Foamed aluminum process parameter optimization method based on physical information deep learning

Abstract

The invention provides a foamed aluminum process parameter optimization method based on physical information deep learning, and relates to the field of deep learning process parameter optimization, and the method comprises the steps of data preprocessing, mechanical property prediction and process parameter optimization. Wherein the data preprocessing comprises generation type data enhancement based on physical information, data standardization and feature dimension reduction; according to the mechanical property prediction, a multi-modal information fusion prediction framework based on a graph neural network is constructed, and enhanced data of foamed aluminum is utilized to perform mechanical property prediction; and in the process parameter optimization, the trained graph neural network is used as a target function and is embedded into an improved Bayesian optimization framework, and a parameter combination capable of preparing the optimal energy absorption performance can be iterated and positioned. The method not only can predict the mechanical property of the foamed aluminum, but also can optimize the technological parameters in the preparation process of the foamed aluminum, obviously reduces the research and development cost, shortens the development period and improves the research and development effect of materials.

Description

Technical Field

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

[0002] Foam aluminum is a material made by adding additives to pure aluminum or aluminum alloy and undergoing a foaming process. Foam aluminum, especially closed-cell foam aluminum, has the characteristics of light weight, high specific strength, excellent energy absorption, sound insulation and vibration reduction. It is known 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 parts), aerospace (such as lightweight structural parts), rail transportation (such as shock and noise reduction parts), military industry and construction (such as explosion-proof and thermal insulation materials), and is highly consistent with the current core goal of "green, low-carbon, and efficient circulation" in the development of the manufacturing industry.

[0003] Currently, the main methods for preparing aluminum foam include melt foaming, powder metallurgy, and metal deposition. The melt foaming method involves adding a foaming agent to molten aluminum to directly generate a bubble structure within the liquid aluminum. The powder metallurgy method involves mixing aluminum powder with a foaming agent and then subjecting the mixture to pressing and sintering to produce the foamed aluminum. The metal deposition method involves depositing aluminum onto a porous substrate through electrochemical or physical deposition to form an aluminum foam layer. The melt foaming method 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 the melt foaming method can achieve high porosity, it is prone to problems such as uneven pore structure and thin pore walls, resulting in insufficient compressive strength, large fluctuations in mechanical properties, and difficulty in precise control. Furthermore, the microscopic pore structure of aluminum foam is complex and difficult to precisely replicate. Optimizing process parameters and improving material properties through traditional experimental methods consumes significant experimental resources and time, is labor-intensive, and achieving optimal process parameter optimization conditions is difficult. Summary of the Invention

[0004] In response to the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a foam aluminum process parameter optimization method based on deep learning of physical information. This method can not only effectively predict the mechanical properties of foam aluminum, but also optimize the process parameters in the melt foaming preparation process, thereby obtaining foam aluminum exhibiting 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 purpose of the present invention is achieved through the following technical solutions: A method for optimizing aluminum foam process parameters based on deep learning of physical information includes: data preprocessing, mechanical property prediction, and process parameter optimization; wherein, data preprocessing includes generative data enhancement based on physical information, data standardization, and feature dimensionality reduction; generative data enhancement based on physical information adopts an adversarial training process of a generator based on a physical constraint conditional generation module and a discriminator to construct an adversarial generative network; mechanical property prediction predicts mechanical properties by constructing a multimodal information fusion prediction framework based on a graph neural network (GNN) and utilizing the enhanced data of aluminum foam; process parameter optimization uses the trained graph neural network (GNN) as the objective function and embeds it into an improved Bayesian optimization framework to iterate and locate the parameter combination that can produce the optimal energy absorption performance.

[0006] Based on the further optimization of the above solution, the generator of the physical constraint conditional generation module is specifically: In order 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:

[0007]

[0008] Where: c pr Indicates process-related conditions (such as foaming agent content range, foaming amount, foaming temperature, etc.); c pe Indicates the energy absorption efficiency of foam aluminum; C i (i=1,2,…,6) represents the constraint condition; Indicates that all constraints must be true at the same time; 1 indicates the corresponding condition information C v Available, 0 means unavailable; The generator is specifically:

[0009] Where: represents the data pair containing CT images and process parameters created by the generator; G() represents the generator neural network; z represents a random noise vector; C Represents the conditional information vector, used to guide the generation direction; The discriminator uses its internal neural network structure to deeply analyze the texture and pore structure of the image, and makes a comprehensive judgment based on process parameters and performance conditions:

[0010] Where: D() represents the discriminator neural network; (I,P,C) Represents an input packet, which can be real , or it can be forged; P rel Represents the output probability value, if P rel Close to 1, indicating that the discriminator believes that the input is real. P rel Close to 0, it means the discriminator thinks the input is fake.

[0011] Based on the further optimization of the above solution, the constraint condition C 1 indicates the viscosity enhancer (calcium) content constraint:

[0012] Where: x Ca Indicates the content of thickener (calcium), that is, the content of thickener does not exceed 2 wt.% ; C 2 represents the collaborative constraint of foaming parameters: The foaming temperature is 750℃,

[0013] Where: x W 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 represents the porosity-performance coupling constraint: Energy absorption rate ≥8.2MJ / m 3 ,but

[0014] Where: P best Indicates the estimated porosity, that is, if the energy absorption rate expected is greater than or equal to 8.2MJ / m 3 When , the porosity is between 75% and 85%; C 4 represents the aperture-performance coupling constraint:

[0015] Where: D best Indicates the estimated aperture, i.e. if excellent energy absorption rate is expected, the estimated aperture is less than 3mm; C 5 represents the uniformity-performance coupling constraint:

[0016] In the formula: CV represents the pore size distribution uniformity. That is, if a highly stable platform stress is expected, the pore size distribution uniformity is less than 0.4. C 6 represents the sphericity - performance coupling constraint:

[0017] In the formula: N represents the pore sphericity. That is, if a peak energy absorption rate is expected, the pore sphericity is greater than 0.75.

[0018] Based on the further optimization of the above - mentioned scheme, the discriminator loss and the generator loss are included in the adversarial generation network. The discriminator loss is used to maximize the adversarial loss, that is, to accurately distinguish between true and false:

[0019] In the formula: L adv represents the adversarial loss; E represents the expected mathematical symbol, used to represent the average expectation of the values taken by a random variable; represents the real sample of the data pair containing CT images and process parameters; 丨 represents under the condition of..., for example: represents under the condition information C of the noise z, that is, the sampling and generation of the noise z are constrained by the condition information C ; The generator loss should not only minimize the adversarial loss but also minimize the physical loss:

[0020] In the formula: represents the weight coefficient of the physical loss; represents the physical loss:

[0021]

[0022] In the formula: L p1 represents the stress - porosity loss function, L p2 represents the buckling - pore size loss function, L p3 represents the stability - uniformity loss function, L p4 represents the toughness - minimum pore size loss function, L p5 represents the stress concentration - sphericity loss function; Represents the corresponding loss function weight coefficient; represents the target platform stress, i.e. the macroscopic compressive strength that the material is expected to achieve; Indicates the yield strength of aluminum, i.e. the strength of the metal itself that makes up the foam; P 0 porosity; k 1 represents the proportional relationship between pore size and stress; d avg represents the average pore size; represents the relative fluctuation of the target platform stress; represents the corresponding material constant; CV k represents the coefficient of variation of the pore size distribution; represents the geometric correction factor; d min Indicates the minimum aperture.

[0023] Based on a further optimization of the above solution, the multimodal information fusion model based on a graph neural network (GNN) receives process parameters (used to describe the manufacturing process, including the range of blowing agent content, blowing dosage, and foaming temperature) after data preprocessing 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, and pore shape). Then, the model abstracts the key structural units into nodes in the graph through a graph construction phase, and the physical adjacency between nodes is defined as edges. Among them, the process parameters are not directly used as static node features, but as a modulator to dynamically respond to the inter-layer message transmission process of the graph neural network (GNN) model, that is, the process parameters can control the intensity of the information flow between nodes; the transmission and aggregation of information after multi-layer modulation of the process parameters can realize the hierarchical representation from the micro environment of a single node to the macro state of the entire graph, and the nodes i In the ( l+1 ) The feature update of the layer is specifically as follows:

[0024] Where: Representation node i In the ( l+1 ) layer’s feature vector; Represents the aggregation function, which is used to aggregate all neighbor information; j Representation node i Neighbor nodes of Representation node i The set of all neighbor nodes; represents the input process parameter vector, g(P pr )represents the gating vector determined by the process parameters, which is a small neural network used to modulate the flow of information; represents the element-wise product, which is used for modulation of the message by the process parameter gating vector; Indicates the l The message function of the layer is used to calculate the neighbor nodes j To Node i news; Represents neighbor nodes j In the l The feature vector of the layer, i.e. the state of the neighbors; E ij Represents a connected node i and nodes j Edge features; represents the update function (using GRU-controlled recurrent unit), which combines the node's own old features with the aggregated new messages 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 (MLP) to output the prediction of the macroscopic mechanical properties of aluminum foam:

[0025] Where: READOUT() represents the graph readout function, which aggregates the final features of all nodes into a vector representing the entire graph; represents the final features of all nodes (i.e. after updating); V Represents the set of all nodes in the graph.

[0026] The traditional loss function only supervises the final macro performance prediction value and ignores the intermediate physical state during the deformation process. Based on the further optimization of the above scheme, three parallel prediction heads are set at the end of the graph neural network (GNN) model, including the macro performance prediction head (outputting the predicted mechanical properties) and the )、 LDOSI Prediction head (output node-level prediction graph LDOSI )and SUEDEF Prediction head (outputs the prediction vector of the balance structure unit SUEDEF ), through the parallel optimization of three prediction heads, the model learns the complete mapping from process parameters to microstructure, then to local physical response, and finally to macroscopic overall performance; The total loss function of the three parallel prediction heads is the weighted sum of the three subtask loss functions, which is used to balance the macro prediction accuracy and the consistency of the microscopic physical process:

[0027] Where: Respectively represent the corresponding weight coefficients; L ma Represents the macroscopic performance loss, which is used to measure the predicted macroscopic mechanical properties The gap between the true value Y (obtained through a large amount of experiments and empirical data):

[0028] Where: M represents the number of samples; L LDOSI represents the local deformation initiation sensitivity loss, which is supervised at the node level and used to calculate the LDOSI Prediction head prediction LDOSI Figure 1 shows the baseline truth obtained by digital image correlation analysis of foam aluminum CT images. The differences between:

[0029] L SUEDEF Represents the energy dissipation efficiency loss of the structural unit, which is supervised at the structural unit level and used to calculate the energy dissipation efficiency loss of the structural unit. SUEDEF Prediction head prediction SUEDEF Factors and digital image correlation analysis benchmark truth for aluminum foam CT images The differences between:

[0030] Where: K Represents the set of all different structural source types in the sample.

[0031] Based on the further optimization of the above scheme, 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 the distribution of the sampled points is fitted by a surrogate model, where the role of the surrogate model is to learn and approximate the true form of the objective function and quantify the uncertainty of the prediction. Specifically,

[0032] Where: f(x) Represents the agent model for process parameters x The prediction of the corresponding mechanical properties is a probability distribution; GP() represents a Gaussian process for integrating physical predictions and data-driven corrections; Represents the feature map of process parameters, which converts the original process parameters x Mapping to a high-dimensional feature space to capture nonlinear relationships; represents the process parameters of the training set; Indicated by the parameter The kernel function is defined as:

[0033] Where: represents the amplitude, represents the length scale; H phy (x) Represents the physical prior mean function:

[0034] Where: f p (x) The porosity of aluminum foam predicted by the objective function; For new points , the mean of the posterior predictive distribution of the Gaussian process for:

[0035] Where: Indicates new point The sum correlation vector with all samples in the training set ，X i Indicates the i Process parameters of training samples; T represents the kernel covariance matrix of the training set; represents the variance of the observation noise; I represents the identity matrix; y Represents the observation vector of 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 :

[0036]

[0037] Where: w x 、 w y 、 w z Respectively represent the corresponding weight coefficients; represents the mean energy absorption rate predicted by the surrogate model; represents the surrogate model prediction LDOSI picture, Var represents variance; represents the surrogate model prediction SUEDEF factor, Mean represents the mean; Indicates that the proxy model is at point x The forecast uncertainty at represents a hyperparameter that controls the exploration effort.

[0038] The following are the technical effects of the solution of the present invention: This invention achieves data augmentation by using a conditional generative adversarial network (GAN) constrained by physical information. This allows for the cost-effective and efficient generation of large quantities of high-fidelity data that conforms to physical laws. This not only addresses the bottlenecks of high experimental costs, long cycles, and insufficient data during actual R&D, but also enriches data types, ensures data relevance and cross-correlation, and enhances the capabilities and accuracy of subsequent training and predictive models. By constructing a predictive model based on a graph neural network (GNN) that integrates multimodal information, this model not only deeply integrates process parameters and microstructural information, further improving prediction accuracy, but also forces the model to focus on more critical physical processes during training, resulting in more robust and physically interpretable prediction results. Through an improved Bayesian optimization framework, the model not only enables physically consistent judgments in data-sparse regions, but also effectively avoids inefficient exploration in physically invalid parameter spaces, accelerating convergence to the optimal solution. Furthermore, by combining energy absorption, deformation stability, and internal structural energy dissipation efficiency, this approach can identify process solutions with superior overall performance, overcoming the limitations of single-objective optimization methods that often focus on one objective but not the other. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Flow chart of aluminum foam preparation.

[0040] Figure 2 To improve the optimization results of the Bayesian optimization framework; the dots are the optimization parameters and the stars are the optimal solutions.

[0041] Figure 3 Schematic diagrams of four different appearances of aluminum foam prepared using the process parameter optimization method in an embodiment of the present invention.

[0042] Figure 4 for Figure 3 CT scan pore structure diagrams of four different foam aluminum appearances.

[0043] Figure 5 This is a schematic diagram of the appearance of foamed aluminum that is not prepared using the process parameter optimization method in the embodiment of the present invention. DETAILED DESCRIPTION

[0044] The technical solutions in the embodiments of the present invention will be described clearly and completely below. In the following description, for the purpose of illustration rather than limitation, specific details such as specific system structures and technologies are proposed to facilitate a thorough understanding of the embodiments of the present invention.

[0045] Example 1: A foam aluminum process parameter optimization method based on physical information deep learning, including: data preprocessing, mechanical property prediction and process parameter optimization; Data preprocessing includes generative data enhancement based on physical information, data standardization, and feature dimensionality reduction. Generative data enhancement based on physical information uses an adversarial training process between a generator based on a physical constraint-conditioned generation module and a discriminator to construct an adversarial generative network. The generator of the generation module based on physical constraints is as follows: In order 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:

[0046]

[0047] Where: c pr Indicates process-related conditions (such as foaming agent content range, foaming amount, foaming temperature, etc.); c pe Indicates the energy absorption efficiency of foam aluminum; C i (i=1,2,…,6) represents the constraint condition; Indicates that all constraints must be true at the same time; 1 indicates the corresponding condition information C v Available, 0 means unavailable; Constraints C 1 indicates the viscosity enhancer (calcium) content constraint:

[0048] Where: x Ca Indicates the content of thickener (calcium), that is, the content of thickener does not exceed 2 wt.% ; C 2 represents the collaborative constraint of foaming parameters: The foaming temperature is 750℃,

[0049] Where: x WIndicates 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 represents the porosity-performance coupling constraint: Energy absorption rate ≥8.2MJ / m 3 ,but

[0050] Where: P best Indicates the estimated porosity, that is, if the energy absorption rate expected is greater than or equal to 8.2MJ / m 3 When , the porosity is between 75% and 85%; C 4 represents the aperture-performance coupling constraint:

[0051] Where: D best Indicates the estimated aperture, i.e. if excellent energy absorption rate is expected, the estimated aperture is less than 3mm; C 5 represents the uniformity-performance coupling constraint:

[0052] Where: CV represents the pore size distribution uniformity, that is, if a high stability platform stress is desired, the pore size distribution uniformity should be less than 0.4; C 6 represents the sphericity-performance coupling constraint:

[0053] Where: N It represents the sphericity of the pores. That is, if the peak energy absorption rate is desired, the sphericity of the pores should be greater than 0.75.

[0054] The generator is specifically:

[0055] Where: represents the data pair containing CT images and process parameters created by the generator; G() represents the generator neural network; z represents a random noise vector; C Represents the conditional information vector, used to guide the generation direction; The discriminator uses its internal neural network structure to deeply analyze the texture and pore structure of the image, and makes a comprehensive judgment based on process parameters and performance conditions:

[0056] In the formula: D() represents a discriminator neural network; (I,P,C) represents an input data packet, which can be real or forged; P rel represents an output probability value. If P rel is close to 1, it means the discriminator believes the input is real. If P rel is close to 0, it means the discriminator believes the input is forged.

[0057] In the adversarial generative network, there are discriminator loss and generator loss. The discriminator loss is used to maximize the adversarial loss, that is, to accurately distinguish between true and false:

[0058] In the formula: L adv represents the adversarial loss; E represents the mathematical symbol of expectation, used to represent the average expectation of the values taken by a random variable; represents a real sample of a data pair containing CT images and process parameters; 丨 represents under the condition of..., for example: represents under the condition information C of the noise z, that is, the sampling and generation of the noise z are constrained by the condition information C ; The generator loss should not only minimize the adversarial loss but also minimize the physical loss:

[0059] In the formula: represents the weight coefficient of the physical loss; represents the physical loss:

[0060]

[0061] 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 represents the toughness-minimum aperture loss function, L p5 represents the stress concentration-sphericity loss function; represents the corresponding loss function weight coefficient; represents the target platform stress, i.e. the macroscopic compressive strength that the material is expected to achieve; Indicates the yield strength of aluminum, i.e. the strength of the metal itself that makes up the foam; P 0 porosity; k 1 represents the proportional relationship between pore size and stress; d avg represents the average pore size; represents the relative fluctuation of the target platform stress; represents the corresponding material constant; CV k represents the coefficient of variation of the pore size distribution; represents the geometric correction factor; d min Indicates the minimum aperture.

[0062] Mechanical properties prediction is performed by constructing a multimodal information fusion prediction framework based on a graph neural network (GNN) and utilizing the enhanced data of aluminum foam. The multimodal information fusion model based on the graph neural network (GNN) receives the process parameters (used to describe the manufacturing process, including the range of foaming agent content, foaming dosage, foaming temperature, etc.) after data preprocessing and CT images (used to reveal the internal microstructure of the material). The CT images are first processed through 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 the graph construction phase, and the physical adjacency relationship between nodes is defined as edges. Among them, the process parameters are not directly used as static node features, but as a modulator to dynamically respond to the inter-layer message transmission process of the graph neural network (GNN) model, that is, the process parameters can control the intensity of the information flow between nodes; the transmission and aggregation of information after multi-layer modulation of the process parameters can realize the hierarchical representation from the micro environment of a single node to the macro state of the entire graph, and the nodes i In the ( l+1 ) The feature update of the layer is specifically as follows:

[0063] Where: Representation node i In the ( l+1 ) layer’s feature vector; Represents the aggregation function, which is used to aggregate all neighbor information; j Representation node i Neighbor nodes of Representation node i The set of all neighbor nodes; represents the input process parameter vector, g(P pr) represents the gating vector determined by the process parameters, which is a small neural network used to modulate the flow of information; represents the element-wise product, which is used for modulation of the message by the process parameter gating vector; Indicates the l The message function of the layer is used to calculate the neighbor nodes j To Node i news; Represents neighbor nodes j In the l The feature vector of the layer, i.e. the state of the neighbors; E ij Represents a connected node i and nodes j Edge features; represents the update function (using GRU-controlled recurrent unit), which combines the node's own old features with the aggregated new messages 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 (MLP) to output the prediction of the macroscopic mechanical properties of aluminum foam:

[0064] Where: READOUT() represents the graph readout function, which aggregates the final features of all nodes into a vector representing the entire graph; represents the final features of all nodes (i.e. after updating); V Represents the set of all nodes in the graph.

[0065] Three parallel prediction heads are set at the end of the graph neural network (GNN) model, including the macro performance prediction head (output predicted mechanical properties )、 LDOSI Prediction head (output node-level prediction graph LDOSI )and SUEDEF Prediction head (outputs the prediction vector of the balance structure unit SUEDEF ), through the parallel optimization of three prediction heads, the model learns the complete mapping from process parameters to microstructure, then to local physical response, and finally to macroscopic overall performance; The total loss function of the three parallel prediction heads is the weighted sum of the three subtask loss functions, which is used to balance the macro prediction accuracy and the consistency of the microscopic physical process:

[0066] Where: Respectively represent the corresponding weight coefficients; L maRepresents the macroscopic performance loss, which is used to measure the predicted macroscopic mechanical properties The gap between the true value Y (obtained through a large amount of experiments and empirical data):

[0067] Where: M represents the number of samples; L LDOSI represents the local deformation initiation sensitivity loss, which is supervised at the node level and used to calculate the LDOSI Prediction head prediction LDOSI Figure 1 shows the baseline truth obtained by digital image correlation analysis of foam aluminum CT images. The differences between:

[0068] L SUEDEF Represents the energy dissipation efficiency loss of the structural unit, which is supervised at the structural unit level and used to calculate the energy dissipation efficiency loss of the structural unit. SUEDEF Prediction head prediction SUEDEF Factors and digital image correlation analysis benchmark truth for aluminum foam CT images The differences between:

[0069] Where: K Represents the set of all different structural source types in the sample.

[0070] The process parameter optimization uses a 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 produces 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, the distribution of the sampled points is fitted using a surrogate model. The role of the surrogate model is to learn and approximate the true form of the objective function while quantifying the uncertainty of the prediction. Specifically,

[0071] Where: f(x) Represents the agent model for process parameters x The prediction of the corresponding mechanical properties is a probability distribution; GP() represents a Gaussian process for integrating physical predictions and data-driven corrections; Represents the feature map of process parameters, which converts the original process parameters x Mapping to a high-dimensional feature space to capture nonlinear relationships; represents the process parameters of the training set; Indicated by the parameter The kernel function is defined as:

[0072] Where: represents the amplitude, represents the length scale; H phy (x) Represents the physical prior mean function:

[0073] Where: f p (x) The porosity of aluminum foam predicted by the objective function; For new points , the mean of the posterior predictive distribution of the Gaussian process for:

[0074] Where: Indicates new point The sum correlation vector with all samples in the training set ，X i Indicates the i Process parameters of training samples; T represents the kernel covariance matrix of the training set; represents the variance of the observation noise; I represents the identity matrix; y Represents the observation vector of 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 :

[0075]

[0076] Where: w x 、 w y 、 w z Respectively represent the corresponding weight coefficients; represents the mean energy absorption rate predicted by the surrogate model; represents the surrogate model prediction LDOSI picture, Var represents variance; represents the surrogate model prediction SUEDEF factor, Mean represents the mean; Indicates that the proxy model is at point x The forecast uncertainty at represents a hyperparameter that controls the exploration effort.

[0077] like Figure 3 、 Figure 4 As shown in the figure, after the process parameters are optimized by the above method, the foam aluminum structure is uniform and consistent; while the image without process parameter optimization is shown in the figure Figure 5 As shown, there are problems such as poor pore uniformity, poor consistency, and large pores.

[0078] Example 2: As another preferred embodiment of the technical solution of the present invention, based on the solution of Example 1 above, data normalization is to normalize the process parameter feature data after data enhancement to eliminate the dimensional differences between different parameters, specifically:

[0079] The specific feature dimensionality reduction is as follows: perform principal component analysis on the standardized high-dimensional feature space to reduce the dimensionality, and project the standardized data matrix onto the matrix obtained by the previous orthogonal projection. k The subspace composed of the principal component directions is used to obtain the data after dimensionality reduction.

Claims

1. A method for optimizing aluminum foam process parameters based on deep learning of physical information, characterized by: include: Data preprocessing, mechanical property prediction, and process parameter optimization; data preprocessing includes generative data enhancement based on physical information, data standardization, and feature dimensionality reduction. Generative data enhancement based on physical information uses an adversarial training process between a generator based on a physical constraint-conditioned generation module and a discriminator to construct an adversarial generative network; mechanical property prediction uses a multimodal information fusion prediction framework based on graph neural networks and utilizes enhanced data of aluminum foam to predict mechanical properties; The process parameter optimization uses the trained graph neural network as the objective function and embeds it into an improved Bayesian optimization framework to iterate and locate the parameter combination that can produce the optimal energy absorption performance.

2. The method for optimizing aluminum foam process parameters based on physical information deep learning according to claim 1, characterized in that: The generator of the physical constraint-based generation module is specifically: The physical constraint-based conditional generation module is used to filter the conditional information before it enters the generator. Specifically: Where: c pr Indicates process-related conditions; c pe Indicates the energy absorption rate of foam aluminum; C i (i=1,2,…,6) represents the constraint condition; Indicates that all constraints must be true at the same time; 1 indicates the corresponding condition information C v Available, 0 means unavailable; The generator is specifically: Where: represents the data pair containing CT images and process parameters created by the generator; G() represents the generator neural network; z represents a random noise vector; C represents the conditional information vector; The discriminator uses its internal neural network structure to deeply analyze the texture and pore structure of the image, and makes a comprehensive judgment based on process parameters and performance conditions: Where: D() represents the discriminator neural network; (I,P,C) Indicates input data packet; P rel Represents the output probability value, if P rel Close to 1, indicating that the discriminator believes that the input is real. P rel Close to 0, it means the discriminator thinks the input is fake.

3. The method for optimizing aluminum foam process parameters based on physical information deep learning according to claim 1 or 2, characterized in that: The constraints C 1 indicates the viscosity enhancer content constraint: Where: x Ca Indicates the content of thickener, that is, the content of thickener does not exceed 2 wt.% ; C 2 represents the collaborative constraint of foaming parameters: The foaming temperature is 750℃, Where: x W 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 represents the porosity-performance coupling constraint: Energy absorption rate ≥8.2MJ / m 3 ,but Where: P best Indicates the estimated porosity, that is, if the energy absorption rate expected is greater than or equal to 8.2MJ / m 3 When , the porosity is between 75% and 85%; C 4 represents the aperture-performance coupling constraint: Where: D best Indicates the estimated aperture, i.e. if excellent energy absorption rate is expected, the estimated aperture is less than 3mm; C 5 represents the uniformity-performance coupling constraint: Where: CV represents the pore size distribution uniformity, that is, if a high stability platform stress is desired, the pore size distribution uniformity should be less than 0.4; C 6 represents the sphericity-performance coupling constraint: Where: N It represents the sphericity of the pores. That is, if the peak energy absorption rate is desired, the sphericity of the pores should be greater than 0.

75.

4. The method for optimizing aluminum foam process parameters based on physical information deep learning according to claim 1 or 3, characterized in that: The adversarial generative network includes discriminator loss and generator loss. The discriminator loss is used to maximize the adversarial loss, that is, to accurately distinguish between true and false: In the formula: L adv represents the adversarial loss; E represents the mathematical symbol of expectation; represents the true sample of the data pair containing the CT image and process parameters; 丨 represents under the condition of... The generator loss minimizes both the adversarial loss and the physical loss: Where: represents the weight coefficient of physical loss; Indicates physical loss: Where: 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 represents the toughness-minimum aperture loss function, L p5 represents the stress concentration-sphericity loss function; Represents the corresponding loss function weight coefficient; represents the target platform stress, i.e. the macroscopic compressive strength that the material is expected to achieve; Indicates the yield strength of aluminum, i.e. the strength of the metal itself that makes up the foam; P 0 porosity; k 1 represents the proportional relationship between pore size and stress; d avg represents the average pore size; represents the relative fluctuation of the target platform stress; represents the corresponding material constant; CV k represents the coefficient of variation of the pore size distribution; represents the geometric correction factor; d min Indicates the minimum aperture.

5. 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 a graph neural network receives process parameters and CT images after data preprocessing. 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 the graph through a graph construction phase, and the physical adjacency between nodes is defined as edges. Among them, the process parameters are not directly used as static node features, but as a modulator to dynamically respond to the inter-layer message transmission process of the graph neural network model, that is, the process parameters can control the intensity of the information flow between nodes; the transmission and aggregation of information after multi-layer modulation of the process parameters can realize the hierarchical representation from the micro environment of a single node to the macro state of the entire graph, and the nodes i In the ( l+1 ) The feature update of the layer is specifically as follows: Where: Representation node i In the ( l+1 ) layer’s feature vector; Represents the aggregation function, which is used to aggregate all neighbor information; j Representation node i Neighbor nodes of Representation node i The set of all neighbor nodes; represents the input process parameter vector, g(P pr ) represents the gating vector determined by the process parameters, which is a small neural network used to modulate the flow of information; represents the element-wise product, which is used for modulation of the message by the process parameter gating vector; Indicates the l The message function of the layer is used to calculate the neighbor nodes j To Node i news; Represents neighbor nodes j In the l The feature vector of the layer, i.e. the state of the neighbors; E ij Represents a connected node i and nodes j Edge features; represents the update function, which combines the node's own old features with the aggregated new messages 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 (MLP) to output the prediction of the macroscopic mechanical properties of aluminum foam: Where: READOUT() represents the graph readout function, which aggregates the final features of all nodes into a vector representing the entire graph; Represents the final features of all nodes; V Represents the set of all nodes in the graph.

6. The method for optimizing aluminum foam process parameters based on physical information deep learning according to claim 5, characterized in that: The terminal of the graph neural network model sets three parallel prediction heads, including macro performance prediction head, LDOSI Prediction head and SUEDEF Prediction head; The total loss function of the three parallel prediction heads is the weighted sum of the three subtask loss functions, which is used to balance the macro prediction accuracy and the consistency of the microscopic physical process: Where: Respectively represent the corresponding weight coefficients; L ma Represents macro performance loss: Where: M represents the number of samples; L LDOSI represents the local deformation initiation sensitivity loss, which is supervised at the node level and used to calculate the LDOSI Prediction head prediction LDOSI Figure 1 shows the baseline truth obtained by digital image correlation analysis of foam aluminum CT images. The differences between: L SUEDEF Represents the energy dissipation efficiency loss of the structural unit, which is supervised at the structural unit level and used to calculate the energy dissipation efficiency loss of the structural unit. SUEDEF Prediction head prediction SUEDEF Factors and digital image correlation analysis benchmark truth for aluminum foam CT images The differences between: Where: K Represents the set of all different structural source types in the sample.

7. The method for optimizing aluminum foam process parameters based on physical information deep learning according to claim 6, characterized in that: 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 the distribution of the sampled points is fitted through a surrogate model, where the role of the surrogate model is to learn and approximate the true form of the objective function and quantify the uncertainty of the prediction. Specifically, Where: f(x) Represents the agent model for process parameters x The prediction of the corresponding mechanical properties is a probability distribution; GP () represents a Gaussian process; Represents the feature map of process parameters, which converts the original process parameters x Mapping to high-dimensional feature space; represents the process parameters of the training set; Indicated by the parameter The kernel function is defined as: Where: represents the amplitude, represents the length scale; H phy (x) Represents the physical prior mean function: Where: f p (x) The porosity of aluminum foam predicted by the objective function; For new points , the mean of the posterior predictive distribution of the Gaussian process for: Where: Indicates new point The sum correlation vector with all samples in the training set ，X i Indicates the i Process parameters of training samples; T represents the kernel covariance matrix of the training set; represents the variance of the observation noise; I represents the identity matrix; y Represents the observation vector of 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 : Where: w x 、 w y 、 w z Respectively represent the corresponding weight coefficients; represents the mean energy absorption rate predicted by the surrogate model; represents the surrogate model prediction LDOSI picture, Var represents variance; represents the surrogate model prediction SUEDEF factor, Mean represents the mean; Indicates that the proxy model is at point x The forecast uncertainty at represents a hyperparameter that controls the exploration effort.

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