A Physics-Based Deep Learning-Based Parameter Optimization Method for Aluminum Foam Process

Abstract

This invention provides a method for optimizing process parameters of aluminum foam based on physical information deep learning, belonging to the field of deep learning-based process parameter optimization. The method includes: data preprocessing, mechanical property prediction, and process parameter optimization. Data preprocessing includes generative data augmentation based on physical information, data standardization, and feature dimensionality reduction. Mechanical property prediction utilizes enhanced data of aluminum foam to predict mechanical properties by constructing a multimodal information fusion prediction framework based on graph neural networks. Process parameter optimization uses a trained graph neural network as the objective function and embeds it into an improved Bayesian optimization framework to iteratively locate the parameter combination that yields the optimal energy absorption performance. This method can not only predict the mechanical properties of aluminum foam but also optimize process parameters during its preparation, significantly reducing R&D costs, shortening the development cycle, and improving the effectiveness of material R&D.

Description

Technical Field

[0001] This invention relates to the field of deep learning optimization of process parameters, specifically to a method for optimizing process parameters of aluminum foam based on physical information deep learning. Background Technology

[0002] Aluminum foam is a material made by adding additives to pure aluminum or aluminum alloys and then performing a foaming process. Aluminum foam, especially closed-cell aluminum foam, has the characteristics of being lightweight, having high specific strength, excellent energy absorption, and sound insulation and vibration reduction. It is hailed as a new type of structural and functional integrated material with great potential in the 21st century. It has broad application prospects in automobile manufacturing (such as collision energy absorption components), aerospace (such as lightweight structural components), rail transportation (such as vibration damping and noise reduction components), military industry and construction (such as explosion-proof and heat insulation materials), which is highly consistent with the current core goal of "green, low-carbon, efficient and circular" manufacturing development.

[0003] Currently, the main methods for preparing aluminum foam include melt foaming, powder metallurgy, and metal deposition. Melt foaming involves adding a foaming agent to molten aluminum to directly generate bubble structures within the liquid aluminum, forming aluminum foam. Powder metallurgy involves mixing aluminum powder with a foaming agent and then pressing and sintering to obtain aluminum foam. Metal deposition involves depositing aluminum onto a porous substrate using electrochemical or physical deposition methods to form an aluminum foam layer. Among these, melt foaming has attracted considerable attention due to its relatively simple process, low cost, and ease of industrialization and mass production. However, while aluminum foam prepared using melt foaming can achieve high porosity, it is prone to problems such as uneven pore structure and thin pore walls, leading to insufficient compressive strength, large fluctuations in mechanical properties, and difficulty in precise control. Furthermore, the complex microstructure of aluminum foam is difficult to replicate precisely. Optimizing process parameters and improving material properties through traditional experimental methods requires significant experimental resources and time, making it time-consuming, labor-intensive, and difficult to achieve optimal process parameter conditions. Summary of the Invention

[0004] To address the problems existing in the prior art, the present invention aims to provide a method for optimizing the process parameters of aluminum foam based on physical information deep learning. This method can not only effectively predict the mechanical properties of aluminum foam, but also optimize the process parameters in the melt foaming process, thereby obtaining aluminum foam with excellent performance, significantly reducing R&D costs, shortening the development cycle of new formulas or new process adjustments, and improving the R&D effect of materials.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A method for optimizing process parameters of aluminum foam based on physical information deep learning includes: data preprocessing, mechanical property prediction, and process parameter optimization. Data preprocessing includes physical information-based generative data augmentation, data standardization, and feature dimensionality reduction. The physical information-based generative data augmentation employs an adversarial training process between a generator based on a physically constrained generative module and a discriminator to construct an adversarial generative network. Mechanical property prediction utilizes augmented data from aluminum foam to predict mechanical properties by constructing a multimodal information fusion prediction framework based on graph neural networks (GNNs). Process parameter optimization uses the trained graph neural network (GNN) as the objective function and embeds it into an improved Bayesian optimization framework to iteratively locate the parameter combination that yields the optimal energy absorption performance.

[0007] Based on further optimization of the above scheme, the generator based on the physical constraint conditional generation module is specifically as follows:

[0008] To improve the effectiveness of generated data from the source, a conditional generation module based on physical constraints is used to filter the conditional information before it enters the generator. Specifically:

[0009]

[0010]

[0011] In the formula: c pr Indicates process-related conditions (such as foaming agent content range, foaming dosage, foaming temperature, etc.); c pe This indicates the energy absorption efficiency of aluminum foam; C i (i=1,2,…,6) represents the constraint conditions; This indicates that all constraints must be true simultaneously; 1 indicates the corresponding condition information. C v Available; 0 indicates unavailable.

[0012] The generator is specifically:

[0013]

[0014] In the formula: This represents the data pair created by the generator, which includes CT images and process parameters; G() This represents a generator neural network; z Represents a random noise vector; C This represents a conditional information vector used to guide the generation direction.

[0015] The discriminator uses its internal neural network structure to deeply analyze the texture and pore structure of an image, and makes a comprehensive judgment based on process parameters and performance conditions.

[0016]

[0017] In the formula: D() This represents a discriminator neural network; (I,P,C) This represents the input data packet, which can be real. It can also be counterfeit; P rel This indicates the output probability value. P rel If the value is close to 1, it means the discriminator considers the input to be true. P rel A value close to 0 indicates that the discriminator considers the input to be forged.

[0018] Based on further optimization of the above scheme, the constraints... C 1 indicates a constraint on the content of the thickener (calcium):

[0019]

[0020] In the formula: x Ca This indicates the content of tackifier (calcium), meaning the tackifier content does not exceed 2%. wt.% ;

[0021] C 2 indicates a collaborative constraint on foaming parameters:

[0022] If the foaming temperature is 750℃, then

[0023] In the formula: x W This indicates the amount of foaming agent used; that is, when the foaming temperature is 750℃, the amount of foaming agent used is less than 2. wt.% ;

[0024] C 3 indicates the porosity-performance coupling constraint:

[0025] Energy absorption rate ≥8.2 MJ / m 3 ,but

[0026] In the formula: P best This indicates the estimated porosity, i.e., if the desired energy absorption rate is greater than or equal to 8.2 MJ / m³. 3 At that time, the porosity is between 75% and 85%;

[0027] C 4 indicates aperture-performance coupling constraint:

[0028]

[0029] In the formula: D best This indicates the estimated pore size, meaning that if excellent energy absorption is desired, the estimated pore size is less than 3 mm.

[0030] C 5 represents the uniformity-performance coupling constraint:

[0031]

[0032] In the formula: CV represents the uniformity of aperture distribution, that is, if a high stability of the plateau stress is desired, the uniformity of aperture distribution should be less than 0.4.

[0033] C 6 indicates a sphericity-performance coupling constraint:

[0034]

[0035] In the formula: N This indicates the porosity; that is, if a peak energy absorption rate is desired, the porosity must be greater than 0.75.

[0036] Based on further optimization of the above scheme, the adversarial generative network includes a discriminator loss and a generator loss. The discriminator loss is used to maximize the adversarial loss, i.e., to accurately distinguish between true and false data.

[0037]

[0038] In the formula: L adv Indicates resistance to loss; E The mathematical symbol for expectation, used to represent the average expected value of a random variable; Represents a real sample containing data pairs of CT images and process parameters; | indicates under the condition of…, for example: Indicates condition information C Under noise z, i.e., the sampling and generation of noise z are conditional information. C Constraints;

[0039] The generator loss should minimize both the adversarial loss and the physical loss.

[0040]

[0041] In the formula: Weighting coefficients representing physical losses;

[0042] Indicates physical loss:

[0043]

[0044]

[0045] In the formula: L p1 Represents the stress-porosity loss function. L p2 Represents the buckling-aperture loss function. L p3 Represents the stability-uniformity loss function. L p4 This represents the toughness-minimum pore size loss function. L p5 This represents the stress concentration-sphericity loss function; This represents the corresponding weight coefficients of the loss function; This represents the target platform stress, i.e., the macroscopic compressive strength that the material is expected to achieve. This indicates the yield strength of aluminum, which is the strength of the metal itself that makes up the foam; P 0 porosity; k 1 indicates the proportional relationship between aperture and stress; d avg Indicates the average aperture; This indicates the relative fluctuation of stress on the target platform; Indicates the corresponding material constant; CV k The coefficient of variation represents the aperture distribution; Indicates the geometric correction factor; d min Indicates the minimum aperture.

[0046] Based on further optimization of the above scheme, the multimodal information fusion model based on graph neural network (GNN) receives preprocessed process parameters (used to describe the manufacturing process, including foaming agent content range, foaming dosage, foaming temperature, etc.) and CT images (used to reveal the internal microstructure of the material). The CT images are first processed by a convolutional neural network to extract key low-dimensional geometric features (including pore size, pore wall thickness, pore shape, etc.). Then, the model abstracts the key structural units into nodes in the graph through a graph construction stage, and the physical adjacency relationship between nodes is defined as an edge.

[0047] In this model, process parameters are not directly used as static node features, but rather as modulators that dynamically respond to the inter-layer message passing process of the Graph Neural Network (GNN) model. That is, process parameters can control the intensity of information flow between nodes. Through the multi-layer modulation of process parameters, information is transmitted and aggregated, thereby achieving a hierarchical representation from the micro-environment of a single node to the macro-state of the entire graph. i In the ( l+1 The feature update of layer ) is specifically as follows:

[0048]

[0049] In the formula: Represents a node i In the ( l+1 ) layer feature vectors; This represents an aggregation function used to gather information about all neighbors; j Represents a node i The neighboring nodes, Represents a node i The set of all neighboring nodes; This represents the input process parameter vector. g(P pr ) This represents a gated vector determined by process parameters, which is a small neural network used to modulate the flow of information. This represents element-wise multiplication, used for modulating messages using process parameter gating vectors; Indicates the first l The message function of the layer is used to calculate neighboring nodes. j To the node i The message; Representing neighboring nodes j In the l The feature vector of a layer, i.e., the state of its neighbors; E ij Indicates the connection node i and nodes j Edge features; The update function (using a GRU-controlled cyclic unit) combines the node's old features with the aggregated new message to generate new features;

[0050] Finally, the graph-level vector representing the material state, formed by aggregating all nodes, is fed into a fully connected network (MLP) to output a prediction of the macroscopic mechanical properties of aluminum foam:

[0051]

[0052] In the formula: READOUT() The graph readout function aggregates the final features of all nodes into a vector representing the entire graph. This represents the final characteristics (i.e., the updated characteristics) of all nodes. V This represents the set of all nodes in the graph.

[0053] Traditional loss functions only supervise the final macroscopic performance prediction value, ignoring the intermediate physical states during deformation. Based on further optimization of the above scheme, the graph neural network (GNN)-based model has three parallel prediction heads at its end, including a macroscopic performance prediction head (outputting the predicted mechanical properties). ), LDOSI Prediction Head (outputs a node-level prediction graph) LDOSI )and SUEDEF Prediction Head (outputs the prediction vector of the remaining structural unit) SUEDEF Through parallel optimization of three prediction heads, the model learns a complete mapping from process parameters to microstructure, then to local physical response, and finally to macroscopic overall performance.

[0054] The total loss function of the three parallel prediction heads is a weighted sum of the loss functions of the three sub-tasks, used to balance the consistency between macroscopic prediction accuracy and microscopic physical processes:

[0055]

[0056] In the formula: These represent the corresponding weight coefficients;

[0057] L ma Represents macroscopic performance loss, used to measure predicted macroscopic mechanical properties. The difference between the actual value Y (obtained through extensive experiments and empirical data) and the true value Y:

[0058]

[0059] In the formula: M Indicates the number of samples;

[0060] L LDOSI This represents the initial sensitivity loss of local deformation, which is supervised at the node level and used to calculate the loss through... LDOSI The prediction head predicts LDOSI The baseline truth obtained by digital image correlation analysis of aluminum foam CT images was obtained. Differences between them:

[0061]

[0062] L SUEDEF This represents the energy dissipation efficiency loss of structural elements, which is monitored at the structural element level and used to calculate the energy loss through structural elements. SUEDEFThe prediction head predicts SUEDEF Factors and the benchmark truth of digital image correlation analysis of aluminum foam CT images Differences between them:

[0063]

[0064] In the formula: K It represents the set of all different structural resource types in the sample.

[0065] Based on further optimization of the above scheme, the specific process of the improved Bayesian optimization framework is as follows: First, randomly sample a small number of points and evaluate their objective function values; then, fit the distribution of the sampled points using a surrogate model. The surrogate model's role is to learn and approximate the true form of the objective function, while simultaneously quantifying the uncertainty of the prediction. Specifically:

[0066]

[0067] In the formula: f(x) This indicates that the surrogate model applies to process parameters. x The prediction of the corresponding mechanical properties is a probability distribution; GP() This represents a Gaussian process used to integrate physics predictions and data-driven corrections. The feature mapping represents the process parameters, which will map the original process parameters. x Mapping to a high-dimensional feature space to capture nonlinear relationships; Represents the process parameters of the training set;

[0068] Indicates by parameters Defined kernel function:

[0069]

[0070] In the formula: Indicates amplitude, Indicates length measurement;

[0071] H phy (x) Represents the physical prior mean function:

[0072]

[0073] In the formula: f p (x) Porosity of aluminum foam predicted by the objective function;

[0074] For new points Mean of the posterior prediction distribution of a Gaussian process for:

[0075]

[0076] In the formula: Indicates a new point The sum and correlation vector of all samples in the training set ，X i Indicates the first i Process parameters for each training sample; T Represents the kernel covariance matrix of the training set; The variance represents the observation noise; I Represents the identity matrix; y Represents the vector of observations in the training set; Represents the residual term;

[0077] In the Bayesian optimization framework, a multi-objective constraint acquisition function is used to obtain the optimal process parameter points. x ne :

[0078]

[0079]

[0080] In the formula: w x , w y , w z These represent the corresponding weight coefficients; This represents the mean energy absorption rate predicted by the surrogate model; Indicates the prediction of the surrogate model LDOSI picture, Var Indicates variance; Indicates the prediction of the surrogate model SUEDEF factor, Mean This represents the mean; This indicates that the proxy model is at the point. x The uncertainty of the forecast, This represents the hyperparameter that controls the exploration intensity.

[0081] The following are the technical effects of the present invention:

[0082] This invention achieves data augmentation through conditional generative adversarial networks constrained by physical information. It can generate large amounts of high-fidelity data that conforms to physical laws at low cost and high efficiency. This not only solves the bottleneck problems of high experimental costs, long cycles, and insufficient quantity in actual R&D processes, but also enriches data types, ensures data correlation and cross-referencing, and improves the ability and accuracy of subsequent training and prediction models. By constructing a prediction model based on a multimodal information fusion graph neural network (GNN), it can not only deeply integrate process parameters and microstructure information to further improve prediction accuracy, but also force the model to focus on more critical physical processes during training, making the prediction results more robust and physically interpretable. Through an improved Bayesian optimization framework, the model can not only make judgments that conform to physical laws in data sparse regions, but also effectively avoid ineffective exploration in physically invalid parameter spaces, accelerating the convergence speed of finding the optimal solution. In addition, it combines energy absorption, deformation process stability, and internal structure energy dissipation efficiency, thereby discovering process solutions with superior overall performance and overcoming the limitations of single-objective optimization methods that neglect other aspects. Attached Figure Description

[0083] Figure 1 A flowchart for the preparation of aluminum foam.

[0084] Figure 2 To improve the optimization results of the Bayesian optimization framework; where dots represent optimization parameters and pentagrams represent the optimal solution.

[0085] Figure 3 These are schematic diagrams of four different appearances of aluminum foam prepared using the process parameter optimization method described in this embodiment of the invention.

[0086] Figure 4 for Figure 3 CT scan pore structure diagrams of four different aluminum foam appearances.

[0087] Figure 5 This is a schematic diagram of the appearance of aluminum foam prepared without using the process parameter optimization method in the embodiments of the present invention. Detailed Implementation

[0088] The technical solutions in the embodiments of the present invention will be clearly and completely described below. In the following description, specific details such as specific system structures and technologies are presented for illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present invention.

[0089] Example 1:

[0090] A method for optimizing process parameters of aluminum foam based on physical information deep learning includes: data preprocessing, mechanical property prediction, and process parameter optimization;

[0091] Among them, data preprocessing includes physical information-based generative data augmentation, data standardization and feature dimensionality reduction. Physical information-based generative data augmentation adopts an adversarial training process of a generator and a discriminator based on a physical constraint-conditional generation module to construct an adversarial generative network.

[0092] The generator based on the physical constraint conditional generation module is specifically as follows:

[0093] To improve the effectiveness of generated data from the source, a conditional generation module based on physical constraints is used to filter the conditional information before it enters the generator. Specifically:

[0094]

[0095]

[0096] In the formula: c pr Indicates process-related conditions (such as foaming agent content range, foaming dosage, foaming temperature, etc.); c pe This indicates the energy absorption efficiency of aluminum foam; C i (i=1,2,…,6) represents the constraint conditions; This indicates that all constraints must be true simultaneously; 1 indicates the corresponding condition information. C v Available; 0 indicates unavailable.

[0097] Constraints C 1 indicates a constraint on the content of the thickener (calcium):

[0098]

[0099] In the formula: x Ca This indicates the content of tackifier (calcium), meaning the tackifier content does not exceed 2%. wt.% ;

[0100] C 2 indicates a collaborative constraint on foaming parameters:

[0101] If the foaming temperature is 750℃, then

[0102] In the formula: x W This indicates the amount of foaming agent used; that is, when the foaming temperature is 750℃, the amount of foaming agent used is less than 2. wt.% ;

[0103] C 3 indicates the porosity-performance coupling constraint:

[0104] Energy absorption rate ≥8.2 MJ / m 3 ,but

[0105] In the formula: P best This indicates the estimated porosity, i.e., if the desired energy absorption rate is greater than or equal to 8.2 MJ / m³. 3 At that time, the porosity is between 75% and 85%;

[0106] C 4 indicates aperture-performance coupling constraint:

[0107]

[0108] In the formula: D best This indicates the estimated pore size, meaning that if excellent energy absorption is desired, the estimated pore size is less than 3 mm.

[0109] C 5 represents the uniformity-performance coupling constraint:

[0110]

[0111] In the formula: CV represents the uniformity of aperture distribution, that is, if a high stability of the plateau stress is desired, the uniformity of aperture distribution should be less than 0.4.

[0112] C 6 indicates a sphericity-performance coupling constraint:

[0113]

[0114] In the formula: N This indicates the porosity; that is, if a peak energy absorption rate is desired, the porosity must be greater than 0.75.

[0115] The generator is specifically:

[0116]

[0117] In the formula: This represents the data pair created by the generator, which includes CT images and process parameters; G() This represents a generator neural network; z Represents a random noise vector; C This represents a conditional information vector used to guide the generation direction.

[0118] The discriminator uses its internal neural network structure to deeply analyze the texture and pore structure of an image, and makes a comprehensive judgment based on process parameters and performance conditions.

[0119]

[0120] In the formula: D() This represents a discriminator neural network; (I,P,C) This represents the input data packet, which can be real. It can also be counterfeit; P rel This indicates the output probability value. P rel If the value is close to 1, it means the discriminator considers the input to be true. P rel A value close to 0 indicates that the discriminator considers the input to be forged.

[0121] Generative adversarial networks (GANs) include discriminator loss and generator loss. The discriminator loss is used to maximize the adversarial loss, i.e., to accurately distinguish between true and false data.

[0122]

[0123] In the formula: L adv Indicates resistance to loss; E The mathematical symbol for expectation, used to represent the average expected value of a random variable; Represents a real sample containing data pairs of CT images and process parameters; | indicates under the condition of…, for example: Indicates condition information C Under noise z, i.e., the sampling and generation of noise z are conditional information. C Constraints;

[0124] The generator loss should minimize both the adversarial loss and the physical loss.

[0125]

[0126] In the formula: Weighting coefficients representing physical losses;

[0127] Indicates physical loss:

[0128]

[0129]

[0130] In the formula: L p1 Represents the stress-porosity loss function. L p2 Represents the buckling-aperture loss function. L p3 Represents the stability-uniformity loss function.L p4 This represents the toughness-minimum pore size loss function. L p5 This represents the stress concentration-sphericity loss function; This represents the corresponding weight coefficients of the loss function; This represents the target platform stress, i.e., the macroscopic compressive strength that the material is expected to achieve. This indicates the yield strength of aluminum, which is the strength of the metal itself that makes up the foam; P 0 porosity; k 1 indicates the proportional relationship between aperture and stress; d avg Indicates the average aperture; This indicates the relative fluctuation of stress on the target platform; Indicates the corresponding material constant; CV k The coefficient of variation represents the aperture distribution; Indicates the geometric correction factor; d min Indicates the minimum aperture.

[0131] Mechanical property prediction is achieved by constructing a multimodal information fusion prediction framework based on graph neural networks (GNNs) and utilizing enhanced data of aluminum foam. The multimodal information fusion model based on graph neural networks (GNNs) receives preprocessed process parameters (used to describe the manufacturing process, including the foaming agent content range, foaming dosage, foaming temperature, etc.) and CT images (used to reveal the internal microstructure of the material). The CT images are first processed by a convolutional neural network to extract key low-dimensional geometric features (including pore size, pore wall thickness, pore shape, etc.). Then, the model abstracts key structural units into nodes in the graph through a graph construction stage, and the physical adjacency relationship between nodes is defined as an edge.

[0132] In this model, process parameters are not directly used as static node features, but rather as modulators that dynamically respond to the inter-layer message passing process of the Graph Neural Network (GNN) model. That is, process parameters can control the intensity of information flow between nodes. Through the multi-layer modulation of process parameters, information is transmitted and aggregated, thereby achieving a hierarchical representation from the micro-environment of a single node to the macro-state of the entire graph. i In the ( l+1 The feature update of layer ) is specifically as follows:

[0133]

[0134] In the formula: Represents a node i In the ( l+1 ) layer feature vectors; This represents an aggregation function used to gather information about all neighbors; j Represents a node i The neighboring nodes, Represents a node i The set of all neighboring nodes; This represents the input process parameter vector. g(P pr ) This represents a gated vector determined by process parameters, which is a small neural network used to modulate the flow of information. This represents element-wise multiplication, used for modulating messages using process parameter gating vectors; Indicates the first l The message function of the layer is used to calculate neighboring nodes. j To the node i The message; Representing neighboring nodes j In the l The feature vector of a layer, i.e., the state of its neighbors; E ij Indicates the connection node i and nodes j Edge features; The update function (using a GRU-controlled cyclic unit) combines the node's old features with the aggregated new message to generate new features;

[0135] Finally, the graph-level vector representing the material state, formed by aggregating all nodes, is fed into a fully connected network (MLP) to output a prediction of the macroscopic mechanical properties of aluminum foam:

[0136]

[0137] In the formula: READOUT() The graph readout function aggregates the final features of all nodes into a vector representing the entire graph. This represents the final characteristics (i.e., the updated characteristics) of all nodes. V This represents the set of all nodes in the graph.

[0138] The model is based on a graph neural network (GNN) and has three parallel prediction heads at the end, including a macroscopic performance prediction head (which outputs the predicted mechanical properties). ), LDOSI Prediction Head (outputs a node-level prediction graph) LDOSI )and SUEDEF Prediction Head (outputs the prediction vector of the remaining structural unit) SUEDEF Through parallel optimization of three prediction heads, the model learns a complete mapping from process parameters to microstructure, then to local physical response, and finally to macroscopic overall performance.

[0139] The total loss function of the three parallel prediction heads is a weighted sum of the loss functions of the three sub-tasks, used to balance the consistency between macroscopic prediction accuracy and microscopic physical processes:

[0140]

[0141] In the formula: These represent the corresponding weight coefficients;

[0142] L ma Represents macroscopic performance loss, used to measure predicted macroscopic mechanical properties. The difference between the actual value Y (obtained through extensive experiments and empirical data) and the true value Y:

[0143]

[0144] In the formula: M Indicates the number of samples;

[0145] L LDOSI This represents the initial sensitivity loss of local deformation, which is supervised at the node level and used to calculate the loss through... LDOSI The prediction head predicts LDOSI The baseline truth obtained by digital image correlation analysis of aluminum foam CT images was obtained. Differences between them:

[0146]

[0147] L SUEDEF This represents the energy dissipation efficiency loss of structural elements, which is monitored at the structural element level and used to calculate the energy loss through structural elements. SUEDEF The prediction head predicts SUEDEF Factors and the benchmark truth of digital image correlation analysis of aluminum foam CT images Differences between them:

[0148]

[0149] In the formula: K It represents the set of all different structural resource types in the sample.

[0150] The process parameter optimization uses a trained graph neural network (GNN) as the objective function and embeds it into an improved Bayesian optimization framework. This framework iteratively locates the parameter combination that yields the optimal energy absorption performance. The specific process of the improved Bayesian optimization framework is as follows: First, a small number of points are randomly sampled, and their objective function values ​​are evaluated. Then, a surrogate model is used to fit the distribution of the sampled points. The surrogate model learns and approximates the true form of the objective function, while quantifying the uncertainty of the prediction. Specifically:

[0151]

[0152] In the formula: f(x) This indicates that the surrogate model applies to process parameters. x The prediction of the corresponding mechanical properties is a probability distribution; GP() This represents a Gaussian process used to integrate physics predictions and data-driven corrections. The feature mapping represents the process parameters, which will map the original process parameters. x Mapping to a high-dimensional feature space to capture nonlinear relationships; Represents the process parameters of the training set;

[0153] Indicates by parameters Defined kernel function:

[0154]

[0155] In the formula: Indicates amplitude, Indicates length measurement;

[0156] H phy (x) Represents the physical prior mean function:

[0157]

[0158] In the formula: f p (x) Porosity of aluminum foam predicted by the objective function;

[0159] For new points Mean of the posterior prediction distribution of a Gaussian process for:

[0160]

[0161] In the formula: Indicates a new point The sum and correlation vector of all samples in the training set ，X iIndicates the first i Process parameters for each training sample; T Represents the kernel covariance matrix of the training set; The variance represents the observation noise; I Represents the identity matrix; y Represents the vector of observations in the training set; Represents the residual term;

[0162] In the Bayesian optimization framework, a multi-objective constraint acquisition function is used to obtain the optimal process parameter points. x ne :

[0163]

[0164]

[0165] In the formula: w x , w y , w z These represent the corresponding weight coefficients; This represents the mean energy absorption rate predicted by the surrogate model; Indicates the prediction of the surrogate model LDOSI picture, Var Indicates variance; Indicates the prediction of the surrogate model SUEDEF factor, Mean This represents the mean; This indicates that the proxy model is at the point. x The uncertainty of the forecast, This represents the hyperparameter that controls the exploration intensity.

[0166] like Figure 3 , Figure 4 As shown, the aluminum foam structure obtained after process parameter optimization using the above method exhibits uniform and consistent pore size; while the image without process parameter optimization is as follows. Figure 5 As shown, there are problems such as poor uniformity of pores, poor consistency, and large pore size.

[0167] Example 2:

[0168] As another preferred embodiment of the technical solution of the present invention, based on the above embodiment 1, data standardization, that is, normalizing the process parameter feature data after data enhancement to eliminate the dimensional differences between different parameters, specifically:

[0169]

[0170] Feature dimensionality reduction specifically involves: performing principal component analysis to reduce the dimensionality of the standardized high-dimensional feature space, and then projecting the standardized data matrix onto the orthogonal feature space using orthogonal projection. k The subspace formed by the directions of the principal components yields the dimensionality-reduced data.

Claims

1. A method for optimizing process parameters of aluminum foam based on physical information deep learning, characterized in that: include: The process includes data preprocessing, mechanical property prediction, and process parameter optimization. Data preprocessing includes physical information-based generative data augmentation, data standardization, and feature dimensionality reduction. Physical information-based generative data augmentation employs an adversarial training process between a generator and a discriminator based on a physically constrained generative module to construct an adversarial generative network. Mechanical property prediction utilizes augmented data from aluminum foam to predict mechanical properties by constructing a multimodal information fusion prediction framework based on graph neural networks. Process parameter optimization uses a trained graph neural network as the objective function and embeds it into an improved Bayesian optimization framework to iteratively locate the parameter combination that can produce aluminum foam with optimal energy absorption performance. Specifically, the generation module based on physical constraints is as follows: By utilizing a physical constraint-based conditional generation module, the conditional information is filtered before entering the generator: In the formula: c pr Indicates process-related conditions; c pe This indicates the energy absorption rate of aluminum foam; C i Indicates constraints. i =1,2,…,6; This indicates that all constraints must be true simultaneously; 1 indicates the corresponding condition information. C v Available; 0 indicates unavailable. The generator is specifically: In the formula: This represents the data pair created by the generator, which includes CT images and process parameters; G() This represents a generator neural network; z Represents a random noise vector; C Represents a conditional information vector; The discriminator uses its internal neural network structure to deeply analyze the texture and pore structure of an image, and makes a comprehensive judgment based on process parameters and performance conditions. In the formula: D() This represents a discriminator neural network; (I,P,C) Indicates the input data packet; P rel This indicates the output probability value. P rel If the value is close to 1, it means the discriminator considers the input to be true. P rel A value close to 0 indicates that the discriminator considers the input to be forged.

2. The method for optimizing aluminum foam process parameters based on physical information deep learning according to claim 1, characterized in that: The constraints C 1 indicates a constraint on the tackifier content: In the formula: x Ca This indicates the content of the tackifier, meaning the tackifier content does not exceed 2%. wt.% ; C 2 indicates a collaborative constraint on foaming parameters: If the foaming temperature is 750℃, then In the formula: x W This indicates the amount of foaming agent used; that is, when the foaming temperature is 750℃, the amount of foaming agent used is less than 2. wt.% ; C 3 indicates the porosity-performance coupling constraint: Energy absorption rate ≥8.2 MJ / m 3 ,but In the formula: P best This indicates the estimated porosity, i.e., if the desired energy absorption rate is greater than or equal to 8.2 MJ / m³. 3 At that time, the porosity is between 75% and 85%; C 4 indicates aperture-performance coupling constraint: In the formula: D best This indicates the estimated pore size, meaning that if excellent energy absorption is desired, the estimated pore size is less than 3 mm. C 5 represents the uniformity-performance coupling constraint: In the formula: CV represents the uniformity of aperture distribution, that is, if a high stability of the plateau stress is desired, the uniformity of aperture distribution should be less than 0.

4. C 6 indicates a sphericity-performance coupling constraint: In the formula: N This indicates the porosity; that is, if a peak energy absorption rate is desired, the porosity must be greater than 0.

75.

3. The method for optimizing aluminum foam process parameters based on deep learning of physical information according to claim 1 or 2, characterized in that: The adversarial generative network includes a discriminator loss and a generator loss. The discriminator loss is used to maximize the adversarial loss, i.e., to accurately distinguish between true and false data. In the formula: L adv Indicates resistance to loss; E Mathematical symbols representing expectations; Represents a real sample containing data pairs of CT images and process parameters; | indicates under the condition of… The generator loss should minimize both the adversarial loss and the physical loss. In the formula: Weighting coefficients representing physical losses; Indicates physical loss: In the formula: L p1 Represents the stress-porosity loss function. L p2 Represents the buckling-aperture loss function. L p3 Represents the stability-uniformity loss function. L p4 This represents the toughness-minimum pore size loss function. L p5 This represents the stress concentration-sphericity loss function; This represents the corresponding weight coefficients of the loss function; This represents the target platform stress, i.e., the macroscopic compressive strength that the material is expected to achieve. This indicates the yield strength of aluminum, which is the strength of the metal itself that makes up the foam; P 0 porosity; k 1 indicates the proportional relationship between aperture and stress; d avg Indicates the average aperture; This indicates the relative fluctuation of stress on the target platform; Indicates the corresponding material constant; CV k The coefficient of variation represents the aperture distribution; Indicates the geometric correction factor; d min Indicates the minimum aperture.

4. The method for optimizing aluminum foam process parameters based on physical information deep learning according to claim 1, characterized in that: The multimodal information fusion model based on graph neural networks receives preprocessed process parameters and CT images. The CT images are first processed by a convolutional neural network to extract key low-dimensional geometric features. Then, the model abstracts key structural units into nodes in a graph through a graph construction phase, and the physical adjacency relationship between nodes is defined as an edge. In this model, process parameters are not directly used as static node features, but rather as modulators that dynamically respond to the inter-layer message passing process in the graph neural network model. That is, process parameters control the intensity of information flow between nodes. Through multi-layer modulation of process parameters, information is transmitted and aggregated, thereby achieving a hierarchical representation from the micro-environment of a single node to the macro-state of the entire graph. i In the ( l+1 The feature update of layer ) is specifically as follows: In the formula: Represents a node i In the ( l+1 ) layer feature vectors; This represents an aggregation function used to gather information about all neighbors; j Represents a node i The neighboring nodes, Represents a node i The set of all neighboring nodes; This represents the input process parameter vector. g(P pr ) This represents a gated vector determined by process parameters, which is a small neural network used to modulate the flow of information. This represents element-wise multiplication, used for modulating messages using process parameter gating vectors; Indicates the first l The message function of the layer is used to calculate neighboring nodes. j To the node i The message; Representing neighboring nodes j In the l The feature vector of a layer, i.e., the state of its neighbors; E ij Indicates the connection node i and nodes j Edge features; This represents the update function, which combines the node's old features with the aggregated new message to generate new features; Finally, the graph-level vector representing the material state, formed by aggregating all nodes, is fed into a fully connected network to output a prediction of the macroscopic mechanical properties of aluminum foam: In the formula: READOUT() The graph readout function aggregates the final features of all nodes into a vector representing the entire graph. Represents the final characteristic of all nodes; V This represents the set of all nodes in the graph.

5. The method for optimizing aluminum foam process parameters based on physical information deep learning according to claim 4, characterized in that: The graph neural network-based model has three parallel prediction heads at its end, including a macroscopic performance prediction head, LDOSI Predicting head and SUEDEF Predicting the head; The total loss function of the three parallel prediction heads is a weighted sum of the loss functions of the three sub-tasks, used to balance the consistency between macroscopic prediction accuracy and microscopic physical processes: In the formula: These represent the corresponding weight coefficients; L ma Indicates macroscopic performance loss: In the formula: M Indicates the number of samples; L LDOSI This represents the initial sensitivity loss of local deformation, which is supervised at the node level and used to calculate the loss through... LDOSI The prediction head predicts LDOSI The baseline truth obtained by digital image correlation analysis of aluminum foam CT images was obtained. Differences between them: L SUEDEF This represents the energy dissipation efficiency loss of structural elements, which is monitored at the structural element level and used to calculate the energy loss through structural elements. SUEDEF The prediction head predicts SUEDEF Factors and the benchmark truth of digital image correlation analysis of aluminum foam CT images Differences between them: In the formula: K It represents the set of all different structural resource types in the sample.

6. The method for optimizing aluminum foam process parameters based on physical information deep learning according to claim 5, characterized in that: The improved Bayesian optimization framework follows this process: First, a small number of points are randomly sampled, and their objective function values ​​are evaluated. Then, a surrogate model is used to fit the distribution of the sampled points. The surrogate model learns and approximates the true form of the objective function, while quantifying the uncertainty of the prediction. Specifically: In the formula: f(x) This indicates that the surrogate model applies to process parameters. x The prediction of the corresponding mechanical properties is a probability distribution; GP () Represent a Gaussian process; The feature mapping represents the process parameters, which will map the original process parameters. x Mapped to a high-dimensional feature space; The process parameters of the training set are represented. Indicates by parameters Defined kernel function: In the formula: Indicates amplitude, Indicates length measurement; H phy (x) Represents the physical prior mean function: In the formula: f p (x) Porosity of aluminum foam predicted by the objective function; For new points Mean of the posterior prediction distribution of a Gaussian process for: In the formula: Indicates a new point The sum and correlation vector of all samples in the training set ，X i Indicates the first i Process parameters for each training sample; T Represents the kernel covariance matrix of the training set; The variance represents the observation noise; I Represents the identity matrix; y Represents the vector of observations in the training set; Represents the residual term; In the Bayesian optimization framework, a multi-objective constraint acquisition function is used to obtain the optimal process parameter points. x ne : In the formula: w x , w y , w z These represent the corresponding weight coefficients; This represents the mean energy absorption rate predicted by the surrogate model; Indicates the prediction of the surrogate model LDOSI picture, Var Indicates variance; Indicates the prediction of the surrogate model SUEDEF factor, Mean This represents the mean; This indicates that the proxy model is at the point. x The uncertainty of the forecast, This represents the hyperparameter that controls the exploration intensity.

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