupling conditions. This invention introduces a non-equilibrium statistical mechanics creep rate field algorithm, rigorously modeling the thermo-mechanical-chemical multi-field coupling effect through the Onsager linear irreversible thermodynamic framework, ensuring the thermodynamic self-consistency of the creep rate field distribution from a physical perspective, and making the selection of process parameters based on thermodynamic evidence rather than solely relying on statistical experience. Second, traditional two-dimensional cross-sectional analysis underestimates the contribution of cell three-dimensional anisotropy to creep behavior. This invention transforms the cell three-dimensional anisotropic morphology into quantitative features through cell three-dimensional reconstruction and shape parameterization models, enabling the creep prediction model to obtain physically meaningful morphological inputs and eliminating the prediction bias introduced by two-dimensional cross-sectional analysis. Furthermore, the traditional time-temperature equivalence principle has an excessively wide confidence interval in nonlinear viscoelastic crosslinking systems, failing to provide reliable quantitative uncertainty basis for engineering decisions. This invention, through a dual-flow parallel creep prediction model and a Monte Carlo random deactivation strategy, achieves accurate extrapolation of long-term creep behavior across formulations and temperature conditions, even with limited training data, and provides quantitative confidence intervals. Finally, traditional methods lack the ability to reverse-engineer formulations from performance targets. This invention, through a flow-matching reverse design algorithm, achieves end-to-end closed-loop generation from performance conditions to formulation composition under Riemannian manifold constraints, transforming formulation design from experience-based forward experimentation to physically constraint-driven reverse design, fundamentally improving the systematic nature and reliability of high-temperature compression set control.

[0124] It should be noted that the variables involved in this invention are explained in detail in Tables 3 and 4.

[0125] Table 3. Variable Explanation Table (Part 1)

[0126]

[0127] Table 4. Variable Explanation Table (Part Two)

[0128]

[0129] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for reducing high-temperature compression deformation of EVA foam shoe sole material, characterized in that, Includes the following steps: After mixing the components according to the basic formula, plasticize them in an internal mixer to obtain the compounded rubber. High-throughput response surface methodology was employed to scan the three-dimensional parameter space of temperature, time and dicumyl peroxide dosage on a flat vulcanizing machine matrix experimental platform. Pareto front was constructed with gel content and compression set as dual objectives to determine the positive vulcanization window and optimize process parameters. The preferred process parameters are input into the non-equilibrium statistical mechanics creep rate field algorithm to obtain the creep rate field distribution results. Based on the comparison between the creep rate field mean and the preset creep rate threshold, if the creep rate field mean exceeds the preset creep rate threshold, return to the previous step to adjust the parameters; otherwise, proceed to the next step. The sample prepared under the preferred process parameters is subjected to micro-computed tomography. The three-dimensional morphology of the bubble is reconstructed using bubble 3D reconstruction and shape parameterization model. The bubble shape parameter set and anisotropy index are extracted. If the anisotropy index exceeds the preset anisotropy threshold, the mold flow channel size or injection direction is adjusted and the sample is remade. Otherwise, proceed to the next step. Multi-temperature short-time compression creep experiments were conducted on the samples. The creep experiment data and the set of pore shape parameters were input into the creep prediction model, and the long-time creep prediction curve containing confidence intervals was output. If the confidence interval width exceeded the preset confidence width threshold, the number of experimental temperature points was increased and the data was collected again. Otherwise, the process proceeded to the next step. The long-term creep prediction curve is matched with the input stream of the cell shape parameter set to reverse design the algorithm, and the optimized formula is generated with the target compression permanent deformation rate and the target springback rate as conditions. The optimized formulation was validated by sample preparation and compression set testing to complete closed-loop validation.

2. The method for reducing high-temperature compression deformation of EVA foam shoe sole material according to claim 1, characterized in that, The basic formula is based on 100 parts by weight of ethylene-vinyl acetate copolymer. The components include ethylene-vinyl acetate copolymer, dicumyl peroxide, azodicarbonamide, zinc oxide, stearic acid, silica, and triallyl isocyanurate. The components are mixed in an internal mixer at a specified temperature for a specified time before being discharged.

3. The method for reducing high-temperature compression deformation of EVA foam shoe sole material according to claim 2, characterized in that, The high-throughput response surface methodology was designed using a combination of response surface methodology and Taguchi orthogonal design. The Pareto front was obtained by multi-objective optimization of the response surface fitting data using a non-dominated sorting genetic algorithm. The objective function was that the gel content was higher than the target value of gel content and the compression set was lower than the target value of compression set.

4. The method for reducing high-temperature compression deformation of EVA foam shoe sole material according to claim 3, characterized in that, The non-equilibrium statistical mechanics creep rate field algorithm is based on the Onsager linear irreversible thermodynamic framework. It describes the high-temperature creep of the ethylene-vinyl acetate copolymer crosslinked network as a process of minimizing the entropy generation rate and constructs the Onsager coefficient matrix between generalized forces and generalized flows. The matrix satisfies the symmetric positive definite condition.

5. The method for reducing high-temperature compression deformation of EVA foam shoe sole material according to claim 4, characterized in that, The non-equilibrium statistical mechanics creep rate field algorithm discretizes the creep equation into a finite volume scheme, minimizes the global entropy generation functional under the constraint that the local entropy generation rate is greater than or equal to zero, and uses the block preconditional conjugate gradient method for iterative solution.

6. The method for reducing high-temperature compression deformation of EVA foam shoe sole material according to claim 5, characterized in that, The encoder of the bubble 3D reconstruction and shape parameterization model adopts a multi-level downsampling path composed of 3D residual convolutional units, and the decoder adopts a symmetrical multi-level upsampling path with skip connections at each level. The output layer outputs a voxel-by-voxel bubble assignment probability map.

7. The method for reducing high-temperature compression deformation of EVA foam shoe sole material according to claim 6, characterized in that, The set of bubble shape parameters is composed of the coefficients of spherical harmonic functions extracted from each connected bubble region. The anisotropy index is defined as the ratio of the maximum to the minimum length of the three principal axes of the bubble, which is obtained by principal component analysis on the bubble voxel coordinate set.

8. The method for reducing high-temperature compression deformation of EVA foam shoe sole material according to claim 7, characterized in that, The creep prediction model adopts a dual-stream parallel coding architecture. The first stream uses a temporal convolutional network to extract local features from short-term stress relaxation signals, while the second stream uses a bidirectional long short-term memory network to perform global temporal modeling of medium- and long-term creep curves. The features from the two streams are fused through a cross-attention mechanism.

9. The method for reducing high-temperature compression deformation of EVA foam shoe sole material according to claim 8, characterized in that, The top layer of the creep prediction model embeds a physical condition location encoding module, which generates a physical condition location encoding vector with temperature, crosslinking density, and vinyl acetate content as conditional variables. The time-temperature superposition shift factor is embedded in the network as a learnable scalar parameter.

10. The method for reducing high-temperature compression deformation of EVA foam shoe sole material according to claim 9, characterized in that, During the inference process of the creep prediction model, a Monte Carlo random deactivation strategy is used to output confidence intervals. The internal iterative feedback loop re-encodes the predicted long-term creep curve and feeds it back to the initial hidden state of the long short-term memory network for refined prediction.

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