Metal matrix composite optimization method and system based on dynamic reverse design

Abstract

The invention relates to the field of metal-based composite materials, and provides a metal-based composite material optimization method based on dynamic reverse design, which comprises the following steps: S1, an early-stage preparation stage of a model: establishing different particle distribution configurations of a particle reinforced metal-based composite material at high flux by utilizing an Abaq us plug-in; s2, a data set construction stage: quantizing the long-range / short-range order degree of an enhancement body through a translation sequence parameter and a radial distribution function, and generating an enhancement body configuration and a random variant thereof; s3, a forward prediction stage: constructing a BPNN-CL model by adopting a back propagation neural network fused with continuous learning, and dynamically mapping the material / structure feature vectors to mechanical properties; and S4, a reverse optimization stage: chaos disturbance, dynamic partition monitoring and an elitism strategy are integrated into an NSGA-I algorithm to form an NSGA-I-PMCP optimizer, and multi-target optimization is carried out by taking BPNN-CL as a real-time agent model. The problem of reasonably designing a matrix, an interface product and a reinforcement of the particle reinforced metal matrix composite to synergistically improve the strength and the toughness of the metal matrix composite is solved.

Description

Technical Field

[0001] This invention relates to the technical field of metal matrix composites, and more particularly to the field of predicting the strength, toughness, modulus, and other properties of particle-reinforced metal matrix composites. Specifically, it relates to an optimization method and system for metal matrix composites based on dynamic reverse design. Background Technology

[0002] The performance of metal matrix composites (MMCs) primarily depends on the matrix composition, interface type, and reinforcing phase characteristics. The matrix composition determines the overall mechanical, thermal, and chemical properties of the material. Interface type directly affects stress transfer efficiency and interfacial bonding strength; chemically bonded interfaces exhibit high stability, while mechanically bonded interfaces rely on roughness and friction. The size, morphology, distribution, and volume fraction of the reinforcing phase significantly regulate the strength, toughness, and wear resistance of the composite material. These three factors work synergistically to optimize the overall performance of the material. However, the inverse relationship between strength and toughness remains a key challenge hindering further improvements in the performance of MMCs. At the microscale, significant differences in mechanical properties (such as elastic modulus and yield strength) between the hard phase and the soft matrix induce strong strain / stress gradients. Therefore, how to precisely design the microscopic characteristics of MMCs (such as the size, distribution, and interfacial properties of hard units) to synergistically optimize strength and toughness has become a core scientific issue for synergistically improving strength and toughness.

[0003] However, the vast design space makes trial-and-error methods impractical; while analytical models are convenient and quick, they can only provide simple physical insights; and high-fidelity numerical methods can capture key physical phenomena, but they incur excessively high computational costs in complex material combinations. To address this issue, recent advancements in machine learning offer a feasible solution. Current literature lacks reports on the joint prediction of properties from three dimensions—composition, interface, and reinforcing phase—for particle-reinforced metal matrix composites, and the synergistic optimization of strength and toughness. Given the "synergistic optimization effect" in materials science, the field of multi-scale design of new materials remains largely unexplored. In recent years, the rapid development of computers has provided impetus for the design of new materials, and the development of machine learning and artificial intelligence algorithms has accelerated the prediction process. Combining machine learning with computational simulation can further broaden the direction of metal matrix composite design. Currently, there are few reports on the synergistic optimization of the "composition-interface-reinforcing phase" of particle-reinforced metal matrix composites. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to provide a method and system for optimizing metal matrix composites based on dynamic reverse design, in order to solve the problem of rationally designing the interface products and reinforcements of particle-reinforced metal matrix composites to synergistically improve the strength and toughness of metal matrix composites.

[0005] The above-mentioned objective of this invention is achieved through the following technical solutions:

[0006] An optimization method for metal matrix composites based on dynamic reverse design includes the following steps:

[0007] S1: Model preparation stage: Using the Abaqus plugin, different particle distribution configurations of particle-reinforced metal matrix composites are established in high throughput.

[0008] S2: Dataset construction phase: Quantify the long-range / short-range order of the augmentation by translation order parameters and radial distribution functions to generate augmentation configurations and their random variants, including random distribution, uniform distribution, layered, network, and micro / nano hybrid structures.

[0009] S3: Forward prediction stage: A BPNN-CL model is constructed using a backpropagation neural network that integrates continuous learning, and the material / structure feature vectors are dynamically mapped to mechanical properties including ultimate tensile strength, toughness, and elastic modulus.

[0010] S4: Inverse optimization stage: Chaotic perturbation, dynamic partition monitoring and elite retention strategy are integrated into the NSGA-II algorithm to form the NSGA-II-PMCP optimizer, and BPNN-CL is used as a real-time agent model for multi-objective optimization design.

[0011] Furthermore, in step S1, using the Abaqus plugin, high-throughput models of different particle distribution configurations of particle-reinforced metal matrix composites are built in batches, and finite element analysis is performed to calculate large amounts of data. Specifically:

[0012] S11: Calls Abaqus / CAE related modules, including Abaqus, abaqusConstants, caeModules, and driverUtils, to achieve seamless interaction with Abaqus software, complete core functions including finite element modeling, material property definition, boundary condition setting, and analysis task submission. It also supports automated operation of the CAE interface and extraction of post-processing results. Calls caeModules and driverUtils modules to provide the functions of Abaqus CAE modules, perform model operations, and call tools.

[0013] S12: Utilize scipy.spatial.cKDTree to construct an efficient spatial index structure, thereby achieving spatial distribution optimization and nearest neighbor search for enhanced phase particles; combine np.meshgrid to generate a regular three-dimensional coordinate grid system, flatten it into a two-dimensional array grid, and use numpy to generate a three-dimensional grid, setting different grid configurations and constructing a non-uniformly distributed grid through grid deformation techniques including radial basis function interpolation, providing a flexible discretization scheme for multi-scale modeling;

[0014] S13: The matrix material adopts the Johnson-Cook plastic constitutive model, which comprehensively considers strain hardening, strain rate effect and temperature softening effect, and can accurately describe the dynamic mechanical response of the metal matrix under high strain rate load.

[0015] S14: The reinforcing phase material is defined as a linear elastic constitutive model, which is coupled with the constitutive model of the matrix to construct a multiphase material system;

[0016] S15: Explicit dynamic methods, including Abaqus / Explicit, are used to simulate the dynamic loading process. Adaptive meshing techniques and contact algorithms, including general contact or surface-to-surface contact, are combined to handle nonlinear behaviors that may occur at the enhanced phase / matrix interface, including separation and slippage, to ensure computational convergence and accuracy.

[0017] Furthermore, in step S13, the matrix material adopts the Johnson-Cook plastic constitutive model, specifically as follows:

[0018] The matrix material was subjected to finite element analysis using the Johnson-Cook plastic constitutive model, and its static yield stress σ was determined. 0 Represented as:

[0019]

[0020] in It is the equivalent plastic strain, where A, B, n, C, and m are the five major material physical property constants, and T is the equivalent plastic strain. room and T melt These represent room temperature and the melting point of the material, respectively. For reference strain, The actual strain is T, and the test temperature is T.

[0021] Further, in step S2, the long-range / short-range order of the reinforcement is quantified by the translational order parameter and the radial distribution function to generate reinforcement configurations and their random variants, including random distribution, uniform distribution, layered, network, and micro / nano hybrid structures, specifically:

[0022] S21: The spatial distribution of the enhancer is extracted as the TOP value using a topological analysis algorithm, assuming that the centroids of all detected particles are... Image size is L x The height is L y Normalize the coordinates of each centroid:

[0023]

[0024] Where i is the index of all detected particles from 1 to N, N is the total number of detected enhancer particles, and x i Let y be the value of the two-dimensional coordinate horizontal direction of the centroid of the i-th particle in the original image coordinate system. i Let be the value of the two-dimensional coordinates of the centroid of the i-th particle in the vertical direction of the original image coordinate system. The normalized x-coordinate For the normalized y-coordinate, min j x j min is the minimum value of the x-coordinate of all particles. j y j It is the minimum value of the y-coordinate of all particles;

[0025] The TOP for each direction is calculated as follows:

[0026]

[0027] in and It is the average normalized coordinate, σ x and σ y The TOP values ​​for the directions are given, and the 2D TOP is finally defined as the Euclidean combination:

[0028]

[0029] S22: Calculate the radial distribution function (RDF) of the reinforcement-matrix using atomized modeling;

[0030] Under periodic boundary conditions, for each particle i, find its nearest non-zero neighbor distance r. i Collect the nearest neighbor distance set of all particles And from the distance interval width Δr to the maximum statistical distance r max Construct a histogram on the interval:

[0031] hist(r k )=#{i|r i ∈[r k ,r k +Δr]},k=1,...,M

[0032] Where k is the interval number, hist(r i ) represents the particle distance count within the distance interval k, M represents the total number of intervals, [r k ,r k +Δr] is the distance of the kth interval;

[0033] According to number density The shell center distance r of the k-th distance interval k The radial distribution function RDF at a given location is defined as:

[0034]

[0035] Wherein, g(r) k ) represents the radial distribution function RDF at a distance r. k The value at;

[0036] Quantifying short-term orderliness deviation using the absolute difference of integrals:

[0037]

[0038] Where RDF_dev is the short-range ordering bias, g(r) is the actual radial distribution function, g0(r) is the radial distribution function of the ideal random distribution, and T max Maximum radial distance;

[0039] S23. When TOP>0.40 and RDF>1.03, it is determined to be a long-range ordered structure; when TOP≤0.40 and RDF≤1.03, it is determined to be a random distribution structure; when TOP≤0.40 but RDF>1.03, it is determined to be a short-range ordered structure.

[0040] Furthermore, in step S3, a BPNN-CL model is constructed using a backpropagation neural network that integrates continuous learning, dynamically mapping the material / structure feature vectors to mechanical properties including ultimate tensile strength, toughness, and elastic modulus. Specifically:

[0041] S31: The network architecture adopts a deep feedforward structure, including: a 13-node input layer corresponding to the material feature dimension; 5 nonlinear transformation hidden layers with the number of nodes decreasing in the order of 128-64-32-16-8; and a 3-node output layer for predicting mechanical properties. The hidden layer activation function adopts the improved LeakyReLU activation function with a negative slope coefficient α = 0.01.

[0042]

[0043] Where f(x) is the improved LeakyReLU activation function, x is the input signal of the hidden layer neuron, a is the slope coefficient in the negative interval, and the output layer uses linear activation;

[0044] S32: The continuous learning mechanism is implemented through dynamic network expansion. Key technologies include: calculation of the difference in distribution between new and old data, network expansion triggering conditions and expansion rules, and weight initialization constraints.

[0045] Calculation of the difference in distribution between old and new data:

[0046]

[0047] Where ΔD represents the difference in distribution between the old and new data, D n For the nth batch of new data, D n-1 For the (n-1)th batch of old data, μ is the mean vector of the dataset, and σ is the standard deviation of the dataset;

[0048] Network expansion trigger conditions and expansion rules:

[0049] If ΔD > 0.3, Nnew = [0.2 × N original ]

[0050] Where, N new To determine the number of newly added neurons, N original This represents the original number of neurons in the network.

[0051] Weight initialization constraints:

[0052] ||W new ||2≤0.05||W old ||2

[0053] Among them, W new For the new neuron connection weights, W old The connection weights of the existing network;

[0054] S33: Use MSE as the loss function to monitor and measure the results of positive prediction in real time;

[0055] S34: The training process employs a dynamic learning rate scheduling strategy, with the dynamic learning rate... The initial learning rate η0 = 0.001, and t is the epoch count, enabling dynamic monitoring and learning;

[0056] S35: Employ an early stopping mechanism to monitor the validation set loss. Training is terminated when the loss decreases below a threshold for 100 consecutive epochs.

[0057] Furthermore, prior to improving the NSGA-II-PMCP optimizer in step S4, the following steps are included:

[0058] The basic genetic operations module employs an improved real-number encoded genetic algorithm framework and includes the following core operations:

[0059] Simulated binary crossover (SBX): Performs a crossover operation on the parent individuals with a probability of 0.9 to generate offspring individuals with similar characteristics. The distribution index is set to 20 to ensure sufficient exploration.

[0060] Multinomial mutation: Local perturbation of offspring individuals with a probability of 0.1, with the mutation index set to 100 to achieve fine-tuning;

[0061] Hybrid selection mechanism: Combining tournament selection and elite retention strategies to ensure population diversity.

[0062] Furthermore, in step S4, the NSGA-II-PMCP optimizer is improved, including:

[0063] S41: Chaotic Perturbation Injection Mechanism: To address the problem of traditional NSGA-II easily getting trapped in local optima, a dynamic chaotic perturbation strategy is introduced:

[0064] Generating chaotic sequences using Logistic mapping:

[0065] x n+1 =μx n (1-x n μ = 3.8

[0066] Where, x n Let x be the nth value of the chaotic sequence. n+1 Let μ be the (n+1)th value of the chaotic sequence, and μ be the control parameter of the Logistic mapping.

[0067] The perturbation intensity decays exponentially with the number of iterations t:

[0068] When local stagnation is detected and the improvement of the optimal solution is less than the threshold for 10 consecutive generations, chaotic perturbation is applied to 5% of the individuals in the population, and the perturbation range is controlled within ±15% of the current search space.

[0069] S42: Dynamic partitioning monitoring strategy: including adaptive mesh division and boundary definition;

[0070] The target space is divided into an adaptive grid, and the grid dimension is dynamically adjusted according to the distribution of non-dominated solutions.

[0071] Boundary definition adopts a dynamic ε-dominance mechanism;

[0072] A judgment is made every 20 generations; if full coverage is not achieved, chaotic perturbation is initiated.

[0073] S43: Improved Elite Retention Strategy:

[0074] The proportion of elites is dynamically adjusted, initially set at 20%, and linearly increased to 40% with iteration;

[0075] An elite memory with a capacity limit of 100 non-dominated solutions is established and maintained using crowding distance sorting.

[0076] S44: Set up a composite constraint handling mechanism: Define composite conditions that include process constraints and performance constraints; adopt a feasibility-first tournament selection mechanism, and reduce the constraint violation threshold from 0.1 to 0.01 with each iteration; implement adaptive penalties for infeasible solutions;

[0077] S45: Pareto solution injection strategy: Inject 20% of known Pareto solutions during the initialization phase to ensure the quality of the search starting point;

[0078] Establish a solution similarity detection mechanism to avoid duplicate solution injection.

[0079] A dynamic inverse design-based metal matrix composite optimization system for performing the aforementioned dynamic inverse design-based metal matrix composite optimization method, characterized in that it comprises:

[0080] The model preparation module is used to establish different particle distribution configurations of particle-reinforced metal matrix composites in high throughput using the Abaqus plugin.

[0081] The dataset construction module is used to quantify the long-range / short-range order of the augmentation through translation order parameters and radial distribution functions, and generate augmentation configurations and their random variants, including random distribution, uniform distribution, layered, network, and micro / nano hybrid structures.

[0082] The forward prediction module is used to construct a BPNN-CL model using a backpropagation neural network that integrates continuous learning, and dynamically maps material / structure feature vectors to mechanical properties including ultimate tensile strength, toughness, and elastic modulus.

[0083] The inverse optimization module integrates chaotic perturbation, dynamic partition monitoring, and elite retention strategies into the NSGA-II algorithm to form the NSGA-II-PMCP optimizer, which uses BPNN-CL as a real-time agent model for multi-objective optimization design.

[0084] A computer device includes a memory and one or more processors, the memory storing computer code that, when executed by the one or more processors, causes the one or more processors to perform the method described above.

[0085] A computer-readable storage medium storing computer code that, when executed, performs the method described above.

[0086] Compared with the prior art, the beneficial effects of the present invention are:

[0087] While maintaining the advantages of the NSGA-II framework, this invention enhances global search capabilities through chaotic perturbation, improves solution set distribution through dynamic partitioning strategy, and ensures the stability of the optimization process through memory mechanism. It is particularly suitable for multi-objective process optimization problems of metal matrix composites. Attached Figure Description

[0088] Figure 1 This is a flowchart of the overall calculation method in one embodiment of the present invention;

[0089] Figure 2 This is a flowchart of the BPNN-CL algorithm in one embodiment of the present invention;

[0090] Figure 3 This is a flowchart of the NSGA-II-PMCP algorithm in one embodiment of the present invention;

[0091] Figure 4 This is a schematic diagram comparing the optimization effects of the NSGA-II-PMCP algorithm in one embodiment of the present invention with those of the traditional NSGA-II algorithm;

[0092] Figure 5 This is a schematic diagram comparing the performance of the NSGA-II-PMCP algorithm in one embodiment of the present invention with that of the traditional NSGA-II and Bayesian optimization algorithms (baseline NSGA-II (M1), NSGA-II-PMCP (M2), Bayesian optimization (M3) and previous work (M4)). Detailed Implementation

[0093] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0094] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0095] First Embodiment

[0096] like Figure 1As shown, this embodiment provides a method for optimizing metal matrix composites based on dynamic reverse design, characterized by the following steps:

[0097] S1: Model preparation stage: Using the Abaqus plugin, different particle distribution configurations of particle-reinforced metal matrix composites are established in high throughput.

[0098] In this embodiment, step S1 is performed using the finite element method to calculate a large amount of data, specifically as follows:

[0099] S11: Calls Abaqus / CAE related modules, including Abaqus, abaqusConstants, caeModules, and driverUtils, to achieve seamless interaction with Abaqus software, complete core functions including finite element modeling, material property definition, boundary condition setting, and analysis task submission. It also supports automated operation of the CAE interface and extraction of post-processing results. Calls caeModules and driverUtils modules to provide the functions of Abaqus CAE modules, perform model operations, and call tools.

[0100] S12: Utilize scipy.spatial.cKDTree to construct an efficient spatial index structure, thereby achieving spatial distribution optimization and nearest neighbor search for enhanced phase particles; combine np.meshgrid to generate a regular three-dimensional coordinate grid system, flatten it into a two-dimensional array grid, and use numpy to generate a three-dimensional grid, setting different grid configurations and constructing a non-uniformly distributed grid through grid deformation techniques including radial basis function interpolation, providing a flexible discretization scheme for multi-scale modeling;

[0101] S13: The matrix material adopts the Johnson-Cook plastic constitutive model, which comprehensively considers strain hardening, strain rate effect and temperature softening effect, and can accurately describe the dynamic mechanical response of the metal matrix under high strain rate load.

[0102] S14: The reinforcing phase material is defined as a linear elastic constitutive model, which is coupled with the constitutive model of the matrix to construct a multiphase material system;

[0103] S15: Explicit dynamic methods, including Abaqus / Explicit, are used to simulate the dynamic loading process. Adaptive meshing techniques and contact algorithms, including general contact or surface-to-surface contact, are combined to handle nonlinear behaviors that may occur at the enhanced phase / matrix interface, including separation and slippage, to ensure computational convergence and accuracy.

[0104] In step S13, the matrix material adopts the Johnson-Cook plastic constitutive model, specifically as follows:

[0105] The matrix material was subjected to finite element analysis using the Johnson-Cook plastic constitutive model, and its static yield stress σ was determined. 0 Represented as:

[0106]

[0107] in It is the equivalent plastic strain, where A, B, n, C, and m are the five major material physical property constants, and T is the equivalent plastic strain. room and T melt These represent room temperature and the melting point of the material, respectively. For reference strain, The actual strain is T, and the test temperature is T.

[0108] S2: Dataset Construction Phase: The long-range / short-range order of the augmentation is quantified by translation order parameters and radial distribution functions to generate augmentation configurations and their random variants, including random distribution, uniform distribution, layered, network, and micro / nano hybrid structures.

[0109] In this embodiment, step S2 specifically includes:

[0110] S21: The spatial distribution of the enhancer is extracted as the TOP value using a topological analysis algorithm, assuming that the centroids of all detected particles are... Image size is L x The height is L y Normalize the coordinates of each centroid:

[0111]

[0112] Where i is the index of all detected particles from 1 to N, N is the total number of detected enhancer particles, and x i Let y be the value of the two-dimensional coordinate horizontal direction of the centroid of the i-th particle in the original image coordinate system. i Let be the value of the two-dimensional coordinates of the centroid of the i-th particle in the vertical direction of the original image coordinate system. The normalized x-coordinate For the normalized y-coordinate, min j x j min is the minimum value of the x-coordinate of all particles. j y j It is the minimum value of the y-coordinate of all particles;

[0113] The TOP for each direction is calculated as follows:

[0114]

[0115] in and It is the average normalized coordinate, σ x and σ y The TOP values ​​for the directions are given, and the 2D TOP is finally defined as the Euclidean combination:

[0116]

[0117] S22: Calculate the radial distribution function (RDF) of the reinforcement-matrix using atomized modeling;

[0118] Under periodic boundary conditions, for each particle i, find its nearest non-zero neighbor distance r. i Collect the nearest neighbor distance set of all particles And from the distance interval width Δr to the maximum statistical distance r max Construct a histogram on the interval:

[0119] hist(r k )=#{i|r i ∈[r k ,r k +Δr]},k=1,...,M

[0120] Where k is the interval number, hist(r i ) represents the particle distance count within the distance interval k, M represents the total number of intervals, [r k ,r k +Δr] is the distance of the kth interval;

[0121] According to number density The shell center distance r of the k-th distance interval k The radial distribution function RDF at a given location is defined as:

[0122]

[0123] Wherein, g(r) k ) represents the radial distribution function RDF at a distance r. k The value at;

[0124] Quantifying short-term orderliness deviation using the absolute difference of integrals:

[0125]

[0126] Where RDF_dev is the short-range ordering bias, g(r) is the actual radial distribution function, g0(r) is the radial distribution function of the ideal random distribution, and T max Maximum radial distance;

[0127] S23. When TOP>0.40 and RDF>1.03, it is determined to be a long-range ordered structure; when TOP≤0.40 and RDF≤1.03, it is determined to be a random distribution structure; when TOP≤0.40 but RDF>1.03, it is determined to be a short-range ordered structure.

[0128] S3: Forward Prediction Phase: Constructing a BPNN-CL model using a backpropagation neural network that incorporates continuous learning (e.g., ...). Figure 2 As shown, material / structure feature vectors are dynamically mapped to mechanical properties including ultimate tensile strength, toughness, and elastic modulus.

[0129] exist Figure 2 In the forward prediction phase, a BPNN-CL model is constructed using a backpropagation neural network with a continuous learning mechanism. First, based on the backpropagation neural network (BPNN), initial data on particle-reinforced metal matrix composites (covering diverse particle distribution configurations and composition information) is used to initially explore the mapping relationship between material characteristics (such as particle distribution and interface properties) and mechanical properties (ultimate tensile strength, toughness, and elastic modulus) to achieve performance prediction. Then, relying on the continuous learning mechanism, the first continuous learning (CL-1) is initiated, introducing new material data (such as samples with different reinforcement distributions and interface products), allowing the model to adapt to new data patterns without forgetting existing knowledge, thus optimizing the mapping accuracy from features to performance. Next, a second continuous learning (CL-2) is initiated, incorporating more diverse material data (such as data from different processes and composition systems), and the model is further iterated and optimized through continuous learning-2. In this way, the BPNN-CL model continuously absorbs new data and dynamically updates knowledge, accurately and efficiently establishing a dynamic mapping from material / structure feature vectors to mechanical properties, laying a solid foundation for performance prediction in subsequent reverse optimization design, and helping to achieve precise control and optimization of the performance of particle-reinforced metal matrix composites.

[0130] In this embodiment, step S3 specifically includes:

[0131] S31: The network architecture adopts a deep feedforward structure, including: a 13-node input layer corresponding to the material feature dimension; 5 nonlinear transformation hidden layers with the number of nodes decreasing in the order of 128-64-32-16-8; and a 3-node output layer for predicting mechanical properties. The hidden layer activation function adopts the improved LeakyReLU activation function with a negative slope coefficient α = 0.01.

[0132]

[0133] Where f(x) is the improved LeakyReLU activation function, x is the input signal of the hidden layer neuron, a is the slope coefficient in the negative interval, and the output layer uses linear activation;

[0134] S32: The continuous learning mechanism is implemented through dynamic network expansion. Key technologies include: calculation of the difference in distribution between new and old data, network expansion triggering conditions and expansion rules, and weight initialization constraints.

[0135] Calculation of the difference in distribution between old and new data:

[0136]

[0137] Where ΔD represents the difference in distribution between the old and new data, D n For the nth batch of new data, D n-1 For the (n-1)th batch of old data, μ is the mean vector of the dataset, and σ is the standard deviation of the dataset;

[0138] Network expansion trigger conditions and expansion rules:

[0139] If ΔD > 0.3, Nnew = [0.2 × N original ]

[0140] Where, N new To determine the number of newly added neurons, N original This represents the original number of neurons in the network.

[0141] Weight initialization constraints:

[0142] ||W new ||2≤0.05||W old ||2

[0143] Among them, W new For the new neuron connection weights, W old The connection weights of the existing network;

[0144] S33: Use MSE as the loss function to monitor and measure the results of positive prediction in real time;

[0145] S34: The training process employs a dynamic learning rate scheduling strategy, with the dynamic learning rate... The initial learning rate η0 = 0.001, and t is the epoch count, enabling dynamic monitoring and learning;

[0146] S35: Employ an early stopping mechanism to monitor the validation set loss. Training is terminated when the loss decreases below a threshold for 100 consecutive epochs.

[0147] S4: Inverse optimization stage: Chaotic perturbation, dynamic partition monitoring and elite retention strategy are integrated into the NSGA-II algorithm to form the NSGA-II-PMCP optimizer, and BPNN-CL is used as a real-time agent model for multi-objective optimization design.

[0148] In this embodiment, the improvement of the NSGA-II-PMCP optimizer in step S4 includes:

[0149] The basic genetic operations module employs an improved real-number encoded genetic algorithm framework and includes the following core operations:

[0150] Simulated binary crossover (SBX): Performs a crossover operation on the parent individuals with a probability of 0.9 to generate offspring individuals with similar characteristics. The distribution index is set to 20 to ensure sufficient exploration.

[0151] Multinomial mutation: Local perturbation of offspring individuals with a probability of 0.1, with the mutation index set to 100 to achieve fine-tuning;

[0152] Hybrid selection mechanism: Combining tournament selection and elite retention strategies to ensure population diversity.

[0153] In step S4, as Figure 3 As shown, improvements to the NSGA-II-PMCP optimizer include:

[0154] S41: Chaotic Perturbation Injection Mechanism: To address the problem of traditional NSGA-II easily getting trapped in local optima, a dynamic chaotic perturbation strategy is introduced:

[0155] Generating chaotic sequences using Logistic mapping:

[0156] x n+1 =μx n (1-x n μ = 3.8

[0157] Where, x n Let x be the nth value of the chaotic sequence. n+1 Let μ be the (n+1)th value of the chaotic sequence, and μ be the control parameter of the Logistic mapping.

[0158] The perturbation intensity decays exponentially with the number of iterations t:

[0159] When local stagnation is detected and the improvement of the optimal solution is less than the threshold for 10 consecutive generations, chaotic perturbation is applied to 5% of the individuals in the population, and the perturbation range is controlled within ±15% of the current search space.

[0160] S42: Dynamic partitioning monitoring strategy: including adaptive mesh division and boundary definition;

[0161] The target space is divided into an adaptive grid, and the grid dimension is dynamically adjusted according to the distribution of non-dominated solutions.

[0162] Boundary definition adopts a dynamic ε-dominance mechanism;

[0163] A judgment is made every 20 generations; if full coverage is not achieved, chaotic perturbation is initiated.

[0164] S43: Improved Elite Retention Strategy:

[0165] The proportion of elites is dynamically adjusted, initially set at 20%, and linearly increased to 40% with iteration;

[0166] An elite memory with a capacity limit of 100 non-dominated solutions is established and maintained using crowding distance sorting.

[0167] S44: Set up a composite constraint handling mechanism: Define composite conditions that include process constraints and performance constraints; adopt a feasibility-first tournament selection mechanism, and reduce the constraint violation threshold from 0.1 to 0.01 with each iteration; implement adaptive penalties for infeasible solutions;

[0168] S45: Pareto solution injection strategy: Inject 20% of known Pareto solutions during the initialization phase to ensure the quality of the search starting point;

[0169] Establish a solution similarity detection mechanism to avoid duplicate solution injection.

[0170] Figure 3 This paper demonstrates the core operational logic of NSGA-II-PMCP (an improved non-dominated sorting genetic algorithm with an elite strategy). In the multi-objective optimization process of particle-reinforced metal matrix composites, the selection, crossover, and mutation operations of the non-dominated algorithm (NSGA-II) are first used to simulate the genetic evolution of material design parameters, continuously generating design combinations. The innovation lies in introducing a partitioned monitoring mechanism to dynamically control the solution distribution in different objective intervals during the optimization process, ensuring a comprehensive exploration of the design space; employing chaotic perturbation to inject a quasi-random global exploration capability into the population, helping to escape local optima and uncover more promising material designs; and simultaneously retaining elite individuals to inherit high-performing design schemes during the optimization process, maintaining the algorithm's optimization efficiency. Finally, the evolved and improved design schemes are checked and predicted, and their corresponding material mechanical properties (such as ultimate tensile strength and toughness) are evaluated, continuously iterating and optimizing to find the optimal design of particle-reinforced metal matrix composites that balances multiple properties.

[0171] The improved NSGA-II-PMCP optimizer scheme described above achieves the same optimization results as the traditional NSGA-II algorithm. Figure 4 As shown in the diagram, the performance comparison diagram between the traditional NSGA-II and the Bayesian optimization algorithm is shown (NSGA-II(Baseline, M1), NSGA-II-PMCP(M2), Bayesian optimization(M3) and previous work(M4)). Figure 4This paper presents the hypervolume and fitness convergence results of the NSGA-II-PMCP (improved algorithm) and the traditional NSGA-II algorithm for three aluminum alloys: Al2014, Al6061, and Al7075. From the hypervolume perspective, at different epochs, the curves corresponding to the NSGA-II-PMCP algorithm show a better growth trend or higher stability values ​​compared to the traditional NSGA-II algorithm. This indicates that the improved algorithm can cover a wider range of high-quality solutions in the solution space, which is more helpful in improving the diversity and quality of multi-objective optimization solutions. Looking at fitness, the fitness curve of NSGA-II-PMCP also shows advantages. Its value is more stable and in most cases higher than that of the traditional NSGA-II. This means that during the optimization process, the improved algorithm can guide the population to move closer to a better goal more efficiently. In the multi-objective optimization design of aluminum alloy materials (such as the synergistic optimization of performance such as strength and toughness), it can converge to a high-quality solution more accurately and quickly, which verifies the effectiveness and superiority of the NSGA-II-PMCP algorithm in the reverse optimization design scenario of aluminum alloy materials.

[0172] Figure 5 For three aluminum alloys, Al2014, Al6061, and Al7075, comparisons were made between baseline NSGA-II (M1), NSGA-II-PMCP (M2), Bayesian optimization (M3), and previous work (M4). The "Strength-Toughness Scatter Plot" subplot presents the relationship between ultimate tensile strength and toughness (K0) under different optimization methods. t In terms of performance, the data optimized by M2 is more concentrated in high UTS and high K. t The subplot "Supervolume + Fitness Changes Over Time" demonstrates that M2, during the optimization process, exhibits a wider supervolume coverage, better fitness convergence, and more efficient exploration of high-quality solutions. The subplot "Comparison of Optimization Method and Original Data" shows that the optimization results of M2 deviate from the original data, extending towards the high-performance range. Overall, this validates that NSGA-II-PMCP demonstrates superior performance synergy and optimization efficiency in multi-objective optimization of three aluminum alloys, accurately identifying design schemes that balance strength and toughness, and providing effective algorithmic support for material inverse optimization.

[0173] Second Embodiment

[0174] This embodiment provides a dynamic inverse design-based metal matrix composite optimization system for performing the dynamic inverse design-based metal matrix composite optimization method as described in the first embodiment, characterized in that it includes:

[0175] The model preparation module is used to establish different particle distribution configurations of particle-reinforced metal matrix composites in high throughput using the Abaqus plugin.

[0176] The dataset construction module is used to quantify the long-range / short-range order of the augmentation through translation order parameters and radial distribution functions, and generate augmentation configurations and their random variants, including random distribution, uniform distribution, layered, network, and micro / nano hybrid structures.

[0177] The forward prediction module is used to construct a BPNN-CL model using a backpropagation neural network that integrates continuous learning, and dynamically maps material / structure feature vectors to mechanical properties including ultimate tensile strength, toughness, and elastic modulus.

[0178] The inverse optimization module integrates chaotic perturbation, dynamic partition monitoring, and elite retention strategies into the NSGA-II algorithm to form the NSGA-II-PMCP optimizer, which uses BPNN-CL as a real-time agent model for multi-objective optimization design.

[0179] A computer-readable storage medium stores computer code that, when executed, performs the methods described above. Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. This program can be stored in a computer-readable storage medium, which may include: read-only memory (ROM), random access memory (RAM), a magnetic disk, or an optical disk, etc.

[0180] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

[0181] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0182] It should be noted that the above embodiments can be freely combined as needed. The above description is only a preferred embodiment of the present invention. It should be pointed out that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing metal matrix composites based on dynamic reverse design, characterized in that, Includes the following steps: S1: Model preparation stage: Using the Abaqus plugin, different particle distribution configurations of particle-reinforced metal matrix composites are established in high throughput. S2: Dataset construction phase: Quantify the long-range / short-range order of the augmentation by translation order parameters and radial distribution functions to generate augmentation configurations and their random variants, including random distribution, uniform distribution, layered, network, and micro / nano hybrid structures. S3: Forward prediction stage: A BPNN-CL model is constructed using a backpropagation neural network that integrates continuous learning, and the material / structure feature vectors are dynamically mapped to mechanical properties including ultimate tensile strength, toughness, and elastic modulus. S4: Inverse optimization stage: Chaotic perturbation, dynamic partition monitoring and elite retention strategy are integrated into the NSGA-II algorithm to form the NSGA-II-PMCP optimizer, and BPNN-CL is used as a real-time agent model for multi-objective optimization design.

2. The optimization method for metal matrix composites based on dynamic reverse design according to claim 1, characterized in that, In step S1, using the Abaqus plugin, high-throughput models of different particle distribution configurations of particle-reinforced metal matrix composites are built in batches, and finite element analysis is performed to calculate large amounts of data. Specifically: S11: Calls Abaqus / CAE related modules, including Abaqus, abaqusConstants, caeModules, and driverUtils, to achieve seamless interaction with Abaqus software, complete core functions including finite element modeling, material property definition, boundary condition setting, and analysis task submission. It also supports automated operation of the CAE interface and extraction of post-processing results. Calls caeModules and driverUtils modules to provide the functions of Abaqus CAE modules, perform model operations, and call tools. S12: Utilize scipy.spatial.cKDTree to construct an efficient spatial index structure, thereby achieving spatial distribution optimization and nearest neighbor search for enhanced phase particles; combine np.meshgrid to generate a regular three-dimensional coordinate grid system, flatten it into a two-dimensional array grid, and use numpy to generate a three-dimensional grid, setting different grid configurations and constructing a non-uniformly distributed grid through grid deformation techniques including radial basis function interpolation, providing a flexible discretization scheme for multi-scale modeling; S13: The matrix material adopts the Johnson-Cook plastic constitutive model, which comprehensively considers strain hardening, strain rate effect and temperature softening effect, and can accurately describe the dynamic mechanical response of the metal matrix under high strain rate load. S14: The reinforcing phase material is defined as a linear elastic constitutive model, which is coupled with the constitutive model of the matrix to construct a multiphase material system; S15: Explicit dynamic methods, including Abaqus / Explicit, are used to simulate the dynamic loading process. Adaptive meshing techniques and contact algorithms, including general contact or surface-to-surface contact, are combined to handle nonlinear behaviors that may occur at the enhanced phase / matrix interface, including separation and slippage, to ensure computational convergence and accuracy.

3. The optimization method for metal matrix composites based on dynamic reverse design according to claim 2, characterized in that, In step S13, the matrix material adopts the Johnson-Cook plastic constitutive model, specifically: The matrix material was subjected to finite element analysis using the Johnson-Cook plastic constitutive model, and its static yield stress σ was determined. 0 Represented as: in It is the equivalent plastic strain, where A, B, n, C, and m are the five major material physical property constants, and T is the equivalent plastic strain. room and T melt These represent room temperature and the melting point of the material, respectively. For reference strain, The actual strain is T, and the test temperature is T.

4. The optimization method for metal matrix composites based on dynamic reverse design according to claim 1, characterized in that, In step S2, the long-range / short-range order of the reinforcement is quantified by the translational order parameter and the radial distribution function, generating reinforcement configurations and their random variants, including random distribution, uniform distribution, layered, network, and micro / nano hybrid structures, specifically: S21: The spatial distribution of the enhancer is extracted as the TOP value using a topological analysis algorithm, assuming that the centroids of all detected particles are... Image size is L x The height is L y Normalize the coordinates of each centroid: Where i is the index of all detected particles from 1 to N, N is the total number of detected enhancer particles, and x i Let y be the value of the two-dimensional coordinate horizontal direction of the centroid of the i-th particle in the original image coordinate system. i Let be the value of the two-dimensional coordinates of the centroid of the i-th particle in the vertical direction of the original image coordinate system. The normalized x-coordinate For the normalized y-coordinate, min j x j min is the minimum value of the x-coordinate of all particles. j yj 为 The minimum value of the y-coordinate of all particles; The TOP for each direction is calculated as follows: in and It is the average normalized coordinate, σ x and σ y The TOP values ​​for the directions are given, and the 2D TOP is finally defined as the Euclidean combination: S22: Calculate the radial distribution function (RDF) of the reinforcement-matrix using atomized modeling; Under periodic boundary conditions, for each particle i, find its nearest non-zero neighbor distance r. i Collect the nearest neighbor distance set of all particles And from the distance interval width Δr to the maximum statistical distance r max Construct a histogram on the interval: hist(r k )=#{i|r i ∈[r k ,r k +Δr]},k=1,...,M Where k is the interval number, hist(r i ) represents the particle distance count within the distance interval k, M represents the total number of intervals, [r k ,r k +Δr] is the distance of the kth interval; According to number density The shell center distance r of the k-th distance interval k The radial distribution function RDF at a given location is defined as: Wherein, g(r) k ) represents the radial distribution function RDF at a distance r. k The value at; Quantifying short-term orderliness deviation using the absolute difference of integrals: Where RDF_dev is the short-range ordering bias, g(r) is the actual radial distribution function, g0(r) is the radial distribution function of the ideal random distribution, and T max Maximum radial distance; S23. When TOP>0.40 and RDF>1.03, it is determined to be a long-range ordered structure; when TOP≤0.40 and RDF≤1.03, it is determined to be a random distribution structure; when TOP≤0.40 but RDF>1.03, it is determined to be a short-range ordered structure.

5. The optimization method for metal matrix composites based on dynamic reverse design according to claim 1, characterized in that, In step S3, a BPNN-CL model is constructed using a backpropagation neural network that integrates continuous learning. This model dynamically maps material / structure feature vectors to mechanical properties, including ultimate tensile strength, toughness, and elastic modulus. Specifically: S31: The network architecture adopts a deep feedforward structure, including: a 13-node input layer corresponding to the material feature dimension; 5 nonlinear transformation hidden layers with the number of nodes decreasing in the order of 128-64-32-16-8; and a 3-node output layer for predicting mechanical properties. The hidden layer activation function adopts the improved LeakyReLU activation function with a negative slope coefficient α = 0.

01. Where f(x) is the improved LeakyReLU activation function, x is the input signal of the hidden layer neuron, a is the slope coefficient in the negative interval, and the output layer uses linear activation; S32: The continuous learning mechanism is implemented through dynamic network expansion. Key technologies include: calculation of the difference in distribution between new and old data, network expansion triggering conditions and expansion rules, and weight initialization constraints. Calculation of the difference in distribution between old and new data: Where ΔD represents the difference in distribution between the old and new data, D n For the nth batch of new data, D n-1 For the (n-1)th batch of old data, μ is the mean vector of the dataset, and σ is the standard deviation of the dataset; Network expansion trigger conditions and expansion rules: ifΔD>0.3,Nnew=[0.2×N original ] Where, N new To determine the number of newly added neurons, N original This represents the original number of neurons in the network. Weight initialization constraints: ||In new ||2≤0.05||W old ||2 Among them, W new For the new neuron connection weights, W old The connection weights of the existing network; S33: Use MSE as the loss function to monitor and measure the results of positive prediction in real time; S34: The training process employs a dynamic learning rate scheduling strategy, with the dynamic learning rate... The initial learning rate η0 = 0.001, and t is the epoch count, enabling dynamic monitoring and learning; S35: Employ an early stopping mechanism to monitor the validation set loss. Training is terminated when the loss decreases below a threshold for 100 consecutive epochs.

6. The optimization method for metal matrix composites based on dynamic reverse design according to claim 1, characterized in that, Before improving the NSGA-II-PMCP optimizer in step S4, the following steps are included: The basic genetic operations module employs an improved real-number encoded genetic algorithm framework and includes the following core operations: Simulated binary crossover (SBX): Performs a crossover operation on the parent individuals with a probability of 0.9 to generate offspring individuals with similar characteristics. The distribution index is set to 20 to ensure sufficient exploration. Multinomial mutation: Local perturbation of offspring individuals with a probability of 0.1, with the mutation index set to 100 to achieve fine-tuning; Hybrid selection mechanism: Combining tournament selection and elite retention strategies to ensure population diversity.

7. The optimization method for metal matrix composites based on dynamic reverse design according to claim 1, characterized in that, In step S4, the NSGA-II-PMCP optimizer is improved, including: S41: Chaotic Perturbation Injection Mechanism: To address the problem of traditional NSGA-II easily getting trapped in local optima, a dynamic chaotic perturbation strategy is introduced: Generating chaotic sequences using Logistic mapping: x n+1 =μx n (1-x n ),μ=3.8 Where, x n Let x be the nth value of the chaotic sequence. n+1 Let μ be the (n+1)th value of the chaotic sequence, and μ be the control parameter of the Logistic mapping. The perturbation intensity decays exponentially with the number of iterations t: When local stagnation is detected and the improvement of the optimal solution is less than the threshold for 10 consecutive generations, chaotic perturbation is applied to 5% of the individuals in the population, and the perturbation range is controlled within ±15% of the current search space. S42: Dynamic partitioning monitoring strategy: including adaptive mesh division and boundary definition; The target space is divided into an adaptive grid, and the grid dimension is dynamically adjusted according to the distribution of non-dominated solutions. Boundary definition adopts a dynamic ε-dominance mechanism; A judgment is made every 20 generations; if full coverage is not achieved, chaotic perturbation is initiated. S43: Improved Elite Retention Strategy: The proportion of elites is dynamically adjusted, initially set at 20%, and linearly increased to 40% with iteration; An elite memory with a capacity limit of 100 non-dominated solutions is established and maintained using crowding distance sorting. S44: Set up a composite constraint handling mechanism: Define composite conditions that include process constraints and performance constraints; adopt a feasibility-first tournament selection mechanism, and reduce the constraint violation threshold from 0.1 to 0.01 with each iteration; implement adaptive penalties for infeasible solutions; S45: Pareto solution injection strategy: Inject 20% of known Pareto solutions during the initialization phase to ensure the quality of the search starting point; Establish a solution similarity detection mechanism to avoid duplicate solution injection.

8. A dynamic inverse design-based metal matrix composite optimization system for performing the dynamic inverse design-based metal matrix composite optimization method as described in any one of claims 1-7, characterized in that, include: The model preparation module is used to establish different particle distribution configurations of particle-reinforced metal matrix composites in high throughput using the Abaqus plugin. The dataset construction module is used to quantify the long-range / short-range order of the augmentation through translation order parameters and radial distribution functions, and generate augmentation configurations and their random variants, including random distribution, uniform distribution, layered, network, and micro / nano hybrid structures. The forward prediction module is used to construct a BPNN-CL model using a backpropagation neural network that integrates continuous learning, and dynamically maps material / structure feature vectors to mechanical properties including ultimate tensile strength, toughness, and elastic modulus. The inverse optimization module integrates chaotic perturbation, dynamic partition monitoring, and elite retention strategies into the NSGA-II algorithm to form the NSGA-II-PMCP optimizer, which uses BPNN-CL as a real-time agent model for multi-objective optimization design.

9. A computer device comprising a memory and one or more processors, the memory storing computer code that, when executed by the one or more processors, causes the one or more processors to perform the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing computer code, wherein when the computer code is executed, the method of any one of claims 1 to 7 is performed.

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